************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Nov 27 13:45:57 2003 Input: 1+1 Output: Magma V2.10-6 Thu Nov 27 2003 13:45:54 on modular [Seed = 217412972] ------------------------------------- 2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Thu Nov 27 17:12:30 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2* (a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))] Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0); Output: Magma V2.10-6 Thu Nov 27 2003 17:12:27 on modular [Seed = 1503662226] ------------------------------------- >> Eigenvalues(M); ^ User error: bad syntax >> Eigenspace(M,1); ^ User error: Identifier 'M' has not been declared or assigned >> Eigenspace(M,0); ^ User error: Identifier 'M' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Thu Nov 27 17:12:40 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2* (a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0); Output: Magma V2.10-6 Thu Nov 27 2003 17:12:37 on modular [Seed = 1637361844] ------------------------------------- { <1, 1>, <(1/3*a - 3)/(a - 5), 1>, <(1/6*a - 5/3)/(a - 5), 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*a + 6)/(a + 2) -2/(a - 1)) Vector space of degree 3, dimension 0 over Univariate rational function field over Rational Field Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Thu Nov 27 17:13:40 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2* (a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,(1/3*a - 3)/(a - 5)); Eigenspace(M,(1/6*a - 5/3)/(a - 5)); Output: Magma V2.10-6 Thu Nov 27 2003 17:13:37 on modular [Seed = 1788027515] ------------------------------------- { <1, 1>, <(1/3*a - 3)/(a - 5), 1>, <(1/6*a - 5/3)/(a - 5), 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*a + 6)/(a + 2) -2/(a - 1)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-1/2*a + 3/2)/(a - 1/2) (-1/2*a - 1)/(a - 1/2)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 -1/3 -2/3) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Thu Nov 27 17:19:05 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(3*a-4)/(5*(a-4)),2*(3*a-4)/(5*(a-4)),4*(a+2)/(5*(4-a)),(a+2)/(5*(4-a)),2*(4*a-7) /(5*(a-4)),2*(a+2)/(5*(4-a)),(a-1)/(a-4),(a-1)/(a-4),(a+2)/(4-a)]; Eigenvalues(M); Eigenspace(M,1); Output: Magma V2.10-6 Thu Nov 27 2003 17:19:02 on modular [Seed = 2072132653] ------------------------------------- { <0, 1>, <1, 1>, <(1/5*a - 8/5)/(a - 4), 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*a + 6)/(a + 2) -2/(a - 1)) Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Thu Nov 27 17:20:00 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(3*a-4)/(5*(a-4)),2*(3*a-4)/(5*(a-4)),4*(a+2)/(5*(4-a)),(a+2)/(5*(4-a)),2*(4*a-7) /(5*(a-4)),2*(a+2)/(5*(4-a)),(a-1)/(a-4),(a-1)/(a-4),(a+2)/(4-a)]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0); Eigenspace(M,(1/5*a - 8/5)/(a - 4)); Output: Magma V2.10-6 Thu Nov 27 2003 17:19:57 on modular [Seed = 2222834441] ------------------------------------- { <0, 1>, <1, 1>, <(1/5*a - 8/5)/(a - 4), 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*a + 6)/(a + 2) -2/(a - 1)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 -1/3 -2/3) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-1/2*a + 3/2)/(a - 1/2) (-1/2*a - 1)/(a - 1/2)) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Thu Nov 27 17:24:13 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2* (a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,(1/3*a - 3)/(a - 5)); Eigenspace(M,(1/6*a - 5/3)/(a - 5)); Output: Magma V2.10-6 Thu Nov 27 2003 17:24:10 on modular [Seed = 2506937119] ------------------------------------- { <1, 1>, <(1/3*a - 3)/(a - 5), 1>, <(1/6*a - 5/3)/(a - 5), 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*a + 6)/(a + 2) -2/(a - 1)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-1/2*a + 3/2)/(a - 1/2) (-1/2*a - 1)/(a - 1/2)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 -1/3 -2/3) Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 20:49:32 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(MOdularSymbols(56,2,+1))))); #A; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),+110))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),-110))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),+54))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),-54))); Output: Magma V2.10-6 Thu Nov 27 2003 20:49:29 on modular [Seed = 417435343] ------------------------------------- >> A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(MOdu ^ User error: Identifier 'MOdularSymbols' has not been declared or assigned >> uspidalSubspace(MOdularSymbols(56,2,+1))))); #A; ^ User error: Identifier 'A' has not been declared or assigned >> al(DualHeckeOperator(A[2],109)),+110))); ^ User error: Identifier 'A' has not been declared or assigned >> al(DualHeckeOperator(A[2],109)),-110))); ^ User error: Identifier 'A' has not been declared or assigned >> al(DualHeckeOperator(A[2],53)),+54))); ^ User error: Identifier 'A' has not been declared or assigned >> al(DualHeckeOperator(A[2],53)),-54))); ^ User error: Identifier 'A' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 20:49:56 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),+110))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),-110))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),+54))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),-54))); Output: Magma V2.10-6 Thu Nov 27 2003 20:49:52 on modular [Seed = 300451759] ------------------------------------- 2 [ <2, 3>, <3, 1>, <5, 1> ] [ <2, 2>, <5, 2> ] [ <2, 4>, <3, 1> ] [ <2, 2>, <3, 1>, <5, 1> ] Total time: 3.609 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 21:02:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A; 56*109; C; E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1); CongruenceGroupAnemic(A[2],Parent(Newform(E)),200); 56*53; D; E:=EllipticCurve(EllipticCurveDatabase(),2968,4,1); CongruenceGroupAnemic(A[2],Parent(Newform(E)),200); Output: Magma V2.10-6 Thu Nov 27 2003 21:02:16 on modular [Seed = 3710144011] ------------------------------------- 2 6104 >> 56*109; C; ^ User error: Identifier 'C' has not been declared or assigned Abelian Group of order 1 2968 >> 56*53; D; ^ User error: Identifier 'D' has not been declared or assigned Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 4.279 seconds, Total memory usage: 5.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 21:07:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A; 56*109; C; E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1); CongruenceGroupAnemic(A[1],Parent(Newform(E)),200); Output: Magma V2.10-6 Thu Nov 27 2003 21:07:09 on modular [Seed = 3426049663] ------------------------------------- 2 6104 >> 56*109; C; ^ User error: Identifier 'C' has not been declared or assigned Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 4.119 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 21:07:59 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A; 56*109; C; E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1); CongruenceGroupAnemic(A[1],Parent(Newform(E)),200); Output: Magma V2.10-6 Thu Nov 27 2003 21:07:55 on modular [Seed = 3292354113] ------------------------------------- 2 6104 >> 56*109; C; ^ User error: Identifier 'C' has not been declared or assigned Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 4.159 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 21:09:03 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A; 56*109; C; E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1); CongruenceGroupAnemic(A[1],Parent(Newform(E)),200); Output: Magma V2.10-6 Thu Nov 27 2003 21:08:58 on modular [Seed = 3124964350] ------------------------------------- 2 6104 >> 56*109; C; ^ User error: Identifier 'C' has not been declared or assigned Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 4.219 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Thu Nov 27 21:37:11 2003 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*(x^6+y^6)+1552*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2)+73*(x-y)-81905; I:=ideal; B:=GroebnerBasis(I); B; Factorization(2749936217096833768575); Bn:=GroebnerBasis(ChangeRing(I,GF(2430902559671))); Bn; PP:=ChangeRing(P,GF(2430902559671)); Factorization(PP!(y^2 + 1852361963659*y + 840678110478)); Output: Magma V2.10-6 Thu Nov 27 2003 21:37:07 on modular [Seed = 2089154514] ------------------------------------- [ x^2 + 3*x + y^3 + 5*y^2 + 2614760142323078757143*y + 550651912315588962426, x*y + 2*x + 2*y^3 + 8*y^2 + 2479584067549323745715*y + 1530544330223333986239, 5*x + 2*y^3 + 8*y^2 + 2479584067549323745712*y + 1101303824631177924868, y^4 + y^3 + 4*y^2 + 2626616282958524270696*y + 2208607045947985918918, 3*y^3 + 12*y^2 + 2344407992775568734288*y + 1946020167765167937252, 15*y^2 + 588128861636802099900*y + 1924284781875100852290, 2749936217096833768575 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <35159, 1>, <2430902559671, 1> ] [ x + 2430902559670*y + 578540596012, y^2 + 1852361963659*y + 840678110478 ] [ ] Total time: 2.999 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Thu Nov 27 21:40:18 2003 Input: // Allan f := SwinnertonDyerPolynomial(5); g := SwinnertonDyerPolynomial(6); time L:=Factorization(f*g); #L; Output: Magma V2.10-6 Thu Nov 27 2003 21:40:14 on modular [Seed = 1872160156] ------------------------------------- Time: 0.660 2 Total time: 3.729 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Thu Nov 27 21:40:30 2003 Input: // Allan f := SwinnertonDyerPolynomial(5); g := SwinnertonDyerPolynomial(6); time L:=Factorization(f*g); #L; L; Output: Magma V2.10-6 Thu Nov 27 2003 21:40:26 on modular [Seed = 1738468736] ------------------------------------- Time: 0.660 2 [ <$.1^32 - 448*$.1^30 + 84864*$.1^28 - 9028096*$.1^26 + 602397952*$.1^24 - 26625650688*$.1^22 + 801918722048*$.1^20 - 16665641517056*$.1^18 + 239210760462336*$.1^16 - 2349014746136576*$.1^14 + 15459151516270592*$.1^12 - 65892492886671360*$.1^10 + 172580952324702208*$.1^8 - 255690851718529024*$.1^6 + 183876928237731840*$.1^4 - 44660812492570624*$.1^2 + 2000989041197056, 1>, <$.1^64 - 1312*$.1^62 + 792048*$.1^60 - 293134944*$.1^58 + 74737287288*$.1^56 - 13981172308896*$.1^54 + 1995413247403984*$.1^52 - 223010452468129504*$.1^50 + 19875965471079809820*$.1^48 - 1431186296399427673760*$.1^46 + 84041236543621002233072*$.1^44 - 4051269676739248306877664*$.1^42 + 161038437520893531719546696*$.1^40 - 5292590468585153795497272608*$.1^38 + 143976257181996292530653998416*$.1^36 - 3240853899326109989616514647392*$.1^34 + 60261059130667890854325275719238*$.1^32 - 922739669127277027441017551584608*$.1^30 + 11582497564629879101390954172990800*$.1^28 - 118444912349891951852181962142375200*$.1^26 + 978878175154164215599705915851796296*$.1^24 - 6471399892949448329687739464771529952*$.1^22 + 33785494292069713784801456649105169648*$.1^20 - 137048942135190916858196960829292680864*$.1^18 + 423140580409718469187953106123559340828*$.1^16 - 968316307427310602872375357706532108000*$.1^14 + 1585722240968892813653220405983168716752*$.1^12 - 1771080720430629161685158978892152599456*$.1^10 + 1258829468814790188483900997578812102776*$.1^8 - 511762449216265420619809586571618679392*$.1^6 + 100392008259975194458539996111340080624*$.1^4 - 8316202966928528723117528333532208416*$.1^2 + 198828783273803025550632280753863681, 1> ] Total time: 3.720 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4) Time: Thu Nov 27 21:41:44 2003 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Nov 27 2003 21:41:41 on modular [Seed = 1471077839] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4) Time: Thu Nov 27 21:42:04 2003 Input: for Output: Magma V2.10-6 Thu Nov 27 2003 21:42:01 on modular [Seed = 1203686851] ------------------------------------- >> for; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4) Time: Thu Nov 27 21:42:15 2003 Input: for Output: Magma V2.10-6 Thu Nov 27 2003 21:42:12 on modular [Seed = 1069987398] ------------------------------------- >> for; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mac174.sm.luth.se. (130.240.15.174) Time: Fri Nov 28 11:24:42 2003 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Nov 28 2003 11:24:38 on modular [Seed = 1370036455] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:20:59 2003 Input: C:=DoublyCirculantQRCode(7); Output: Magma V2.10-6 Fri Nov 28 2003 12:20:56 on modular [Seed = 4228137076] ------------------------------------- Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:21:16 2003 Input: C:=DoublyCirculantQRCode(7); C; Output: Magma V2.10-6 Fri Nov 28 2003 12:21:13 on modular [Seed = 3827064733] ------------------------------------- [14, 7, 3] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 1 1 1 0 1 0 0] [0 1 0 0 0 0 0 0 1 1 1 0 1 0] [0 0 1 0 0 0 0 0 0 1 1 1 0 1] [0 0 0 1 0 0 0 1 0 0 1 1 1 0] [0 0 0 0 1 0 0 0 1 0 0 1 1 1] [0 0 0 0 0 1 0 1 0 1 0 0 1 1] [0 0 0 0 0 0 1 1 1 0 1 0 0 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:22:54 2003 Input: C:=DoublyCirculantQRCode(11); C; Output: Magma V2.10-6 Fri Nov 28 2003 12:22:50 on modular [Seed = 3960756215] ------------------------------------- [22, 11, 7] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1] [0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1] [0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:24:07 2003 Input: C:=DoublyCirculantQRCode(13); C; Output: Magma V2.10-6 Fri Nov 28 2003 12:24:04 on modular [Seed = 3576524305] ------------------------------------- [26, 13, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:24:47 2003 Input: C:=DoublyCirculantQRCode(17); C; Output: Magma V2.10-6 Fri Nov 28 2003 12:24:44 on modular [Seed = 3710215793] ------------------------------------- [34, 17] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:25:22 2003 Input: C:=DoublyCirculantQRCode(17); C; MinimalDistance(C); Output: Magma V2.10-6 Fri Nov 28 2003 12:25:19 on modular [Seed = 3375460934] ------------------------------------- [34, 17] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1] >> MinimalDistance(C);; ^ User error: Identifier 'MinimalDistance' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:26:25 2003 Input: C:=DoublyCirculantQRCode(17); C; MinimumDistance(C); Output: Magma V2.10-6 Fri Nov 28 2003 12:26:22 on modular [Seed = 2974354431] ------------------------------------- [34, 17] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1] 6 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:27:10 2003 Input: C:=DoublyCirculantQRCode(19); C; MinimumDistance(C); Output: Magma V2.10-6 Fri Nov 28 2003 12:27:06 on modular [Seed = 3108045731] ------------------------------------- [38, 19] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1] 7 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:27:44 2003 Input: C:=DoublyCirculantQRCode(23); C; MinimumDistance(C); Output: Magma V2.10-6 Fri Nov 28 2003 12:27:41 on modular [Seed = 2706971484] ------------------------------------- [46, 23] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1] 7 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:28:15 2003 Input: C:=DoublyCirculantQRCode(29); C; MinimumDistance(C); Output: Magma V2.10-6 Fri Nov 28 2003 12:28:11 on modular [Seed = 2840662898] ------------------------------------- [58, 29] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1] 12 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:28:49 2003 Input: C:=DoublyCirculantQRCode(31); C; MinimumDistance(C); Output: Magma V2.10-6 Fri Nov 28 2003 12:28:46 on modular [Seed = 2439588655] ------------------------------------- [62, 31] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1] 7 Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Fri Nov 28 12:29:44 2003 Input: C:=DoublyCirculantQRCode(37); C; MinimumDistance(C); Output: Magma V2.10-6 Fri Nov 28 2003 12:29:41 on modular [Seed = 2590122991] ------------------------------------- [74, 37] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1] 12 Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:26:17 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=1366076058403; f1:=2590764387755; f2:=3192785289108; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:26:13 on modular [Seed = 868982553] ------------------------------------- [] 27 [] 36 Total time: 3.269 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:27:04 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=1237559558535; f1:=4618476257611; f2:=1771339940640; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:27:00 on modular [Seed = 200517392] ------------------------------------- [ <366427174246, 936139050903, 0>, <729572566429, 2655705066073, 0>, <799473895704, 2681189646640, 0>, <1408904790141, 246104236481, 0>, <2825450335113, 961623631470, 0>, <3329120936973, 2565788990989, 0>, <3581194270392, 2540304410422, 0>, <4301697223593, 1850269596000, 0>, <4528551981581, 1965670251651, 0> ] [ , ] [ ] [ , ] [ ] [ , ] [ ] [ , ] [ , ] [ , ] 27 [ <111999871605, 4899443106346, 3257828155161>, <219250367204, 2184697719270, 3477945283971>, <821787457239, 441403113397, 4365987944593>, <2226239470925, 2896939759078, 1856574669973>, <2419571365379, 2129255421068, 4712633972520>, <5136348054734, 3851055761470, 4199423147954> ] [ , , ] [ , , ] [ , , ] [ , , ] [ , ] [ , ] [ , ] [ , ] [ , ] [ , ] [ , , ] [ , , ] 36 Total time: 3.399 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:27:26 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=5200520646404; f1:=1150349096740; f2:=4237089101808; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:27:23 on modular [Seed = 66826215] ------------------------------------- [ <3370307863942, 5011329312978, 0>, <3721693715583, 3443373886111, 0>, <3843195007561, 2480493387997, 0> ] [ ] [ ] [ ] 27 [] 36 Total time: 3.349 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:27:51 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=2327136090767; f1:=2647590640482; f2:=4900698753729; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:27:48 on modular [Seed = 467908560] ------------------------------------- [] 27 [] 36 Total time: 3.259 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:28:32 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=1388631197972; f1:=5181403620092; f2:=908395318285; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:28:28 on modular [Seed = 334217136] ------------------------------------- [ <542463558561, 2113471712437, 0>, <896193300545, 2307476134461, 0>, <4028941434437, 1046650446645, 0> ] [ , ] [ , ] [ , ] 27 [] 36 Total time: 3.399 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:28:51 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=4748886167107; f1:=725507982392; f2:=3499950548075; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:28:48 on modular [Seed = 3943909220] ------------------------------------- [] 27 [] 36 Total time: 3.279 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:29:22 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=2591961607789; f1:=36769060797; f2:=2811170238233; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:29:19 on modular [Seed = 3793374834] ------------------------------------- [] 27 [] 36 Total time: 3.299 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:29:37 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=2591961607789; f1:=36769060797; f2:=2811170238233; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:29:34 on modular [Seed = 4194455963] ------------------------------------- [] 27 [] 36 Total time: 3.229 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:30:03 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=1446741701307; f1:=3194847765863; f2:=3304559678408; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:30:00 on modular [Seed = 4060764597] ------------------------------------- [] 27 [ <1441432152364, 5075630842515, 1564835826223>, <4419698336419, 5158967442712, 3600217769814>, <5074066098303, 700598301859, 302544697506> ] [ , , ] [ , , ] [ , , ] [ , , ] [ , , ] [ , , ] 36 Total time: 3.499 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:30:26 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=5057832268023; f1:=2457454435757; f2:=5009798957119; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:30:23 on modular [Seed = 3275450515] ------------------------------------- [] 27 [] 36 Total time: 3.339 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:31:07 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=3908044323274; f1:=474141643354; f2:=3392077099935; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:31:04 on modular [Seed = 3676532956] ------------------------------------- [] 27 [ <1432718350231, 2577269460898, 1249229038910>, <4398886853922, 1664548382069, 4886036004408>, <5103591382933, 1225780450576, 4799931543768> ] [ ] [ ] [ ] [ ] [ ] [ ] 36 Total time: 3.339 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:31:28 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=5359564472347; f1:=1557625926929; f2:=2432895672430; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:31:24 on modular [Seed = 3542841536] ------------------------------------- [] 27 [ <2822438931716, 5357631023947, 1632327600978>, <3877337861163, 4930213235167, 4744243650287>, <4235419794207, 647352327972, 4558625335821> ] [ , ] [ , ] [ , ] [ , ] [ , ] [ , ] 36 Total time: 3.269 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:31:56 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=69275895431; f1:=2558966378446; f2:=2889492328518; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:31:53 on modular [Seed = 2874343517] ------------------------------------- [] 27 [ <1444534880264, 638408936802, 3517999112870>, <4292471587785, 2719758364766, 1257974476022>, <5198190119037, 2109430991975, 691624704651> ] [ , ] [ , ] [ , ] [ , ] [ , ] [ , ] 36 Total time: 3.279 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:32:07 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=69275895431; f1:=2558966378446; f2:=2889492328518; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:32:04 on modular [Seed = 2740652136] ------------------------------------- [] 27 [ <1444534880264, 638408936802, 3517999112870>, <4292471587785, 2719758364766, 1257974476022>, <5198190119037, 2109430991975, 691624704651> ] [ , ] [ , ] [ , ] [ , ] [ , ] [ , ] 36 Total time: 3.329 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:32:27 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=69275895431; f1:=2558966378446; f2:=2889492328518; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:32:23 on modular [Seed = 3141734508] ------------------------------------- [] 27 [ <1444534880264, 638408936802, 3517999112870>, <4292471587785, 2719758364766, 1257974476022>, <5198190119037, 2109430991975, 691624704651> ] [ , ] [ , ] [ , ] [ , ] [ , ] [ , ] 36 Total time: 3.319 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:32:46 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=2188720769727; f1:=2489747699477; f2:=2101389220360; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:32:43 on modular [Seed = 3008043031] ------------------------------------- [] 27 [ <2633972796332, 389071919784, 2945581151314>, <3337747150862, 3103654715067, 4108440050501>, <4963476639892, 1974871658692, 3881175385271> ] [ ] [ ] [ ] [ ] [ ] [ ] 36 Total time: 3.319 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host encserver1.math.ucalgary.ca. (136.159.61.73) Time: Fri Nov 28 13:33:08 2003 Input: p:= 5467598293543; K:=GF(p); P:=PolynomialRing(K,3); f0:=5050278591955; f1:=4076806917888; f2:=1296058978637; f3:=0; poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2); poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3); poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2* x^4-64*x^3*f2; poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24 *x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1; poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z -192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0- 256*x^5*z^3; I1:=ideal; V1:=Variety(I1); V1; for v in V1 do s1:=(f3+v[2]^3)/2; s0:=(f2+3*v[2]^2*v[1]-s1^2)/2; S:=x^2+s1*x+s0; Factorization(S); end for; VarietySizeOverAlgebraicClosure(I1); I2:=ideal; V2:=Variety(I2); V2; for v in V2 do if v[1] ne 0 then u2:=v[1]; u1:=v[2]; u0:=v[3]; U:=u2*x^2+u1*x+u0; s2:=(3*u1*u2^2)/(2*u2^3); s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3); s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3); S:=x^3+s2*x^2+s1*x+s0; Factorization(S); Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3); end if; end for; VarietySizeOverAlgebraicClosure(I2); Output: Magma V2.10-6 Fri Nov 28 2003 13:33:05 on modular [Seed = 2339577861] ------------------------------------- [] 27 [ <790394822678, 4568695114671, 3434700804444>, <2154255580542, 3238405308559, 5381764533926>, <2522947890323, 3128096163856, 2118731248716> ] [ ] [ ] [ ] [ ] [ ] [ ] 36 Total time: 3.319 seconds, Total memory usage: 1.95MB ************** MAGMA ***************** Host pcp238458pcs.elictc01.md.comcast.net. (68.55.164.65) Time: Fri Nov 28 16:03:21 2003 Input: F:=GF(97); a:=F!87; b:=F!46; E:=EllipticCurve([0,0,0,a,b]); order(E); Output: Magma V2.10-6 Fri Nov 28 2003 16:03:18 on modular [Seed = 2808029404] ------------------------------------- >> order(E);; ^ User error: Identifier 'order' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcp238458pcs.elictc01.md.comcast.net. (68.55.164.65) Time: Fri Nov 28 16:03:39 2003 Input: F:=GF(97); a:=F!87; b:=F!46; E:=EllipticCurve([0,0,0,a,b]); Order(E); Output: Magma V2.10-6 Fri Nov 28 2003 16:03:36 on modular [Seed = 3209115898] ------------------------------------- 111 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h-68-165-78-41.MIATFLAD.dynamic.covad.net. (68.165.78.41) Time: Fri Nov 28 18:09:47 2003 Input: sqrt{4} Output: Magma V2.10-6 Fri Nov 28 2003 18:09:44 on modular [Seed = 2874360191] ------------------------------------- >> sqrt{4} ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:26:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do print([N,i,(2),CP(DH(A[i],2)),(3),CP(DH(A[i],3)),(5),CP(DH(A[i],5)),(7),CP(DH(A[i],7)),(11),CP(DH(A[i],11)),(13),CP(DH(A[i],13))]); end for; Output: Magma V2.10-6 Sat Nov 29 2003 03:25:55 on modular [Seed = 3409751231] ------------------------------------- [ 364, 1, 2, $.1, 3, $.1 + 2, 5, $.1 - 1, 7, $.1 + 1, 11, $.1 + 4, 13, $.1 - 1 ] [ 364, 2, 2, $.1, 3, $.1, 5, $.1 + 3, 7, $.1 - 1, 11, $.1 + 2, 13, $.1 + 1 ] [ 364, 3, 2, $.1^2, 3, $.1^2 - 6, 5, $.1^2 + 2*$.1 - 5, 7, $.1^2 + 2*$.1 + 1, 11, $.1^2 - 8*$.1 + 10, 13, $.1^2 + 2*$.1 + 1 ] [ 364, 4, 2, $.1^2, 3, $.1^2 - 2*$.1 - 2, 5, $.1^2 - 3, 7, $.1^2 - 2*$.1 + 1, 11, $.1^2 - 6*$.1 + 6, 13, $.1^2 - 2*$.1 + 1 ] Total time: 6.919 seconds, Total memory usage: 3.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:33:30 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print([N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]); end for; Output: Magma V2.10-6 Sat Nov 29 2003 03:33:23 on modular [Seed = 2790375442] ------------------------------------- [ 364, 1, 2, $.1, 3, $.1 + 2, 5, $.1 - 1, 7, $.1 + 1, 11, $.1 + 4, 13, $.1 - 1 ] [ 364, 2, 2, $.1, 3, $.1, 5, $.1 + 3, 7, $.1 - 1, 11, $.1 + 2, 13, $.1 + 1 ] [ 364, 3, 2, $.1^2, 3, $.1^2 - 6, 5, $.1^2 + 2*$.1 - 5, 7, $.1^2 + 2*$.1 + 1, 11, $.1^2 - 8*$.1 + 10, 13, $.1^2 + 2*$.1 + 1 ] [ 364, 4, 2, $.1^2, 3, $.1^2 - 2*$.1 - 2, 5, $.1^2 - 3, 7, $.1^2 - 2*$.1 + 1, 11, $.1^2 - 6*$.1 + 6, 13, $.1^2 - 2*$.1 + 1 ] Total time: 6.819 seconds, Total memory usage: 3.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:36:38 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; print B; end for; Output: Magma V2.10-6 Sat Nov 29 2003 03:36:30 on modular [Seed = 2824850753] ------------------------------------- [ 364, 1, 2, $.1, 3, $.1 + 2, 5, $.1 - 1, 7, $.1 + 1, 11, $.1 + 4, 13, $.1 - 1 ] [ 364, 2, 2, $.1, 3, $.1, 5, $.1 + 3, 7, $.1 - 1, 11, $.1 + 2, 13, $.1 + 1 ] [ 364, 3, 2, $.1^2, 3, $.1^2 - 6, 5, $.1^2 + 2*$.1 - 5, 7, $.1^2 + 2*$.1 + 1, 11, $.1^2 - 8*$.1 + 10, 13, $.1^2 + 2*$.1 + 1 ] [ 364, 4, 2, $.1^2, 3, $.1^2 - 2*$.1 - 2, 5, $.1^2 - 3, 7, $.1^2 - 2*$.1 + 1, 11, $.1^2 - 6*$.1 + 6, 13, $.1^2 - 2*$.1 + 1 ] Total time: 6.739 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:39:56 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; print [B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]]; end for; Output: Magma V2.10-6 Sat Nov 29 2003 03:39:50 on modular [Seed = 3192511119] ------------------------------------- [ 364, 1, 2, $.1, 3, $.1 + 2, 5, $.1 - 1, 7, $.1 + 1, 11, $.1 + 4, 13, $.1 - 1 ] [ 364, 2, 2, $.1, 3, $.1, 5, $.1 + 3, 7, $.1 - 1, 11, $.1 + 2, 13, $.1 + 1 ] [ 364, 3, 2, $.1^2, 3, $.1^2 - 6, 5, $.1^2 + 2*$.1 - 5, 7, $.1^2 + 2*$.1 + 1, 11, $.1^2 - 8*$.1 + 10, 13, $.1^2 + 2*$.1 + 1 ] [ 364, 4, 2, $.1^2, 3, $.1^2 - 2*$.1 - 2, 5, $.1^2 - 3, 7, $.1^2 - 2*$.1 + 1, 11, $.1^2 - 6*$.1 + 6, 13, $.1^2 - 2*$.1 + 1 ] Total time: 6.659 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:41:21 2003 Input: print [1,2,3,4,5,6,7,8,9,10,11,12,13,14]; Output: Magma V2.10-6 Sat Nov 29 2003 03:41:18 on modular [Seed = 2407066438] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:41:38 2003 Input: print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14]; Output: Magma V2.10-6 Sat Nov 29 2003 03:41:35 on modular [Seed = 2539713359] ------------------------------------- >> print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:44:24 2003 Input: R:=PolynomialRing(Q); print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14]; Output: Magma V2.10-6 Sat Nov 29 2003 03:44:21 on modular [Seed = 2641034911] ------------------------------------- >> R:=PolynomialRing(Q); ^ User error: Identifier 'Q' has not been declared or assigned >> print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:44:49 2003 Input: R:=PolynomialRing(Integer); print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14]; Output: Magma V2.10-6 Sat Nov 29 2003 03:44:46 on modular [Seed = 1687357308] ------------------------------------- >> R:=PolynomialRing(Integer); ^ User error: Identifier 'Integer' has not been declared or assigned >> print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:46:16 2003 Input: R:=PolynomialRing(RationalField()); print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14]; Output: Magma V2.10-6 Sat Nov 29 2003 03:46:13 on modular [Seed = 1771965146] ------------------------------------- [ x + 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:46:44 2003 Input: R:=PolynomialRing(RationalField()); print [1,2,3,4,5,6,7,8,9,10,11,12,13,14]; Output: Magma V2.10-6 Sat Nov 29 2003 03:46:41 on modular [Seed = 1904612070] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:54:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "B[1]"; printf "B[2]"; printf "B[3]"; printf "B[4]"; printf "B[5]"; printf "B[6]"; printf "B[7]"; printf "B[8]"; printf "B[9]"; printf "B[10]"; printf "B[11]"; printf "B[12]"; printf "B[13]"; printf "B[14]"; end for; Output: Magma V2.10-6 Sat Nov 29 2003 03:53:53 on modular [Seed = 1270622860] ------------------------------------- B[1]B[2]B[3]B[4]B[5]B[6]B[7]B[8]B[9]B[10]B[11]B[12]B[13]B[14]B[1]B[2]B[3]B[4]B[\ 5]B[6]B[7]B[8]B[9]B[10]B[11]B[12]B[13]B[14]B[1]B[2]B[3]B[4]B[5]B[6]B[7]B[8]B[9]\ B[10]B[11]B[12]B[13]B[14]B[1]B[2]B[3]B[4]B[5]B[6]B[7]B[8]B[9]B[10]B[11]B[12]B[1\ 3]B[14] Total time: 6.869 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 03:59:27 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf B[1]; printf B[2]; printf B[3]; printf B[4]; printf B[5]; printf B[6]; printf B[7]; printf B[8]; printf B[9]; printf B[10]; printf B[11]; printf B[12]; printf B[13]; printf B[14]; end for; Output: Magma V2.10-6 Sat Nov 29 2003 03:59:20 on modular [Seed = 1538014165] ------------------------------------- >> printf B[1]; printf B[2]; printf B[3]; printf B[4]; printf B[5]; printf B[6 ^ Runtime error in printf: Argument 1 should be a format string Total time: 6.929 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:00:56 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; print B[1]; print B[2]; print B[3]; print B[4]; print B[5]; print B[6]; print B[7]; print B[8]; print B[9]; print B[10]; print B[11]; print B[12]; print B[13]; print B[14]; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:00:49 on modular [Seed = 735867916] ------------------------------------- 364 1 2 $.1 3 $.1 + 2 5 $.1 - 1 7 $.1 + 1 11 $.1 + 4 13 $.1 - 1 364 2 2 $.1 3 $.1 5 $.1 + 3 7 $.1 - 1 11 $.1 + 2 13 $.1 + 1 364 3 2 $.1^2 3 $.1^2 - 6 5 $.1^2 + 2*$.1 - 5 7 $.1^2 + 2*$.1 + 1 11 $.1^2 - 8*$.1 + 10 13 $.1^2 + 2*$.1 + 1 364 4 2 $.1^2 3 $.1^2 - 2*$.1 - 2 5 $.1^2 - 3 7 $.1^2 - 2*$.1 + 1 11 $.1^2 - 6*$.1 + 6 13 $.1^2 - 2*$.1 + 1 Total time: 6.919 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:07:56 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:07:49 on modular [Seed = 1436683220] ------------------------------------- 364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1 Total time: 7.369 seconds, Total memory usage: 3.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:08:38 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%on",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:08:31 on modular [Seed = 1571422262] ------------------------------------- 364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1n364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1n364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1n364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1n Total time: 7.099 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:09:04 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%on",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:08:57 on modular [Seed = 634550376] ------------------------------------- 364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1n364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1n364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1n364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1n Total time: 6.869 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:11:08 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; print [N,i]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12]; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:11:01 on modular [Seed = 918645751] ------------------------------------- [ 364, 1 ] 2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[ 364, 2 ] 2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1[ 364, 3 ] 2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1[ 364, 4 ] 2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1 Total time: 6.969 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:12:50 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=364; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:12:43 on modular [Seed = 1070097232] ------------------------------------- 364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[] 364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1[] 364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1[] 364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1[] Total time: 7.059 seconds, Total memory usage: 3.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:15:25 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [364..365] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:15:17 on modular [Seed = 4245332284] ------------------------------------- 364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[] 364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1[] 364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1[] 364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1[] 365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x + 6,13,x^2 - 12[] 365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[] 365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x + 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 - 16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3 + 9*x^2 - 28*x - 4[] 365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 - 14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 - 352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x - 3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[] 365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x + 3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x + 32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 - 7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 + 7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8 - 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[] Total time: 8.319 seconds, Total memory usage: 3.97MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:16:56 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [361..365] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:16:41 on modular [Seed = 3325139547] ------------------------------------- 361,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 - 3,11,$.1 + 5,13,$.1[] 361,2,2,$.1,3,$.1 - 2,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 - 4[] 361,3,2,$.1^2 - 5,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 361,4,2,$.1^2 - 5,3,$.1^2 + 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 + 3*$.1 - 9[] 361,5,2,$.1^2 - $.1 - 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1 + 9,11,$.1^2 + $.1 - 1,13,$.1^2 + 2*$.1 + 1[] 361,6,2,$.1^2 + $.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1 + 9,11,$.1^2 + $.1 - 1,13,$.1^2 - 2*$.1 + 1[] 361,7,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 + 37[] 361,8,2,$.1^3 - 3*$.1^2 + 3,3,$.1^3 - 3*$.1^2 + 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 - 37[] 361,9,2,$.1^4 - 5*$.1^2 + 5,3,$.1^4 - 5*$.1^2 + 5,5,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,7,$.1^4 + 8*$.1^3 + 14*$.1^2 - 8*$.1 + 1,11,$.1^4 + 10*$.1^3 + 35*$.1^2 + 50*$.1 + 25,13,$.1^4 - 10*$.1^2 + 5[] 362,1,2,x + 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x - 4[] 362,2,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x + 1,13,x + 4[] 362,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + x - 1,7,x^2 + 3*x + 1,11,x^2 + 2*x - 4,13,x^2 + 7*x + 11[] 362,4,2,x^2 - 2*x + 1,3,x^2 - 2*x - 1,5,x^2 - 4*x + 2,7,x^2 - 8,11,x^2 + 10*x + 23,13,x^2 - 8*x + 14[] 362,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 4*x^4 - 2*x^3 + 17*x^2 - x - 17,5,x^5 - 18*x^3 + 8*x^2 + 56*x - 48,7,x^5 - 5*x^4 - 9*x^3 + 61*x^2 - 136,11,x^5 - 4*x^4 - 4*x^3 + 13*x^2 + 5*x - 9,13,x^5 - 10*x^4 + 22*x^3 + 20*x^2 - 48*x + 16[] 362,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 13*x^3 + 3*x^2 + 38*x - 28,5,x^5 + x^4 - 17*x^3 - 16*x^2 + 68*x + 72,7,x^5 - 6*x^4 - 3*x^3 + 51*x^2 - 6*x - 109,11,x^5 - 4*x^4 - 23*x^3 + 139*x^2 - 214*x + 84,13,x^5 + 5*x^4 - 31*x^3 - 90*x^2 + 328*x + 8[] 363,1,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x - 2[] 363,2,2,x - 2,3,x + 1,5,x - 4,7,x + 1,11,x,13,x - 2[] 363,3,2,x + 2,3,x + 1,5,x - 4,7,x - 1,11,x,13,x + 2[] 363,4,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 3[] 363,5,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x + 1,11,x^2,13,x^2 + 4*x - 1[] 363,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x + 1,11,x^2,13,x^2 - 4*x - 1[] 363,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 20,11,x^2,13,x^2[] 363,8,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 6*x + 9,11,x^2,13,x^2 - 8*x + 11[] 363,9,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x + 9,11,x^2,13,x^2 + 8*x + 11[] 363,10,2,x^4 - 7*x^2 + 4,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 15*x^2 + 16*x + 64,7,x^4 - 7*x^2 + 4,11,x^4,13,x^4 - 51*x^2 + 576[] 364,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x + 4,13,x - 1[] 364,2,2,x,3,x,5,x + 3,7,x - 1,11,x + 2,13,x + 1[] 364,3,2,x^2,3,x^2 - 6,5,x^2 + 2*x - 5,7,x^2 + 2*x + 1,11,x^2 - 8*x + 10,13,x^2 + 2*x + 1[] 364,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 6*x + 6,13,x^2 - 2*x + 1[] 365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x + 6,13,x^2 - 12[] 365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[] 365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x + 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 - 16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3 + 9*x^2 - 28*x - 4[] 365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 - 14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 - 352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x - 3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[] 365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x + 3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x + 32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 - 7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 + 7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8 - 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[] Total time: 14.479 seconds, Total memory usage: 5.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:18:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [361..368] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 04:17:52 on modular [Seed = 3459880426] ------------------------------------- 361,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 - 3,11,$.1 + 5,13,$.1[] 361,2,2,$.1,3,$.1 - 2,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 - 4[] 361,3,2,$.1^2 - 5,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 361,4,2,$.1^2 - 5,3,$.1^2 + 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 + 3*$.1 - 9[] 361,5,2,$.1^2 - $.1 - 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1 + 9,11,$.1^2 + $.1 - 1,13,$.1^2 + 2*$.1 + 1[] 361,6,2,$.1^2 + $.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1 + 9,11,$.1^2 + $.1 - 1,13,$.1^2 - 2*$.1 + 1[] 361,7,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 + 37[] 361,8,2,$.1^3 - 3*$.1^2 + 3,3,$.1^3 - 3*$.1^2 + 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 - 37[] 361,9,2,$.1^4 - 5*$.1^2 + 5,3,$.1^4 - 5*$.1^2 + 5,5,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,7,$.1^4 + 8*$.1^3 + 14*$.1^2 - 8*$.1 + 1,11,$.1^4 + 10*$.1^3 + 35*$.1^2 + 50*$.1 + 25,13,$.1^4 - 10*$.1^2 + 5[] 362,1,2,x + 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x - 4[] 362,2,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x + 1,13,x + 4[] 362,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + x - 1,7,x^2 + 3*x + 1,11,x^2 + 2*x - 4,13,x^2 + 7*x + 11[] 362,4,2,x^2 - 2*x + 1,3,x^2 - 2*x - 1,5,x^2 - 4*x + 2,7,x^2 - 8,11,x^2 + 10*x + 23,13,x^2 - 8*x + 14[] 362,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 4*x^4 - 2*x^3 + 17*x^2 - x - 17,5,x^5 - 18*x^3 + 8*x^2 + 56*x - 48,7,x^5 - 5*x^4 - 9*x^3 + 61*x^2 - 136,11,x^5 - 4*x^4 - 4*x^3 + 13*x^2 + 5*x - 9,13,x^5 - 10*x^4 + 22*x^3 + 20*x^2 - 48*x + 16[] 362,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 13*x^3 + 3*x^2 + 38*x - 28,5,x^5 + x^4 - 17*x^3 - 16*x^2 + 68*x + 72,7,x^5 - 6*x^4 - 3*x^3 + 51*x^2 - 6*x - 109,11,x^5 - 4*x^4 - 23*x^3 + 139*x^2 - 214*x + 84,13,x^5 + 5*x^4 - 31*x^3 - 90*x^2 + 328*x + 8[] 363,1,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x - 2[] 363,2,2,x - 2,3,x + 1,5,x - 4,7,x + 1,11,x,13,x - 2[] 363,3,2,x + 2,3,x + 1,5,x - 4,7,x - 1,11,x,13,x + 2[] 363,4,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 3[] 363,5,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x + 1,11,x^2,13,x^2 + 4*x - 1[] 363,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x + 1,11,x^2,13,x^2 - 4*x - 1[] 363,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 20,11,x^2,13,x^2[] 363,8,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 6*x + 9,11,x^2,13,x^2 - 8*x + 11[] 363,9,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x + 9,11,x^2,13,x^2 + 8*x + 11[] 363,10,2,x^4 - 7*x^2 + 4,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 15*x^2 + 16*x + 64,7,x^4 - 7*x^2 + 4,11,x^4,13,x^4 - 51*x^2 + 576[] 364,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x + 4,13,x - 1[] 364,2,2,x,3,x,5,x + 3,7,x - 1,11,x + 2,13,x + 1[] 364,3,2,x^2,3,x^2 - 6,5,x^2 + 2*x - 5,7,x^2 + 2*x + 1,11,x^2 - 8*x + 10,13,x^2 + 2*x + 1[] 364,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 6*x + 6,13,x^2 - 2*x + 1[] 365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x + 6,13,x^2 - 12[] 365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[] 365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x + 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 - 16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3 + 9*x^2 - 28*x - 4[] 365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 - 14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 - 352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x - 3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[] 365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x + 3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x + 32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 - 7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 + 7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8 - 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[] 366,1,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x + 2[] 366,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 6,13,x[] 366,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x + 3,13,x + 1[] 366,4,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 2,13,x - 4[] 366,5,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x + 1,13,x + 5[] 366,6,2,x - 1,3,x - 1,5,x - 1,7,x - 1,11,x + 1,13,x + 5[] 366,7,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x - 4[] 366,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 17,7,x^2 + 3*x - 2,11,x^2 - 3*x - 2,13,x^2 - 7*x + 8[] 367,1,2,x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 61*x^6 + 197*x^5 + 212*x^4 - 66*x^3 - 132*x^2 - 12*x + 13,3,x^11 + 6*x^10 + 3*x^9 - 41*x^8 - 64*x^7 + 64*x^6 + 158*x^5 - 9*x^4 - 118*x^3 - 14*x^2 + 24*x - 1,5,x^11 + 8*x^10 + 7*x^9 - 85*x^8 - 191*x^7 + 190*x^6 + 791*x^5 + 247*x^4 - 815*x^3 - 687*x^2 - 128*x + 5,7,x^11 + 7*x^10 - 13*x^9 - 186*x^8 - 277*x^7 + 859*x^6 + 2780*x^5 + 1778*x^4 - 1871*x^3 - 2671*x^2 - 799*x + 25,11,x^11 + 10*x^10 - 12*x^9 - 313*x^8 - 120*x^7 + 3196*x^6 + 661*x^5 - 11246*x^4 + 2768*x^3 + 5371*x^2 - 892*x - 743,13,x^11 + 5*x^10 - 48*x^9 - 277*x^8 + 569*x^7 + 4656*x^6 + 745*x^5 - 22685*x^4 - 14329*x^3 + 25989*x^2 - 1682*x - 2621[] 367,2,2,x^19 - 9*x^18 + 11*x^17 + 123*x^16 - 372*x^15 - 469*x^14 + 2884*x^13 - 550*x^12 - 10042*x^11 + 8029*x^10 + 17059*x^9 - 20350*x^8 - 12836*x^7 + 20779*x^6 + 2682*x^5 - 7739*x^4 + 63*x^3 + 899*x^2 - 27*x - 29,3,x^19 - 4*x^18 - 35*x^17 + 149*x^16 + 486*x^15 - 2260*x^14 - 3442*x^13 + 18203*x^12 + 13108*x^11 - 84580*x^10 - 25304*x^9 + 229397*x^8 + 19212*x^7 - 348172*x^6 - 3000*x^5 + 262144*x^4 + 15968*x^3 - 68672*x^2 - 21504*x - 1792,5,x^19 - 6*x^18 - 43*x^17 + 309*x^16 + 595*x^15 - 6046*x^14 - 2461*x^13 + 58707*x^12 - 5347*x^11 - 322649*x^10 + 48332*x^9 + 1052323*x^8 + 41520*x^7 - 1950148*x^6 - 697328*x^5 + 1640832*x^4 + 1181408*x^3 - 153984*x^2 - 315520*x - 68864,7,x^19 - x^18 - 68*x^17 + 93*x^16 + 1821*x^15 - 3162*x^14 - 24162*x^13 + 51825*x^12 + 161877*x^11 - 438685*x^10 - 465321*x^9 + 1870316*x^8 + 63387*x^7 - 3600393*x^6 + 1757269*x^5 + 2308835*x^4 - 1465397*x^3 - 561533*x^2 + 257949*x + 75177,11,x^19 - 4*x^18 - 120*x^17 + 545*x^16 + 5632*x^15 - 29392*x^14 - 128435*x^13 + 812306*x^12 + 1363286*x^11 - 12382021*x^10 - 2606314*x^9 + 102742747*x^8 - 71962574*x^7 - 413796744*x^6 + 565237368*x^5 + 539820496*x^4 - 1225061216*x^3 + 173670080*x^2 + 608625792*x - 263379712,13,x^19 - 5*x^18 - 99*x^17 + 398*x^16 + 4006*x^15 - 11816*x^14 - 82529*x^13 + 167855*x^12 + 890309*x^11 - 1326823*x^10 - 4991303*x^9 + 6366113*x^8 + 13486540*x^7 - 17861951*x^6 - 12151477*x^5 + 22331038*x^4 - 6313452*x^3 - 683605*x^2 + 175252*x - 2548[] Errors: /home/mfd/gomagma: line 2: 23466 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 04:18:46 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [361..367] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 04:18:24 on modular [Seed = 3609234643] ------------------------------------- 361,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 - 3,11,$.1 + 5,13,$.1[] 361,2,2,$.1,3,$.1 - 2,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 - 4[] 361,3,2,$.1^2 - 5,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 361,4,2,$.1^2 - 5,3,$.1^2 + 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 + 3*$.1 - 9[] 361,5,2,$.1^2 - $.1 - 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1 + 9,11,$.1^2 + $.1 - 1,13,$.1^2 + 2*$.1 + 1[] 361,6,2,$.1^2 + $.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1 + 9,11,$.1^2 + $.1 - 1,13,$.1^2 - 2*$.1 + 1[] 361,7,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 + 37[] 361,8,2,$.1^3 - 3*$.1^2 + 3,3,$.1^3 - 3*$.1^2 + 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 - 37[] 361,9,2,$.1^4 - 5*$.1^2 + 5,3,$.1^4 - 5*$.1^2 + 5,5,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,7,$.1^4 + 8*$.1^3 + 14*$.1^2 - 8*$.1 + 1,11,$.1^4 + 10*$.1^3 + 35*$.1^2 + 50*$.1 + 25,13,$.1^4 - 10*$.1^2 + 5[] 362,1,2,x + 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x - 4[] 362,2,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x + 1,13,x + 4[] 362,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + x - 1,7,x^2 + 3*x + 1,11,x^2 + 2*x - 4,13,x^2 + 7*x + 11[] 362,4,2,x^2 - 2*x + 1,3,x^2 - 2*x - 1,5,x^2 - 4*x + 2,7,x^2 - 8,11,x^2 + 10*x + 23,13,x^2 - 8*x + 14[] 362,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 4*x^4 - 2*x^3 + 17*x^2 - x - 17,5,x^5 - 18*x^3 + 8*x^2 + 56*x - 48,7,x^5 - 5*x^4 - 9*x^3 + 61*x^2 - 136,11,x^5 - 4*x^4 - 4*x^3 + 13*x^2 + 5*x - 9,13,x^5 - 10*x^4 + 22*x^3 + 20*x^2 - 48*x + 16[] 362,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 13*x^3 + 3*x^2 + 38*x - 28,5,x^5 + x^4 - 17*x^3 - 16*x^2 + 68*x + 72,7,x^5 - 6*x^4 - 3*x^3 + 51*x^2 - 6*x - 109,11,x^5 - 4*x^4 - 23*x^3 + 139*x^2 - 214*x + 84,13,x^5 + 5*x^4 - 31*x^3 - 90*x^2 + 328*x + 8[] 363,1,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x - 2[] 363,2,2,x - 2,3,x + 1,5,x - 4,7,x + 1,11,x,13,x - 2[] 363,3,2,x + 2,3,x + 1,5,x - 4,7,x - 1,11,x,13,x + 2[] 363,4,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 3[] 363,5,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x + 1,11,x^2,13,x^2 + 4*x - 1[] 363,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x + 1,11,x^2,13,x^2 - 4*x - 1[] 363,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 20,11,x^2,13,x^2[] 363,8,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 6*x + 9,11,x^2,13,x^2 - 8*x + 11[] 363,9,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x + 9,11,x^2,13,x^2 + 8*x + 11[] 363,10,2,x^4 - 7*x^2 + 4,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 15*x^2 + 16*x + 64,7,x^4 - 7*x^2 + 4,11,x^4,13,x^4 - 51*x^2 + 576[] 364,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x + 4,13,x - 1[] 364,2,2,x,3,x,5,x + 3,7,x - 1,11,x + 2,13,x + 1[] 364,3,2,x^2,3,x^2 - 6,5,x^2 + 2*x - 5,7,x^2 + 2*x + 1,11,x^2 - 8*x + 10,13,x^2 + 2*x + 1[] 364,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 6*x + 6,13,x^2 - 2*x + 1[] 365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x + 6,13,x^2 - 12[] 365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[] 365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x + 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 - 16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3 + 9*x^2 - 28*x - 4[] 365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 - 14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 - 352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x - 3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[] 365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x + 3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x + 32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 - 7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 + 7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8 - 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[] 366,1,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x + 2[] 366,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 6,13,x[] 366,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x + 3,13,x + 1[] 366,4,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 2,13,x - 4[] 366,5,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x + 1,13,x + 5[] 366,6,2,x - 1,3,x - 1,5,x - 1,7,x - 1,11,x + 1,13,x + 5[] 366,7,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x - 4[] 366,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 17,7,x^2 + 3*x - 2,11,x^2 - 3*x - 2,13,x^2 - 7*x + 8[] 367,1,2,x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 61*x^6 + 197*x^5 + 212*x^4 - 66*x^3 - 132*x^2 - 12*x + 13,3,x^11 + 6*x^10 + 3*x^9 - 41*x^8 - 64*x^7 + 64*x^6 + 158*x^5 - 9*x^4 - 118*x^3 - 14*x^2 + 24*x - 1,5,x^11 + 8*x^10 + 7*x^9 - 85*x^8 - 191*x^7 + 190*x^6 + 791*x^5 + 247*x^4 - 815*x^3 - 687*x^2 - 128*x + 5,7,x^11 + 7*x^10 - 13*x^9 - 186*x^8 - 277*x^7 + 859*x^6 + 2780*x^5 + 1778*x^4 - 1871*x^3 - 2671*x^2 - 799*x + 25,11,x^11 + 10*x^10 - 12*x^9 - 313*x^8 - 120*x^7 + 3196*x^6 + 661*x^5 - 11246*x^4 + 2768*x^3 + 5371*x^2 - 892*x - 743,13,x^11 + 5*x^10 - 48*x^9 - 277*x^8 + 569*x^7 + 4656*x^6 + 745*x^5 - 22685*x^4 - 14329*x^3 + 25989*x^2 - 1682*x - 2621[] 367,2,2,x^19 - 9*x^18 + 11*x^17 + 123*x^16 - 372*x^15 - 469*x^14 + 2884*x^13 - 550*x^12 - 10042*x^11 + 8029*x^10 + 17059*x^9 - 20350*x^8 - 12836*x^7 + 20779*x^6 + 2682*x^5 - 7739*x^4 + 63*x^3 + 899*x^2 - 27*x - 29,3,x^19 - 4*x^18 - 35*x^17 + 149*x^16 + 486*x^15 - 2260*x^14 - 3442*x^13 + 18203*x^12 + 13108*x^11 - 84580*x^10 - 25304*x^9 + 229397*x^8 + 19212*x^7 - 348172*x^6 - 3000*x^5 + 262144*x^4 + 15968*x^3 - 68672*x^2 - 21504*x - 1792,5,x^19 - 6*x^18 - 43*x^17 + 309*x^16 + 595*x^15 - 6046*x^14 - 2461*x^13 + 58707*x^12 - 5347*x^11 - 322649*x^10 + 48332*x^9 + 1052323*x^8 + 41520*x^7 - 1950148*x^6 - 697328*x^5 + 1640832*x^4 + 1181408*x^3 - 153984*x^2 - 315520*x - 68864,7,x^19 - x^18 - 68*x^17 + 93*x^16 + 1821*x^15 - 3162*x^14 - 24162*x^13 + 51825*x^12 + 161877*x^11 - 438685*x^10 - 465321*x^9 + 1870316*x^8 + 63387*x^7 - 3600393*x^6 + 1757269*x^5 + 2308835*x^4 - 1465397*x^3 - 561533*x^2 + 257949*x + 75177,11,x^19 - 4*x^18 - 120*x^17 + 545*x^16 + 5632*x^15 - 29392*x^14 - 128435*x^13 + 812306*x^12 + 1363286*x^11 - 12382021*x^10 - 2606314*x^9 + 102742747*x^8 - 71962574*x^7 - 413796744*x^6 + 565237368*x^5 + 539820496*x^4 - 1225061216*x^3 + 173670080*x^2 + 608625792*x - 263379712,13,x^19 - 5*x^18 - 99*x^17 + 398*x^16 + 4006*x^15 - 11816*x^14 - 82529*x^13 + 167855*x^12 + 890309*x^11 - 1326823*x^10 - 4991303*x^9 + 6366113*x^8 + 13486540*x^7 - 17861951*x^6 - 12151477*x^5 + 22331038*x^4 - 6313452*x^3 - 683605*x^2 + 175252*x - 2548[] Total time: 21.159 seconds, Total memory usage: 6.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 06:46:22 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [11..20] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 06:46:17 on modular [Seed = 1036682582] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 14,1,2,x + 1,3,x + 2,5,x,7,x - 1,11,x,13,x + 4[] 15,1,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 4,13,x + 2[] 17,1,2,x + 1,3,x,5,x + 2,7,x - 4,11,x,13,x + 2[] 19,1,2,x,3,x + 2,5,x - 3,7,x + 1,11,x - 3,13,x + 4[] 20,1,2,x,3,x + 2,5,x + 1,7,x - 2,11,x,13,x - 2[] Total time: 4.049 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 06:46:35 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [11..20] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 06:46:31 on modular [Seed = 99794288] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 14,1,2,x + 1,3,x + 2,5,x,7,x - 1,11,x,13,x + 4[] 15,1,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 4,13,x + 2[] 17,1,2,x + 1,3,x,5,x + 2,7,x - 4,11,x,13,x + 2[] 19,1,2,x,3,x + 2,5,x - 3,7,x + 1,11,x - 3,13,x + 4[] 20,1,2,x,3,x + 2,5,x + 1,7,x - 2,11,x,13,x - 2[] Total time: 4.159 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 06:49:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [20..40] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 06:48:54 on modular [Seed = 317041366] ------------------------------------- 20,1,2,$.1,3,$.1 + 2,5,$.1 + 1,7,$.1 - 2,11,$.1,13,$.1 - 2[] 21,1,2,x + 1,3,x - 1,5,x + 2,7,x + 1,11,x - 4,13,x + 2[] 23,1,2,x^2 + x - 1,3,x^2 - 5,5,x^2 + 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 6*x + 4,13,x^2 - 6*x + 9[] 24,1,2,x,3,x + 1,5,x + 2,7,x,11,x - 4,13,x + 2[] 26,1,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x - 6,13,x - 1[] 26,2,2,x - 1,3,x + 3,5,x + 1,7,x - 1,11,x + 2,13,x + 1[] 27,1,2,x,3,x,5,x,7,x + 1,11,x,13,x - 5[] 29,1,2,x^2 + 2*x - 1,3,x^2 - 2*x - 1,5,x^2 + 2*x + 1,7,x^2 - 8,11,x^2 - 2*x - 1,13,x^2 + 2*x - 7[] 30,1,2,x + 1,3,x - 1,5,x + 1,7,x + 4,11,x,13,x - 2[] 31,1,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 - 4*x + 4,13,x^2 + 2*x - 4[] 32,1,2,x,3,x,5,x + 2,7,x,11,x,13,x - 6[] 33,1,2,x - 1,3,x + 1,5,x + 2,7,x - 4,11,x - 1,13,x + 2[] 34,1,2,x - 1,3,x + 2,5,x,7,x + 4,11,x - 6,13,x - 2[] 35,1,2,x,3,x - 1,5,x + 1,7,x - 1,11,x + 3,13,x - 5[] 35,2,2,x^2 + x - 4,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - x - 4,13,x^2 - 5*x + 2[] 36,1,2,x,3,x,5,x,7,x + 4,11,x,13,x - 2[] 37,1,2,x + 2,3,x + 3,5,x + 2,7,x + 1,11,x + 5,13,x + 2[] 37,2,2,x,3,x - 1,5,x,7,x + 1,11,x - 3,13,x + 4[] 38,1,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 6,13,x - 5[] 38,2,2,x - 1,3,x + 1,5,x + 4,7,x - 3,11,x - 2,13,x + 1[] 39,1,2,x - 1,3,x + 1,5,x - 2,7,x + 4,11,x - 4,13,x - 1[] 39,2,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 + 4*x + 4,13,x^2 + 2*x + 1[] 40,1,2,x,3,x,5,x - 1,7,x + 4,11,x - 4,13,x + 2[] Total time: 7.539 seconds, Total memory usage: 4.93MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 06:51:39 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [40..80] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 06:51:21 on modular [Seed = 3809760440] ------------------------------------- 40,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 + 4,11,$.1 - 4,13,$.1 + 2[] 41,1,2,x^3 + x^2 - 5*x - 1,3,x^3 - 4*x + 2,5,x^3 + 2*x^2 - 4*x - 4,7,x^3 - 6*x^2 + 8*x - 2,11,x^3 - 2*x^2 - 20*x + 50,13,x^3 + 2*x^2 - 12*x - 8[] 42,1,2,x - 1,3,x + 1,5,x + 2,7,x + 1,11,x + 4,13,x - 6[] 43,1,2,x + 2,3,x + 2,5,x + 4,7,x,11,x - 3,13,x + 5[] 43,2,2,x^2 - 2,3,x^2 - 2,5,x^2 - 4*x + 2,7,x^2 + 4*x + 2,11,x^2 + 2*x - 7,13,x^2 - 2*x - 7[] 44,1,2,x,3,x - 1,5,x + 3,7,x - 2,11,x + 1,13,x + 4[] 45,1,2,x - 1,3,x,5,x + 1,7,x,11,x - 4,13,x + 2[] 46,1,2,x + 1,3,x,5,x - 4,7,x + 4,11,x - 2,13,x + 2[] 47,1,2,x^4 - x^3 - 5*x^2 + 5*x - 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 + 2*x^3 - 16*x^2 - 16*x + 48,7,x^4 - 4*x^3 - 7*x^2 + 44*x - 43,11,x^4 + 6*x^3 - 4*x^2 - 56*x - 48,13,x^4 - 8*x^3 + 56*x + 48[] 48,1,2,x,3,x - 1,5,x + 2,7,x,11,x + 4,13,x + 2[] 49,1,2,x - 1,3,x,5,x,7,x,11,x - 4,13,x[] 50,1,2,x + 1,3,x - 1,5,x,7,x - 2,11,x + 3,13,x + 4[] 50,2,2,x - 1,3,x + 1,5,x,7,x + 2,11,x + 3,13,x - 4[] 51,1,2,x,3,x - 1,5,x - 3,7,x + 4,11,x + 3,13,x + 1[] 51,2,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2,11,x^2 + x - 4,13,x^2 - 5*x + 2[] 52,1,2,x,3,x,5,x - 2,7,x + 2,11,x + 2,13,x + 1[] 53,1,2,x + 1,3,x + 3,5,x,7,x + 4,11,x,13,x + 3[] 53,2,2,x^3 + x^2 - 3*x - 1,3,x^3 - 3*x^2 - x + 1,5,x^3 + 2*x^2 - 4*x - 4,7,x^3 - 4*x^2 + 4,11,x^3 + 4*x^2 - 4*x - 20,13,x^3 - 3*x^2 + 3*x - 1[] 54,1,2,x + 1,3,x,5,x - 3,7,x + 1,11,x + 3,13,x + 4[] 54,2,2,x - 1,3,x,5,x + 3,7,x + 1,11,x - 3,13,x + 4[] 55,1,2,x - 1,3,x,5,x - 1,7,x,11,x + 1,13,x - 2[] 55,2,2,x^2 - 2*x - 1,3,x^2 - 8,5,x^2 + 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 2*x + 1,13,x^2 + 8*x + 8[] 56,1,2,x,3,x - 2,5,x + 4,7,x - 1,11,x,13,x[] 56,2,2,x,3,x,5,x - 2,7,x + 1,11,x + 4,13,x - 2[] 57,1,2,x + 2,3,x + 1,5,x + 3,7,x + 5,11,x - 1,13,x - 2[] 57,2,2,x - 1,3,x - 1,5,x + 2,7,x,11,x,13,x - 6[] 57,3,2,x + 2,3,x - 1,5,x - 1,7,x - 3,11,x + 3,13,x + 6[] 58,1,2,x + 1,3,x + 3,5,x + 3,7,x + 2,11,x + 1,13,x - 3[] 58,2,2,x - 1,3,x + 1,5,x - 1,7,x + 2,11,x + 3,13,x + 1[] 59,1,2,x^5 - 9*x^3 + 2*x^2 + 16*x - 8,3,x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 13*x - 1,5,x^5 - 2*x^4 - 14*x^3 + 23*x^2 + 19*x + 1,7,x^5 - 2*x^4 - 16*x^3 + 43*x^2 + 13*x - 71,11,x^5 + 2*x^4 - 24*x^3 - 24*x^2 + 128*x - 64,13,x^5 - 8*x^4 + 88*x^2 - 48*x - 224[] 61,1,2,x + 1,3,x + 2,5,x + 3,7,x - 1,11,x + 5,13,x - 1[] 61,2,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 + x^2 - 9*x - 13,7,x^3 + 3*x^2 - x - 1,11,x^3 - 13*x^2 + 53*x - 67,13,x^3 + 9*x^2 + 11*x - 37[] 62,1,2,x - 1,3,x,5,x + 2,7,x,11,x,13,x - 2[] 62,2,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 + 6*x + 6,13,x^2 + 2*x - 26[] 63,1,2,x - 1,3,x,5,x - 2,7,x + 1,11,x + 4,13,x + 2[] 63,2,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2 - 2*x + 1,11,x^2 - 12,13,x^2 - 4*x + 4[] 64,1,2,x,3,x,5,x - 2,7,x,11,x,13,x + 6[] 65,1,2,x + 1,3,x + 2,5,x + 1,7,x + 4,11,x - 2,13,x + 1[] 65,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 6*x + 6,13,x^2 - 2*x + 1[] 65,3,2,x^2 + 2*x - 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 4*x - 4,11,x^2 - 4*x + 2,13,x^2 + 2*x + 1[] 66,1,2,x + 1,3,x - 1,5,x,7,x - 2,11,x + 1,13,x + 4[] 66,2,2,x - 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x + 6[] 66,3,2,x - 1,3,x - 1,5,x + 4,7,x + 2,11,x - 1,13,x - 4[] 67,1,2,x - 2,3,x + 2,5,x - 2,7,x + 2,11,x + 4,13,x - 2[] 67,2,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 + 6*x + 9,7,x^2 + x - 11,11,x^2 - 5,13,x^2 + 7*x + 1[] 67,3,2,x^2 + x - 1,3,x^2 - x - 1,5,x^2 - 4*x - 1,7,x^2 - x - 1,11,x^2 - 2*x + 1,13,x^2 + x - 1[] 68,1,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 + 2*x - 2,11,x^2 + 6*x + 6,13,x^2 - 4*x - 8[] 69,1,2,x - 1,3,x - 1,5,x,7,x + 2,11,x - 4,13,x + 6[] 69,2,2,x^2 - 5,3,x^2 + 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 2*x - 4,11,x^2 - 8*x + 16,13,x^2 - 20[] 70,1,2,x - 1,3,x,5,x + 1,7,x + 1,11,x - 4,13,x + 6[] 71,1,2,x^3 - 5*x + 3,3,x^3 + x^2 - 8*x - 3,5,x^3 + 3*x^2 - 2*x - 7,7,x^3 - 2*x^2 - 16*x + 24,11,x^3 + 2*x^2 - 16*x - 24,13,x^3 - 12*x^2 + 48*x - 64[] 71,2,2,x^3 + x^2 - 4*x - 3,3,x^3 - x^2 - 4*x + 3,5,x^3 - 5*x^2 - 2*x + 25,7,x^3 - 2*x^2 - 16*x + 24,11,x^3 - 20*x + 24,13,x^3 + 6*x^2 - 8*x - 56[] 72,1,2,x,3,x,5,x - 2,7,x,11,x + 4,13,x + 2[] 73,1,2,x - 1,3,x,5,x - 2,7,x - 2,11,x + 2,13,x + 6[] 73,2,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x + 9,11,x^2 + 3*x + 1,13,x^2 - x - 11[] 73,3,2,x^2 - x - 3,3,x^2 - x - 3,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 7*x + 9,13,x^2 + x - 3[] 74,1,2,x^2 + 2*x + 1,3,x^2 - 3*x - 1,5,x^2 + x - 3,7,x^2 - 2*x - 12,11,x^2 + x - 3,13,x^2 + x - 3[] 74,2,2,x^2 - 2*x + 1,3,x^2 + x - 1,5,x^2 - x - 11,7,x^2 + 2*x - 4,11,x^2 + 5*x + 5,13,x^2 - x - 11[] 75,1,2,x - 2,3,x + 1,5,x,7,x + 3,11,x - 2,13,x - 1[] 75,2,2,x - 1,3,x - 1,5,x,7,x,11,x + 4,13,x - 2[] 75,3,2,x + 2,3,x - 1,5,x,7,x - 3,11,x - 2,13,x + 1[] 76,1,2,x,3,x - 2,5,x + 1,7,x + 3,11,x - 5,13,x + 4[] 77,1,2,x,3,x + 3,5,x + 1,7,x + 1,11,x + 1,13,x + 4[] 77,2,2,x - 1,3,x - 2,5,x + 2,7,x + 1,11,x - 1,13,x - 4[] 77,3,2,x,3,x - 1,5,x - 3,7,x - 1,11,x + 1,13,x + 4[] 77,4,2,x^2 - 5,3,x^2 - 2*x - 4,5,x^2 + 4*x + 4,7,x^2 - 2*x + 1,11,x^2 + 2*x + 1,13,x^2 - 2*x - 4[] 78,1,2,x + 1,3,x + 1,5,x - 2,7,x - 4,11,x + 4,13,x - 1[] 79,1,2,x + 1,3,x + 1,5,x + 3,7,x + 1,11,x + 2,13,x - 3[] 79,2,2,x^5 - 6*x^3 + 8*x - 1,3,x^5 - x^4 - 12*x^3 + 8*x^2 + 24*x - 16,5,x^5 - 7*x^4 + 9*x^3 + 27*x^2 - 65*x + 31,7,x^5 + 5*x^4 - 6*x^3 - 52*x^2 - 56*x - 16,11,x^5 - 2*x^4 - 35*x^3 + 34*x^2 + 185*x + 106,13,x^5 + 3*x^4 - 23*x^3 - 123*x^2 - 197*x - 103[] 80,1,2,x,3,x,5,x - 1,7,x - 4,11,x + 4,13,x + 2[] 80,2,2,x,3,x - 2,5,x + 1,7,x + 2,11,x,13,x - 2[] Total time: 18.260 seconds, Total memory usage: 7.05MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Nov 29 07:00:46 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [80..110] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 07:00:23 on modular [Seed = 4161752525] ------------------------------------- 80,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 - 4,11,$.1 + 4,13,$.1 + 2[] 80,2,2,$.1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 2,11,$.1,13,$.1 - 2[] 81,1,2,x^2 - 3,3,x^2,5,x^2 - 3,7,x^2 - 4*x + 4,11,x^2 - 12,13,x^2 + 2*x + 1[] 82,1,2,x + 1,3,x + 2,5,x + 2,7,x + 4,11,x + 2,13,x - 4[] 82,2,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 8,7,x^2 + 4*x + 2,11,x^2 - 18,13,x^2[] 83,1,2,x + 1,3,x + 1,5,x + 2,7,x + 3,11,x - 3,13,x + 6[] 83,2,2,x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8,3,x^6 - x^5 - 10*x^4 + 5*x^3 + 30*x^2 - 4*x - 25,5,x^6 - 2*x^5 - 20*x^4 + 28*x^3 + 104*x^2 - 64*x - 160,7,x^6 - 3*x^5 - 22*x^4 + 55*x^3 + 154*x^2 - 228*x - 409,11,x^6 + 3*x^5 - 26*x^4 - 83*x^3 + 66*x^2 + 156*x - 113,13,x^6 - 14*x^5 + 44*x^4 + 108*x^3 - 488*x^2 - 288*x + 992[] 84,1,2,x,3,x + 1,5,x - 4,7,x + 1,11,x - 2,13,x + 6[] 84,2,2,x,3,x - 1,5,x,7,x - 1,11,x + 6,13,x - 2[] 85,1,2,x - 1,3,x - 2,5,x + 1,7,x + 2,11,x - 2,13,x - 2[] 85,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 + 4*x + 2,11,x^2 + 8*x + 14,13,x^2 - 8[] 85,3,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 + 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 8*x + 16[] 86,1,2,x^2 + 2*x + 1,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 4*x + 4[] 86,2,2,x^2 - 2*x + 1,3,x^2 - x - 1,5,x^2 + 3*x + 1,7,x^2 - 20,11,x^2 + 4*x - 16,13,x^2 - 20[] 87,1,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x - 1,11,x^2 - 4*x - 1,13,x^2 + 2*x - 19[] 87,2,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 16*x + 8,7,x^3 - 4*x^2 - x + 8,11,x^3 + 8*x^2 + 15*x + 4,13,x^3 - 4*x^2 - 7*x + 26[] 88,1,2,x,3,x + 3,5,x + 3,7,x + 2,11,x + 1,13,x[] 88,2,2,x^2,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2 + 2*x - 16,11,x^2 + 2*x + 1,13,x^2 + 2*x - 16[] 89,1,2,x + 1,3,x + 1,5,x + 1,7,x + 4,11,x + 2,13,x - 2[] 89,2,2,x - 1,3,x - 2,5,x + 2,7,x - 2,11,x + 4,13,x - 2[] 89,3,2,x^5 + x^4 - 10*x^3 - 10*x^2 + 21*x + 17,3,x^5 + 3*x^4 - 4*x^3 - 16*x^2 - 9*x - 1,5,x^5 + x^4 - 14*x^3 - 14*x^2 + 29*x + 13,7,x^5 - 8*x^4 + 10*x^3 + 36*x^2 - 68*x + 28,11,x^5 - 6*x^4 - 20*x^3 + 112*x^2 + 80*x - 112,13,x^5 - 28*x^3 - 56*x^2 + 16[] 90,1,2,x + 1,3,x,5,x - 1,7,x - 2,11,x - 6,13,x + 4[] 90,2,2,x - 1,3,x,5,x + 1,7,x - 2,11,x + 6,13,x + 4[] 90,3,2,x - 1,3,x,5,x - 1,7,x + 4,11,x,13,x - 2[] 91,1,2,x + 2,3,x,5,x + 3,7,x + 1,11,x + 6,13,x + 1[] 91,2,2,x,3,x + 2,5,x + 3,7,x - 1,11,x,13,x - 1[] 91,3,2,x^2 - 2,3,x^2 - 2,5,x^2 - 6*x + 7,7,x^2 - 2*x + 1,11,x^2 - 18,13,x^2 + 2*x + 1[] 91,4,2,x^3 - x^2 - 4*x + 2,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 - 2*x^2 - 3*x + 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 2*x^2 - 6*x + 8,13,x^3 - 3*x^2 + 3*x - 1[] 92,1,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x + 1[] 92,2,2,x,3,x + 3,5,x + 2,7,x + 4,11,x - 2,13,x + 5[] 93,1,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 4*x - 1,7,x^2 + 4*x - 1,11,x^2 + 6*x + 4,13,x^2 + 2*x - 4[] 93,2,2,x^3 - 4*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 - 4*x^2 - x + 8,11,x^3 + 2*x^2 - 20*x + 16,13,x^3 - 4*x^2 - 16*x + 56[] 94,1,2,x - 1,3,x,5,x,7,x,11,x - 2,13,x + 4[] 94,2,2,x^2 + 2*x + 1,3,x^2 - 8,5,x^2 - 4*x + 2,7,x^2 + 4*x - 4,11,x^2 - 8*x + 14,13,x^2 + 4*x + 2[] 95,1,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 16*x + 16,11,x^3 + 8*x^2 + 8*x - 16,13,x^3 - 8*x^2 + 12*x - 4[] 95,2,2,x^4 + 2*x^3 - 6*x^2 - 8*x + 9,3,x^4 - 2*x^3 - 8*x^2 + 16*x - 4,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 4*x^3 - 16*x^2 + 48*x + 32,11,x^4 - 4*x^3 - 16*x^2 + 32*x + 48,13,x^4 - 2*x^3 - 24*x^2 + 32*x + 20[] 96,1,2,x,3,x - 1,5,x - 2,7,x + 4,11,x - 4,13,x + 2[] 96,2,2,x,3,x + 1,5,x - 2,7,x - 4,11,x + 4,13,x + 2[] 97,1,2,x^3 + 4*x^2 + 3*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x + 1,7,x^3 + 7*x^2 + 14*x + 7,11,x^3 + 7*x^2 + 14*x + 7,13,x^3 + 2*x^2 - x - 1[] 97,2,2,x^4 - 3*x^3 - x^2 + 6*x - 1,3,x^4 - 5*x^2 - x + 4,5,x^4 - x^3 - 4*x^2 + x + 2,7,x^4 - 3*x^3 - 6*x^2 + 23*x - 16,11,x^4 - 5*x^3 - 14*x^2 + 47*x + 92,13,x^4 + 6*x^3 - 29*x^2 - 167*x - 122[] 98,1,2,x + 1,3,x - 2,5,x,7,x,11,x,13,x - 4[] 98,2,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 8,7,x^2,11,x^2 + 4*x + 4,13,x^2[] 99,1,2,x + 1,3,x,5,x + 4,7,x + 2,11,x + 1,13,x + 2[] 99,2,2,x - 1,3,x,5,x - 4,7,x + 2,11,x - 1,13,x + 2[] 99,3,2,x + 1,3,x,5,x - 2,7,x - 4,11,x + 1,13,x + 2[] 99,4,2,x - 2,3,x,5,x + 1,7,x + 2,11,x + 1,13,x - 4[] 100,1,2,x,3,x - 2,5,x,7,x + 2,11,x,13,x + 2[] 101,1,2,x,3,x + 2,5,x + 1,7,x + 2,11,x + 2,13,x - 1[] 101,2,2,x^7 - 13*x^5 + 2*x^4 + 47*x^3 - 16*x^2 - 43*x + 14,3,x^7 - 4*x^6 - 7*x^5 + 38*x^4 + 4*x^3 - 96*x^2 + 13*x + 68,5,x^7 + 3*x^6 - 13*x^5 - 33*x^4 + 48*x^3 + 94*x^2 - 43*x - 67,7,x^7 - 2*x^6 - 25*x^5 + 66*x^4 + 90*x^3 - 326*x^2 + 165*x + 14,11,x^7 - 8*x^6 - x^5 + 114*x^4 - 72*x^3 - 554*x^2 + 213*x + 878,13,x^7 + x^6 - 45*x^5 - 59*x^4 + 664*x^3 + 1066*x^2 - 3203*x - 6001[] 102,1,2,x + 1,3,x + 1,5,x + 4,7,x + 2,11,x,13,x + 6[] 102,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 102,3,2,x - 1,3,x - 1,5,x + 2,7,x,11,x + 4,13,x + 2[] 103,1,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 + 3*x + 1,13,x^2 + 3*x - 9[] 103,2,2,x^6 - 4*x^5 - x^4 + 17*x^3 - 9*x^2 - 16*x + 11,3,x^6 - 13*x^4 + 40*x^2 - 8*x - 16,5,x^6 - 3*x^5 - 11*x^4 + 34*x^3 + 12*x^2 - 40*x - 16,7,x^6 + 2*x^5 - 18*x^4 - 26*x^3 + 74*x^2 + 66*x + 1,11,x^6 + x^5 - 41*x^4 - 68*x^3 + 416*x^2 + 968*x + 272,13,x^6 + x^5 - 28*x^4 + 53*x^3 + 20*x^2 - 103*x + 55[] 104,1,2,x,3,x - 1,5,x + 1,7,x - 5,11,x + 2,13,x + 1[] 104,2,2,x^2,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2 + x - 4,11,x^2 + 2*x - 16,13,x^2 - 2*x + 1[] 105,1,2,x - 1,3,x - 1,5,x - 1,7,x - 1,11,x,13,x + 6[] 105,2,2,x^2 - 5,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x - 16,13,x^2 - 20[] 106,1,2,x + 1,3,x + 1,5,x + 4,7,x,11,x + 4,13,x - 1[] 106,2,2,x + 1,3,x - 2,5,x - 1,7,x + 2,11,x - 5,13,x + 4[] 106,3,2,x - 1,3,x - 1,5,x,7,x + 4,11,x,13,x - 5[] 106,4,2,x - 1,3,x + 2,5,x - 3,7,x - 2,11,x + 3,13,x + 4[] 107,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 - 4*x - 1,13,x^2 + 12*x + 36[] 107,2,2,x^7 + x^6 - 10*x^5 - 7*x^4 + 29*x^3 + 12*x^2 - 20*x - 8,3,x^7 - 3*x^6 - 9*x^5 + 29*x^4 + 14*x^3 - 69*x^2 + 12*x + 29,5,x^7 - 5*x^6 - 9*x^5 + 64*x^4 - 28*x^3 - 152*x^2 + 192*x - 64,7,x^7 - 4*x^6 - 23*x^5 + 114*x^4 - 32*x^3 - 360*x^2 + 448*x - 128,11,x^7 + 2*x^6 - 41*x^5 - 95*x^4 + 361*x^3 + 950*x^2 + 519*x + 47,13,x^7 - 18*x^6 + 98*x^5 + x^4 - 1649*x^3 + 4855*x^2 - 3548*x - 1244[] 108,1,2,x,3,x,5,x,7,x - 5,11,x,13,x + 7[] 109,1,2,x - 1,3,x,5,x - 3,7,x - 2,11,x - 1,13,x[] 109,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 5*x - 13,7,x^3 + x^2 - 16*x + 13,11,x^3 + 13*x^2 + 54*x + 71,13,x^3 + x^2 - 16*x + 13[] 109,3,2,x^4 + x^3 - 5*x^2 - 4*x + 3,3,x^4 - 4*x^3 - x^2 + 15*x - 8,5,x^4 - x^3 - 5*x^2 + 4*x + 3,7,x^4 + 3*x^3 - 10*x^2 - 23*x - 2,11,x^4 - 12*x^3 + 33*x^2 + 47*x - 177,13,x^4 + 7*x^3 - 10*x^2 - 93*x + 16[] 110,1,2,x + 1,3,x - 1,5,x + 1,7,x - 5,11,x - 1,13,x - 2[] 110,2,2,x - 1,3,x - 1,5,x + 1,7,x + 1,11,x + 1,13,x - 2[] 110,3,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 1,13,x + 6[] 110,4,2,x^2 + 2*x + 1,3,x^2 + x - 8,5,x^2 - 2*x + 1,7,x^2 - x - 8,11,x^2 + 2*x + 1,13,x^2 - 4*x + 4[] Total time: 22.149 seconds, Total memory usage: 7.83MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Nov 29 07:12:30 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [110..130] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 07:12:08 on modular [Seed = 2807043549] ------------------------------------- 110,1,2,$.1 + 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 5,11,$.1 - 1,13,$.1 - 2[] 110,2,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 1,13,$.1 - 2[] 110,3,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1 - 3,11,$.1 - 1,13,$.1 + 6[] 110,4,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + $.1 - 8,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - $.1 - 8,11,$.1^2 + 2*$.1 + 1,13,$.1^2 - 4*$.1 + 4[] 111,1,2,x^3 - 3*x^2 - x + 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 4*x + 20,7,x^3 + 4*x^2 - 8*x - 16,11,x^3 - 4*x^2 - 16*x + 32,13,x^3 + 2*x^2 - 20*x - 8[] 111,2,2,x^4 - 6*x^2 + 2*x + 5,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 2*x^3 - 8*x^2 + 4,7,x^4 - 4*x^3 - 16*x^2 + 64*x - 16,11,x^4 - 32*x^2 - 32*x + 64,13,x^4 - 4*x^3 - 32*x^2 + 144*x - 80[] 112,1,2,x,3,x + 2,5,x + 4,7,x + 1,11,x,13,x[] 112,2,2,x,3,x,5,x - 2,7,x - 1,11,x - 4,13,x - 2[] 112,3,2,x,3,x - 2,5,x,7,x + 1,11,x,13,x + 4[] 113,1,2,x + 1,3,x - 2,5,x - 2,7,x,11,x,13,x - 2[] 113,2,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 - 8*x + 16,11,x^2 + 4*x - 8,13,x^2 + 4*x - 8[] 113,3,2,x^3 + 2*x^2 - x - 1,3,x^3 + 5*x^2 + 6*x + 1,5,x^3 + x^2 - 9*x - 1,7,x^3 + 10*x^2 + 31*x + 29,11,x^3 - 2*x^2 - 15*x - 13,13,x^3 + 8*x^2 + 5*x - 43[] 113,4,2,x^3 + 2*x^2 - 5*x - 9,3,x^3 + x^2 - 4*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 6*x^2 + 3*x + 9,11,x^3 - 2*x^2 - 3*x + 3,13,x^3 - 8*x^2 + 17*x - 7[] 114,1,2,x + 1,3,x + 1,5,x,7,x - 4,11,x - 4,13,x[] 114,2,2,x - 1,3,x + 1,5,x - 2,7,x,11,x + 4,13,x - 2[] 114,3,2,x - 1,3,x - 1,5,x,7,x + 4,11,x,13,x + 4[] 115,1,2,x - 2,3,x,5,x + 1,7,x - 1,11,x - 2,13,x + 2[] 115,2,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 + 2*x - 4,13,x^2 + 8*x + 11[] 115,3,2,x^4 - 2*x^3 - 4*x^2 + 5*x + 2,3,x^4 + 2*x^3 - 7*x^2 - 8*x + 16,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 3*x^3 - 14*x^2 - 52*x - 32,11,x^4 - 4*x^3 - 16*x^2 + 40*x + 32,13,x^4 - 41*x^2 + 212[] 116,1,2,x,3,x - 1,5,x - 3,7,x + 4,11,x - 3,13,x - 5[] 116,2,2,x,3,x - 2,5,x + 2,7,x - 4,11,x + 6,13,x - 2[] 116,3,2,x,3,x + 3,5,x - 3,7,x - 4,11,x + 1,13,x + 3[] 117,1,2,x + 1,3,x,5,x + 2,7,x + 4,11,x + 4,13,x - 1[] 117,2,2,x^2 - 3,3,x^2,5,x^2,7,x^2 - 4*x + 4,11,x^2 - 12,13,x^2 - 2*x + 1[] 117,3,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 8,7,x^2 - 8,11,x^2 - 4*x + 4,13,x^2 + 2*x + 1[] 118,1,2,x + 1,3,x + 1,5,x + 3,7,x + 1,11,x + 2,13,x + 2[] 118,2,2,x + 1,3,x - 2,5,x - 2,7,x + 3,11,x - 1,13,x - 3[] 118,3,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 6[] 118,4,2,x - 1,3,x - 2,5,x + 2,7,x + 3,11,x + 1,13,x + 3[] 119,1,2,x^4 + x^3 - 5*x^2 - x + 3,3,x^4 - 2*x^3 - 7*x^2 + 12*x - 1,5,x^4 - 2*x^3 - 7*x^2 + 4*x + 3,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 20*x^2 + 8*x + 48,13,x^4 - 8*x^3 - 16*x^2 + 216*x - 368[] 119,2,2,x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 14*x - 17,3,x^5 + 2*x^4 - 11*x^3 - 12*x^2 + 31*x - 12,5,x^5 - 23*x^3 + 18*x^2 + 131*x - 178,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 + 2*x^4 - 44*x^3 - 40*x^2 + 496*x - 192,13,x^5 - 2*x^4 - 40*x^3 + 56*x^2 + 352*x - 544[] 120,1,2,x,3,x - 1,5,x + 1,7,x - 4,11,x,13,x + 6[] 120,2,2,x,3,x - 1,5,x - 1,7,x,11,x + 4,13,x - 6[] 121,1,2,x,3,x + 1,5,x + 3,7,x,11,x,13,x[] 121,2,2,x - 1,3,x - 2,5,x - 1,7,x + 2,11,x,13,x - 1[] 121,3,2,x + 1,3,x - 2,5,x - 1,7,x - 2,11,x,13,x + 1[] 121,4,2,x - 2,3,x + 1,5,x - 1,7,x - 2,11,x,13,x + 4[] 122,1,2,x + 1,3,x + 2,5,x - 1,7,x + 5,11,x + 3,13,x + 3[] 122,2,2,x^2 + 2*x + 1,3,x^2 - x - 3,5,x^2,7,x^2 - 5*x + 3,11,x^2 - 2*x - 12,13,x^2 - 6*x - 4[] 122,3,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + x^2 - 5*x + 2,5,x^3 - x^2 - 12*x + 16,7,x^3 - 4*x^2 - 10*x + 41,11,x^3 + 7*x^2 + 10*x - 4,13,x^3 + x^2 - 6*x - 4[] 123,1,2,x,3,x + 1,5,x + 2,7,x + 4,11,x - 5,13,x + 4[] 123,2,2,x + 2,3,x - 1,5,x + 4,7,x + 2,11,x + 3,13,x + 6[] 123,3,2,x^2 - 2,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 2*x - 1,13,x^2 - 4*x - 14[] 123,4,2,x^3 - x^2 - 4*x + 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 2*x + 4,7,x^3 - 2*x^2 - 14*x + 32,11,x^3 + 4*x^2 + x - 4,13,x^3 - 8*x^2 + 14*x + 4[] 124,1,2,x,3,x,5,x - 1,7,x - 3,11,x - 6,13,x + 4[] 124,2,2,x,3,x + 2,5,x + 3,7,x + 1,11,x + 6,13,x - 2[] 125,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2,7,x^2 + 6*x + 9,11,x^2 + 6*x + 9,13,x^2 + 3*x - 9[] 125,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2,7,x^2 - 6*x + 9,11,x^2 + 6*x + 9,13,x^2 - 3*x - 9[] 125,3,2,x^4 - 8*x^2 + 11,3,x^4 - 7*x^2 + 11,5,x^4,7,x^4 - 13*x^2 + 11,11,x^4 - 8*x^3 + 24*x^2 - 32*x + 16,13,x^4 - 32*x^2 + 176[] 126,1,2,x + 1,3,x,5,x - 2,7,x + 1,11,x - 4,13,x - 6[] 126,2,2,x - 1,3,x,5,x,7,x - 1,11,x,13,x + 4[] 127,1,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 + 3*x^2 - 3,11,x^3 - 21*x - 37,13,x^3 + 3*x^2 - 18*x - 37[] 127,2,2,x^7 - 2*x^6 - 8*x^5 + 15*x^4 + 17*x^3 - 28*x^2 - 11*x + 15,3,x^7 - 3*x^6 - 12*x^5 + 39*x^4 + 26*x^3 - 128*x^2 + 64*x + 16,5,x^7 - 8*x^6 + 11*x^5 + 53*x^4 - 146*x^3 + 32*x^2 + 128*x - 48,7,x^7 + 3*x^6 - 20*x^5 - 41*x^4 + 114*x^3 + 64*x^2 - 112*x - 16,11,x^7 - 28*x^5 - 17*x^4 + 88*x^3 - 37*x^2 - 5*x + 3,13,x^7 + x^6 - 69*x^5 - 38*x^4 + 1515*x^3 + 52*x^2 - 10416*x + 5383[] 128,1,2,x,3,x + 2,5,x + 2,7,x + 4,11,x - 2,13,x + 2[] 128,2,2,x,3,x - 2,5,x - 2,7,x + 4,11,x + 2,13,x - 2[] 128,3,2,x,3,x - 2,5,x + 2,7,x - 4,11,x + 2,13,x + 2[] 128,4,2,x,3,x + 2,5,x - 2,7,x - 4,11,x - 2,13,x - 2[] 129,1,2,x,3,x + 1,5,x + 2,7,x + 2,11,x + 5,13,x - 3[] 129,2,2,x - 1,3,x - 1,5,x - 2,7,x,11,x,13,x + 2[] 129,3,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 1,7,x^2 - 2*x - 7,11,x^2 - 6*x + 7,13,x^2 + 10*x + 25[] 129,4,2,x^3 + 2*x^2 - 5*x - 8,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 4*x^2 - x - 2,7,x^3 - 4*x^2 - 3*x + 10,11,x^3 - x^2 - 19*x - 25,13,x^3 - 9*x^2 + 27*x - 27[] 130,1,2,x + 1,3,x + 2,5,x - 1,7,x + 4,11,x + 6,13,x - 1[] 130,2,2,x - 1,3,x - 2,5,x + 1,7,x + 4,11,x + 2,13,x + 1[] 130,3,2,x - 1,3,x,5,x - 1,7,x,11,x,13,x - 1[] Total time: 21.549 seconds, Total memory usage: 7.15MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Nov 29 07:19:56 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [130..150] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 07:19:33 on modular [Seed = 3041002498] ------------------------------------- 130,1,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 1[] 130,2,2,$.1 - 1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[] 130,3,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1,13,$.1 - 1[] 131,1,2,x,3,x + 1,5,x + 2,7,x + 1,11,x,13,x + 3[] 131,2,2,x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 + 16*x - 32,3,x^10 - x^9 - 22*x^8 + 24*x^7 + 157*x^6 - 184*x^5 - 403*x^4 + 533*x^3 + 222*x^2 - 390*x + 67,5,x^10 - 4*x^9 - 26*x^8 + 116*x^7 + 155*x^6 - 988*x^5 + 138*x^4 + 2384*x^3 - 763*x^2 - 1856*x + 8,7,x^10 - x^9 - 46*x^8 + 36*x^7 + 701*x^6 - 376*x^5 - 3971*x^4 + 929*x^3 + 7566*x^2 + 738*x - 1213,11,x^10 - 2*x^9 - 48*x^8 + 76*x^7 + 829*x^6 - 1032*x^5 - 6248*x^4 + 6058*x^3 + 19601*x^2 - 12860*x - 17852,13,x^10 - 11*x^9 - 4*x^8 + 386*x^7 - 1069*x^6 - 1056*x^5 + 5897*x^4 - 2717*x^3 - 6108*x^2 + 4764*x - 31[] 132,1,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x - 6[] 132,2,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x + 2[] 133,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2 + 9*x + 19,13,x^2 - 2*x + 1[] 133,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 1,13,x^2 + 2*x + 1[] 133,3,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 + 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 5*x + 3,13,x^2 + 4*x - 9[] 133,4,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 - x + 4,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 7*x^2 + 11*x - 4,13,x^3 + 2*x^2 - 5*x - 2[] 134,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - 3*x^2 - 2*x + 3,7,x^3 - 20*x + 8,11,x^3 + x^2 - 16*x + 9,13,x^3 - 11*x^2 + 30*x - 9[] 134,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 - 12*x - 8,11,x^3 + 3*x^2 - 24*x - 53,13,x^3 + 3*x^2 - 18*x - 3[] 135,1,2,x + 2,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 5[] 135,2,2,x - 2,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 5[] 135,3,2,x^2 + x - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 12,11,x^2 - 2*x - 12,13,x^2 - 6*x - 4[] 135,4,2,x^2 - x - 3,3,x^2,5,x^2 + 2*x + 1,7,x^2 - 2*x - 12,11,x^2 + 2*x - 12,13,x^2 - 6*x - 4[] 136,1,2,x,3,x - 2,5,x,7,x,11,x - 2,13,x + 6[] 136,2,2,x,3,x + 2,5,x + 2,7,x + 2,11,x + 6,13,x - 2[] 136,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 4,11,x^2 - 2*x - 4,13,x^2 - 20[] 137,1,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,5,x^4 + 2*x^3 - 12*x^2 - 23*x + 1,7,x^4 + 13*x^3 + 60*x^2 + 116*x + 79,11,x^4 - x^3 - 38*x^2 + 76*x + 101,13,x^4 + 8*x^3 + 10*x^2 - 49*x - 101[] 137,2,2,x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7,3,x^7 - 3*x^6 - 8*x^5 + 26*x^4 + 11*x^3 - 58*x^2 + 16*x + 14,5,x^7 + 2*x^6 - 18*x^5 - 21*x^4 + 103*x^3 + 26*x^2 - 188*x + 88,7,x^7 - 15*x^6 + 80*x^5 - 168*x^4 + 43*x^3 + 300*x^2 - 352*x + 112,11,x^7 + 3*x^6 - 26*x^5 - 140*x^4 - 219*x^3 - 92*x^2 + 24*x + 16,13,x^7 - 12*x^6 + 32*x^5 + 85*x^4 - 351*x^3 - 202*x^2 + 876*x + 488[] 138,1,2,x + 1,3,x + 1,5,x + 2,7,x + 2,11,x + 6,13,x + 2[] 138,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 138,3,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x + 2[] 138,4,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 20,11,x^2 + 6*x + 4,13,x^2 - 20[] 139,1,2,x - 1,3,x - 2,5,x + 1,7,x - 3,11,x - 5,13,x + 7[] 139,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 8*x^2 + 19*x + 13,7,x^3 - 7*x + 7,11,x^3 + 7*x^2 - 49,13,x^3 - x^2 - 16*x - 13[] 139,3,2,x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8,3,x^7 + 2*x^6 - 15*x^5 - 25*x^4 + 56*x^3 + 52*x^2 - 56*x - 16,5,x^7 - 11*x^6 + 36*x^5 + 2*x^4 - 211*x^3 + 319*x^2 - 55*x - 83,7,x^7 + 5*x^6 - 8*x^5 - 82*x^4 - 155*x^3 - 109*x^2 - 31*x - 3,11,x^7 - 2*x^6 - 36*x^5 + 82*x^4 + 186*x^3 - 314*x^2 - 294*x + 229,13,x^7 - 6*x^6 - 2*x^5 + 64*x^4 - 108*x^3 + 38*x^2 + 6*x - 1[] 140,1,2,x,3,x - 3,5,x + 1,7,x + 1,11,x + 5,13,x + 3[] 140,2,2,x,3,x - 1,5,x - 1,7,x - 1,11,x - 3,13,x + 1[] 141,1,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 3,13,x + 4[] 141,2,2,x + 1,3,x + 1,5,x,7,x - 4,11,x,13,x - 6[] 141,3,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 141,4,2,x - 2,3,x - 1,5,x + 1,7,x + 3,11,x - 1,13,x + 2[] 141,5,2,x + 2,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x - 2[] 141,6,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x + 8,13,x^2 + 6*x - 8[] 142,1,2,x + 1,3,x + 1,5,x + 2,7,x + 1,11,x + 2,13,x + 3[] 142,2,2,x + 1,3,x,5,x - 2,7,x,11,x - 6,13,x - 4[] 142,3,2,x + 1,3,x - 3,5,x - 2,7,x + 3,11,x + 6,13,x + 5[] 142,4,2,x - 1,3,x - 1,5,x,7,x + 1,11,x,13,x + 1[] 142,5,2,x - 1,3,x + 3,5,x + 4,7,x + 3,11,x,13,x - 1[] 143,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x + 1,13,x + 1[] 143,2,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 - 16*x^2 + 8*x + 16,7,x^4 - 6*x^3 + x^2 + 44*x - 61,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 143,3,2,x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12,3,x^6 - 3*x^5 - 11*x^4 + 33*x^3 + 25*x^2 - 91*x + 28,5,x^6 - x^5 - 26*x^4 + 32*x^3 + 152*x^2 - 256*x + 96,7,x^6 - 4*x^5 - 23*x^4 + 66*x^3 + 187*x^2 - 210*x - 448,11,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 144,1,2,x,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[] 144,2,2,x,3,x,5,x,7,x - 4,11,x,13,x - 2[] 145,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x + 6,13,x - 2[] 145,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 + 4*x - 4,13,x^2 + 4*x + 4[] 145,3,2,x^3 - 3*x^2 - x + 5,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 6*x^2 - 4*x - 8[] 145,4,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 4*x^2 + 4,11,x^3 - 2*x^2 - 8*x - 4,13,x^3 + 2*x^2 - 12*x - 8[] 146,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 8*x + 4,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 - 8*x^2 + 16*x - 2,11,x^3 - 2*x^2 - 28*x + 72,13,x^3 - 4*x^2 + 2[] 146,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 8*x^2 + 4*x + 4,5,x^4 - 2*x^3 - 14*x^2 + 26*x + 2,7,x^4 - 22*x^2 + 6*x + 2,11,x^4 - 24*x^2 - 16*x + 80,13,x^4 + 4*x^3 - 38*x^2 - 106*x + 314[] 147,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[] 147,2,2,x - 2,3,x + 1,5,x - 2,7,x,11,x + 2,13,x + 1[] 147,3,2,x - 2,3,x - 1,5,x + 2,7,x,11,x + 2,13,x - 1[] 147,4,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 2,7,x^2,11,x^2 + 4*x + 4,13,x^2 + 8*x + 14[] 147,5,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2,11,x^2 + 4*x + 4,13,x^2 - 8*x + 14[] 148,1,2,x,3,x + 1,5,x + 4,7,x + 3,11,x - 5,13,x[] 148,2,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - x - 4,13,x^2 - 4*x + 4[] 149,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x - 13,7,x^3 + 5*x^2 + 6*x + 1,11,x^3 + 5*x^2 - 8*x + 1,13,x^3 + 3*x^2 - 4*x - 13[] 149,2,2,x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x + 39,3,x^9 - 6*x^8 + 55*x^6 - 67*x^5 - 125*x^4 + 235*x^3 - 6*x^2 - 117*x + 27,5,x^9 + x^8 - 25*x^7 - 4*x^6 + 202*x^5 - 83*x^4 - 529*x^3 + 305*x^2 + 392*x - 221,7,x^9 - 3*x^8 - 34*x^7 + 117*x^6 + 208*x^5 - 916*x^4 + 144*x^3 + 1056*x^2 - 128*x - 64,11,x^9 - 5*x^8 - 33*x^7 + 202*x^6 + 66*x^5 - 1503*x^4 + 997*x^3 + 2817*x^2 - 3392*x + 981,13,x^9 - 7*x^8 - 28*x^7 + 277*x^6 - 152*x^5 - 2028*x^4 + 3072*x^3 + 32*x^2 - 512*x - 64[] Errors: /home/mfd/gomagma: line 2: 24023 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Nov 29 07:20:45 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [130..150] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 07:20:22 on modular [Seed = 2222142688] ------------------------------------- 130,1,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 1[] 130,2,2,$.1 - 1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[] 130,3,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1,13,$.1 - 1[] 131,1,2,x,3,x + 1,5,x + 2,7,x + 1,11,x,13,x + 3[] 131,2,2,x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 + 16*x - 32,3,x^10 - x^9 - 22*x^8 + 24*x^7 + 157*x^6 - 184*x^5 - 403*x^4 + 533*x^3 + 222*x^2 - 390*x + 67,5,x^10 - 4*x^9 - 26*x^8 + 116*x^7 + 155*x^6 - 988*x^5 + 138*x^4 + 2384*x^3 - 763*x^2 - 1856*x + 8,7,x^10 - x^9 - 46*x^8 + 36*x^7 + 701*x^6 - 376*x^5 - 3971*x^4 + 929*x^3 + 7566*x^2 + 738*x - 1213,11,x^10 - 2*x^9 - 48*x^8 + 76*x^7 + 829*x^6 - 1032*x^5 - 6248*x^4 + 6058*x^3 + 19601*x^2 - 12860*x - 17852,13,x^10 - 11*x^9 - 4*x^8 + 386*x^7 - 1069*x^6 - 1056*x^5 + 5897*x^4 - 2717*x^3 - 6108*x^2 + 4764*x - 31[] 132,1,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x - 6[] 132,2,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x + 2[] 133,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2 + 9*x + 19,13,x^2 - 2*x + 1[] 133,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 1,13,x^2 + 2*x + 1[] 133,3,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 + 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 5*x + 3,13,x^2 + 4*x - 9[] 133,4,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 - x + 4,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 7*x^2 + 11*x - 4,13,x^3 + 2*x^2 - 5*x - 2[] 134,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - 3*x^2 - 2*x + 3,7,x^3 - 20*x + 8,11,x^3 + x^2 - 16*x + 9,13,x^3 - 11*x^2 + 30*x - 9[] 134,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 - 12*x - 8,11,x^3 + 3*x^2 - 24*x - 53,13,x^3 + 3*x^2 - 18*x - 3[] 135,1,2,x + 2,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 5[] 135,2,2,x - 2,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 5[] 135,3,2,x^2 + x - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 12,11,x^2 - 2*x - 12,13,x^2 - 6*x - 4[] 135,4,2,x^2 - x - 3,3,x^2,5,x^2 + 2*x + 1,7,x^2 - 2*x - 12,11,x^2 + 2*x - 12,13,x^2 - 6*x - 4[] 136,1,2,x,3,x - 2,5,x,7,x,11,x - 2,13,x + 6[] 136,2,2,x,3,x + 2,5,x + 2,7,x + 2,11,x + 6,13,x - 2[] 136,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 4,11,x^2 - 2*x - 4,13,x^2 - 20[] 137,1,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,5,x^4 + 2*x^3 - 12*x^2 - 23*x + 1,7,x^4 + 13*x^3 + 60*x^2 + 116*x + 79,11,x^4 - x^3 - 38*x^2 + 76*x + 101,13,x^4 + 8*x^3 + 10*x^2 - 49*x - 101[] 137,2,2,x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7,3,x^7 - 3*x^6 - 8*x^5 + 26*x^4 + 11*x^3 - 58*x^2 + 16*x + 14,5,x^7 + 2*x^6 - 18*x^5 - 21*x^4 + 103*x^3 + 26*x^2 - 188*x + 88,7,x^7 - 15*x^6 + 80*x^5 - 168*x^4 + 43*x^3 + 300*x^2 - 352*x + 112,11,x^7 + 3*x^6 - 26*x^5 - 140*x^4 - 219*x^3 - 92*x^2 + 24*x + 16,13,x^7 - 12*x^6 + 32*x^5 + 85*x^4 - 351*x^3 - 202*x^2 + 876*x + 488[] 138,1,2,x + 1,3,x + 1,5,x + 2,7,x + 2,11,x + 6,13,x + 2[] 138,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 138,3,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x + 2[] 138,4,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 20,11,x^2 + 6*x + 4,13,x^2 - 20[] 139,1,2,x - 1,3,x - 2,5,x + 1,7,x - 3,11,x - 5,13,x + 7[] 139,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 8*x^2 + 19*x + 13,7,x^3 - 7*x + 7,11,x^3 + 7*x^2 - 49,13,x^3 - x^2 - 16*x - 13[] 139,3,2,x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8,3,x^7 + 2*x^6 - 15*x^5 - 25*x^4 + 56*x^3 + 52*x^2 - 56*x - 16,5,x^7 - 11*x^6 + 36*x^5 + 2*x^4 - 211*x^3 + 319*x^2 - 55*x - 83,7,x^7 + 5*x^6 - 8*x^5 - 82*x^4 - 155*x^3 - 109*x^2 - 31*x - 3,11,x^7 - 2*x^6 - 36*x^5 + 82*x^4 + 186*x^3 - 314*x^2 - 294*x + 229,13,x^7 - 6*x^6 - 2*x^5 + 64*x^4 - 108*x^3 + 38*x^2 + 6*x - 1[] 140,1,2,x,3,x - 3,5,x + 1,7,x + 1,11,x + 5,13,x + 3[] 140,2,2,x,3,x - 1,5,x - 1,7,x - 1,11,x - 3,13,x + 1[] 141,1,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 3,13,x + 4[] 141,2,2,x + 1,3,x + 1,5,x,7,x - 4,11,x,13,x - 6[] 141,3,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 141,4,2,x - 2,3,x - 1,5,x + 1,7,x + 3,11,x - 1,13,x + 2[] 141,5,2,x + 2,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x - 2[] 141,6,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x + 8,13,x^2 + 6*x - 8[] 142,1,2,x + 1,3,x + 1,5,x + 2,7,x + 1,11,x + 2,13,x + 3[] 142,2,2,x + 1,3,x,5,x - 2,7,x,11,x - 6,13,x - 4[] 142,3,2,x + 1,3,x - 3,5,x - 2,7,x + 3,11,x + 6,13,x + 5[] 142,4,2,x - 1,3,x - 1,5,x,7,x + 1,11,x,13,x + 1[] 142,5,2,x - 1,3,x + 3,5,x + 4,7,x + 3,11,x,13,x - 1[] 143,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x + 1,13,x + 1[] 143,2,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 - 16*x^2 + 8*x + 16,7,x^4 - 6*x^3 + x^2 + 44*x - 61,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 143,3,2,x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12,3,x^6 - 3*x^5 - 11*x^4 + 33*x^3 + 25*x^2 - 91*x + 28,5,x^6 - x^5 - 26*x^4 + 32*x^3 + 152*x^2 - 256*x + 96,7,x^6 - 4*x^5 - 23*x^4 + 66*x^3 + 187*x^2 - 210*x - 448,11,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 144,1,2,x,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[] 144,2,2,x,3,x,5,x,7,x - 4,11,x,13,x - 2[] 145,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x + 6,13,x - 2[] 145,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 + 4*x - 4,13,x^2 + 4*x + 4[] 145,3,2,x^3 - 3*x^2 - x + 5,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 6*x^2 - 4*x - 8[] 145,4,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 4*x^2 + 4,11,x^3 - 2*x^2 - 8*x - 4,13,x^3 + 2*x^2 - 12*x - 8[] 146,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 8*x + 4,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 - 8*x^2 + 16*x - 2,11,x^3 - 2*x^2 - 28*x + 72,13,x^3 - 4*x^2 + 2[] 146,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 8*x^2 + 4*x + 4,5,x^4 - 2*x^3 - 14*x^2 + 26*x + 2,7,x^4 - 22*x^2 + 6*x + 2,11,x^4 - 24*x^2 - 16*x + 80,13,x^4 + 4*x^3 - 38*x^2 - 106*x + 314[] 147,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[] 147,2,2,x - 2,3,x + 1,5,x - 2,7,x,11,x + 2,13,x + 1[] 147,3,2,x - 2,3,x - 1,5,x + 2,7,x,11,x + 2,13,x - 1[] 147,4,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 2,7,x^2,11,x^2 + 4*x + 4,13,x^2 + 8*x + 14[] 147,5,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2,11,x^2 + 4*x + 4,13,x^2 - 8*x + 14[] 148,1,2,x,3,x + 1,5,x + 4,7,x + 3,11,x - 5,13,x[] 148,2,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - x - 4,13,x^2 - 4*x + 4[] 149,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x - 13,7,x^3 + 5*x^2 + 6*x + 1,11,x^3 + 5*x^2 - 8*x + 1,13,x^3 + 3*x^2 - 4*x - 13[] 149,2,2,x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x + 39,3,x^9 - 6*x^8 + 55*x^6 - 67*x^5 - 125*x^4 + 235*x^3 - 6*x^2 - 117*x + 27,5,x^9 + x^8 - 25*x^7 - 4*x^6 + 202*x^5 - 83*x^4 - 529*x^3 + 305*x^2 + 392*x - 221,7,x^9 - 3*x^8 - 34*x^7 + 117*x^6 + 208*x^5 - 916*x^4 + 144*x^3 + 1056*x^2 - 128*x - 64,11,x^9 - 5*x^8 - 33*x^7 + 202*x^6 + 66*x^5 - 1503*x^4 + 997*x^3 + 2817*x^2 - 3392*x + 981,13,x^9 - 7*x^8 - 28*x^7 + 277*x^6 - 152*x^5 - 2028*x^4 + 3072*x^3 + 32*x^2 - 512*x - 64[] Errors: /home/mfd/gomagma: line 2: 24038 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Nov 29 07:25:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [130..148] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 07:24:52 on modular [Seed = 2472819941] ------------------------------------- 130,1,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 1[] 130,2,2,$.1 - 1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[] 130,3,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1,13,$.1 - 1[] 131,1,2,x,3,x + 1,5,x + 2,7,x + 1,11,x,13,x + 3[] 131,2,2,x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 + 16*x - 32,3,x^10 - x^9 - 22*x^8 + 24*x^7 + 157*x^6 - 184*x^5 - 403*x^4 + 533*x^3 + 222*x^2 - 390*x + 67,5,x^10 - 4*x^9 - 26*x^8 + 116*x^7 + 155*x^6 - 988*x^5 + 138*x^4 + 2384*x^3 - 763*x^2 - 1856*x + 8,7,x^10 - x^9 - 46*x^8 + 36*x^7 + 701*x^6 - 376*x^5 - 3971*x^4 + 929*x^3 + 7566*x^2 + 738*x - 1213,11,x^10 - 2*x^9 - 48*x^8 + 76*x^7 + 829*x^6 - 1032*x^5 - 6248*x^4 + 6058*x^3 + 19601*x^2 - 12860*x - 17852,13,x^10 - 11*x^9 - 4*x^8 + 386*x^7 - 1069*x^6 - 1056*x^5 + 5897*x^4 - 2717*x^3 - 6108*x^2 + 4764*x - 31[] 132,1,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x - 6[] 132,2,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x + 2[] 133,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2 + 9*x + 19,13,x^2 - 2*x + 1[] 133,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 1,13,x^2 + 2*x + 1[] 133,3,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 + 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 5*x + 3,13,x^2 + 4*x - 9[] 133,4,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 - x + 4,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 7*x^2 + 11*x - 4,13,x^3 + 2*x^2 - 5*x - 2[] 134,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - 3*x^2 - 2*x + 3,7,x^3 - 20*x + 8,11,x^3 + x^2 - 16*x + 9,13,x^3 - 11*x^2 + 30*x - 9[] 134,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 - 12*x - 8,11,x^3 + 3*x^2 - 24*x - 53,13,x^3 + 3*x^2 - 18*x - 3[] 135,1,2,x + 2,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 5[] 135,2,2,x - 2,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 5[] 135,3,2,x^2 + x - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 12,11,x^2 - 2*x - 12,13,x^2 - 6*x - 4[] 135,4,2,x^2 - x - 3,3,x^2,5,x^2 + 2*x + 1,7,x^2 - 2*x - 12,11,x^2 + 2*x - 12,13,x^2 - 6*x - 4[] 136,1,2,x,3,x - 2,5,x,7,x,11,x - 2,13,x + 6[] 136,2,2,x,3,x + 2,5,x + 2,7,x + 2,11,x + 6,13,x - 2[] 136,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 4,11,x^2 - 2*x - 4,13,x^2 - 20[] 137,1,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,5,x^4 + 2*x^3 - 12*x^2 - 23*x + 1,7,x^4 + 13*x^3 + 60*x^2 + 116*x + 79,11,x^4 - x^3 - 38*x^2 + 76*x + 101,13,x^4 + 8*x^3 + 10*x^2 - 49*x - 101[] 137,2,2,x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7,3,x^7 - 3*x^6 - 8*x^5 + 26*x^4 + 11*x^3 - 58*x^2 + 16*x + 14,5,x^7 + 2*x^6 - 18*x^5 - 21*x^4 + 103*x^3 + 26*x^2 - 188*x + 88,7,x^7 - 15*x^6 + 80*x^5 - 168*x^4 + 43*x^3 + 300*x^2 - 352*x + 112,11,x^7 + 3*x^6 - 26*x^5 - 140*x^4 - 219*x^3 - 92*x^2 + 24*x + 16,13,x^7 - 12*x^6 + 32*x^5 + 85*x^4 - 351*x^3 - 202*x^2 + 876*x + 488[] 138,1,2,x + 1,3,x + 1,5,x + 2,7,x + 2,11,x + 6,13,x + 2[] 138,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 138,3,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x + 2[] 138,4,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 20,11,x^2 + 6*x + 4,13,x^2 - 20[] 139,1,2,x - 1,3,x - 2,5,x + 1,7,x - 3,11,x - 5,13,x + 7[] 139,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 8*x^2 + 19*x + 13,7,x^3 - 7*x + 7,11,x^3 + 7*x^2 - 49,13,x^3 - x^2 - 16*x - 13[] 139,3,2,x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8,3,x^7 + 2*x^6 - 15*x^5 - 25*x^4 + 56*x^3 + 52*x^2 - 56*x - 16,5,x^7 - 11*x^6 + 36*x^5 + 2*x^4 - 211*x^3 + 319*x^2 - 55*x - 83,7,x^7 + 5*x^6 - 8*x^5 - 82*x^4 - 155*x^3 - 109*x^2 - 31*x - 3,11,x^7 - 2*x^6 - 36*x^5 + 82*x^4 + 186*x^3 - 314*x^2 - 294*x + 229,13,x^7 - 6*x^6 - 2*x^5 + 64*x^4 - 108*x^3 + 38*x^2 + 6*x - 1[] 140,1,2,x,3,x - 3,5,x + 1,7,x + 1,11,x + 5,13,x + 3[] 140,2,2,x,3,x - 1,5,x - 1,7,x - 1,11,x - 3,13,x + 1[] 141,1,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 3,13,x + 4[] 141,2,2,x + 1,3,x + 1,5,x,7,x - 4,11,x,13,x - 6[] 141,3,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 141,4,2,x - 2,3,x - 1,5,x + 1,7,x + 3,11,x - 1,13,x + 2[] 141,5,2,x + 2,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x - 2[] 141,6,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x + 8,13,x^2 + 6*x - 8[] 142,1,2,x + 1,3,x + 1,5,x + 2,7,x + 1,11,x + 2,13,x + 3[] 142,2,2,x + 1,3,x,5,x - 2,7,x,11,x - 6,13,x - 4[] 142,3,2,x + 1,3,x - 3,5,x - 2,7,x + 3,11,x + 6,13,x + 5[] 142,4,2,x - 1,3,x - 1,5,x,7,x + 1,11,x,13,x + 1[] 142,5,2,x - 1,3,x + 3,5,x + 4,7,x + 3,11,x,13,x - 1[] 143,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x + 1,13,x + 1[] 143,2,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 - 16*x^2 + 8*x + 16,7,x^4 - 6*x^3 + x^2 + 44*x - 61,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 143,3,2,x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12,3,x^6 - 3*x^5 - 11*x^4 + 33*x^3 + 25*x^2 - 91*x + 28,5,x^6 - x^5 - 26*x^4 + 32*x^3 + 152*x^2 - 256*x + 96,7,x^6 - 4*x^5 - 23*x^4 + 66*x^3 + 187*x^2 - 210*x - 448,11,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 144,1,2,x,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[] 144,2,2,x,3,x,5,x,7,x - 4,11,x,13,x - 2[] 145,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x + 6,13,x - 2[] 145,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 + 4*x - 4,13,x^2 + 4*x + 4[] 145,3,2,x^3 - 3*x^2 - x + 5,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 6*x^2 - 4*x - 8[] 145,4,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 4*x^2 + 4,11,x^3 - 2*x^2 - 8*x - 4,13,x^3 + 2*x^2 - 12*x - 8[] 146,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 8*x + 4,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 - 8*x^2 + 16*x - 2,11,x^3 - 2*x^2 - 28*x + 72,13,x^3 - 4*x^2 + 2[] 146,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 8*x^2 + 4*x + 4,5,x^4 - 2*x^3 - 14*x^2 + 26*x + 2,7,x^4 - 22*x^2 + 6*x + 2,11,x^4 - 24*x^2 - 16*x + 80,13,x^4 + 4*x^3 - 38*x^2 - 106*x + 314[] 147,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[] 147,2,2,x - 2,3,x + 1,5,x - 2,7,x,11,x + 2,13,x + 1[] 147,3,2,x - 2,3,x - 1,5,x + 2,7,x,11,x + 2,13,x - 1[] 147,4,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 2,7,x^2,11,x^2 + 4*x + 4,13,x^2 + 8*x + 14[] 147,5,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2,11,x^2 + 4*x + 4,13,x^2 - 8*x + 14[] 148,1,2,x,3,x + 1,5,x + 4,7,x + 3,11,x - 5,13,x[] 148,2,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - x - 4,13,x^2 - 4*x + 4[] Total time: 21.689 seconds, Total memory usage: 8.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 07:35:31 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [148..160] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 07:35:14 on modular [Seed = 1822146959] ------------------------------------- 148,1,2,$.1,3,$.1 + 1,5,$.1 + 4,7,$.1 + 3,11,$.1 - 5,13,$.1[] 148,2,2,$.1^2,3,$.1^2 + $.1 - 4,5,$.1^2 - 4*$.1 + 4,7,$.1^2 - $.1 - 4,11,$.1^2 - $.1 - 4,13,$.1^2 - 4*$.1 + 4[] 149,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x - 13,7,x^3 + 5*x^2 + 6*x + 1,11,x^3 + 5*x^2 - 8*x + 1,13,x^3 + 3*x^2 - 4*x - 13[] 149,2,2,x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x + 39,3,x^9 - 6*x^8 + 55*x^6 - 67*x^5 - 125*x^4 + 235*x^3 - 6*x^2 - 117*x + 27,5,x^9 + x^8 - 25*x^7 - 4*x^6 + 202*x^5 - 83*x^4 - 529*x^3 + 305*x^2 + 392*x - 221,7,x^9 - 3*x^8 - 34*x^7 + 117*x^6 + 208*x^5 - 916*x^4 + 144*x^3 + 1056*x^2 - 128*x - 64,11,x^9 - 5*x^8 - 33*x^7 + 202*x^6 + 66*x^5 - 1503*x^4 + 997*x^3 + 2817*x^2 - 3392*x + 981,13,x^9 - 7*x^8 - 28*x^7 + 277*x^6 - 152*x^5 - 2028*x^4 + 3072*x^3 + 32*x^2 - 512*x - 64[] 150,1,2,x + 1,3,x + 1,5,x,7,x - 2,11,x - 2,13,x - 6[] 150,2,2,x - 1,3,x + 1,5,x,7,x - 4,11,x,13,x + 2[] 150,3,2,x - 1,3,x - 1,5,x,7,x + 2,11,x - 2,13,x + 6[] 151,1,2,x^3 + 2*x^2 - x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 7*x^2 + 14*x + 7,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 5*x^2 - x - 13,13,x^3 + x^2 - 16*x + 13[] 151,2,2,x^3 - 5*x + 3,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 5*x^2 - 2*x + 25,7,x^3 + 6*x^2 + 12*x + 8,11,x^3 + x^2 - 20*x + 25,13,x^3 + 2*x^2 - 32*x - 24[] 151,3,2,x^6 - x^5 - 7*x^4 + 3*x^3 + 13*x^2 + 3*x - 1,3,x^6 + 5*x^5 - 4*x^4 - 51*x^3 - 68*x^2 - 12*x + 8,5,x^6 - 6*x^5 + 5*x^4 + 16*x^3 - 8*x^2 - 12*x - 1,7,x^6 - 3*x^5 - 33*x^4 + 119*x^3 + 200*x^2 - 1100*x + 1000,11,x^6 - 8*x^5 + 14*x^4 + 23*x^3 - 64*x^2 - 7*x + 49,13,x^6 + x^5 - 40*x^4 - x^3 + 236*x^2 - 36*x - 328[] 152,1,2,x,3,x + 2,5,x + 1,7,x + 3,11,x + 3,13,x + 4[] 152,2,2,x,3,x - 1,5,x,7,x - 3,11,x - 2,13,x - 1[] 152,3,2,x^3,3,x^3 - x^2 - 10*x + 8,5,x^3 - x^2 - 10*x + 8,7,x^3 - 4*x^2 - 5*x + 16,11,x^3 + 5*x^2 - 2*x - 8,13,x^3 - 5*x^2 - 2*x + 8[] 153,1,2,x + 2,3,x,5,x + 1,7,x + 2,11,x + 3,13,x + 5[] 153,2,2,x - 2,3,x,5,x - 1,7,x + 2,11,x - 3,13,x + 5[] 153,3,2,x - 1,3,x,5,x - 2,7,x - 4,11,x,13,x + 2[] 153,4,2,x,3,x,5,x + 3,7,x + 4,11,x - 3,13,x + 1[] 153,5,2,x^2 - x - 4,3,x^2,5,x^2 + 3*x - 2,7,x^2,11,x^2 - x - 4,13,x^2 - 5*x + 2[] 154,1,2,x + 1,3,x,5,x + 4,7,x + 1,11,x + 1,13,x - 2[] 154,2,2,x + 1,3,x - 2,5,x - 2,7,x + 1,11,x - 1,13,x + 4[] 154,3,2,x - 1,3,x,5,x - 2,7,x + 1,11,x + 1,13,x - 2[] 154,4,2,x^2 - 2*x + 1,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 - 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + 2*x - 4[] 155,1,2,x,3,x + 1,5,x + 1,7,x,11,x + 4,13,x + 6[] 155,2,2,x + 1,3,x - 2,5,x + 1,7,x - 4,11,x - 4,13,x[] 155,3,2,x + 2,3,x + 1,5,x - 1,7,x + 2,11,x - 2,13,x + 6[] 155,4,2,x^4 + x^3 - 8*x^2 - 4*x + 12,3,x^4 + x^3 - 9*x^2 - 9*x - 2,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 12*x^2 - 4*x + 16,11,x^4 + 6*x^3 - 16*x^2 - 124*x - 144,13,x^4 - 16*x^3 + 84*x^2 - 156*x + 64[] 155,5,2,x^4 - x^3 - 6*x^2 + 4*x + 4,3,x^4 - x^3 - 5*x^2 + 3*x + 4,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 2*x^3 - 20*x^2 + 52*x - 32,11,x^4 + 4*x^3 - 8*x^2 - 12*x + 16,13,x^4 - 10*x^3 + 20*x^2 + 52*x - 136[] 156,1,2,x,3,x + 1,5,x + 4,7,x + 2,11,x + 4,13,x - 1[] 156,2,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x - 1[] 157,1,2,x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 7*x + 1,3,x^5 + 7*x^4 + 15*x^3 + 7*x^2 - 8*x - 5,5,x^5 + 3*x^4 - 12*x^3 - 39*x^2 - x + 25,7,x^5 + 3*x^4 - 15*x^3 - 26*x^2 + 61*x + 17,11,x^5 + 14*x^4 + 64*x^3 + 91*x^2 - 20*x + 1,13,x^5 + 7*x^4 + 9*x^3 - 32*x^2 - 89*x - 59[] 157,2,2,x^7 - 5*x^6 + 2*x^5 + 21*x^4 - 22*x^3 - 21*x^2 + 27*x - 1,3,x^7 - 5*x^6 - x^5 + 31*x^4 - 20*x^3 - 45*x^2 + 44*x - 4,5,x^7 + x^6 - 16*x^5 + 3*x^4 + 73*x^3 - 87*x^2 + 8*x + 16,7,x^7 - x^6 - 16*x^5 + 19*x^4 + 56*x^3 - 75*x^2 + 19*x - 1,11,x^7 - 10*x^6 + 28*x^5 - 9*x^4 - 44*x^3 + 33*x^2 + 8*x - 8,13,x^7 + 5*x^6 - 16*x^5 - 63*x^4 + 128*x^3 + 187*x^2 - 407*x + 113[] 158,1,2,x + 1,3,x + 1,5,x + 1,7,x + 3,11,x - 4,13,x + 7[] 158,2,2,x + 1,3,x - 1,5,x - 3,7,x + 1,11,x,13,x - 5[] 158,3,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 1[] 158,4,2,x - 1,3,x - 2,5,x + 2,7,x,11,x + 4,13,x - 2[] 158,5,2,x - 1,3,x + 3,5,x + 3,7,x + 3,11,x + 2,13,x + 5[] 158,6,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2 + 4*x + 4,7,x^2 - 8*x + 16,11,x^2,13,x^2 - 4*x - 20[] 159,1,2,x^4 - 3*x^3 - x^2 + 7*x - 3,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 11*x^2 + 32*x - 21,7,x^4 + 4*x^3 - 7*x^2 - 44*x - 43,11,x^4 - 6*x^3 - 28*x^2 + 232*x - 336,13,x^4 + 6*x^3 - 9*x^2 - 70*x + 1[] 159,2,2,x^5 - 10*x^3 + 22*x + 5,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 - 19*x^3 + 6*x^2 + 67*x - 2,7,x^5 - 4*x^4 - 23*x^3 + 92*x^2 + 117*x - 472,11,x^5 - 2*x^4 - 28*x^3 + 72*x^2 + 16*x - 64,13,x^5 - 8*x^4 - 13*x^3 + 136*x^2 + 101*x - 110[] 160,1,2,x,3,x + 2,5,x + 1,7,x + 2,11,x + 4,13,x + 6[] 160,2,2,x,3,x - 2,5,x + 1,7,x - 2,11,x - 4,13,x + 6[] 160,3,2,x^2,3,x^2 - 8,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 - 32,13,x^2 + 4*x + 4[] Total time: 17.389 seconds, Total memory usage: 7.25MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 07:44:16 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [160..170] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 07:44:01 on modular [Seed = 1102506673] ------------------------------------- 160,1,2,$.1,3,$.1 + 2,5,$.1 + 1,7,$.1 + 2,11,$.1 + 4,13,$.1 + 6[] 160,2,2,$.1,3,$.1 - 2,5,$.1 + 1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 6[] 160,3,2,$.1^2,3,$.1^2 - 8,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 8,11,$.1^2 - 32,13,$.1^2 + 4*$.1 + 4[] 161,1,2,x + 1,3,x,5,x - 2,7,x - 1,11,x - 4,13,x - 6[] 161,2,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x - 4,7,x^2 + 2*x + 1,11,x^2 - 20,13,x^2 + 4*x - 1[] 161,3,2,x^3 + x^2 - 5*x - 1,3,x^3 - 2*x^2 - 2*x + 2,5,x^3 - 2*x^2 - 2*x + 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 4*x^2 + 4,13,x^3 - 2*x^2 - 12*x + 8[] 161,4,2,x^5 - 2*x^4 - 9*x^3 + 17*x^2 + 16*x - 27,3,x^5 - 13*x^3 + 38*x + 10,5,x^5 + 4*x^4 - 14*x^3 - 54*x^2 + 52*x + 168,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 + 4*x^4 - 28*x^3 - 148*x^2 - 160*x - 48,13,x^5 + 6*x^4 - 9*x^3 - 46*x^2 + 12*x + 56[] 162,1,2,x + 1,3,x,5,x + 3,7,x + 4,11,x,13,x + 1[] 162,2,2,x + 1,3,x,5,x,7,x - 2,11,x - 3,13,x - 2[] 162,3,2,x - 1,3,x,5,x,7,x - 2,11,x + 3,13,x - 2[] 162,4,2,x - 1,3,x,5,x - 3,7,x + 4,11,x,13,x + 1[] 163,1,2,x,3,x,5,x + 4,7,x - 2,11,x + 6,13,x - 4[] 163,2,2,x^5 + 5*x^4 + 3*x^3 - 15*x^2 - 16*x + 3,3,x^5 + 5*x^4 + x^3 - 23*x^2 - 28*x - 9,5,x^5 + 9*x^4 + 23*x^3 + 12*x^2 - x - 1,7,x^5 + 6*x^4 - 5*x^3 - 48*x^2 + 18*x - 1,11,x^5 - 2*x^4 - 26*x^3 + 57*x^2 - 32*x + 3,13,x^5 + 14*x^4 + 73*x^3 + 173*x^2 + 179*x + 61[] 163,3,2,x^7 - 3*x^6 - 5*x^5 + 19*x^4 - 23*x^2 + 4*x + 6,3,x^7 - x^6 - 11*x^5 + 13*x^4 + 26*x^3 - 39*x^2 + 16*x - 2,5,x^7 - 11*x^6 + 41*x^5 - 44*x^4 - 73*x^3 + 199*x^2 - 136*x + 24,7,x^7 - 21*x^5 - 18*x^4 + 104*x^3 + 115*x^2 - 136*x - 158,11,x^7 - 2*x^6 - 20*x^5 + 67*x^4 - 34*x^3 - 49*x^2 + 20*x + 12,13,x^7 - 10*x^6 + 11*x^5 + 149*x^4 - 493*x^3 + 311*x^2 + 402*x - 334[] 164,1,2,x^4,3,x^4 - 2*x^3 - 10*x^2 + 22*x - 2,5,x^4 - 4*x^3 - 8*x^2 + 44*x - 36,7,x^4 - 22*x^2 + 26*x + 38,11,x^4 - 4*x^3 - 18*x^2 + 18*x + 54,13,x^4 - 40*x^2 - 48*x + 144[] 165,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 4*x - 4,11,x^2 + 2*x + 1,13,x^2 - 32[] 165,2,2,x^2 - 3,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 2*x + 1,13,x^2 - 4*x - 8[] 165,3,2,x^3 + x^2 - 5*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 16*x + 16,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 2*x^2 - 12*x - 8[] 166,1,2,x + 1,3,x + 1,5,x + 2,7,x - 1,11,x + 5,13,x + 2[] 166,2,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 - 3*x + 1,7,x^2 + 3*x + 1,11,x^2 - 6*x + 4,13,x^2 - 3*x + 1[] 166,3,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 6*x + 4,5,x^3 + x^2 - 5*x + 2,7,x^3 - 2*x^2 - 14*x - 13,11,x^3 - 5*x^2 + 2*x + 4,13,x^3 + 9*x^2 + 23*x + 14[] 167,1,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + 2*x + 1,7,x^2 + 5*x + 5,11,x^2,13,x^2 + 5*x + 5[] 167,2,2,x^12 - 2*x^11 - 17*x^10 + 33*x^9 + 103*x^8 - 189*x^7 - 277*x^6 + 447*x^5 + 363*x^4 - 433*x^3 - 205*x^2 + 120*x + 9,3,x^12 - 3*x^11 - 22*x^10 + 71*x^9 + 145*x^8 - 552*x^7 - 243*x^6 + 1577*x^5 - 122*x^4 - 1737*x^3 + 384*x^2 + 599*x - 91,5,x^12 - 4*x^11 - 41*x^10 + 152*x^9 + 648*x^8 - 2136*x^7 - 4816*x^6 + 13568*x^5 + 15616*x^4 - 37632*x^3 - 12544*x^2 + 33792*x - 9216,7,x^12 - 11*x^11 + 4*x^10 + 335*x^9 - 965*x^8 - 2308*x^7 + 11629*x^6 - 1491*x^5 - 39468*x^4 + 30443*x^3 + 38438*x^2 - 37689*x - 1557,11,x^12 - 77*x^10 - 12*x^9 + 2080*x^8 + 500*x^7 - 24675*x^6 - 6388*x^5 + 127975*x^4 + 29620*x^3 - 237953*x^2 - 23960*x + 86192,13,x^12 - 9*x^11 - 47*x^10 + 642*x^9 - 396*x^8 - 12320*x^7 + 32400*x^6 + 35904*x^5 - 180288*x^4 + 58880*x^3 + 179456*x^2 - 38912*x - 37888[] 168,1,2,x,3,x + 1,5,x - 2,7,x - 1,11,x,13,x - 6[] 168,2,2,x,3,x - 1,5,x - 2,7,x + 1,11,x,13,x + 2[] 169,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 3,7,x^2,11,x^2,13,x^2[] 169,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3 + 3*x^2 - 4*x - 13,11,x^3 + 8*x^2 + 19*x + 13,13,x^3[] 169,3,2,x^3 - 2*x^2 - x + 1,3,x^3 + 2*x^2 - x - 1,5,x^3 - 4*x^2 + 3*x + 1,7,x^3 - 3*x^2 - 4*x + 13,11,x^3 - 8*x^2 + 19*x - 13,13,x^3[] 170,1,2,x + 1,3,x + 2,5,x + 1,7,x - 2,11,x - 6,13,x - 2[] 170,2,2,x + 1,3,x - 3,5,x + 1,7,x - 2,11,x + 4,13,x + 3[] 170,3,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 5[] 170,4,2,x + 1,3,x + 2,5,x - 1,7,x + 2,11,x + 2,13,x + 6[] 170,5,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x + 1[] 170,6,2,x^2 - 2*x + 1,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 + 8*x + 16,13,x^2 - 5*x + 2[] Total time: 14.729 seconds, Total memory usage: 6.70MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:15:59 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [170..180] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:15:42 on modular [Seed = 333756300] ------------------------------------- 170,1,2,$.1 + 1,3,$.1 + 2,5,$.1 + 1,7,$.1 - 2,11,$.1 - 6,13,$.1 - 2[] 170,2,2,$.1 + 1,3,$.1 - 3,5,$.1 + 1,7,$.1 - 2,11,$.1 + 4,13,$.1 + 3[] 170,3,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 2,11,$.1,13,$.1 - 5[] 170,4,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 6[] 170,5,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 2,11,$.1,13,$.1 + 1[] 170,6,2,$.1^2 - 2*$.1 + 1,3,$.1^2 + $.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 2*$.1 - 16,11,$.1^2 + 8*$.1 + 16,13,$.1^2 - 5*$.1 + 2[] 171,1,2,x + 1,3,x,5,x - 2,7,x,11,x,13,x - 6[] 171,2,2,x - 2,3,x,5,x + 1,7,x - 3,11,x - 3,13,x + 6[] 171,3,2,x - 2,3,x,5,x - 3,7,x + 5,11,x + 1,13,x - 2[] 171,4,2,x,3,x,5,x + 3,7,x + 1,11,x + 3,13,x + 4[] 171,5,2,x^4 - 9*x^2 + 12,3,x^4,5,x^4 - 15*x^2 + 48,7,x^4 - 2*x^3 - 15*x^2 + 16*x + 64,11,x^4 - 27*x^2 + 108,13,x^4 - 8*x^3 + 24*x^2 - 32*x + 16[] 172,1,2,x,3,x + 2,5,x,7,x + 4,11,x + 3,13,x + 1[] 172,2,2,x^2,3,x^2 - 4*x + 2,5,x^2 - 2,7,x^2 - 2,11,x^2 - 2*x - 7,13,x^2 + 6*x + 1[] 173,1,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 6*x^3 + 10*x^2 + 3*x - 1,5,x^4 + x^3 - 5*x^2 - 7*x - 1,7,x^4 + 9*x^3 + 27*x^2 + 31*x + 11,11,x^4 + 5*x^3 - 11*x^2 - 65*x - 31,13,x^4 + 5*x^3 - 30*x^2 - 200*x - 275[] 173,2,2,x^10 - x^9 - 16*x^8 + 16*x^7 + 85*x^6 - 80*x^5 - 175*x^4 + 136*x^3 + 138*x^2 - 71*x - 25,3,x^10 - 8*x^9 + 11*x^8 + 59*x^7 - 165*x^6 - 55*x^5 + 484*x^4 - 202*x^3 - 390*x^2 + 169*x + 113,5,x^10 - x^9 - 29*x^8 + 41*x^7 + 253*x^6 - 452*x^5 - 548*x^4 + 1344*x^3 - 544*x^2 - 128*x + 64,7,x^10 - 11*x^9 + 20*x^8 + 168*x^7 - 704*x^6 + 235*x^5 + 2126*x^4 - 1607*x^3 - 2023*x^2 + 1319*x + 577,11,x^10 - 5*x^9 - 34*x^8 + 188*x^7 + 194*x^6 - 1935*x^5 + 1554*x^4 + 2983*x^3 - 2373*x^2 - 1687*x - 25,13,x^10 - x^9 - 63*x^8 + 59*x^7 + 1259*x^6 - 1496*x^5 - 9134*x^4 + 13207*x^3 + 14308*x^2 - 19944*x + 5285[] 174,1,2,x + 1,3,x + 1,5,x - 3,7,x + 3,11,x - 6,13,x[] 174,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x + 4,13,x - 6[] 174,3,2,x + 1,3,x - 1,5,x + 3,7,x - 5,11,x - 6,13,x + 4[] 174,4,2,x - 1,3,x + 1,5,x - 1,7,x - 1,11,x - 6,13,x + 4[] 174,5,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x + 2,13,x[] 175,1,2,x,3,x + 1,5,x,7,x + 1,11,x + 3,13,x + 5[] 175,2,2,x - 2,3,x - 1,5,x,7,x + 1,11,x + 3,13,x - 1[] 175,3,2,x + 2,3,x + 1,5,x,7,x - 1,11,x + 3,13,x + 1[] 175,4,2,x^2 - x - 4,3,x^2 - x - 4,5,x^2,7,x^2 - 2*x + 1,11,x^2 - x - 4,13,x^2 + 5*x + 2[] 175,5,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 4*x - 1,13,x^2 + 2*x - 4[] 175,6,2,x^2 + x - 1,3,x^2 - 2*x - 4,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x - 1,13,x^2 - 2*x - 4[] 176,1,2,x,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x[] 176,2,2,x,3,x - 1,5,x - 1,7,x - 2,11,x + 1,13,x - 4[] 176,3,2,x,3,x + 1,5,x + 3,7,x + 2,11,x - 1,13,x + 4[] 176,4,2,x^2,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 - 2*x - 16,11,x^2 - 2*x + 1,13,x^2 + 2*x - 16[] 177,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - 5,7,x^2 + 7*x + 11,11,x^2 - 5,13,x^2 + 8*x + 11[] 177,2,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - x - 1,11,x^2 - 4*x - 1,13,x^2 + 2*x + 1[] 177,3,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 6*x + 9,7,x^2 + 7*x + 11,11,x^2 + 2*x - 19,13,x^2 - 45[] 177,4,2,x^3 - 4*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 - 9*x^2 + 23*x - 16,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 - 4*x^2 - 7*x + 26[] 178,1,2,x + 1,3,x - 2,5,x - 2,7,x,11,x,13,x + 4[] 178,2,2,x - 1,3,x - 1,5,x - 3,7,x + 4,11,x + 6,13,x - 2[] 178,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 1,5,x^2 + 2*x - 7,7,x^2 + 4*x + 4,11,x^2 + 4*x - 4,13,x^2 + 4*x + 4[] 178,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 8*x + 4,5,x^3 + x^2 - 8*x - 4,7,x^3 - 10*x + 8,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 2*x^2 - 18*x - 44[] 179,1,2,x - 2,3,x,5,x - 3,7,x + 4,11,x - 4,13,x + 1[] 179,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3 + 4*x^2 + 3*x - 1,11,x^3 + 3*x^2 - 4*x + 1,13,x^3 + 11*x^2 + 38*x + 41[] 179,3,2,x^11 + 3*x^10 - 14*x^9 - 45*x^8 + 59*x^7 + 225*x^6 - 58*x^5 - 427*x^4 - 76*x^3 + 240*x^2 + 56*x - 16,3,x^11 - 25*x^9 + 5*x^8 + 219*x^7 - 98*x^6 - 781*x^5 + 589*x^4 + 901*x^3 - 1000*x^2 + 185*x - 9,5,x^11 - 3*x^10 - 28*x^9 + 65*x^8 + 310*x^7 - 499*x^6 - 1680*x^5 + 1613*x^4 + 4325*x^3 - 1977*x^2 - 4019*x + 663,7,x^11 - 8*x^10 - 19*x^9 + 281*x^8 - 202*x^7 - 2904*x^6 + 4160*x^5 + 12464*x^4 - 18560*x^3 - 26624*x^2 + 25728*x + 27392,11,x^11 + 9*x^10 - 24*x^9 - 359*x^8 + 4*x^7 + 5052*x^6 + 2592*x^5 - 32352*x^4 - 15552*x^3 + 94144*x^2 + 21504*x - 95488,13,x^11 - 24*x^10 + 206*x^9 - 583*x^8 - 1712*x^7 + 14840*x^6 - 30091*x^5 + 2233*x^4 + 47058*x^3 - 11030*x^2 - 30872*x - 7499[] 180,1,2,x,3,x,5,x - 1,7,x - 2,11,x,13,x - 2[] Total time: 16.819 seconds, Total memory usage: 7.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:22:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [180..190] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:21:39 on modular [Seed = 3876603365] ------------------------------------- 180,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 - 2,11,$.1,13,$.1 - 2[] 181,1,2,x^5 + 3*x^4 - x^3 - 7*x^2 - 2*x + 1,3,x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 9*x - 1,5,x^5 + 5*x^4 - 5*x^3 - 55*x^2 - 88*x - 43,7,x^5 + 2*x^4 - 19*x^3 - 42*x^2 + 66*x + 149,11,x^5 + 20*x^4 + 153*x^3 + 554*x^2 + 936*x + 575,13,x^5 + 2*x^4 - 40*x^3 - 53*x^2 + 222*x + 293[] 181,2,2,x^9 - 3*x^8 - 9*x^7 + 29*x^6 + 23*x^5 - 84*x^4 - 23*x^3 + 89*x^2 + 8*x - 27,3,x^9 - 3*x^8 - 15*x^7 + 46*x^6 + 63*x^5 - 213*x^4 - 32*x^3 + 272*x^2 - 144*x + 16,5,x^9 - x^8 - 24*x^7 + 28*x^6 + 170*x^5 - 181*x^4 - 441*x^3 + 340*x^2 + 326*x - 3,7,x^9 - 2*x^8 - 26*x^7 + 42*x^6 + 152*x^5 - 195*x^4 - 331*x^3 + 259*x^2 + 268*x - 31,11,x^9 - 24*x^8 + 221*x^7 - 898*x^6 + 832*x^5 + 5259*x^4 - 15404*x^3 + 5356*x^2 + 22256*x - 19056,13,x^9 + 8*x^8 - 17*x^7 - 333*x^6 - 1035*x^5 - 252*x^4 + 4742*x^3 + 10438*x^2 + 9148*x + 2993[] 182,1,2,x + 1,3,x - 1,5,x - 4,7,x + 1,11,x + 1,13,x - 1[] 182,2,2,x + 1,3,x - 3,5,x,7,x - 1,11,x + 5,13,x + 1[] 182,3,2,x - 1,3,x,5,x - 2,7,x + 1,11,x - 4,13,x + 1[] 182,4,2,x - 1,3,x - 3,5,x + 4,7,x + 1,11,x - 1,13,x + 1[] 182,5,2,x - 1,3,x - 1,5,x,7,x - 1,11,x + 3,13,x - 1[] 183,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x - 1,11,x^2 + 2*x - 1,13,x^2 + 6*x + 9[] 183,2,2,x^3 - x^2 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 6*x^2 + 12*x - 8,7,x^3 - 16*x - 16,11,x^3 - 2*x^2 - 4*x + 4,13,x^3 - 6*x^2 - 4*x + 40[] 183,3,2,x^6 - 11*x^4 + 2*x^3 + 31*x^2 - 10*x - 17,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 2*x^5 - 23*x^4 + 28*x^3 + 144*x^2 - 80*x - 144,7,x^6 - 2*x^5 - 25*x^4 + 60*x^3 + 128*x^2 - 432*x + 288,11,x^6 + 8*x^5 - 5*x^4 - 110*x^3 - 68*x^2 + 8*x + 4,13,x^6 - 6*x^5 - 23*x^4 + 116*x^3 + 168*x^2 - 464*x - 608[] 184,1,2,x,3,x + 1,5,x + 2,7,x + 4,11,x + 2,13,x - 7[] 184,2,2,x,3,x,5,x,7,x - 4,11,x - 6,13,x + 2[] 184,3,2,x,3,x - 3,5,x,7,x + 2,11,x,13,x + 5[] 184,4,2,x,3,x + 1,5,x + 4,7,x - 2,11,x + 4,13,x + 5[] 184,5,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2,11,x^2 - 2*x - 16,13,x^2 - 5*x + 2[] 185,1,2,x - 1,3,x + 2,5,x + 1,7,x + 2,11,x,13,x + 2[] 185,2,2,x + 2,3,x - 1,5,x + 1,7,x + 5,11,x - 3,13,x + 2[] 185,3,2,x,3,x + 1,5,x - 1,7,x + 3,11,x + 5,13,x - 4[] 185,4,2,x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 11*x - 12,3,x^5 - 3*x^4 - 6*x^3 + 20*x^2 + 4*x - 22,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 - 11*x^4 + 32*x^3 + 32*x^2 - 268*x + 302,11,x^5 + 5*x^4 - 8*x^3 - 48*x^2 + 16*x + 96,13,x^5 - 4*x^4 - 28*x^3 + 60*x^2 + 148*x - 256[] 185,5,2,x^5 - 8*x^3 + 2*x^2 + 11*x - 2,3,x^5 + x^4 - 8*x^3 - 4*x^2 + 4*x + 2,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - 7*x^4 + 6*x^3 + 24*x^2 - 2,11,x^5 - 7*x^4 - 12*x^3 + 144*x^2 - 176*x - 32,13,x^5 - 2*x^4 - 20*x^3 + 20*x^2 + 76*x - 88[] 186,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x - 3,13,x - 3[] 186,2,2,x + 1,3,x - 1,5,x - 3,7,x + 2,11,x - 5,13,x + 7[] 186,3,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x + 3,13,x + 1[] 186,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2 - 2*x - 16,11,x^2 + x - 4,13,x^2 - 3*x - 2[] 187,1,2,x - 2,3,x,5,x - 4,7,x + 5,11,x + 1,13,x - 4[] 187,2,2,x,3,x - 1,5,x - 3,7,x - 2,11,x - 1,13,x - 2[] 187,3,2,x^2 - 4*x + 4,3,x^2 + x - 4,5,x^2 - x - 4,7,x^2 - 3*x - 2,11,x^2 - 2*x + 1,13,x^2[] 187,4,2,x^2 + 2*x - 2,3,x^2 - 3,5,x^2 + 4*x + 1,7,x^2 + 4*x + 4,11,x^2 - 2*x + 1,13,x^2 + 10*x + 22[] 187,5,2,x^3 + 2*x^2 - 2*x - 2,3,x^3 + 3*x^2 - x - 5,5,x^3 + 7*x^2 + 13*x + 5,7,x^3 - 16*x + 16,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 30*x - 2[] 187,6,2,x^4 - x^3 - 6*x^2 + 2*x + 2,3,x^4 - x^3 - 11*x^2 + 9*x + 20,5,x^4 - 3*x^3 - 3*x^2 + 9*x - 2,7,x^4,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 2*x^3 - 28*x^2 - 90*x - 36[] 188,1,2,x^2,3,x^2 - x - 3,5,x^2,7,x^2 - 5*x + 3,11,x^2 - 2*x - 12,13,x^2 - 4*x + 4[] 188,2,2,x^2,3,x^2 + 3*x + 1,5,x^2 + 2*x - 4,7,x^2 + 7*x + 11,11,x^2 + 4*x - 16,13,x^2 + 4*x - 16[] 189,1,2,x + 2,3,x,5,x + 1,7,x + 1,11,x + 4,13,x + 2[] 189,2,2,x,3,x,5,x - 3,7,x - 1,11,x - 6,13,x + 4[] 189,3,2,x - 2,3,x,5,x - 1,7,x + 1,11,x - 4,13,x + 2[] 189,4,2,x,3,x,5,x + 3,7,x - 1,11,x + 6,13,x + 4[] 189,5,2,x^2 - 3,3,x^2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 3,13,x^2 - 4*x + 4[] 189,6,2,x^2 - 7,3,x^2,5,x^2 - 7,7,x^2 + 2*x + 1,11,x^2 - 7,13,x^2 + 4*x + 4[] 190,1,2,x + 1,3,x + 1,5,x + 1,7,x + 1,11,x,13,x + 3[] 190,2,2,x - 1,3,x + 3,5,x + 1,7,x + 5,11,x + 4,13,x + 1[] 190,3,2,x - 1,3,x - 1,5,x - 1,7,x + 1,11,x,13,x + 1[] 190,4,2,x^2 + 2*x + 1,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + x - 4,11,x^2 - 8*x + 16,13,x^2 + x - 38[] Total time: 19.180 seconds, Total memory usage: 7.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:28:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [190..200] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:27:58 on modular [Seed = 4093859147] ------------------------------------- 190,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1,13,$.1 + 3[] 190,2,2,$.1 - 1,3,$.1 + 3,5,$.1 + 1,7,$.1 + 5,11,$.1 + 4,13,$.1 + 1[] 190,3,2,$.1 - 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1,13,$.1 + 1[] 190,4,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + $.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 + $.1 - 4,11,$.1^2 - 8*$.1 + 16,13,$.1^2 + $.1 - 38[] 191,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 + x - 1,7,x^2 + x - 1,11,x^2 + x - 1,13,x^2 + 7*x + 1[] 191,2,2,x^14 - 23*x^12 + x^11 + 205*x^10 - 13*x^9 - 895*x^8 + 35*x^7 + 1993*x^6 + 103*x^5 - 2135*x^4 - 465*x^3 + 853*x^2 + 374*x + 41,3,x^14 - 2*x^13 - 30*x^12 + 58*x^11 + 334*x^10 - 630*x^9 - 1667*x^8 + 3160*x^7 + 3418*x^6 - 7088*x^5 - 1483*x^4 + 5142*x^3 - 940*x^2 - 122*x + 5,5,x^14 - x^13 - 48*x^12 + 63*x^11 + 860*x^10 - 1339*x^9 - 6923*x^8 + 11842*x^7 + 23938*x^6 - 41166*x^5 - 31785*x^4 + 51275*x^3 + 6610*x^2 - 21509*x + 5527,7,x^14 - 3*x^13 - 71*x^12 + 236*x^11 + 1872*x^10 - 7064*x^9 - 21808*x^8 + 101248*x^7 + 85248*x^6 - 691840*x^5 + 303360*x^4 + 1703424*x^3 - 2363392*x^2 + 942080*x - 69632,11,x^14 + 3*x^13 - 103*x^12 - 332*x^11 + 3764*x^10 + 13152*x^9 - 56816*x^8 - 222400*x^7 + 288512*x^6 + 1458688*x^5 + 131840*x^4 - 2122240*x^3 - 254976*x^2 + 892928*x - 167936,13,x^14 - 19*x^13 + 62*x^12 + 949*x^11 - 7606*x^10 + 503*x^9 + 166303*x^8 - 478782*x^7 - 645034*x^6 + 5011874*x^5 - 6716001*x^4 - 1704311*x^3 + 7511848*x^2 - 1293835*x - 1553539[] 192,1,2,x,3,x + 1,5,x + 2,7,x + 4,11,x + 4,13,x - 2[] 192,2,2,x,3,x - 1,5,x - 2,7,x,11,x + 4,13,x - 2[] 192,3,2,x,3,x - 1,5,x + 2,7,x - 4,11,x - 4,13,x - 2[] 192,4,2,x,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[] 193,1,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - 5,7,x^2 + x - 11,11,x^2 - 3*x - 9,13,x^2 + 6*x + 9[] 193,2,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,3,x^5 + 5*x^4 - x^3 - 27*x^2 - 10*x + 23,5,x^5 + 8*x^4 + 15*x^3 - 26*x^2 - 106*x - 83,7,x^5 + 10*x^4 + 27*x^3 + 5*x^2 - 25*x - 11,11,x^5 + 10*x^4 + 5*x^3 - 162*x^2 - 162*x + 729,13,x^5 - 2*x^4 - 45*x^3 + 50*x^2 + 350*x - 23[] 193,3,2,x^8 - 2*x^7 - 9*x^6 + 18*x^5 + 21*x^4 - 44*x^3 - 11*x^2 + 27*x + 1,3,x^8 - 5*x^7 - 2*x^6 + 40*x^5 - 37*x^4 - 48*x^3 + 36*x^2 + 31*x + 4,5,x^8 - 8*x^7 + 16*x^6 + 8*x^5 - 35*x^4 + x^3 + 16*x^2 - x - 2,7,x^8 - 5*x^7 - 10*x^6 + 62*x^5 - 9*x^4 - 71*x^3 + 28*x^2 + 17*x - 8,11,x^8 - 9*x^7 + 8*x^6 + 121*x^5 - 279*x^4 - 301*x^3 + 1067*x^2 - 333*x - 4,13,x^8 + 4*x^7 - 18*x^6 - 70*x^5 + 49*x^4 + 307*x^3 + 144*x^2 - 199*x - 118[] 194,1,2,x - 1,3,x,5,x - 4,7,x + 4,11,x - 4,13,x + 4[] 194,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 2*x^3 - 9*x^2 + 18*x + 1,5,x^4 + 2*x^3 - 15*x^2 - 26*x + 27,7,x^4 - 6*x^3 + 7*x^2 + 10*x - 13,11,x^4 - 2*x^3 - 9*x^2 + 2*x + 9,13,x^4 - 4*x^3 - 20*x^2 + 80*x - 16[] 194,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 9*x^2 + 18*x - 7,5,x^4 + 2*x^3 - 5*x^2 - 6*x + 7,7,x^4 - 2*x^3 - 19*x^2 + 62*x - 49,11,x^4 + 2*x^3 - 41*x^2 - 66*x + 193,13,x^4 - 4*x^3 - 20*x^2 + 48*x + 112[] 195,1,2,x - 2,3,x + 1,5,x - 1,7,x - 3,11,x + 1,13,x + 1[] 195,2,2,x - 2,3,x - 1,5,x + 1,7,x + 1,11,x - 5,13,x + 1[] 195,3,2,x + 1,3,x - 1,5,x - 1,7,x,11,x - 4,13,x - 1[] 195,4,2,x - 2,3,x - 1,5,x - 1,7,x + 3,11,x + 5,13,x - 1[] 195,5,2,x^3 - 7*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - x^2 - 16*x - 16,11,x^3 - x^2 - 16*x - 16,13,x^3 - 3*x^2 + 3*x - 1[] 196,1,2,x,3,x - 1,5,x - 3,7,x,11,x + 3,13,x - 2[] 196,2,2,x,3,x + 1,5,x + 3,7,x,11,x + 3,13,x + 2[] 196,3,2,x^2,3,x^2 - 8,5,x^2 - 2,7,x^2,11,x^2 - 8*x + 16,13,x^2 - 18[] 197,1,2,x + 2,3,x,5,x,7,x + 3,11,x - 4,13,x + 2[] 197,2,2,x^5 - 5*x^3 + x^2 + 3*x - 1,3,x^5 + 8*x^4 + 18*x^3 - x^2 - 38*x - 25,5,x^5 + 4*x^4 - 8*x^3 - 37*x^2 + 16*x + 85,7,x^5 + 10*x^4 + 27*x^3 - 9*x^2 - 97*x - 53,11,x^5 + 8*x^4 + x^3 - 68*x^2 + 22*x + 59,13,x^5 + 8*x^4 - 18*x^3 - 163*x^2 + 188*x + 493[] 197,3,2,x^10 - 15*x^8 + x^7 + 78*x^6 - 7*x^5 - 165*x^4 + 15*x^3 + 123*x^2 - 9*x - 26,3,x^10 - 10*x^9 + 29*x^8 + 17*x^7 - 227*x^6 + 316*x^5 + 184*x^4 - 784*x^3 + 646*x^2 - 175*x + 2,5,x^10 - 2*x^9 - 26*x^8 + 59*x^7 + 180*x^6 - 465*x^5 - 194*x^4 + 804*x^3 - 200*x^2 - 176*x + 32,7,x^10 - 11*x^9 + 25*x^8 + 100*x^7 - 420*x^6 - 24*x^5 + 1485*x^4 - 1136*x^3 - 496*x^2 + 384*x + 64,11,x^10 - 2*x^9 - 48*x^8 + 128*x^7 + 590*x^6 - 1633*x^5 - 2727*x^4 + 6561*x^3 + 5866*x^2 - 7319*x - 5906,13,x^10 - 8*x^9 - 14*x^8 + 189*x^7 - 28*x^6 - 1145*x^5 + 116*x^4 + 2160*x^3 - 352*x^2 - 1264*x + 448[] 198,1,2,x + 1,3,x,5,x,7,x - 2,11,x - 1,13,x - 2[] 198,2,2,x + 1,3,x,5,x - 4,7,x + 2,11,x + 1,13,x - 4[] 198,3,2,x + 1,3,x,5,x + 2,7,x + 4,11,x - 1,13,x + 6[] 198,4,2,x - 1,3,x,5,x,7,x - 2,11,x + 1,13,x - 2[] 198,5,2,x - 1,3,x,5,x,7,x - 2,11,x - 1,13,x + 4[] 199,1,2,x^2 + x - 1,3,x^2 - 4*x + 4,5,x^2 - 6*x + 9,7,x^2,11,x^2 + 6*x + 4,13,x^2 - 2*x - 19[] 199,2,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 2*x^3 - x^2 - 2*x + 1,5,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,7,x^4 + 3*x^3 - 10*x^2 + 6*x - 1,11,x^4 + 7*x^3 + 10*x^2 - 6*x - 11,13,x^4 - 14*x^2 + 25*x - 11[] 199,3,2,x^10 - 5*x^9 - 4*x^8 + 51*x^7 - 32*x^6 - 154*x^5 + 151*x^4 + 168*x^3 - 168*x^2 - 54*x + 27,3,x^10 + 4*x^9 - 19*x^8 - 88*x^7 + 73*x^6 + 552*x^5 + 200*x^4 - 784*x^3 - 480*x^2 + 96*x + 64,5,x^10 + x^9 - 26*x^8 - 26*x^7 + 216*x^6 + 219*x^5 - 607*x^4 - 571*x^3 + 317*x^2 + 156*x - 63,7,x^10 + 3*x^9 - 41*x^8 - 135*x^7 + 504*x^6 + 2027*x^5 - 1160*x^4 - 10173*x^3 - 8697*x^2 + 1110*x + 497,11,x^10 - 17*x^9 + 84*x^8 + 80*x^7 - 1875*x^6 + 4370*x^5 + 4696*x^4 - 27992*x^3 + 16544*x^2 + 42144*x - 45504,13,x^10 - 60*x^8 - 21*x^7 + 1174*x^6 + 364*x^5 - 9433*x^4 - 593*x^3 + 30585*x^2 - 5033*x - 26803[] 200,1,2,x,3,x - 2,5,x,7,x - 2,11,x + 4,13,x - 4[] 200,2,2,x,3,x + 3,5,x,7,x - 2,11,x - 1,13,x - 4[] 200,3,2,x,3,x,5,x,7,x - 4,11,x - 4,13,x - 2[] 200,4,2,x,3,x - 3,5,x,7,x + 2,11,x - 1,13,x + 4[] 200,5,2,x,3,x + 2,5,x,7,x + 2,11,x + 4,13,x + 4[] Total time: 16.959 seconds, Total memory usage: 7.28MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:36:31 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [200..210] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:36:08 on modular [Seed = 3508948600] ------------------------------------- 200,1,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 + 4,13,$.1 - 4[] 200,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 - 1,13,$.1 - 4[] 200,3,2,$.1,3,$.1,5,$.1,7,$.1 - 4,11,$.1 - 4,13,$.1 - 2[] 200,4,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 - 1,13,$.1 + 4[] 200,5,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 + 4,13,$.1 + 4[] 201,1,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x,13,x - 4[] 201,2,2,x + 2,3,x + 1,5,x,7,x,11,x + 6,13,x - 4[] 201,3,2,x + 1,3,x - 1,5,x + 1,7,x + 5,11,x + 4,13,x + 4[] 201,4,2,x^3 - 3*x^2 - x + 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - x^2 - 3*x + 1,7,x^3 - x^2 - 5*x + 1,11,x^3 - 10*x^2 + 24*x + 4,13,x^3 + 8*x^2 + 12*x + 4[] 201,5,2,x^5 - 8*x^3 + 13*x + 2,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 + 3*x^4 - 9*x^3 - 19*x^2 + 10*x + 16,7,x^5 - 7*x^4 + 3*x^3 + 63*x^2 - 128*x + 64,11,x^5 - 20*x^3 - 4*x^2 + 56*x - 32,13,x^5 - 10*x^4 + 20*x^3 + 36*x^2 - 88*x - 32[] 202,1,2,x + 1,3,x,5,x - 2,7,x - 1,11,x - 4,13,x[] 202,2,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 - 6*x - 17,7,x^3 + 3*x^2 - 18*x - 37,11,x^3 + 9*x^2 + 24*x + 17,13,x^3 + 3*x^2 - 36*x - 127[] 202,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + x^3 - 8*x^2 + x + 8,5,x^4 - 3*x^3 - 4*x^2 + 7*x - 2,7,x^4 - 2*x^3 - 9*x^2 + 3*x + 13,11,x^4 - x^3 - 28*x^2 + 39*x - 8,13,x^4 - x^3 - 16*x^2 - 19*x - 4[] 203,1,2,x - 1,3,x - 2,5,x - 2,7,x - 1,11,x + 4,13,x + 2[] 203,2,2,x + 2,3,x + 1,5,x + 4,7,x - 1,11,x - 2,13,x - 4[] 203,3,2,x + 1,3,x + 1,5,x - 1,7,x - 1,11,x + 5,13,x + 5[] 203,4,2,x^2 + 2*x + 1,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 + 2*x + 1,11,x^2 + x - 4,13,x^2 - 5*x + 2[] 203,5,2,x^2 - 4*x + 4,3,x^2 - 2*x - 1,5,x^2 - 8,7,x^2 + 2*x + 1,11,x^2 + 4*x - 4,13,x^2 - 8*x + 8[] 203,6,2,x^3 + x^2 - 3*x - 1,3,x^3 + 3*x^2 - x - 5,5,x^3 + 5*x^2 + 3*x - 5,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 5*x^2 - 5*x - 1,13,x^3 + 15*x^2 + 75*x + 125[] 203,7,2,x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 9*x - 6,3,x^5 + 2*x^4 - 10*x^3 - 18*x^2 + 11*x + 2,5,x^5 - 5*x^4 - 3*x^3 + 29*x^2 + 6*x - 24,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - 3*x^4 - 39*x^3 + 117*x^2 + 270*x - 648,13,x^5 - 15*x^4 + 53*x^3 + 147*x^2 - 1082*x + 1432[] 204,1,2,x,3,x + 1,5,x + 1,7,x - 4,11,x - 3,13,x - 3[] 204,2,2,x,3,x - 1,5,x - 1,7,x,11,x - 5,13,x + 5[] 205,1,2,x + 1,3,x - 2,5,x + 1,7,x - 2,11,x - 6,13,x - 2[] 205,2,2,x - 1,3,x - 2,5,x - 1,7,x - 2,11,x,13,x + 4[] 205,3,2,x + 1,3,x,5,x - 1,7,x + 4,11,x,13,x + 2[] 205,4,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 3*x - 9,11,x^2 + 8*x + 11,13,x^2 + 3*x - 9[] 205,5,2,x^2 + x - 3,3,x^2 + 6*x + 9,5,x^2 - 2*x + 1,7,x^2 + 3*x - 1,11,x^2 + 6*x + 9,13,x^2 + x - 29[] 205,6,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 2*x^2 - 5*x + 2,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 9*x^2 + 23*x + 14,11,x^3 - 4*x^2 - 7*x + 26,13,x^3 + 3*x^2 - x - 2[] 205,7,2,x^3 - 4*x - 1,3,x^3 - 2*x^2 - 5*x + 2,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - x^2 - 5*x - 2,11,x^3 - 4*x^2 - x + 8,13,x^3 - x^2 - 15*x + 28[] 206,1,2,x + 1,3,x - 2,5,x - 4,7,x,11,x + 6,13,x + 2[] 206,2,2,x^2 + 2*x + 1,3,x^2 - x - 7,5,x^2 - x - 7,7,x^2 + 3*x - 5,11,x^2 - 8*x + 16,13,x^2 - 2*x - 28[] 206,3,2,x^2 + 2*x + 1,3,x^2 + 3*x - 1,5,x^2 + 5*x + 3,7,x^2 - 5*x + 3,11,x^2,13,x^2 - 6*x - 4[] 206,4,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 5*x^2 + 12*x - 5,5,x^4 - 7*x^2 + 6*x - 1,7,x^4 - 2*x^3 - 17*x^2 + 50*x - 31,11,x^4 - 4*x^3 - 24*x^2 + 48*x + 80,13,x^4 - 28*x^2 - 48*x - 16[] 207,1,2,x + 1,3,x,5,x,7,x + 2,11,x + 4,13,x + 6[] 207,2,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 8,13,x^2[] 207,3,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 8,13,x^2[] 207,4,2,x^2 - 5,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 8*x + 16,13,x^2 - 20[] 207,5,2,x^2 - x - 1,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 - 6*x + 4,13,x^2 - 6*x + 9[] 208,1,2,x,3,x + 1,5,x + 1,7,x + 5,11,x - 2,13,x + 1[] 208,2,2,x,3,x,5,x - 2,7,x - 2,11,x - 2,13,x + 1[] 208,3,2,x,3,x - 3,5,x + 1,7,x + 1,11,x - 2,13,x + 1[] 208,4,2,x,3,x + 1,5,x + 3,7,x - 1,11,x + 6,13,x - 1[] 208,5,2,x^2,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 - x - 4,11,x^2 - 2*x - 16,13,x^2 - 2*x + 1[] 209,1,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x - 2[] 209,2,2,x^2 - 2,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2 + 4*x + 2,11,x^2 + 2*x + 1,13,x^2 + 4*x - 14[] 209,3,2,x^5 - 2*x^4 - 6*x^3 + 10*x^2 + 5*x - 4,3,x^5 - x^4 - 9*x^3 + 11*x^2 + 7*x - 1,5,x^5 + 5*x^4 - 3*x^3 - 33*x^2 - 9*x + 19,7,x^5 - 6*x^4 - x^3 + 62*x^2 - 119*x + 64,11,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,13,x^5 - 4*x^4 - 9*x^3 + 26*x^2 + 37*x + 2[] 209,4,2,x^7 + x^6 - 14*x^5 - 10*x^4 + 59*x^3 + 27*x^2 - 66*x - 30,3,x^7 - 2*x^6 - 14*x^5 + 28*x^4 + 46*x^3 - 100*x^2 - 17*x + 64,5,x^7 - 2*x^6 - 20*x^5 + 34*x^4 + 88*x^3 - 156*x^2 + 57*x - 6,7,x^7 - 10*x^6 + 17*x^5 + 86*x^4 - 185*x^3 - 316*x^2 + 394*x + 512,11,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,13,x^7 + 4*x^6 - 51*x^5 - 194*x^4 + 639*x^3 + 2082*x^2 - 2550*x - 5716[] 210,1,2,x + 1,3,x + 1,5,x + 1,7,x + 1,11,x + 4,13,x + 2[] 210,2,2,x + 1,3,x - 1,5,x - 1,7,x - 1,11,x,13,x - 2[] 210,3,2,x - 1,3,x + 1,5,x - 1,7,x - 1,11,x - 4,13,x + 2[] 210,4,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x,13,x - 2[] 210,5,2,x - 1,3,x - 1,5,x - 1,7,x + 1,11,x + 4,13,x + 2[] Total time: 21.779 seconds, Total memory usage: 8.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:42:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [210..220] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 08:41:52 on modular [Seed = 2740207330] ------------------------------------- 210,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 210,2,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,3,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1 - 1,11,$.1 - 4,13,$.1 + 2[] 210,4,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,5,2,$.1 - 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 211,1,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - x - 1,11,x^2 + 6*x + 9,13,x^2 - 8*x + 11[] 211,2,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 - x - 4,5,x^3 + 5*x^2 + 2*x - 4,7,x^3 + 3*x^2 - x - 2,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 - x^2 - 21*x + 37[] 211,3,2,x^3 + 2*x^2 - x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 8*x^2 + 19*x + 13,7,x^3 - 2*x^2 - 15*x + 29,11,x^3 + 2*x^2 - 29*x - 71,13,x^3 + 3*x^2 - 4*x + 1[] 211,4,2,x^9 + x^8 - 14*x^7 - 11*x^6 + 66*x^5 + 36*x^4 - 123*x^3 - 38*x^2 + 72*x + 8,3,x^9 + x^8 - 20*x^7 - 17*x^6 + 128*x^5 + 80*x^4 - 292*x^3 - 72*x^2 + 224*x - 32,5,x^9 - 15*x^8 + 83*x^7 - 189*x^6 + 63*x^5 + 377*x^4 - 410*x^3 + 10*x^2 + 51*x - 3,7,x^9 + 2*x^8 - 35*x^7 - 57*x^6 + 322*x^5 + 200*x^4 - 984*x^3 + 352*x^2 + 384*x - 192,11,x^9 - 13*x^8 + 31*x^7 + 235*x^6 - 1233*x^5 + 671*x^4 + 5452*x^3 - 9568*x^2 + 3705*x - 333,13,x^9 + 4*x^8 - 37*x^7 - 52*x^6 + 480*x^5 - 186*x^4 - 1768*x^3 + 2169*x^2 + 272*x - 931[] 212,1,2,x,3,x - 2,5,x - 2,7,x,11,x + 4,13,x + 2[] 212,2,2,x,3,x + 1,5,x + 2,7,x + 2,11,x - 2,13,x + 7[] 212,3,2,x^3,3,x^3 + 3*x^2 - 3*x - 7,5,x^3 - 12*x - 12,7,x^3 - 6*x^2 + 28,11,x^3 - 6*x^2 - 12*x + 84,13,x^3 - 15*x^2 + 75*x - 125[] 213,1,2,x - 1,3,x - 1,5,x - 2,7,x - 2,11,x,13,x + 2[] 213,2,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 6*x + 9,11,x^2 + 4*x - 1,13,x^2 + 5*x - 5[] 213,3,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 + 3*x - 1[] 213,4,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 + 8*x + 11,13,x^2 + x - 11[] 213,5,2,x^4 - 3*x^3 - 2*x^2 + 7*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 3*x^3 - 5*x^2 - 4*x + 4,7,x^4 - 6*x^3 + 7*x^2 + 6*x - 4,11,x^4 - 2*x^3 - 15*x^2 + 36*x - 16,13,x^4 - 5*x^3 - 11*x^2 + 40*x + 4[] 214,1,2,x + 1,3,x - 1,5,x + 4,7,x + 2,11,x + 3,13,x + 1[] 214,2,2,x + 1,3,x + 2,5,x + 1,7,x - 4,11,x + 6,13,x + 4[] 214,3,2,x - 1,3,x - 1,5,x,7,x - 2,11,x + 3,13,x + 1[] 214,4,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x + 2,13,x - 4[] 214,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 4*x + 1,7,x^2 + 2*x - 2,11,x^2 - 2*x - 2,13,x^2 - 2*x - 2[] 214,6,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 + 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 2*x - 2[] 215,1,2,x,3,x,5,x + 1,7,x + 2,11,x + 1,13,x + 1[] 215,2,2,x^3 + 2*x^2 - 3*x - 3,3,x^3 - x^2 - 4*x + 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 3*x^2 - 6*x - 7,11,x^3 - 9*x^2 + 107,13,x^3 + 2*x^2 - 16*x - 8[] 215,3,2,x^5 - 2*x^4 - 7*x^3 + 13*x^2 + 5*x - 4,3,x^5 + x^4 - 16*x^3 - 7*x^2 + 64*x - 16,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - 5*x^4 - 14*x^3 + 97*x^2 - 58*x - 160,11,x^5 + 6*x^4 + x^3 - 43*x^2 - 59*x - 12,13,x^5 - 5*x^4 - 50*x^3 + 284*x^2 + 224*x - 2000[] 215,4,2,x^6 - 3*x^5 - 5*x^4 + 17*x^3 + 3*x^2 - 17*x - 3,3,x^6 - 4*x^5 - 5*x^4 + 30*x^3 - 20*x^2 + 1,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,7,x^6 - 8*x^5 + x^4 + 92*x^3 - 72*x^2 - 194*x - 31,11,x^6 - 41*x^4 + 12*x^3 + 322*x^2 + 88*x - 93,13,x^6 - 6*x^5 - 20*x^4 + 104*x^3 + 144*x^2 - 352*x - 448[] 216,1,2,x,3,x,5,x + 4,7,x + 3,11,x + 4,13,x - 1[] 216,2,2,x,3,x,5,x + 1,7,x - 3,11,x - 5,13,x - 4[] 216,3,2,x,3,x,5,x - 1,7,x - 3,11,x + 5,13,x - 4[] 216,4,2,x,3,x,5,x - 4,7,x + 3,11,x - 4,13,x - 1[] 217,1,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 9*x - 9,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 6*x^2 + 3*x - 19,13,x^3 + 3*x^2 - 18*x - 37[] 217,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 27*x + 27,13,x^3 + 3*x^2 - 24*x + 1[] 217,3,2,x^4 - 5*x^2 + x + 1,3,x^4 - 3*x^3 - 2*x^2 + 9*x - 4,5,x^4 - 4*x^3 + x^2 + 5*x - 2,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 23*x^2 + 81*x - 68,13,x^4 + x^3 - 18*x^2 - 37*x - 2[] 217,4,2,x^5 - 3*x^4 - 5*x^3 + 16*x^2 + 6*x - 19,3,x^5 - 3*x^4 - 6*x^3 + 15*x^2 + 8*x - 16,5,x^5 - 17*x^3 - 5*x^2 + 56*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 13*x^3 + 39*x^2 + 48*x + 8,13,x^5 + 3*x^4 - 14*x^3 - 47*x^2 - 36*x - 4[] 218,1,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x - 3,13,x + 4[] 218,2,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 - 2*x - 1,7,x^2 + 4*x + 2,11,x^2 + 2*x - 7,13,x^2 + 8*x + 8[] 218,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2 - 2*x + 1,13,x^2 - 4*x - 8[] 218,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x + 4,11,x^2 + 6*x + 4,13,x^2 - 3*x - 9[] 218,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 3*x + 8,5,x^3 + 3*x^2 - 6*x - 12,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 3*x^2 - 6*x + 12,13,x^3 - 9*x^2 + 15*x + 16[] 219,1,2,x - 1,3,x + 1,5,x + 4,7,x - 2,11,x + 4,13,x + 2[] 219,2,2,x + 2,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x + 2[] 219,3,2,x,3,x - 1,5,x + 3,7,x + 4,11,x,13,x + 4[] 219,4,2,x^4 - x^3 - 6*x^2 + 4*x + 4,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 9*x^3 + 25*x^2 - 21*x + 2,7,x^4 + 4*x^3 - 8*x^2 - 12*x + 16,11,x^4 - 2*x^3 - 20*x^2 + 52*x - 32,13,x^4 - 6*x^3 - 4*x^2 + 12*x + 8[] 219,5,2,x^6 + x^5 - 9*x^4 - 5*x^3 + 20*x^2 + 4*x - 4,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 5*x^5 - 7*x^4 + 49*x^3 + 20*x^2 - 128*x - 64,7,x^6 - 8*x^5 + 4*x^4 + 92*x^3 - 216*x^2 + 160*x - 32,11,x^6 + 2*x^5 - 40*x^4 - 20*x^3 + 336*x^2 - 240*x + 32,13,x^6 - 4*x^5 - 28*x^4 + 108*x^3 + 88*x^2 - 240*x + 32[] Errors: /home/mfd/gomagma: line 2: 24258 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:43:11 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [210..218] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:42:52 on modular [Seed = 2874947222] ------------------------------------- 210,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 210,2,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,3,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1 - 1,11,$.1 - 4,13,$.1 + 2[] 210,4,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,5,2,$.1 - 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 211,1,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - x - 1,11,x^2 + 6*x + 9,13,x^2 - 8*x + 11[] 211,2,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 - x - 4,5,x^3 + 5*x^2 + 2*x - 4,7,x^3 + 3*x^2 - x - 2,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 - x^2 - 21*x + 37[] 211,3,2,x^3 + 2*x^2 - x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 8*x^2 + 19*x + 13,7,x^3 - 2*x^2 - 15*x + 29,11,x^3 + 2*x^2 - 29*x - 71,13,x^3 + 3*x^2 - 4*x + 1[] 211,4,2,x^9 + x^8 - 14*x^7 - 11*x^6 + 66*x^5 + 36*x^4 - 123*x^3 - 38*x^2 + 72*x + 8,3,x^9 + x^8 - 20*x^7 - 17*x^6 + 128*x^5 + 80*x^4 - 292*x^3 - 72*x^2 + 224*x - 32,5,x^9 - 15*x^8 + 83*x^7 - 189*x^6 + 63*x^5 + 377*x^4 - 410*x^3 + 10*x^2 + 51*x - 3,7,x^9 + 2*x^8 - 35*x^7 - 57*x^6 + 322*x^5 + 200*x^4 - 984*x^3 + 352*x^2 + 384*x - 192,11,x^9 - 13*x^8 + 31*x^7 + 235*x^6 - 1233*x^5 + 671*x^4 + 5452*x^3 - 9568*x^2 + 3705*x - 333,13,x^9 + 4*x^8 - 37*x^7 - 52*x^6 + 480*x^5 - 186*x^4 - 1768*x^3 + 2169*x^2 + 272*x - 931[] 212,1,2,x,3,x - 2,5,x - 2,7,x,11,x + 4,13,x + 2[] 212,2,2,x,3,x + 1,5,x + 2,7,x + 2,11,x - 2,13,x + 7[] 212,3,2,x^3,3,x^3 + 3*x^2 - 3*x - 7,5,x^3 - 12*x - 12,7,x^3 - 6*x^2 + 28,11,x^3 - 6*x^2 - 12*x + 84,13,x^3 - 15*x^2 + 75*x - 125[] 213,1,2,x - 1,3,x - 1,5,x - 2,7,x - 2,11,x,13,x + 2[] 213,2,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 6*x + 9,11,x^2 + 4*x - 1,13,x^2 + 5*x - 5[] 213,3,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 + 3*x - 1[] 213,4,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 + 8*x + 11,13,x^2 + x - 11[] 213,5,2,x^4 - 3*x^3 - 2*x^2 + 7*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 3*x^3 - 5*x^2 - 4*x + 4,7,x^4 - 6*x^3 + 7*x^2 + 6*x - 4,11,x^4 - 2*x^3 - 15*x^2 + 36*x - 16,13,x^4 - 5*x^3 - 11*x^2 + 40*x + 4[] 214,1,2,x + 1,3,x - 1,5,x + 4,7,x + 2,11,x + 3,13,x + 1[] 214,2,2,x + 1,3,x + 2,5,x + 1,7,x - 4,11,x + 6,13,x + 4[] 214,3,2,x - 1,3,x - 1,5,x,7,x - 2,11,x + 3,13,x + 1[] 214,4,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x + 2,13,x - 4[] 214,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 4*x + 1,7,x^2 + 2*x - 2,11,x^2 - 2*x - 2,13,x^2 - 2*x - 2[] 214,6,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 + 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 2*x - 2[] 215,1,2,x,3,x,5,x + 1,7,x + 2,11,x + 1,13,x + 1[] 215,2,2,x^3 + 2*x^2 - 3*x - 3,3,x^3 - x^2 - 4*x + 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 3*x^2 - 6*x - 7,11,x^3 - 9*x^2 + 107,13,x^3 + 2*x^2 - 16*x - 8[] 215,3,2,x^5 - 2*x^4 - 7*x^3 + 13*x^2 + 5*x - 4,3,x^5 + x^4 - 16*x^3 - 7*x^2 + 64*x - 16,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - 5*x^4 - 14*x^3 + 97*x^2 - 58*x - 160,11,x^5 + 6*x^4 + x^3 - 43*x^2 - 59*x - 12,13,x^5 - 5*x^4 - 50*x^3 + 284*x^2 + 224*x - 2000[] 215,4,2,x^6 - 3*x^5 - 5*x^4 + 17*x^3 + 3*x^2 - 17*x - 3,3,x^6 - 4*x^5 - 5*x^4 + 30*x^3 - 20*x^2 + 1,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,7,x^6 - 8*x^5 + x^4 + 92*x^3 - 72*x^2 - 194*x - 31,11,x^6 - 41*x^4 + 12*x^3 + 322*x^2 + 88*x - 93,13,x^6 - 6*x^5 - 20*x^4 + 104*x^3 + 144*x^2 - 352*x - 448[] 216,1,2,x,3,x,5,x + 4,7,x + 3,11,x + 4,13,x - 1[] 216,2,2,x,3,x,5,x + 1,7,x - 3,11,x - 5,13,x - 4[] 216,3,2,x,3,x,5,x - 1,7,x - 3,11,x + 5,13,x - 4[] 216,4,2,x,3,x,5,x - 4,7,x + 3,11,x - 4,13,x - 1[] 217,1,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 9*x - 9,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 6*x^2 + 3*x - 19,13,x^3 + 3*x^2 - 18*x - 37[] 217,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 27*x + 27,13,x^3 + 3*x^2 - 24*x + 1[] 217,3,2,x^4 - 5*x^2 + x + 1,3,x^4 - 3*x^3 - 2*x^2 + 9*x - 4,5,x^4 - 4*x^3 + x^2 + 5*x - 2,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 23*x^2 + 81*x - 68,13,x^4 + x^3 - 18*x^2 - 37*x - 2[] 217,4,2,x^5 - 3*x^4 - 5*x^3 + 16*x^2 + 6*x - 19,3,x^5 - 3*x^4 - 6*x^3 + 15*x^2 + 8*x - 16,5,x^5 - 17*x^3 - 5*x^2 + 56*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 13*x^3 + 39*x^2 + 48*x + 8,13,x^5 + 3*x^4 - 14*x^3 - 47*x^2 - 36*x - 4[] 218,1,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x - 3,13,x + 4[] 218,2,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 - 2*x - 1,7,x^2 + 4*x + 2,11,x^2 + 2*x - 7,13,x^2 + 8*x + 8[] 218,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2 - 2*x + 1,13,x^2 - 4*x - 8[] 218,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x + 4,11,x^2 + 6*x + 4,13,x^2 - 3*x - 9[] 218,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 3*x + 8,5,x^3 + 3*x^2 - 6*x - 12,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 3*x^2 - 6*x + 12,13,x^3 - 9*x^2 + 15*x + 16[] Total time: 18.959 seconds, Total memory usage: 7.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:49:40 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [218..226] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:49:21 on modular [Seed = 3092194360] ------------------------------------- 218,1,2,$.1 - 1,3,$.1 + 2,5,$.1 + 3,7,$.1 + 4,11,$.1 - 3,13,$.1 + 4[] 218,2,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + 4*$.1 + 2,5,$.1^2 - 2*$.1 - 1,7,$.1^2 + 4*$.1 + 2,11,$.1^2 + 2*$.1 - 7,13,$.1^2 + 8*$.1 + 8[] 218,3,2,$.1^2 - 2*$.1 + 1,3,$.1^2 + 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 6*$.1 + 6,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 - 8[] 218,4,2,$.1^2 - 2*$.1 + 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 + 4*$.1 + 4,11,$.1^2 + 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 218,5,2,$.1^3 + 3*$.1^2 + 3*$.1 + 1,3,$.1^3 - 3*$.1^2 - 3*$.1 + 8,5,$.1^3 + 3*$.1^2 - 6*$.1 - 12,7,$.1^3 - 6*$.1^2 + 12*$.1 - 8,11,$.1^3 - 3*$.1^2 - 6*$.1 + 12,13,$.1^3 - 9*$.1^2 + 15*$.1 + 16[] 219,1,2,x - 1,3,x + 1,5,x + 4,7,x - 2,11,x + 4,13,x + 2[] 219,2,2,x + 2,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x + 2[] 219,3,2,x,3,x - 1,5,x + 3,7,x + 4,11,x,13,x + 4[] 219,4,2,x^4 - x^3 - 6*x^2 + 4*x + 4,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 9*x^3 + 25*x^2 - 21*x + 2,7,x^4 + 4*x^3 - 8*x^2 - 12*x + 16,11,x^4 - 2*x^3 - 20*x^2 + 52*x - 32,13,x^4 - 6*x^3 - 4*x^2 + 12*x + 8[] 219,5,2,x^6 + x^5 - 9*x^4 - 5*x^3 + 20*x^2 + 4*x - 4,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 5*x^5 - 7*x^4 + 49*x^3 + 20*x^2 - 128*x - 64,7,x^6 - 8*x^5 + 4*x^4 + 92*x^3 - 216*x^2 + 160*x - 32,11,x^6 + 2*x^5 - 40*x^4 - 20*x^3 + 336*x^2 - 240*x + 32,13,x^6 - 4*x^5 - 28*x^4 + 108*x^3 + 88*x^2 - 240*x + 32[] 220,1,2,x,3,x + 2,5,x - 1,7,x + 4,11,x + 1,13,x + 4[] 220,2,2,x,3,x - 2,5,x - 1,7,x,11,x - 1,13,x[] 221,1,2,x - 1,3,x - 2,5,x - 2,7,x - 2,11,x + 6,13,x + 1[] 221,2,2,x + 1,3,x,5,x - 4,7,x + 2,11,x - 6,13,x + 1[] 221,3,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + x - 1,11,x^2 + 3*x - 9,13,x^2 + 2*x + 1[] 221,4,2,x^2 - 5,3,x^2 - 2*x - 4,5,x^2 + 2*x - 4,7,x^2 - 4*x + 4,11,x^2 - 4*x + 4,13,x^2 + 2*x + 1[] 221,5,2,x^2 + x - 5,3,x^2 - x - 5,5,x^2 + 2*x + 1,7,x^2 + 5*x + 1,11,x^2 - 3*x - 3,13,x^2 + 2*x + 1[] 221,6,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 - x - 4,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 + 9*x^2 + 23*x + 16,11,x^3 + 7*x^2 + 11*x + 4,13,x^3 - 3*x^2 + 3*x - 1[] 221,7,2,x^6 - x^5 - 9*x^4 + 6*x^3 + 19*x^2 - 5*x - 3,3,x^6 - x^5 - 11*x^4 + 12*x^3 + 28*x^2 - 36*x + 4,5,x^6 + 2*x^5 - 15*x^4 - 16*x^3 + 60*x^2 - 16*x - 12,7,x^6 - 7*x^5 - 7*x^4 + 112*x^3 - 56*x^2 - 400*x + 208,11,x^6 + x^5 - 19*x^4 - 8*x^3 + 88*x^2 + 16*x - 48,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 222,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x + 4,13,x - 6[] 222,2,2,x + 1,3,x + 1,5,x + 4,7,x - 3,11,x - 5,13,x - 3[] 222,3,2,x + 1,3,x - 1,5,x - 4,7,x + 1,11,x + 1,13,x + 3[] 222,4,2,x - 1,3,x + 1,5,x,7,x - 3,11,x - 1,13,x - 1[] 222,5,2,x - 1,3,x - 1,5,x,7,x + 1,11,x - 3,13,x + 1[] 223,1,2,x^2 + 2*x - 1,3,x^2 + 2*x - 1,5,x^2 + 4*x + 2,7,x^2 - 2,11,x^2 - 2*x - 1,13,x^2 - 4*x + 2[] 223,2,2,x^4 + 4*x^3 + 2*x^2 - 5*x - 3,3,x^4 - 4*x^2 + x + 1,5,x^4 + 3*x^3 - x^2 - 7*x - 3,7,x^4 + 6*x^3 - 31*x - 3,11,x^4 + 10*x^3 + 24*x^2 - 21*x - 83,13,x^4 + 9*x^3 + 13*x^2 - 19*x - 31[] 223,3,2,x^12 - 7*x^11 + 6*x^10 + 57*x^9 - 122*x^8 - 105*x^7 + 430*x^6 - 73*x^5 - 499*x^4 + 242*x^3 + 143*x^2 - 52*x - 19,3,x^12 - 27*x^10 + 7*x^9 + 263*x^8 - 131*x^7 - 1091*x^6 + 816*x^5 + 1600*x^4 - 1752*x^3 + 128*x^2 + 288*x - 64,5,x^12 - 7*x^11 - 11*x^10 + 157*x^9 - 97*x^8 - 1096*x^7 + 1354*x^6 + 2692*x^5 - 3952*x^4 - 1744*x^3 + 3200*x^2 - 512*x - 128,7,x^12 - 2*x^11 - 35*x^10 + 55*x^9 + 385*x^8 - 527*x^7 - 1444*x^6 + 2034*x^5 + 1158*x^4 - 2761*x^3 + 1299*x^2 - 174*x + 2,11,x^12 - 6*x^11 - 53*x^10 + 329*x^9 + 919*x^8 - 6597*x^7 - 4941*x^6 + 58510*x^5 - 14616*x^4 - 213896*x^3 + 167520*x^2 + 204800*x - 194048,13,x^12 - x^11 - 81*x^10 + 89*x^9 + 2061*x^8 - 2766*x^7 - 17434*x^6 + 27992*x^5 + 28880*x^4 - 34320*x^3 - 26304*x^2 - 1216*x + 896[] 224,1,2,x,3,x + 2,5,x,7,x + 1,11,x + 4,13,x + 4[] 224,2,2,x,3,x - 2,5,x,7,x - 1,11,x - 4,13,x + 4[] 224,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 - 2*x + 1,11,x^2 + 4*x - 16,13,x^2 - 6*x + 4[] 224,4,2,x^2,3,x^2 - 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 2*x + 1,11,x^2 - 4*x - 16,13,x^2 - 6*x + 4[] 225,1,2,x,3,x,5,x,7,x + 5,11,x,13,x + 5[] 225,2,2,x,3,x,5,x,7,x - 5,11,x,13,x - 5[] 225,3,2,x + 1,3,x,5,x,7,x,11,x - 4,13,x - 2[] 225,4,2,x - 2,3,x,5,x,7,x - 3,11,x + 2,13,x + 1[] 225,5,2,x + 2,3,x,5,x,7,x + 3,11,x + 2,13,x - 1[] 225,6,2,x^2 - 5,3,x^2,5,x^2,7,x^2,11,x^2,13,x^2[] 226,1,2,x - 1,3,x + 2,5,x + 4,7,x,11,x + 4,13,x + 2[] 226,2,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 + 4*x + 2,7,x^2 + 4*x - 4,11,x^2 + 8*x + 16,13,x^2 - 4*x + 4[] 226,3,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 4*x + 4,7,x^2,11,x^2 - 4*x - 8,13,x^2 + 4*x - 8[] 226,4,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 6*x^2 + 12*x - 4,5,x^4 - 4*x^3 - 4*x^2 + 16*x - 4,7,x^4 + 4*x^3 - 4*x^2 - 16*x + 16,11,x^4 - 20*x^2 + 80,13,x^4 - 4*x^3 - 24*x^2 + 96*x - 64[] Total time: 18.139 seconds, Total memory usage: 7.55MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 09:26:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [226..234] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 09:26:19 on modular [Seed = 1470153916] ------------------------------------- 226,1,2,$.1 - 1,3,$.1 + 2,5,$.1 + 4,7,$.1,11,$.1 + 4,13,$.1 + 2[] 226,2,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2,5,$.1^2 + 4*$.1 + 2,7,$.1^2 + 4*$.1 - 4,11,$.1^2 + 8*$.1 + 16,13,$.1^2 - 4*$.1 + 4[] 226,3,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 4*$.1 + 4,7,$.1^2,11,$.1^2 - 4*$.1 - 8,13,$.1^2 + 4*$.1 - 8[] 226,4,2,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,3,$.1^4 - 2*$.1^3 - 6*$.1^2 + 12*$.1 - 4,5,$.1^4 - 4*$.1^3 - 4*$.1^2 + 16*$.1 - 4,7,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,11,$.1^4 - 20*$.1^2 + 80,13,$.1^4 - 4*$.1^3 - 24*$.1^2 + 96*$.1 - 64[] 227,1,2,x^2 - 2,3,x^2 + 4*x + 4,5,x^2 - 2,7,x^2 + 2*x - 7,11,x^2 - 2*x - 7,13,x^2 + 8*x + 8[] 227,2,2,x^2 - 5,3,x^2 - 3*x + 1,5,x^2 + 4*x + 4,7,x^2 - 7*x + 11,11,x^2 - x - 1,13,x^2 + 2*x - 4[] 227,3,2,x^2 - 2*x + 1,3,x^2 + x - 7,5,x^2 - 4*x + 4,7,x^2 - 3*x - 5,11,x^2 - 5*x - 1,13,x^2 - 2*x - 28[] 227,4,2,x^3 + 2*x^2 - x - 1,3,x^3 - x^2 - 2*x + 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3 + 6*x^2 + 5*x - 13,11,x^3 + x^2 - 16*x - 29,13,x^3 + 9*x^2 + 27*x + 27[] 227,5,2,x^10 - 17*x^8 - 3*x^7 + 98*x^6 + 40*x^5 - 218*x^4 - 148*x^3 + 136*x^2 + 144*x + 32,3,x^10 - x^9 - 17*x^8 + 8*x^7 + 99*x^6 - 8*x^5 - 210*x^4 + 5*x^3 + 152*x^2 - 20*x - 4,5,x^10 - 7*x^9 - 18*x^8 + 205*x^7 - 66*x^6 - 1746*x^5 + 1594*x^4 + 5648*x^3 - 5408*x^2 - 5712*x + 5472,7,x^10 - 37*x^8 + 3*x^7 + 422*x^6 - 37*x^5 - 1575*x^4 - 216*x^3 + 2014*x^2 + 774*x - 265,11,x^10 + 3*x^9 - 64*x^8 - 165*x^7 + 1442*x^6 + 2675*x^5 - 14456*x^4 - 11754*x^3 + 61970*x^2 - 14195*x - 38209,13,x^10 - 23*x^9 + 191*x^8 - 505*x^7 - 2032*x^6 + 17104*x^5 - 37704*x^4 - 11504*x^3 + 184640*x^2 - 292992*x + 151808[] 228,1,2,x,3,x + 1,5,x - 2,7,x,11,x - 2,13,x - 2[] 228,2,2,x,3,x + 1,5,x + 3,7,x - 1,11,x + 5,13,x + 6[] 228,3,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 3*x - 6,7,x^2 - x - 8,11,x^2 + 3*x - 6,13,x^2 - 4*x + 4[] 229,1,2,x + 1,3,x - 1,5,x + 3,7,x - 2,11,x + 3,13,x + 6[] 229,2,2,x^6 + 4*x^5 - 12*x^3 - 3*x^2 + 9*x - 1,3,x^6 + 6*x^5 + 7*x^4 - 17*x^3 - 36*x^2 - 6*x + 13,5,x^6 + 3*x^5 - 12*x^4 - 39*x^3 + 19*x^2 + 121*x + 79,7,x^6 + 5*x^5 - 16*x^4 - 127*x^3 - 155*x^2 + 213*x + 386,11,x^6 + 22*x^5 + 190*x^4 + 815*x^3 + 1815*x^2 + 1996*x + 853,13,x^6 - x^5 - 34*x^4 + 121*x^3 - 111*x^2 - 21*x + 46[] 229,3,2,x^11 - 5*x^10 - 4*x^9 + 50*x^8 - 26*x^7 - 165*x^6 + 152*x^5 + 193*x^4 - 207*x^3 - 50*x^2 + 52*x + 1,3,x^11 - 3*x^10 - 19*x^9 + 60*x^8 + 109*x^7 - 402*x^6 - 133*x^5 + 987*x^4 - 332*x^3 - 572*x^2 + 288*x - 16,5,x^11 - 28*x^9 + 3*x^8 + 204*x^7 - 23*x^6 - 397*x^5 + 238*x^3 + 21*x^2 - 44*x - 7,7,x^11 - x^10 - 33*x^9 + 26*x^8 + 342*x^7 - 293*x^6 - 1477*x^5 + 1416*x^4 + 2679*x^3 - 2815*x^2 - 1556*x + 1736,11,x^11 - 27*x^10 + 288*x^9 - 1447*x^8 + 2508*x^7 + 7057*x^6 - 38171*x^5 + 44023*x^4 + 51012*x^3 - 149100*x^2 + 103664*x - 22384,13,x^11 + 7*x^10 - 28*x^9 - 203*x^8 + 311*x^7 + 1849*x^6 - 1432*x^5 - 6708*x^4 + 1776*x^3 + 8528*x^2 + 1984*x - 128[] 230,1,2,x^2 + 2*x + 1,3,x^2 + x - 5,5,x^2 + 2*x + 1,7,x^2 - x - 5,11,x^2 - 3*x - 3,13,x^2 - 7*x + 7[] 230,2,2,x^2 + 2*x + 1,3,x^2 - 3*x - 1,5,x^2 - 2*x + 1,7,x^2 - 3*x - 1,11,x^2 + 7*x + 9,13,x^2 - 3*x - 1[] 230,3,2,x^2 - 2*x + 1,3,x^2 - x - 1,5,x^2 - 2*x + 1,7,x^2 - x - 1,11,x^2 - x - 11,13,x^2 + 3*x - 29[] 230,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 9*x + 12,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 3*x^2 - 21*x + 64,11,x^3 - 3*x^2 - 39*x + 144,13,x^3 + x^2 - 15*x - 18[] 231,1,2,x + 1,3,x + 1,5,x + 2,7,x - 1,11,x + 1,13,x - 6[] 231,2,2,x^2 + x - 5,3,x^2 + 2*x + 1,5,x^2 - 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 2*x + 1,13,x^2 - 2*x + 1[] 231,3,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + 2*x - 19[] 231,4,2,x^3 - 6*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 15*x + 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 15*x + 2[] 231,5,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 - 7*x + 26,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 4*x^2 - 27*x - 94[] 232,1,2,x,3,x + 1,5,x + 3,7,x - 2,11,x + 3,13,x + 5[] 232,2,2,x,3,x - 1,5,x - 1,7,x - 2,11,x - 3,13,x + 1[] 232,3,2,x^2,3,x^2 + 2*x - 1,5,x^2 + 2*x - 7,7,x^2 + 8*x + 16,11,x^2 + 2*x - 1,13,x^2 + 2*x - 31[] 232,4,2,x^3,3,x^3 - 2*x^2 - 5*x + 8,5,x^3 - 4*x^2 - 3*x + 10,7,x^3,11,x^3 - 2*x^2 - 29*x + 80,13,x^3 - 4*x^2 - 19*x + 2[] 233,1,2,x - 1,3,x + 2,5,x - 2,7,x - 4,11,x - 6,13,x - 6[] 233,2,2,x^7 + 2*x^6 - 6*x^5 - 10*x^4 + 10*x^3 + 8*x^2 - 7*x + 1,3,x^7 + 8*x^6 + 18*x^5 - 3*x^4 - 44*x^3 - 20*x^2 + 12*x + 1,5,x^7 + 3*x^6 - 15*x^5 - 40*x^4 + 41*x^3 + 79*x^2 - 29*x - 43,7,x^7 + 17*x^6 + 112*x^5 + 351*x^4 + 494*x^3 + 157*x^2 - 182*x - 41,11,x^7 - x^6 - 37*x^5 + 34*x^4 + 402*x^3 - 271*x^2 - 1242*x + 471,13,x^7 + 12*x^6 + 4*x^5 - 464*x^4 - 2100*x^3 - 2956*x^2 - 753*x + 687[] 233,3,2,x^11 + 2*x^10 - 16*x^9 - 30*x^8 + 91*x^7 + 158*x^6 - 213*x^5 - 349*x^4 + 152*x^3 + 290*x^2 + 41*x - 19,3,x^11 - 10*x^10 + 28*x^9 + 29*x^8 - 277*x^7 + 394*x^6 + 162*x^5 - 716*x^4 + 250*x^3 + 312*x^2 - 138*x - 29,5,x^11 + x^10 - 35*x^9 - 20*x^8 + 429*x^7 + 109*x^6 - 2119*x^5 - 265*x^4 + 3880*x^3 + 336*x^2 - 1280*x - 128,7,x^11 - 15*x^10 + 72*x^9 - 53*x^8 - 514*x^7 + 1169*x^6 + 434*x^5 - 3161*x^4 + 1712*x^3 + 1552*x^2 - 1056*x - 144,11,x^11 + 5*x^10 - 23*x^9 - 164*x^8 - 92*x^7 + 1161*x^6 + 3112*x^5 + 2905*x^4 + 272*x^3 - 1248*x^2 - 720*x - 108,13,x^11 - 4*x^10 - 50*x^9 + 188*x^8 + 557*x^7 - 2440*x^6 - 237*x^5 + 6067*x^4 - 766*x^3 - 4762*x^2 + 247*x + 687[] 234,1,2,x + 1,3,x,5,x + 2,7,x + 2,11,x + 4,13,x + 1[] 234,2,2,x + 1,3,x,5,x - 1,7,x - 1,11,x - 2,13,x + 1[] 234,3,2,x - 1,3,x,5,x - 2,7,x + 2,11,x - 4,13,x + 1[] 234,4,2,x - 1,3,x,5,x + 2,7,x - 4,11,x - 4,13,x - 1[] 234,5,2,x - 1,3,x,5,x - 3,7,x + 1,11,x + 6,13,x - 1[] Total time: 18.119 seconds, Total memory usage: 7.48MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 09:34:18 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [234..240] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 09:34:00 on modular [Seed = 719174418] ------------------------------------- 234,1,2,$.1 + 1,3,$.1,5,$.1 + 2,7,$.1 + 2,11,$.1 + 4,13,$.1 + 1[] 234,2,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 - 1,11,$.1 - 2,13,$.1 + 1[] 234,3,2,$.1 - 1,3,$.1,5,$.1 - 2,7,$.1 + 2,11,$.1 - 4,13,$.1 + 1[] 234,4,2,$.1 - 1,3,$.1,5,$.1 + 2,7,$.1 - 4,11,$.1 - 4,13,$.1 - 1[] 234,5,2,$.1 - 1,3,$.1,5,$.1 - 3,7,$.1 + 1,11,$.1 + 6,13,$.1 - 1[] 235,1,2,x + 1,3,x + 1,5,x + 1,7,x - 1,11,x - 3,13,x - 3[] 235,2,2,x - 2,3,x - 2,5,x + 1,7,x + 2,11,x,13,x - 3[] 235,3,2,x + 1,3,x + 1,5,x - 1,7,x - 1,11,x + 3,13,x + 3[] 235,4,2,x^5 + 4*x^4 - 12*x^2 - 4*x + 7,3,x^5 + 5*x^4 + 3*x^3 - 13*x^2 - 13*x + 1,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 - 17*x^3 - 83*x^2 + 61*x + 227,11,x^5 + x^4 - 46*x^3 - 72*x^2 + 368*x + 656,13,x^5 + 11*x^4 + 18*x^3 - 156*x^2 - 632*x - 656[] 235,5,2,x^7 - x^6 - 10*x^5 + 8*x^4 + 28*x^3 - 17*x^2 - 19*x + 2,3,x^7 - x^6 - 15*x^5 + 13*x^4 + 57*x^3 - 37*x^2 - 42*x - 8,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 23*x^5 - 53*x^4 + 91*x^3 + 29*x^2 - 66*x + 16,11,x^7 - x^6 - 46*x^5 + 40*x^4 + 512*x^3 - 80*x^2 - 1408*x - 256,13,x^7 - 2*x^6 - 35*x^5 + 36*x^4 + 128*x^3 - 96*x^2 - 96*x + 32[] 236,1,2,x,3,x - 1,5,x - 3,7,x + 1,11,x - 6,13,x + 4[] 236,2,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 2,13,x[] 236,3,2,x^3,3,x^3 - 9*x + 1,5,x^3 + 4*x^2 + x - 3,7,x^3 - 8*x^2 + 15*x + 3,11,x^3 - 2*x^2 - 16*x + 8,13,x^3 - 4*x^2 - 12*x + 24[] 237,1,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 6*x + 7,13,x^2 + 2*x - 7[] 237,2,2,x^4 + 3*x^3 - x^2 - 5*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 4*x^3 - x^2 - 14*x - 9,7,x^4 + 2*x^3 - 20*x^2 - 40*x - 16,11,x^4 + 8*x^3 + 11*x^2 - 42*x - 89,13,x^4 + 6*x^3 - 21*x^2 - 74*x + 141[] 237,3,2,x^7 - 2*x^6 - 11*x^5 + 22*x^4 + 30*x^3 - 65*x^2 - 2*x + 23,3,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,5,x^7 + 2*x^6 - 25*x^5 - 32*x^4 + 191*x^3 + 102*x^2 - 416*x + 32,7,x^7 - 4*x^6 - 23*x^5 + 98*x^4 + 12*x^3 - 264*x^2 + 48*x + 128,11,x^7 - 2*x^6 - 42*x^5 + 40*x^4 + 416*x^3 - 52*x^2 - 611*x + 116,13,x^7 - 6*x^6 - 16*x^5 + 194*x^4 - 528*x^3 + 616*x^2 - 315*x + 58[] 238,1,2,x + 1,3,x,5,x + 2,7,x + 1,11,x + 2,13,x[] 238,2,2,x + 1,3,x - 2,5,x - 4,7,x - 1,11,x + 4,13,x + 4[] 238,3,2,x - 1,3,x - 2,5,x,7,x + 1,11,x + 2,13,x + 2[] 238,4,2,x - 1,3,x + 2,5,x + 4,7,x - 1,11,x + 6,13,x + 2[] 238,5,2,x - 1,3,x,5,x - 2,7,x - 1,11,x,13,x + 2[] 238,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 2*x + 1,11,x^2 - 6*x + 4,13,x^2 - 4*x - 16[] 239,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + x^2 - 2*x - 1,13,x^3 + 7*x^2 + 14*x + 7[] 239,2,2,x^17 - 28*x^15 + x^14 + 319*x^13 - 17*x^12 - 1903*x^11 + 91*x^10 + 6377*x^9 - 125*x^8 - 11967*x^7 - 233*x^6 + 11733*x^5 + 503*x^4 - 5015*x^3 - 94*x^2 + 609*x + 49,3,x^17 - 3*x^16 - 35*x^15 + 110*x^14 + 468*x^13 - 1573*x^12 - 2977*x^11 + 11197*x^10 + 8880*x^9 - 42041*x^8 - 8213*x^7 + 80809*x^6 - 11957*x^5 - 70374*x^4 + 23710*x^3 + 20383*x^2 - 9684*x + 592,5,x^17 - 6*x^16 - 44*x^15 + 311*x^14 + 647*x^13 - 6439*x^12 - 1715*x^11 + 66664*x^10 - 47987*x^9 - 345487*x^8 + 500506*x^7 + 707930*x^6 - 1708498*x^5 + 168922*x^4 + 1466245*x^3 - 775724*x^2 - 64969*x + 43871,7,x^17 - 5*x^16 - 77*x^15 + 393*x^14 + 2276*x^13 - 12292*x^12 - 31088*x^11 + 193664*x^10 + 166432*x^9 - 1590464*x^8 + 251392*x^7 + 6211328*x^6 - 5164544*x^5 - 8086528*x^4 + 10784768*x^3 - 540672*x^2 - 1900544*x - 262144,11,x^17 + x^16 - 123*x^15 - 202*x^14 + 6056*x^13 + 13619*x^12 - 149697*x^11 - 427543*x^10 + 1893660*x^9 + 6787983*x^8 - 10803586*x^7 - 53477248*x^6 + 15048164*x^5 + 195019206*x^4 + 50388863*x^3 - 305552905*x^2 - 115295798*x + 151629817,13,x^17 - 15*x^16 - 30*x^15 + 1407*x^14 - 3250*x^13 - 47272*x^12 + 199728*x^11 + 647712*x^10 - 4205376*x^9 - 2052928*x^8 + 38764288*x^7 - 25163008*x^6 - 147311616*x^5 + 180070400*x^4 + 144123904*x^3 - 224333824*x^2 + 9224192*x + 11583488[] 240,1,2,x,3,x + 1,5,x + 1,7,x + 4,11,x,13,x + 6[] 240,2,2,x,3,x + 1,5,x - 1,7,x,11,x - 4,13,x - 6[] 240,3,2,x,3,x + 1,5,x + 1,7,x - 4,11,x,13,x - 2[] 240,4,2,x,3,x - 1,5,x - 1,7,x,11,x - 4,13,x + 2[] Total time: 18.079 seconds, Total memory usage: 7.16MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 09:40:29 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [240..248] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 09:40:08 on modular [Seed = 32936361] ------------------------------------- 240,1,2,$.1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 4,11,$.1,13,$.1 + 6[] 240,2,2,$.1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 - 4,13,$.1 - 6[] 240,3,2,$.1,3,$.1 + 1,5,$.1 + 1,7,$.1 - 4,11,$.1,13,$.1 - 2[] 240,4,2,$.1,3,$.1 - 1,5,$.1 - 1,7,$.1,11,$.1 - 4,13,$.1 + 2[] 241,1,2,x^7 + 4*x^6 - 14*x^4 - 10*x^3 + 6*x^2 + 3*x - 1,3,x^7 + 3*x^6 - 5*x^5 - 19*x^4 - 4*x^3 + 14*x^2 + 8*x + 1,5,x^7 + 8*x^6 + 12*x^5 - 50*x^4 - 165*x^3 - 93*x^2 + 137*x + 127,7,x^7 + 7*x^6 - 3*x^5 - 98*x^4 - 138*x^3 + 127*x^2 + 260*x + 61,11,x^7 + 18*x^6 + 117*x^5 + 283*x^4 - 137*x^3 - 1559*x^2 - 1281*x + 1069,13,x^7 + x^6 - 48*x^5 - 62*x^4 + 533*x^3 + 860*x^2 + 13*x - 1[] 241,2,2,x^12 - 3*x^11 - 14*x^10 + 44*x^9 + 65*x^8 - 219*x^7 - 123*x^6 + 444*x^5 + 105*x^4 - 328*x^3 - 45*x^2 + 18*x - 1,3,x^12 - x^11 - 25*x^10 + 25*x^9 + 224*x^8 - 210*x^7 - 888*x^6 + 725*x^5 + 1540*x^4 - 960*x^3 - 992*x^2 + 400*x + 64,5,x^12 - 6*x^11 - 14*x^10 + 134*x^9 - 68*x^8 - 797*x^7 + 1301*x^6 + 497*x^5 - 2193*x^4 + 1071*x^3 + 339*x^2 - 347*x + 62,7,x^12 - 3*x^11 - 33*x^10 + 96*x^9 + 245*x^8 - 854*x^7 + 263*x^6 + 855*x^5 - 588*x^4 - 131*x^3 + 200*x^2 - 53*x + 4,11,x^12 - 22*x^11 + 177*x^10 - 553*x^9 - 215*x^8 + 5545*x^7 - 12739*x^6 + 9811*x^5 + 3100*x^4 - 9672*x^3 + 5900*x^2 - 1460*x + 128,13,x^12 + 5*x^11 - 62*x^10 - 296*x^9 + 1425*x^8 + 6470*x^7 - 15049*x^6 - 64645*x^5 + 69802*x^4 + 288472*x^3 - 90512*x^2 - 441248*x - 52672[] 242,1,2,x + 1,3,x + 2,5,x + 3,7,x - 2,11,x,13,x - 5[] 242,2,2,x - 1,3,x + 2,5,x + 3,7,x + 2,11,x,13,x + 5[] 242,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 + 6*x + 6,11,x^2,13,x^2 + 6*x + 9[] 242,4,2,x^2 + 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 2*x - 4[] 242,5,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2,13,x^2 - 6*x + 9[] 242,6,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x + 4,11,x^2,13,x^2 + 2*x - 4[] 243,1,2,x,3,x,5,x,7,x + 4,11,x,13,x + 7[] 243,2,2,x,3,x,5,x,7,x - 5,11,x,13,x - 2[] 243,3,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2 + 2*x + 1,11,x^2 - 12,13,x^2 - 10*x + 25[] 243,4,2,x^2 - 6,3,x^2,5,x^2 - 6,7,x^2 - 4*x + 4,11,x^2 - 6,13,x^2 + 2*x + 1[] 243,5,2,x^3 + 3*x^2 - 3,3,x^3,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 + 3*x^2 - 6*x - 17,11,x^3 + 3*x^2 - 18*x - 3,13,x^3 + 3*x^2 - 6*x - 17[] 243,6,2,x^3 - 3*x^2 + 3,3,x^3,5,x^3 - 6*x^2 + 9*x - 3,7,x^3 + 3*x^2 - 6*x - 17,11,x^3 - 3*x^2 - 18*x + 3,13,x^3 + 3*x^2 - 6*x - 17[] 244,1,2,x,3,x,5,x + 3,7,x + 3,11,x + 1,13,x - 1[] 244,2,2,x^4,3,x^4 - 12*x^2 + 4*x + 16,5,x^4 - 5*x^3 + x^2 + 13*x + 2,7,x^4 + x^3 - 9*x^2 - 9*x - 2,11,x^4 + x^3 - 23*x^2 + 41*x - 18,13,x^4 - 5*x^3 - 3*x^2 + 17*x + 6[] 245,1,2,x + 2,3,x - 3,5,x + 1,7,x,11,x - 1,13,x - 3[] 245,2,2,x,3,x + 1,5,x - 1,7,x,11,x + 3,13,x + 5[] 245,3,2,x + 2,3,x + 3,5,x - 1,7,x,11,x - 1,13,x + 3[] 245,4,2,x^2 - 2,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2,11,x^2 + 6*x + 1,13,x^2 + 6*x + 7[] 245,5,2,x^2 + x - 4,3,x^2 - x - 4,5,x^2 + 2*x + 1,7,x^2,11,x^2 - x - 4,13,x^2 + 5*x + 2[] 245,6,2,x^2 - 2*x - 1,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2,11,x^2 - 4*x - 4,13,x^2 - 4*x - 4[] 245,7,2,x^2 - 2,3,x^2 - 2*x - 1,5,x^2 - 2*x + 1,7,x^2,11,x^2 + 6*x + 1,13,x^2 - 6*x + 7[] 245,8,2,x^2 - 2*x - 1,3,x^2 - 2*x - 1,5,x^2 - 2*x + 1,7,x^2,11,x^2 - 4*x - 4,13,x^2 + 4*x - 4[] 246,1,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x + 4,13,x + 4[] 246,2,2,x + 1,3,x + 1,5,x - 3,7,x + 2,11,x - 2,13,x - 1[] 246,3,2,x + 1,3,x - 1,5,x + 2,7,x - 2,11,x - 4,13,x - 4[] 246,4,2,x + 1,3,x - 1,5,x - 3,7,x - 2,11,x + 6,13,x + 1[] 246,5,2,x - 1,3,x + 1,5,x - 1,7,x - 2,11,x - 2,13,x + 7[] 246,6,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x + 1[] 246,7,2,x - 1,3,x - 1,5,x + 2,7,x - 4,11,x + 4,13,x - 2[] 247,1,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 4*x + 4,11,x^2 + 6*x + 4,13,x^2 - 2*x + 1[] 247,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 - 9*x - 9,13,x^3 - 3*x^2 + 3*x - 1[] 247,3,2,x^4 + 3*x^3 - 2*x^2 - 9*x - 4,3,x^4 + x^3 - 6*x^2 - 3*x + 8,5,x^4 + 8*x^3 + 19*x^2 + 13*x - 1,7,x^4 + 2*x^3 - 11*x^2 - 23*x - 1,11,x^4 + 5*x^3 - 9*x^2 - 66*x - 55,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 247,4,2,x^5 - 4*x^4 + 12*x^2 - 5*x - 5,3,x^5 - 3*x^4 - 4*x^3 + 11*x^2 + 6*x - 4,5,x^5 - 3*x^4 - 8*x^3 + 17*x^2 + 18*x + 4,7,x^5 + x^4 - 12*x^3 + x^2 + 12*x + 4,11,x^5 + 2*x^4 - 39*x^3 - 51*x^2 + 338*x + 428,13,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1[] 247,5,2,x^5 - 9*x^3 - x^2 + 19*x + 4,3,x^5 - 3*x^4 - 8*x^3 + 25*x^2 - 16,5,x^5 - 2*x^4 - 15*x^3 + 25*x^2 + 9*x - 2,7,x^5 - 4*x^4 - 15*x^3 + 47*x^2 + 59*x - 32,11,x^5 - 7*x^4 + 9*x^3 + 8*x^2 - 11*x - 4,13,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1[] 248,1,2,x,3,x + 2,5,x - 1,7,x + 3,11,x + 2,13,x + 2[] 248,2,2,x,3,x + 2,5,x - 2,7,x,11,x - 2,13,x - 4[] 248,3,2,x,3,x,5,x + 3,7,x + 3,11,x - 2,13,x + 4[] 248,4,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 3*x - 6,7,x^2 - x - 8,11,x^2 + 4*x + 4,13,x^2 - 2*x - 32[] 248,5,2,x^3,3,x^3 - 2*x^2 - 6*x + 8,5,x^3 + 3*x^2 - 4*x - 4,7,x^3 - 5*x^2 - 8*x + 44,11,x^3 - 8*x^2 + 6*x + 44,13,x^3 - 2*x^2 - 14*x + 32[] Total time: 20.190 seconds, Total memory usage: 7.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 09:46:25 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [248..256] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 09:46:06 on modular [Seed = 283614814] ------------------------------------- 248,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 3,11,$.1 + 2,13,$.1 + 2[] 248,2,2,$.1,3,$.1 + 2,5,$.1 - 2,7,$.1,11,$.1 - 2,13,$.1 - 4[] 248,3,2,$.1,3,$.1,5,$.1 + 3,7,$.1 + 3,11,$.1 - 2,13,$.1 + 4[] 248,4,2,$.1^2,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - 3*$.1 - 6,7,$.1^2 - $.1 - 8,11,$.1^2 + 4*$.1 + 4,13,$.1^2 - 2*$.1 - 32[] 248,5,2,$.1^3,3,$.1^3 - 2*$.1^2 - 6*$.1 + 8,5,$.1^3 + 3*$.1^2 - 4*$.1 - 4,7,$.1^3 - 5*$.1^2 - 8*$.1 + 44,11,$.1^3 - 8*$.1^2 + 6*$.1 + 44,13,$.1^3 - 2*$.1^2 - 14*$.1 + 32[] 249,1,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 3,13,x - 2[] 249,2,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 3,13,x + 6[] 249,3,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 6*x + 7,7,x^2 + 4*x + 4,11,x^2 + 6*x + 1,13,x^2[] 249,4,2,x^4 - 2*x^3 - 4*x^2 + 8*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 6*x^3 + 8*x^2 - 1,7,x^4 - 8*x^2 - 4*x + 4,11,x^4 - 4*x^3 - 14*x^2 + 32*x + 37,13,x^4 + 6*x^3 + 4*x^2 - 24*x - 28[] 249,5,2,x^5 + 3*x^4 - 4*x^3 - 14*x^2 - 3*x + 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 2*x^4 - 12*x^3 - 10*x^2 + 43*x - 22,7,x^5 - 8*x^4 + 12*x^3 + 36*x^2 - 92*x + 32,11,x^5 - 4*x^4 - 14*x^3 + 4*x^2 + 13*x - 4,13,x^5 - 4*x^4 - 24*x^3 + 144*x^2 - 220*x + 104[] 250,1,2,x^2 + 2*x + 1,3,x^2 + 3*x + 1,5,x^2,7,x^2 + x - 11,11,x^2 + 6*x + 4,13,x^2 - 2*x - 4[] 250,2,2,x^2 + 2*x + 1,3,x^2 - 2*x - 4,5,x^2,7,x^2 + x - 1,11,x^2 - 9*x + 19,13,x^2 + 3*x + 1[] 250,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 4,5,x^2,7,x^2 - x - 1,11,x^2 - 9*x + 19,13,x^2 - 3*x + 1[] 250,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2,7,x^2 - x - 11,11,x^2 + 6*x + 4,13,x^2 + 2*x - 4[] 251,1,2,x^4 + 2*x^3 - x^2 - 2*x + 1,3,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,5,x^4 + 3*x^3 - 2*x^2 - 2*x + 1,7,x^4 + 3*x^3 - 5*x^2 - 19*x - 11,11,x^4 + 3*x^3 - 4*x - 1,13,x^4 + 12*x^3 + 48*x^2 + 77*x + 41[] 251,2,2,x^17 - 2*x^16 - 28*x^15 + 54*x^14 + 317*x^13 - 582*x^12 - 1867*x^11 + 3178*x^10 + 6186*x^9 - 9216*x^8 - 11921*x^7 + 13680*x^6 + 13752*x^5 - 9400*x^4 - 8800*x^3 + 1920*x^2 + 2240*x + 256,3,x^17 - 38*x^15 + 5*x^14 + 582*x^13 - 142*x^12 - 4602*x^11 + 1445*x^10 + 20039*x^9 - 6280*x^8 - 48174*x^7 + 10424*x^6 + 63091*x^5 - 3260*x^4 - 41362*x^3 - 5377*x^2 + 10587*x + 3164,5,x^17 - 3*x^16 - 54*x^15 + 168*x^14 + 1118*x^13 - 3641*x^12 - 11152*x^11 + 38721*x^10 + 56108*x^9 - 215683*x^8 - 141507*x^7 + 649211*x^6 + 155977*x^5 - 1041793*x^4 - 22991*x^3 + 813550*x^2 - 51713*x - 228857,7,x^17 - 3*x^16 - 71*x^15 + 203*x^14 + 2030*x^13 - 5579*x^12 - 29805*x^11 + 80756*x^10 + 235362*x^9 - 668242*x^8 - 922654*x^7 + 3176896*x^6 + 1056610*x^5 - 7921027*x^4 + 3243764*x^3 + 7315324*x^2 - 7772692*x + 2209789,11,x^17 + x^16 - 122*x^15 - 152*x^14 + 5977*x^13 + 9162*x^12 - 151560*x^11 - 278496*x^10 + 2100848*x^9 + 4542848*x^8 - 15007296*x^7 - 38411776*x^6 + 41462784*x^5 + 139814400*x^4 + 18051072*x^3 - 84443136*x^2 - 11018240*x + 10657792,13,x^17 - 22*x^16 + 106*x^15 + 985*x^14 - 11180*x^13 + 18658*x^12 + 166344*x^11 - 636123*x^10 - 596895*x^9 + 5242340*x^8 - 1749194*x^7 - 16832410*x^6 + 11584495*x^5 + 21090650*x^4 - 16505080*x^3 - 6409715*x^2 + 5938307*x - 504874[] 252,1,2,x,3,x,5,x + 4,7,x + 1,11,x + 2,13,x + 6[] 252,2,2,x,3,x,5,x,7,x - 1,11,x - 6,13,x - 2[] 253,1,2,x^3 - 3*x^2 + 3,3,x^3 - 3*x^2 + 3,5,x^3 - 3*x^2 + 3,7,x^3 - 3*x^2 + 3,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 - 6*x - 17[] 253,2,2,x^3 + x^2 - 4*x + 1,3,x^3 + 5*x^2 + 4*x - 5,5,x^3 + 5*x^2 + 4*x - 5,7,x^3 + 3*x^2 - 10*x + 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + x^2 - 4*x + 1[] 253,3,2,x^5 + 4*x^4 - 14*x^2 - 13*x - 1,3,x^5 + 5*x^4 + 3*x^3 - 10*x^2 - 4*x + 1,5,x^5 + 3*x^4 - 14*x^3 - 43*x^2 - 12*x + 16,7,x^5 + 3*x^4 - 20*x^3 - 71*x^2 - 6*x + 92,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 + 15*x^4 + 83*x^3 + 208*x^2 + 232*x + 89[] 253,4,2,x^6 - 3*x^5 - 4*x^4 + 16*x^3 - 3*x^2 - 10*x + 1,3,x^6 - 7*x^5 + 11*x^4 + 18*x^3 - 56*x^2 + 33*x - 4,5,x^6 - 3*x^5 - 12*x^4 + 25*x^3 + 38*x^2 - 40*x - 32,7,x^6 + x^5 - 18*x^4 + 7*x^3 + 70*x^2 - 92*x + 32,11,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,13,x^6 + 3*x^5 - 33*x^4 - 94*x^3 + 226*x^2 + 783*x + 502[] 254,1,2,x + 1,3,x,5,x + 1,7,x + 3,11,x - 1,13,x + 2[] 254,2,2,x - 1,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[] 254,3,2,x - 1,3,x + 2,5,x,7,x - 4,11,x,13,x - 6[] 254,4,2,x - 1,3,x + 2,5,x + 3,7,x + 1,11,x + 3,13,x + 4[] 254,5,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 + x - 4,7,x^2 - x - 4,11,x^2 + 7*x + 8,13,x^2 + 2*x - 16[] 254,6,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + 2*x^4 - 10*x^3 - 16*x^2 + 10*x + 16,5,x^5 + x^4 - 20*x^3 - 18*x^2 + 54*x + 54,7,x^5 - 3*x^4 - 20*x^3 + 40*x^2 + 96*x - 32,11,x^5 - x^4 - 44*x^3 + 72*x^2 + 480*x - 1056,13,x^5 - 10*x^4 + 40*x^3 - 80*x^2 + 80*x - 32[] 255,1,2,x^2 - x - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 13,11,x^2 - 10*x + 25,13,x^2 + 6*x - 4[] 255,2,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 5,11,x^2 - 2*x - 19,13,x^2 - 6*x + 4[] 255,3,2,x^3 - 4*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 4*x^2 - x + 8,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 - 4*x^2 - 16*x + 56[] 255,4,2,x^4 - x^3 - 8*x^2 + 7*x + 9,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 4*x^3 - 17*x^2 + 80*x - 64,11,x^4 - 2*x^3 - 31*x^2 + 112*x - 96,13,x^4 + 2*x^3 - 48*x^2 - 120*x + 208[] 256,1,2,x,3,x,5,x + 4,7,x,11,x,13,x + 4[] 256,2,2,x,3,x + 2,5,x,7,x,11,x + 6,13,x[] 256,3,2,x,3,x,5,x - 4,7,x,11,x,13,x - 4[] 256,4,2,x,3,x - 2,5,x,7,x,11,x - 6,13,x[] 256,5,2,x^2,3,x^2 - 8,5,x^2,7,x^2,11,x^2 - 8,13,x^2[] Total time: 19.180 seconds, Total memory usage: 8.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 09:54:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [256..264] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 09:53:43 on modular [Seed = 3793055605] ------------------------------------- 256,1,2,$.1,3,$.1,5,$.1 + 4,7,$.1,11,$.1,13,$.1 + 4[] 256,2,2,$.1,3,$.1 + 2,5,$.1,7,$.1,11,$.1 + 6,13,$.1[] 256,3,2,$.1,3,$.1,5,$.1 - 4,7,$.1,11,$.1,13,$.1 - 4[] 256,4,2,$.1,3,$.1 - 2,5,$.1,7,$.1,11,$.1 - 6,13,$.1[] 256,5,2,$.1^2,3,$.1^2 - 8,5,$.1^2,7,$.1^2,11,$.1^2 - 8,13,$.1^2[] 257,1,2,x^7 + 3*x^6 - 3*x^5 - 11*x^4 + 3*x^3 + 10*x^2 - x - 1,3,x^7 + 5*x^6 + x^5 - 22*x^4 - 17*x^3 + 15*x^2 + 8*x - 4,5,x^7 + x^6 - 15*x^5 - 5*x^4 + 52*x^3 - 35*x^2 - 2*x + 4,7,x^7 + 18*x^6 + 125*x^5 + 410*x^4 + 586*x^3 + 91*x^2 - 496*x - 256,11,x^7 + 2*x^6 - 35*x^5 - 53*x^4 + 264*x^3 + 110*x^2 - 630*x + 337,13,x^7 + 10*x^6 - 287*x^4 - 976*x^3 - 752*x^2 + 489*x + 491[] 257,2,2,x^14 - 2*x^13 - 21*x^12 + 42*x^11 + 163*x^10 - 327*x^9 - 568*x^8 + 1153*x^7 + 830*x^6 - 1755*x^5 - 318*x^4 + 825*x^3 + 10*x^2 - 96*x - 1,3,x^14 - 3*x^13 - 23*x^12 + 74*x^11 + 173*x^10 - 627*x^9 - 500*x^8 + 2254*x^7 + 726*x^6 - 3988*x^5 - 858*x^4 + 3536*x^3 + 960*x^2 - 1280*x - 512,5,x^14 + x^13 - 45*x^12 - 21*x^11 + 740*x^10 - 41*x^9 - 5360*x^8 + 2796*x^7 + 16632*x^6 - 14736*x^5 - 18208*x^4 + 23232*x^3 - 384*x^2 - 5120*x + 512,7,x^14 - 24*x^13 + 227*x^12 - 988*x^11 + 1160*x^10 + 6413*x^9 - 24968*x^8 + 15746*x^7 + 66718*x^6 - 119942*x^5 + 11018*x^4 + 91024*x^3 - 28632*x^2 - 20096*x + 256,11,x^14 - 2*x^13 - 79*x^12 + 131*x^11 + 2172*x^10 - 2382*x^9 - 27190*x^8 + 14565*x^7 + 162892*x^6 - 16416*x^5 - 440000*x^4 - 68608*x^3 + 440448*x^2 + 66560*x - 145408,13,x^14 - 12*x^13 - 4*x^12 + 513*x^11 - 1358*x^10 - 5248*x^9 + 22253*x^8 + 12589*x^7 - 129450*x^6 + 57348*x^5 + 309368*x^4 - 309776*x^3 - 210288*x^2 + 382080*x - 128192[] 258,1,2,x + 1,3,x + 1,5,x - 1,7,x + 5,11,x - 1,13,x + 3[] 258,2,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x,13,x - 2[] 258,3,2,x + 1,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x + 3[] 258,4,2,x - 1,3,x + 1,5,x + 2,7,x - 4,11,x - 4,13,x - 6[] 258,5,2,x - 1,3,x + 1,5,x - 3,7,x + 1,11,x + 1,13,x - 1[] 258,6,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x - 5,13,x + 7[] 258,7,2,x - 1,3,x - 1,5,x - 2,7,x + 2,11,x + 4,13,x - 2[] 259,1,2,x - 1,3,x,5,x - 4,7,x - 1,11,x - 4,13,x - 4[] 259,2,2,x^2,3,x^2 - 8,5,x^2 - 6*x + 7,7,x^2 + 2*x + 1,11,x^2 + 6*x + 1,13,x^2 - 2*x - 17[] 259,3,2,x^2 - x - 4,3,x^2,5,x^2 - x - 4,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 - x - 4[] 259,4,2,x^3 - x^2 - 2*x + 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 6*x^2 + 5*x - 13,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + x^2 - 2*x - 1,13,x^3 - x^2 - 16*x - 13[] 259,5,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 9*x^2 + 18*x - 9,13,x^3 + 3*x^2 - 24*x - 53[] 259,6,2,x^4 - 9*x^2 + x + 17,3,x^4 - 2*x^3 - 5*x^2 + 7*x + 4,5,x^4 - 6*x^3 + 7*x^2 + 5*x - 2,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 - 3*x^3 - 22*x^2 + 99*x - 100,13,x^4 - 5*x^3 - 16*x^2 + 47*x + 62[] 259,7,2,x^4 - x^3 - 6*x^2 + 5*x + 4,3,x^4 - 15*x^2 + 3*x + 48,5,x^4 - x^3 - 9*x^2 + 8*x + 13,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 10*x^3 + 15*x^2 + 77*x - 137,13,x^4 + 8*x^3 + 9*x^2 - 7*x + 1[] 260,1,2,x,3,x - 2,5,x + 1,7,x - 2,11,x - 4,13,x + 1[] 260,2,2,x^3,3,x^3 - 2*x^2 - 8*x + 12,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 2*x^2 - 20*x - 24,11,x^3 - 24*x + 36,13,x^3 - 3*x^2 + 3*x - 1[] 261,1,2,x^2 + x - 1,3,x^2,5,x^2 + 4*x + 4,7,x^2 - 5,11,x^2 + 8*x + 11,13,x^2 + 2*x - 19[] 261,2,2,x^2 - x - 1,3,x^2,5,x^2 - 4*x + 4,7,x^2 - 5,11,x^2 - 8*x + 11,13,x^2 + 2*x - 19[] 261,3,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 + 2*x - 1,13,x^2 + 2*x - 7[] 261,4,2,x^2 + x - 1,3,x^2,5,x^2 + 2*x - 4,7,x^2 + 4*x - 1,11,x^2 + 4*x - 1,13,x^2 + 2*x - 19[] 261,5,2,x^3 + 2*x^2 - 4*x - 7,3,x^3,5,x^3 - 16*x - 8,7,x^3 - 4*x^2 - x + 8,11,x^3 - 8*x^2 + 15*x - 4,13,x^3 - 4*x^2 - 7*x + 26[] 262,1,2,x + 1,3,x,5,x,7,x + 5,11,x - 2,13,x + 2[] 262,2,2,x - 1,3,x + 2,5,x + 2,7,x + 3,11,x + 6,13,x - 4[] 262,3,2,x^2 + 2*x + 1,3,x^2 + x - 3,5,x^2 + 5*x + 3,7,x^2 - 3*x - 1,11,x^2 + 7*x + 9,13,x^2 + 5*x + 3[] 262,4,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 - 4*x + 2,7,x^2 - 2*x - 1,11,x^2 - 4*x - 4,13,x^2 - 18[] 262,5,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 4*x + 1,11,x^2 - 12,13,x^2 + 6*x + 6[] 262,6,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 + x - 1,7,x^2 + x - 1,11,x^2 - 5*x + 5,13,x^2 - 3*x - 9[] 263,1,2,x^5 + 2*x^4 - 3*x^3 - 6*x^2 + 1,3,x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 7*x + 1,5,x^5 + 3*x^4 - x^3 - 7*x^2 - 2*x + 1,7,x^5 + 5*x^4 + 4*x^3 - 5*x^2 - 5*x - 1,11,x^5 - 2*x^4 - 22*x^3 - 13*x^2 + 24*x + 17,13,x^5 + 15*x^4 + 79*x^3 + 167*x^2 + 96*x - 53[] 263,2,2,x^17 - x^16 - 26*x^15 + 24*x^14 + 274*x^13 - 225*x^12 - 1505*x^11 + 1041*x^10 + 4613*x^9 - 2467*x^8 - 7815*x^7 + 2761*x^6 + 6709*x^5 - 974*x^4 - 2284*x^3 - 239*x^2 + 135*x + 19,3,x^17 - 7*x^16 - 14*x^15 + 191*x^14 - 93*x^13 - 1956*x^12 + 2598*x^11 + 9587*x^10 - 17149*x^9 - 23845*x^8 + 50477*x^7 + 30119*x^6 - 69326*x^5 - 20491*x^4 + 39160*x^3 + 7677*x^2 - 4259*x - 119,5,x^17 - 3*x^16 - 61*x^15 + 185*x^14 + 1458*x^13 - 4495*x^12 - 17168*x^11 + 54320*x^10 + 102152*x^9 - 337584*x^8 - 280480*x^7 + 1002880*x^6 + 291584*x^5 - 1189120*x^4 - 151040*x^3 + 473088*x^2 + 65536*x - 4096,7,x^17 - 7*x^16 - 56*x^15 + 477*x^14 + 905*x^13 - 12145*x^12 + 584*x^11 + 144260*x^10 - 136136*x^9 - 814096*x^8 + 1150112*x^7 + 1950144*x^6 - 3208448*x^5 - 1505280*x^4 + 2396160*x^3 + 698368*x^2 - 483328*x - 151552,11,x^17 + 2*x^16 - 109*x^15 - 179*x^14 + 4639*x^13 + 5830*x^12 - 98806*x^11 - 85828*x^10 + 1119162*x^9 + 563445*x^8 - 6608205*x^7 - 1222544*x^6 + 18228623*x^5 - 405279*x^4 - 17443186*x^3 - 1627778*x^2 + 3900240*x + 800389,13,x^17 - 27*x^16 + 232*x^15 + 48*x^14 - 12494*x^13 + 65067*x^12 + 39521*x^11 - 1344086*x^10 + 3360234*x^9 + 5503401*x^8 - 36994803*x^7 + 35699891*x^6 + 94564718*x^5 - 233875954*x^4 + 105306969*x^3 + 161866750*x^2 - 192628894*x + 58427707[] 264,1,2,x,3,x + 1,5,x - 2,7,x,11,x - 1,13,x - 2[] 264,2,2,x,3,x - 1,5,x + 2,7,x - 4,11,x + 1,13,x - 6[] 264,3,2,x,3,x - 1,5,x - 4,7,x + 2,11,x + 1,13,x[] 264,4,2,x,3,x - 1,5,x,7,x - 2,11,x - 1,13,x[] Total time: 19.250 seconds, Total memory usage: 6.26MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:02:44 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [264..272] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:02:22 on modular [Seed = 3409723477] ------------------------------------- 264,1,2,$.1,3,$.1 + 1,5,$.1 - 2,7,$.1,11,$.1 - 1,13,$.1 - 2[] 264,2,2,$.1,3,$.1 - 1,5,$.1 + 2,7,$.1 - 4,11,$.1 + 1,13,$.1 - 6[] 264,3,2,$.1,3,$.1 - 1,5,$.1 - 4,7,$.1 + 2,11,$.1 + 1,13,$.1[] 264,4,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 1,13,$.1[] 265,1,2,x + 1,3,x,5,x + 1,7,x - 2,11,x,13,x + 6[] 265,2,2,x^2 + x - 5,3,x^2 + x - 5,5,x^2 + 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + 10*x + 25,13,x^2 - 21[] 265,3,2,x^2 + 2*x - 1,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2 + 4*x - 4,11,x^2 - 4*x + 4,13,x^2 - 2*x - 7[] 265,4,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 + 2*x + 1,7,x^2 - 2*x - 2,11,x^2 - 4*x - 8,13,x^2 - 12[] 265,5,2,x^2 - 3*x + 1,3,x^2 + 3*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x - 1,11,x^2 - 6*x + 9,13,x^2 - 2*x + 1[] 265,6,2,x^2 + x - 3,3,x^2 - x - 3,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 + 4*x - 9[] 265,7,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 + 10*x + 25,13,x^2 - 2*x - 19[] 265,8,2,x^4 - 4*x^3 + 2*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 4*x + 4,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 4*x^3 - 6*x^2 + 24*x + 8,11,x^4 - 4*x^3 - 20*x^2 + 64*x + 32,13,x^4 + 2*x^3 - 27*x^2 - 92*x - 68[] 266,1,2,x^2 + 2*x + 1,3,x^2 - x - 7,5,x^2 + x - 7,7,x^2 + 2*x + 1,11,x^2 - 3*x - 5,13,x^2 + 2*x - 28[] 266,2,2,x^2 + 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - x - 11,7,x^2 - 2*x + 1,11,x^2 - 7*x + 11,13,x^2 - 6*x + 4[] 266,3,2,x^2 - 2*x + 1,3,x^2 - x - 3,5,x^2 - x - 3,7,x^2 - 2*x + 1,11,x^2 + 5*x + 3,13,x^2 - 6*x - 4[] 266,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + x^2 - 7*x + 4,5,x^3 - 5*x^2 + 3*x + 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 3*x^2 - 25*x + 76,13,x^3 + 4*x^2 - 16*x - 8[] 267,1,2,x,3,x + 1,5,x - 4,7,x + 2,11,x - 2,13,x - 6[] 267,2,2,x,3,x - 1,5,x,7,x - 2,11,x - 6,13,x - 2[] 267,3,2,x^3 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 + 6*x^2 + 9*x + 1,11,x^3 - 6*x^2 - 9*x + 71,13,x^3 + 15*x^2 + 72*x + 109[] 267,4,2,x^3 - 2*x^2 - 3*x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 5*x^2 + 4*x + 5,7,x^3 + 4*x^2 + x - 1,11,x^3 + 4*x^2 + x - 1,13,x^3 - 3*x^2 - 10*x - 1[] 267,5,2,x^3 + 4*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 7*x^2 + 14*x + 7,7,x^3 + 4*x^2 - 11*x - 43,11,x^3 + 8*x^2 + 19*x + 13,13,x^3 + 11*x^2 + 38*x + 41[] 267,6,2,x^4 - x^3 - 7*x^2 + 6*x + 7,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 3*x^3 - 6*x^2 + 19*x - 2,7,x^4 - 6*x^3 + x^2 + 19*x - 16,11,x^4 + 6*x^3 - 3*x^2 - 7*x + 4,13,x^4 - 9*x^3 + 10*x^2 + 91*x - 202[] 268,1,2,x,3,x - 2,5,x - 2,7,x - 2,11,x + 4,13,x + 6[] 268,2,2,x^2,3,x^2 - x - 5,5,x^2 + 2*x + 1,7,x^2 - x - 5,11,x^2 - 10*x + 25,13,x^2 - 3*x - 3[] 268,3,2,x^2,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 5*x + 5,11,x^2 + 4*x - 1,13,x^2 + 3*x - 9[] 269,1,2,x,3,x,5,x - 1,7,x + 4,11,x + 3,13,x - 2[] 269,2,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 5*x + 3,3,x^5 + 5*x^4 + 3*x^3 - 15*x^2 - 16*x + 3,5,x^5 + 4*x^4 - x^3 - 16*x^2 - 14*x - 1,7,x^5 + 5*x^4 - 4*x^3 - 25*x^2 - x + 19,11,x^5 + 9*x^4 + 23*x^3 - 59*x - 45,13,x^5 + 5*x^4 - 35*x^3 - 205*x^2 - 192*x + 61[] 269,3,2,x^16 - x^15 - 28*x^14 + 27*x^13 + 314*x^12 - 283*x^11 - 1803*x^10 + 1435*x^9 + 5637*x^8 - 3547*x^7 - 9470*x^6 + 3701*x^5 + 7860*x^4 - 1001*x^3 - 2363*x^2 - 43*x + 172,3,x^16 - 5*x^15 - 22*x^14 + 138*x^13 + 139*x^12 - 1450*x^11 + 41*x^10 + 7440*x^9 - 3354*x^8 - 20186*x^7 + 12462*x^6 + 28989*x^5 - 18771*x^4 - 19974*x^3 + 12032*x^2 + 4633*x - 2654,5,x^16 + x^15 - 46*x^14 - 32*x^13 + 861*x^12 + 316*x^11 - 8506*x^10 - 222*x^9 + 47729*x^8 - 14650*x^7 - 149888*x^6 + 92967*x^5 + 233992*x^4 - 219530*x^3 - 113145*x^2 + 177883*x - 48947,7,x^16 - 11*x^15 - 9*x^14 + 492*x^13 - 1053*x^12 - 7914*x^11 + 30314*x^10 + 46584*x^9 - 336651*x^8 + 83088*x^7 + 1695664*x^6 - 2025023*x^5 - 3085559*x^4 + 6658712*x^3 - 1044425*x^2 - 3548057*x + 1239286,11,x^16 - 16*x^15 + 30*x^14 + 693*x^13 - 3163*x^12 - 8622*x^11 + 61745*x^10 + 35024*x^9 - 506404*x^8 - 53136*x^7 + 1984496*x^6 + 581824*x^5 - 3521152*x^4 - 2514944*x^3 + 1231616*x^2 + 1575936*x + 369664,13,x^16 + x^15 - 118*x^14 + 40*x^13 + 5257*x^12 - 7276*x^11 - 105245*x^10 + 222524*x^9 + 949298*x^8 - 2595172*x^7 - 3434680*x^6 + 13153571*x^5 + 1070523*x^4 - 26094100*x^3 + 13603562*x^2 + 10842305*x - 7490278[] 270,1,2,x + 1,3,x,5,x - 1,7,x - 2,11,x + 3,13,x - 5[] 270,2,2,x + 1,3,x,5,x + 1,7,x - 2,11,x - 3,13,x + 1[] 270,3,2,x - 1,3,x,5,x + 1,7,x - 2,11,x - 3,13,x - 5[] 270,4,2,x - 1,3,x,5,x - 1,7,x - 2,11,x + 3,13,x + 1[] 271,1,2,x^6 + 4*x^5 + x^4 - 9*x^3 - 4*x^2 + 5*x + 1,3,x^6 + x^5 - 5*x^4 - 4*x^3 + 5*x^2 + 2*x - 1,5,x^6 + 8*x^5 + 20*x^4 + 16*x^3 - 2*x^2 - 5*x - 1,7,x^6 + 3*x^5 - 13*x^4 - 20*x^3 + 58*x^2 - 37*x + 7,11,x^6 + 11*x^5 + 34*x^4 + 5*x^3 - 137*x^2 - 214*x - 97,13,x^6 + 2*x^5 - 18*x^4 - 9*x^3 + 44*x^2 + 40*x + 7[] 271,2,2,x^16 - 5*x^15 - 12*x^14 + 91*x^13 + 11*x^12 - 620*x^11 + 381*x^10 + 1953*x^9 - 1863*x^8 - 2853*x^7 + 3137*x^6 + 1830*x^5 - 1758*x^4 - 831*x^3 + 308*x^2 + 204*x + 27,3,x^16 - x^15 - 41*x^14 + 44*x^13 + 663*x^12 - 746*x^11 - 5343*x^10 + 6132*x^9 + 22208*x^8 - 25016*x^7 - 43952*x^6 + 44896*x^5 + 33280*x^4 - 22016*x^3 - 13056*x^2 + 1536*x + 1024,5,x^16 - 10*x^15 + x^14 + 274*x^13 - 606*x^12 - 2545*x^11 + 8910*x^10 + 7903*x^9 - 50940*x^8 + 8944*x^7 + 123487*x^6 - 78423*x^5 - 108147*x^4 + 82115*x^3 + 37001*x^2 - 22695*x - 4725,7,x^16 + 3*x^15 - 58*x^14 - 187*x^13 + 1263*x^12 + 4399*x^11 - 13026*x^10 - 50956*x^9 + 62459*x^8 + 310197*x^7 - 82378*x^6 - 956996*x^5 - 315162*x^4 + 1239685*x^3 + 899123*x^2 - 257399*x - 263719,11,x^16 - 17*x^15 + 49*x^14 + 642*x^13 - 4059*x^12 - 4187*x^11 + 78189*x^10 - 77707*x^9 - 587886*x^8 + 995074*x^7 + 2122184*x^6 - 3966954*x^5 - 4261574*x^4 + 5963025*x^3 + 4848166*x^2 - 1967190*x - 1319031,13,x^16 + 4*x^15 - 122*x^14 - 493*x^13 + 5358*x^12 + 21292*x^11 - 104611*x^10 - 394880*x^9 + 887112*x^8 + 2958088*x^7 - 2769360*x^6 - 6121088*x^5 + 4984960*x^4 + 1402624*x^3 - 961792*x^2 - 98304*x + 44032[] 272,1,2,x,3,x + 2,5,x,7,x,11,x + 2,13,x + 6[] 272,2,2,x,3,x - 2,5,x + 2,7,x - 2,11,x - 6,13,x - 2[] 272,3,2,x,3,x - 2,5,x,7,x - 4,11,x + 6,13,x - 2[] 272,4,2,x,3,x,5,x + 2,7,x + 4,11,x,13,x + 2[] 272,5,2,x^2,3,x^2 - 2*x - 4,5,x^2 - 4*x + 4,7,x^2 + 2*x - 4,11,x^2 + 2*x - 4,13,x^2 - 20[] 272,6,2,x^2,3,x^2 + 2*x - 2,5,x^2 - 12,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2 - 4*x - 8[] Total time: 21.510 seconds, Total memory usage: 6.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:11:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [272..280] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:10:37 on modular [Seed = 2740202030] ------------------------------------- 272,1,2,$.1,3,$.1 + 2,5,$.1,7,$.1,11,$.1 + 2,13,$.1 + 6[] 272,2,2,$.1,3,$.1 - 2,5,$.1 + 2,7,$.1 - 2,11,$.1 - 6,13,$.1 - 2[] 272,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 4,11,$.1 + 6,13,$.1 - 2[] 272,4,2,$.1,3,$.1,5,$.1 + 2,7,$.1 + 4,11,$.1,13,$.1 + 2[] 272,5,2,$.1^2,3,$.1^2 - 2*$.1 - 4,5,$.1^2 - 4*$.1 + 4,7,$.1^2 + 2*$.1 - 4,11,$.1^2 + 2*$.1 - 4,13,$.1^2 - 20[] 272,6,2,$.1^2,3,$.1^2 + 2*$.1 - 2,5,$.1^2 - 12,7,$.1^2 - 2*$.1 - 2,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 4*$.1 - 8[] 273,1,2,x + 2,3,x + 1,5,x + 1,7,x - 1,11,x + 2,13,x - 1[] 273,2,2,x - 2,3,x - 1,5,x - 1,7,x + 1,11,x + 2,13,x + 1[] 273,3,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 4*x + 4,13,x^2 + 2*x + 1[] 273,4,2,x^3 + 2*x^2 - 3*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 4*x - 8,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 2*x^2 - 28*x + 8,13,x^3 + 3*x^2 + 3*x + 1[] 273,5,2,x^4 - x^3 - 7*x^2 + 5*x + 6,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 3*x^3 - 10*x^2 - 20*x + 24,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 + 2*x^3 - 24*x^2 - 32*x + 96,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 274,1,2,x + 1,3,x,5,x,7,x + 4,11,x + 4,13,x - 4[] 274,2,2,x + 1,3,x,5,x + 3,7,x - 2,11,x + 1,13,x + 2[] 274,3,2,x - 1,3,x + 2,5,x + 3,7,x,11,x + 3,13,x + 6[] 274,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 5*x^2 + 5*x + 1,7,x^3 - 2*x^2 - 8*x - 4,11,x^3 - 5*x^2 - 5*x + 17,13,x^3 + 8*x^2 + 12*x + 4[] 274,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 2*x^4 - 10*x^3 + 20*x^2 - 8,5,x^5 - 5*x^4 - x^3 + 19*x^2 - 16,7,x^5 + 4*x^4 - 8*x^3 - 28*x^2 + 16*x + 32,11,x^5 + x^4 - 21*x^3 - 21*x^2 + 72*x - 16,13,x^5 - 4*x^4 - 20*x^3 + 76*x^2 + 64*x - 256[] 275,1,2,x + 1,3,x,5,x,7,x,11,x + 1,13,x + 2[] 275,2,2,x - 2,3,x - 1,5,x,7,x - 2,11,x - 1,13,x + 4[] 275,3,2,x^2 + x - 3,3,x^2 + x - 3,5,x^2,7,x^2 + 5*x + 3,11,x^2 + 2*x + 1,13,x^2 + 10*x + 25[] 275,4,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2,7,x^2 - x - 11,11,x^2 - 2*x + 1,13,x^2 - 8*x + 11[] 275,5,2,x^2 + 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 - 4*x + 4,11,x^2 - 2*x + 1,13,x^2 - 8*x + 8[] 275,6,2,x^2 - x - 3,3,x^2 - x - 3,5,x^2,7,x^2 - 5*x + 3,11,x^2 + 2*x + 1,13,x^2 - 10*x + 25[] 275,7,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2,7,x^2 + x - 11,11,x^2 - 2*x + 1,13,x^2 + 8*x + 11[] 275,8,2,x^4 - 7*x^2 + 4,3,x^4 - 7*x^2 + 4,5,x^4,7,x^4 - 24*x^2 + 144,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4[] 276,1,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 10,7,x^2 - 4*x - 6,11,x^2,13,x^2 - 8*x + 16[] 276,2,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2 - 2,11,x^2 - 32,13,x^2 - 32[] 277,1,2,x - 1,3,x + 2,5,x - 2,7,x + 4,11,x - 1,13,x + 5[] 277,2,2,x^3 + x^2 - 3*x - 1,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 4*x^2 + 4,7,x^3 - 4*x^2 - 4*x + 20,11,x^3 - 11*x^2 + 37*x - 37,13,x^3 - x^2 - 13*x + 5[] 277,3,2,x^9 + 6*x^8 + 4*x^7 - 37*x^6 - 69*x^5 + 24*x^4 + 119*x^3 + 34*x^2 - 52*x - 25,3,x^9 + 10*x^8 + 31*x^7 + 10*x^6 - 100*x^5 - 105*x^4 + 75*x^3 + 92*x^2 + 4*x - 5,5,x^9 + 12*x^8 + 43*x^7 - 13*x^6 - 390*x^5 - 673*x^4 + 123*x^3 + 1036*x^2 + 635*x + 109,7,x^9 + 2*x^8 - 35*x^7 - 69*x^6 + 420*x^5 + 812*x^4 - 1983*x^3 - 3735*x^2 + 3119*x + 5743,11,x^9 + 14*x^8 + 43*x^7 - 140*x^6 - 653*x^5 + 475*x^4 + 2394*x^3 - 1469*x^2 - 1131*x - 9,13,x^9 + 2*x^8 - 63*x^7 - 164*x^6 + 1169*x^5 + 3371*x^4 - 7559*x^3 - 23687*x^2 + 10754*x + 42085[] 277,4,2,x^9 - 4*x^8 - 6*x^7 + 37*x^6 - 3*x^5 - 100*x^4 + 49*x^3 + 64*x^2 - 20*x - 1,3,x^9 - 6*x^8 - x^7 + 50*x^6 - 20*x^5 - 141*x^4 + 23*x^3 + 120*x^2 + 24*x - 1,5,x^9 - 4*x^8 - 15*x^7 + 69*x^6 + 32*x^5 - 337*x^4 + 237*x^3 + 330*x^2 - 459*x + 145,7,x^9 + 2*x^8 - 23*x^7 - 41*x^6 + 136*x^5 + 228*x^4 - 51*x^3 - 203*x^2 - 77*x - 1,11,x^9 - 2*x^8 - 45*x^7 + 102*x^6 + 519*x^5 - 1187*x^4 - 1370*x^3 + 2773*x^2 + 763*x + 43,13,x^9 + 2*x^8 - 35*x^7 - 40*x^6 + 401*x^5 + 179*x^4 - 1395*x^3 - 547*x^2 + 1010*x + 461[] 278,1,2,x + 1,3,x + 2,5,x - 3,7,x + 1,11,x + 3,13,x - 5[] 278,2,2,x - 1,3,x + 2,5,x + 1,7,x + 5,11,x + 3,13,x - 1[] 278,3,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 + 2*x - 1,7,x^2 + 6*x + 7,11,x^2 - 2*x - 7,13,x^2 + 10*x + 23[] 278,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 + 3,5,x^3 - 12*x - 8,7,x^3 - 9*x^2 + 24*x - 17,11,x^3 - 12*x + 8,13,x^3 - 36*x + 72[] 278,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2,5,x^5 + 2*x^4 - 9*x^3 - 12*x^2 + 20*x + 8,7,x^5 - 7*x^4 + x^3 + 76*x^2 - 146*x + 61,11,x^5 - 6*x^4 - 19*x^3 + 116*x^2 + 84*x - 376,13,x^5 - 2*x^4 - 33*x^3 + 64*x^2 + 140*x + 56[] 279,1,2,x^2 - 3*x + 1,3,x^2,5,x^2 - 4*x - 1,7,x^2 + 4*x - 1,11,x^2 - 6*x + 4,13,x^2 + 2*x - 4[] 279,2,2,x^2 + x - 1,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 4*x - 1,11,x^2 + 4*x + 4,13,x^2 + 2*x - 4[] 279,3,2,x^3 - 4*x - 1,3,x^3,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 - 4*x^2 - x + 8,11,x^3 - 2*x^2 - 20*x - 16,13,x^3 - 4*x^2 - 16*x + 56[] 279,4,2,x^6 - 12*x^4 + 40*x^2 - 27,3,x^6,5,x^6 - 26*x^4 + 181*x^2 - 192,7,x^6 - 8*x^5 - 2*x^4 + 136*x^3 - 175*x^2 - 576*x + 1024,11,x^6 - 68*x^4 + 1168*x^2 - 768,13,x^6 - 64*x^4 - 80*x^3 + 1024*x^2 + 2560*x + 1600[] 280,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x + 5,13,x - 1[] 280,2,2,x,3,x + 3,5,x - 1,7,x - 1,11,x + 5,13,x + 5[] 280,3,2,x^2,3,x^2 + x - 8,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 7*x + 4,13,x^2 - 3*x - 6[] 280,4,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 - x - 38[] Total time: 22.579 seconds, Total memory usage: 6.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:18:38 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [280..287] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:18:17 on modular [Seed = 2990880107] ------------------------------------- 280,1,2,$.1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 5,13,$.1 - 1[] 280,2,2,$.1,3,$.1 + 3,5,$.1 - 1,7,$.1 - 1,11,$.1 + 5,13,$.1 + 5[] 280,3,2,$.1^2,3,$.1^2 + $.1 - 8,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 7*$.1 + 4,13,$.1^2 - 3*$.1 - 6[] 280,4,2,$.1^2,3,$.1^2 - $.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 2*$.1 + 1,11,$.1^2 + $.1 - 4,13,$.1^2 - $.1 - 38[] 281,1,2,x^7 + 2*x^6 - 5*x^5 - 9*x^4 + 7*x^3 + 10*x^2 - 2*x - 1,3,x^7 + 4*x^6 - 2*x^5 - 23*x^4 - 20*x^3 + 6*x^2 + 4*x - 1,5,x^7 + 4*x^6 - 13*x^5 - 58*x^4 - 9*x^3 + 76*x^2 + 51*x + 9,7,x^7 + 12*x^6 + 49*x^5 + 55*x^4 - 147*x^3 - 490*x^2 - 504*x - 177,11,x^7 + 7*x^6 - 22*x^5 - 275*x^4 - 484*x^3 + 1097*x^2 + 4016*x + 3121,13,x^7 + 7*x^6 - 16*x^5 - 167*x^4 - 146*x^3 + 295*x^2 + 376*x + 107[] 281,2,2,x^16 + x^15 - 27*x^14 - 24*x^13 + 294*x^12 + 229*x^11 - 1650*x^10 - 1115*x^9 + 5054*x^8 + 2991*x^7 - 8223*x^6 - 4526*x^5 + 6338*x^4 + 3707*x^3 - 1604*x^2 - 1215*x - 167,3,x^16 - 4*x^15 - 24*x^14 + 105*x^13 + 213*x^12 - 1086*x^11 - 824*x^10 + 5694*x^9 + 911*x^8 - 16142*x^7 + 2792*x^6 + 24266*x^5 - 9130*x^4 - 17154*x^3 + 8640*x^2 + 3847*x - 2158,5,x^16 - 2*x^15 - 51*x^14 + 108*x^13 + 1004*x^12 - 2272*x^11 - 9528*x^10 + 23527*x^9 + 43544*x^8 - 123838*x^7 - 76110*x^6 + 302357*x^5 - 7165*x^4 - 254732*x^3 + 24591*x^2 + 71803*x + 9158,7,x^16 - 16*x^15 + 57*x^14 + 359*x^13 - 2779*x^12 + 222*x^11 + 40216*x^10 - 69329*x^9 - 249828*x^8 + 742632*x^7 + 554336*x^6 - 3298448*x^5 + 664384*x^4 + 6373504*x^3 - 3933952*x^2 - 4035328*x + 2987008,11,x^16 - x^15 - 100*x^14 + 53*x^13 + 3851*x^12 - 544*x^11 - 72826*x^10 - 11166*x^9 + 728551*x^8 + 294344*x^7 - 3800998*x^6 - 2455896*x^5 + 9048488*x^4 + 8109681*x^3 - 5657184*x^2 - 6858135*x - 1476306,13,x^16 - 9*x^15 - 74*x^14 + 859*x^13 + 1328*x^12 - 31309*x^11 + 25786*x^10 + 524405*x^9 - 1198822*x^8 - 3471696*x^7 + 14389568*x^6 - 2926160*x^5 - 51577696*x^4 + 88267136*x^3 - 53487616*x^2 + 6349568*x + 3121664[] 282,1,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x - 2[] 282,2,2,x - 1,3,x + 1,5,x + 4,7,x + 4,11,x,13,x + 2[] 282,3,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 - 12,11,x^2 + 6*x + 6,13,x^2 + 2*x - 26[] 282,4,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 6,7,x^2 - 4*x + 4,11,x^2 - 6,13,x^2 - 4*x - 2[] 282,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 8*x - 4,7,x^3 - 16*x - 16,11,x^3 + 6*x^2 - 16*x - 100,13,x^3 - 28*x - 52[] 283,1,2,x^9 + 6*x^8 + 5*x^7 - 29*x^6 - 50*x^5 + 27*x^4 + 83*x^3 + 19*x^2 - 13*x + 1,3,x^9 + 6*x^8 + 5*x^7 - 27*x^6 - 41*x^5 + 33*x^4 + 64*x^3 - 8*x^2 - 28*x - 4,5,x^9 + 14*x^8 + 70*x^7 + 119*x^6 - 162*x^5 - 897*x^4 - 1200*x^3 - 568*x^2 - 56*x + 4,7,x^9 + 2*x^8 - 35*x^7 - 59*x^6 + 388*x^5 + 485*x^4 - 1723*x^3 - 1021*x^2 + 2753*x - 919,11,x^9 + 5*x^8 - 53*x^7 - 250*x^6 + 908*x^5 + 4006*x^4 - 5573*x^3 - 24230*x^2 + 8533*x + 42269,13,x^9 + 9*x^8 - 24*x^7 - 353*x^6 - 302*x^5 + 2456*x^4 + 2108*x^3 - 5681*x^2 - 3119*x + 3881[] 283,2,2,x^14 - 6*x^13 - 4*x^12 + 83*x^11 - 77*x^10 - 394*x^9 + 617*x^8 + 724*x^7 - 1566*x^6 - 370*x^5 + 1489*x^4 - 153*x^3 - 410*x^2 + 120*x - 8,3,x^14 - 4*x^13 - 21*x^12 + 95*x^11 + 143*x^10 - 815*x^9 - 330*x^8 + 3158*x^7 + 32*x^6 - 5740*x^5 + 524*x^4 + 4204*x^3 - 144*x^2 - 432*x + 32,5,x^14 - 14*x^13 + 52*x^12 + 115*x^11 - 1100*x^10 + 919*x^9 + 7116*x^8 - 13162*x^7 - 17292*x^6 + 49668*x^5 + 8200*x^4 - 66620*x^3 + 10736*x^2 + 21744*x + 2848,7,x^14 - 47*x^12 + 8*x^11 + 729*x^10 - 377*x^9 - 4485*x^8 + 4037*x^7 + 10435*x^6 - 13019*x^5 - 5943*x^4 + 12435*x^3 - 3633*x^2 - 108*x + 31,11,x^14 - 5*x^13 - 67*x^12 + 361*x^11 + 1322*x^10 - 9059*x^9 - 3449*x^8 + 83611*x^7 - 97383*x^6 - 138728*x^5 + 241269*x^4 + 50916*x^3 - 153904*x^2 + 4920*x + 14419,13,x^14 - 9*x^13 - 60*x^12 + 688*x^11 + 1058*x^10 - 20258*x^9 + 202*x^8 + 291882*x^7 - 190576*x^6 - 2108657*x^5 + 1914633*x^4 + 6666922*x^3 - 5938267*x^2 - 4997192*x + 391681[] 284,1,2,x^3,3,x^3 - x^2 - 4*x + 1,5,x^3 - x^2 - 6*x - 3,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 4*x^2 - 12*x + 24,13,x^3 - 4*x^2 - 20*x + 72[] 284,2,2,x^3,3,x^3 + 3*x^2 - 3,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 + 6*x^2 - 24,11,x^3 + 6*x^2 - 24,13,x^3 + 6*x^2 - 24*x - 136[] 285,1,2,x - 1,3,x + 1,5,x + 1,7,x + 2,11,x + 2,13,x + 4[] 285,2,2,x - 1,3,x + 1,5,x - 1,7,x - 4,11,x - 4,13,x - 2[] 285,3,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 6,13,x[] 285,4,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x + 2,11,x^2 - 2,13,x^2 - 8*x + 14[] 285,5,2,x^2 - 7,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 2*x - 6,11,x^2 - 6*x + 2,13,x^2 + 6*x + 2[] 285,6,2,x^2 - 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2,11,x^2 - 4*x - 14,13,x^2 + 4*x + 2[] 285,7,2,x^2 - 3,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 2*x - 2[] 286,1,2,x + 1,3,x + 1,5,x + 1,7,x - 1,11,x + 1,13,x + 1[] 286,2,2,x + 1,3,x + 2,5,x - 3,7,x + 1,11,x + 1,13,x - 1[] 286,3,2,x - 1,3,x - 2,5,x + 1,7,x - 1,11,x + 1,13,x + 1[] 286,4,2,x - 1,3,x + 1,5,x + 3,7,x + 5,11,x + 1,13,x - 1[] 286,5,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 1,13,x - 1[] 286,6,2,x - 1,3,x - 2,5,x - 1,7,x + 3,11,x - 1,13,x - 1[] 286,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 10*x + 8,5,x^3 - 2*x^2 - 9*x + 2,7,x^3 + 4*x^2 - 5*x - 16,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 + 3*x + 1[] 287,1,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 - x - 1,7,x^2 + 2*x + 1,11,x^2 + 2*x + 1,13,x^2 + 8*x + 11[] 287,2,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 + x - 1,7,x^2 - 2*x + 1,11,x^2 - 5,13,x^2 + 6*x + 9[] 287,3,2,x^3 - 4*x^2 + 3*x + 1,3,x^3 - 5*x^2 + 6*x - 1,5,x^3 - 2*x^2 - 8*x + 8,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 - 4*x - 8,13,x^3 - 7*x^2 + 49[] 287,4,2,x^3 - x^2 - 4*x + 3,3,x^3 + x^2 - 8*x - 3,5,x^3 - 6*x^2 + 12*x - 8,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 6*x^2 + 12*x + 8,13,x^3 - 9*x^2 + 22*x - 15[] 287,5,2,x^5 + x^4 - 6*x^3 - 4*x^2 + 6*x + 3,3,x^5 - 4*x^4 + 10*x^2 - 3*x - 1,5,x^5 + 5*x^4 - 11*x^3 - 86*x^2 - 96*x + 24,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - 2*x^4 - 63*x^3 + 140*x^2 + 972*x - 2472,13,x^5 - 5*x^4 - 9*x^3 + 80*x^2 - 120*x + 49[] 287,6,2,x^6 + x^5 - 10*x^4 - 10*x^3 + 23*x^2 + 24*x + 5,3,x^6 + 4*x^5 - 8*x^4 - 46*x^3 - 13*x^2 + 111*x + 100,5,x^6 + x^5 - 29*x^4 - 16*x^3 + 200*x^2 - 16*x - 16,7,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 - 6*x^5 - 29*x^4 + 218*x^3 + 28*x^2 - 1928*x + 2720,13,x^6 - 7*x^5 - 49*x^4 + 330*x^3 + 400*x^2 - 1917*x - 1546[] Total time: 21.100 seconds, Total memory usage: 6.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:29:27 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [287..294] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:29:07 on modular [Seed = 2407009196] ------------------------------------- 287,1,2,$.1^2 + $.1 - 1,3,$.1^2 + $.1 - 1,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 8*$.1 + 11[] 287,2,2,$.1^2 + $.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 + $.1 - 1,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 5,13,$.1^2 + 6*$.1 + 9[] 287,3,2,$.1^3 - 4*$.1^2 + 3*$.1 + 1,3,$.1^3 - 5*$.1^2 + 6*$.1 - 1,5,$.1^3 - 2*$.1^2 - 8*$.1 + 8,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 - 4*$.1 - 8,13,$.1^3 - 7*$.1^2 + 49[] 287,4,2,$.1^3 - $.1^2 - 4*$.1 + 3,3,$.1^3 + $.1^2 - 8*$.1 - 3,5,$.1^3 - 6*$.1^2 + 12*$.1 - 8,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 + 6*$.1^2 + 12*$.1 + 8,13,$.1^3 - 9*$.1^2 + 22*$.1 - 15[] 287,5,2,$.1^5 + $.1^4 - 6*$.1^3 - 4*$.1^2 + 6*$.1 + 3,3,$.1^5 - 4*$.1^4 + 10*$.1^2 - 3*$.1 - 1,5,$.1^5 + 5*$.1^4 - 11*$.1^3 - 86*$.1^2 - 96*$.1 + 24,7,$.1^5 - 5*$.1^4 + 10*$.1^3 - 10*$.1^2 + 5*$.1 - 1,11,$.1^5 - 2*$.1^4 - 63*$.1^3 + 140*$.1^2 + 972*$.1 - 2472,13,$.1^5 - 5*$.1^4 - 9*$.1^3 + 80*$.1^2 - 120*$.1 + 49[] 287,6,2,$.1^6 + $.1^5 - 10*$.1^4 - 10*$.1^3 + 23*$.1^2 + 24*$.1 + 5,3,$.1^6 + 4*$.1^5 - 8*$.1^4 - 46*$.1^3 - 13*$.1^2 + 111*$.1 + 100,5,$.1^6 + $.1^5 - 29*$.1^4 - 16*$.1^3 + 200*$.1^2 - 16*$.1 - 16,7,$.1^6 + 6*$.1^5 + 15*$.1^4 + 20*$.1^3 + 15*$.1^2 + 6*$.1 + 1,11,$.1^6 - 6*$.1^5 - 29*$.1^4 + 218*$.1^3 + 28*$.1^2 - 1928*$.1 + 2720,13,$.1^6 - 7*$.1^5 - 49*$.1^4 + 330*$.1^3 + 400*$.1^2 - 1917*$.1 - 1546[] 288,1,2,x,3,x,5,x + 4,7,x,11,x,13,x + 6[] 288,2,2,x,3,x,5,x - 2,7,x,11,x,13,x - 6[] 288,3,2,x,3,x,5,x + 2,7,x - 4,11,x - 4,13,x + 2[] 288,4,2,x,3,x,5,x - 4,7,x,11,x,13,x + 6[] 288,5,2,x,3,x,5,x + 2,7,x + 4,11,x + 4,13,x + 2[] 289,1,2,x + 1,3,x,5,x - 2,7,x + 4,11,x,13,x + 2[] 289,2,2,x^2 + x - 3,3,x^2 + x - 3,5,x^2 + x - 3,7,x^2 + 3*x - 1,11,x^2 + 6*x + 9,13,x^2 + 3*x - 1[] 289,3,2,x^2 + x - 3,3,x^2 - x - 3,5,x^2 - x - 3,7,x^2 - 3*x - 1,11,x^2 - 6*x + 9,13,x^2 + 3*x - 1[] 289,4,2,x^3 - 3*x + 1,3,x^3 + 3*x^2 - 3,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 - 3*x + 1,11,x^3 + 6*x^2 - 24,13,x^3 - 6*x^2 - 9*x + 71[] 289,5,2,x^3 - 3*x + 1,3,x^3 - 3*x^2 + 3,5,x^3 - 6*x^2 + 9*x - 1,7,x^3 - 3*x - 1,11,x^3 - 6*x^2 + 24,13,x^3 - 6*x^2 - 9*x + 71[] 289,6,2,x^4 - 4*x^3 + 2*x^2 + 4*x + 1,3,x^4 - 8*x^2 + 8,5,x^4 - 4*x^2 + 2,7,x^4 - 8*x^2 + 8,11,x^4 - 8*x^2 + 8,13,x^4 - 4*x^2 + 4[] 290,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 2,13,x + 6[] 290,2,2,x^2 + 2*x + 1,3,x^2 - x - 3,5,x^2 + 2*x + 1,7,x^2 - 5*x + 3,11,x^2 + 2*x - 12,13,x^2 - 9*x + 17[] 290,3,2,x^2 + 2*x + 1,3,x^2 - x - 3,5,x^2 - 2*x + 1,7,x^2 - 3*x - 1,11,x^2 - 2*x - 12,13,x^2 + x - 3[] 290,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 3*x + 8,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 3*x^2 - 15*x + 46,11,x^3 - 24*x - 24,13,x^3 - 3*x^2 - 33*x + 118[] 290,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + x^2 - 7*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + x^2 - 5*x - 4,11,x^3 - 2*x^2 - 20*x + 32,13,x^3 - 5*x^2 - 21*x + 98[] 291,1,2,x + 1,3,x + 1,5,x,7,x - 2,11,x + 4,13,x + 2[] 291,2,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x - 4,13,x - 6[] 291,3,2,x - 2,3,x + 1,5,x - 1,7,x - 2,11,x - 4,13,x[] 291,4,2,x + 2,3,x + 1,5,x - 3,7,x + 2,11,x,13,x + 4[] 291,5,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 3*x - 1,11,x^2 + 3*x - 1,13,x^2 + 3*x - 1[] 291,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - 6*x + 9,7,x^2 + 3*x - 9,11,x^2 + 7*x + 11,13,x^2 - 7*x + 11[] 291,7,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 4*x - 1,7,x^2 + 7*x + 11,11,x^2 - x - 11,13,x^2 + 9*x + 19[] 291,8,2,x^7 - 11*x^5 + x^4 + 34*x^3 - 5*x^2 - 24*x - 4,3,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,5,x^7 - 4*x^6 - 16*x^5 + 52*x^4 + 111*x^3 - 168*x^2 - 336*x - 64,7,x^7 - 9*x^6 + 13*x^5 + 62*x^4 - 124*x^3 - 96*x^2 + 192*x - 32,11,x^7 + 3*x^6 - 39*x^5 - 88*x^4 + 328*x^3 + 672*x^2 - 384*x - 512,13,x^7 - 11*x^6 + 25*x^5 + 82*x^4 - 276*x^3 - 200*x^2 + 640*x + 448[] 292,1,2,x^2,3,x^2 + x - 1,5,x^2 + 5*x + 5,7,x^2 - 5,11,x^2 + 7*x + 11,13,x^2 + x - 31[] 292,2,2,x^4,3,x^4 - 3*x^3 - 5*x^2 + 16*x - 8,5,x^4 - 5*x^3 + x^2 + 8*x - 4,7,x^4 - 7*x^2 + 2,11,x^4 - 3*x^3 - 15*x^2 - 10*x + 2,13,x^4 - 5*x^3 + x^2 + 8*x - 4[] 293,1,2,x^8 + 3*x^7 - 4*x^6 - 15*x^5 + 4*x^4 + 21*x^3 - 2*x^2 - 8*x + 1,3,x^8 + 8*x^7 + 17*x^6 - 11*x^5 - 61*x^4 - 12*x^3 + 54*x^2 - 9,5,x^8 + x^7 - 14*x^6 - 12*x^5 + 49*x^4 + 39*x^3 - 43*x^2 - 21*x + 13,7,x^8 + 13*x^7 + 50*x^6 + 4*x^5 - 322*x^4 - 409*x^3 + 356*x^2 + 551*x - 107,11,x^8 + 9*x^7 - 17*x^6 - 299*x^5 - 255*x^4 + 1950*x^3 + 1347*x^2 - 3162*x - 1777,13,x^8 + 8*x^7 - 10*x^6 - 179*x^5 - 66*x^4 + 1301*x^3 + 838*x^2 - 3003*x - 1993[] 293,2,2,x^16 - 3*x^15 - 22*x^14 + 69*x^13 + 184*x^12 - 621*x^11 - 716*x^10 + 2758*x^9 + 1234*x^8 - 6287*x^7 - 554*x^6 + 7023*x^5 - 572*x^4 - 3385*x^3 + 508*x^2 + 526*x - 111,3,x^16 - 10*x^15 + 16*x^14 + 145*x^13 - 539*x^12 - 391*x^11 + 4186*x^10 - 2997*x^9 - 12471*x^8 + 19066*x^7 + 10434*x^6 - 35185*x^5 + 12204*x^4 + 17688*x^3 - 17052*x^2 + 5482*x - 613,5,x^16 - x^15 - 50*x^14 + 52*x^13 + 967*x^12 - 1133*x^11 - 9107*x^10 + 12731*x^9 + 42279*x^8 - 74396*x^7 - 78548*x^6 + 202208*x^5 - 13072*x^4 - 176512*x^3 + 104320*x^2 - 7424*x - 2304,7,x^16 - 15*x^15 + 47*x^14 + 355*x^13 - 2587*x^12 + 1270*x^11 + 31866*x^10 - 82216*x^9 - 81204*x^8 + 587973*x^7 - 541623*x^6 - 957347*x^5 + 2078389*x^4 - 767685*x^3 - 751840*x^2 + 444163*x + 39801,11,x^16 - 9*x^15 - 66*x^14 + 748*x^13 + 1441*x^12 - 24992*x^11 - 9096*x^10 + 443284*x^9 - 82288*x^8 - 4603767*x^7 + 1256495*x^6 + 28598848*x^5 - 2437626*x^4 - 100143384*x^3 - 26960213*x^2 + 154057944*x + 107176896,13,x^16 - 10*x^15 - 54*x^14 + 839*x^13 - 450*x^12 - 21927*x^11 + 62138*x^10 + 151969*x^9 - 882035*x^8 + 825676*x^7 + 1529916*x^6 - 3032400*x^5 + 775008*x^4 + 1156352*x^3 - 760128*x^2 + 136192*x - 4096[] 294,1,2,x + 1,3,x + 1,5,x + 3,7,x,11,x - 3,13,x - 4[] 294,2,2,x + 1,3,x + 1,5,x - 4,7,x,11,x + 4,13,x - 4[] 294,3,2,x + 1,3,x - 1,5,x - 3,7,x,11,x - 3,13,x + 4[] 294,4,2,x + 1,3,x - 1,5,x + 4,7,x,11,x + 4,13,x + 4[] 294,5,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 5,13,x[] 294,6,2,x - 1,3,x - 1,5,x + 1,7,x,11,x - 5,13,x[] 294,7,2,x - 1,3,x - 1,5,x - 2,7,x,11,x + 4,13,x + 6[] Total time: 19.629 seconds, Total memory usage: 6.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:36:04 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [294..301] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 10:35:41 on modular [Seed = 1504631499] ------------------------------------- 294,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 3,7,$.1,11,$.1 - 3,13,$.1 - 4[] 294,2,2,$.1 + 1,3,$.1 + 1,5,$.1 - 4,7,$.1,11,$.1 + 4,13,$.1 - 4[] 294,3,2,$.1 + 1,3,$.1 - 1,5,$.1 - 3,7,$.1,11,$.1 - 3,13,$.1 + 4[] 294,4,2,$.1 + 1,3,$.1 - 1,5,$.1 + 4,7,$.1,11,$.1 + 4,13,$.1 + 4[] 294,5,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 - 5,13,$.1[] 294,6,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 - 5,13,$.1[] 294,7,2,$.1 - 1,3,$.1 - 1,5,$.1 - 2,7,$.1,11,$.1 + 4,13,$.1 + 6[] 295,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 7*x + 7,11,x^3 + 9*x^2 + 20*x + 13,13,x^3 - x^2 - 9*x + 1[] 295,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 6*x^2 + 3*x - 19,11,x^3 - 3*x^2 - 6*x + 17,13,x^3 + 9*x^2 + 15*x - 17[] 295,3,2,x^6 - 2*x^5 - 6*x^4 + 11*x^3 + 8*x^2 - 11*x - 3,3,x^6 - x^5 - 12*x^4 + 13*x^3 + 28*x^2 - 16*x - 16,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 2*x^5 - 21*x^4 + 57*x^3 + 12*x^2 - 104*x + 48,11,x^6 - 3*x^5 - 12*x^4 + 33*x^3 + 32*x^2 - 80*x + 32,13,x^6 - 11*x^5 + 23*x^4 + 83*x^3 - 268*x^2 - 64*x + 452[] 295,4,2,x^7 - x^6 - 10*x^5 + 7*x^4 + 27*x^3 - 11*x^2 - 10*x - 1,3,x^7 - 3*x^6 - 14*x^5 + 39*x^4 + 52*x^3 - 128*x^2 - 16*x + 32,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 4*x^6 - 23*x^5 - 105*x^4 + 40*x^3 + 488*x^2 + 400*x - 32,11,x^7 - 3*x^6 - 66*x^5 + 221*x^4 + 1252*x^3 - 4368*x^2 - 7168*x + 25408,13,x^7 + 9*x^6 - 19*x^5 - 301*x^4 - 6*x^3 + 3276*x^2 + 980*x - 11564[] 296,1,2,x,3,x + 1,5,x + 2,7,x - 1,11,x - 1,13,x + 6[] 296,2,2,x,3,x + 1,5,x,7,x + 3,11,x + 3,13,x[] 296,3,2,x^3,3,x^3 - 2*x^2 - 4*x + 7,5,x^3 + x^2 - 5*x + 2,7,x^3 - 7*x^2 + 10*x + 4,11,x^3 - 36*x + 27,13,x^3 - 3*x^2 - 33*x + 62[] 296,4,2,x^4,3,x^4 - 2*x^3 - 8*x^2 + 15*x + 4,5,x^4 - 5*x^3 - x^2 + 26*x - 16,7,x^4 + x^3 - 18*x^2 - 4*x + 64,11,x^4 - 4*x^3 - 12*x^2 + 63*x - 52,13,x^4 - 5*x^3 - 17*x^2 + 122*x - 160[] 297,1,2,x + 1,3,x,5,x - 2,7,x + 5,11,x + 1,13,x + 2[] 297,2,2,x - 2,3,x,5,x - 2,7,x - 1,11,x + 1,13,x + 5[] 297,3,2,x - 1,3,x,5,x + 2,7,x + 5,11,x - 1,13,x + 2[] 297,4,2,x + 2,3,x,5,x + 2,7,x - 1,11,x - 1,13,x + 5[] 297,5,2,x^2 + 2*x - 2,3,x^2,5,x^2 + 2*x - 2,7,x^2 + 4*x + 1,11,x^2 + 2*x + 1,13,x^2 + 4*x + 1[] 297,6,2,x^2 - 2*x - 2,3,x^2,5,x^2 - 2*x - 2,7,x^2 + 4*x + 1,11,x^2 - 2*x + 1,13,x^2 + 4*x + 1[] 297,7,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 - 2*x^2 - 8*x + 12,7,x^3 - 7*x^2 + 11*x + 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 4*x^2 - 4*x + 4[] 297,8,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 + 2*x^2 - 8*x - 12,7,x^3 - 7*x^2 + 11*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 4*x^2 - 4*x + 4[] 298,1,2,x + 1,3,x,5,x + 4,7,x - 4,11,x - 2,13,x + 5[] 298,2,2,x - 1,3,x + 2,5,x + 2,7,x + 2,11,x,13,x + 5[] 298,3,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 4*x + 1[] 298,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 5*x^2 + 4*x - 5,5,x^3 - x^2 - 4*x - 1,7,x^3 + 4*x^2 - 12*x - 40,11,x^3 + 5*x^2 - 22*x - 109,13,x^3[] 298,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2,5,x^5 - 5*x^4 + 2*x^3 + 9*x^2 - 2,7,x^5 - 18*x^3 + 8*x^2 + 40*x + 16,11,x^5 + 3*x^4 - 16*x^3 - 73*x^2 - 84*x - 22,13,x^5 - 6*x^4 - 37*x^3 + 236*x^2 + 32*x - 704[] 299,1,2,x^2 - x - 1,3,x^2 + x - 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 + 3*x + 1,13,x^2 + 2*x + 1[] 299,2,2,x^2 - 5,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 6*x + 4,13,x^2 - 2*x + 1[] 299,3,2,x^2 - x - 4,3,x^2 - x - 4,5,x^2 - x - 4,7,x^2 - 2*x - 16,11,x^2 - 5*x + 2,13,x^2 - 2*x + 1[] 299,4,2,x^2 + x - 5,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 - 2*x + 1,11,x^2 - 3*x - 3,13,x^2 - 2*x + 1[] 299,5,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 + 4*x - 1,11,x^2 - x - 1,13,x^2 - 2*x + 1[] 299,6,2,x^3,3,x^3 + x^2 - 9*x - 5,5,x^3 - x^2 - 7*x - 3,7,x^3 - 2*x^2 - 8*x + 4,11,x^3 - 5*x^2 - 5*x + 27,13,x^3 - 3*x^2 + 3*x - 1[] 299,7,2,x^10 - x^9 - 19*x^8 + 18*x^7 + 127*x^6 - 109*x^5 - 357*x^4 + 252*x^3 + 400*x^2 - 192*x - 128,3,x^10 - 3*x^9 - 19*x^8 + 58*x^7 + 107*x^6 - 343*x^5 - 181*x^4 + 720*x^3 - 56*x^2 - 400*x + 112,5,x^10 - 3*x^9 - 37*x^8 + 112*x^7 + 443*x^6 - 1401*x^5 - 1817*x^4 + 6424*x^3 + 1108*x^2 - 6140*x - 2372,7,x^10 + 2*x^9 - 53*x^8 - 70*x^7 + 1044*x^6 + 640*x^5 - 9072*x^4 + 456*x^3 + 29888*x^2 - 18272*x - 5936,11,x^10 - 3*x^9 - 71*x^8 + 200*x^7 + 1777*x^6 - 4449*x^5 - 19765*x^4 + 39328*x^3 + 100444*x^2 - 119916*x - 190148,13,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1[] 300,1,2,x,3,x + 1,5,x,7,x - 1,11,x - 6,13,x + 5[] Errors: /home/mfd/gomagma: line 2: 24582 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:37:09 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [294..299] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:36:52 on modular [Seed = 1369887514] ------------------------------------- 294,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 3,7,$.1,11,$.1 - 3,13,$.1 - 4[] 294,2,2,$.1 + 1,3,$.1 + 1,5,$.1 - 4,7,$.1,11,$.1 + 4,13,$.1 - 4[] 294,3,2,$.1 + 1,3,$.1 - 1,5,$.1 - 3,7,$.1,11,$.1 - 3,13,$.1 + 4[] 294,4,2,$.1 + 1,3,$.1 - 1,5,$.1 + 4,7,$.1,11,$.1 + 4,13,$.1 + 4[] 294,5,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 - 5,13,$.1[] 294,6,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 - 5,13,$.1[] 294,7,2,$.1 - 1,3,$.1 - 1,5,$.1 - 2,7,$.1,11,$.1 + 4,13,$.1 + 6[] 295,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 7*x + 7,11,x^3 + 9*x^2 + 20*x + 13,13,x^3 - x^2 - 9*x + 1[] 295,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 6*x^2 + 3*x - 19,11,x^3 - 3*x^2 - 6*x + 17,13,x^3 + 9*x^2 + 15*x - 17[] 295,3,2,x^6 - 2*x^5 - 6*x^4 + 11*x^3 + 8*x^2 - 11*x - 3,3,x^6 - x^5 - 12*x^4 + 13*x^3 + 28*x^2 - 16*x - 16,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 2*x^5 - 21*x^4 + 57*x^3 + 12*x^2 - 104*x + 48,11,x^6 - 3*x^5 - 12*x^4 + 33*x^3 + 32*x^2 - 80*x + 32,13,x^6 - 11*x^5 + 23*x^4 + 83*x^3 - 268*x^2 - 64*x + 452[] 295,4,2,x^7 - x^6 - 10*x^5 + 7*x^4 + 27*x^3 - 11*x^2 - 10*x - 1,3,x^7 - 3*x^6 - 14*x^5 + 39*x^4 + 52*x^3 - 128*x^2 - 16*x + 32,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 4*x^6 - 23*x^5 - 105*x^4 + 40*x^3 + 488*x^2 + 400*x - 32,11,x^7 - 3*x^6 - 66*x^5 + 221*x^4 + 1252*x^3 - 4368*x^2 - 7168*x + 25408,13,x^7 + 9*x^6 - 19*x^5 - 301*x^4 - 6*x^3 + 3276*x^2 + 980*x - 11564[] 296,1,2,x,3,x + 1,5,x + 2,7,x - 1,11,x - 1,13,x + 6[] 296,2,2,x,3,x + 1,5,x,7,x + 3,11,x + 3,13,x[] 296,3,2,x^3,3,x^3 - 2*x^2 - 4*x + 7,5,x^3 + x^2 - 5*x + 2,7,x^3 - 7*x^2 + 10*x + 4,11,x^3 - 36*x + 27,13,x^3 - 3*x^2 - 33*x + 62[] 296,4,2,x^4,3,x^4 - 2*x^3 - 8*x^2 + 15*x + 4,5,x^4 - 5*x^3 - x^2 + 26*x - 16,7,x^4 + x^3 - 18*x^2 - 4*x + 64,11,x^4 - 4*x^3 - 12*x^2 + 63*x - 52,13,x^4 - 5*x^3 - 17*x^2 + 122*x - 160[] 297,1,2,x + 1,3,x,5,x - 2,7,x + 5,11,x + 1,13,x + 2[] 297,2,2,x - 2,3,x,5,x - 2,7,x - 1,11,x + 1,13,x + 5[] 297,3,2,x - 1,3,x,5,x + 2,7,x + 5,11,x - 1,13,x + 2[] 297,4,2,x + 2,3,x,5,x + 2,7,x - 1,11,x - 1,13,x + 5[] 297,5,2,x^2 + 2*x - 2,3,x^2,5,x^2 + 2*x - 2,7,x^2 + 4*x + 1,11,x^2 + 2*x + 1,13,x^2 + 4*x + 1[] 297,6,2,x^2 - 2*x - 2,3,x^2,5,x^2 - 2*x - 2,7,x^2 + 4*x + 1,11,x^2 - 2*x + 1,13,x^2 + 4*x + 1[] 297,7,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 - 2*x^2 - 8*x + 12,7,x^3 - 7*x^2 + 11*x + 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 4*x^2 - 4*x + 4[] 297,8,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 + 2*x^2 - 8*x - 12,7,x^3 - 7*x^2 + 11*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 4*x^2 - 4*x + 4[] 298,1,2,x + 1,3,x,5,x + 4,7,x - 4,11,x - 2,13,x + 5[] 298,2,2,x - 1,3,x + 2,5,x + 2,7,x + 2,11,x,13,x + 5[] 298,3,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 4*x + 1[] 298,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 5*x^2 + 4*x - 5,5,x^3 - x^2 - 4*x - 1,7,x^3 + 4*x^2 - 12*x - 40,11,x^3 + 5*x^2 - 22*x - 109,13,x^3[] 298,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2,5,x^5 - 5*x^4 + 2*x^3 + 9*x^2 - 2,7,x^5 - 18*x^3 + 8*x^2 + 40*x + 16,11,x^5 + 3*x^4 - 16*x^3 - 73*x^2 - 84*x - 22,13,x^5 - 6*x^4 - 37*x^3 + 236*x^2 + 32*x - 704[] 299,1,2,x^2 - x - 1,3,x^2 + x - 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 + 3*x + 1,13,x^2 + 2*x + 1[] 299,2,2,x^2 - 5,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 6*x + 4,13,x^2 - 2*x + 1[] 299,3,2,x^2 - x - 4,3,x^2 - x - 4,5,x^2 - x - 4,7,x^2 - 2*x - 16,11,x^2 - 5*x + 2,13,x^2 - 2*x + 1[] 299,4,2,x^2 + x - 5,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 - 2*x + 1,11,x^2 - 3*x - 3,13,x^2 - 2*x + 1[] 299,5,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 + 4*x - 1,11,x^2 - x - 1,13,x^2 - 2*x + 1[] 299,6,2,x^3,3,x^3 + x^2 - 9*x - 5,5,x^3 - x^2 - 7*x - 3,7,x^3 - 2*x^2 - 8*x + 4,11,x^3 - 5*x^2 - 5*x + 27,13,x^3 - 3*x^2 + 3*x - 1[] 299,7,2,x^10 - x^9 - 19*x^8 + 18*x^7 + 127*x^6 - 109*x^5 - 357*x^4 + 252*x^3 + 400*x^2 - 192*x - 128,3,x^10 - 3*x^9 - 19*x^8 + 58*x^7 + 107*x^6 - 343*x^5 - 181*x^4 + 720*x^3 - 56*x^2 - 400*x + 112,5,x^10 - 3*x^9 - 37*x^8 + 112*x^7 + 443*x^6 - 1401*x^5 - 1817*x^4 + 6424*x^3 + 1108*x^2 - 6140*x - 2372,7,x^10 + 2*x^9 - 53*x^8 - 70*x^7 + 1044*x^6 + 640*x^5 - 9072*x^4 + 456*x^3 + 29888*x^2 - 18272*x - 5936,11,x^10 - 3*x^9 - 71*x^8 + 200*x^7 + 1777*x^6 - 4449*x^5 - 19765*x^4 + 39328*x^3 + 100444*x^2 - 119916*x - 190148,13,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1[] Total time: 16.529 seconds, Total memory usage: 5.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:43:14 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [299..301] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:43:02 on modular [Seed = 2139684518] ------------------------------------- 299,1,2,$.1^2 - $.1 - 1,3,$.1^2 + $.1 - 1,5,$.1^2 + 3*$.1 + 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 + 3*$.1 + 1,13,$.1^2 + 2*$.1 + 1[] 299,2,2,$.1^2 - 5,3,$.1^2,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 2*$.1 - 4,11,$.1^2 + 6*$.1 + 4,13,$.1^2 - 2*$.1 + 1[] 299,3,2,$.1^2 - $.1 - 4,3,$.1^2 - $.1 - 4,5,$.1^2 - $.1 - 4,7,$.1^2 - 2*$.1 - 16,11,$.1^2 - 5*$.1 + 2,13,$.1^2 - 2*$.1 + 1[] 299,4,2,$.1^2 + $.1 - 5,3,$.1^2 + $.1 - 5,5,$.1^2 - 3*$.1 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 3*$.1 - 3,13,$.1^2 - 2*$.1 + 1[] 299,5,2,$.1^2 + $.1 - 1,3,$.1^2 + $.1 - 1,5,$.1^2 + $.1 - 1,7,$.1^2 + 4*$.1 - 1,11,$.1^2 - $.1 - 1,13,$.1^2 - 2*$.1 + 1[] 299,6,2,$.1^3,3,$.1^3 + $.1^2 - 9*$.1 - 5,5,$.1^3 - $.1^2 - 7*$.1 - 3,7,$.1^3 - 2*$.1^2 - 8*$.1 + 4,11,$.1^3 - 5*$.1^2 - 5*$.1 + 27,13,$.1^3 - 3*$.1^2 + 3*$.1 - 1[] 299,7,2,$.1^10 - $.1^9 - 19*$.1^8 + 18*$.1^7 + 127*$.1^6 - 109*$.1^5 - 357*$.1^4 + 252*$.1^3 + 400*$.1^2 - 192*$.1 - 128,3,$.1^10 - 3*$.1^9 - 19*$.1^8 + 58*$.1^7 + 107*$.1^6 - 343*$.1^5 - 181*$.1^4 + 720*$.1^3 - 56*$.1^2 - 400*$.1 + 112,5,$.1^10 - 3*$.1^9 - 37*$.1^8 + 112*$.1^7 + 443*$.1^6 - 1401*$.1^5 - 1817*$.1^4 + 6424*$.1^3 + 1108*$.1^2 - 6140*$.1 - 2372,7,$.1^10 + 2*$.1^9 - 53*$.1^8 - 70*$.1^7 + 1044*$.1^6 + 640*$.1^5 - 9072*$.1^4 + 456*$.1^3 + 29888*$.1^2 - 18272*$.1 - 5936,11,$.1^10 - 3*$.1^9 - 71*$.1^8 + 200*$.1^7 + 1777*$.1^6 - 4449*$.1^5 - 19765*$.1^4 + 39328*$.1^3 + 100444*$.1^2 - 119916*$.1 - 190148,13,$.1^10 + 10*$.1^9 + 45*$.1^8 + 120*$.1^7 + 210*$.1^6 + 252*$.1^5 + 210*$.1^4 + 120*$.1^3 + 45*$.1^2 + 10*$.1 + 1[] 300,1,2,x,3,x + 1,5,x,7,x - 1,11,x - 6,13,x + 5[] 300,2,2,x,3,x + 1,5,x,7,x + 4,11,x + 4,13,x[] 300,3,2,x,3,x - 1,5,x,7,x + 1,11,x - 6,13,x - 5[] 300,4,2,x,3,x - 1,5,x,7,x - 4,11,x + 4,13,x[] 301,1,2,x^4 + 4*x^3 + 2*x^2 - 5*x - 3,3,x^4 + 3*x^3 - 2*x^2 - 4*x - 1,5,x^4 + 4*x^3 - 7*x + 3,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 + 15*x^3 + 80*x^2 + 176*x + 129,13,x^4 - x^3 - 30*x^2 + 12*x + 217[] 301,2,2,x^5 - 6*x^3 + x^2 + 5*x - 2,3,x^5 + 3*x^4 - 6*x^3 - 18*x^2 + x + 2,5,x^5 + 6*x^4 - 49*x^2 - 67*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 + 16*x^4 + 83*x^3 + 120*x^2 - 155*x - 283,13,x^5 + 2*x^4 - 35*x^3 - 80*x^2 + 81*x + 193[] 301,3,2,x^5 - x^4 - 6*x^3 + 5*x^2 + 6*x - 1,3,x^5 - 5*x^4 + 2*x^3 + 18*x^2 - 15*x - 8,5,x^5 - 4*x^4 - 4*x^3 + 15*x^2 + 17*x + 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 13*x^4 + 52*x^3 - 56*x^2 - 23*x + 32,13,x^5 + x^4 - 36*x^3 - 26*x^2 + 147*x - 86[] 301,4,2,x^7 - 4*x^6 - 3*x^5 + 25*x^4 - 13*x^3 - 23*x^2 + 11*x + 2,3,x^7 - x^6 - 14*x^5 + 16*x^4 + 43*x^3 - 54*x^2 - 24*x + 32,5,x^7 - 16*x^5 + 9*x^4 + 57*x^3 - 54*x^2 - 12*x + 16,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,11,x^7 - 16*x^6 + 83*x^5 - 104*x^4 - 347*x^3 + 881*x^2 - 52*x - 688,13,x^7 + 2*x^6 - 35*x^5 - 102*x^4 + 9*x^3 + 247*x^2 + 220*x + 52[] Total time: 11.500 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:47:52 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [301..306] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:47:35 on modular [Seed = 267947975] ------------------------------------- 301,1,2,$.1^4 + 4*$.1^3 + 2*$.1^2 - 5*$.1 - 3,3,$.1^4 + 3*$.1^3 - 2*$.1^2 - 4*$.1 - 1,5,$.1^4 + 4*$.1^3 - 7*$.1 + 3,7,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,11,$.1^4 + 15*$.1^3 + 80*$.1^2 + 176*$.1 + 129,13,$.1^4 - $.1^3 - 30*$.1^2 + 12*$.1 + 217[] 301,2,2,$.1^5 - 6*$.1^3 + $.1^2 + 5*$.1 - 2,3,$.1^5 + 3*$.1^4 - 6*$.1^3 - 18*$.1^2 + $.1 + 2,5,$.1^5 + 6*$.1^4 - 49*$.1^2 - 67*$.1 - 4,7,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,11,$.1^5 + 16*$.1^4 + 83*$.1^3 + 120*$.1^2 - 155*$.1 - 283,13,$.1^5 + 2*$.1^4 - 35*$.1^3 - 80*$.1^2 + 81*$.1 + 193[] 301,3,2,$.1^5 - $.1^4 - 6*$.1^3 + 5*$.1^2 + 6*$.1 - 1,3,$.1^5 - 5*$.1^4 + 2*$.1^3 + 18*$.1^2 - 15*$.1 - 8,5,$.1^5 - 4*$.1^4 - 4*$.1^3 + 15*$.1^2 + 17*$.1 + 4,7,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,11,$.1^5 - 13*$.1^4 + 52*$.1^3 - 56*$.1^2 - 23*$.1 + 32,13,$.1^5 + $.1^4 - 36*$.1^3 - 26*$.1^2 + 147*$.1 - 86[] 301,4,2,$.1^7 - 4*$.1^6 - 3*$.1^5 + 25*$.1^4 - 13*$.1^3 - 23*$.1^2 + 11*$.1 + 2,3,$.1^7 - $.1^6 - 14*$.1^5 + 16*$.1^4 + 43*$.1^3 - 54*$.1^2 - 24*$.1 + 32,5,$.1^7 - 16*$.1^5 + 9*$.1^4 + 57*$.1^3 - 54*$.1^2 - 12*$.1 + 16,7,$.1^7 - 7*$.1^6 + 21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1,11,$.1^7 - 16*$.1^6 + 83*$.1^5 - 104*$.1^4 - 347*$.1^3 + 881*$.1^2 - 52*$.1 - 688,13,$.1^7 + 2*$.1^6 - 35*$.1^5 - 102*$.1^4 + 9*$.1^3 + 247*$.1^2 + 220*$.1 + 52[] 302,1,2,x + 1,3,x - 2,5,x - 2,7,x - 4,11,x + 4,13,x[] 302,2,2,x - 1,3,x + 1,5,x + 4,7,x + 2,11,x - 2,13,x + 6[] 302,3,2,x - 1,3,x + 3,5,x,7,x + 2,11,x + 6,13,x + 2[] 302,4,2,x^2 + 2*x + 1,3,x^2 + 2*x - 1,5,x^2,7,x^2 + 4*x - 4,11,x^2 - 4*x - 4,13,x^2 + 8*x + 8[] 302,5,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 10*x^2 - 6*x + 9,5,x^4 + 4*x^3 - 8*x^2 - 44*x - 36,7,x^4 - 2*x^3 - 8*x^2 + 8*x + 4,11,x^4 - 36*x^2 + 4*x + 12,13,x^4 - 14*x^3 + 64*x^2 - 104*x + 36[] 302,6,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 4*x^2 + 8*x - 1,5,x^4 - 8*x^2 - 4*x + 4,7,x^4 - 6*x^3 + 4*x^2 + 24*x - 28,11,x^4 - 20*x^2 - 4*x + 52,13,x^4 - 6*x^3 - 12*x^2 + 64*x - 52[] 303,1,2,x,3,x - 1,5,x + 3,7,x,11,x + 2,13,x + 3[] 303,2,2,x + 2,3,x - 1,5,x + 1,7,x + 2,11,x + 6,13,x - 1[] 303,3,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 1,7,x^2 + 4*x + 2,11,x^2 - 4*x + 4,13,x^2 + 6*x + 1[] 303,4,2,x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 6,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 6*x^5 + x^4 + 34*x^3 - 16*x^2 - 32*x + 16,7,x^6 - 18*x^4 + 4*x^3 + 80*x^2 - 32*x - 32,11,x^6 - 10*x^5 + 5*x^4 + 144*x^3 - 125*x^2 - 388*x - 164,13,x^6 - 44*x^4 + 14*x^3 + 444*x^2 - 492*x + 53[] 303,5,2,x^7 - 12*x^5 + 40*x^3 + x^2 - 24*x - 4,3,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,5,x^7 - 6*x^6 - 15*x^5 + 132*x^4 - 20*x^3 - 768*x^2 + 688*x + 544,7,x^7 - 6*x^6 - 20*x^5 + 136*x^4 + 112*x^3 - 832*x^2 - 192*x + 1024,11,x^7 + 10*x^6 + x^5 - 312*x^4 - 1293*x^3 - 1600*x^2 + 700*x + 2000,13,x^7 - 10*x^6 + 210*x^4 - 396*x^3 - 104*x^2 + 425*x - 62[] 304,1,2,x,3,x + 1,5,x,7,x + 3,11,x + 2,13,x - 1[] 304,2,2,x,3,x - 2,5,x + 1,7,x - 3,11,x - 3,13,x + 4[] 304,3,2,x,3,x + 1,5,x,7,x - 1,11,x - 6,13,x - 5[] 304,4,2,x,3,x - 2,5,x - 3,7,x - 1,11,x + 3,13,x + 4[] 304,5,2,x,3,x - 1,5,x + 4,7,x + 3,11,x + 2,13,x + 1[] 304,6,2,x,3,x + 2,5,x + 1,7,x - 3,11,x + 5,13,x + 4[] 304,7,2,x^3,3,x^3 + x^2 - 10*x - 8,5,x^3 - x^2 - 10*x + 8,7,x^3 + 4*x^2 - 5*x - 16,11,x^3 - 5*x^2 - 2*x + 8,13,x^3 - 5*x^2 - 2*x + 8[] 305,1,2,x^3 - 3*x + 1,3,x^3 - 3*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 6*x^2 + 3*x - 19,11,x^3 + 6*x^2 + 3*x - 1,13,x^3 + 3*x^2 - 36*x - 127[] 305,2,2,x^4 + 3*x^3 - x^2 - 6*x - 1,3,x^4 + 6*x^3 + 9*x^2 - x - 4,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 10*x^3 + 33*x^2 + 41*x + 16,11,x^4 + 2*x^3 - 23*x^2 - 53*x + 32,13,x^4 + x^3 - 8*x^2 + 5*x + 2[] 305,3,2,x^7 + 2*x^6 - 11*x^5 - 19*x^4 + 35*x^3 + 48*x^2 - 25*x - 27,3,x^7 - 15*x^5 + 3*x^4 + 64*x^3 - 8*x^2 - 76*x - 20,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 12*x^6 + 33*x^5 + 101*x^4 - 568*x^3 + 472*x^2 + 464*x + 80,11,x^7 - 2*x^6 - 27*x^5 + 15*x^4 + 220*x^3 + 152*x^2 - 148*x + 12,13,x^7 - 9*x^6 + 12*x^5 + 73*x^4 - 128*x^3 - 200*x^2 + 192*x + 144[] 305,4,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 19*x^3 - 36*x^2 + 5*x + 1,3,x^7 - 6*x^6 + 5*x^5 + 23*x^4 - 28*x^3 - 24*x^2 + 24*x + 8,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,7,x^7 - 8*x^6 + 7*x^5 + 65*x^4 - 96*x^3 - 120*x^2 + 144*x + 16,11,x^7 + 6*x^6 - 25*x^5 - 153*x^4 + 100*x^3 + 840*x^2 + 216*x + 8,13,x^7 - 5*x^6 - 46*x^5 + 289*x^4 + 176*x^3 - 3560*x^2 + 6432*x - 2864[] 306,1,2,x + 1,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[] 306,2,2,x + 1,3,x,5,x,7,x + 4,11,x + 6,13,x - 2[] 306,3,2,x - 1,3,x,5,x,7,x - 2,11,x,13,x - 2[] 306,4,2,x - 1,3,x,5,x - 4,7,x + 2,11,x,13,x + 6[] 306,5,2,x^2 + 2*x + 1,3,x^2,5,x^2 - 6,7,x^2 - 4*x - 2,11,x^2 - 24,13,x^2 - 4*x - 20[] 306,6,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 6,7,x^2 - 4*x - 2,11,x^2 - 24,13,x^2 - 4*x - 20[] Total time: 17.329 seconds, Total memory usage: 5.70MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 11:40:11 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [306..312] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 11:39:48 on modular [Seed = 2472830744] ------------------------------------- 306,1,2,$.1 + 1,3,$.1,5,$.1 - 2,7,$.1,11,$.1 - 4,13,$.1 + 2[] 306,2,2,$.1 + 1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 2[] 306,3,2,$.1 - 1,3,$.1,5,$.1,7,$.1 - 2,11,$.1,13,$.1 - 2[] 306,4,2,$.1 - 1,3,$.1,5,$.1 - 4,7,$.1 + 2,11,$.1,13,$.1 + 6[] 306,5,2,$.1^2 + 2*$.1 + 1,3,$.1^2,5,$.1^2 - 6,7,$.1^2 - 4*$.1 - 2,11,$.1^2 - 24,13,$.1^2 - 4*$.1 - 20[] 306,6,2,$.1^2 - 2*$.1 + 1,3,$.1^2,5,$.1^2 - 6,7,$.1^2 - 4*$.1 - 2,11,$.1^2 - 24,13,$.1^2 - 4*$.1 - 20[] 307,1,2,x,3,x,5,x - 4,7,x,11,x - 3,13,x - 6[] 307,2,2,x - 1,3,x - 2,5,x,7,x - 3,11,x - 5,13,x[] 307,3,2,x - 2,3,x,5,x - 2,7,x - 3,11,x + 4,13,x[] 307,4,2,x - 2,3,x - 2,5,x,7,x + 3,11,x - 1,13,x - 6[] 307,5,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 - 6*x + 9,7,x^2 - 5*x + 3,11,x^2 - 7*x + 9,13,x^2 + 4*x - 9[] 307,6,2,x^9 - 3*x^8 - 11*x^7 + 30*x^6 + 46*x^5 - 87*x^4 - 91*x^3 + 50*x^2 + 62*x + 13,3,x^9 - x^8 - 21*x^7 + 11*x^6 + 162*x^5 - 10*x^4 - 525*x^3 - 169*x^2 + 547*x + 286,5,x^9 - 5*x^8 - 16*x^7 + 83*x^6 + 116*x^5 - 450*x^4 - 482*x^3 + 765*x^2 + 735*x - 100,7,x^9 + 5*x^8 - 17*x^7 - 99*x^6 - 7*x^5 + 432*x^4 + 428*x^3 - 318*x^2 - 558*x - 169,11,x^9 - 47*x^7 - 27*x^6 + 568*x^5 + 650*x^4 - 842*x^3 - 1219*x^2 - 269*x + 5,13,x^9 + 3*x^8 - 49*x^7 - 26*x^6 + 690*x^5 - 968*x^4 - 798*x^3 + 2165*x^2 - 1263*x + 220[] 307,7,2,x^10 + 7*x^9 + 10*x^8 - 28*x^7 - 73*x^6 + 16*x^5 + 128*x^4 + 26*x^3 - 69*x^2 - 18*x - 1,3,x^10 + 4*x^9 - 7*x^8 - 41*x^7 - 8*x^6 + 107*x^5 + 79*x^4 - 50*x^3 - 35*x^2 + 10*x + 1,5,x^10 + 15*x^9 + 83*x^8 + 184*x^7 - 637*x^5 - 732*x^4 + 223*x^3 + 495*x^2 - 45*x + 1,7,x^10 + 3*x^9 - 38*x^8 - 93*x^7 + 522*x^6 + 968*x^5 - 3021*x^4 - 4037*x^3 + 6345*x^2 + 5886*x - 2403,11,x^10 + 10*x^9 - 270*x^7 - 716*x^6 + 1135*x^5 + 7015*x^4 + 9900*x^3 + 4990*x^2 + 171*x - 361,13,x^10 + 11*x^9 - 30*x^8 - 623*x^7 - 559*x^6 + 10436*x^5 + 22728*x^4 - 41589*x^3 - 148643*x^2 - 84705*x + 31181[] 308,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 1,13,x + 4[] 308,2,2,x^2,3,x^2 - 6,5,x^2 - 4*x + 4,7,x^2 + 2*x + 1,11,x^2 + 2*x + 1,13,x^2 - 4*x - 2[] 308,3,2,x^3,3,x^3 + x^2 - 6*x - 2,5,x^3 + x^2 - 16*x - 12,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 12*x^2 + 34*x + 8[] 309,1,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 2,13,x + 5[] 309,2,2,x^3 - x^2 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - x^2 - 3*x + 1,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 3*x^2 - 13*x - 31[] 309,3,2,x^5 + 2*x^4 - 4*x^3 - 6*x^2 + 4*x + 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 5*x^4 - 6*x^3 - 56*x^2 - 64*x - 16,7,x^5 + 2*x^4 - 27*x^3 - 42*x^2 + 129*x + 134,11,x^5 + 12*x^4 + 36*x^3 - 16*x^2 - 112*x + 32,13,x^5 - x^4 - 51*x^3 + 25*x^2 + 375*x + 9[] 309,4,2,x^8 + x^7 - 13*x^6 - 11*x^5 + 52*x^4 + 35*x^3 - 59*x^2 - 27*x + 1,3,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,5,x^8 + x^7 - 27*x^6 - 17*x^5 + 196*x^4 - 4*x^3 - 432*x^2 + 304*x - 32,7,x^8 - 6*x^7 - 19*x^6 + 162*x^5 - 55*x^4 - 1022*x^3 + 1544*x^2 - 220*x - 32,11,x^8 - 6*x^7 - 32*x^6 + 228*x^5 + 88*x^4 - 2144*x^3 + 2880*x^2 - 64*x - 256,13,x^8 - 9*x^7 - 18*x^6 + 354*x^5 - 798*x^4 - 620*x^3 + 2881*x^2 - 1377*x + 106[] 310,1,2,x - 1,3,x - 2,5,x + 1,7,x,11,x - 2,13,x[] 310,2,2,x - 1,3,x + 2,5,x + 1,7,x + 4,11,x,13,x + 4[] 310,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 12,11,x^2 + 2*x - 2,13,x^2 + 6*x + 6[] 310,4,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 4*x - 2,13,x^2 - 4*x - 2[] 310,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 16*x + 16,11,x^3 - 28*x - 52,13,x^3 + 8*x^2 + 16*x + 4[] 311,1,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 2*x^3 - x^2 - 2*x + 1,5,x^4 + x^3 - 3*x^2 - x + 1,7,x^4 + 4*x^3 - 13*x - 11,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 6*x^3 + 10*x^2 + 3*x - 1[] 311,2,2,x^22 - 2*x^21 - 35*x^20 + 70*x^19 + 517*x^18 - 1033*x^17 - 4195*x^16 + 8357*x^15 + 20417*x^14 - 40403*x^13 - 61287*x^12 + 119701*x^11 + 113017*x^10 - 215615*x^9 - 124399*x^8 + 228609*x^7 + 76453*x^6 - 133295*x^5 - 23503*x^4 + 36742*x^3 + 3587*x^2 - 3200*x - 473,3,x^22 - 2*x^21 - 50*x^20 + 100*x^19 + 1054*x^18 - 2090*x^17 - 12220*x^16 + 23710*x^15 + 85436*x^14 - 158732*x^13 - 372823*x^12 + 638428*x^11 + 1021312*x^10 - 1499190*x^9 - 1731753*x^8 + 1880136*x^7 + 1732827*x^6 - 997894*x^5 - 846784*x^4 + 56220*x^3 + 63398*x^2 + 2766*x - 581,5,x^22 - x^21 - 80*x^20 + 80*x^19 + 2734*x^18 - 2781*x^17 - 52218*x^16 + 54799*x^15 + 611842*x^14 - 669446*x^13 - 4539481*x^12 + 5216024*x^11 + 21207760*x^10 - 25736951*x^9 - 59717725*x^8 + 77226576*x^7 + 90576343*x^6 - 128165703*x^5 - 52348978*x^4 + 91996538*x^3 - 8405884*x^2 - 5816731*x - 405143,7,x^22 - 8*x^21 - 77*x^20 + 751*x^19 + 2057*x^18 - 29039*x^17 - 15212*x^16 + 602096*x^15 - 293191*x^14 - 7369509*x^13 + 7091610*x^12 + 56125407*x^11 - 61368055*x^10 - 277132225*x^9 + 260009583*x^8 + 899877452*x^7 - 487207047*x^6 - 1807798930*x^5 + 21068313*x^4 + 1718049915*x^3 + 879292937*x^2 + 12987869*x - 24640261,11,x^22 - 6*x^21 - 158*x^20 + 1020*x^19 + 10177*x^18 - 72814*x^17 - 340516*x^16 + 2847992*x^15 + 6126512*x^14 - 66931488*x^13 - 50088768*x^12 + 977963776*x^11 - 74690304*x^10 - 8923385856*x^9 + 4847145984*x^8 + 50054287360*x^7 - 36928937984*x^6 - 166727901184*x^5 + 110340030464*x^4 + 310715056128*x^3 - 85162852352*x^2 - 275443089408*x - 86332669952,13,x^22 - 12*x^21 - 125*x^20 + 1895*x^19 + 5527*x^18 - 128259*x^17 - 57828*x^16 + 4864982*x^15 - 3711305*x^14 - 113354343*x^13 + 167980932*x^12 + 1669526673*x^11 - 3271781053*x^10 - 15371842897*x^9 + 35453664037*x^8 + 83993883166*x^7 - 216607237743*x^6 - 242692713398*x^5 + 680115803253*x^4 + 290042852541*x^3 - 834033148105*x^2 - 92013030575*x + 78103127827[] 312,1,2,x,3,x + 1,5,x,7,x + 4,11,x + 2,13,x + 1[] 312,2,2,x,3,x + 1,5,x + 2,7,x - 4,11,x,13,x - 1[] 312,3,2,x,3,x - 1,5,x,7,x,11,x - 6,13,x + 1[] 312,4,2,x,3,x + 1,5,x - 4,7,x,11,x + 2,13,x + 1[] 312,5,2,x,3,x - 1,5,x + 4,7,x + 4,11,x + 2,13,x + 1[] 312,6,2,x,3,x - 1,5,x - 2,7,x,11,x,13,x - 1[] Total time: 21.170 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 11:49:21 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [312..318] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 11:48:59 on modular [Seed = 3159051800] ------------------------------------- 312,1,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[] 312,2,2,$.1,3,$.1 + 1,5,$.1 + 2,7,$.1 - 4,11,$.1,13,$.1 - 1[] 312,3,2,$.1,3,$.1 - 1,5,$.1,7,$.1,11,$.1 - 6,13,$.1 + 1[] 312,4,2,$.1,3,$.1 + 1,5,$.1 - 4,7,$.1,11,$.1 + 2,13,$.1 + 1[] 312,5,2,$.1,3,$.1 - 1,5,$.1 + 4,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[] 312,6,2,$.1,3,$.1 - 1,5,$.1 - 2,7,$.1,11,$.1,13,$.1 - 1[] 313,1,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 3*x + 1,7,x^2 - 2*x - 4,11,x^2 - 5,13,x^2 - 7*x + 1[] 313,2,2,x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 62*x^6 + 190*x^5 + 196*x^4 - 76*x^3 - 122*x^2 + 2*x + 17,3,x^11 + 8*x^10 + 13*x^9 - 43*x^8 - 138*x^7 - 31*x^6 + 171*x^5 + 33*x^4 - 90*x^3 + 18*x^2 + 4*x - 1,5,x^11 + 6*x^10 - 13*x^9 - 135*x^8 - 82*x^7 + 822*x^6 + 1216*x^5 - 1314*x^4 - 3151*x^3 - 661*x^2 + 1307*x + 577,7,x^11 + 14*x^10 + 51*x^9 - 111*x^8 - 1036*x^7 - 1273*x^6 + 3469*x^5 + 8394*x^4 + 1303*x^3 - 8825*x^2 - 7006*x - 1532,11,x^11 + 11*x^10 - 9*x^9 - 464*x^8 - 1090*x^7 + 4831*x^6 + 21347*x^5 + 7358*x^4 - 75753*x^3 - 132533*x^2 - 81996*x - 17107,13,x^11 + 7*x^10 - 60*x^9 - 429*x^8 + 1344*x^7 + 9070*x^6 - 15848*x^5 - 78846*x^4 + 106546*x^3 + 225219*x^2 - 305054*x + 84043[] 313,3,2,x^12 - 6*x^11 - 2*x^10 + 69*x^9 - 68*x^8 - 268*x^7 + 399*x^6 + 368*x^5 - 701*x^4 - 57*x^3 + 262*x^2 - 22*x - 19,3,x^12 - x^11 - 23*x^10 + 21*x^9 + 188*x^8 - 152*x^7 - 657*x^6 + 438*x^5 + 945*x^4 - 469*x^3 - 416*x^2 + 112*x + 32,5,x^12 + x^11 - 33*x^10 - 27*x^9 + 346*x^8 + 149*x^7 - 1349*x^6 - 40*x^5 + 1388*x^4 + 101*x^3 - 406*x^2 - 124*x - 8,7,x^12 - 6*x^11 - 19*x^10 + 177*x^9 - 90*x^8 - 1449*x^7 + 2931*x^6 + 1340*x^5 - 9553*x^4 + 10497*x^3 - 4166*x^2 + 250*x + 106,11,x^12 - 9*x^11 - 20*x^10 + 343*x^9 - 218*x^8 - 3962*x^7 + 4665*x^6 + 19396*x^5 - 21956*x^4 - 43205*x^3 + 29428*x^2 + 40512*x + 928,13,x^12 + 8*x^11 - 35*x^10 - 382*x^9 + 251*x^8 + 6461*x^7 + 1748*x^6 - 49207*x^5 - 19779*x^4 + 172081*x^3 + 17354*x^2 - 230320*x + 79108[] 314,1,2,x + 1,3,x,5,x,7,x + 3,11,x + 2,13,x + 1[] 314,2,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 3*x^5 - 9*x^4 + 26*x^3 + 20*x^2 - 43*x - 25,5,x^6 - x^5 - 23*x^4 + 18*x^3 + 112*x^2 - 123*x - 3,7,x^6 - 3*x^5 - 27*x^4 + 102*x^3 + 98*x^2 - 701*x + 649,11,x^6 - 9*x^5 - 11*x^4 + 282*x^3 - 520*x^2 - 1137*x + 2793,13,x^6 - 4*x^5 - 40*x^4 + 192*x^3 + 64*x^2 - 672*x - 320[] 314,3,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 + x^6 - 17*x^5 - 6*x^4 + 84*x^3 - 19*x^2 - 73*x + 4,5,x^7 - 3*x^6 - 19*x^5 + 58*x^4 + 80*x^3 - 237*x^2 - 115*x + 232,7,x^7 - 4*x^6 - 24*x^5 + 87*x^4 + 136*x^3 - 425*x^2 + 126*x + 5,11,x^7 + x^6 - 61*x^5 + 988*x^3 - 913*x^2 - 989*x + 90,13,x^7 - 7*x^6 - 44*x^5 + 344*x^4 + 464*x^3 - 4928*x^2 + 352*x + 16832[] 315,1,2,x + 1,3,x,5,x + 1,7,x - 1,11,x,13,x + 6[] 315,2,2,x,3,x,5,x - 1,7,x - 1,11,x - 3,13,x - 5[] 315,3,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 + 4*x - 4,13,x^2 + 4*x - 4[] 315,4,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 4*x - 4,13,x^2 + 4*x - 4[] 315,5,2,x^2 - x - 4,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 + x - 4,13,x^2 - 5*x + 2[] 315,6,2,x^2 - 5,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 4*x - 16,13,x^2 - 20[] 316,1,2,x,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 1[] 316,2,2,x,3,x + 3,5,x - 1,7,x - 1,11,x + 6,13,x + 1[] 316,3,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 3*x - 1,7,x^2,11,x^2 - 3*x - 1,13,x^2 - x - 29[] 316,4,2,x^2,3,x^2,5,x^2 + 5*x + 3,7,x^2 + 2*x - 12,11,x^2 + 5*x + 3,13,x^2 + 3*x - 1[] 317,1,2,x^11 + 3*x^10 - 10*x^9 - 32*x^8 + 31*x^7 + 109*x^6 - 42*x^5 - 147*x^4 + 35*x^3 + 68*x^2 - 19*x - 1,3,x^11 + 11*x^10 + 37*x^9 - x^8 - 239*x^7 - 350*x^6 + 238*x^5 + 755*x^4 + 211*x^3 - 383*x^2 - 252*x - 37,5,x^11 + 4*x^10 - 22*x^9 - 103*x^8 + 78*x^7 + 628*x^6 + 55*x^5 - 1302*x^4 - 253*x^3 + 973*x^2 + 48*x - 144,7,x^11 + 20*x^10 + 147*x^9 + 403*x^8 - 427*x^7 - 4935*x^6 - 9052*x^5 + 1349*x^4 + 21886*x^3 + 24083*x^2 + 8658*x + 324,11,x^11 + 10*x^10 - 19*x^9 - 466*x^8 - 729*x^7 + 6130*x^6 + 16960*x^5 - 24515*x^4 - 94320*x^3 + 27939*x^2 + 142806*x - 55628,13,x^11 + 16*x^10 + 35*x^9 - 700*x^8 - 4497*x^7 - 2129*x^6 + 49343*x^5 + 107373*x^4 - 116494*x^3 - 489295*x^2 - 146956*x + 342164[] 317,2,2,x^15 - x^14 - 22*x^13 + 22*x^12 + 188*x^11 - 184*x^10 - 786*x^9 + 723*x^8 + 1666*x^7 - 1315*x^6 - 1715*x^5 + 910*x^4 + 829*x^3 - 168*x^2 - 129*x + 1,3,x^15 - 11*x^14 + 30*x^13 + 84*x^12 - 549*x^11 + 414*x^10 + 2378*x^9 - 4600*x^8 - 1888*x^7 + 10118*x^6 - 3013*x^5 - 8337*x^4 + 4287*x^3 + 2636*x^2 - 1282*x - 251,5,x^15 - 2*x^14 - 40*x^13 + 81*x^12 + 594*x^11 - 1222*x^10 - 4105*x^9 + 8538*x^8 + 13937*x^7 - 28221*x^6 - 24938*x^5 + 43708*x^4 + 24072*x^3 - 25832*x^2 - 10832*x + 80,7,x^15 - 20*x^14 + 139*x^13 - 213*x^12 - 2063*x^11 + 10345*x^10 - 5644*x^9 - 69675*x^8 + 158086*x^7 + 47475*x^6 - 475434*x^5 + 288528*x^4 + 405976*x^3 - 373400*x^2 - 23248*x + 2704,11,x^15 - 6*x^14 - 67*x^13 + 382*x^12 + 1823*x^11 - 9214*x^10 - 26096*x^9 + 105977*x^8 + 202604*x^7 - 602465*x^6 - 756834*x^5 + 1659924*x^4 + 1044856*x^3 - 1851192*x^2 - 19776*x + 266288,13,x^15 - 14*x^14 + 11*x^13 + 648*x^12 - 2745*x^11 - 5247*x^10 + 52647*x^9 - 69155*x^8 - 196166*x^7 + 590465*x^6 - 229832*x^5 - 847068*x^4 + 1214792*x^3 - 646464*x^2 + 152304*x - 13232[] 318,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x + 1,13,x + 2[] 318,2,2,x + 1,3,x + 1,5,x - 4,7,x - 1,11,x + 1,13,x + 4[] 318,3,2,x + 1,3,x - 1,5,x,7,x - 5,11,x + 3,13,x + 4[] 318,4,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 5,13,x[] 318,5,2,x - 1,3,x + 1,5,x + 3,7,x + 4,11,x + 5,13,x + 2[] 318,6,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - x - 10,7,x^2,11,x^2 - 3*x - 8,13,x^2 - 12*x + 36[] 318,7,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 + 2*x + 1,13,x^2 + 2*x - 16[] Total time: 21.840 seconds, Total memory usage: 6.58MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 11:57:21 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [318..324] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 11:56:59 on modular [Seed = 2773636385] ------------------------------------- 318,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1,11,$.1 + 1,13,$.1 + 2[] 318,2,2,$.1 + 1,3,$.1 + 1,5,$.1 - 4,7,$.1 - 1,11,$.1 + 1,13,$.1 + 4[] 318,3,2,$.1 + 1,3,$.1 - 1,5,$.1,7,$.1 - 5,11,$.1 + 3,13,$.1 + 4[] 318,4,2,$.1 - 1,3,$.1 + 1,5,$.1,7,$.1 - 1,11,$.1 - 5,13,$.1[] 318,5,2,$.1 - 1,3,$.1 + 1,5,$.1 + 3,7,$.1 + 4,11,$.1 + 5,13,$.1 + 2[] 318,6,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2*$.1 + 1,5,$.1^2 - $.1 - 10,7,$.1^2,11,$.1^2 - 3*$.1 - 8,13,$.1^2 - 12*$.1 + 36[] 318,7,2,$.1^2 - 2*$.1 + 1,3,$.1^2 - 2*$.1 + 1,5,$.1^2 - $.1 - 4,7,$.1^2 - $.1 - 4,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 2*$.1 - 16[] 319,1,2,x - 2,3,x + 3,5,x - 1,7,x - 4,11,x + 1,13,x - 6[] 319,2,2,x^3 - 3*x - 1,3,x^3 - 3*x + 1,5,x^3 + 6*x^2 + 3*x - 19,7,x^3 + 3*x^2 - 9*x - 19,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 6*x^2 + 3*x - 19[] 319,3,2,x^4 + 2*x^3 - 3*x^2 - 3*x + 2,3,x^4 + 3*x^3 - x^2 - 6*x - 1,5,x^4 + 5*x^3 + 5*x^2 - 2*x - 1,7,x^4 - x^3 - 9*x^2 + 9*x + 8,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 2*x^3 - 29*x^2 + 27*x + 46[] 319,4,2,x^7 - 3*x^6 - 4*x^5 + 15*x^4 + x^3 - 14*x^2 + 1,3,x^7 - 17*x^5 + 3*x^4 + 78*x^3 - 8*x^2 - 96*x + 16,5,x^7 - 4*x^6 - 14*x^5 + 59*x^4 + 36*x^3 - 225*x^2 + 81*x + 81,7,x^7 - x^6 - 25*x^5 + 9*x^4 + 136*x^3 - 56*x^2 - 152*x + 16,11,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,13,x^7 - 51*x^5 + 57*x^4 + 440*x^3 - 768*x^2 - 152*x + 464[] 319,5,2,x^8 - 13*x^6 - x^5 + 50*x^4 + 7*x^3 - 54*x^2 - 5*x + 1,3,x^8 - 4*x^7 - 11*x^6 + 55*x^5 + 10*x^4 - 184*x^3 + 80*x^2 + 112*x - 64,5,x^8 - 10*x^7 + 18*x^6 + 107*x^5 - 406*x^4 + 115*x^3 + 887*x^2 - 641*x - 94,7,x^8 + 7*x^7 - 13*x^6 - 155*x^5 - 128*x^4 + 416*x^3 + 168*x^2 - 432*x + 128,11,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,13,x^8 + 4*x^7 - 43*x^6 - 193*x^5 + 522*x^4 + 3000*x^3 - 520*x^2 - 15168*x - 15520[] 320,1,2,x,3,x,5,x + 1,7,x + 4,11,x + 4,13,x - 2[] 320,2,2,x,3,x - 2,5,x - 1,7,x - 2,11,x,13,x + 2[] 320,3,2,x,3,x - 2,5,x - 1,7,x + 2,11,x - 4,13,x - 6[] 320,4,2,x,3,x + 2,5,x - 1,7,x - 2,11,x + 4,13,x - 6[] 320,5,2,x,3,x,5,x + 1,7,x - 4,11,x - 4,13,x - 2[] 320,6,2,x,3,x + 2,5,x - 1,7,x + 2,11,x,13,x + 2[] 320,7,2,x^2,3,x^2 - 8,5,x^2 + 2*x + 1,7,x^2 - 8,11,x^2 - 32,13,x^2 - 4*x + 4[] 321,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 + 6*x + 4,13,x^2 + 2*x + 1[] 321,2,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 6*x + 9,7,x^2 + 2*x - 4,11,x^2 + 4*x + 4,13,x^2 + 2*x + 1[] 321,3,2,x^6 - 3*x^5 - 5*x^4 + 18*x^3 + x^2 - 19*x + 3,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 6*x^5 + 2*x^4 + 28*x^3 - 10*x^2 - 16*x - 3,7,x^6 - 15*x^4 + 18*x^3 + 13*x^2 - 14*x - 4,11,x^6 - 6*x^5 - 21*x^4 + 138*x^3 - 7*x^2 - 632*x + 636,13,x^6 + 8*x^5 - 4*x^4 - 122*x^3 - 20*x^2 + 500*x - 359[] 321,4,2,x^7 - 14*x^5 - x^4 + 55*x^3 + 8*x^2 - 46*x - 19,3,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,5,x^7 + 8*x^6 + 6*x^5 - 76*x^4 - 102*x^3 + 240*x^2 + 225*x - 250,7,x^7 - 6*x^6 - 15*x^5 + 124*x^4 + 33*x^3 - 788*x^2 + 188*x + 1424,11,x^7 - 4*x^6 - 33*x^5 + 112*x^4 + 277*x^3 - 610*x^2 - 556*x + 976,13,x^7 - 6*x^6 - 20*x^5 + 94*x^4 + 152*x^3 - 276*x^2 - 351*x - 94[] 322,1,2,x + 1,3,x - 2,5,x,7,x - 1,11,x - 4,13,x[] 322,2,2,x + 1,3,x,5,x + 2,7,x - 1,11,x + 4,13,x - 4[] 322,3,2,x - 1,3,x + 2,5,x + 2,7,x + 1,11,x + 2,13,x + 4[] 322,4,2,x - 1,3,x - 2,5,x + 2,7,x - 1,11,x - 6,13,x + 4[] 322,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x - 4,7,x^2 + 2*x + 1,11,x^2,13,x^2 + 4*x - 16[] 322,6,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 2*x + 1,11,x^2 - 12,13,x^2 - 4*x - 8[] 322,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 6*x + 8,5,x^3 - 4*x^2 - 2*x + 4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 - 12*x - 16,13,x^3 - 2*x^2 - 16*x + 16[] 323,1,2,x,3,x - 3,5,x + 2,7,x - 4,11,x + 2,13,x - 6[] 323,2,2,x^2 + x - 4,3,x^2 - x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 16,11,x^2 + 4*x + 4,13,x^2 - 4*x + 4[] 323,3,2,x^4 - 6*x^2 - x + 7,3,x^4 + x^3 - 8*x^2 - 10*x - 3,5,x^4 + 7*x^3 + 14*x^2 + 6*x - 1,7,x^4 + 11*x^3 + 41*x^2 + 57*x + 19,11,x^4 + 2*x^3 - 18*x^2 + 7*x + 27,13,x^4 + 10*x^3 + 15*x^2 - 66*x - 71[] 323,4,2,x^5 + 3*x^4 - 2*x^3 - 7*x^2 + 2*x + 1,3,x^5 + 3*x^4 - 4*x^3 - 8*x^2 + 9*x - 2,5,x^5 + 3*x^4 - 6*x^3 - 8*x^2 + x + 2,7,x^5 + 5*x^4 - 3*x^3 - 31*x^2 - 23*x + 8,11,x^5 - 36*x^3 + 31*x^2 + 265*x - 304,13,x^5 + 20*x^4 + 153*x^3 + 558*x^2 + 967*x + 634[] 323,5,2,x^6 - 2*x^5 - 9*x^4 + 15*x^3 + 23*x^2 - 23*x - 21,3,x^6 + 3*x^5 - 6*x^4 - 14*x^3 + 11*x^2 + 6*x - 4,5,x^6 + x^5 - 24*x^4 - 20*x^3 + 149*x^2 + 104*x - 84,7,x^6 - 5*x^5 - x^4 + 27*x^3 - 9*x^2 - 26*x - 4,11,x^6 - 2*x^5 - 40*x^4 + 15*x^3 + 347*x^2 + 146*x + 12,13,x^6 - 14*x^5 + 43*x^4 + 146*x^3 - 743*x^2 - 268*x + 2852[] 323,6,2,x^7 - x^6 - 10*x^5 + 9*x^4 + 26*x^3 - 19*x^2 - 12*x + 8,3,x^7 - 3*x^6 - 9*x^5 + 29*x^4 + 17*x^3 - 68*x^2 + 7*x + 8,5,x^7 - 7*x^6 + 4*x^5 + 54*x^4 - 73*x^3 - 90*x^2 + 124*x - 8,7,x^7 - x^6 - 27*x^5 + 29*x^4 + 227*x^3 - 256*x^2 - 568*x + 608,11,x^7 - 2*x^6 - 46*x^5 + 7*x^4 + 559*x^3 + 592*x^2 - 516*x - 288,13,x^7 - 20*x^6 + 141*x^5 - 342*x^4 - 393*x^3 + 2734*x^2 - 1876*x - 2344[] 324,1,2,x,3,x,5,x - 3,7,x + 1,11,x - 3,13,x + 1[] 324,2,2,x,3,x,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 324,3,2,x,3,x,5,x + 3,7,x - 2,11,x - 6,13,x - 5[] 324,4,2,x,3,x,5,x + 3,7,x + 1,11,x + 3,13,x + 1[] Total time: 21.039 seconds, Total memory usage: 6.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:04:28 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [324..330] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 12:04:05 on modular [Seed = 1921359017] ------------------------------------- 324,1,2,$.1,3,$.1,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 + 1[] 324,2,2,$.1,3,$.1,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[] 324,3,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 2,11,$.1 - 6,13,$.1 - 5[] 324,4,2,$.1,3,$.1,5,$.1 + 3,7,$.1 + 1,11,$.1 + 3,13,$.1 + 1[] 325,1,2,x,3,x + 1,5,x,7,x - 4,11,x + 6,13,x + 1[] 325,2,2,x - 1,3,x - 2,5,x,7,x - 4,11,x - 2,13,x - 1[] 325,3,2,x + 2,3,x + 1,5,x,7,x + 2,11,x - 2,13,x - 1[] 325,4,2,x - 2,3,x - 1,5,x,7,x - 2,11,x - 2,13,x + 1[] 325,5,2,x,3,x - 1,5,x,7,x + 4,11,x + 6,13,x - 1[] 325,6,2,x^2 - 3,3,x^2 + 2*x - 2,5,x^2,7,x^2 + 4*x + 4,11,x^2 + 6*x + 6,13,x^2 + 2*x + 1[] 325,7,2,x^2 - 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 - 2*x - 1,11,x^2 - 10*x + 23,13,x^2 - 2*x + 1[] 325,8,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2,7,x^2 + 4*x - 4,11,x^2 - 4*x + 2,13,x^2 - 2*x + 1[] 325,9,2,x^2 + 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 + 2*x - 1,11,x^2 - 10*x + 23,13,x^2 + 2*x + 1[] 325,10,2,x^3 - 3*x^2 - x + 5,3,x^3 - 4*x^2 + 2*x + 2,5,x^3,7,x^3 - 2*x^2 - 4*x + 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 + 3*x^2 + 3*x + 1[] 325,11,2,x^3 + 3*x^2 - x - 5,3,x^3 + 4*x^2 + 2*x - 2,5,x^3,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 - 3*x^2 + 3*x - 1[] 326,1,2,x + 1,3,x,5,x + 1,7,x + 1,11,x,13,x + 5[] 326,2,2,x + 1,3,x + 2,5,x + 3,7,x + 1,11,x,13,x - 5[] 326,3,2,x - 1,3,x + 2,5,x + 1,7,x + 3,11,x + 4,13,x + 1[] 326,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 3*x^4 - 8*x^3 + 27*x^2 - 5*x - 17,5,x^5 - 9*x^4 + 20*x^3 + 19*x^2 - 77*x + 5,7,x^5 - 4*x^4 - 20*x^3 + 64*x^2 + 64*x - 32,11,x^5 + x^4 - 42*x^3 - 35*x^2 + 383*x + 17,13,x^5 - x^4 - 24*x^3 + 17*x^2 + 121*x - 139[] 326,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 5*x^5 + 29*x^3 - 25*x^2 - 35*x + 36,5,x^6 - 13*x^4 + x^3 + 42*x^2 + 4*x - 31,7,x^6 - 5*x^5 - 20*x^4 + 132*x^3 - 144*x^2 + 32,11,x^6 - x^5 - 38*x^4 + 63*x^3 + 351*x^2 - 837*x + 324,13,x^6 + 4*x^5 - 73*x^4 - 289*x^3 + 1230*x^2 + 4306*x - 1891[] 327,1,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 1,13,x + 4[] 327,2,2,x^3 + 3*x^2 - x - 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + x^2 - 3*x - 1,13,x^3 + 2*x^2 - 4*x - 4[] 327,3,2,x^6 - 4*x^5 - 2*x^4 + 20*x^3 - 8*x^2 - 16*x + 1,3,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,5,x^6 - 5*x^5 - 10*x^4 + 68*x^3 - 40*x^2 - 48*x + 32,7,x^6 + 2*x^5 - 18*x^4 - 44*x^3 + 17*x^2 + 42*x - 16,11,x^6 - 7*x^5 + 52*x^3 - 32*x^2 - 80*x + 64,13,x^6 - 6*x^5 - 20*x^4 + 136*x^3 - 80*x^2 - 160*x + 128[] 327,4,2,x^9 - 3*x^8 - 11*x^7 + 35*x^6 + 34*x^5 - 122*x^4 - 29*x^3 + 127*x^2 + 9*x - 5,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 - x^8 - 33*x^7 + 29*x^6 + 324*x^5 - 248*x^4 - 992*x^3 + 640*x^2 + 64*x - 64,7,x^9 - 6*x^8 - 22*x^7 + 192*x^6 - 151*x^5 - 934*x^4 + 1372*x^3 + 940*x^2 - 1920*x + 512,11,x^9 + 5*x^8 - 51*x^7 - 225*x^6 + 732*x^5 + 2840*x^4 - 2160*x^3 - 7552*x^2 + 1792*x + 5696,13,x^9 - 6*x^8 - 52*x^7 + 284*x^6 + 832*x^5 - 3840*x^4 - 3776*x^3 + 12288*x^2 + 2560*x - 7936[] 328,1,2,x,3,x,5,x + 2,7,x + 2,11,x,13,x + 4[] 328,2,2,x,3,x - 2,5,x - 2,7,x + 2,11,x - 2,13,x - 6[] 328,3,2,x^2,3,x^2 - 2*x - 2,5,x^2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2[] 328,4,2,x^3,3,x^3 + 2*x^2 - 6*x - 10,5,x^3 - 2*x^2 - 8*x + 4,7,x^3 - 4*x^2 - 2*x + 2,11,x^3 + 4*x^2 - 2*x - 2,13,x^3 + 2*x^2 - 28*x + 24[] 328,5,2,x^3,3,x^3 + 4*x^2 + 2*x - 2,5,x^3 + 2*x^2 - 8*x + 4,7,x^3 + 2*x^2 - 14*x + 10,11,x^3 + 10*x^2 + 18*x - 34,13,x^3 + 2*x^2 - 12*x - 8[] 329,1,2,x + 1,3,x + 1,5,x - 3,7,x + 1,11,x - 3,13,x + 6[] 329,2,2,x^2 + 2*x + 1,3,x^2 - x - 4,5,x^2 + 3*x - 2,7,x^2 - 2*x + 1,11,x^2 + 7*x + 8,13,x^2 - 4*x + 4[] 329,3,2,x^3 + x^2 - 2*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 + 3*x - 1,13,x^3 - x^2 - 16*x - 13[] 329,4,2,x^3 - x^2 - 5*x + 1,3,x^3 - x^2 - 9*x + 13,5,x^3 + x^2 - 15*x - 25,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 13*x + 23,13,x^3 + 4*x^2 - 4[] 329,5,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 7*x - 7,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 21*x - 7,13,x^3 + 11*x^2 + 38*x + 41[] 329,6,2,x^5 - x^4 - 11*x^3 + 12*x^2 + 28*x - 33,3,x^5 - 2*x^4 - 9*x^3 + 11*x^2 + 16*x - 16,5,x^5 + 4*x^4 - 5*x^3 - 17*x^2 + 20*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 35*x^3 + 139*x^2 + 188*x - 664,13,x^5 - x^4 - 46*x^3 + 39*x^2 + 112*x + 44[] 329,7,2,x^6 - 12*x^4 + 5*x^3 + 36*x^2 - 29*x + 3,3,x^6 - 3*x^5 - 6*x^4 + 17*x^3 + 12*x^2 - 22*x - 11,5,x^6 - 5*x^5 + 23*x^3 - 4*x^2 - 32*x - 9,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 7*x^5 - 8*x^4 + 111*x^3 - 208*x^2 + 136*x - 27,13,x^6 - 5*x^5 - 28*x^4 + 177*x^3 - 92*x^2 - 528*x + 396[] Errors: /home/mfd/gomagma: line 2: 24876 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:05:06 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [324..329] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:04:49 on modular [Seed = 1805419908] ------------------------------------- 324,1,2,$.1,3,$.1,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 + 1[] 324,2,2,$.1,3,$.1,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[] 324,3,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 2,11,$.1 - 6,13,$.1 - 5[] 324,4,2,$.1,3,$.1,5,$.1 + 3,7,$.1 + 1,11,$.1 + 3,13,$.1 + 1[] 325,1,2,x,3,x + 1,5,x,7,x - 4,11,x + 6,13,x + 1[] 325,2,2,x - 1,3,x - 2,5,x,7,x - 4,11,x - 2,13,x - 1[] 325,3,2,x + 2,3,x + 1,5,x,7,x + 2,11,x - 2,13,x - 1[] 325,4,2,x - 2,3,x - 1,5,x,7,x - 2,11,x - 2,13,x + 1[] 325,5,2,x,3,x - 1,5,x,7,x + 4,11,x + 6,13,x - 1[] 325,6,2,x^2 - 3,3,x^2 + 2*x - 2,5,x^2,7,x^2 + 4*x + 4,11,x^2 + 6*x + 6,13,x^2 + 2*x + 1[] 325,7,2,x^2 - 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 - 2*x - 1,11,x^2 - 10*x + 23,13,x^2 - 2*x + 1[] 325,8,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2,7,x^2 + 4*x - 4,11,x^2 - 4*x + 2,13,x^2 - 2*x + 1[] 325,9,2,x^2 + 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 + 2*x - 1,11,x^2 - 10*x + 23,13,x^2 + 2*x + 1[] 325,10,2,x^3 - 3*x^2 - x + 5,3,x^3 - 4*x^2 + 2*x + 2,5,x^3,7,x^3 - 2*x^2 - 4*x + 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 + 3*x^2 + 3*x + 1[] 325,11,2,x^3 + 3*x^2 - x - 5,3,x^3 + 4*x^2 + 2*x - 2,5,x^3,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 - 3*x^2 + 3*x - 1[] 326,1,2,x + 1,3,x,5,x + 1,7,x + 1,11,x,13,x + 5[] 326,2,2,x + 1,3,x + 2,5,x + 3,7,x + 1,11,x,13,x - 5[] 326,3,2,x - 1,3,x + 2,5,x + 1,7,x + 3,11,x + 4,13,x + 1[] 326,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 3*x^4 - 8*x^3 + 27*x^2 - 5*x - 17,5,x^5 - 9*x^4 + 20*x^3 + 19*x^2 - 77*x + 5,7,x^5 - 4*x^4 - 20*x^3 + 64*x^2 + 64*x - 32,11,x^5 + x^4 - 42*x^3 - 35*x^2 + 383*x + 17,13,x^5 - x^4 - 24*x^3 + 17*x^2 + 121*x - 139[] 326,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 5*x^5 + 29*x^3 - 25*x^2 - 35*x + 36,5,x^6 - 13*x^4 + x^3 + 42*x^2 + 4*x - 31,7,x^6 - 5*x^5 - 20*x^4 + 132*x^3 - 144*x^2 + 32,11,x^6 - x^5 - 38*x^4 + 63*x^3 + 351*x^2 - 837*x + 324,13,x^6 + 4*x^5 - 73*x^4 - 289*x^3 + 1230*x^2 + 4306*x - 1891[] 327,1,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 1,13,x + 4[] 327,2,2,x^3 + 3*x^2 - x - 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + x^2 - 3*x - 1,13,x^3 + 2*x^2 - 4*x - 4[] 327,3,2,x^6 - 4*x^5 - 2*x^4 + 20*x^3 - 8*x^2 - 16*x + 1,3,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,5,x^6 - 5*x^5 - 10*x^4 + 68*x^3 - 40*x^2 - 48*x + 32,7,x^6 + 2*x^5 - 18*x^4 - 44*x^3 + 17*x^2 + 42*x - 16,11,x^6 - 7*x^5 + 52*x^3 - 32*x^2 - 80*x + 64,13,x^6 - 6*x^5 - 20*x^4 + 136*x^3 - 80*x^2 - 160*x + 128[] 327,4,2,x^9 - 3*x^8 - 11*x^7 + 35*x^6 + 34*x^5 - 122*x^4 - 29*x^3 + 127*x^2 + 9*x - 5,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 - x^8 - 33*x^7 + 29*x^6 + 324*x^5 - 248*x^4 - 992*x^3 + 640*x^2 + 64*x - 64,7,x^9 - 6*x^8 - 22*x^7 + 192*x^6 - 151*x^5 - 934*x^4 + 1372*x^3 + 940*x^2 - 1920*x + 512,11,x^9 + 5*x^8 - 51*x^7 - 225*x^6 + 732*x^5 + 2840*x^4 - 2160*x^3 - 7552*x^2 + 1792*x + 5696,13,x^9 - 6*x^8 - 52*x^7 + 284*x^6 + 832*x^5 - 3840*x^4 - 3776*x^3 + 12288*x^2 + 2560*x - 7936[] 328,1,2,x,3,x,5,x + 2,7,x + 2,11,x,13,x + 4[] 328,2,2,x,3,x - 2,5,x - 2,7,x + 2,11,x - 2,13,x - 6[] 328,3,2,x^2,3,x^2 - 2*x - 2,5,x^2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2[] 328,4,2,x^3,3,x^3 + 2*x^2 - 6*x - 10,5,x^3 - 2*x^2 - 8*x + 4,7,x^3 - 4*x^2 - 2*x + 2,11,x^3 + 4*x^2 - 2*x - 2,13,x^3 + 2*x^2 - 28*x + 24[] 328,5,2,x^3,3,x^3 + 4*x^2 + 2*x - 2,5,x^3 + 2*x^2 - 8*x + 4,7,x^3 + 2*x^2 - 14*x + 10,11,x^3 + 10*x^2 + 18*x - 34,13,x^3 + 2*x^2 - 12*x - 8[] 329,1,2,x + 1,3,x + 1,5,x - 3,7,x + 1,11,x - 3,13,x + 6[] 329,2,2,x^2 + 2*x + 1,3,x^2 - x - 4,5,x^2 + 3*x - 2,7,x^2 - 2*x + 1,11,x^2 + 7*x + 8,13,x^2 - 4*x + 4[] 329,3,2,x^3 + x^2 - 2*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 + 3*x - 1,13,x^3 - x^2 - 16*x - 13[] 329,4,2,x^3 - x^2 - 5*x + 1,3,x^3 - x^2 - 9*x + 13,5,x^3 + x^2 - 15*x - 25,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 13*x + 23,13,x^3 + 4*x^2 - 4[] 329,5,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 7*x - 7,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 21*x - 7,13,x^3 + 11*x^2 + 38*x + 41[] 329,6,2,x^5 - x^4 - 11*x^3 + 12*x^2 + 28*x - 33,3,x^5 - 2*x^4 - 9*x^3 + 11*x^2 + 16*x - 16,5,x^5 + 4*x^4 - 5*x^3 - 17*x^2 + 20*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 35*x^3 + 139*x^2 + 188*x - 664,13,x^5 - x^4 - 46*x^3 + 39*x^2 + 112*x + 44[] 329,7,2,x^6 - 12*x^4 + 5*x^3 + 36*x^2 - 29*x + 3,3,x^6 - 3*x^5 - 6*x^4 + 17*x^3 + 12*x^2 - 22*x - 11,5,x^6 - 5*x^5 + 23*x^3 - 4*x^2 - 32*x - 9,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 7*x^5 - 8*x^4 + 111*x^3 - 208*x^2 + 136*x - 27,13,x^6 - 5*x^5 - 28*x^4 + 177*x^3 - 92*x^2 - 528*x + 396[] Total time: 16.949 seconds, Total memory usage: 5.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:10:42 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [329..335] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:10:20 on modular [Seed = 367196343] ------------------------------------- 329,1,2,$.1 + 1,3,$.1 + 1,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 + 6[] 329,2,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - $.1 - 4,5,$.1^2 + 3*$.1 - 2,7,$.1^2 - 2*$.1 + 1,11,$.1^2 + 7*$.1 + 8,13,$.1^2 - 4*$.1 + 4[] 329,3,2,$.1^3 + $.1^2 - 2*$.1 - 1,3,$.1^3 + 2*$.1^2 - $.1 - 1,5,$.1^3 + 2*$.1^2 - $.1 - 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 + 3*$.1 - 1,13,$.1^3 - $.1^2 - 16*$.1 - 13[] 329,4,2,$.1^3 - $.1^2 - 5*$.1 + 1,3,$.1^3 - $.1^2 - 9*$.1 + 13,5,$.1^3 + $.1^2 - 15*$.1 - 25,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 - $.1^2 - 13*$.1 + 23,13,$.1^3 + 4*$.1^2 - 4[] 329,5,2,$.1^3 + $.1^2 - 2*$.1 - 1,3,$.1^3 + 4*$.1^2 + 3*$.1 - 1,5,$.1^3 - 7*$.1 - 7,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 21*$.1 - 7,13,$.1^3 + 11*$.1^2 + 38*$.1 + 41[] 329,6,2,$.1^5 - $.1^4 - 11*$.1^3 + 12*$.1^2 + 28*$.1 - 33,3,$.1^5 - 2*$.1^4 - 9*$.1^3 + 11*$.1^2 + 16*$.1 - 16,5,$.1^5 + 4*$.1^4 - 5*$.1^3 - 17*$.1^2 + 20*$.1 - 4,7,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,11,$.1^5 - 4*$.1^4 - 35*$.1^3 + 139*$.1^2 + 188*$.1 - 664,13,$.1^5 - $.1^4 - 46*$.1^3 + 39*$.1^2 + 112*$.1 + 44[] 329,7,2,$.1^6 - 12*$.1^4 + 5*$.1^3 + 36*$.1^2 - 29*$.1 + 3,3,$.1^6 - 3*$.1^5 - 6*$.1^4 + 17*$.1^3 + 12*$.1^2 - 22*$.1 - 11,5,$.1^6 - 5*$.1^5 + 23*$.1^3 - 4*$.1^2 - 32*$.1 - 9,7,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1,11,$.1^6 - 7*$.1^5 - 8*$.1^4 + 111*$.1^3 - 208*$.1^2 + 136*$.1 - 27,13,$.1^6 - 5*$.1^5 - 28*$.1^4 + 177*$.1^3 - 92*$.1^2 - 528*$.1 + 396[] 330,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x - 1,13,x - 2[] 330,2,2,x + 1,3,x + 1,5,x - 1,7,x + 4,11,x - 1,13,x + 2[] 330,3,2,x - 1,3,x + 1,5,x + 1,7,x - 4,11,x + 1,13,x - 2[] 330,4,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 1,13,x - 6[] 330,5,2,x - 1,3,x - 1,5,x - 1,7,x,11,x + 1,13,x + 2[] 331,1,2,x + 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x + 4[] 331,2,2,x^3 + 2*x^2 - 4*x - 7,3,x^3 + x^2 - 5*x + 2,5,x^3 + 6*x^2 + 8*x + 1,7,x^3 - 3*x^2 - x + 2,11,x^3 + 7*x^2 + 11*x + 4,13,x^3 + 13*x^2 + 41*x - 8[] 331,3,2,x^7 + 2*x^6 - 6*x^5 - 8*x^4 + 11*x^3 + 3*x^2 - 5*x + 1,3,x^7 - 10*x^5 - 3*x^4 + 12*x^3 - 4*x + 1,5,x^7 + 13*x^6 + 58*x^5 + 79*x^4 - 114*x^3 - 335*x^2 - 28*x + 257,7,x^7 + 8*x^6 - 6*x^5 - 184*x^4 - 329*x^3 + 834*x^2 + 2988*x + 2377,11,x^7 + 10*x^6 + 4*x^5 - 206*x^4 - 431*x^3 + 865*x^2 + 2851*x + 1857,13,x^7 - 5*x^6 - 30*x^5 + 189*x^4 - 66*x^3 - 815*x^2 + 906*x - 79[] 331,4,2,x^16 - 3*x^15 - 19*x^14 + 60*x^13 + 136*x^12 - 465*x^11 - 448*x^10 + 1747*x^9 + 657*x^8 - 3241*x^7 - 375*x^6 + 2695*x^5 + 230*x^4 - 855*x^3 - 110*x^2 + 56*x + 8,3,x^16 + x^15 - 33*x^14 - 25*x^13 + 435*x^12 + 233*x^11 - 2896*x^10 - 999*x^9 + 10181*x^8 + 1965*x^7 - 18302*x^6 - 1340*x^5 + 15636*x^4 - 732*x^3 - 5032*x^2 + 880*x - 32,5,x^16 - 20*x^15 + 151*x^14 - 449*x^13 - 320*x^12 + 5338*x^11 - 9611*x^10 - 11154*x^9 + 52289*x^8 - 26196*x^7 - 82111*x^6 + 92087*x^5 + 30651*x^4 - 65686*x^3 + 3649*x^2 + 10584*x + 157,7,x^16 - x^15 - 61*x^14 + 94*x^13 + 1377*x^12 - 2767*x^11 - 13815*x^10 + 34139*x^9 + 58089*x^8 - 185433*x^7 - 71396*x^6 + 456052*x^5 - 122644*x^4 - 438388*x^3 + 285488*x^2 + 60464*x - 61216,11,x^16 - 9*x^15 - 61*x^14 + 676*x^13 + 1209*x^12 - 19382*x^11 - 8279*x^10 + 274731*x^9 + 13224*x^8 - 2094871*x^7 - 157490*x^6 + 8344536*x^5 + 2432928*x^4 - 14003660*x^3 - 8064856*x^2 + 1680768*x + 888416,13,x^16 - 8*x^15 - 80*x^14 + 838*x^13 + 1115*x^12 - 28708*x^11 + 40887*x^10 + 359296*x^9 - 1099387*x^8 - 989469*x^7 + 7476312*x^6 - 6763164*x^5 - 9092696*x^4 + 18873408*x^3 - 8460480*x^2 - 2000000*x + 1682176[] 332,1,2,x^2,3,x^2 - 7,5,x^2 + 2*x - 6,7,x^2 - 7,11,x^2 - 4*x - 3,13,x^2 + 6*x + 2[] 332,2,2,x^2,3,x^2 + 2*x - 1,5,x^2 - 2,7,x^2 + 6*x + 7,11,x^2 + 6*x + 7,13,x^2 - 2[] 332,3,2,x^3,3,x^3 - 4*x^2 + 3*x + 1,5,x^3 - 2*x^2 - 8*x + 8,7,x^3 - 8*x^2 + 19*x - 13,11,x^3 + 4*x^2 - 25*x - 71,13,x^3 - 6*x^2 - 16*x + 104[] 333,1,2,x - 1,3,x,5,x + 2,7,x + 4,11,x - 4,13,x + 2[] 333,2,2,x + 1,3,x,5,x - 2,7,x + 4,11,x + 4,13,x + 2[] 333,3,2,x - 2,3,x,5,x - 2,7,x + 1,11,x - 5,13,x + 2[] 333,4,2,x,3,x,5,x,7,x + 1,11,x + 3,13,x + 4[] 333,5,2,x^3 + 3*x^2 - x - 5,3,x^3,5,x^3 + 4*x^2 - 4*x - 20,7,x^3 + 4*x^2 - 8*x - 16,11,x^3 + 4*x^2 - 16*x - 32,13,x^3 + 2*x^2 - 20*x - 8[] 333,6,2,x^4 - 6*x^2 + 3,3,x^4,5,x^4 - 12*x^2 + 12,7,x^4 - 8*x^3 + 24*x^2 - 32*x + 16,11,x^4,13,x^4 - 8*x^3 + 24*x^2 - 32*x + 16[] 333,7,2,x^4 - 6*x^2 - 2*x + 5,3,x^4,5,x^4 - 2*x^3 - 8*x^2 + 4,7,x^4 - 4*x^3 - 16*x^2 + 64*x - 16,11,x^4 - 32*x^2 + 32*x + 64,13,x^4 - 4*x^3 - 32*x^2 + 144*x - 80[] 334,1,2,x - 1,3,x,5,x - 3,7,x - 1,11,x,13,x + 2[] 334,2,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2 + 2*x + 1,7,x^2 - 5,11,x^2 + 5*x + 5,13,x^2 - 5[] 334,3,2,x^2 + 2*x + 1,3,x^2 - 8,5,x^2 - 2*x - 1,7,x^2 + 6*x + 9,11,x^2 - 8,13,x^2 - 8*x + 8[] 334,4,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 4*x - 1,7,x^2 + 6*x + 9,11,x^2 + 9*x + 19,13,x^2 - 2*x - 19[] 334,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 5*x - 4,5,x^3 - 13*x + 16,7,x^3 - 13*x + 16,11,x^3 - 11*x^2 + 33*x - 16,13,x^3 + 10*x^2 + 21*x - 4[] 334,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 7*x + 8,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 7*x^2 - 9*x + 88,13,x^3 - 2*x^2 - 9*x + 14[] 335,1,2,x,3,x,5,x - 1,7,x + 2,11,x + 2,13,x + 2[] 335,2,2,x^2 - 2,3,x^2 - 2,5,x^2 + 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 2,13,x^2 + 4*x + 4[] 335,3,2,x^2 - x - 1,3,x^2 - 5,5,x^2 + 2*x + 1,7,x^2 - 5,11,x^2 + 6*x + 4,13,x^2 - 12*x + 36[] 335,4,2,x^7 - 2*x^6 - 12*x^5 + 21*x^4 + 42*x^3 - 52*x^2 - 39*x - 6,3,x^7 - 4*x^6 - 8*x^5 + 46*x^4 - 27*x^3 - 36*x^2 - x + 2,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 10*x^6 + 12*x^5 + 176*x^4 - 757*x^3 + 1136*x^2 - 673*x + 134,11,x^7 - 6*x^6 - 32*x^5 + 184*x^4 + 240*x^3 - 1408*x^2 - 576*x + 3072,13,x^7 - 4*x^6 - 45*x^5 + 134*x^4 + 639*x^3 - 1016*x^2 - 2835*x - 778[] 335,5,2,x^11 - 18*x^9 + 2*x^8 + 114*x^7 - 24*x^6 - 306*x^5 + 86*x^4 + 332*x^3 - 109*x^2 - 114*x + 46,3,x^11 - 27*x^9 + 2*x^8 + 263*x^7 - 42*x^6 - 1148*x^5 + 290*x^4 + 2249*x^3 - 858*x^2 - 1622*x + 872,5,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,7,x^11 - 4*x^10 - 49*x^9 + 184*x^8 + 911*x^7 - 2998*x^6 - 8264*x^5 + 20214*x^4 + 39089*x^3 - 44972*x^2 - 84588*x - 15680,11,x^11 - 6*x^10 - 86*x^9 + 536*x^8 + 2496*x^7 - 15968*x^6 - 32384*x^5 + 195968*x^4 + 219648*x^3 - 888064*x^2 - 844288*x + 542720,13,x^11 - 4*x^10 - 69*x^9 + 330*x^8 + 1207*x^7 - 7760*x^6 - 315*x^5 + 50266*x^4 - 58056*x^3 - 40752*x^2 + 77328*x - 18144[] Total time: 21.489 seconds, Total memory usage: 6.27MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:20:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [335..341] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:19:39 on modular [Seed = 66382193] ------------------------------------- 335,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 2[] 335,2,2,$.1^2 - 2,3,$.1^2 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 4*$.1 + 4,11,$.1^2 - 2,13,$.1^2 + 4*$.1 + 4[] 335,3,2,$.1^2 - $.1 - 1,3,$.1^2 - 5,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 5,11,$.1^2 + 6*$.1 + 4,13,$.1^2 - 12*$.1 + 36[] 335,4,2,$.1^7 - 2*$.1^6 - 12*$.1^5 + 21*$.1^4 + 42*$.1^3 - 52*$.1^2 - 39*$.1 - 6,3,$.1^7 - 4*$.1^6 - 8*$.1^5 + 46*$.1^4 - 27*$.1^3 - 36*$.1^2 - $.1 + 2,5,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,7,$.1^7 - 10*$.1^6 + 12*$.1^5 + 176*$.1^4 - 757*$.1^3 + 1136*$.1^2 - 673*$.1 + 134,11,$.1^7 - 6*$.1^6 - 32*$.1^5 + 184*$.1^4 + 240*$.1^3 - 1408*$.1^2 - 576*$.1 + 3072,13,$.1^7 - 4*$.1^6 - 45*$.1^5 + 134*$.1^4 + 639*$.1^3 - 1016*$.1^2 - 2835*$.1 - 778[] 335,5,2,$.1^11 - 18*$.1^9 + 2*$.1^8 + 114*$.1^7 - 24*$.1^6 - 306*$.1^5 + 86*$.1^4 + 332*$.1^3 - 109*$.1^2 - 114*$.1 + 46,3,$.1^11 - 27*$.1^9 + 2*$.1^8 + 263*$.1^7 - 42*$.1^6 - 1148*$.1^5 + 290*$.1^4 + 2249*$.1^3 - 858*$.1^2 - 1622*$.1 + 872,5,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 + 330*$.1^7 - 462*$.1^6 + 462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1,7,$.1^11 - 4*$.1^10 - 49*$.1^9 + 184*$.1^8 + 911*$.1^7 - 2998*$.1^6 - 8264*$.1^5 + 20214*$.1^4 + 39089*$.1^3 - 44972*$.1^2 - 84588*$.1 - 15680,11,$.1^11 - 6*$.1^10 - 86*$.1^9 + 536*$.1^8 + 2496*$.1^7 - 15968*$.1^6 - 32384*$.1^5 + 195968*$.1^4 + 219648*$.1^3 - 888064*$.1^2 - 844288*$.1 + 542720,13,$.1^11 - 4*$.1^10 - 69*$.1^9 + 330*$.1^8 + 1207*$.1^7 - 7760*$.1^6 - 315*$.1^5 + 50266*$.1^4 - 58056*$.1^3 - 40752*$.1^2 + 77328*$.1 - 18144[] 336,1,2,x,3,x + 1,5,x - 2,7,x - 1,11,x,13,x + 2[] 336,2,2,x,3,x - 1,5,x - 2,7,x + 1,11,x,13,x - 6[] 336,3,2,x,3,x + 1,5,x,7,x + 1,11,x - 6,13,x - 2[] 336,4,2,x,3,x + 1,5,x + 2,7,x - 1,11,x + 4,13,x + 2[] 336,5,2,x,3,x - 1,5,x + 2,7,x - 1,11,x - 4,13,x - 6[] 336,6,2,x,3,x - 1,5,x - 4,7,x - 1,11,x + 2,13,x + 6[] 337,1,2,x^12 + 6*x^11 + x^10 - 54*x^9 - 76*x^8 + 135*x^7 + 289*x^6 - 97*x^5 - 392*x^4 - 28*x^3 + 201*x^2 + 36*x - 27,3,x^12 + 11*x^11 + 38*x^10 + 6*x^9 - 236*x^8 - 429*x^7 + 35*x^6 + 621*x^5 + 253*x^4 - 297*x^3 - 156*x^2 + 47*x + 25,5,x^12 + 10*x^11 + 17*x^10 - 132*x^9 - 527*x^8 + 35*x^7 + 2998*x^6 + 4271*x^5 - 2229*x^4 - 10525*x^3 - 10100*x^2 - 4125*x - 625,7,x^12 + 13*x^11 + 32*x^10 - 261*x^9 - 1569*x^8 - 1265*x^7 + 9845*x^6 + 26080*x^5 + 10940*x^4 - 30124*x^3 - 31288*x^2 - 4948*x - 9,11,x^12 + 7*x^11 - 46*x^10 - 401*x^9 + 236*x^8 + 6118*x^7 + 6069*x^6 - 24890*x^5 - 28251*x^4 + 44478*x^3 + 28863*x^2 - 36612*x + 6075,13,x^12 + 6*x^11 - 84*x^10 - 532*x^9 + 2177*x^8 + 15792*x^7 - 14373*x^6 - 176312*x^5 - 87376*x^4 + 624217*x^3 + 864963*x^2 + 200995*x - 101313[] 337,2,2,x^15 - 3*x^14 - 18*x^13 + 56*x^12 + 123*x^11 - 402*x^10 - 400*x^9 + 1395*x^8 + 643*x^7 - 2406*x^6 - 496*x^5 + 1843*x^4 + 200*x^3 - 388*x^2 - 69*x + 1,3,x^15 - 9*x^14 + 10*x^13 + 126*x^12 - 356*x^11 - 473*x^10 + 2511*x^9 - 147*x^8 - 7503*x^7 + 3919*x^6 + 10704*x^5 - 6921*x^4 - 7307*x^3 + 3460*x^2 + 2216*x + 64,5,x^15 - 10*x^14 + 11*x^13 + 170*x^12 - 433*x^11 - 1061*x^10 + 3724*x^9 + 2939*x^8 - 14061*x^7 - 3535*x^6 + 24746*x^5 + 2311*x^4 - 17969*x^3 - 3070*x^2 + 3900*x + 1048,7,x^15 - 7*x^14 - 28*x^13 + 263*x^12 + 187*x^11 - 3733*x^10 + 949*x^9 + 25860*x^8 - 16912*x^7 - 91924*x^6 + 79452*x^5 + 153600*x^4 - 164337*x^3 - 77896*x^2 + 127336*x - 33056,11,x^15 - 9*x^14 - 44*x^13 + 659*x^12 - 596*x^11 - 14278*x^10 + 43871*x^9 + 85358*x^8 - 535343*x^7 + 275388*x^6 + 1943157*x^5 - 2657068*x^4 - 1775361*x^3 + 3954164*x^2 + 281822*x - 1662812,13,x^15 + 4*x^14 - 80*x^13 - 228*x^12 + 2533*x^11 + 4102*x^10 - 39373*x^9 - 19254*x^8 + 294312*x^7 - 117851*x^6 - 821659*x^5 + 811293*x^4 + 186277*x^3 - 340210*x^2 + 7376*x + 33040[] 338,1,2,x + 1,3,x,5,x - 1,7,x + 4,11,x + 4,13,x[] 338,2,2,x + 1,3,x + 3,5,x - 1,7,x + 1,11,x - 2,13,x[] 338,3,2,x + 1,3,x + 1,5,x - 3,7,x - 3,11,x,13,x[] 338,4,2,x - 1,3,x,5,x + 1,7,x - 4,11,x - 4,13,x[] 338,5,2,x - 1,3,x - 1,5,x - 3,7,x - 1,11,x + 6,13,x[] 338,6,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x,13,x[] 338,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 4*x + 13,5,x^3 + 2*x^2 - 8*x - 8,7,x^3 - 4*x^2 - 4*x + 8,11,x^3 + 3*x^2 - 4*x - 13,13,x^3[] 338,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 4*x + 13,5,x^3 - 2*x^2 - 8*x + 8,7,x^3 + 4*x^2 - 4*x - 8,11,x^3 - 3*x^2 - 4*x + 13,13,x^3[] 339,1,2,x - 2,3,x + 1,5,x - 2,7,x - 3,11,x + 6,13,x - 5[] 339,2,2,x,3,x - 1,5,x + 1,7,x + 3,11,x + 4,13,x + 2[] 339,3,2,x + 2,3,x - 1,5,x + 3,7,x - 1,11,x + 2,13,x + 2[] 339,4,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 1,7,x^2 + 2*x + 1,11,x^2 - 2,13,x^2 + 8*x + 8[] 339,5,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 7,7,x^2 - 6*x + 9,11,x^2 - 4*x - 4,13,x^2 - 10*x + 25[] 339,6,2,x^2 - 4*x + 4,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 + x - 4,11,x^2 + 2*x - 16,13,x^2 + 6*x + 9[] 339,7,2,x^5 - x^4 - 10*x^3 + 6*x^2 + 22*x + 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 2*x^4 - 20*x^3 - 42*x^2 + 93*x + 202,7,x^5 + 5*x^4 - 5*x^3 - 57*x^2 - 84*x - 32,11,x^5 - 4*x^4 - 20*x^3 + 86*x^2 - 96*x + 32,13,x^5 + 3*x^4 - 24*x^3 - 92*x^2 - 52*x - 8[] 339,8,2,x^5 - 7*x^3 - 4*x^2 + 6*x + 2,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 - 3*x^4 - 6*x^3 + 16*x^2 + x - 1,7,x^5 + 3*x^4 - 18*x^3 - 18*x^2 + 89*x - 41,11,x^5 - 2*x^4 - 30*x^3 + 58*x^2 + 224*x - 424,13,x^5 - 8*x^4 - 11*x^3 + 150*x^2 - 56*x - 92[] 340,1,2,x,3,x,5,x + 1,7,x + 4,11,x - 2,13,x + 6[] 340,2,2,x^3,3,x^3 - 8*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 8*x + 4,11,x^3 - 2*x^2 - 16*x - 4,13,x^3 - 2*x^2 - 28*x + 72[] 341,1,2,x^2 - x - 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - x - 11,11,x^2 - 2*x + 1,13,x^2 + 2*x - 19[] 341,2,2,x^4 + 2*x^3 - x^2 - 2*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 6*x + 4,5,x^4 + x^3 - 8*x^2 - 11*x + 1,7,x^4 + 5*x^3 + 4*x^2 - 5*x - 1,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 6*x^3 + 7*x^2 - 6*x - 4[] 341,3,2,x^8 - x^7 - 14*x^6 + 11*x^5 + 60*x^4 - 31*x^3 - 74*x^2 + 5*x + 3,3,x^8 - 4*x^7 - 6*x^6 + 34*x^5 - x^4 - 74*x^3 + 19*x^2 + 42*x + 1,5,x^8 + 5*x^7 - 12*x^6 - 77*x^5 - 11*x^4 + 176*x^3 + 35*x^2 - 77*x + 9,7,x^8 - 7*x^7 - 8*x^6 + 127*x^5 - 137*x^4 - 434*x^3 + 657*x^2 + 393*x - 659,11,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,13,x^8 - 8*x^7 - 10*x^6 + 130*x^5 + 139*x^4 - 600*x^3 - 1171*x^2 - 538*x + 37[] 341,4,2,x^11 - x^10 - 20*x^9 + 20*x^8 + 141*x^7 - 135*x^6 - 421*x^5 + 347*x^4 + 530*x^3 - 288*x^2 - 239*x + 17,3,x^11 - 4*x^10 - 20*x^9 + 88*x^8 + 129*x^7 - 684*x^6 - 233*x^5 + 2146*x^4 - 269*x^3 - 2130*x^2 + 268*x + 304,5,x^11 - 3*x^10 - 35*x^9 + 106*x^8 + 423*x^7 - 1261*x^6 - 2318*x^5 + 6533*x^4 + 5956*x^3 - 14599*x^2 - 6045*x + 10618,7,x^11 - 5*x^10 - 41*x^9 + 234*x^8 + 471*x^7 - 3723*x^6 - 266*x^5 + 23865*x^4 - 21440*x^3 - 48211*x^2 + 83151*x - 32728,11,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,13,x^11 + 2*x^10 - 96*x^9 - 188*x^8 + 3497*x^7 + 6824*x^6 - 58955*x^5 - 115484*x^4 + 433915*x^3 + 842512*x^2 - 913120*x - 1575176[] Total time: 20.420 seconds, Total memory usage: 6.25MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:30:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [341..347] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:30:18 on modular [Seed = 601148375] ------------------------------------- 341,1,2,$.1^2 - $.1 - 1,3,$.1^2 + 2*$.1 + 1,5,$.1^2 + 3*$.1 + 1,7,$.1^2 - $.1 - 11,11,$.1^2 - 2*$.1 + 1,13,$.1^2 + 2*$.1 - 19[] 341,2,2,$.1^4 + 2*$.1^3 - $.1^2 - 2*$.1 + 1,3,$.1^4 + 2*$.1^3 - 5*$.1^2 - 6*$.1 + 4,5,$.1^4 + $.1^3 - 8*$.1^2 - 11*$.1 + 1,7,$.1^4 + 5*$.1^3 + 4*$.1^2 - 5*$.1 - 1,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 6*$.1^3 + 7*$.1^2 - 6*$.1 - 4[] 341,3,2,$.1^8 - $.1^7 - 14*$.1^6 + 11*$.1^5 + 60*$.1^4 - 31*$.1^3 - 74*$.1^2 + 5*$.1 + 3,3,$.1^8 - 4*$.1^7 - 6*$.1^6 + 34*$.1^5 - $.1^4 - 74*$.1^3 + 19*$.1^2 + 42*$.1 + 1,5,$.1^8 + 5*$.1^7 - 12*$.1^6 - 77*$.1^5 - 11*$.1^4 + 176*$.1^3 + 35*$.1^2 - 77*$.1 + 9,7,$.1^8 - 7*$.1^7 - 8*$.1^6 + 127*$.1^5 - 137*$.1^4 - 434*$.1^3 + 657*$.1^2 + 393*$.1 - 659,11,$.1^8 + 8*$.1^7 + 28*$.1^6 + 56*$.1^5 + 70*$.1^4 + 56*$.1^3 + 28*$.1^2 + 8*$.1 + 1,13,$.1^8 - 8*$.1^7 - 10*$.1^6 + 130*$.1^5 + 139*$.1^4 - 600*$.1^3 - 1171*$.1^2 - 538*$.1 + 37[] 341,4,2,$.1^11 - $.1^10 - 20*$.1^9 + 20*$.1^8 + 141*$.1^7 - 135*$.1^6 - 421*$.1^5 + 347*$.1^4 + 530*$.1^3 - 288*$.1^2 - 239*$.1 + 17,3,$.1^11 - 4*$.1^10 - 20*$.1^9 + 88*$.1^8 + 129*$.1^7 - 684*$.1^6 - 233*$.1^5 + 2146*$.1^4 - 269*$.1^3 - 2130*$.1^2 + 268*$.1 + 304,5,$.1^11 - 3*$.1^10 - 35*$.1^9 + 106*$.1^8 + 423*$.1^7 - 1261*$.1^6 - 2318*$.1^5 + 6533*$.1^4 + 5956*$.1^3 - 14599*$.1^2 - 6045*$.1 + 10618,7,$.1^11 - 5*$.1^10 - 41*$.1^9 + 234*$.1^8 + 471*$.1^7 - 3723*$.1^6 - 266*$.1^5 + 23865*$.1^4 - 21440*$.1^3 - 48211*$.1^2 + 83151*$.1 - 32728,11,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 + 330*$.1^7 - 462*$.1^6 + 462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1,13,$.1^11 + 2*$.1^10 - 96*$.1^9 - 188*$.1^8 + 3497*$.1^7 + 6824*$.1^6 - 58955*$.1^5 - 115484*$.1^4 + 433915*$.1^3 + 842512*$.1^2 - 913120*$.1 - 1575176[] 342,1,2,x + 1,3,x,5,x + 2,7,x,11,x + 2,13,x + 4[] 342,2,2,x + 1,3,x,5,x + 2,7,x,11,x - 4,13,x - 2[] 342,3,2,x + 1,3,x,5,x - 4,7,x - 3,11,x + 2,13,x + 1[] 342,4,2,x + 1,3,x,5,x,7,x + 4,11,x,13,x + 4[] 342,5,2,x - 1,3,x,5,x - 2,7,x,11,x - 2,13,x + 4[] 342,6,2,x - 1,3,x,5,x,7,x + 1,11,x - 6,13,x - 5[] 342,7,2,x - 1,3,x,5,x,7,x - 4,11,x + 4,13,x[] 343,1,2,x^3 + 4*x^2 + 3*x - 1,3,x^3,5,x^3,7,x^3,11,x^3 + 9*x^2 + 20*x + 13,13,x^3[] 343,2,2,x^3 - 3*x^2 - 4*x + 13,3,x^3,5,x^3,7,x^3,11,x^3 - 5*x^2 - 36*x + 167,13,x^3[] 343,3,2,x^6 + 2*x^5 - 6*x^4 - 10*x^3 + 10*x^2 + 11*x - 1,3,x^6 + 5*x^5 - x^4 - 34*x^3 - 28*x^2 + 49*x + 49,5,x^6 + 11*x^5 + 38*x^4 + 20*x^3 - 126*x^2 - 196*x - 49,7,x^6,11,x^6 + x^5 - 26*x^4 - 10*x^3 + 159*x^2 + 43*x - 239,13,x^6 + 7*x^5 - 14*x^4 - 154*x^3 - 147*x^2 + 343*x + 343[] 343,4,2,x^6 + 2*x^5 - 6*x^4 - 10*x^3 + 10*x^2 + 11*x - 1,3,x^6 - 5*x^5 - x^4 + 34*x^3 - 28*x^2 - 49*x + 49,5,x^6 - 11*x^5 + 38*x^4 - 20*x^3 - 126*x^2 + 196*x - 49,7,x^6,11,x^6 + x^5 - 26*x^4 - 10*x^3 + 159*x^2 + 43*x - 239,13,x^6 - 7*x^5 - 14*x^4 + 154*x^3 - 147*x^2 - 343*x + 343[] 343,5,2,x^6 - 4*x^5 + 2*x^4 + 6*x^3 - 3*x^2 - 2*x + 1,3,x^6 - 20*x^4 + 124*x^2 - 232,5,x^6 - 24*x^4 + 164*x^2 - 232,7,x^6,11,x^6 - 2*x^5 - 3*x^4 + 6*x^3 + 2*x^2 - 4*x + 1,13,x^6 - 70*x^4 + 1568*x^2 - 11368[] 344,1,2,x,3,x,5,x + 2,7,x + 2,11,x - 1,13,x + 1[] 344,2,2,x^2,3,x^2 + 2*x - 2,5,x^2 + 2*x - 2,7,x^2 + 2*x - 2,11,x^2 + 6*x + 9,13,x^2 + 6*x + 9[] 344,3,2,x^3,3,x^3 - 3*x^2 - x + 4,5,x^3 - x^2 - 5*x - 2,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - x^2 - 32*x + 64,13,x^3 - 3*x^2 - 40*x + 148[] 344,4,2,x^5,3,x^5 + x^4 - 13*x^3 - 8*x^2 + 42*x + 8,5,x^5 - x^4 - 21*x^3 + 26*x^2 + 110*x - 164,7,x^5 - 2*x^4 - 22*x^3 + 24*x^2 + 104*x - 64,11,x^5 - 2*x^4 - 31*x^3 + 48*x^2 + 192*x - 320,13,x^5 - 8*x^4 - 7*x^3 + 106*x^2 + 28*x - 8[] 345,1,2,x,3,x + 1,5,x + 1,7,x - 1,11,x - 4,13,x[] 345,2,2,x - 2,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 2[] 345,3,2,x - 1,3,x - 1,5,x + 1,7,x - 4,11,x - 4,13,x - 6[] 345,4,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x + 4,13,x + 2[] 345,5,2,x,3,x - 1,5,x + 1,7,x + 3,11,x + 4,13,x[] 345,6,2,x + 2,3,x - 1,5,x - 1,7,x + 5,11,x + 2,13,x + 6[] 345,7,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x - 7,11,x^2 + 8*x + 14,13,x^2 - 4*x + 2[] 345,8,2,x^2 + 2*x - 2,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + 2*x - 2,13,x^2 - 2*x - 26[] 345,9,2,x^2 - 6,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 6,13,x^2 - 4*x - 2[] 345,10,2,x^3 + x^2 - 4*x - 2,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 6*x^2 + 5*x + 8,11,x^3 + 2*x^2 - 6*x - 8,13,x^3 - 4*x^2 - 2*x + 4[] 346,1,2,x - 1,3,x - 1,5,x + 1,7,x - 4,11,x - 4,13,x + 6[] 346,2,2,x - 1,3,x + 1,5,x + 3,7,x + 2,11,x + 4,13,x[] 346,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 6*x + 4,5,x^3 - 4*x - 1,7,x^3 + 3*x^2 - x - 4,11,x^3 - 12*x^2 + 48*x - 64,13,x^3 - 16*x - 8[] 346,4,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 5*x - 1,5,x^4 + 5*x^3 - 20*x - 8,7,x^4 + x^3 - 22*x^2 - x + 82,11,x^4 + 13*x^3 + 46*x^2 - 3*x - 164,13,x^4 - 3*x^3 - 18*x^2 + 37*x - 16[] 346,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 + 3*x^4 - 8*x^3 - 21*x^2 + 18*x + 28,5,x^5 - 5*x^4 - 7*x^3 + 60*x^2 - 44*x - 56,7,x^5 + 2*x^4 - 12*x^3 - 20*x^2 + 33*x + 43,11,x^5 - 5*x^4 - 14*x^3 + 55*x^2 + 52*x - 48,13,x^5 - 9*x^4 + 16*x^3 + 49*x^2 - 158*x + 108[] 347,1,2,x + 2,3,x - 1,5,x,7,x + 2,11,x + 3,13,x + 2[] 347,2,2,x^2 - 2*x + 1,3,x^2 + x - 1,5,x^2 + 2*x - 4,7,x^2 + 4*x + 4,11,x^2 - 3*x + 1,13,x^2 + 7*x + 11[] 347,3,2,x^7 + 2*x^6 - 7*x^5 - 15*x^4 + 6*x^3 + 22*x^2 + 9*x + 1,3,x^7 + 7*x^6 + 9*x^5 - 33*x^4 - 88*x^3 - 29*x^2 + 74*x + 52,5,x^7 + 8*x^6 + 17*x^5 - 5*x^4 - 34*x^3 + 4*x^2 + 20*x - 7,7,x^7 + 5*x^6 - 16*x^5 - 101*x^4 + 2*x^3 + 391*x^2 + 131*x - 241,11,x^7 - 2*x^6 - 49*x^5 + 42*x^4 + 708*x^3 - 178*x^2 - 3012*x - 241,13,x^7 + 22*x^6 + 171*x^5 + 483*x^4 - 188*x^3 - 2572*x^2 - 1463*x + 439[] 347,4,2,x^19 - 30*x^17 + x^16 + 374*x^15 - 21*x^14 - 2509*x^13 + 166*x^12 + 9794*x^11 - 586*x^10 - 22435*x^9 + 749*x^8 + 28885*x^7 + 329*x^6 - 18752*x^5 - 878*x^4 + 4788*x^3 - 64*x^2 - 352*x + 32,3,x^19 - 7*x^18 - 15*x^17 + 200*x^16 - 82*x^15 - 2248*x^14 + 3021*x^13 + 12520*x^12 - 24550*x^11 - 35088*x^10 + 93955*x^9 + 40425*x^8 - 182034*x^7 + 6073*x^6 + 166727*x^5 - 35466*x^4 - 62207*x^3 + 9197*x^2 + 8954*x + 332,5,x^19 - 10*x^18 - 13*x^17 + 407*x^16 - 538*x^15 - 6534*x^14 + 15728*x^13 + 51265*x^12 - 171692*x^11 - 187966*x^10 + 951140*x^9 + 150336*x^8 - 2755080*x^7 + 848464*x^6 + 3887232*x^5 - 1878368*x^4 - 2406336*x^3 + 916352*x^2 + 595200*x + 24064,7,x^19 - 9*x^18 - 42*x^17 + 573*x^16 + 128*x^15 - 13897*x^14 + 17867*x^13 + 161413*x^12 - 344862*x^11 - 910492*x^10 + 2632844*x^9 + 2154744*x^8 - 9084272*x^7 - 1049520*x^6 + 13525472*x^5 - 1666496*x^4 - 6550400*x^3 - 194304*x^2 + 728064*x + 74752,11,x^19 - 113*x^17 + 71*x^16 + 5073*x^15 - 6646*x^14 - 115317*x^13 + 234224*x^12 + 1356714*x^11 - 3949803*x^10 - 6819222*x^9 + 32420953*x^8 - 4265833*x^7 - 107914763*x^6 + 130828209*x^5 + 30172714*x^4 - 139580357*x^3 + 81655891*x^2 - 16016817*x + 661909,13,x^19 - 39*x^18 + 622*x^17 - 4840*x^16 + 12521*x^15 + 92504*x^14 - 951637*x^13 + 3328320*x^12 - 1975275*x^11 - 22577295*x^10 + 69174531*x^9 - 27939688*x^8 - 216015592*x^7 + 379040948*x^6 + 16430721*x^5 - 577483356*x^4 + 441702328*x^3 + 48794013*x^2 - 132517280*x + 23914336[] Total time: 18.969 seconds, Total memory usage: 6.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:40:40 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [347..353] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:40:20 on modular [Seed = 3325109148] ------------------------------------- 347,1,2,$.1 + 2,3,$.1 - 1,5,$.1,7,$.1 + 2,11,$.1 + 3,13,$.1 + 2[] 347,2,2,$.1^2 - 2*$.1 + 1,3,$.1^2 + $.1 - 1,5,$.1^2 + 2*$.1 - 4,7,$.1^2 + 4*$.1 + 4,11,$.1^2 - 3*$.1 + 1,13,$.1^2 + 7*$.1 + 11[] 347,3,2,$.1^7 + 2*$.1^6 - 7*$.1^5 - 15*$.1^4 + 6*$.1^3 + 22*$.1^2 + 9*$.1 + 1,3,$.1^7 + 7*$.1^6 + 9*$.1^5 - 33*$.1^4 - 88*$.1^3 - 29*$.1^2 + 74*$.1 + 52,5,$.1^7 + 8*$.1^6 + 17*$.1^5 - 5*$.1^4 - 34*$.1^3 + 4*$.1^2 + 20*$.1 - 7,7,$.1^7 + 5*$.1^6 - 16*$.1^5 - 101*$.1^4 + 2*$.1^3 + 391*$.1^2 + 131*$.1 - 241,11,$.1^7 - 2*$.1^6 - 49*$.1^5 + 42*$.1^4 + 708*$.1^3 - 178*$.1^2 - 3012*$.1 - 241,13,$.1^7 + 22*$.1^6 + 171*$.1^5 + 483*$.1^4 - 188*$.1^3 - 2572*$.1^2 - 1463*$.1 + 439[] 347,4,2,$.1^19 - 30*$.1^17 + $.1^16 + 374*$.1^15 - 21*$.1^14 - 2509*$.1^13 + 166*$.1^12 + 9794*$.1^11 - 586*$.1^10 - 22435*$.1^9 + 749*$.1^8 + 28885*$.1^7 + 329*$.1^6 - 18752*$.1^5 - 878*$.1^4 + 4788*$.1^3 - 64*$.1^2 - 352*$.1 + 32,3,$.1^19 - 7*$.1^18 - 15*$.1^17 + 200*$.1^16 - 82*$.1^15 - 2248*$.1^14 + 3021*$.1^13 + 12520*$.1^12 - 24550*$.1^11 - 35088*$.1^10 + 93955*$.1^9 + 40425*$.1^8 - 182034*$.1^7 + 6073*$.1^6 + 166727*$.1^5 - 35466*$.1^4 - 62207*$.1^3 + 9197*$.1^2 + 8954*$.1 + 332,5,$.1^19 - 10*$.1^18 - 13*$.1^17 + 407*$.1^16 - 538*$.1^15 - 6534*$.1^14 + 15728*$.1^13 + 51265*$.1^12 - 171692*$.1^11 - 187966*$.1^10 + 951140*$.1^9 + 150336*$.1^8 - 2755080*$.1^7 + 848464*$.1^6 + 3887232*$.1^5 - 1878368*$.1^4 - 2406336*$.1^3 + 916352*$.1^2 + 595200*$.1 + 24064,7,$.1^19 - 9*$.1^18 - 42*$.1^17 + 573*$.1^16 + 128*$.1^15 - 13897*$.1^14 + 17867*$.1^13 + 161413*$.1^12 - 344862*$.1^11 - 910492*$.1^10 + 2632844*$.1^9 + 2154744*$.1^8 - 9084272*$.1^7 - 1049520*$.1^6 + 13525472*$.1^5 - 1666496*$.1^4 - 6550400*$.1^3 - 194304*$.1^2 + 728064*$.1 + 74752,11,$.1^19 - 113*$.1^17 + 71*$.1^16 + 5073*$.1^15 - 6646*$.1^14 - 115317*$.1^13 + 234224*$.1^12 + 1356714*$.1^11 - 3949803*$.1^10 - 6819222*$.1^9 + 32420953*$.1^8 - 4265833*$.1^7 - 107914763*$.1^6 + 130828209*$.1^5 + 30172714*$.1^4 - 139580357*$.1^3 + 81655891*$.1^2 - 16016817*$.1 + 661909,13,$.1^19 - 39*$.1^18 + 622*$.1^17 - 4840*$.1^16 + 12521*$.1^15 + 92504*$.1^14 - 951637*$.1^13 + 3328320*$.1^12 - 1975275*$.1^11 - 22577295*$.1^10 + 69174531*$.1^9 - 27939688*$.1^8 - 216015592*$.1^7 + 379040948*$.1^6 + 16430721*$.1^5 - 577483356*$.1^4 + 441702328*$.1^3 + 48794013*$.1^2 - 132517280*$.1 + 23914336[] 348,1,2,x,3,x + 1,5,x + 2,7,x - 1,11,x - 3,13,x - 5[] 348,2,2,x,3,x + 1,5,x,7,x + 3,11,x + 3,13,x + 3[] 348,3,2,x,3,x - 1,5,x + 4,7,x + 3,11,x + 1,13,x + 3[] 348,4,2,x,3,x - 1,5,x - 2,7,x - 1,11,x - 1,13,x + 3[] 349,1,2,x^11 + 5*x^10 - x^9 - 35*x^8 - 24*x^7 + 80*x^6 + 66*x^5 - 77*x^4 - 56*x^3 + 31*x^2 + 15*x - 4,3,x^11 + 6*x^10 - 55*x^8 - 64*x^7 + 135*x^6 + 218*x^5 - 47*x^4 - 98*x^3 + 25*x^2 + 4*x - 1,5,x^11 + 9*x^10 + 8*x^9 - 129*x^8 - 295*x^7 + 570*x^6 + 1931*x^5 - 533*x^4 - 4548*x^3 - 1490*x^2 + 3401*x + 2066,7,x^11 + 3*x^10 - 41*x^9 - 137*x^8 + 487*x^7 + 1943*x^6 - 1428*x^5 - 9862*x^4 - 3862*x^3 + 11740*x^2 + 4981*x - 4808,11,x^11 + 31*x^10 + 410*x^9 + 3003*x^8 + 13177*x^7 + 34629*x^6 + 49499*x^5 + 22418*x^4 - 30350*x^3 - 38416*x^2 - 8307*x + 1366,13,x^11 + 4*x^10 - 73*x^9 - 315*x^8 + 1748*x^7 + 8617*x^6 - 12681*x^5 - 90736*x^4 - 38072*x^3 + 237723*x^2 + 314825*x + 110828[] 349,2,2,x^17 - 5*x^16 - 14*x^15 + 102*x^14 + 26*x^13 - 792*x^12 + 474*x^11 + 2887*x^10 - 3021*x^9 - 4835*x^8 + 6673*x^7 + 2880*x^6 - 5373*x^5 - 164*x^4 + 1075*x^3 + 75*x^2 - 41*x - 4,3,x^17 - 6*x^16 - 20*x^15 + 177*x^14 + 48*x^13 - 1985*x^12 + 1406*x^11 + 10845*x^10 - 12658*x^9 - 31199*x^8 + 44236*x^7 + 48099*x^6 - 74028*x^5 - 39044*x^4 + 57120*x^3 + 17296*x^2 - 15296*x - 5056,5,x^17 - 5*x^16 - 37*x^15 + 214*x^14 + 419*x^13 - 3319*x^12 - 857*x^11 + 23008*x^10 - 10989*x^9 - 73502*x^8 + 63382*x^7 + 97594*x^6 - 116692*x^5 - 24693*x^4 + 66466*x^3 - 24778*x^2 + 2789*x + 2,7,x^17 - x^16 - 62*x^15 + 108*x^14 + 1446*x^13 - 3592*x^12 - 14668*x^11 + 50964*x^10 + 46043*x^9 - 311849*x^8 + 167240*x^7 + 607051*x^6 - 885383*x^5 + 307370*x^4 + 57048*x^3 - 28554*x^2 - 2663*x + 142,11,x^17 - 39*x^16 + 637*x^15 - 5462*x^14 + 23655*x^13 - 18200*x^12 - 307653*x^11 + 1355416*x^10 - 1191873*x^9 - 6344921*x^8 + 18465668*x^7 - 7646257*x^6 - 33914554*x^5 + 47577880*x^4 - 10495234*x^3 - 12511566*x^2 + 6304189*x - 778568,13,x^17 + 6*x^16 - 87*x^15 - 529*x^14 + 2510*x^13 + 16439*x^12 - 28043*x^11 - 226068*x^10 + 81674*x^9 + 1436433*x^8 + 514933*x^7 - 3879170*x^6 - 3100324*x^5 + 3028472*x^4 + 3960064*x^3 + 1329408*x^2 + 137408*x - 896[] 350,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x - 3,13,x + 2[] 350,2,2,x + 1,3,x,5,x,7,x - 1,11,x - 4,13,x - 6[] 350,3,2,x + 1,3,x - 3,5,x,7,x - 1,11,x + 5,13,x - 6[] 350,4,2,x - 1,3,x - 2,5,x,7,x + 1,11,x,13,x - 4[] 350,5,2,x - 1,3,x + 3,5,x,7,x + 1,11,x + 5,13,x + 6[] 350,6,2,x - 1,3,x - 1,5,x,7,x - 1,11,x - 3,13,x - 2[] 350,7,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 24,13,x^2 - 4*x - 2[] 350,8,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 24,13,x^2 + 4*x - 2[] 351,1,2,x^2 + x - 1,3,x^2,5,x^2 + 3*x + 1,7,x^2 - 5,11,x^2 + 5*x - 5,13,x^2 + 2*x + 1[] 351,2,2,x^2 - x - 3,3,x^2,5,x^2 - 5*x + 3,7,x^2 + 2*x + 1,11,x^2 - x - 3,13,x^2 - 2*x + 1[] 351,3,2,x^2 - x - 1,3,x^2,5,x^2 - 3*x + 1,7,x^2 - 5,11,x^2 - 5*x - 5,13,x^2 + 2*x + 1[] 351,4,2,x^2 + x - 3,3,x^2,5,x^2 + 5*x + 3,7,x^2 + 2*x + 1,11,x^2 + x - 3,13,x^2 - 2*x + 1[] 351,5,2,x^4 - 7*x^2 + 3,3,x^4,5,x^4 - 16*x^2 + 27,7,x^4 - 8*x^3 + 24*x^2 - 32*x + 16,11,x^4 - 28*x^2 + 48,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 351,6,2,x^4 - 9*x^2 + 19,3,x^4,5,x^4 - 16*x^2 + 19,7,x^4 - 40*x^2 + 400,11,x^4 - 44*x^2 + 304,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 352,1,2,x,3,x + 1,5,x - 1,7,x + 4,11,x + 1,13,x + 2[] 352,2,2,x,3,x + 1,5,x + 3,7,x - 4,11,x + 1,13,x + 2[] 352,3,2,x,3,x - 1,5,x - 1,7,x - 4,11,x - 1,13,x + 2[] 352,4,2,x,3,x - 3,5,x - 1,7,x,11,x + 1,13,x + 6[] 352,5,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x + 2[] 352,6,2,x,3,x + 3,5,x - 1,7,x,11,x - 1,13,x + 6[] 352,7,2,x^2,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2,11,x^2 - 2*x + 1,13,x^2 - 4*x + 4[] 352,8,2,x^2,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2,11,x^2 + 2*x + 1,13,x^2 - 4*x + 4[] 353,1,2,x + 1,3,x - 2,5,x - 2,7,x + 2,11,x - 4,13,x - 2[] 353,2,2,x^3 - x^2 - 6*x + 4,3,x^3 - 3*x^2 - x + 2,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 - 2*x^2 - 5*x + 2,11,x^3 - 3*x^2 - x + 4,13,x^3 - 11*x^2 + 35*x - 26[] 353,3,2,x^11 + 5*x^10 - x^9 - 36*x^8 - 28*x^7 + 82*x^6 + 87*x^5 - 65*x^4 - 71*x^3 + 21*x^2 + 14*x - 4,3,x^11 + 5*x^10 - 7*x^9 - 64*x^8 - 36*x^7 + 175*x^6 + 126*x^5 - 186*x^4 - 104*x^3 + 72*x^2 + 18*x + 1,5,x^11 + 4*x^10 - 18*x^9 - 81*x^8 + 53*x^7 + 384*x^6 + 56*x^5 - 495*x^4 - 148*x^3 + 153*x^2 + 26*x + 1,7,x^11 + 25*x^10 + 259*x^9 + 1407*x^8 + 4053*x^7 + 4609*x^6 - 4827*x^5 - 17025*x^4 - 6326*x^3 + 14629*x^2 + 6466*x - 5575,11,x^11 + 4*x^10 - 64*x^9 - 310*x^8 + 1013*x^7 + 7581*x^6 + 4661*x^5 - 50668*x^4 - 142459*x^3 - 159283*x^2 - 80334*x - 14697,13,x^11 + 13*x^10 + 17*x^9 - 425*x^8 - 1863*x^7 + 1016*x^6 + 18114*x^5 + 21395*x^4 - 38907*x^3 - 81473*x^2 - 11214*x + 32157[] 353,4,2,x^14 - 4*x^13 - 14*x^12 + 71*x^11 + 47*x^10 - 452*x^9 + 101*x^8 + 1251*x^7 - 740*x^6 - 1488*x^5 + 1096*x^4 + 600*x^3 - 410*x^2 - 42*x - 1,3,x^14 + 2*x^13 - 26*x^12 - 48*x^11 + 262*x^10 + 447*x^9 - 1279*x^8 - 2024*x^7 + 3081*x^6 + 4547*x^5 - 3326*x^4 - 4522*x^3 + 1322*x^2 + 1308*x - 322,5,x^14 + 4*x^13 - 39*x^12 - 151*x^11 + 592*x^10 + 2235*x^9 - 4272*x^8 - 16368*x^7 + 13846*x^6 + 60545*x^5 - 10522*x^4 - 98304*x^3 - 25184*x^2 + 36240*x + 10400,7,x^14 - 29*x^13 + 352*x^12 - 2260*x^11 + 7591*x^10 - 6997*x^9 - 45654*x^8 + 210050*x^7 - 425708*x^6 + 476445*x^5 - 279130*x^4 + 48708*x^3 + 31114*x^2 - 16770*x + 2290,11,x^14 + 7*x^13 - 70*x^12 - 473*x^11 + 1808*x^10 + 10840*x^9 - 21587*x^8 - 101229*x^7 + 105583*x^6 + 399873*x^5 - 195880*x^4 - 578384*x^3 + 168704*x^2 + 229888*x - 57856,13,x^14 - 2*x^13 - 92*x^12 + 219*x^11 + 3314*x^10 - 8885*x^9 - 59691*x^8 + 176589*x^7 + 560201*x^6 - 1845067*x^5 - 2466086*x^4 + 9702888*x^3 + 2569392*x^2 - 20177168*x + 8277472[] Total time: 19.059 seconds, Total memory usage: 6.15MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:48:56 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [353..359] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:48:36 on modular [Seed = 4127265372] ------------------------------------- 353,1,2,$.1 + 1,3,$.1 - 2,5,$.1 - 2,7,$.1 + 2,11,$.1 - 4,13,$.1 - 2[] 353,2,2,$.1^3 - $.1^2 - 6*$.1 + 4,3,$.1^3 - 3*$.1^2 - $.1 + 2,5,$.1^3 - 2*$.1^2 - 5*$.1 + 2,7,$.1^3 - 2*$.1^2 - 5*$.1 + 2,11,$.1^3 - 3*$.1^2 - $.1 + 4,13,$.1^3 - 11*$.1^2 + 35*$.1 - 26[] 353,3,2,$.1^11 + 5*$.1^10 - $.1^9 - 36*$.1^8 - 28*$.1^7 + 82*$.1^6 + 87*$.1^5 - 65*$.1^4 - 71*$.1^3 + 21*$.1^2 + 14*$.1 - 4,3,$.1^11 + 5*$.1^10 - 7*$.1^9 - 64*$.1^8 - 36*$.1^7 + 175*$.1^6 + 126*$.1^5 - 186*$.1^4 - 104*$.1^3 + 72*$.1^2 + 18*$.1 + 1,5,$.1^11 + 4*$.1^10 - 18*$.1^9 - 81*$.1^8 + 53*$.1^7 + 384*$.1^6 + 56*$.1^5 - 495*$.1^4 - 148*$.1^3 + 153*$.1^2 + 26*$.1 + 1,7,$.1^11 + 25*$.1^10 + 259*$.1^9 + 1407*$.1^8 + 4053*$.1^7 + 4609*$.1^6 - 4827*$.1^5 - 17025*$.1^4 - 6326*$.1^3 + 14629*$.1^2 + 6466*$.1 - 5575,11,$.1^11 + 4*$.1^10 - 64*$.1^9 - 310*$.1^8 + 1013*$.1^7 + 7581*$.1^6 + 4661*$.1^5 - 50668*$.1^4 - 142459*$.1^3 - 159283*$.1^2 - 80334*$.1 - 14697,13,$.1^11 + 13*$.1^10 + 17*$.1^9 - 425*$.1^8 - 1863*$.1^7 + 1016*$.1^6 + 18114*$.1^5 + 21395*$.1^4 - 38907*$.1^3 - 81473*$.1^2 - 11214*$.1 + 32157[] 353,4,2,$.1^14 - 4*$.1^13 - 14*$.1^12 + 71*$.1^11 + 47*$.1^10 - 452*$.1^9 + 101*$.1^8 + 1251*$.1^7 - 740*$.1^6 - 1488*$.1^5 + 1096*$.1^4 + 600*$.1^3 - 410*$.1^2 - 42*$.1 - 1,3,$.1^14 + 2*$.1^13 - 26*$.1^12 - 48*$.1^11 + 262*$.1^10 + 447*$.1^9 - 1279*$.1^8 - 2024*$.1^7 + 3081*$.1^6 + 4547*$.1^5 - 3326*$.1^4 - 4522*$.1^3 + 1322*$.1^2 + 1308*$.1 - 322,5,$.1^14 + 4*$.1^13 - 39*$.1^12 - 151*$.1^11 + 592*$.1^10 + 2235*$.1^9 - 4272*$.1^8 - 16368*$.1^7 + 13846*$.1^6 + 60545*$.1^5 - 10522*$.1^4 - 98304*$.1^3 - 25184*$.1^2 + 36240*$.1 + 10400,7,$.1^14 - 29*$.1^13 + 352*$.1^12 - 2260*$.1^11 + 7591*$.1^10 - 6997*$.1^9 - 45654*$.1^8 + 210050*$.1^7 - 425708*$.1^6 + 476445*$.1^5 - 279130*$.1^4 + 48708*$.1^3 + 31114*$.1^2 - 16770*$.1 + 2290,11,$.1^14 + 7*$.1^13 - 70*$.1^12 - 473*$.1^11 + 1808*$.1^10 + 10840*$.1^9 - 21587*$.1^8 - 101229*$.1^7 + 105583*$.1^6 + 399873*$.1^5 - 195880*$.1^4 - 578384*$.1^3 + 168704*$.1^2 + 229888*$.1 - 57856,13,$.1^14 - 2*$.1^13 - 92*$.1^12 + 219*$.1^11 + 3314*$.1^10 - 8885*$.1^9 - 59691*$.1^8 + 176589*$.1^7 + 560201*$.1^6 - 1845067*$.1^5 - 2466086*$.1^4 + 9702888*$.1^3 + 2569392*$.1^2 - 20177168*$.1 + 8277472[] 354,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x + 5,13,x - 1[] 354,2,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x + 6[] 354,3,2,x + 1,3,x - 1,5,x,7,x + 1,11,x - 3,13,x - 5[] 354,4,2,x - 1,3,x + 1,5,x,7,x,11,x - 4,13,x - 4[] 354,5,2,x - 1,3,x + 1,5,x - 4,7,x,11,x + 4,13,x[] 354,6,2,x - 1,3,x + 1,5,x + 4,7,x + 1,11,x + 3,13,x + 1[] 354,7,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x - 10,7,x^2 - 8*x + 16,11,x^2 + 4*x + 4,13,x^2 + 2*x - 10[] 354,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 6*x + 8,7,x^3 + x^2 - 16*x + 16,11,x^3 - x^2 - 32*x + 76,13,x^3 - x^2 - 4*x + 2[] 355,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x,13,x - 5[] 355,2,2,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,3,x^4 + x^3 - 3*x^2 - x + 1,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - x^3 - 10*x^2 - 8*x - 1,11,x^4 + 9*x^3 + 22*x^2 + 16*x + 1,13,x^4 + 2*x^3 - 20*x^2 + 29*x - 11[] 355,3,2,x^4 + 4*x^3 + 2*x^2 - 5*x - 3,3,x^4 + 3*x^3 - x^2 - 5*x + 1,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 5*x^3 - 6*x^2 - 36*x - 27,11,x^4 + x^3 - 24*x^2 - 12*x + 43,13,x^4 + 14*x^3 + 54*x^2 + 9*x - 161[] 355,4,2,x^6 - 3*x^5 - 6*x^4 + 21*x^3 + 4*x^2 - 35*x + 16,3,x^6 - 3*x^5 - 7*x^4 + 25*x^3 - 5*x^2 - 18*x + 8,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 6*x^5 + 3*x^4 + 24*x^3 - 15*x^2 - 13*x + 8,11,x^6 - 3*x^5 - 22*x^4 + 4*x^3 + 73*x^2 + 4*x - 64,13,x^6 - 5*x^5 - 30*x^4 + 129*x^3 + 80*x^2 - x - 2[] 355,5,2,x^8 - 4*x^7 - 5*x^6 + 31*x^5 - 3*x^4 - 57*x^3 + 5*x^2 + 32*x + 8,3,x^8 + x^7 - 19*x^6 - 13*x^5 + 113*x^4 + 48*x^3 - 204*x^2 - 64*x + 64,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 5*x^7 - 25*x^6 - 97*x^5 + 291*x^4 + 472*x^3 - 1421*x^2 + 188*x + 668,11,x^8 - 7*x^7 - 40*x^6 + 336*x^5 + 259*x^4 - 4496*x^3 + 3144*x^2 + 11008*x - 4096,13,x^8 + 4*x^7 - 49*x^6 - 99*x^5 + 877*x^4 + 223*x^3 - 4755*x^2 + 1312*x + 6352[] 356,1,2,x,3,x + 1,5,x + 1,7,x,11,x,13,x + 4[] 356,2,2,x^7,3,x^7 - x^6 - 18*x^5 + 18*x^4 + 93*x^3 - 95*x^2 - 126*x + 134,5,x^7 - 3*x^6 - 22*x^5 + 54*x^4 + 117*x^3 - 215*x^2 + 96*x - 12,7,x^7 - 36*x^5 + 8*x^4 + 360*x^3 - 244*x^2 - 952*x + 872,11,x^7 - 8*x^6 - 28*x^5 + 304*x^4 + 16*x^3 - 2800*x^2 + 1152*x + 6912,13,x^7 - 10*x^6 - 32*x^5 + 576*x^4 - 848*x^3 - 7344*x^2 + 27072*x - 26048[] 357,1,2,x,3,x + 1,5,x - 1,7,x + 1,11,x - 3,13,x - 3[] 357,2,2,x,3,x + 1,5,x - 1,7,x - 1,11,x + 5,13,x + 5[] 357,3,2,x - 2,3,x - 1,5,x - 1,7,x + 1,11,x - 1,13,x - 1[] 357,4,2,x + 2,3,x - 1,5,x + 3,7,x - 1,11,x + 3,13,x - 1[] 357,5,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 1,7,x^2 + 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + 6*x + 7[] 357,6,2,x^2 + 2*x - 2,3,x^2 - 2*x + 1,5,x^2 + 4*x + 1,7,x^2 + 2*x + 1,11,x^2 + 10*x + 25,13,x^2 + 4*x - 23[] 357,7,2,x^3 - x^2 - 4*x + 2,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 3*x + 2,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 5*x + 4,13,x^3 + 2*x^2 - 23*x - 62[] 357,8,2,x^4 - 2*x^3 - 5*x^2 + 8*x + 2,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 2*x^3 - 13*x^2 - 20*x - 4,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 23*x^2 + 80*x - 64,13,x^4 - 2*x^3 - 13*x^2 + 20*x - 4[] 358,1,2,x + 1,3,x - 2,5,x,7,x + 2,11,x - 5,13,x - 6[] 358,2,2,x - 1,3,x + 2,5,x,7,x - 2,11,x - 3,13,x - 2[] 358,3,2,x^2 + 2*x + 1,3,x^2 - x - 5,5,x^2 - 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 2*x + 1,13,x^2 + 3*x - 3[] 358,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - x - 11,7,x^2 - 4*x + 4,11,x^2 + 2*x - 4,13,x^2 + 11*x + 29[] 358,5,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 - 4*x - 1,13,x^2 - 3*x + 1[] 358,6,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 4*x - 1,7,x^2 + 6*x + 9,11,x^2 - 5,13,x^2 + 3*x - 9[] 358,7,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 7*x^2 - 8*x - 1,5,x^4 + 7*x^3 + 12*x^2 - 3*x - 13,7,x^4 - 17*x^2 + 68,11,x^4 + 4*x^3 - 11*x^2 - 30*x + 52,13,x^4 + 8*x^3 + 7*x^2 - 70*x - 137[] 359,1,2,x - 1,3,x + 2,5,x - 1,7,x - 1,11,x + 2,13,x + 6[] 359,2,2,x + 1,3,x,5,x - 1,7,x + 1,11,x + 2,13,x[] 359,3,2,x^4 + 2*x^3 - 3*x^2 - 5*x + 1,3,x^4 + x^3 - 4*x^2 - x + 2,5,x^4 + 6*x^3 + 9*x^2 + x - 1,7,x^4 + 3*x^3 - x^2 - 6*x - 1,11,x^4 - x^3 - 4*x^2 + x + 2,13,x^4 + 5*x^3 - 5*x - 2[] 359,4,2,x^24 - x^23 - 39*x^22 + 38*x^21 + 658*x^20 - 619*x^19 - 6300*x^18 + 5654*x^17 + 37740*x^16 - 31780*x^15 - 147096*x^14 + 113400*x^13 + 376092*x^12 - 255412*x^11 - 621508*x^10 + 349080*x^9 + 638532*x^8 - 266744*x^7 - 378124*x^6 + 98609*x^5 + 110695*x^4 - 14509*x^3 - 11972*x^2 + 780*x + 381,3,x^24 - 5*x^23 - 43*x^22 + 244*x^21 + 730*x^20 - 5047*x^19 - 5907*x^18 + 57923*x^17 + 17687*x^16 - 406074*x^15 + 67031*x^14 + 1808670*x^13 - 762586*x^12 - 5180837*x^11 + 2757430*x^10 + 9527658*x^9 - 4960839*x^8 - 11153867*x^7 + 4462237*x^6 + 8084680*x^5 - 1630622*x^4 - 3295895*x^3 - 52340*x^2 + 569928*x + 116220,5,x^24 - 6*x^23 - 69*x^22 + 467*x^21 + 1858*x^20 - 15164*x^19 - 23636*x^18 + 267639*x^17 + 117204*x^16 - 2810581*x^15 + 361049*x^14 + 18183228*x^13 - 6736119*x^12 - 73400500*x^11 + 27673727*x^10 + 184563711*x^9 - 40548680*x^8 - 273285446*x^7 - 1013221*x^6 + 201596727*x^5 + 30252732*x^4 - 60035364*x^3 - 9319637*x^2 + 6343389*x + 470595,7,x^24 - 5*x^23 - 114*x^22 + 641*x^21 + 5174*x^20 - 34398*x^19 - 112225*x^18 + 995574*x^17 + 887868*x^16 - 16586560*x^15 + 9274640*x^14 + 154492864*x^13 - 258142784*x^12 - 667474304*x^11 + 2055038208*x^10 + 84195328*x^9 - 5784735744*x^8 + 6531266560*x^7 - 286748672*x^6 - 3293741056*x^5 + 1408040960*x^4 + 294420480*x^3 - 233504768*x^2 + 6422528*x + 7602176,11,x^24 - x^23 - 169*x^22 + 126*x^21 + 12398*x^20 - 6197*x^19 - 519473*x^18 + 142367*x^17 + 13756217*x^16 - 1107152*x^15 - 240666717*x^14 - 16619292*x^13 + 2827831610*x^12 + 467702785*x^11 - 22280707192*x^10 - 4576511138*x^9 + 115550031501*x^8 + 22525582681*x^7 - 376953626781*x^6 - 55187488438*x^5 + 699077626886*x^4 + 52803563063*x^3 - 563144202202*x^2 + 519529404*x + 10936677960,13,x^24 - 19*x^23 - 40*x^22 + 2811*x^21 - 8740*x^20 - 166732*x^19 + 940532*x^18 + 4929984*x^17 - 42016912*x^16 - 66630272*x^15 + 1059257920*x^14 - 100152576*x^13 - 16382637568*x^12 + 17675379712*x^11 + 158158316544*x^10 - 281003210752*x^9 - 924055621632*x^8 + 2228757315584*x^7 + 2924503531520*x^6 - 9682178965504*x^5 - 3197478961152*x^4 + 21392562978816*x^3 - 4807181991936*x^2 - 17987890839552*x + 9644547244032[] Total time: 19.760 seconds, Total memory usage: 6.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:58:17 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [359..361] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:58:04 on modular [Seed = 2657714156] ------------------------------------- 359,1,2,$.1 - 1,3,$.1 + 2,5,$.1 - 1,7,$.1 - 1,11,$.1 + 2,13,$.1 + 6[] 359,2,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1 + 2,13,$.1[] 359,3,2,$.1^4 + 2*$.1^3 - 3*$.1^2 - 5*$.1 + 1,3,$.1^4 + $.1^3 - 4*$.1^2 - $.1 + 2,5,$.1^4 + 6*$.1^3 + 9*$.1^2 + $.1 - 1,7,$.1^4 + 3*$.1^3 - $.1^2 - 6*$.1 - 1,11,$.1^4 - $.1^3 - 4*$.1^2 + $.1 + 2,13,$.1^4 + 5*$.1^3 - 5*$.1 - 2[] 359,4,2,$.1^24 - $.1^23 - 39*$.1^22 + 38*$.1^21 + 658*$.1^20 - 619*$.1^19 - 6300*$.1^18 + 5654*$.1^17 + 37740*$.1^16 - 31780*$.1^15 - 147096*$.1^14 + 113400*$.1^13 + 376092*$.1^12 - 255412*$.1^11 - 621508*$.1^10 + 349080*$.1^9 + 638532*$.1^8 - 266744*$.1^7 - 378124*$.1^6 + 98609*$.1^5 + 110695*$.1^4 - 14509*$.1^3 - 11972*$.1^2 + 780*$.1 + 381,3,$.1^24 - 5*$.1^23 - 43*$.1^22 + 244*$.1^21 + 730*$.1^20 - 5047*$.1^19 - 5907*$.1^18 + 57923*$.1^17 + 17687*$.1^16 - 406074*$.1^15 + 67031*$.1^14 + 1808670*$.1^13 - 762586*$.1^12 - 5180837*$.1^11 + 2757430*$.1^10 + 9527658*$.1^9 - 4960839*$.1^8 - 11153867*$.1^7 + 4462237*$.1^6 + 8084680*$.1^5 - 1630622*$.1^4 - 3295895*$.1^3 - 52340*$.1^2 + 569928*$.1 + 116220,5,$.1^24 - 6*$.1^23 - 69*$.1^22 + 467*$.1^21 + 1858*$.1^20 - 15164*$.1^19 - 23636*$.1^18 + 267639*$.1^17 + 117204*$.1^16 - 2810581*$.1^15 + 361049*$.1^14 + 18183228*$.1^13 - 6736119*$.1^12 - 73400500*$.1^11 + 27673727*$.1^10 + 184563711*$.1^9 - 40548680*$.1^8 - 273285446*$.1^7 - 1013221*$.1^6 + 201596727*$.1^5 + 30252732*$.1^4 - 60035364*$.1^3 - 9319637*$.1^2 + 6343389*$.1 + 470595,7,$.1^24 - 5*$.1^23 - 114*$.1^22 + 641*$.1^21 + 5174*$.1^20 - 34398*$.1^19 - 112225*$.1^18 + 995574*$.1^17 + 887868*$.1^16 - 16586560*$.1^15 + 9274640*$.1^14 + 154492864*$.1^13 - 258142784*$.1^12 - 667474304*$.1^11 + 2055038208*$.1^10 + 84195328*$.1^9 - 5784735744*$.1^8 + 6531266560*$.1^7 - 286748672*$.1^6 - 3293741056*$.1^5 + 1408040960*$.1^4 + 294420480*$.1^3 - 233504768*$.1^2 + 6422528*$.1 + 7602176,11,$.1^24 - $.1^23 - 169*$.1^22 + 126*$.1^21 + 12398*$.1^20 - 6197*$.1^19 - 519473*$.1^18 + 142367*$.1^17 + 13756217*$.1^16 - 1107152*$.1^15 - 240666717*$.1^14 - 16619292*$.1^13 + 2827831610*$.1^12 + 467702785*$.1^11 - 22280707192*$.1^10 - 4576511138*$.1^9 + 115550031501*$.1^8 + 22525582681*$.1^7 - 376953626781*$.1^6 - 55187488438*$.1^5 + 699077626886*$.1^4 + 52803563063*$.1^3 - 563144202202*$.1^2 + 519529404*$.1 + 10936677960,13,$.1^24 - 19*$.1^23 - 40*$.1^22 + 2811*$.1^21 - 8740*$.1^20 - 166732*$.1^19 + 940532*$.1^18 + 4929984*$.1^17 - 42016912*$.1^16 - 66630272*$.1^15 + 1059257920*$.1^14 - 100152576*$.1^13 - 16382637568*$.1^12 + 17675379712*$.1^11 + 158158316544*$.1^10 - 281003210752*$.1^9 - 924055621632*$.1^8 + 2228757315584*$.1^7 + 2924503531520*$.1^6 - 9682178965504*$.1^5 - 3197478961152*$.1^4 + 21392562978816*$.1^3 - 4807181991936*$.1^2 - 17987890839552*$.1 + 9644547244032[] 360,1,2,x,3,x,5,x - 1,7,x - 2,11,x + 2,13,x - 4[] 360,2,2,x,3,x,5,x + 1,7,x,11,x - 4,13,x - 6[] 360,3,2,x,3,x,5,x + 1,7,x - 2,11,x - 2,13,x - 4[] 360,4,2,x,3,x,5,x + 1,7,x + 4,11,x + 4,13,x + 2[] 360,5,2,x,3,x,5,x - 1,7,x - 4,11,x,13,x + 6[] 361,1,2,x,3,x,5,x + 1,7,x - 3,11,x + 5,13,x[] 361,2,2,x,3,x - 2,5,x - 3,7,x + 1,11,x - 3,13,x - 4[] 361,3,2,x^2 - 5,3,x^2 - 4*x + 4,5,x^2 - x - 1,7,x^2 + 2*x - 4,11,x^2 - 6*x + 4,13,x^2 - 3*x - 9[] 361,4,2,x^2 - 5,3,x^2 + 4*x + 4,5,x^2 - x - 1,7,x^2 + 2*x - 4,11,x^2 - 6*x + 4,13,x^2 + 3*x - 9[] 361,5,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 6*x + 9,11,x^2 + x - 1,13,x^2 + 2*x + 1[] 361,6,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 6*x + 9,11,x^2 + x - 1,13,x^2 - 2*x + 1[] 361,7,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 - 3,7,x^3 - 3*x + 1,11,x^3 - 9*x - 9,13,x^3 - 21*x + 37[] 361,8,2,x^3 - 3*x^2 + 3,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 3,7,x^3 - 3*x + 1,11,x^3 - 9*x - 9,13,x^3 - 21*x - 37[] 361,9,2,x^4 - 5*x^2 + 5,3,x^4 - 5*x^2 + 5,5,x^4 + 4*x^3 - 4*x^2 - 16*x + 16,7,x^4 + 8*x^3 + 14*x^2 - 8*x + 1,11,x^4 + 10*x^3 + 35*x^2 + 50*x + 25,13,x^4 - 10*x^2 + 5[] Total time: 13.529 seconds, Total memory usage: 4.75MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:01:27 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [367..373] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 13:01:07 on modular [Seed = 3175767040] ------------------------------------- 367,1,2,$.1^11 + 8*$.1^10 + 16*$.1^9 - 26*$.1^8 - 121*$.1^7 - 61*$.1^6 + 197*$.1^5 + 212*$.1^4 - 66*$.1^3 - 132*$.1^2 - 12*$.1 + 13,3,$.1^11 + 6*$.1^10 + 3*$.1^9 - 41*$.1^8 - 64*$.1^7 + 64*$.1^6 + 158*$.1^5 - 9*$.1^4 - 118*$.1^3 - 14*$.1^2 + 24*$.1 - 1,5,$.1^11 + 8*$.1^10 + 7*$.1^9 - 85*$.1^8 - 191*$.1^7 + 190*$.1^6 + 791*$.1^5 + 247*$.1^4 - 815*$.1^3 - 687*$.1^2 - 128*$.1 + 5,7,$.1^11 + 7*$.1^10 - 13*$.1^9 - 186*$.1^8 - 277*$.1^7 + 859*$.1^6 + 2780*$.1^5 + 1778*$.1^4 - 1871*$.1^3 - 2671*$.1^2 - 799*$.1 + 25,11,$.1^11 + 10*$.1^10 - 12*$.1^9 - 313*$.1^8 - 120*$.1^7 + 3196*$.1^6 + 661*$.1^5 - 11246*$.1^4 + 2768*$.1^3 + 5371*$.1^2 - 892*$.1 - 743,13,$.1^11 + 5*$.1^10 - 48*$.1^9 - 277*$.1^8 + 569*$.1^7 + 4656*$.1^6 + 745*$.1^5 - 22685*$.1^4 - 14329*$.1^3 + 25989*$.1^2 - 1682*$.1 - 2621[] 367,2,2,$.1^19 - 9*$.1^18 + 11*$.1^17 + 123*$.1^16 - 372*$.1^15 - 469*$.1^14 + 2884*$.1^13 - 550*$.1^12 - 10042*$.1^11 + 8029*$.1^10 + 17059*$.1^9 - 20350*$.1^8 - 12836*$.1^7 + 20779*$.1^6 + 2682*$.1^5 - 7739*$.1^4 + 63*$.1^3 + 899*$.1^2 - 27*$.1 - 29,3,$.1^19 - 4*$.1^18 - 35*$.1^17 + 149*$.1^16 + 486*$.1^15 - 2260*$.1^14 - 3442*$.1^13 + 18203*$.1^12 + 13108*$.1^11 - 84580*$.1^10 - 25304*$.1^9 + 229397*$.1^8 + 19212*$.1^7 - 348172*$.1^6 - 3000*$.1^5 + 262144*$.1^4 + 15968*$.1^3 - 68672*$.1^2 - 21504*$.1 - 1792,5,$.1^19 - 6*$.1^18 - 43*$.1^17 + 309*$.1^16 + 595*$.1^15 - 6046*$.1^14 - 2461*$.1^13 + 58707*$.1^12 - 5347*$.1^11 - 322649*$.1^10 + 48332*$.1^9 + 1052323*$.1^8 + 41520*$.1^7 - 1950148*$.1^6 - 697328*$.1^5 + 1640832*$.1^4 + 1181408*$.1^3 - 153984*$.1^2 - 315520*$.1 - 68864,7,$.1^19 - $.1^18 - 68*$.1^17 + 93*$.1^16 + 1821*$.1^15 - 3162*$.1^14 - 24162*$.1^13 + 51825*$.1^12 + 161877*$.1^11 - 438685*$.1^10 - 465321*$.1^9 + 1870316*$.1^8 + 63387*$.1^7 - 3600393*$.1^6 + 1757269*$.1^5 + 2308835*$.1^4 - 1465397*$.1^3 - 561533*$.1^2 + 257949*$.1 + 75177,11,$.1^19 - 4*$.1^18 - 120*$.1^17 + 545*$.1^16 + 5632*$.1^15 - 29392*$.1^14 - 128435*$.1^13 + 812306*$.1^12 + 1363286*$.1^11 - 12382021*$.1^10 - 2606314*$.1^9 + 102742747*$.1^8 - 71962574*$.1^7 - 413796744*$.1^6 + 565237368*$.1^5 + 539820496*$.1^4 - 1225061216*$.1^3 + 173670080*$.1^2 + 608625792*$.1 - 263379712,13,$.1^19 - 5*$.1^18 - 99*$.1^17 + 398*$.1^16 + 4006*$.1^15 - 11816*$.1^14 - 82529*$.1^13 + 167855*$.1^12 + 890309*$.1^11 - 1326823*$.1^10 - 4991303*$.1^9 + 6366113*$.1^8 + 13486540*$.1^7 - 17861951*$.1^6 - 12151477*$.1^5 + 22331038*$.1^4 - 6313452*$.1^3 - 683605*$.1^2 + 175252*$.1 - 2548[] 368,1,2,x,3,x,5,x,7,x + 4,11,x + 6,13,x + 2[] 368,2,2,x,3,x - 1,5,x + 4,7,x + 2,11,x - 4,13,x + 5[] 368,3,2,x,3,x + 3,5,x,7,x - 2,11,x,13,x + 5[] 368,4,2,x,3,x - 1,5,x + 2,7,x - 4,11,x - 2,13,x - 7[] 368,5,2,x,3,x,5,x - 4,7,x - 4,11,x + 2,13,x + 2[] 368,6,2,x,3,x - 3,5,x + 2,7,x - 4,11,x + 2,13,x + 5[] 368,7,2,x,3,x + 1,5,x,7,x + 2,11,x,13,x + 1[] 368,8,2,x^2,3,x^2 - x - 4,5,x^2 - 4*x + 4,7,x^2,11,x^2 + 2*x - 16,13,x^2 - 5*x + 2[] 368,9,2,x^2,3,x^2 - 5,5,x^2 + 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 6*x + 4,13,x^2 - 6*x + 9[] 369,1,2,x - 2,3,x,5,x - 4,7,x + 2,11,x - 3,13,x + 6[] 369,2,2,x,3,x,5,x - 2,7,x + 4,11,x + 5,13,x + 4[] 369,3,2,x^2 - 2,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 + 2*x - 1,13,x^2 - 4*x - 14[] 369,4,2,x^3 + 2*x^2 - 2*x - 2,3,x^3,5,x^3 + 4*x^2 + 2*x - 2,7,x^3 - 4*x - 2,11,x^3 + 11*x^2 + 37*x + 37,13,x^3 + 2*x^2 - 12*x + 10[] 369,5,2,x^3 - 2*x^2 - 2*x + 2,3,x^3,5,x^3 - 4*x^2 + 2*x + 2,7,x^3 - 4*x - 2,11,x^3 - 11*x^2 + 37*x - 37,13,x^3 + 2*x^2 - 12*x + 10[] 369,6,2,x^3 - x^2 - 5*x + 1,3,x^3,5,x^3 - 2*x^2 - 4*x + 4,7,x^3 - 6*x^2 + 8*x - 2,11,x^3 + 2*x^2 - 20*x - 50,13,x^3 + 2*x^2 - 12*x - 8[] 369,7,2,x^3 + x^2 - 4*x - 2,3,x^3,5,x^3 + 4*x^2 - 2*x - 4,7,x^3 - 2*x^2 - 14*x + 32,11,x^3 - 4*x^2 + x + 4,13,x^3 - 8*x^2 + 14*x + 4[] 370,1,2,x + 1,3,x,5,x + 1,7,x,11,x + 4,13,x - 2[] 370,2,2,x + 1,3,x + 2,5,x + 1,7,x + 1,11,x - 3,13,x + 4[] 370,3,2,x + 1,3,x - 2,5,x - 1,7,x - 1,11,x - 3,13,x[] 370,4,2,x - 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x - 2[] 370,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 + 4*x - 8,13,x^2 + 4*x - 8[] 370,6,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 3*x - 6,11,x^2 + x - 8,13,x^2 - 2*x - 32[] 370,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 10*x + 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + x^2 - 8*x - 10,11,x^3 - 11*x^2 + 28*x + 8,13,x^3 - 40*x - 32[] 371,1,2,x - 1,3,x + 1,5,x,7,x + 1,11,x,13,x - 1[] 371,2,2,x - 2,3,x,5,x - 3,7,x - 1,11,x - 3,13,x + 6[] 371,3,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + 3*x + 1,7,x^2 - 2*x + 1,11,x^2 - 5,13,x^2 + 3*x + 1[] 371,4,2,x^3 - 4*x - 1,3,x^3 - 4*x + 1,5,x^3 + 5*x^2 + 3*x - 8,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 - x - 8,13,x^3 + 12*x^2 + 44*x + 47[] 371,5,2,x^9 - 15*x^7 + x^6 + 74*x^5 - 9*x^4 - 132*x^3 + 24*x^2 + 64*x - 16,3,x^9 - 3*x^8 - 15*x^7 + 42*x^6 + 76*x^5 - 172*x^4 - 172*x^3 + 192*x^2 + 176*x + 32,5,x^9 - 9*x^8 + 9*x^7 + 130*x^6 - 395*x^5 - 83*x^4 + 1495*x^3 - 1218*x^2 - 960*x + 1112,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,11,x^9 - 59*x^7 + 56*x^6 + 1139*x^5 - 1836*x^4 - 7209*x^3 + 12916*x^2 + 14240*x - 23872,13,x^9 - 13*x^8 + 3*x^7 + 590*x^6 - 2604*x^5 + 1880*x^4 + 7728*x^3 - 13600*x^2 + 6720*x - 896[] 371,6,2,x^11 + x^10 - 20*x^9 - 19*x^8 + 140*x^7 + 125*x^6 - 396*x^5 - 333*x^4 + 359*x^3 + 298*x^2 - 4*x - 24,3,x^11 + x^10 - 26*x^9 - 17*x^8 + 251*x^7 + 86*x^6 - 1088*x^5 - 144*x^4 + 2012*x^3 + 248*x^2 - 1296*x - 400,5,x^11 - 2*x^10 - 37*x^9 + 49*x^8 + 514*x^7 - 359*x^6 - 3152*x^5 + 632*x^4 + 7624*x^3 + 916*x^2 - 3680*x + 768,7,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,11,x^11 - 5*x^10 - 58*x^9 + 238*x^8 + 1089*x^7 - 2465*x^6 - 9480*x^5 + 1576*x^4 + 19376*x^3 + 7984*x^2 - 6272*x - 3072,13,x^11 - 13*x^10 + 2*x^9 + 537*x^8 - 1277*x^7 - 7054*x^6 + 21444*x^5 + 35208*x^4 - 113840*x^3 - 47264*x^2 + 181184*x - 73600[] 372,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x,13,x + 6[] 372,2,2,x,3,x - 1,5,x + 3,7,x + 5,11,x - 2,13,x + 4[] 372,3,2,x,3,x - 1,5,x + 2,7,x - 4,11,x,13,x - 2[] 372,4,2,x,3,x - 1,5,x - 3,7,x + 1,11,x,13,x - 2[] 372,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2 + x - 4,11,x^2 - 2*x - 16,13,x^2 - 6*x - 8[] 373,1,2,x + 2,3,x - 1,5,x - 2,7,x + 4,11,x + 6,13,x + 1[] 373,2,2,x^12 + 4*x^11 - 8*x^10 - 43*x^9 + 14*x^8 + 161*x^7 + 17*x^6 - 260*x^5 - 53*x^4 + 177*x^3 + 18*x^2 - 42*x + 7,3,x^12 + 15*x^11 + 88*x^10 + 237*x^9 + 183*x^8 - 518*x^7 - 1320*x^6 - 819*x^5 + 588*x^4 + 1026*x^3 + 491*x^2 + 98*x + 7,5,x^12 + 11*x^11 + 26*x^10 - 118*x^9 - 605*x^8 - 182*x^7 + 3140*x^6 + 4749*x^5 - 2919*x^4 - 10800*x^3 - 6876*x^2 - 689*x + 331,7,x^12 + x^11 - 47*x^10 - 41*x^9 + 841*x^8 + 585*x^7 - 7225*x^6 - 3446*x^5 + 30765*x^4 + 7470*x^3 - 59872*x^2 - 3760*x + 40397,11,x^12 + 8*x^11 - 35*x^10 - 352*x^9 + 261*x^8 + 4248*x^7 - 2641*x^6 - 19126*x^5 + 22857*x^4 + 10925*x^3 - 20993*x^2 + 1383*x + 3397,13,x^12 + 10*x^11 - 36*x^10 - 625*x^9 - 608*x^8 + 11245*x^7 + 29822*x^6 - 48645*x^5 - 246092*x^4 - 198302*x^3 + 119773*x^2 + 149389*x + 33169[] 373,3,2,x^17 - 4*x^16 - 18*x^15 + 85*x^14 + 111*x^13 - 713*x^12 - 211*x^11 + 3017*x^10 - 469*x^9 - 6832*x^8 + 2513*x^7 + 8146*x^6 - 3634*x^5 - 4743*x^4 + 2092*x^3 + 1142*x^2 - 417*x - 62,3,x^17 - 14*x^16 + 61*x^15 + 17*x^14 - 866*x^13 + 1843*x^12 + 2698*x^11 - 13639*x^10 + 5907*x^9 + 34646*x^8 - 42911*x^7 - 24721*x^6 + 64125*x^5 - 14879*x^4 - 21272*x^3 + 6996*x^2 + 2464*x - 464,5,x^17 - 9*x^16 - 8*x^15 + 282*x^14 - 461*x^13 - 2974*x^12 + 8406*x^11 + 12105*x^10 - 55679*x^9 - 6974*x^8 + 171042*x^7 - 73089*x^6 - 246837*x^5 + 168692*x^4 + 161652*x^3 - 131216*x^2 - 38512*x + 33856,7,x^17 - 3*x^16 - 59*x^15 + 203*x^14 + 1181*x^13 - 4735*x^12 - 9117*x^11 + 47250*x^10 + 20329*x^9 - 220646*x^8 + 65432*x^7 + 456300*x^6 - 320455*x^5 - 299884*x^4 + 290500*x^3 - 8688*x^2 - 27600*x + 2944,11,x^17 - 16*x^16 + 36*x^15 + 706*x^14 - 4217*x^13 - 5808*x^12 + 101605*x^11 - 143010*x^10 - 915761*x^9 + 2938069*x^8 + 1586119*x^7 - 17823126*x^6 + 18908999*x^5 + 25080886*x^4 - 70775476*x^3 + 60414065*x^2 - 22749671*x + 3214412,13,x^17 + x^16 - 93*x^15 - 138*x^14 + 3054*x^13 + 5139*x^12 - 44918*x^11 - 72993*x^10 + 331571*x^9 + 471762*x^8 - 1261603*x^7 - 1397971*x^6 + 2332782*x^5 + 1584167*x^4 - 1689197*x^3 - 199911*x^2 + 270108*x - 36259[] Total time: 20.369 seconds, Total memory usage: 6.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:11:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [373..379] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 13:10:40 on modular [Seed = 2723511516] ------------------------------------- 373,1,2,$.1 + 2,3,$.1 - 1,5,$.1 - 2,7,$.1 + 4,11,$.1 + 6,13,$.1 + 1[] 373,2,2,$.1^12 + 4*$.1^11 - 8*$.1^10 - 43*$.1^9 + 14*$.1^8 + 161*$.1^7 + 17*$.1^6 - 260*$.1^5 - 53*$.1^4 + 177*$.1^3 + 18*$.1^2 - 42*$.1 + 7,3,$.1^12 + 15*$.1^11 + 88*$.1^10 + 237*$.1^9 + 183*$.1^8 - 518*$.1^7 - 1320*$.1^6 - 819*$.1^5 + 588*$.1^4 + 1026*$.1^3 + 491*$.1^2 + 98*$.1 + 7,5,$.1^12 + 11*$.1^11 + 26*$.1^10 - 118*$.1^9 - 605*$.1^8 - 182*$.1^7 + 3140*$.1^6 + 4749*$.1^5 - 2919*$.1^4 - 10800*$.1^3 - 6876*$.1^2 - 689*$.1 + 331,7,$.1^12 + $.1^11 - 47*$.1^10 - 41*$.1^9 + 841*$.1^8 + 585*$.1^7 - 7225*$.1^6 - 3446*$.1^5 + 30765*$.1^4 + 7470*$.1^3 - 59872*$.1^2 - 3760*$.1 + 40397,11,$.1^12 + 8*$.1^11 - 35*$.1^10 - 352*$.1^9 + 261*$.1^8 + 4248*$.1^7 - 2641*$.1^6 - 19126*$.1^5 + 22857*$.1^4 + 10925*$.1^3 - 20993*$.1^2 + 1383*$.1 + 3397,13,$.1^12 + 10*$.1^11 - 36*$.1^10 - 625*$.1^9 - 608*$.1^8 + 11245*$.1^7 + 29822*$.1^6 - 48645*$.1^5 - 246092*$.1^4 - 198302*$.1^3 + 119773*$.1^2 + 149389*$.1 + 33169[] 373,3,2,$.1^17 - 4*$.1^16 - 18*$.1^15 + 85*$.1^14 + 111*$.1^13 - 713*$.1^12 - 211*$.1^11 + 3017*$.1^10 - 469*$.1^9 - 6832*$.1^8 + 2513*$.1^7 + 8146*$.1^6 - 3634*$.1^5 - 4743*$.1^4 + 2092*$.1^3 + 1142*$.1^2 - 417*$.1 - 62,3,$.1^17 - 14*$.1^16 + 61*$.1^15 + 17*$.1^14 - 866*$.1^13 + 1843*$.1^12 + 2698*$.1^11 - 13639*$.1^10 + 5907*$.1^9 + 34646*$.1^8 - 42911*$.1^7 - 24721*$.1^6 + 64125*$.1^5 - 14879*$.1^4 - 21272*$.1^3 + 6996*$.1^2 + 2464*$.1 - 464,5,$.1^17 - 9*$.1^16 - 8*$.1^15 + 282*$.1^14 - 461*$.1^13 - 2974*$.1^12 + 8406*$.1^11 + 12105*$.1^10 - 55679*$.1^9 - 6974*$.1^8 + 171042*$.1^7 - 73089*$.1^6 - 246837*$.1^5 + 168692*$.1^4 + 161652*$.1^3 - 131216*$.1^2 - 38512*$.1 + 33856,7,$.1^17 - 3*$.1^16 - 59*$.1^15 + 203*$.1^14 + 1181*$.1^13 - 4735*$.1^12 - 9117*$.1^11 + 47250*$.1^10 + 20329*$.1^9 - 220646*$.1^8 + 65432*$.1^7 + 456300*$.1^6 - 320455*$.1^5 - 299884*$.1^4 + 290500*$.1^3 - 8688*$.1^2 - 27600*$.1 + 2944,11,$.1^17 - 16*$.1^16 + 36*$.1^15 + 706*$.1^14 - 4217*$.1^13 - 5808*$.1^12 + 101605*$.1^11 - 143010*$.1^10 - 915761*$.1^9 + 2938069*$.1^8 + 1586119*$.1^7 - 17823126*$.1^6 + 18908999*$.1^5 + 25080886*$.1^4 - 70775476*$.1^3 + 60414065*$.1^2 - 22749671*$.1 + 3214412,13,$.1^17 + $.1^16 - 93*$.1^15 - 138*$.1^14 + 3054*$.1^13 + 5139*$.1^12 - 44918*$.1^11 - 72993*$.1^10 + 331571*$.1^9 + 471762*$.1^8 - 1261603*$.1^7 - 1397971*$.1^6 + 2332782*$.1^5 + 1584167*$.1^4 - 1689197*$.1^3 - 199911*$.1^2 + 270108*$.1 - 36259[] 374,1,2,x + 1,3,x,5,x,7,x + 2,11,x + 1,13,x + 2[] 374,2,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 6*x - 5,5,x^3 + x^2 - 10*x - 15,7,x^3 - x^2 - 16*x + 25,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 11*x^2 + 34*x - 29[] 374,3,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 2*x + 7,5,x^3 + x^2 - 10*x + 9,7,x^3 - 7*x^2 + 12*x - 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 - 2*x - 7[] 374,4,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - x^3 - 10*x^2 + 9*x + 16,5,x^4 - 5*x^3 - 6*x^2 + 47*x - 36,7,x^4 - x^3 - 22*x^2 + 3*x + 98,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + 3*x^3 - 44*x^2 - 65*x + 350[] 374,5,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 13*x - 4,5,x^4 + x^3 - 12*x^2 - 13*x - 2,7,x^4 - x^3 - 16*x^2 + 37*x - 16,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + x^3 - 44*x^2 - 67*x + 2[] 375,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 + x - 1,11,x^2 - 4*x - 1,13,x^2 + 8*x + 11[] 375,2,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 5*x + 5,11,x^2 + 8*x + 11,13,x^2 - 6*x + 9[] 375,3,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 - x - 1,11,x^2 - 4*x - 1,13,x^2 - 8*x + 11[] 375,4,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 5*x + 5,11,x^2 + 8*x + 11,13,x^2 + 6*x + 9[] 375,5,2,x^4 + 3*x^3 - 3*x^2 - 11*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4,7,x^4 - 4*x^3 - 16*x^2 + 40*x + 80,11,x^4 - 6*x^3 - 12*x^2 + 88*x - 16,13,x^4 - 8*x^3 - 8*x^2 + 136*x - 176[] 375,6,2,x^4 - 3*x^3 - 3*x^2 + 11*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4,7,x^4 + 4*x^3 - 16*x^2 - 40*x + 80,11,x^4 - 6*x^3 - 12*x^2 + 88*x - 16,13,x^4 + 8*x^3 - 8*x^2 - 136*x - 176[] 376,1,2,x^2,3,x^2 + x - 1,5,x^2 + 2*x - 4,7,x^2 + 3*x + 1,11,x^2 + 6*x + 4,13,x^2 - 2*x - 4[] 376,2,2,x^2,3,x^2 + x - 1,5,x^2 + 4*x + 4,7,x^2 - x - 11,11,x^2 + 4*x + 4,13,x^2 + 6*x + 4[] 376,3,2,x^4,3,x^4 - 3*x^3 - 5*x^2 + 16*x - 8,5,x^4 - 14*x^2 + 8,7,x^4 - 5*x^3 + x^2 + 8*x - 4,11,x^4 - 8*x^3 - 2*x^2 + 72*x + 40,13,x^4 + 10*x^3 + 10*x^2 - 116*x - 200[] 376,4,2,x^4,3,x^4 + x^3 - 9*x^2 - 4*x + 16,5,x^4 - 4*x^3 - 4*x^2 + 16*x + 16,7,x^4 + 3*x^3 - 11*x^2 - 8*x + 16,11,x^4 - 4*x^3 - 4*x^2 + 16*x + 16,13,x^4 - 12*x^3 + 44*x^2 - 48*x + 16[] 377,1,2,x - 1,3,x,5,x + 2,7,x,11,x + 4,13,x - 1[] 377,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 - 4*x + 4,13,x^2 + 2*x + 1[] 377,3,2,x^5 + x^4 - 5*x^3 - 3*x^2 + 6*x + 1,3,x^5 + 4*x^4 + x^3 - 6*x^2 + 1,5,x^5 + 2*x^4 - 10*x^3 - 11*x^2 + 10*x + 9,7,x^5 + 11*x^4 + 41*x^3 + 64*x^2 + 41*x + 9,11,x^5 - 3*x^4 - 24*x^3 + 73*x^2 + 61*x - 179,13,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1[] 377,4,2,x^5 + 3*x^4 - 3*x^3 - 13*x^2 - 8*x - 1,3,x^5 + 4*x^4 - 5*x^3 - 30*x^2 - 16*x + 7,5,x^5 - 2*x^4 - 12*x^3 + 27*x^2 + 2*x - 3,7,x^5 + 15*x^4 + 79*x^3 + 166*x^2 + 109*x + 21,11,x^5 + 7*x^4 - 67*x^2 - 71*x + 27,13,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1[] 377,5,2,x^7 - 3*x^6 - 8*x^5 + 26*x^4 + 9*x^3 - 36*x^2 - 14*x + 3,3,x^7 - 2*x^6 - 11*x^5 + 16*x^4 + 30*x^3 - 33*x^2 - 6*x + 2,5,x^7 + 2*x^6 - 18*x^5 - 7*x^4 + 106*x^3 - 111*x^2 - 8*x + 36,7,x^7 - 7*x^6 + 5*x^5 + 52*x^4 - 117*x^3 + 51*x^2 + 40*x - 18,11,x^7 + 3*x^6 - 66*x^5 - 159*x^4 + 1199*x^3 + 1051*x^2 - 8080*x + 6508,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 377,6,2,x^9 - x^8 - 13*x^7 + 13*x^6 + 51*x^5 - 50*x^4 - 59*x^3 + 45*x^2 + 20*x - 3,3,x^9 - 19*x^7 + 6*x^6 + 120*x^5 - 59*x^4 - 304*x^3 + 184*x^2 + 264*x - 184,5,x^9 - 2*x^8 - 24*x^7 + 39*x^6 + 178*x^5 - 247*x^4 - 400*x^3 + 536*x^2 + 32*x - 48,7,x^9 - 17*x^8 + 99*x^7 - 150*x^6 - 655*x^5 + 2625*x^4 - 1932*x^3 - 2672*x^2 + 2032*x + 1352,11,x^9 - 3*x^8 - 38*x^7 + 145*x^6 + 151*x^5 - 747*x^4 - 272*x^3 + 984*x^2 + 464*x - 48,13,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1[] 378,1,2,x + 1,3,x,5,x + 1,7,x + 1,11,x + 5,13,x[] 378,2,2,x + 1,3,x,5,x,7,x - 1,11,x,13,x - 5[] 378,3,2,x + 1,3,x,5,x + 4,7,x + 1,11,x - 4,13,x - 3[] 378,4,2,x + 1,3,x,5,x + 3,7,x - 1,11,x - 3,13,x + 4[] 378,5,2,x - 1,3,x,5,x - 1,7,x + 1,11,x - 5,13,x[] 378,6,2,x - 1,3,x,5,x - 4,7,x + 1,11,x + 4,13,x - 3[] 378,7,2,x - 1,3,x,5,x,7,x - 1,11,x,13,x - 5[] 378,8,2,x - 1,3,x,5,x - 3,7,x - 1,11,x + 3,13,x + 4[] 379,1,2,x^13 + 5*x^12 - 5*x^11 - 56*x^10 - 27*x^9 + 210*x^8 + 184*x^7 - 347*x^6 - 346*x^5 + 252*x^4 + 246*x^3 - 60*x^2 - 48*x - 1,3,x^13 + 5*x^12 - 9*x^11 - 76*x^10 - 29*x^9 + 318*x^8 + 271*x^7 - 507*x^6 - 493*x^5 + 280*x^4 + 291*x^3 - 22*x^2 - 37*x - 2,5,x^13 + 20*x^12 + 156*x^11 + 555*x^10 + 551*x^9 - 2138*x^8 - 6937*x^7 - 5820*x^6 + 2699*x^5 + 6331*x^4 + 3300*x^3 + 684*x^2 + 45*x - 1,7,x^13 + 3*x^12 - 51*x^11 - 165*x^10 + 927*x^9 + 3231*x^8 - 7121*x^7 - 26856*x^6 + 22770*x^5 + 88955*x^4 - 44958*x^3 - 103932*x^2 + 61419*x - 6962,11,x^13 + 20*x^12 + 118*x^11 - 159*x^10 - 4297*x^9 - 13356*x^8 + 15642*x^7 + 163400*x^6 + 305266*x^5 + 144171*x^4 - 90510*x^3 - 63404*x^2 + 4863*x + 982,13,x^13 + 11*x^12 - 19*x^11 - 598*x^10 - 1283*x^9 + 8493*x^8 + 33160*x^7 - 21888*x^6 - 215862*x^5 - 127992*x^4 + 378558*x^3 + 364127*x^2 - 41109*x - 77076[] 379,2,2,x^18 - 3*x^17 - 22*x^16 + 69*x^15 + 190*x^14 - 638*x^13 - 807*x^12 + 3041*x^11 + 1680*x^10 - 7967*x^9 - 1220*x^8 + 11334*x^7 - 1006*x^6 - 8079*x^5 + 1938*x^4 + 2287*x^3 - 752*x^2 - 68*x + 24,3,x^18 - x^17 - 37*x^16 + 36*x^15 + 559*x^14 - 528*x^13 - 4439*x^12 + 4029*x^11 + 19833*x^10 - 16844*x^9 - 49523*x^8 + 37022*x^7 + 65433*x^6 - 37568*x^5 - 43264*x^4 + 15784*x^3 + 12768*x^2 - 1952*x - 1216,5,x^18 - 22*x^17 + 186*x^16 - 638*x^15 - 432*x^14 + 10139*x^13 - 24686*x^12 - 19276*x^11 + 178471*x^10 - 200705*x^9 - 313477*x^8 + 829502*x^7 - 236421*x^6 - 754823*x^5 + 554475*x^4 + 137385*x^3 - 165124*x^2 - 5558*x + 13539,7,x^18 - x^17 - 71*x^16 + 103*x^15 + 1973*x^14 - 3563*x^13 - 27635*x^12 + 57544*x^11 + 212620*x^10 - 495675*x^9 - 908364*x^8 + 2385308*x^7 + 2003077*x^6 - 6316692*x^5 - 1626708*x^4 + 8415004*x^3 - 938464*x^2 - 4314960*x + 1667936,11,x^18 - 10*x^17 - 56*x^16 + 835*x^15 + 139*x^14 - 25232*x^13 + 44874*x^12 + 320464*x^11 - 991608*x^10 - 1295023*x^9 + 7267954*x^8 - 2597706*x^7 - 15131019*x^6 + 10747474*x^5 + 12487788*x^4 - 8891044*x^3 - 4374984*x^2 + 1890416*x + 722208,13,x^18 - 9*x^17 - 73*x^16 + 808*x^15 + 1737*x^14 - 29343*x^13 - 4988*x^12 + 551478*x^11 - 460270*x^10 - 5643760*x^9 + 8372598*x^8 + 29575499*x^7 - 60491577*x^6 - 59028994*x^5 + 179211796*x^4 - 27182716*x^3 - 123218944*x^2 + 59018432*x + 568064[] Total time: 19.579 seconds, Total memory usage: 6.48MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:21:31 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [379..385] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 13:21:08 on modular [Seed = 1270650754] ------------------------------------- 379,1,2,$.1^13 + 5*$.1^12 - 5*$.1^11 - 56*$.1^10 - 27*$.1^9 + 210*$.1^8 + 184*$.1^7 - 347*$.1^6 - 346*$.1^5 + 252*$.1^4 + 246*$.1^3 - 60*$.1^2 - 48*$.1 - 1,3,$.1^13 + 5*$.1^12 - 9*$.1^11 - 76*$.1^10 - 29*$.1^9 + 318*$.1^8 + 271*$.1^7 - 507*$.1^6 - 493*$.1^5 + 280*$.1^4 + 291*$.1^3 - 22*$.1^2 - 37*$.1 - 2,5,$.1^13 + 20*$.1^12 + 156*$.1^11 + 555*$.1^10 + 551*$.1^9 - 2138*$.1^8 - 6937*$.1^7 - 5820*$.1^6 + 2699*$.1^5 + 6331*$.1^4 + 3300*$.1^3 + 684*$.1^2 + 45*$.1 - 1,7,$.1^13 + 3*$.1^12 - 51*$.1^11 - 165*$.1^10 + 927*$.1^9 + 3231*$.1^8 - 7121*$.1^7 - 26856*$.1^6 + 22770*$.1^5 + 88955*$.1^4 - 44958*$.1^3 - 103932*$.1^2 + 61419*$.1 - 6962,11,$.1^13 + 20*$.1^12 + 118*$.1^11 - 159*$.1^10 - 4297*$.1^9 - 13356*$.1^8 + 15642*$.1^7 + 163400*$.1^6 + 305266*$.1^5 + 144171*$.1^4 - 90510*$.1^3 - 63404*$.1^2 + 4863*$.1 + 982,13,$.1^13 + 11*$.1^12 - 19*$.1^11 - 598*$.1^10 - 1283*$.1^9 + 8493*$.1^8 + 33160*$.1^7 - 21888*$.1^6 - 215862*$.1^5 - 127992*$.1^4 + 378558*$.1^3 + 364127*$.1^2 - 41109*$.1 - 77076[] 379,2,2,$.1^18 - 3*$.1^17 - 22*$.1^16 + 69*$.1^15 + 190*$.1^14 - 638*$.1^13 - 807*$.1^12 + 3041*$.1^11 + 1680*$.1^10 - 7967*$.1^9 - 1220*$.1^8 + 11334*$.1^7 - 1006*$.1^6 - 8079*$.1^5 + 1938*$.1^4 + 2287*$.1^3 - 752*$.1^2 - 68*$.1 + 24,3,$.1^18 - $.1^17 - 37*$.1^16 + 36*$.1^15 + 559*$.1^14 - 528*$.1^13 - 4439*$.1^12 + 4029*$.1^11 + 19833*$.1^10 - 16844*$.1^9 - 49523*$.1^8 + 37022*$.1^7 + 65433*$.1^6 - 37568*$.1^5 - 43264*$.1^4 + 15784*$.1^3 + 12768*$.1^2 - 1952*$.1 - 1216,5,$.1^18 - 22*$.1^17 + 186*$.1^16 - 638*$.1^15 - 432*$.1^14 + 10139*$.1^13 - 24686*$.1^12 - 19276*$.1^11 + 178471*$.1^10 - 200705*$.1^9 - 313477*$.1^8 + 829502*$.1^7 - 236421*$.1^6 - 754823*$.1^5 + 554475*$.1^4 + 137385*$.1^3 - 165124*$.1^2 - 5558*$.1 + 13539,7,$.1^18 - $.1^17 - 71*$.1^16 + 103*$.1^15 + 1973*$.1^14 - 3563*$.1^13 - 27635*$.1^12 + 57544*$.1^11 + 212620*$.1^10 - 495675*$.1^9 - 908364*$.1^8 + 2385308*$.1^7 + 2003077*$.1^6 - 6316692*$.1^5 - 1626708*$.1^4 + 8415004*$.1^3 - 938464*$.1^2 - 4314960*$.1 + 1667936,11,$.1^18 - 10*$.1^17 - 56*$.1^16 + 835*$.1^15 + 139*$.1^14 - 25232*$.1^13 + 44874*$.1^12 + 320464*$.1^11 - 991608*$.1^10 - 1295023*$.1^9 + 7267954*$.1^8 - 2597706*$.1^7 - 15131019*$.1^6 + 10747474*$.1^5 + 12487788*$.1^4 - 8891044*$.1^3 - 4374984*$.1^2 + 1890416*$.1 + 722208,13,$.1^18 - 9*$.1^17 - 73*$.1^16 + 808*$.1^15 + 1737*$.1^14 - 29343*$.1^13 - 4988*$.1^12 + 551478*$.1^11 - 460270*$.1^10 - 5643760*$.1^9 + 8372598*$.1^8 + 29575499*$.1^7 - 60491577*$.1^6 - 59028994*$.1^5 + 179211796*$.1^4 - 27182716*$.1^3 - 123218944*$.1^2 + 59018432*$.1 + 568064[] 380,1,2,x,3,x - 2,5,x + 1,7,x - 2,11,x,13,x - 6[] 380,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 4,13,x + 4[] 380,3,2,x^2,3,x^2 + 4*x + 2,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 + 4*x + 4,13,x^2 + 4*x - 14[] 380,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 - 4*x + 4,11,x^2 - 12,13,x^2 + 2*x - 2[] 381,1,2,x - 2,3,x - 1,5,x - 3,7,x + 4,11,x - 6,13,x + 7[] 381,2,2,x,3,x - 1,5,x + 1,7,x + 2,11,x + 4,13,x + 3[] 381,3,2,x^5 + x^4 - 5*x^3 - 3*x^2 + 5*x + 2,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 5*x^4 - 2*x^3 - 24*x^2 + 16,7,x^5 - 24*x^3 + 8*x^2 + 80*x - 64,11,x^5 + 16*x^4 + 91*x^3 + 220*x^2 + 193*x + 2,13,x^5 - 3*x^4 - 11*x^3 + 47*x^2 - 41*x - 1[] 381,4,2,x^5 - 2*x^4 - 6*x^3 + 10*x^2 + 5*x - 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 - x^4 - 9*x^3 + 11*x^2 + 7*x - 1,7,x^5 - 13*x^3 - 4*x^2 + 33*x + 2,11,x^5 - 14*x^4 + 63*x^3 - 96*x^2 + 33*x + 8,13,x^5 + 5*x^4 - 3*x^3 - 33*x^2 - 9*x + 19[] 381,5,2,x^9 + 2*x^8 - 14*x^7 - 26*x^6 + 59*x^5 + 99*x^4 - 66*x^3 - 102*x^2 - 24*x - 1,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 + 4*x^8 - 25*x^7 - 94*x^6 + 185*x^5 + 524*x^4 - 612*x^3 - 384*x^2 + 592*x - 160,7,x^9 - 10*x^8 + 7*x^7 + 222*x^6 - 707*x^5 - 532*x^4 + 5304*x^3 - 7544*x^2 + 2352*x + 1152,11,x^9 - 8*x^8 - 18*x^7 + 238*x^6 - 29*x^5 - 2258*x^4 + 1474*x^3 + 7234*x^2 - 3671*x - 5644,13,x^9 - 14*x^8 + 30*x^7 + 344*x^6 - 1521*x^5 - 894*x^4 + 10198*x^3 - 5728*x^2 - 4575*x + 418[] 382,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 4*x + 1,5,x^3 + 4*x^2 + x - 1,7,x^3 + x^2 - 4*x + 1,11,x^3 + 3*x^2 - 10*x - 25,13,x^3 + 3*x^2 + 3*x + 1[] 382,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 5*x^2 + 6*x + 1,5,x^3 + 6*x^2 + 5*x - 13,7,x^3 + 5*x^2 - 8*x - 41,11,x^3 + 3*x^2 - 18*x - 27,13,x^3 + 11*x^2 + 31*x + 13[] 382,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 3*x^3 - 2*x^2 + 9*x - 4,5,x^4 - 4*x^3 + x^2 + 5*x - 2,7,x^4 - x^3 - 6*x^2 + 3*x + 8,11,x^4 - 3*x^3 - 10*x^2 + 33*x - 20,13,x^4 + x^3 - 11*x^2 - x + 2[] 382,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 3*x^4 - 8*x^3 + 25*x^2 + 8*x - 32,5,x^5 - 8*x^4 + 13*x^3 + 23*x^2 - 36*x - 36,7,x^5 - x^4 - 18*x^3 - 23*x^2 + 8*x + 16,11,x^5 - 5*x^4 - 22*x^3 + 113*x^2 + 62*x - 446,13,x^5 - x^4 - 33*x^3 + 73*x^2 + 44*x + 4[] 383,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - x - 1,7,x^2 + 4*x - 1,11,x^2 - 5*x + 5,13,x^2[] 383,2,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 - x^2 + 8*x + 3,3,x^6 - x^5 - 6*x^4 + 5*x^3 + 5*x^2 - 2*x - 1,5,x^6 + 4*x^5 - 15*x^3 - 14*x^2 + 2*x + 3,7,x^6 + 7*x^5 + 12*x^4 - 14*x^3 - 55*x^2 - 39*x - 1,11,x^6 + 7*x^5 + 8*x^4 - 32*x^3 - 66*x^2 + 2*x + 43,13,x^6 + 18*x^5 + 122*x^4 + 376*x^3 + 482*x^2 + 139*x + 11[] 383,3,2,x^24 - 5*x^23 - 26*x^22 + 160*x^21 + 244*x^20 - 2173*x^19 - 711*x^18 + 16368*x^17 - 4007*x^16 - 75111*x^15 + 42025*x^14 + 217575*x^13 - 160547*x^12 - 399209*x^11 + 331301*x^10 + 452295*x^9 - 388291*x^8 - 296126*x^7 + 247918*x^6 + 96139*x^5 - 75925*x^4 - 9553*x^3 + 8302*x^2 - 342*x - 49,3,x^24 - 2*x^23 - 51*x^22 + 104*x^21 + 1109*x^20 - 2290*x^19 - 13450*x^18 + 27911*x^17 + 100018*x^16 - 206849*x^15 - 472337*x^14 + 965359*x^13 + 1415309*x^12 - 2843156*x^11 - 2583424*x^10 + 5141445*x^9 + 2555730*x^8 - 5332948*x^7 - 929626*x^6 + 2720600*x^5 - 153532*x^4 - 425022*x^3 + 17806*x^2 + 19571*x + 743,5,x^24 - 3*x^23 - 89*x^22 + 259*x^21 + 3375*x^20 - 9557*x^19 - 70951*x^18 + 196783*x^17 + 899813*x^16 - 2474270*x^15 - 6999964*x^14 + 19514728*x^13 + 32247680*x^12 - 95294656*x^11 - 78085888*x^10 + 273042688*x^9 + 61524736*x^8 - 408682496*x^7 + 74373120*x^6 + 247068672*x^5 - 100229120*x^4 - 38567936*x^3 + 23134208*x^2 - 2490368*x - 65536,7,x^24 - 17*x^23 + 36*x^22 + 942*x^21 - 5769*x^20 - 11929*x^19 + 182178*x^18 - 205659*x^17 - 2403957*x^16 + 6825011*x^15 + 13078328*x^14 - 71066450*x^13 - 1315722*x^12 + 361882707*x^11 - 292414708*x^10 - 990516687*x^9 + 1345964622*x^8 + 1461617571*x^7 - 2834498399*x^6 - 1056451767*x^5 + 3147665499*x^4 + 245611927*x^3 - 1779168466*x^2 + 40526951*x + 405907721,11,x^24 - 170*x^22 + 3*x^21 + 12126*x^20 - 670*x^19 - 473243*x^18 + 52527*x^17 + 11062807*x^16 - 1980462*x^15 - 159713668*x^14 + 39812152*x^13 + 1420991840*x^12 - 438268128*x^11 - 7585055872*x^10 + 2621443712*x^9 + 23139197184*x^8 - 8438759936*x^7 - 37824342016*x^6 + 15647381504*x^5 + 29517463552*x^4 - 15904178176*x^3 - 7621558272*x^2 + 6398541824*x - 1074200576,13,x^24 - 28*x^23 + 178*x^22 + 2020*x^21 - 29764*x^20 + 23887*x^19 + 1415095*x^18 - 6150628*x^17 - 25591408*x^16 + 225928952*x^15 - 9428192*x^14 - 3724661216*x^13 + 6876164864*x^12 + 29302047872*x^11 - 100363459584*x^10 - 79709571072*x^9 + 627035143168*x^8 - 242064082944*x^7 - 1764248862720*x^6 + 1677457481728*x^5 + 1825612185600*x^4 - 2161780850688*x^3 - 781524729856*x^2 + 821170274304*x + 147586023424[] 384,1,2,x,3,x + 1,5,x,7,x + 2,11,x + 4,13,x + 6[] 384,2,2,x,3,x - 1,5,x,7,x - 2,11,x - 4,13,x + 6[] 384,3,2,x,3,x - 1,5,x,7,x + 2,11,x - 4,13,x - 6[] 384,4,2,x,3,x - 1,5,x - 4,7,x - 2,11,x + 4,13,x + 2[] 384,5,2,x,3,x + 1,5,x,7,x - 2,11,x + 4,13,x - 6[] 384,6,2,x,3,x + 1,5,x - 4,7,x + 2,11,x - 4,13,x + 2[] 384,7,2,x,3,x + 1,5,x + 4,7,x - 2,11,x - 4,13,x - 2[] 384,8,2,x,3,x - 1,5,x + 4,7,x + 2,11,x + 4,13,x - 2[] 385,1,2,x + 1,3,x,5,x - 1,7,x + 1,11,x - 1,13,x + 6[] 385,2,2,x + 1,3,x + 2,5,x - 1,7,x - 1,11,x + 1,13,x - 4[] 385,3,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 2*x + 1,13,x^2 - 4*x + 2[] 385,4,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 2*x + 1,13,x^2 + 2*x - 2[] 385,5,2,x^3 + 3*x^2 - x - 5,3,x^3 + 2*x^2 - 2*x - 2,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 2*x^2 - 22*x - 2[] 385,6,2,x^3 + 3*x^2 - x - 5,3,x^3 + 4*x^2 + 2*x - 2,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 8*x^2 + 18*x + 10[] 385,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 4*x + 2,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 4*x + 2[] 385,8,2,x^4 - 2*x^3 - 6*x^2 + 8*x + 7,3,x^4 - 2*x^3 - 8*x^2 + 10*x + 16,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 8*x^3 - 8*x^2 - 162*x - 236[] Total time: 22.049 seconds, Total memory usage: 6.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:31:39 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [385..391] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 13:31:16 on modular [Seed = 1921362139] ------------------------------------- 385,1,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 1,13,$.1 + 6[] 385,2,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 - 1,11,$.1 + 1,13,$.1 - 4[] 385,3,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 + 2[] 385,4,2,$.1^2 - 3,3,$.1^2 - 2*$.1 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 2*$.1 + 1,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 2*$.1 - 2[] 385,5,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 2*$.1^2 - 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 3*$.1^2 + 3*$.1 + 1,13,$.1^3 - 2*$.1^2 - 22*$.1 - 2[] 385,6,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 4*$.1^2 + 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 + 8*$.1^2 + 18*$.1 + 10[] 385,7,2,$.1^3 - $.1^2 - 3*$.1 + 1,3,$.1^3 - 4*$.1 + 2,5,$.1^3 - 3*$.1^2 + 3*$.1 - 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 - 4*$.1 + 2[] 385,8,2,$.1^4 - 2*$.1^3 - 6*$.1^2 + 8*$.1 + 7,3,$.1^4 - 2*$.1^3 - 8*$.1^2 + 10*$.1 + 16,5,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 8*$.1^3 - 8*$.1^2 - 162*$.1 - 236[] 386,1,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2 - x - 1,7,x^2 + 4*x + 4,11,x^2 + 4*x + 4,13,x^2 + 3*x - 9[] 386,2,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 5*x + 5,7,x^2 + 2*x - 4,11,x^2 + 2*x - 4,13,x^2 + 7*x + 1[] 386,3,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - x^5 - 12*x^4 + 7*x^3 + 40*x^2 - 13*x - 37,5,x^6 + 5*x^5 - 8*x^4 - 49*x^3 + 22*x^2 + 103*x - 63,7,x^6 - 8*x^5 + 136*x^3 - 320*x^2 + 80*x + 176,11,x^6 + 2*x^5 - 36*x^4 - 56*x^3 + 344*x^2 + 352*x - 336,13,x^6 - 9*x^5 - 8*x^4 + 227*x^3 - 448*x^2 - 221*x + 773[] 386,4,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - 3*x^6 - 10*x^5 + 33*x^4 + 14*x^3 - 91*x^2 + 45*x + 16,5,x^7 - 5*x^6 - 8*x^5 + 59*x^4 + 14*x^3 - 227*x^2 + 3*x + 284,7,x^7 - 2*x^6 - 24*x^5 + 40*x^4 + 152*x^3 - 112*x^2 - 336*x - 128,11,x^7 - 2*x^6 - 36*x^5 + 16*x^4 + 256*x^3 - 96*x^2 - 496*x + 352,13,x^7 - 5*x^6 - 56*x^5 + 249*x^4 + 788*x^3 - 2689*x^2 - 2317*x + 3076[] 387,1,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 3,13,x + 5[] 387,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 3,13,x + 5[] 387,3,2,x,3,x,5,x - 2,7,x + 2,11,x - 5,13,x - 3[] 387,4,2,x + 1,3,x,5,x + 2,7,x,11,x,13,x + 2[] 387,5,2,x - 2,3,x,5,x - 4,7,x,11,x + 3,13,x + 5[] 387,6,2,x^2,3,x^2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 - 27,13,x^2 - 10*x + 25[] 387,7,2,x^2 - 2,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 2*x - 7,13,x^2 - 2*x - 7[] 387,8,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 2*x - 1,7,x^2 - 2*x - 7,11,x^2 + 6*x + 7,13,x^2 + 10*x + 25[] 387,9,2,x^3 - 2*x^2 - 5*x + 8,3,x^3,5,x^3 - 4*x^2 - x + 2,7,x^3 - 4*x^2 - 3*x + 10,11,x^3 + x^2 - 19*x + 25,13,x^3 - 9*x^2 + 27*x - 27[] 387,10,2,x^4 - 10*x^2 + 25,3,x^4,5,x^4 - 9*x^2 + 4,7,x^4 + 2*x^3 - 31*x^2 - 32*x + 256,11,x^4 - 9*x^2 + 4,13,x^4 - 10*x^3 + 5*x^2 + 100*x + 100[] 388,1,2,x^3,3,x^3 + 2*x^2 - x - 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3 - x^2 - 16*x - 13,11,x^3 + 7*x^2 - 49,13,x^3 + 4*x^2 + 3*x - 1[] 388,2,2,x^5,3,x^5 - 2*x^4 - 9*x^3 + 15*x^2 + 20*x - 24,5,x^5 - 5*x^4 - 4*x^3 + 41*x^2 - 8*x - 76,7,x^5 - x^4 - 12*x^3 + x^2 + 10*x + 2,11,x^5 - 5*x^4 - 4*x^3 + 23*x^2 + 28*x + 8,13,x^5 - 6*x^4 - 21*x^3 + 115*x^2 + 100*x - 500[] 389,1,2,x + 2,3,x + 2,5,x + 3,7,x + 5,11,x + 4,13,x + 3[] 389,2,2,x^2 - 2,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 + 2*x - 7,11,x^2 + 4*x + 4,13,x^2 - 2*x - 7[] 389,3,2,x^3 - 4*x - 2,3,x^3 - 4*x + 2,5,x^3 + 5*x^2 + 3*x - 5,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 - 4,13,x^3 + 9*x^2 + 27*x + 27[] 389,4,2,x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1,3,x^6 + 5*x^5 + 4*x^4 - 13*x^3 - 21*x^2 - 6*x + 1,5,x^6 - 3*x^5 - 11*x^4 + 30*x^3 + 38*x^2 - 67*x - 59,7,x^6 + 4*x^5 - 18*x^4 - 110*x^3 - 136*x^2 + 61*x + 139,11,x^6 + 2*x^5 - 39*x^4 - 136*x^3 + 89*x^2 + 655*x + 409,13,x^6 + 5*x^5 - 33*x^4 - 238*x^3 - 409*x^2 - 148*x + 1[] 389,5,2,x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 - 2023*x^14 + 7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 + 6954*x^8 - 74752*x^7 + 1407*x^6 + 46330*x^5 - 1087*x^4 - 12558*x^3 - 942*x^2 + 960*x + 148,3,x^20 - 11*x^19 + 19*x^18 + 204*x^17 - 845*x^16 - 781*x^15 + 8883*x^14 - 6177*x^13 - 40916*x^12 + 63058*x^11 + 85034*x^10 - 215618*x^9 - 46920*x^8 + 342529*x^7 - 84612*x^6 - 241030*x^5 + 112365*x^4 + 51018*x^3 - 28526*x^2 + 3560*x - 100,5,x^20 - x^19 - 58*x^18 + 69*x^17 + 1338*x^16 - 1962*x^15 - 15578*x^14 + 28633*x^13 + 93460*x^12 - 224324*x^11 - 236982*x^10 + 902782*x^9 - 92649*x^8 - 1549758*x^7 + 1240027*x^6 + 457997*x^5 - 897661*x^4 + 293181*x^3 + 17361*x^2 - 16713*x + 757,7,x^20 - 12*x^19 - 8*x^18 + 602*x^17 - 1355*x^16 - 11751*x^15 + 44797*x^14 + 105012*x^13 - 632038*x^12 - 274991*x^11 + 4756743*x^10 - 2413492*x^9 - 19377380*x^8 + 21737168*x^7 + 37613472*x^6 - 64826048*x^5 - 17117376*x^4 + 68169472*x^3 - 23637760*x^2 - 4162560*x + 1715200,11,x^20 - 10*x^19 - 71*x^18 + 1000*x^17 + 825*x^16 - 38773*x^15 + 56185*x^14 + 714296*x^13 - 2098532*x^12 - 5826144*x^11 + 28736608*x^10 + 7095232*x^9 - 174873152*x^8 + 152530432*x^7 + 436532992*x^6 - 742544384*x^5 - 208098304*x^4 + 1038184448*x^3 - 471076864*x^2 - 156303360*x + 92979200,13,x^20 - 17*x^19 + 12*x^18 + 1261*x^17 - 5711*x^16 - 29277*x^15 + 237009*x^14 + 79260*x^13 - 3979139*x^12 + 6049839*x^11 + 28107002*x^10 - 83032878*x^9 - 46796396*x^8 + 371031699*x^7 - 191435207*x^6 - 567769995*x^5 + 474808960*x^4 + 358305542*x^3 - 255218964*x^2 - 124967058*x - 4360151[] Errors: /home/mfd/gomagma: line 2: 25135 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:32:35 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [385..389] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 13:32:20 on modular [Seed = 1788719875] ------------------------------------- 385,1,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 1,13,$.1 + 6[] 385,2,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 - 1,11,$.1 + 1,13,$.1 - 4[] 385,3,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 + 2[] 385,4,2,$.1^2 - 3,3,$.1^2 - 2*$.1 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 2*$.1 + 1,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 2*$.1 - 2[] 385,5,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 2*$.1^2 - 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 3*$.1^2 + 3*$.1 + 1,13,$.1^3 - 2*$.1^2 - 22*$.1 - 2[] 385,6,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 4*$.1^2 + 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 + 8*$.1^2 + 18*$.1 + 10[] 385,7,2,$.1^3 - $.1^2 - 3*$.1 + 1,3,$.1^3 - 4*$.1 + 2,5,$.1^3 - 3*$.1^2 + 3*$.1 - 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 - 4*$.1 + 2[] 385,8,2,$.1^4 - 2*$.1^3 - 6*$.1^2 + 8*$.1 + 7,3,$.1^4 - 2*$.1^3 - 8*$.1^2 + 10*$.1 + 16,5,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 8*$.1^3 - 8*$.1^2 - 162*$.1 - 236[] 386,1,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2 - x - 1,7,x^2 + 4*x + 4,11,x^2 + 4*x + 4,13,x^2 + 3*x - 9[] 386,2,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 5*x + 5,7,x^2 + 2*x - 4,11,x^2 + 2*x - 4,13,x^2 + 7*x + 1[] 386,3,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - x^5 - 12*x^4 + 7*x^3 + 40*x^2 - 13*x - 37,5,x^6 + 5*x^5 - 8*x^4 - 49*x^3 + 22*x^2 + 103*x - 63,7,x^6 - 8*x^5 + 136*x^3 - 320*x^2 + 80*x + 176,11,x^6 + 2*x^5 - 36*x^4 - 56*x^3 + 344*x^2 + 352*x - 336,13,x^6 - 9*x^5 - 8*x^4 + 227*x^3 - 448*x^2 - 221*x + 773[] 386,4,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - 3*x^6 - 10*x^5 + 33*x^4 + 14*x^3 - 91*x^2 + 45*x + 16,5,x^7 - 5*x^6 - 8*x^5 + 59*x^4 + 14*x^3 - 227*x^2 + 3*x + 284,7,x^7 - 2*x^6 - 24*x^5 + 40*x^4 + 152*x^3 - 112*x^2 - 336*x - 128,11,x^7 - 2*x^6 - 36*x^5 + 16*x^4 + 256*x^3 - 96*x^2 - 496*x + 352,13,x^7 - 5*x^6 - 56*x^5 + 249*x^4 + 788*x^3 - 2689*x^2 - 2317*x + 3076[] 387,1,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 3,13,x + 5[] 387,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 3,13,x + 5[] 387,3,2,x,3,x,5,x - 2,7,x + 2,11,x - 5,13,x - 3[] 387,4,2,x + 1,3,x,5,x + 2,7,x,11,x,13,x + 2[] 387,5,2,x - 2,3,x,5,x - 4,7,x,11,x + 3,13,x + 5[] 387,6,2,x^2,3,x^2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 - 27,13,x^2 - 10*x + 25[] 387,7,2,x^2 - 2,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 2*x - 7,13,x^2 - 2*x - 7[] 387,8,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 2*x - 1,7,x^2 - 2*x - 7,11,x^2 + 6*x + 7,13,x^2 + 10*x + 25[] 387,9,2,x^3 - 2*x^2 - 5*x + 8,3,x^3,5,x^3 - 4*x^2 - x + 2,7,x^3 - 4*x^2 - 3*x + 10,11,x^3 + x^2 - 19*x + 25,13,x^3 - 9*x^2 + 27*x - 27[] 387,10,2,x^4 - 10*x^2 + 25,3,x^4,5,x^4 - 9*x^2 + 4,7,x^4 + 2*x^3 - 31*x^2 - 32*x + 256,11,x^4 - 9*x^2 + 4,13,x^4 - 10*x^3 + 5*x^2 + 100*x + 100[] 388,1,2,x^3,3,x^3 + 2*x^2 - x - 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3 - x^2 - 16*x - 13,11,x^3 + 7*x^2 - 49,13,x^3 + 4*x^2 + 3*x - 1[] 388,2,2,x^5,3,x^5 - 2*x^4 - 9*x^3 + 15*x^2 + 20*x - 24,5,x^5 - 5*x^4 - 4*x^3 + 41*x^2 - 8*x - 76,7,x^5 - x^4 - 12*x^3 + x^2 + 10*x + 2,11,x^5 - 5*x^4 - 4*x^3 + 23*x^2 + 28*x + 8,13,x^5 - 6*x^4 - 21*x^3 + 115*x^2 + 100*x - 500[] 389,1,2,x + 2,3,x + 2,5,x + 3,7,x + 5,11,x + 4,13,x + 3[] 389,2,2,x^2 - 2,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 + 2*x - 7,11,x^2 + 4*x + 4,13,x^2 - 2*x - 7[] 389,3,2,x^3 - 4*x - 2,3,x^3 - 4*x + 2,5,x^3 + 5*x^2 + 3*x - 5,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 - 4,13,x^3 + 9*x^2 + 27*x + 27[] 389,4,2,x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1,3,x^6 + 5*x^5 + 4*x^4 - 13*x^3 - 21*x^2 - 6*x + 1,5,x^6 - 3*x^5 - 11*x^4 + 30*x^3 + 38*x^2 - 67*x - 59,7,x^6 + 4*x^5 - 18*x^4 - 110*x^3 - 136*x^2 + 61*x + 139,11,x^6 + 2*x^5 - 39*x^4 - 136*x^3 + 89*x^2 + 655*x + 409,13,x^6 + 5*x^5 - 33*x^4 - 238*x^3 - 409*x^2 - 148*x + 1[] 389,5,2,x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 - 2023*x^14 + 7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 + 6954*x^8 - 74752*x^7 + 1407*x^6 + 46330*x^5 - 1087*x^4 - 12558*x^3 - 942*x^2 + 960*x + 148,3,x^20 - 11*x^19 + 19*x^18 + 204*x^17 - 845*x^16 - 781*x^15 + 8883*x^14 - 6177*x^13 - 40916*x^12 + 63058*x^11 + 85034*x^10 - 215618*x^9 - 46920*x^8 + 342529*x^7 - 84612*x^6 - 241030*x^5 + 112365*x^4 + 51018*x^3 - 28526*x^2 + 3560*x - 100,5,x^20 - x^19 - 58*x^18 + 69*x^17 + 1338*x^16 - 1962*x^15 - 15578*x^14 + 28633*x^13 + 93460*x^12 - 224324*x^11 - 236982*x^10 + 902782*x^9 - 92649*x^8 - 1549758*x^7 + 1240027*x^6 + 457997*x^5 - 897661*x^4 + 293181*x^3 + 17361*x^2 - 16713*x + 757,7,x^20 - 12*x^19 - 8*x^18 + 602*x^17 - 1355*x^16 - 11751*x^15 + 44797*x^14 + 105012*x^13 - 632038*x^12 - 274991*x^11 + 4756743*x^10 - 2413492*x^9 - 19377380*x^8 + 21737168*x^7 + 37613472*x^6 - 64826048*x^5 - 17117376*x^4 + 68169472*x^3 - 23637760*x^2 - 4162560*x + 1715200,11,x^20 - 10*x^19 - 71*x^18 + 1000*x^17 + 825*x^16 - 38773*x^15 + 56185*x^14 + 714296*x^13 - 2098532*x^12 - 5826144*x^11 + 28736608*x^10 + 7095232*x^9 - 174873152*x^8 + 152530432*x^7 + 436532992*x^6 - 742544384*x^5 - 208098304*x^4 + 1038184448*x^3 - 471076864*x^2 - 156303360*x + 92979200,13,x^20 - 17*x^19 + 12*x^18 + 1261*x^17 - 5711*x^16 - 29277*x^15 + 237009*x^14 + 79260*x^13 - 3979139*x^12 + 6049839*x^11 + 28107002*x^10 - 83032878*x^9 - 46796396*x^8 + 371031699*x^7 - 191435207*x^6 - 567769995*x^5 + 474808960*x^4 + 358305542*x^3 - 255218964*x^2 - 124967058*x - 4360151[] Total time: 15.179 seconds, Total memory usage: 5.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:40:17 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [389..395] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 13:39:54 on modular [Seed = 367185330] ------------------------------------- 389,1,2,$.1 + 2,3,$.1 + 2,5,$.1 + 3,7,$.1 + 5,11,$.1 + 4,13,$.1 + 3[] 389,2,2,$.1^2 - 2,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 - 7,11,$.1^2 + 4*$.1 + 4,13,$.1^2 - 2*$.1 - 7[] 389,3,2,$.1^3 - 4*$.1 - 2,3,$.1^3 - 4*$.1 + 2,5,$.1^3 + 5*$.1^2 + 3*$.1 - 5,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 - 4,13,$.1^3 + 9*$.1^2 + 27*$.1 + 27[] 389,4,2,$.1^6 + 3*$.1^5 - 2*$.1^4 - 8*$.1^3 + 2*$.1^2 + 4*$.1 - 1,3,$.1^6 + 5*$.1^5 + 4*$.1^4 - 13*$.1^3 - 21*$.1^2 - 6*$.1 + 1,5,$.1^6 - 3*$.1^5 - 11*$.1^4 + 30*$.1^3 + 38*$.1^2 - 67*$.1 - 59,7,$.1^6 + 4*$.1^5 - 18*$.1^4 - 110*$.1^3 - 136*$.1^2 + 61*$.1 + 139,11,$.1^6 + 2*$.1^5 - 39*$.1^4 - 136*$.1^3 + 89*$.1^2 + 655*$.1 + 409,13,$.1^6 + 5*$.1^5 - 33*$.1^4 - 238*$.1^3 - 409*$.1^2 - 148*$.1 + 1[] 389,5,2,$.1^20 - 3*$.1^19 - 29*$.1^18 + 91*$.1^17 + 338*$.1^16 - 1130*$.1^15 - 2023*$.1^14 + 7432*$.1^13 + 6558*$.1^12 - 28021*$.1^11 - 10909*$.1^10 + 61267*$.1^9 + 6954*$.1^8 - 74752*$.1^7 + 1407*$.1^6 + 46330*$.1^5 - 1087*$.1^4 - 12558*$.1^3 - 942*$.1^2 + 960*$.1 + 148,3,$.1^20 - 11*$.1^19 + 19*$.1^18 + 204*$.1^17 - 845*$.1^16 - 781*$.1^15 + 8883*$.1^14 - 6177*$.1^13 - 40916*$.1^12 + 63058*$.1^11 + 85034*$.1^10 - 215618*$.1^9 - 46920*$.1^8 + 342529*$.1^7 - 84612*$.1^6 - 241030*$.1^5 + 112365*$.1^4 + 51018*$.1^3 - 28526*$.1^2 + 3560*$.1 - 100,5,$.1^20 - $.1^19 - 58*$.1^18 + 69*$.1^17 + 1338*$.1^16 - 1962*$.1^15 - 15578*$.1^14 + 28633*$.1^13 + 93460*$.1^12 - 224324*$.1^11 - 236982*$.1^10 + 902782*$.1^9 - 92649*$.1^8 - 1549758*$.1^7 + 1240027*$.1^6 + 457997*$.1^5 - 897661*$.1^4 + 293181*$.1^3 + 17361*$.1^2 - 16713*$.1 + 757,7,$.1^20 - 12*$.1^19 - 8*$.1^18 + 602*$.1^17 - 1355*$.1^16 - 11751*$.1^15 + 44797*$.1^14 + 105012*$.1^13 - 632038*$.1^12 - 274991*$.1^11 + 4756743*$.1^10 - 2413492*$.1^9 - 19377380*$.1^8 + 21737168*$.1^7 + 37613472*$.1^6 - 64826048*$.1^5 - 17117376*$.1^4 + 68169472*$.1^3 - 23637760*$.1^2 - 4162560*$.1 + 1715200,11,$.1^20 - 10*$.1^19 - 71*$.1^18 + 1000*$.1^17 + 825*$.1^16 - 38773*$.1^15 + 56185*$.1^14 + 714296*$.1^13 - 2098532*$.1^12 - 5826144*$.1^11 + 28736608*$.1^10 + 7095232*$.1^9 - 174873152*$.1^8 + 152530432*$.1^7 + 436532992*$.1^6 - 742544384*$.1^5 - 208098304*$.1^4 + 1038184448*$.1^3 - 471076864*$.1^2 - 156303360*$.1 + 92979200,13,$.1^20 - 17*$.1^19 + 12*$.1^18 + 1261*$.1^17 - 5711*$.1^16 - 29277*$.1^15 + 237009*$.1^14 + 79260*$.1^13 - 3979139*$.1^12 + 6049839*$.1^11 + 28107002*$.1^10 - 83032878*$.1^9 - 46796396*$.1^8 + 371031699*$.1^7 - 191435207*$.1^6 - 567769995*$.1^5 + 474808960*$.1^4 + 358305542*$.1^3 - 255218964*$.1^2 - 124967058*$.1 - 4360151[] 390,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x,13,x + 1[] 390,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 4,13,x + 1[] 390,3,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x,13,x + 1[] 390,4,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 1[] 390,5,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 4,13,x + 1[] 390,6,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x - 1[] 390,7,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x - 1[] 390,8,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 - 32,13,x^2 + 2*x + 1[] 391,1,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 + 2*x - 4,11,x^2 + 8*x + 16,13,x^2 + 2*x + 1[] 391,2,2,x^3 + x^2 - 4*x - 3,3,x^3 + 6*x^2 + 12*x + 8,5,x^3 + 3*x^2 - 2*x - 7,7,x^3 - x^2 - 4*x + 3,11,x^3 - x^2 - 8*x + 3,13,x^3 - x^2 - 26*x - 15[] 391,3,2,x^3 + x^2 - 4*x + 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 5*x^2 + 4*x - 5,11,x^3 + 3*x^2 - 10*x - 25,13,x^3 + 3*x^2 - 10*x + 1[] 391,4,2,x^9 - 2*x^8 - 12*x^7 + 23*x^6 + 43*x^5 - 79*x^4 - 43*x^3 + 78*x^2 + 11*x - 21,3,x^9 - 2*x^8 - 20*x^7 + 36*x^6 + 124*x^5 - 192*x^4 - 248*x^3 + 256*x^2 + 160*x - 64,5,x^9 - 7*x^8 + x^7 + 92*x^6 - 216*x^5 + 15*x^4 + 421*x^3 - 391*x^2 + 64*x + 3,7,x^9 - 3*x^8 - 27*x^7 + 94*x^6 + 194*x^5 - 863*x^4 - 215*x^3 + 2593*x^2 - 918*x - 1493,11,x^9 - 11*x^8 + 11*x^7 + 246*x^6 - 834*x^5 - 213*x^4 + 3633*x^3 - 2305*x^2 - 4100*x + 3723,13,x^9 + 9*x^8 - 35*x^7 - 454*x^6 - 132*x^5 + 5675*x^4 + 8067*x^3 - 10191*x^2 - 13434*x + 5161[] 391,5,2,x^12 - 4*x^11 - 12*x^10 + 62*x^9 + 27*x^8 - 321*x^7 + 108*x^6 + 625*x^5 - 362*x^4 - 372*x^3 + 116*x^2 + 97*x + 13,3,x^12 - 2*x^11 - 31*x^10 + 60*x^9 + 348*x^8 - 652*x^7 - 1708*x^6 + 3064*x^5 + 3608*x^4 - 5728*x^3 - 3424*x^2 + 3264*x + 1792,5,x^12 - 5*x^11 - 33*x^10 + 178*x^9 + 338*x^8 - 2109*x^7 - 1131*x^6 + 9799*x^5 + 574*x^4 - 15637*x^3 - 3040*x^2 + 7912*x + 3080,7,x^12 + 9*x^11 - 13*x^10 - 286*x^9 - 174*x^8 + 3313*x^7 + 2875*x^6 - 18363*x^5 - 8640*x^4 + 46363*x^3 - 10702*x^2 - 19252*x + 7264,11,x^12 - 11*x^11 - 27*x^10 + 610*x^9 - 492*x^8 - 11697*x^7 + 21625*x^6 + 87835*x^5 - 213962*x^4 - 184849*x^3 + 691228*x^2 - 260608*x - 179200,13,x^12 - 7*x^11 - 58*x^10 + 525*x^9 + 327*x^8 - 10629*x^7 + 16951*x^6 + 54704*x^5 - 178361*x^4 + 133768*x^3 + 14316*x^2 - 18959*x + 50[] 392,1,2,x,3,x + 1,5,x + 1,7,x,11,x - 3,13,x + 6[] 392,2,2,x,3,x - 1,5,x - 1,7,x,11,x - 3,13,x - 6[] 392,3,2,x,3,x + 2,5,x - 4,7,x,11,x,13,x[] 392,4,2,x,3,x - 3,5,x + 1,7,x,11,x + 1,13,x - 2[] 392,5,2,x,3,x,5,x + 2,7,x,11,x + 4,13,x + 2[] 392,6,2,x,3,x + 3,5,x - 1,7,x,11,x + 1,13,x + 2[] 392,7,2,x^2,3,x^2 - 8,5,x^2 - 8,7,x^2,11,x^2 + 8*x + 16,13,x^2 - 8[] 392,8,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2,11,x^2 - 12*x + 36,13,x^2 - 32[] 393,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2*x + 1,13,x^2 - 10*x + 25[] 393,2,2,x^4 + x^3 - 4*x^2 - 2*x + 3,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 6*x^2 + x + 7,7,x^4 + 8*x^3 + 17*x^2 - 19,11,x^4 - 2*x^3 - 26*x^2 - 13*x + 3,13,x^4 + 9*x^3 + 12*x^2 - 44*x - 21[] 393,3,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 8*x^3 + 18*x^2 + 3*x - 19,7,x^4 + 8*x^3 + 13*x^2 - 12*x + 1,11,x^4 + 4*x^3 - 30*x^2 - 103*x + 109,13,x^4 + 5*x^3 - 24*x^2 - 80*x + 139[] 393,4,2,x^5 - 2*x^4 - 7*x^3 + 12*x^2 + 9*x - 9,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 2*x^4 - 14*x^3 - 23*x^2 + 17*x - 2,7,x^5 - 4*x^4 - 7*x^3 + 48*x^2 - 63*x + 24,11,x^5 + 6*x^4 - 38*x^3 - 229*x^2 + 183*x + 1388,13,x^5 + 3*x^4 - 38*x^3 - 76*x^2 + 303*x + 158[] 393,5,2,x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 5,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 8*x^5 + 18*x^4 - x^3 - 27*x^2 + 8*x + 8,7,x^6 - 4*x^5 - 11*x^4 + 28*x^3 + 45*x^2 - 48*x - 64,11,x^6 - 6*x^5 - x^4 + 45*x^3 - 19*x^2 - 69*x + 5,13,x^6 + 3*x^5 - 29*x^4 - 75*x^3 - 29*x^2 + 18*x - 1[] Errors: /home/mfd/gomagma: line 2: 25160 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:41:09 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [389..393] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 13:40:49 on modular [Seed = 184409446] ------------------------------------- 389,1,2,$.1 + 2,3,$.1 + 2,5,$.1 + 3,7,$.1 + 5,11,$.1 + 4,13,$.1 + 3[] 389,2,2,$.1^2 - 2,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 - 7,11,$.1^2 + 4*$.1 + 4,13,$.1^2 - 2*$.1 - 7[] 389,3,2,$.1^3 - 4*$.1 - 2,3,$.1^3 - 4*$.1 + 2,5,$.1^3 + 5*$.1^2 + 3*$.1 - 5,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 - 4,13,$.1^3 + 9*$.1^2 + 27*$.1 + 27[] 389,4,2,$.1^6 + 3*$.1^5 - 2*$.1^4 - 8*$.1^3 + 2*$.1^2 + 4*$.1 - 1,3,$.1^6 + 5*$.1^5 + 4*$.1^4 - 13*$.1^3 - 21*$.1^2 - 6*$.1 + 1,5,$.1^6 - 3*$.1^5 - 11*$.1^4 + 30*$.1^3 + 38*$.1^2 - 67*$.1 - 59,7,$.1^6 + 4*$.1^5 - 18*$.1^4 - 110*$.1^3 - 136*$.1^2 + 61*$.1 + 139,11,$.1^6 + 2*$.1^5 - 39*$.1^4 - 136*$.1^3 + 89*$.1^2 + 655*$.1 + 409,13,$.1^6 + 5*$.1^5 - 33*$.1^4 - 238*$.1^3 - 409*$.1^2 - 148*$.1 + 1[] 389,5,2,$.1^20 - 3*$.1^19 - 29*$.1^18 + 91*$.1^17 + 338*$.1^16 - 1130*$.1^15 - 2023*$.1^14 + 7432*$.1^13 + 6558*$.1^12 - 28021*$.1^11 - 10909*$.1^10 + 61267*$.1^9 + 6954*$.1^8 - 74752*$.1^7 + 1407*$.1^6 + 46330*$.1^5 - 1087*$.1^4 - 12558*$.1^3 - 942*$.1^2 + 960*$.1 + 148,3,$.1^20 - 11*$.1^19 + 19*$.1^18 + 204*$.1^17 - 845*$.1^16 - 781*$.1^15 + 8883*$.1^14 - 6177*$.1^13 - 40916*$.1^12 + 63058*$.1^11 + 85034*$.1^10 - 215618*$.1^9 - 46920*$.1^8 + 342529*$.1^7 - 84612*$.1^6 - 241030*$.1^5 + 112365*$.1^4 + 51018*$.1^3 - 28526*$.1^2 + 3560*$.1 - 100,5,$.1^20 - $.1^19 - 58*$.1^18 + 69*$.1^17 + 1338*$.1^16 - 1962*$.1^15 - 15578*$.1^14 + 28633*$.1^13 + 93460*$.1^12 - 224324*$.1^11 - 236982*$.1^10 + 902782*$.1^9 - 92649*$.1^8 - 1549758*$.1^7 + 1240027*$.1^6 + 457997*$.1^5 - 897661*$.1^4 + 293181*$.1^3 + 17361*$.1^2 - 16713*$.1 + 757,7,$.1^20 - 12*$.1^19 - 8*$.1^18 + 602*$.1^17 - 1355*$.1^16 - 11751*$.1^15 + 44797*$.1^14 + 105012*$.1^13 - 632038*$.1^12 - 274991*$.1^11 + 4756743*$.1^10 - 2413492*$.1^9 - 19377380*$.1^8 + 21737168*$.1^7 + 37613472*$.1^6 - 64826048*$.1^5 - 17117376*$.1^4 + 68169472*$.1^3 - 23637760*$.1^2 - 4162560*$.1 + 1715200,11,$.1^20 - 10*$.1^19 - 71*$.1^18 + 1000*$.1^17 + 825*$.1^16 - 38773*$.1^15 + 56185*$.1^14 + 714296*$.1^13 - 2098532*$.1^12 - 5826144*$.1^11 + 28736608*$.1^10 + 7095232*$.1^9 - 174873152*$.1^8 + 152530432*$.1^7 + 436532992*$.1^6 - 742544384*$.1^5 - 208098304*$.1^4 + 1038184448*$.1^3 - 471076864*$.1^2 - 156303360*$.1 + 92979200,13,$.1^20 - 17*$.1^19 + 12*$.1^18 + 1261*$.1^17 - 5711*$.1^16 - 29277*$.1^15 + 237009*$.1^14 + 79260*$.1^13 - 3979139*$.1^12 + 6049839*$.1^11 + 28107002*$.1^10 - 83032878*$.1^9 - 46796396*$.1^8 + 371031699*$.1^7 - 191435207*$.1^6 - 567769995*$.1^5 + 474808960*$.1^4 + 358305542*$.1^3 - 255218964*$.1^2 - 124967058*$.1 - 4360151[] 390,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x,13,x + 1[] 390,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 4,13,x + 1[] 390,3,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x,13,x + 1[] 390,4,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 1[] 390,5,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 4,13,x + 1[] 390,6,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x - 1[] 390,7,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x - 1[] 390,8,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 - 32,13,x^2 + 2*x + 1[] 391,1,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 + 2*x - 4,11,x^2 + 8*x + 16,13,x^2 + 2*x + 1[] 391,2,2,x^3 + x^2 - 4*x - 3,3,x^3 + 6*x^2 + 12*x + 8,5,x^3 + 3*x^2 - 2*x - 7,7,x^3 - x^2 - 4*x + 3,11,x^3 - x^2 - 8*x + 3,13,x^3 - x^2 - 26*x - 15[] 391,3,2,x^3 + x^2 - 4*x + 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 5*x^2 + 4*x - 5,11,x^3 + 3*x^2 - 10*x - 25,13,x^3 + 3*x^2 - 10*x + 1[] 391,4,2,x^9 - 2*x^8 - 12*x^7 + 23*x^6 + 43*x^5 - 79*x^4 - 43*x^3 + 78*x^2 + 11*x - 21,3,x^9 - 2*x^8 - 20*x^7 + 36*x^6 + 124*x^5 - 192*x^4 - 248*x^3 + 256*x^2 + 160*x - 64,5,x^9 - 7*x^8 + x^7 + 92*x^6 - 216*x^5 + 15*x^4 + 421*x^3 - 391*x^2 + 64*x + 3,7,x^9 - 3*x^8 - 27*x^7 + 94*x^6 + 194*x^5 - 863*x^4 - 215*x^3 + 2593*x^2 - 918*x - 1493,11,x^9 - 11*x^8 + 11*x^7 + 246*x^6 - 834*x^5 - 213*x^4 + 3633*x^3 - 2305*x^2 - 4100*x + 3723,13,x^9 + 9*x^8 - 35*x^7 - 454*x^6 - 132*x^5 + 5675*x^4 + 8067*x^3 - 10191*x^2 - 13434*x + 5161[] 391,5,2,x^12 - 4*x^11 - 12*x^10 + 62*x^9 + 27*x^8 - 321*x^7 + 108*x^6 + 625*x^5 - 362*x^4 - 372*x^3 + 116*x^2 + 97*x + 13,3,x^12 - 2*x^11 - 31*x^10 + 60*x^9 + 348*x^8 - 652*x^7 - 1708*x^6 + 3064*x^5 + 3608*x^4 - 5728*x^3 - 3424*x^2 + 3264*x + 1792,5,x^12 - 5*x^11 - 33*x^10 + 178*x^9 + 338*x^8 - 2109*x^7 - 1131*x^6 + 9799*x^5 + 574*x^4 - 15637*x^3 - 3040*x^2 + 7912*x + 3080,7,x^12 + 9*x^11 - 13*x^10 - 286*x^9 - 174*x^8 + 3313*x^7 + 2875*x^6 - 18363*x^5 - 8640*x^4 + 46363*x^3 - 10702*x^2 - 19252*x + 7264,11,x^12 - 11*x^11 - 27*x^10 + 610*x^9 - 492*x^8 - 11697*x^7 + 21625*x^6 + 87835*x^5 - 213962*x^4 - 184849*x^3 + 691228*x^2 - 260608*x - 179200,13,x^12 - 7*x^11 - 58*x^10 + 525*x^9 + 327*x^8 - 10629*x^7 + 16951*x^6 + 54704*x^5 - 178361*x^4 + 133768*x^3 + 14316*x^2 - 18959*x + 50[] 392,1,2,x,3,x + 1,5,x + 1,7,x,11,x - 3,13,x + 6[] 392,2,2,x,3,x - 1,5,x - 1,7,x,11,x - 3,13,x - 6[] 392,3,2,x,3,x + 2,5,x - 4,7,x,11,x,13,x[] 392,4,2,x,3,x - 3,5,x + 1,7,x,11,x + 1,13,x - 2[] 392,5,2,x,3,x,5,x + 2,7,x,11,x + 4,13,x + 2[] 392,6,2,x,3,x + 3,5,x - 1,7,x,11,x + 1,13,x + 2[] 392,7,2,x^2,3,x^2 - 8,5,x^2 - 8,7,x^2,11,x^2 + 8*x + 16,13,x^2 - 8[] 392,8,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2,11,x^2 - 12*x + 36,13,x^2 - 32[] 393,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2*x + 1,13,x^2 - 10*x + 25[] 393,2,2,x^4 + x^3 - 4*x^2 - 2*x + 3,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 6*x^2 + x + 7,7,x^4 + 8*x^3 + 17*x^2 - 19,11,x^4 - 2*x^3 - 26*x^2 - 13*x + 3,13,x^4 + 9*x^3 + 12*x^2 - 44*x - 21[] 393,3,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 8*x^3 + 18*x^2 + 3*x - 19,7,x^4 + 8*x^3 + 13*x^2 - 12*x + 1,11,x^4 + 4*x^3 - 30*x^2 - 103*x + 109,13,x^4 + 5*x^3 - 24*x^2 - 80*x + 139[] 393,4,2,x^5 - 2*x^4 - 7*x^3 + 12*x^2 + 9*x - 9,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 2*x^4 - 14*x^3 - 23*x^2 + 17*x - 2,7,x^5 - 4*x^4 - 7*x^3 + 48*x^2 - 63*x + 24,11,x^5 + 6*x^4 - 38*x^3 - 229*x^2 + 183*x + 1388,13,x^5 + 3*x^4 - 38*x^3 - 76*x^2 + 303*x + 158[] 393,5,2,x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 5,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 8*x^5 + 18*x^4 - x^3 - 27*x^2 + 8*x + 8,7,x^6 - 4*x^5 - 11*x^4 + 28*x^3 + 45*x^2 - 48*x - 64,11,x^6 - 6*x^5 - x^4 + 45*x^3 - 19*x^2 - 69*x + 5,13,x^6 + 3*x^5 - 29*x^4 - 75*x^3 - 29*x^2 + 18*x - 1[] Total time: 19.360 seconds, Total memory usage: 6.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:46:53 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [393..397] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 13:46:34 on modular [Seed = 1003285996] ------------------------------------- 393,1,2,$.1^2 + 2*$.1 - 1,3,$.1^2 + 2*$.1 + 1,5,$.1^2 - 8,7,$.1^2 - 8*$.1 + 16,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 10*$.1 + 25[] 393,2,2,$.1^4 + $.1^3 - 4*$.1^2 - 2*$.1 + 3,3,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,5,$.1^4 - 6*$.1^2 + $.1 + 7,7,$.1^4 + 8*$.1^3 + 17*$.1^2 - 19,11,$.1^4 - 2*$.1^3 - 26*$.1^2 - 13*$.1 + 3,13,$.1^4 + 9*$.1^3 + 12*$.1^2 - 44*$.1 - 21[] 393,3,2,$.1^4 + 3*$.1^3 - 4*$.1 - 1,3,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,5,$.1^4 + 8*$.1^3 + 18*$.1^2 + 3*$.1 - 19,7,$.1^4 + 8*$.1^3 + 13*$.1^2 - 12*$.1 + 1,11,$.1^4 + 4*$.1^3 - 30*$.1^2 - 103*$.1 + 109,13,$.1^4 + 5*$.1^3 - 24*$.1^2 - 80*$.1 + 139[] 393,4,2,$.1^5 - 2*$.1^4 - 7*$.1^3 + 12*$.1^2 + 9*$.1 - 9,3,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,5,$.1^5 + 2*$.1^4 - 14*$.1^3 - 23*$.1^2 + 17*$.1 - 2,7,$.1^5 - 4*$.1^4 - 7*$.1^3 + 48*$.1^2 - 63*$.1 + 24,11,$.1^5 + 6*$.1^4 - 38*$.1^3 - 229*$.1^2 + 183*$.1 + 1388,13,$.1^5 + 3*$.1^4 - 38*$.1^3 - 76*$.1^2 + 303*$.1 + 158[] 393,5,2,$.1^6 - $.1^5 - 7*$.1^4 + 5*$.1^3 + 13*$.1^2 - 4*$.1 - 5,3,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1,5,$.1^6 - 8*$.1^5 + 18*$.1^4 - $.1^3 - 27*$.1^2 + 8*$.1 + 8,7,$.1^6 - 4*$.1^5 - 11*$.1^4 + 28*$.1^3 + 45*$.1^2 - 48*$.1 - 64,11,$.1^6 - 6*$.1^5 - $.1^4 + 45*$.1^3 - 19*$.1^2 - 69*$.1 + 5,13,$.1^6 + 3*$.1^5 - 29*$.1^4 - 75*$.1^3 - 29*$.1^2 + 18*$.1 - 1[] 394,1,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 3*x - 5,7,x^2 - 4*x + 4,11,x^2 - 2*x - 28,13,x^2 - 3*x - 5[] 394,2,2,x^2 - 2*x + 1,3,x^2 - 5,5,x^2 - 5*x + 5,7,x^2 + 6*x + 9,11,x^2 - 3*x - 9,13,x^2 - 6*x + 9[] 394,3,2,x^2 - 2*x + 1,3,x^2 + x - 5,5,x^2,7,x^2 - 4*x + 4,11,x^2 + 3*x - 3,13,x^2 + 2*x - 20[] 394,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 + 5*x + 5,13,x^2 + 2*x - 19[] 394,5,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 3*x^3 - 2*x^2 - 7*x + 1,5,x^4 + 5*x^3 + x^2 - 20*x - 16,7,x^4 - 2*x^3 - 15*x^2 - 4*x + 4,11,x^4 + 8*x^3 + 15*x^2 + 6*x - 1,13,x^4 - 4*x^3 - 15*x^2 - 2*x + 4[] 394,6,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 2*x^3 - 7*x^2 + 8*x + 16,5,x^4 - 2*x^3 - 7*x^2 + 8*x - 1,7,x^4 - 17*x^2 + 68,11,x^4 - 11*x^3 + 39*x^2 - 46*x + 4,13,x^4 + 5*x^3 - 14*x^2 - 91*x - 89[] 395,1,2,x + 1,3,x,5,x - 1,7,x + 4,11,x - 4,13,x - 6[] 395,2,2,x + 1,3,x - 2,5,x - 1,7,x - 2,11,x - 4,13,x + 6[] 395,3,2,x + 2,3,x + 1,5,x - 1,7,x - 3,11,x + 3,13,x - 4[] 395,4,2,x^3 - 3*x + 1,3,x^3 - 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 + 6*x^2 + 3*x - 19,13,x^3 + 6*x^2 + 9*x + 3[] 395,5,2,x^3 - 6*x^2 + 12*x - 8,3,x^3 - x^2 - 5*x + 3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 3*x^2 - 15*x + 43,11,x^3 - 3*x^2 - 21*x - 13,13,x^3[] 395,6,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 3*x^2 - 4*x - 13,11,x^3 - 2*x^2 - x + 1,13,x^3 + 10*x^2 + 31*x + 29[] 395,7,2,x^4 - x^3 - 7*x^2 + 6*x - 1,3,x^4 - 2*x^3 - 9*x^2 + 17*x + 6,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 3*x^3 - 4*x^2 + 7*x - 2,11,x^4 + 6*x^3 + 3*x^2 - 11*x + 4,13,x^4 - 8*x^3 - 9*x^2 + 167*x - 234[] 395,8,2,x^11 - 21*x^9 + x^8 + 159*x^7 - 18*x^6 - 511*x^5 + 105*x^4 + 604*x^3 - 208*x^2 - 128*x + 48,3,x^11 + 2*x^10 - 25*x^9 - 45*x^8 + 223*x^7 + 334*x^6 - 901*x^5 - 1011*x^4 + 1640*x^3 + 1180*x^2 - 1060*x - 284,5,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,7,x^11 - 7*x^10 - 32*x^9 + 303*x^8 + 79*x^7 - 4099*x^6 + 5048*x^5 + 15889*x^4 - 36724*x^3 + 20024*x^2 - 3584*x + 196,11,x^11 - 6*x^10 - 59*x^9 + 421*x^8 + 827*x^7 - 9196*x^6 + 2851*x^5 + 68405*x^4 - 81792*x^3 - 90008*x^2 + 86480*x - 11952,13,x^11 - 14*x^10 - 3*x^9 + 735*x^8 - 1604*x^7 - 13832*x^6 + 40784*x^5 + 105456*x^4 - 368960*x^3 - 182272*x^2 + 1167360*x - 763904[] 396,1,2,x,3,x,5,x + 2,7,x + 2,11,x + 1,13,x + 2[] 396,2,2,x,3,x,5,x + 2,7,x - 2,11,x - 1,13,x - 6[] 396,3,2,x,3,x,5,x - 3,7,x - 2,11,x - 1,13,x + 4[] 397,1,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 4*x + 4,7,x^2 - 6*x + 7,11,x^2 - 8,13,x^2 + 8*x + 8[] 397,2,2,x^2 - 2*x - 1,3,x^2 - 4*x + 2,5,x^2 - 2,7,x^2 + 2*x - 7,11,x^2 - 4*x + 2,13,x^2 - 4*x - 14[] 397,3,2,x^5 - 6*x^3 + x^2 + 7*x - 1,3,x^5 - 5*x^4 + 4*x^3 + 9*x^2 - 8*x - 2,5,x^5 + 2*x^4 - 9*x^3 - x^2 + 6*x + 2,7,x^5 - x^4 - 11*x^3 + 16*x^2 + 16*x - 25,11,x^5 - 6*x^4 - 6*x^3 + 84*x^2 - 112*x - 16,13,x^5 - 2*x^4 - 19*x^3 - 29*x^2 - 14*x - 2[] 397,4,2,x^10 - 7*x^9 + 8*x^8 + 43*x^7 - 105*x^6 - 26*x^5 + 234*x^4 - 119*x^3 - 82*x^2 + 47*x + 3,3,x^10 - 19*x^8 + 3*x^7 + 132*x^6 - 36*x^5 - 397*x^4 + 120*x^3 + 468*x^2 - 71*x - 177,5,x^10 - 7*x^9 - 9*x^8 + 145*x^7 - 124*x^6 - 766*x^5 + 891*x^4 + 1276*x^3 - 841*x^2 - 648*x + 81,7,x^10 - 10*x^9 + 17*x^8 + 97*x^7 - 277*x^6 - 250*x^5 + 1035*x^4 + 112*x^3 - 1154*x^2 - 7*x + 239,11,x^10 - 15*x^9 + 55*x^8 + 188*x^7 - 1775*x^6 + 4272*x^5 - 3580*x^4 - 367*x^3 + 1360*x^2 + 39*x - 81,13,x^10 + 7*x^9 - 14*x^8 - 161*x^7 + 15*x^6 + 1275*x^5 + 254*x^4 - 4036*x^3 + 247*x^2 + 4260*x - 1777[] 397,5,2,x^13 + 7*x^12 + 5*x^11 - 63*x^10 - 124*x^9 + 157*x^8 + 526*x^7 + 2*x^6 - 794*x^5 - 328*x^4 + 408*x^3 + 203*x^2 - 66*x - 23,3,x^13 + 11*x^12 + 31*x^11 - 67*x^10 - 461*x^9 - 347*x^8 + 1652*x^7 + 2845*x^6 - 1038*x^5 - 4630*x^4 - 2122*x^3 + 459*x^2 + 185*x - 31,5,x^13 + 5*x^12 - 30*x^11 - 165*x^10 + 298*x^9 + 1906*x^8 - 1254*x^7 - 9724*x^6 + 2486*x^5 + 21499*x^4 - 2856*x^3 - 15007*x^2 + 915*x + 25,7,x^13 + 17*x^12 + 91*x^11 - 15*x^10 - 1968*x^9 - 7460*x^8 - 8546*x^7 + 8484*x^6 + 23360*x^5 + 936*x^4 - 19934*x^3 - 2011*x^2 + 6421*x - 593,11,x^13 + 31*x^12 + 381*x^11 + 2186*x^10 + 3741*x^9 - 21606*x^8 - 122592*x^7 - 153927*x^6 + 381830*x^5 + 1323595*x^4 + 1292273*x^3 + 383314*x^2 - 48624*x - 21272,13,x^13 - x^12 - 83*x^11 + 135*x^10 + 2434*x^9 - 4874*x^8 - 31822*x^7 + 72166*x^6 + 183608*x^5 - 469892*x^4 - 317478*x^3 + 1110975*x^2 - 429135*x + 37507[] Total time: 18.250 seconds, Total memory usage: 6.06MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 13:53:50 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [397..400] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 13:53:36 on modular [Seed = 634581320] ------------------------------------- 397,1,2,$.1^2 + 2*$.1 - 1,3,$.1^2,5,$.1^2 + 4*$.1 + 4,7,$.1^2 - 6*$.1 + 7,11,$.1^2 - 8,13,$.1^2 + 8*$.1 + 8[] 397,2,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2 - 2,7,$.1^2 + 2*$.1 - 7,11,$.1^2 - 4*$.1 + 2,13,$.1^2 - 4*$.1 - 14[] 397,3,2,$.1^5 - 6*$.1^3 + $.1^2 + 7*$.1 - 1,3,$.1^5 - 5*$.1^4 + 4*$.1^3 + 9*$.1^2 - 8*$.1 - 2,5,$.1^5 + 2*$.1^4 - 9*$.1^3 - $.1^2 + 6*$.1 + 2,7,$.1^5 - $.1^4 - 11*$.1^3 + 16*$.1^2 + 16*$.1 - 25,11,$.1^5 - 6*$.1^4 - 6*$.1^3 + 84*$.1^2 - 112*$.1 - 16,13,$.1^5 - 2*$.1^4 - 19*$.1^3 - 29*$.1^2 - 14*$.1 - 2[] 397,4,2,$.1^10 - 7*$.1^9 + 8*$.1^8 + 43*$.1^7 - 105*$.1^6 - 26*$.1^5 + 234*$.1^4 - 119*$.1^3 - 82*$.1^2 + 47*$.1 + 3,3,$.1^10 - 19*$.1^8 + 3*$.1^7 + 132*$.1^6 - 36*$.1^5 - 397*$.1^4 + 120*$.1^3 + 468*$.1^2 - 71*$.1 - 177,5,$.1^10 - 7*$.1^9 - 9*$.1^8 + 145*$.1^7 - 124*$.1^6 - 766*$.1^5 + 891*$.1^4 + 1276*$.1^3 - 841*$.1^2 - 648*$.1 + 81,7,$.1^10 - 10*$.1^9 + 17*$.1^8 + 97*$.1^7 - 277*$.1^6 - 250*$.1^5 + 1035*$.1^4 + 112*$.1^3 - 1154*$.1^2 - 7*$.1 + 239,11,$.1^10 - 15*$.1^9 + 55*$.1^8 + 188*$.1^7 - 1775*$.1^6 + 4272*$.1^5 - 3580*$.1^4 - 367*$.1^3 + 1360*$.1^2 + 39*$.1 - 81,13,$.1^10 + 7*$.1^9 - 14*$.1^8 - 161*$.1^7 + 15*$.1^6 + 1275*$.1^5 + 254*$.1^4 - 4036*$.1^3 + 247*$.1^2 + 4260*$.1 - 1777[] 397,5,2,$.1^13 + 7*$.1^12 + 5*$.1^11 - 63*$.1^10 - 124*$.1^9 + 157*$.1^8 + 526*$.1^7 + 2*$.1^6 - 794*$.1^5 - 328*$.1^4 + 408*$.1^3 + 203*$.1^2 - 66*$.1 - 23,3,$.1^13 + 11*$.1^12 + 31*$.1^11 - 67*$.1^10 - 461*$.1^9 - 347*$.1^8 + 1652*$.1^7 + 2845*$.1^6 - 1038*$.1^5 - 4630*$.1^4 - 2122*$.1^3 + 459*$.1^2 + 185*$.1 - 31,5,$.1^13 + 5*$.1^12 - 30*$.1^11 - 165*$.1^10 + 298*$.1^9 + 1906*$.1^8 - 1254*$.1^7 - 9724*$.1^6 + 2486*$.1^5 + 21499*$.1^4 - 2856*$.1^3 - 15007*$.1^2 + 915*$.1 + 25,7,$.1^13 + 17*$.1^12 + 91*$.1^11 - 15*$.1^10 - 1968*$.1^9 - 7460*$.1^8 - 8546*$.1^7 + 8484*$.1^6 + 23360*$.1^5 + 936*$.1^4 - 19934*$.1^3 - 2011*$.1^2 + 6421*$.1 - 593,11,$.1^13 + 31*$.1^12 + 381*$.1^11 + 2186*$.1^10 + 3741*$.1^9 - 21606*$.1^8 - 122592*$.1^7 - 153927*$.1^6 + 381830*$.1^5 + 1323595*$.1^4 + 1292273*$.1^3 + 383314*$.1^2 - 48624*$.1 - 21272,13,$.1^13 - $.1^12 - 83*$.1^11 + 135*$.1^10 + 2434*$.1^9 - 4874*$.1^8 - 31822*$.1^7 + 72166*$.1^6 + 183608*$.1^5 - 469892*$.1^4 - 317478*$.1^3 + 1110975*$.1^2 - 429135*$.1 + 37507[] 398,1,2,x + 1,3,x - 2,5,x + 2,7,x,11,x - 2,13,x - 6[] 398,2,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2,7,x^2 + 3*x + 1,11,x^2 - x - 11,13,x^2 + 6*x + 4[] 398,3,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 2*x - 4,7,x^2 + 7*x + 11,11,x^2 + 7*x + 11,13,x^2 + 4*x + 4[] 398,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - x^5 - 14*x^4 + 5*x^3 + 54*x^2 + 9*x - 27,5,x^6 - 4*x^5 - 20*x^4 + 84*x^3 + 32*x^2 - 224*x + 48,7,x^6 - 11*x^5 + 22*x^4 + 117*x^3 - 414*x^2 - 3*x + 737,11,x^6 + 7*x^5 - 26*x^4 - 159*x^3 + 314*x^2 + 533*x - 933,13,x^6 + 2*x^5 - 44*x^4 - 92*x^3 + 416*x^2 + 1104*x + 656[] 398,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 3*x^5 - 6*x^4 + 21*x^3 + 2*x^2 - 21*x - 5,5,x^6 - 2*x^5 - 16*x^4 + 28*x^3 + 32*x^2 - 64*x + 16,7,x^6 - 7*x^5 + 8*x^4 + 37*x^3 - 96*x^2 + 69*x - 13,11,x^6 - 5*x^5 - 18*x^4 + 67*x^3 + 130*x^2 - 71*x + 5,13,x^6 - 52*x^4 + 60*x^3 + 712*x^2 - 1520*x - 16[] 399,1,2,x - 1,3,x + 1,5,x,7,x + 1,11,x + 2,13,x + 4[] 399,2,2,x + 1,3,x + 1,5,x,7,x - 1,11,x + 2,13,x[] 399,3,2,x + 1,3,x - 1,5,x - 4,7,x + 1,11,x + 2,13,x - 4[] 399,4,2,x^3 - x^2 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 + 4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 16*x - 16,13,x^3 - 6*x^2 - 4*x + 8[] 399,5,2,x^3 - x^2 - 7*x + 9,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 8*x - 4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 4*x^2 - 16*x + 48,13,x^3 - 2*x^2 - 20*x - 8[] 399,6,2,x^5 - 3*x^4 - 4*x^3 + 14*x^2 - 3*x - 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 - 4*x^4 - 12*x^3 + 48*x^2 + 4*x - 8,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - 8*x^4 - 32*x^3 + 304*x^2 + 224*x - 2816,13,x^5 + 6*x^4 - 40*x^3 - 224*x^2 + 384*x + 1984[] 399,7,2,x^5 - x^4 - 8*x^3 + 6*x^2 + 13*x - 3,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 + 2*x^4 - 16*x^3 - 8*x^2 + 68*x - 48,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 + 2*x^4 - 32*x^3 - 16*x^2 + 256*x - 192,13,x^5 - 8*x^4 - 8*x^3 + 112*x^2 + 32*x - 256[] 400,1,2,x,3,x,5,x,7,x + 4,11,x + 4,13,x - 2[] 400,2,2,x,3,x + 3,5,x,7,x - 2,11,x + 1,13,x + 4[] 400,3,2,x,3,x - 2,5,x,7,x - 2,11,x - 4,13,x + 4[] 400,4,2,x,3,x + 2,5,x,7,x + 2,11,x - 4,13,x - 4[] 400,5,2,x,3,x - 3,5,x,7,x + 2,11,x + 1,13,x - 4[] 400,6,2,x,3,x - 1,5,x,7,x - 2,11,x - 3,13,x - 4[] 400,7,2,x,3,x + 2,5,x,7,x - 2,11,x,13,x + 2[] 400,8,2,x,3,x + 1,5,x,7,x + 2,11,x - 3,13,x + 4[] Total time: 14.039 seconds, Total memory usage: 5.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:46:06 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [400..406] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 02:45:39 on modular [Seed = 4161693582] ------------------------------------- 400,1,2,$.1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 4,13,$.1 - 2[] 400,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 + 1,13,$.1 + 4[] 400,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 4[] 400,4,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 - 4,13,$.1 - 4[] 400,5,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 + 1,13,$.1 - 4[] 400,6,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 3,13,$.1 - 4[] 400,7,2,$.1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1,13,$.1 + 2[] 400,8,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 2,11,$.1 - 3,13,$.1 + 4[] 401,1,2,x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4,3,x^12 + 5*x^11 - 7*x^10 - 66*x^9 - 33*x^8 + 249*x^7 + 270*x^6 - 258*x^5 - 363*x^4 + 54*x^3 + 136*x^2 - 16,5,x^12 + 7*x^11 - 9*x^10 - 142*x^9 - 93*x^8 + 880*x^7 + 869*x^6 - 2355*x^5 - 1980*x^4 + 3042*x^3 + 1412*x^2 - 1552*x - 79,7,x^12 + 20*x^11 + 155*x^10 + 516*x^9 + 46*x^8 - 5172*x^7 - 15538*x^6 - 11740*x^5 + 30845*x^4 + 83664*x^3 + 81306*x^2 + 32396*x + 2657,11,x^12 + 11*x^11 - 9*x^10 - 451*x^9 - 829*x^8 + 5973*x^7 + 17916*x^6 - 24578*x^5 - 119209*x^4 - 29312*x^3 + 224591*x^2 + 217928*x + 41849,13,x^12 + 11*x^11 - 17*x^10 - 534*x^9 - 1050*x^8 + 5361*x^7 + 13008*x^6 - 23718*x^5 - 42795*x^4 + 49694*x^3 + 21668*x^2 - 9160*x - 272[] 401,2,2,x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44,3,x^21 - 3*x^20 - 37*x^19 + 112*x^18 + 572*x^17 - 1750*x^16 - 4821*x^15 + 14940*x^14 + 24209*x^13 - 76294*x^12 - 74001*x^11 + 239594*x^10 + 133106*x^9 - 457051*x^8 - 121988*x^7 + 501440*x^6 + 21445*x^5 - 278838*x^4 + 44972*x^3 + 55992*x^2 - 21840*x + 2176,5,x^21 - 3*x^20 - 61*x^19 + 194*x^18 + 1512*x^17 - 5215*x^16 - 19300*x^15 + 75661*x^14 + 128652*x^13 - 640637*x^12 - 336982*x^11 + 3173409*x^10 - 785768*x^9 - 8594568*x^8 + 7111131*x^7 + 10298067*x^6 - 15120487*x^5 - 1215456*x^4 + 10541238*x^3 - 4468704*x^2 - 686527*x + 543818,7,x^21 - 24*x^20 + 195*x^19 - 236*x^18 - 5466*x^17 + 28324*x^16 + 9918*x^15 - 432740*x^14 + 844081*x^13 + 2219324*x^12 - 9342038*x^11 + 830912*x^10 + 38273997*x^9 - 42544268*x^8 - 54586056*x^7 + 119960784*x^6 - 13453488*x^5 - 96133952*x^4 + 56121600*x^3 + 6590464*x^2 - 9138432*x + 667648,11,x^21 - x^20 - 133*x^19 + 169*x^18 + 7471*x^17 - 11763*x^16 - 229832*x^15 + 438954*x^14 + 4175027*x^13 - 9581728*x^12 - 44526253*x^11 + 124643620*x^10 + 251896037*x^9 - 934300300*x^8 - 464605776*x^7 + 3623452320*x^6 - 1606573440*x^5 - 5297593344*x^4 + 6110001408*x^3 - 1368589312*x^2 - 367203328*x + 18550784,13,x^21 - 9*x^20 - 109*x^19 + 1118*x^18 + 4634*x^17 - 58263*x^16 - 90876*x^15 + 1658206*x^14 + 519427*x^13 - 28086092*x^12 + 11520128*x^11 + 288867488*x^10 - 257320016*x^9 - 1759190240*x^8 + 2219776000*x^7 + 5836035584*x^6 - 9500805376*x^5 - 8335835648*x^4 + 18968096768*x^3 + 139124736*x^2 - 12677169152*x + 5112193024[] 402,1,2,x + 1,3,x + 1,5,x - 1,7,x + 3,11,x,13,x + 4[] 402,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 402,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 4[] 402,4,2,x - 1,3,x + 1,5,x - 2,7,x - 2,11,x + 4,13,x[] 402,5,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 + 4*x + 4,13,x^2 + 2*x - 2[] 402,6,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 10,7,x^2 + x - 10,11,x^2 - 8*x + 16,13,x^2 - 8*x + 16[] 402,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - x^2 - 4*x + 2,11,x^3 - 28*x + 16,13,x^3 + 6*x^2 - 22*x - 136[] 403,1,2,x^2 - 3*x + 1,3,x^2 + 4*x + 4,5,x^2 - 5,7,x^2 - 2*x + 1,11,x^2 - 20,13,x^2 - 2*x + 1[] 403,2,2,x^6 + 2*x^5 - 7*x^4 - 13*x^3 + 6*x^2 + 7*x - 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 11*x^2 + x + 1,5,x^6 + 9*x^5 + 20*x^4 - 19*x^3 - 75*x^2 + 14*x + 39,7,x^6 - 29*x^4 - 6*x^3 + 175*x^2 + 121*x - 113,11,x^6 + 5*x^5 - 18*x^4 - 49*x^3 + 147*x^2 - 76*x + 9,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 403,3,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 20*x^3 - 37*x^2 + x + 4,3,x^7 - 5*x^6 + 28*x^4 - 25*x^3 - 21*x^2 + 15*x + 8,5,x^7 - 11*x^6 + 38*x^5 - 27*x^4 - 75*x^3 + 80*x^2 + 39*x - 4,7,x^7 - 4*x^6 - 7*x^5 + 24*x^4 + 7*x^3 - 23*x^2 - 7*x + 2,11,x^7 - 8*x^6 - 3*x^5 + 99*x^4 + 10*x^3 - 307*x^2 - 17*x + 283,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 403,4,2,x^8 + 5*x^7 - 30*x^5 - 24*x^4 + 54*x^3 + 54*x^2 - 28*x - 29,3,x^8 + 3*x^7 - 12*x^6 - 36*x^5 + 31*x^4 + 97*x^3 - 29*x^2 - 72*x + 12,5,x^8 + 15*x^7 + 83*x^6 + 192*x^5 + 99*x^4 - 225*x^3 - 158*x^2 + 90*x + 3,7,x^8 + 4*x^7 - 20*x^6 - 88*x^5 + 46*x^4 + 335*x^3 + 50*x^2 - 181*x + 29,11,x^8 + 5*x^7 - 56*x^6 - 309*x^5 + 705*x^4 + 4994*x^3 + 769*x^2 - 17712*x - 14580,13,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[] 403,5,2,x^8 + x^7 - 11*x^6 - 10*x^5 + 37*x^4 + 33*x^3 - 36*x^2 - 33*x - 4,3,x^8 - 7*x^7 + 8*x^6 + 42*x^5 - 107*x^4 + 15*x^3 + 141*x^2 - 104*x + 16,5,x^8 - 11*x^7 + 32*x^6 + 35*x^5 - 263*x^4 + 126*x^3 + 537*x^2 - 346*x - 232,7,x^8 + 2*x^7 - 39*x^6 - 42*x^5 + 527*x^4 + 185*x^3 - 2717*x^2 + 250*x + 3824,11,x^8 + 2*x^7 - 31*x^6 - 51*x^5 + 238*x^4 + 267*x^3 - 631*x^2 - 319*x + 484,13,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1[] 404,1,2,x,3,x + 2,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 404,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 2,13,x + 3[] 404,3,2,x^7,3,x^7 - 2*x^6 - 17*x^5 + 36*x^4 + 64*x^3 - 148*x^2 + 11*x + 58,5,x^7 - 31*x^5 + 8*x^4 + 262*x^3 - 160*x^2 - 503*x + 250,7,x^7 - 2*x^6 - 39*x^5 + 62*x^4 + 438*x^3 - 474*x^2 - 1365*x + 698,11,x^7 - 4*x^6 - 43*x^5 + 122*x^4 + 548*x^3 - 1178*x^2 - 2085*x + 3482,13,x^7 - 4*x^6 - 55*x^5 + 244*x^4 + 534*x^3 - 2528*x^2 + 25*x + 58[] 405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[] 405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[] 405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[] Errors: /home/mfd/gomagma: line 2: 27309 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:46:57 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [400..405] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 02:46:33 on modular [Seed = 3759570924] ------------------------------------- 400,1,2,$.1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 4,13,$.1 - 2[] 400,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 + 1,13,$.1 + 4[] 400,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 4[] 400,4,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 - 4,13,$.1 - 4[] 400,5,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 + 1,13,$.1 - 4[] 400,6,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 3,13,$.1 - 4[] 400,7,2,$.1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1,13,$.1 + 2[] 400,8,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 2,11,$.1 - 3,13,$.1 + 4[] 401,1,2,x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4,3,x^12 + 5*x^11 - 7*x^10 - 66*x^9 - 33*x^8 + 249*x^7 + 270*x^6 - 258*x^5 - 363*x^4 + 54*x^3 + 136*x^2 - 16,5,x^12 + 7*x^11 - 9*x^10 - 142*x^9 - 93*x^8 + 880*x^7 + 869*x^6 - 2355*x^5 - 1980*x^4 + 3042*x^3 + 1412*x^2 - 1552*x - 79,7,x^12 + 20*x^11 + 155*x^10 + 516*x^9 + 46*x^8 - 5172*x^7 - 15538*x^6 - 11740*x^5 + 30845*x^4 + 83664*x^3 + 81306*x^2 + 32396*x + 2657,11,x^12 + 11*x^11 - 9*x^10 - 451*x^9 - 829*x^8 + 5973*x^7 + 17916*x^6 - 24578*x^5 - 119209*x^4 - 29312*x^3 + 224591*x^2 + 217928*x + 41849,13,x^12 + 11*x^11 - 17*x^10 - 534*x^9 - 1050*x^8 + 5361*x^7 + 13008*x^6 - 23718*x^5 - 42795*x^4 + 49694*x^3 + 21668*x^2 - 9160*x - 272[] 401,2,2,x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44,3,x^21 - 3*x^20 - 37*x^19 + 112*x^18 + 572*x^17 - 1750*x^16 - 4821*x^15 + 14940*x^14 + 24209*x^13 - 76294*x^12 - 74001*x^11 + 239594*x^10 + 133106*x^9 - 457051*x^8 - 121988*x^7 + 501440*x^6 + 21445*x^5 - 278838*x^4 + 44972*x^3 + 55992*x^2 - 21840*x + 2176,5,x^21 - 3*x^20 - 61*x^19 + 194*x^18 + 1512*x^17 - 5215*x^16 - 19300*x^15 + 75661*x^14 + 128652*x^13 - 640637*x^12 - 336982*x^11 + 3173409*x^10 - 785768*x^9 - 8594568*x^8 + 7111131*x^7 + 10298067*x^6 - 15120487*x^5 - 1215456*x^4 + 10541238*x^3 - 4468704*x^2 - 686527*x + 543818,7,x^21 - 24*x^20 + 195*x^19 - 236*x^18 - 5466*x^17 + 28324*x^16 + 9918*x^15 - 432740*x^14 + 844081*x^13 + 2219324*x^12 - 9342038*x^11 + 830912*x^10 + 38273997*x^9 - 42544268*x^8 - 54586056*x^7 + 119960784*x^6 - 13453488*x^5 - 96133952*x^4 + 56121600*x^3 + 6590464*x^2 - 9138432*x + 667648,11,x^21 - x^20 - 133*x^19 + 169*x^18 + 7471*x^17 - 11763*x^16 - 229832*x^15 + 438954*x^14 + 4175027*x^13 - 9581728*x^12 - 44526253*x^11 + 124643620*x^10 + 251896037*x^9 - 934300300*x^8 - 464605776*x^7 + 3623452320*x^6 - 1606573440*x^5 - 5297593344*x^4 + 6110001408*x^3 - 1368589312*x^2 - 367203328*x + 18550784,13,x^21 - 9*x^20 - 109*x^19 + 1118*x^18 + 4634*x^17 - 58263*x^16 - 90876*x^15 + 1658206*x^14 + 519427*x^13 - 28086092*x^12 + 11520128*x^11 + 288867488*x^10 - 257320016*x^9 - 1759190240*x^8 + 2219776000*x^7 + 5836035584*x^6 - 9500805376*x^5 - 8335835648*x^4 + 18968096768*x^3 + 139124736*x^2 - 12677169152*x + 5112193024[] 402,1,2,x + 1,3,x + 1,5,x - 1,7,x + 3,11,x,13,x + 4[] 402,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 402,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 4[] 402,4,2,x - 1,3,x + 1,5,x - 2,7,x - 2,11,x + 4,13,x[] 402,5,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 + 4*x + 4,13,x^2 + 2*x - 2[] 402,6,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 10,7,x^2 + x - 10,11,x^2 - 8*x + 16,13,x^2 - 8*x + 16[] 402,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - x^2 - 4*x + 2,11,x^3 - 28*x + 16,13,x^3 + 6*x^2 - 22*x - 136[] 403,1,2,x^2 - 3*x + 1,3,x^2 + 4*x + 4,5,x^2 - 5,7,x^2 - 2*x + 1,11,x^2 - 20,13,x^2 - 2*x + 1[] 403,2,2,x^6 + 2*x^5 - 7*x^4 - 13*x^3 + 6*x^2 + 7*x - 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 11*x^2 + x + 1,5,x^6 + 9*x^5 + 20*x^4 - 19*x^3 - 75*x^2 + 14*x + 39,7,x^6 - 29*x^4 - 6*x^3 + 175*x^2 + 121*x - 113,11,x^6 + 5*x^5 - 18*x^4 - 49*x^3 + 147*x^2 - 76*x + 9,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 403,3,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 20*x^3 - 37*x^2 + x + 4,3,x^7 - 5*x^6 + 28*x^4 - 25*x^3 - 21*x^2 + 15*x + 8,5,x^7 - 11*x^6 + 38*x^5 - 27*x^4 - 75*x^3 + 80*x^2 + 39*x - 4,7,x^7 - 4*x^6 - 7*x^5 + 24*x^4 + 7*x^3 - 23*x^2 - 7*x + 2,11,x^7 - 8*x^6 - 3*x^5 + 99*x^4 + 10*x^3 - 307*x^2 - 17*x + 283,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 403,4,2,x^8 + 5*x^7 - 30*x^5 - 24*x^4 + 54*x^3 + 54*x^2 - 28*x - 29,3,x^8 + 3*x^7 - 12*x^6 - 36*x^5 + 31*x^4 + 97*x^3 - 29*x^2 - 72*x + 12,5,x^8 + 15*x^7 + 83*x^6 + 192*x^5 + 99*x^4 - 225*x^3 - 158*x^2 + 90*x + 3,7,x^8 + 4*x^7 - 20*x^6 - 88*x^5 + 46*x^4 + 335*x^3 + 50*x^2 - 181*x + 29,11,x^8 + 5*x^7 - 56*x^6 - 309*x^5 + 705*x^4 + 4994*x^3 + 769*x^2 - 17712*x - 14580,13,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[] 403,5,2,x^8 + x^7 - 11*x^6 - 10*x^5 + 37*x^4 + 33*x^3 - 36*x^2 - 33*x - 4,3,x^8 - 7*x^7 + 8*x^6 + 42*x^5 - 107*x^4 + 15*x^3 + 141*x^2 - 104*x + 16,5,x^8 - 11*x^7 + 32*x^6 + 35*x^5 - 263*x^4 + 126*x^3 + 537*x^2 - 346*x - 232,7,x^8 + 2*x^7 - 39*x^6 - 42*x^5 + 527*x^4 + 185*x^3 - 2717*x^2 + 250*x + 3824,11,x^8 + 2*x^7 - 31*x^6 - 51*x^5 + 238*x^4 + 267*x^3 - 631*x^2 - 319*x + 484,13,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1[] 404,1,2,x,3,x + 2,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 404,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 2,13,x + 3[] 404,3,2,x^7,3,x^7 - 2*x^6 - 17*x^5 + 36*x^4 + 64*x^3 - 148*x^2 + 11*x + 58,5,x^7 - 31*x^5 + 8*x^4 + 262*x^3 - 160*x^2 - 503*x + 250,7,x^7 - 2*x^6 - 39*x^5 + 62*x^4 + 438*x^3 - 474*x^2 - 1365*x + 698,11,x^7 - 4*x^6 - 43*x^5 + 122*x^4 + 548*x^3 - 1178*x^2 - 2085*x + 3482,13,x^7 - 4*x^6 - 55*x^5 + 244*x^4 + 534*x^3 - 2528*x^2 + 25*x + 58[] 405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[] 405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[] 405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[] 405,4,2,x,3,x,5,x - 1,7,x - 2,11,x - 3,13,x + 4[] 405,5,2,x - 2,3,x,5,x - 1,7,x,11,x - 5,13,x - 4[] 405,6,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 2[] 405,7,2,x^2 - 2*x - 2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 8*x + 13,13,x^2 + 4*x - 8[] 405,8,2,x^2 + 2*x - 2,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 + 8*x + 13,13,x^2 + 4*x - 8[] 405,9,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 + 2*x^2 - 8*x - 12,13,x^3 - 4*x^2 - 4*x + 4[] 405,10,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 - 2*x^2 - 8*x + 12,13,x^3 - 4*x^2 - 4*x + 4[] Errors: /home/mfd/gomagma: line 2: 27317 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:47:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [400..404] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 02:47:16 on modular [Seed = 3894310713] ------------------------------------- 400,1,2,$.1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 4,13,$.1 - 2[] 400,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 + 1,13,$.1 + 4[] 400,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 4[] 400,4,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 - 4,13,$.1 - 4[] 400,5,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 + 1,13,$.1 - 4[] 400,6,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 3,13,$.1 - 4[] 400,7,2,$.1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1,13,$.1 + 2[] 400,8,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 2,11,$.1 - 3,13,$.1 + 4[] 401,1,2,x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4,3,x^12 + 5*x^11 - 7*x^10 - 66*x^9 - 33*x^8 + 249*x^7 + 270*x^6 - 258*x^5 - 363*x^4 + 54*x^3 + 136*x^2 - 16,5,x^12 + 7*x^11 - 9*x^10 - 142*x^9 - 93*x^8 + 880*x^7 + 869*x^6 - 2355*x^5 - 1980*x^4 + 3042*x^3 + 1412*x^2 - 1552*x - 79,7,x^12 + 20*x^11 + 155*x^10 + 516*x^9 + 46*x^8 - 5172*x^7 - 15538*x^6 - 11740*x^5 + 30845*x^4 + 83664*x^3 + 81306*x^2 + 32396*x + 2657,11,x^12 + 11*x^11 - 9*x^10 - 451*x^9 - 829*x^8 + 5973*x^7 + 17916*x^6 - 24578*x^5 - 119209*x^4 - 29312*x^3 + 224591*x^2 + 217928*x + 41849,13,x^12 + 11*x^11 - 17*x^10 - 534*x^9 - 1050*x^8 + 5361*x^7 + 13008*x^6 - 23718*x^5 - 42795*x^4 + 49694*x^3 + 21668*x^2 - 9160*x - 272[] 401,2,2,x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44,3,x^21 - 3*x^20 - 37*x^19 + 112*x^18 + 572*x^17 - 1750*x^16 - 4821*x^15 + 14940*x^14 + 24209*x^13 - 76294*x^12 - 74001*x^11 + 239594*x^10 + 133106*x^9 - 457051*x^8 - 121988*x^7 + 501440*x^6 + 21445*x^5 - 278838*x^4 + 44972*x^3 + 55992*x^2 - 21840*x + 2176,5,x^21 - 3*x^20 - 61*x^19 + 194*x^18 + 1512*x^17 - 5215*x^16 - 19300*x^15 + 75661*x^14 + 128652*x^13 - 640637*x^12 - 336982*x^11 + 3173409*x^10 - 785768*x^9 - 8594568*x^8 + 7111131*x^7 + 10298067*x^6 - 15120487*x^5 - 1215456*x^4 + 10541238*x^3 - 4468704*x^2 - 686527*x + 543818,7,x^21 - 24*x^20 + 195*x^19 - 236*x^18 - 5466*x^17 + 28324*x^16 + 9918*x^15 - 432740*x^14 + 844081*x^13 + 2219324*x^12 - 9342038*x^11 + 830912*x^10 + 38273997*x^9 - 42544268*x^8 - 54586056*x^7 + 119960784*x^6 - 13453488*x^5 - 96133952*x^4 + 56121600*x^3 + 6590464*x^2 - 9138432*x + 667648,11,x^21 - x^20 - 133*x^19 + 169*x^18 + 7471*x^17 - 11763*x^16 - 229832*x^15 + 438954*x^14 + 4175027*x^13 - 9581728*x^12 - 44526253*x^11 + 124643620*x^10 + 251896037*x^9 - 934300300*x^8 - 464605776*x^7 + 3623452320*x^6 - 1606573440*x^5 - 5297593344*x^4 + 6110001408*x^3 - 1368589312*x^2 - 367203328*x + 18550784,13,x^21 - 9*x^20 - 109*x^19 + 1118*x^18 + 4634*x^17 - 58263*x^16 - 90876*x^15 + 1658206*x^14 + 519427*x^13 - 28086092*x^12 + 11520128*x^11 + 288867488*x^10 - 257320016*x^9 - 1759190240*x^8 + 2219776000*x^7 + 5836035584*x^6 - 9500805376*x^5 - 8335835648*x^4 + 18968096768*x^3 + 139124736*x^2 - 12677169152*x + 5112193024[] 402,1,2,x + 1,3,x + 1,5,x - 1,7,x + 3,11,x,13,x + 4[] 402,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 402,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 4[] 402,4,2,x - 1,3,x + 1,5,x - 2,7,x - 2,11,x + 4,13,x[] 402,5,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 + 4*x + 4,13,x^2 + 2*x - 2[] 402,6,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 10,7,x^2 + x - 10,11,x^2 - 8*x + 16,13,x^2 - 8*x + 16[] 402,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - x^2 - 4*x + 2,11,x^3 - 28*x + 16,13,x^3 + 6*x^2 - 22*x - 136[] 403,1,2,x^2 - 3*x + 1,3,x^2 + 4*x + 4,5,x^2 - 5,7,x^2 - 2*x + 1,11,x^2 - 20,13,x^2 - 2*x + 1[] 403,2,2,x^6 + 2*x^5 - 7*x^4 - 13*x^3 + 6*x^2 + 7*x - 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 11*x^2 + x + 1,5,x^6 + 9*x^5 + 20*x^4 - 19*x^3 - 75*x^2 + 14*x + 39,7,x^6 - 29*x^4 - 6*x^3 + 175*x^2 + 121*x - 113,11,x^6 + 5*x^5 - 18*x^4 - 49*x^3 + 147*x^2 - 76*x + 9,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 403,3,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 20*x^3 - 37*x^2 + x + 4,3,x^7 - 5*x^6 + 28*x^4 - 25*x^3 - 21*x^2 + 15*x + 8,5,x^7 - 11*x^6 + 38*x^5 - 27*x^4 - 75*x^3 + 80*x^2 + 39*x - 4,7,x^7 - 4*x^6 - 7*x^5 + 24*x^4 + 7*x^3 - 23*x^2 - 7*x + 2,11,x^7 - 8*x^6 - 3*x^5 + 99*x^4 + 10*x^3 - 307*x^2 - 17*x + 283,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 403,4,2,x^8 + 5*x^7 - 30*x^5 - 24*x^4 + 54*x^3 + 54*x^2 - 28*x - 29,3,x^8 + 3*x^7 - 12*x^6 - 36*x^5 + 31*x^4 + 97*x^3 - 29*x^2 - 72*x + 12,5,x^8 + 15*x^7 + 83*x^6 + 192*x^5 + 99*x^4 - 225*x^3 - 158*x^2 + 90*x + 3,7,x^8 + 4*x^7 - 20*x^6 - 88*x^5 + 46*x^4 + 335*x^3 + 50*x^2 - 181*x + 29,11,x^8 + 5*x^7 - 56*x^6 - 309*x^5 + 705*x^4 + 4994*x^3 + 769*x^2 - 17712*x - 14580,13,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[] 403,5,2,x^8 + x^7 - 11*x^6 - 10*x^5 + 37*x^4 + 33*x^3 - 36*x^2 - 33*x - 4,3,x^8 - 7*x^7 + 8*x^6 + 42*x^5 - 107*x^4 + 15*x^3 + 141*x^2 - 104*x + 16,5,x^8 - 11*x^7 + 32*x^6 + 35*x^5 - 263*x^4 + 126*x^3 + 537*x^2 - 346*x - 232,7,x^8 + 2*x^7 - 39*x^6 - 42*x^5 + 527*x^4 + 185*x^3 - 2717*x^2 + 250*x + 3824,11,x^8 + 2*x^7 - 31*x^6 - 51*x^5 + 238*x^4 + 267*x^3 - 631*x^2 - 319*x + 484,13,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1[] 404,1,2,x,3,x + 2,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 404,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 2,13,x + 3[] 404,3,2,x^7,3,x^7 - 2*x^6 - 17*x^5 + 36*x^4 + 64*x^3 - 148*x^2 + 11*x + 58,5,x^7 - 31*x^5 + 8*x^4 + 262*x^3 - 160*x^2 - 503*x + 250,7,x^7 - 2*x^6 - 39*x^5 + 62*x^4 + 438*x^3 - 474*x^2 - 1365*x + 698,11,x^7 - 4*x^6 - 43*x^5 + 122*x^4 + 548*x^3 - 1178*x^2 - 2085*x + 3482,13,x^7 - 4*x^6 - 55*x^5 + 244*x^4 + 534*x^3 - 2528*x^2 + 25*x + 58[] Total time: 18.969 seconds, Total memory usage: 6.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:58:13 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [404..408] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 02:57:49 on modular [Seed = 2205490731] ------------------------------------- 404,1,2,$.1,3,$.1 + 2,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[] 404,2,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 3[] 404,3,2,$.1^7,3,$.1^7 - 2*$.1^6 - 17*$.1^5 + 36*$.1^4 + 64*$.1^3 - 148*$.1^2 + 11*$.1 + 58,5,$.1^7 - 31*$.1^5 + 8*$.1^4 + 262*$.1^3 - 160*$.1^2 - 503*$.1 + 250,7,$.1^7 - 2*$.1^6 - 39*$.1^5 + 62*$.1^4 + 438*$.1^3 - 474*$.1^2 - 1365*$.1 + 698,11,$.1^7 - 4*$.1^6 - 43*$.1^5 + 122*$.1^4 + 548*$.1^3 - 1178*$.1^2 - 2085*$.1 + 3482,13,$.1^7 - 4*$.1^6 - 55*$.1^5 + 244*$.1^4 + 534*$.1^3 - 2528*$.1^2 + 25*$.1 + 58[] 405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[] 405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[] 405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[] 405,4,2,x,3,x,5,x - 1,7,x - 2,11,x - 3,13,x + 4[] 405,5,2,x - 2,3,x,5,x - 1,7,x,11,x - 5,13,x - 4[] 405,6,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 2[] 405,7,2,x^2 - 2*x - 2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 8*x + 13,13,x^2 + 4*x - 8[] 405,8,2,x^2 + 2*x - 2,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 + 8*x + 13,13,x^2 + 4*x - 8[] 405,9,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 + 2*x^2 - 8*x - 12,13,x^3 - 4*x^2 - 4*x + 4[] 405,10,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 - 2*x^2 - 8*x + 12,13,x^3 - 4*x^2 - 4*x + 4[] 406,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 4,13,x[] 406,2,2,x + 1,3,x - 2,5,x - 2,7,x - 1,11,x - 4,13,x + 2[] 406,3,2,x + 1,3,x - 1,5,x + 3,7,x - 1,11,x + 3,13,x + 1[] 406,4,2,x - 1,3,x + 1,5,x + 3,7,x + 1,11,x + 1,13,x + 1[] 406,5,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x - 2,7,x^2 + 2*x + 1,11,x^2 - 12,13,x^2 + 2*x - 2[] 406,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 4,5,x^3 - 5*x^2 + 2*x + 10,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 24*x - 20,13,x^3 - 7*x^2 + 10*x - 2[] 406,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 4*x + 8,5,x^4 + x^3 - 14*x^2 - 24*x + 4,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 7*x^3 + 8*x^2 + 16*x - 16,13,x^4 + 7*x^3 - 26*x^2 - 176*x + 28[] 407,1,2,x^4 + x^3 - 4*x^2 + 1,3,x^4 - 4*x^2 - x + 1,5,x^4 - x^3 - 4*x^2 + 2*x + 3,7,x^4 + 7*x^3 + 8*x^2 - 30*x - 53,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 10*x^3 + 24*x^2 + 11*x - 3[] 407,2,2,x^4 - x^3 - 4*x^2 + 2*x + 3,3,x^4 + 4*x^3 - 9*x + 1,5,x^4 + 5*x^3 + 4*x^2 - 8*x - 9,7,x^4 + x^3 - 4*x^2 + 1,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + 12*x^3 + 48*x^2 + 71*x + 31[] 407,3,2,x^11 - 2*x^10 - 16*x^9 + 32*x^8 + 89*x^7 - 179*x^6 - 201*x^5 + 407*x^4 + 168*x^3 - 333*x^2 - 51*x + 75,3,x^11 - 24*x^9 + 3*x^8 + 209*x^7 - 48*x^6 - 824*x^5 + 260*x^4 + 1448*x^3 - 560*x^2 - 880*x + 400,5,x^11 - x^10 - 46*x^9 + 48*x^8 + 767*x^7 - 786*x^6 - 5700*x^5 + 5224*x^4 + 19152*x^3 - 13536*x^2 - 24000*x + 9600,7,x^11 - 9*x^10 - 8*x^9 + 250*x^8 - 297*x^7 - 2188*x^6 + 3800*x^5 + 6880*x^4 - 12736*x^3 - 5632*x^2 + 10240*x + 1024,11,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,13,x^11 - 22*x^10 + 156*x^9 - 153*x^8 - 2747*x^7 + 9382*x^6 + 6848*x^5 - 61630*x^4 + 35796*x^3 + 77376*x^2 - 42204*x - 10228[] 407,4,2,x^12 - x^11 - 18*x^10 + 18*x^9 + 111*x^8 - 104*x^7 - 274*x^6 + 212*x^5 + 255*x^4 - 129*x^3 - 78*x^2 + 4*x + 1,3,x^12 - 8*x^11 + 4*x^10 + 115*x^9 - 251*x^8 - 396*x^7 + 1528*x^6 - 220*x^5 - 2592*x^4 + 1440*x^3 + 1328*x^2 - 752*x - 208,5,x^12 - 5*x^11 - 32*x^10 + 182*x^9 + 275*x^8 - 2228*x^7 + 120*x^6 + 10912*x^5 - 10016*x^4 - 15424*x^3 + 29312*x^2 - 15872*x + 2816,7,x^12 - 7*x^11 - 44*x^10 + 416*x^9 + 229*x^8 - 8052*x^7 + 11288*x^6 + 50304*x^5 - 133760*x^4 + 8320*x^3 + 173056*x^2 - 45056*x - 38912,11,x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1,13,x^12 - 14*x^11 + 735*x^9 - 1983*x^8 - 13336*x^7 + 54856*x^6 + 81234*x^5 - 560040*x^4 + 178164*x^3 + 1945404*x^2 - 2543220*x + 604836[] Errors: /home/mfd/gomagma: line 2: 27350 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:59:03 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [404..407] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 02:58:46 on modular [Seed = 2340231144] ------------------------------------- 404,1,2,$.1,3,$.1 + 2,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[] 404,2,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 3[] 404,3,2,$.1^7,3,$.1^7 - 2*$.1^6 - 17*$.1^5 + 36*$.1^4 + 64*$.1^3 - 148*$.1^2 + 11*$.1 + 58,5,$.1^7 - 31*$.1^5 + 8*$.1^4 + 262*$.1^3 - 160*$.1^2 - 503*$.1 + 250,7,$.1^7 - 2*$.1^6 - 39*$.1^5 + 62*$.1^4 + 438*$.1^3 - 474*$.1^2 - 1365*$.1 + 698,11,$.1^7 - 4*$.1^6 - 43*$.1^5 + 122*$.1^4 + 548*$.1^3 - 1178*$.1^2 - 2085*$.1 + 3482,13,$.1^7 - 4*$.1^6 - 55*$.1^5 + 244*$.1^4 + 534*$.1^3 - 2528*$.1^2 + 25*$.1 + 58[] 405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[] 405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[] 405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[] 405,4,2,x,3,x,5,x - 1,7,x - 2,11,x - 3,13,x + 4[] 405,5,2,x - 2,3,x,5,x - 1,7,x,11,x - 5,13,x - 4[] 405,6,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 2[] 405,7,2,x^2 - 2*x - 2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 8*x + 13,13,x^2 + 4*x - 8[] 405,8,2,x^2 + 2*x - 2,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 + 8*x + 13,13,x^2 + 4*x - 8[] 405,9,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 + 2*x^2 - 8*x - 12,13,x^3 - 4*x^2 - 4*x + 4[] 405,10,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 - 2*x^2 - 8*x + 12,13,x^3 - 4*x^2 - 4*x + 4[] 406,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 4,13,x[] 406,2,2,x + 1,3,x - 2,5,x - 2,7,x - 1,11,x - 4,13,x + 2[] 406,3,2,x + 1,3,x - 1,5,x + 3,7,x - 1,11,x + 3,13,x + 1[] 406,4,2,x - 1,3,x + 1,5,x + 3,7,x + 1,11,x + 1,13,x + 1[] 406,5,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x - 2,7,x^2 + 2*x + 1,11,x^2 - 12,13,x^2 + 2*x - 2[] 406,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 4,5,x^3 - 5*x^2 + 2*x + 10,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 24*x - 20,13,x^3 - 7*x^2 + 10*x - 2[] 406,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 4*x + 8,5,x^4 + x^3 - 14*x^2 - 24*x + 4,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 7*x^3 + 8*x^2 + 16*x - 16,13,x^4 + 7*x^3 - 26*x^2 - 176*x + 28[] 407,1,2,x^4 + x^3 - 4*x^2 + 1,3,x^4 - 4*x^2 - x + 1,5,x^4 - x^3 - 4*x^2 + 2*x + 3,7,x^4 + 7*x^3 + 8*x^2 - 30*x - 53,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 10*x^3 + 24*x^2 + 11*x - 3[] 407,2,2,x^4 - x^3 - 4*x^2 + 2*x + 3,3,x^4 + 4*x^3 - 9*x + 1,5,x^4 + 5*x^3 + 4*x^2 - 8*x - 9,7,x^4 + x^3 - 4*x^2 + 1,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + 12*x^3 + 48*x^2 + 71*x + 31[] 407,3,2,x^11 - 2*x^10 - 16*x^9 + 32*x^8 + 89*x^7 - 179*x^6 - 201*x^5 + 407*x^4 + 168*x^3 - 333*x^2 - 51*x + 75,3,x^11 - 24*x^9 + 3*x^8 + 209*x^7 - 48*x^6 - 824*x^5 + 260*x^4 + 1448*x^3 - 560*x^2 - 880*x + 400,5,x^11 - x^10 - 46*x^9 + 48*x^8 + 767*x^7 - 786*x^6 - 5700*x^5 + 5224*x^4 + 19152*x^3 - 13536*x^2 - 24000*x + 9600,7,x^11 - 9*x^10 - 8*x^9 + 250*x^8 - 297*x^7 - 2188*x^6 + 3800*x^5 + 6880*x^4 - 12736*x^3 - 5632*x^2 + 10240*x + 1024,11,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,13,x^11 - 22*x^10 + 156*x^9 - 153*x^8 - 2747*x^7 + 9382*x^6 + 6848*x^5 - 61630*x^4 + 35796*x^3 + 77376*x^2 - 42204*x - 10228[] 407,4,2,x^12 - x^11 - 18*x^10 + 18*x^9 + 111*x^8 - 104*x^7 - 274*x^6 + 212*x^5 + 255*x^4 - 129*x^3 - 78*x^2 + 4*x + 1,3,x^12 - 8*x^11 + 4*x^10 + 115*x^9 - 251*x^8 - 396*x^7 + 1528*x^6 - 220*x^5 - 2592*x^4 + 1440*x^3 + 1328*x^2 - 752*x - 208,5,x^12 - 5*x^11 - 32*x^10 + 182*x^9 + 275*x^8 - 2228*x^7 + 120*x^6 + 10912*x^5 - 10016*x^4 - 15424*x^3 + 29312*x^2 - 15872*x + 2816,7,x^12 - 7*x^11 - 44*x^10 + 416*x^9 + 229*x^8 - 8052*x^7 + 11288*x^6 + 50304*x^5 - 133760*x^4 + 8320*x^3 + 173056*x^2 - 45056*x - 38912,11,x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1,13,x^12 - 14*x^11 + 735*x^9 - 1983*x^8 - 13336*x^7 + 54856*x^6 + 81234*x^5 - 560040*x^4 + 178164*x^3 + 1945404*x^2 - 2543220*x + 604836[] Total time: 16.229 seconds, Total memory usage: 5.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:04:39 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [407..413] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 03:04:15 on modular [Seed = 1453378946] ------------------------------------- 407,1,2,$.1^4 + $.1^3 - 4*$.1^2 + 1,3,$.1^4 - 4*$.1^2 - $.1 + 1,5,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,7,$.1^4 + 7*$.1^3 + 8*$.1^2 - 30*$.1 - 53,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 10*$.1^3 + 24*$.1^2 + 11*$.1 - 3[] 407,2,2,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,3,$.1^4 + 4*$.1^3 - 9*$.1 + 1,5,$.1^4 + 5*$.1^3 + 4*$.1^2 - 8*$.1 - 9,7,$.1^4 + $.1^3 - 4*$.1^2 + 1,11,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,13,$.1^4 + 12*$.1^3 + 48*$.1^2 + 71*$.1 + 31[] 407,3,2,$.1^11 - 2*$.1^10 - 16*$.1^9 + 32*$.1^8 + 89*$.1^7 - 179*$.1^6 - 201*$.1^5 + 407*$.1^4 + 168*$.1^3 - 333*$.1^2 - 51*$.1 + 75,3,$.1^11 - 24*$.1^9 + 3*$.1^8 + 209*$.1^7 - 48*$.1^6 - 824*$.1^5 + 260*$.1^4 + 1448*$.1^3 - 560*$.1^2 - 880*$.1 + 400,5,$.1^11 - $.1^10 - 46*$.1^9 + 48*$.1^8 + 767*$.1^7 - 786*$.1^6 - 5700*$.1^5 + 5224*$.1^4 + 19152*$.1^3 - 13536*$.1^2 - 24000*$.1 + 9600,7,$.1^11 - 9*$.1^10 - 8*$.1^9 + 250*$.1^8 - 297*$.1^7 - 2188*$.1^6 + 3800*$.1^5 + 6880*$.1^4 - 12736*$.1^3 - 5632*$.1^2 + 10240*$.1 + 1024,11,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3 + 55*$.1^2 + 11*$.1 + 1,13,$.1^11 - 22*$.1^10 + 156*$.1^9 - 153*$.1^8 - 2747*$.1^7 + 9382*$.1^6 + 6848*$.1^5 - 61630*$.1^4 + 35796*$.1^3 + 77376*$.1^2 - 42204*$.1 - 10228[] 407,4,2,$.1^12 - $.1^11 - 18*$.1^10 + 18*$.1^9 + 111*$.1^8 - 104*$.1^7 - 274*$.1^6 + 212*$.1^5 + 255*$.1^4 - 129*$.1^3 - 78*$.1^2 + 4*$.1 + 1,3,$.1^12 - 8*$.1^11 + 4*$.1^10 + 115*$.1^9 - 251*$.1^8 - 396*$.1^7 + 1528*$.1^6 - 220*$.1^5 - 2592*$.1^4 + 1440*$.1^3 + 1328*$.1^2 - 752*$.1 - 208,5,$.1^12 - 5*$.1^11 - 32*$.1^10 + 182*$.1^9 + 275*$.1^8 - 2228*$.1^7 + 120*$.1^6 + 10912*$.1^5 - 10016*$.1^4 - 15424*$.1^3 + 29312*$.1^2 - 15872*$.1 + 2816,7,$.1^12 - 7*$.1^11 - 44*$.1^10 + 416*$.1^9 + 229*$.1^8 - 8052*$.1^7 + 11288*$.1^6 + 50304*$.1^5 - 133760*$.1^4 + 8320*$.1^3 + 173056*$.1^2 - 45056*$.1 - 38912,11,$.1^12 - 12*$.1^11 + 66*$.1^10 - 220*$.1^9 + 495*$.1^8 - 792*$.1^7 + 924*$.1^6 - 792*$.1^5 + 495*$.1^4 - 220*$.1^3 + 66*$.1^2 - 12*$.1 + 1,13,$.1^12 - 14*$.1^11 + 735*$.1^9 - 1983*$.1^8 - 13336*$.1^7 + 54856*$.1^6 + 81234*$.1^5 - 560040*$.1^4 + 178164*$.1^3 + 1945404*$.1^2 - 2543220*$.1 + 604836[] 408,1,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 408,2,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x + 5[] 408,3,2,x,3,x + 1,5,x - 3,7,x,11,x + 1,13,x - 3[] 408,4,2,x,3,x - 1,5,x - 2,7,x + 4,11,x - 4,13,x - 6[] 408,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 4,7,x^2 + 2*x - 16,11,x^2 + 9*x + 16,13,x^2 + 3*x - 2[] 408,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 + x - 14,7,x^2 - 8*x + 16,11,x^2 + 3*x - 12,13,x^2 - x - 14[] 409,1,2,x^13 + 6*x^12 + 2*x^11 - 47*x^10 - 64*x^9 + 117*x^8 + 226*x^7 - 94*x^6 - 278*x^5 + 9*x^4 + 134*x^3 + 15*x^2 - 22*x - 4,3,x^13 + 3*x^12 - 15*x^11 - 49*x^10 + 62*x^9 + 246*x^8 - 55*x^7 - 408*x^6 + 38*x^5 + 272*x^4 - 51*x^3 - 64*x^2 + 22*x - 1,5,x^13 + 10*x^12 + 15*x^11 - 147*x^10 - 503*x^9 + 467*x^8 + 3660*x^7 + 1621*x^6 - 9806*x^5 - 9811*x^4 + 7795*x^3 + 11811*x^2 + 2790*x - 171,7,x^13 + 9*x^12 - 8*x^11 - 272*x^10 - 526*x^9 + 1605*x^8 + 4612*x^7 - 2986*x^6 - 12805*x^5 - 85*x^4 + 11495*x^3 + 4353*x^2 - 893*x - 361,11,x^13 + 26*x^12 + 258*x^11 + 1081*x^10 + 210*x^9 - 14427*x^8 - 44686*x^7 - 9053*x^6 + 177762*x^5 + 263786*x^4 - 79735*x^3 - 414834*x^2 - 243630*x - 14347,13,x^13 + 3*x^12 - 69*x^11 - 218*x^10 + 1639*x^9 + 5759*x^8 - 14252*x^7 - 65061*x^6 + 5742*x^5 + 252815*x^4 + 321799*x^3 + 128485*x^2 + 8065*x - 1831[] 409,2,2,x^20 - 5*x^19 - 19*x^18 + 126*x^17 + 100*x^16 - 1283*x^15 + 247*x^14 + 6767*x^13 - 4554*x^12 - 19689*x^11 + 18771*x^10 + 31011*x^9 - 35515*x^8 - 23548*x^7 + 31466*x^6 + 5354*x^5 - 10552*x^4 + 1129*x^3 + 523*x^2 - 54*x - 4,3,x^20 - x^19 - 43*x^18 + 43*x^17 + 770*x^16 - 742*x^15 - 7523*x^14 + 6640*x^13 + 44254*x^12 - 33176*x^11 - 163247*x^10 + 91556*x^9 + 379858*x^8 - 121845*x^7 - 538772*x^6 + 24992*x^5 + 417136*x^4 + 98080*x^3 - 123840*x^2 - 64128*x - 7936,5,x^20 - 8*x^19 - 25*x^18 + 339*x^17 - 73*x^16 - 5519*x^15 + 7786*x^14 + 43033*x^13 - 93848*x^12 - 160799*x^11 + 500285*x^10 + 218665*x^9 - 1333960*x^8 + 220157*x^7 + 1717578*x^6 - 875008*x^5 - 838232*x^4 + 649944*x^3 - 13040*x^2 - 35916*x - 2412,7,x^20 - 5*x^19 - 60*x^18 + 340*x^17 + 1276*x^16 - 8885*x^15 - 11420*x^14 + 119286*x^13 + 20939*x^12 - 909731*x^11 + 382277*x^10 + 4046437*x^9 - 3102111*x^8 - 10182997*x^7 + 9750164*x^6 + 13080780*x^5 - 12859068*x^4 - 7114292*x^3 + 4115996*x^2 + 2565948*x + 334126,11,x^20 - 30*x^19 + 340*x^18 - 1391*x^17 - 5028*x^16 + 75155*x^15 - 248768*x^14 - 310789*x^13 + 4354008*x^12 - 9372430*x^11 - 10656087*x^10 + 76307340*x^9 - 82153612*x^8 - 142849065*x^7 + 383618660*x^6 - 114166400*x^5 - 435600764*x^4 + 422353454*x^3 + 18207646*x^2 - 154653238*x + 45344434,13,x^20 + 7*x^19 - 107*x^18 - 824*x^17 + 4419*x^16 + 39503*x^15 - 86484*x^14 - 1001445*x^13 + 721924*x^12 + 14609397*x^11 + 640203*x^10 - 125194851*x^9 - 53698305*x^8 + 614885465*x^7 + 339715190*x^6 - 1594500300*x^5 - 703861704*x^4 + 1761581616*x^3 + 174121440*x^2 - 226273216*x - 38869888[] 410,1,2,x + 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x + 4[] 410,2,2,x + 1,3,x,5,x - 1,7,x + 2,11,x + 6,13,x + 2[] 410,3,2,x - 1,3,x + 2,5,x + 1,7,x + 2,11,x - 2,13,x + 6[] 410,4,2,x - 1,3,x,5,x - 1,7,x - 4,11,x,13,x + 2[] 410,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 - 2*x - 4,13,x^2 + 8*x + 16[] 410,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 4*x - 8[] 410,7,2,x^2 + 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 - 2*x - 16,13,x^2 - 8*x + 16[] 410,8,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 24,13,x^2 - 8*x + 16[] 410,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 8*x + 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 + 4*x^2 - 16*x - 48,13,x^3 - 8*x^2 - 8*x + 112[] 411,1,2,x^3 - x^2 - 2*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 - 4*x + 1,11,x^3 + 3*x^2 - 4*x - 13,13,x^3 + 11*x^2 + 38*x + 41[] 411,2,2,x^3 - 6*x^2 + 12*x - 8,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 3*x + 5,7,x^3 - 13*x + 13,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 2*x^2 - 16*x - 8[] 411,3,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 + 3*x^2 - 3,11,x^3 + 9*x^2 + 24*x + 19,13,x^3 + 3*x^2 - 6*x - 17[] 411,4,2,x^5 + x^4 - 7*x^3 - 10*x^2 + 1,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 - 6*x^4 + 2*x^3 + 29*x^2 - 13*x - 41,7,x^5 + x^4 - 9*x^3 - 8*x^2 + 18*x + 13,11,x^5 - x^4 - 22*x^3 + 31*x^2 + 120*x - 208,13,x^5 + x^4 - 54*x^3 + 33*x^2 + 784*x - 1516[] 411,5,2,x^9 - 16*x^7 + x^6 + 82*x^5 - 9*x^4 - 141*x^3 + 18*x^2 + 52*x + 8,3,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,5,x^9 - 6*x^8 - 15*x^7 + 130*x^6 + x^5 - 816*x^4 + 464*x^3 + 1608*x^2 - 925*x - 482,7,x^9 - 7*x^8 - 18*x^7 + 212*x^6 - 196*x^5 - 1292*x^4 + 2254*x^3 + 1409*x^2 - 3651*x + 584,11,x^9 - 7*x^8 - 50*x^7 + 395*x^6 + 520*x^5 - 6292*x^4 + 3112*x^3 + 22496*x^2 - 23040*x - 2048,13,x^9 - 7*x^8 - 38*x^7 + 275*x^6 + 244*x^5 - 2072*x^4 - 856*x^3 + 2976*x^2 - 160*x - 320[] Errors: /home/mfd/gomagma: line 2: 27394 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:05:26 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [407..411] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 03:05:04 on modular [Seed = 1538113727] ------------------------------------- 407,1,2,$.1^4 + $.1^3 - 4*$.1^2 + 1,3,$.1^4 - 4*$.1^2 - $.1 + 1,5,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,7,$.1^4 + 7*$.1^3 + 8*$.1^2 - 30*$.1 - 53,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 10*$.1^3 + 24*$.1^2 + 11*$.1 - 3[] 407,2,2,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,3,$.1^4 + 4*$.1^3 - 9*$.1 + 1,5,$.1^4 + 5*$.1^3 + 4*$.1^2 - 8*$.1 - 9,7,$.1^4 + $.1^3 - 4*$.1^2 + 1,11,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,13,$.1^4 + 12*$.1^3 + 48*$.1^2 + 71*$.1 + 31[] 407,3,2,$.1^11 - 2*$.1^10 - 16*$.1^9 + 32*$.1^8 + 89*$.1^7 - 179*$.1^6 - 201*$.1^5 + 407*$.1^4 + 168*$.1^3 - 333*$.1^2 - 51*$.1 + 75,3,$.1^11 - 24*$.1^9 + 3*$.1^8 + 209*$.1^7 - 48*$.1^6 - 824*$.1^5 + 260*$.1^4 + 1448*$.1^3 - 560*$.1^2 - 880*$.1 + 400,5,$.1^11 - $.1^10 - 46*$.1^9 + 48*$.1^8 + 767*$.1^7 - 786*$.1^6 - 5700*$.1^5 + 5224*$.1^4 + 19152*$.1^3 - 13536*$.1^2 - 24000*$.1 + 9600,7,$.1^11 - 9*$.1^10 - 8*$.1^9 + 250*$.1^8 - 297*$.1^7 - 2188*$.1^6 + 3800*$.1^5 + 6880*$.1^4 - 12736*$.1^3 - 5632*$.1^2 + 10240*$.1 + 1024,11,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3 + 55*$.1^2 + 11*$.1 + 1,13,$.1^11 - 22*$.1^10 + 156*$.1^9 - 153*$.1^8 - 2747*$.1^7 + 9382*$.1^6 + 6848*$.1^5 - 61630*$.1^4 + 35796*$.1^3 + 77376*$.1^2 - 42204*$.1 - 10228[] 407,4,2,$.1^12 - $.1^11 - 18*$.1^10 + 18*$.1^9 + 111*$.1^8 - 104*$.1^7 - 274*$.1^6 + 212*$.1^5 + 255*$.1^4 - 129*$.1^3 - 78*$.1^2 + 4*$.1 + 1,3,$.1^12 - 8*$.1^11 + 4*$.1^10 + 115*$.1^9 - 251*$.1^8 - 396*$.1^7 + 1528*$.1^6 - 220*$.1^5 - 2592*$.1^4 + 1440*$.1^3 + 1328*$.1^2 - 752*$.1 - 208,5,$.1^12 - 5*$.1^11 - 32*$.1^10 + 182*$.1^9 + 275*$.1^8 - 2228*$.1^7 + 120*$.1^6 + 10912*$.1^5 - 10016*$.1^4 - 15424*$.1^3 + 29312*$.1^2 - 15872*$.1 + 2816,7,$.1^12 - 7*$.1^11 - 44*$.1^10 + 416*$.1^9 + 229*$.1^8 - 8052*$.1^7 + 11288*$.1^6 + 50304*$.1^5 - 133760*$.1^4 + 8320*$.1^3 + 173056*$.1^2 - 45056*$.1 - 38912,11,$.1^12 - 12*$.1^11 + 66*$.1^10 - 220*$.1^9 + 495*$.1^8 - 792*$.1^7 + 924*$.1^6 - 792*$.1^5 + 495*$.1^4 - 220*$.1^3 + 66*$.1^2 - 12*$.1 + 1,13,$.1^12 - 14*$.1^11 + 735*$.1^9 - 1983*$.1^8 - 13336*$.1^7 + 54856*$.1^6 + 81234*$.1^5 - 560040*$.1^4 + 178164*$.1^3 + 1945404*$.1^2 - 2543220*$.1 + 604836[] 408,1,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 408,2,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x + 5[] 408,3,2,x,3,x + 1,5,x - 3,7,x,11,x + 1,13,x - 3[] 408,4,2,x,3,x - 1,5,x - 2,7,x + 4,11,x - 4,13,x - 6[] 408,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 4,7,x^2 + 2*x - 16,11,x^2 + 9*x + 16,13,x^2 + 3*x - 2[] 408,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 + x - 14,7,x^2 - 8*x + 16,11,x^2 + 3*x - 12,13,x^2 - x - 14[] 409,1,2,x^13 + 6*x^12 + 2*x^11 - 47*x^10 - 64*x^9 + 117*x^8 + 226*x^7 - 94*x^6 - 278*x^5 + 9*x^4 + 134*x^3 + 15*x^2 - 22*x - 4,3,x^13 + 3*x^12 - 15*x^11 - 49*x^10 + 62*x^9 + 246*x^8 - 55*x^7 - 408*x^6 + 38*x^5 + 272*x^4 - 51*x^3 - 64*x^2 + 22*x - 1,5,x^13 + 10*x^12 + 15*x^11 - 147*x^10 - 503*x^9 + 467*x^8 + 3660*x^7 + 1621*x^6 - 9806*x^5 - 9811*x^4 + 7795*x^3 + 11811*x^2 + 2790*x - 171,7,x^13 + 9*x^12 - 8*x^11 - 272*x^10 - 526*x^9 + 1605*x^8 + 4612*x^7 - 2986*x^6 - 12805*x^5 - 85*x^4 + 11495*x^3 + 4353*x^2 - 893*x - 361,11,x^13 + 26*x^12 + 258*x^11 + 1081*x^10 + 210*x^9 - 14427*x^8 - 44686*x^7 - 9053*x^6 + 177762*x^5 + 263786*x^4 - 79735*x^3 - 414834*x^2 - 243630*x - 14347,13,x^13 + 3*x^12 - 69*x^11 - 218*x^10 + 1639*x^9 + 5759*x^8 - 14252*x^7 - 65061*x^6 + 5742*x^5 + 252815*x^4 + 321799*x^3 + 128485*x^2 + 8065*x - 1831[] 409,2,2,x^20 - 5*x^19 - 19*x^18 + 126*x^17 + 100*x^16 - 1283*x^15 + 247*x^14 + 6767*x^13 - 4554*x^12 - 19689*x^11 + 18771*x^10 + 31011*x^9 - 35515*x^8 - 23548*x^7 + 31466*x^6 + 5354*x^5 - 10552*x^4 + 1129*x^3 + 523*x^2 - 54*x - 4,3,x^20 - x^19 - 43*x^18 + 43*x^17 + 770*x^16 - 742*x^15 - 7523*x^14 + 6640*x^13 + 44254*x^12 - 33176*x^11 - 163247*x^10 + 91556*x^9 + 379858*x^8 - 121845*x^7 - 538772*x^6 + 24992*x^5 + 417136*x^4 + 98080*x^3 - 123840*x^2 - 64128*x - 7936,5,x^20 - 8*x^19 - 25*x^18 + 339*x^17 - 73*x^16 - 5519*x^15 + 7786*x^14 + 43033*x^13 - 93848*x^12 - 160799*x^11 + 500285*x^10 + 218665*x^9 - 1333960*x^8 + 220157*x^7 + 1717578*x^6 - 875008*x^5 - 838232*x^4 + 649944*x^3 - 13040*x^2 - 35916*x - 2412,7,x^20 - 5*x^19 - 60*x^18 + 340*x^17 + 1276*x^16 - 8885*x^15 - 11420*x^14 + 119286*x^13 + 20939*x^12 - 909731*x^11 + 382277*x^10 + 4046437*x^9 - 3102111*x^8 - 10182997*x^7 + 9750164*x^6 + 13080780*x^5 - 12859068*x^4 - 7114292*x^3 + 4115996*x^2 + 2565948*x + 334126,11,x^20 - 30*x^19 + 340*x^18 - 1391*x^17 - 5028*x^16 + 75155*x^15 - 248768*x^14 - 310789*x^13 + 4354008*x^12 - 9372430*x^11 - 10656087*x^10 + 76307340*x^9 - 82153612*x^8 - 142849065*x^7 + 383618660*x^6 - 114166400*x^5 - 435600764*x^4 + 422353454*x^3 + 18207646*x^2 - 154653238*x + 45344434,13,x^20 + 7*x^19 - 107*x^18 - 824*x^17 + 4419*x^16 + 39503*x^15 - 86484*x^14 - 1001445*x^13 + 721924*x^12 + 14609397*x^11 + 640203*x^10 - 125194851*x^9 - 53698305*x^8 + 614885465*x^7 + 339715190*x^6 - 1594500300*x^5 - 703861704*x^4 + 1761581616*x^3 + 174121440*x^2 - 226273216*x - 38869888[] 410,1,2,x + 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x + 4[] 410,2,2,x + 1,3,x,5,x - 1,7,x + 2,11,x + 6,13,x + 2[] 410,3,2,x - 1,3,x + 2,5,x + 1,7,x + 2,11,x - 2,13,x + 6[] 410,4,2,x - 1,3,x,5,x - 1,7,x - 4,11,x,13,x + 2[] 410,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 - 2*x - 4,13,x^2 + 8*x + 16[] 410,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 4*x - 8[] 410,7,2,x^2 + 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 - 2*x - 16,13,x^2 - 8*x + 16[] 410,8,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 24,13,x^2 - 8*x + 16[] 410,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 8*x + 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 + 4*x^2 - 16*x - 48,13,x^3 - 8*x^2 - 8*x + 112[] 411,1,2,x^3 - x^2 - 2*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 - 4*x + 1,11,x^3 + 3*x^2 - 4*x - 13,13,x^3 + 11*x^2 + 38*x + 41[] 411,2,2,x^3 - 6*x^2 + 12*x - 8,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 3*x + 5,7,x^3 - 13*x + 13,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 2*x^2 - 16*x - 8[] 411,3,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 + 3*x^2 - 3,11,x^3 + 9*x^2 + 24*x + 19,13,x^3 + 3*x^2 - 6*x - 17[] 411,4,2,x^5 + x^4 - 7*x^3 - 10*x^2 + 1,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 - 6*x^4 + 2*x^3 + 29*x^2 - 13*x - 41,7,x^5 + x^4 - 9*x^3 - 8*x^2 + 18*x + 13,11,x^5 - x^4 - 22*x^3 + 31*x^2 + 120*x - 208,13,x^5 + x^4 - 54*x^3 + 33*x^2 + 784*x - 1516[] 411,5,2,x^9 - 16*x^7 + x^6 + 82*x^5 - 9*x^4 - 141*x^3 + 18*x^2 + 52*x + 8,3,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,5,x^9 - 6*x^8 - 15*x^7 + 130*x^6 + x^5 - 816*x^4 + 464*x^3 + 1608*x^2 - 925*x - 482,7,x^9 - 7*x^8 - 18*x^7 + 212*x^6 - 196*x^5 - 1292*x^4 + 2254*x^3 + 1409*x^2 - 3651*x + 584,11,x^9 - 7*x^8 - 50*x^7 + 395*x^6 + 520*x^5 - 6292*x^4 + 3112*x^3 + 22496*x^2 - 23040*x - 2048,13,x^9 - 7*x^8 - 38*x^7 + 275*x^6 + 244*x^5 - 2072*x^4 - 856*x^3 + 2976*x^2 - 160*x - 320[] Total time: 21.010 seconds, Total memory usage: 6.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:13:36 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [411..415] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 03:13:15 on modular [Seed = 1988161465] ------------------------------------- 411,1,2,$.1^3 - $.1^2 - 2*$.1 + 1,3,$.1^3 + 3*$.1^2 + 3*$.1 + 1,5,$.1^3 + 2*$.1^2 - $.1 - 1,7,$.1^3 + 3*$.1^2 - 4*$.1 + 1,11,$.1^3 + 3*$.1^2 - 4*$.1 - 13,13,$.1^3 + 11*$.1^2 + 38*$.1 + 41[] 411,2,2,$.1^3 - 6*$.1^2 + 12*$.1 - 8,3,$.1^3 - 3*$.1^2 + 3*$.1 - 1,5,$.1^3 - 2*$.1^2 - 3*$.1 + 5,7,$.1^3 - 13*$.1 + 13,11,$.1^3 - 4*$.1^2 - 12*$.1 + 40,13,$.1^3 - 2*$.1^2 - 16*$.1 - 8[] 411,3,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 - 3*$.1^2 + 3*$.1 - 1,5,$.1^3 + 6*$.1^2 + 9*$.1 + 1,7,$.1^3 + 3*$.1^2 - 3,11,$.1^3 + 9*$.1^2 + 24*$.1 + 19,13,$.1^3 + 3*$.1^2 - 6*$.1 - 17[] 411,4,2,$.1^5 + $.1^4 - 7*$.1^3 - 10*$.1^2 + 1,3,$.1^5 - 5*$.1^4 + 10*$.1^3 - 10*$.1^2 + 5*$.1 - 1,5,$.1^5 - 6*$.1^4 + 2*$.1^3 + 29*$.1^2 - 13*$.1 - 41,7,$.1^5 + $.1^4 - 9*$.1^3 - 8*$.1^2 + 18*$.1 + 13,11,$.1^5 - $.1^4 - 22*$.1^3 + 31*$.1^2 + 120*$.1 - 208,13,$.1^5 + $.1^4 - 54*$.1^3 + 33*$.1^2 + 784*$.1 - 1516[] 411,5,2,$.1^9 - 16*$.1^7 + $.1^6 + 82*$.1^5 - 9*$.1^4 - 141*$.1^3 + 18*$.1^2 + 52*$.1 + 8,3,$.1^9 + 9*$.1^8 + 36*$.1^7 + 84*$.1^6 + 126*$.1^5 + 126*$.1^4 + 84*$.1^3 + 36*$.1^2 + 9*$.1 + 1,5,$.1^9 - 6*$.1^8 - 15*$.1^7 + 130*$.1^6 + $.1^5 - 816*$.1^4 + 464*$.1^3 + 1608*$.1^2 - 925*$.1 - 482,7,$.1^9 - 7*$.1^8 - 18*$.1^7 + 212*$.1^6 - 196*$.1^5 - 1292*$.1^4 + 2254*$.1^3 + 1409*$.1^2 - 3651*$.1 + 584,11,$.1^9 - 7*$.1^8 - 50*$.1^7 + 395*$.1^6 + 520*$.1^5 - 6292*$.1^4 + 3112*$.1^3 + 22496*$.1^2 - 23040*$.1 - 2048,13,$.1^9 - 7*$.1^8 - 38*$.1^7 + 275*$.1^6 + 244*$.1^5 - 2072*$.1^4 - 856*$.1^3 + 2976*$.1^2 - 160*$.1 - 320[] 412,1,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 5,7,x^2 - 21,11,x^2 + 3*x - 3,13,x^2 + 7*x + 7[] 412,2,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 2*x - 4,7,x^2 + 3*x + 1,11,x^2 + 4*x + 4,13,x^2 + x - 1[] 412,3,2,x^4,3,x^4 - 2*x^3 - 5*x^2 + 6*x + 4,5,x^4 - 3*x^3 - 7*x^2 + 12*x - 4,7,x^4 - 5*x^3 + 4*x^2 + 5*x - 1,11,x^4 - 7*x^3 + 3*x^2 + 48*x - 64,13,x^4 - 19*x^2 + 89[] 413,1,2,x^2 - 5,3,x^2 + x - 1,5,x^2 - 2*x - 4,7,x^2 + 2*x + 1,11,x^2 + 5*x + 5,13,x^2 - x - 11[] 413,2,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - x + 4,5,x^3 - 16*x + 8,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 3*x^2 - x + 4,13,x^3 + 3*x^2 - 43*x - 98[] 413,3,2,x^5 + 2*x^4 - 3*x^3 - 5*x^2 + x + 1,3,x^5 + 5*x^4 + 4*x^3 - 7*x^2 - 7*x + 1,5,x^5 - x^4 - 5*x^3 + 3*x^2 + 2*x - 1,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 + 7*x^4 + 6*x^3 - 31*x^2 - 35*x + 25,13,x^5 + 3*x^4 - 21*x^3 - 23*x^2 + 112*x - 47[] 413,4,2,x^5 - 4*x^4 - 3*x^3 + 29*x^2 - 35*x + 11,3,x^5 - 7*x^4 + 8*x^3 + 33*x^2 - 67*x + 13,5,x^5 + 3*x^4 - 5*x^3 - 5*x^2 + 6*x - 1,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 9*x^4 + 129*x^2 - 73*x - 481,13,x^5 + x^4 - 13*x^3 - 15*x^2 + 42*x + 55[] 413,5,2,x^5 - 5*x^3 - x^2 + 5*x + 1,3,x^5 + 7*x^4 + 14*x^3 + 3*x^2 - 9*x + 1,5,x^5 + 5*x^4 - x^3 - 27*x^2 - 24*x - 1,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - x^4 - 36*x^3 - 15*x^2 + 199*x + 157,13,x^5 + 17*x^4 + 95*x^3 + 165*x^2 - 78*x - 139[] 413,6,2,x^9 - 13*x^7 + x^6 + 54*x^5 - 7*x^4 - 75*x^3 + 9*x^2 + 17*x - 3,3,x^9 - 7*x^8 + 7*x^7 + 46*x^6 - 94*x^5 - 69*x^4 + 243*x^3 - 32*x^2 - 171*x + 73,5,x^9 - 3*x^8 - 25*x^7 + 77*x^6 + 188*x^5 - 589*x^4 - 460*x^3 + 1340*x^2 + 448*x - 432,7,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,11,x^9 - 3*x^8 - 47*x^7 + 164*x^6 + 492*x^5 - 2085*x^4 + 417*x^3 + 2270*x^2 - 113*x - 423,13,x^9 - 13*x^8 + 22*x^7 + 416*x^6 - 2398*x^5 + 2337*x^4 + 16559*x^3 - 59020*x^2 + 75478*x - 34703[] 414,1,2,x + 1,3,x,5,x + 2,7,x,11,x,13,x + 2[] 414,2,2,x - 1,3,x,5,x + 4,7,x + 4,11,x + 2,13,x + 2[] 414,3,2,x - 1,3,x,5,x,7,x - 2,11,x,13,x - 2[] 414,4,2,x - 1,3,x,5,x - 2,7,x + 2,11,x - 6,13,x + 2[] 414,5,2,x^2 + 2*x + 1,3,x^2,5,x^2 + 2*x - 6,7,x^2 - 4*x + 4,11,x^2 - 2*x - 6,13,x^2 - 28[] 414,6,2,x^2 + 2*x + 1,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 20,11,x^2 - 6*x + 4,13,x^2 - 20[] 414,7,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 2*x - 6,7,x^2 - 4*x + 4,11,x^2 + 2*x - 6,13,x^2 - 28[] 415,1,2,x - 1,3,x - 3,5,x - 1,7,x - 1,11,x - 3,13,x + 6[] 415,2,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 - 2*x + 1,7,x^2 - 5,11,x^2 + 4*x + 4,13,x^2 + 3*x + 1[] 415,3,2,x^6 - 2*x^5 - 5*x^4 + 9*x^3 + 5*x^2 - 6*x - 1,3,x^6 - 3*x^5 - 9*x^4 + 26*x^3 + 16*x^2 - 48*x + 16,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,7,x^6 - 15*x^4 - 2*x^3 + 52*x^2 + 8*x - 16,11,x^6 - 4*x^5 - 27*x^4 + 108*x^3 + 9*x^2 - 256*x + 92,13,x^6 - 7*x^5 - 4*x^4 + 29*x^3 - 4*x^2 - 7*x - 1[] 415,4,2,x^7 + 3*x^6 - 6*x^5 - 19*x^4 + 9*x^3 + 28*x^2 - 4*x - 8,3,x^7 + 5*x^6 + x^5 - 21*x^4 - 10*x^3 + 23*x^2 - 2*x - 1,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 6*x^6 + x^5 - 41*x^4 - 51*x^3 + 10*x^2 + 9*x + 1,11,x^7 + 2*x^6 - 48*x^5 - 83*x^4 + 617*x^3 + 907*x^2 - 1276*x - 508,13,x^7 + 5*x^6 - 39*x^5 - 156*x^4 + 308*x^3 + 656*x^2 - 832*x - 256[] 415,5,2,x^11 - 20*x^9 - x^8 + 146*x^7 + 15*x^6 - 464*x^5 - 76*x^4 + 567*x^3 + 136*x^2 - 100*x - 8,3,x^11 - 27*x^9 + 4*x^8 + 258*x^7 - 71*x^6 - 1041*x^5 + 362*x^4 + 1712*x^3 - 448*x^2 - 1008*x + 64,5,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,7,x^11 + 3*x^10 - 50*x^9 - 97*x^8 + 968*x^7 + 664*x^6 - 8499*x^5 + 3974*x^4 + 25460*x^3 - 34872*x^2 + 10640*x + 1024,11,x^11 + x^10 - 76*x^9 - 49*x^8 + 1991*x^7 + 67*x^6 - 21282*x^5 + 19366*x^4 + 75983*x^3 - 162888*x^2 + 113756*x - 26896,13,x^11 - x^10 - 88*x^9 + 43*x^8 + 2724*x^7 + 615*x^6 - 36217*x^5 - 34976*x^4 + 170244*x^3 + 283536*x^2 + 56960*x - 23296[] Total time: 19.989 seconds, Total memory usage: 6.11MB ************** MAGMA ***************** Host AAnnecy-103-1-7-127.w80-15.abo.wanadoo.fr. (80.15.12.127) Time: Sun Nov 30 03:18:04 2003 Input: 123*3456 Output: Magma V2.10-6 Sun Nov 30 2003 03:18:00 on modular [Seed = 1704197513] ------------------------------------- 425088 Total time: 3.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:20:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [415..419] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 03:19:56 on modular [Seed = 283543400] ------------------------------------- 415,1,2,$.1 - 1,3,$.1 - 3,5,$.1 - 1,7,$.1 - 1,11,$.1 - 3,13,$.1 + 6[] 415,2,2,$.1^2 + $.1 - 1,3,$.1^2 + $.1 - 1,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 5,11,$.1^2 + 4*$.1 + 4,13,$.1^2 + 3*$.1 + 1[] 415,3,2,$.1^6 - 2*$.1^5 - 5*$.1^4 + 9*$.1^3 + 5*$.1^2 - 6*$.1 - 1,3,$.1^6 - 3*$.1^5 - 9*$.1^4 + 26*$.1^3 + 16*$.1^2 - 48*$.1 + 16,5,$.1^6 + 6*$.1^5 + 15*$.1^4 + 20*$.1^3 + 15*$.1^2 + 6*$.1 + 1,7,$.1^6 - 15*$.1^4 - 2*$.1^3 + 52*$.1^2 + 8*$.1 - 16,11,$.1^6 - 4*$.1^5 - 27*$.1^4 + 108*$.1^3 + 9*$.1^2 - 256*$.1 + 92,13,$.1^6 - 7*$.1^5 - 4*$.1^4 + 29*$.1^3 - 4*$.1^2 - 7*$.1 - 1[] 415,4,2,$.1^7 + 3*$.1^6 - 6*$.1^5 - 19*$.1^4 + 9*$.1^3 + 28*$.1^2 - 4*$.1 - 8,3,$.1^7 + 5*$.1^6 + $.1^5 - 21*$.1^4 - 10*$.1^3 + 23*$.1^2 - 2*$.1 - 1,5,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,7,$.1^7 + 6*$.1^6 + $.1^5 - 41*$.1^4 - 51*$.1^3 + 10*$.1^2 + 9*$.1 + 1,11,$.1^7 + 2*$.1^6 - 48*$.1^5 - 83*$.1^4 + 617*$.1^3 + 907*$.1^2 - 1276*$.1 - 508,13,$.1^7 + 5*$.1^6 - 39*$.1^5 - 156*$.1^4 + 308*$.1^3 + 656*$.1^2 - 832*$.1 - 256[] 415,5,2,$.1^11 - 20*$.1^9 - $.1^8 + 146*$.1^7 + 15*$.1^6 - 464*$.1^5 - 76*$.1^4 + 567*$.1^3 + 136*$.1^2 - 100*$.1 - 8,3,$.1^11 - 27*$.1^9 + 4*$.1^8 + 258*$.1^7 - 71*$.1^6 - 1041*$.1^5 + 362*$.1^4 + 1712*$.1^3 - 448*$.1^2 - 1008*$.1 + 64,5,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 + 330*$.1^7 - 462*$.1^6 + 462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1,7,$.1^11 + 3*$.1^10 - 50*$.1^9 - 97*$.1^8 + 968*$.1^7 + 664*$.1^6 - 8499*$.1^5 + 3974*$.1^4 + 25460*$.1^3 - 34872*$.1^2 + 10640*$.1 + 1024,11,$.1^11 + $.1^10 - 76*$.1^9 - 49*$.1^8 + 1991*$.1^7 + 67*$.1^6 - 21282*$.1^5 + 19366*$.1^4 + 75983*$.1^3 - 162888*$.1^2 + 113756*$.1 - 26896,13,$.1^11 - $.1^10 - 88*$.1^9 + 43*$.1^8 + 2724*$.1^7 + 615*$.1^6 - 36217*$.1^5 - 34976*$.1^4 + 170244*$.1^3 + 283536*$.1^2 + 56960*$.1 - 23296[] 416,1,2,x,3,x - 1,5,x - 1,7,x - 3,11,x - 2,13,x - 1[] 416,2,2,x,3,x + 1,5,x - 1,7,x + 3,11,x + 2,13,x - 1[] 416,3,2,x^2,3,x^2 + x - 4,5,x^2 + 3*x - 2,7,x^2 + 3*x - 2,11,x^2 + 4*x + 4,13,x^2 + 2*x + 1[] 416,4,2,x^2,3,x^2 - 5,5,x^2 - 6*x + 9,7,x^2 - 5,11,x^2 - 20,13,x^2 + 2*x + 1[] 416,5,2,x^2,3,x^2 - x - 4,5,x^2 + 3*x - 2,7,x^2 - 3*x - 2,11,x^2 - 4*x + 4,13,x^2 + 2*x + 1[] 416,6,2,x^4,3,x^4 - 13*x^2 + 32,5,x^4 + 2*x^3 - 19*x^2 - 20*x + 100,7,x^4 - 29*x^2 + 200,11,x^4 - 28*x^2 + 32,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 417,1,2,x - 1,3,x + 1,5,x - 2,7,x,11,x - 5,13,x - 5[] 417,2,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 7*x + 11,11,x^2 - 5,13,x^2 + 6*x + 4[] 417,3,2,x^3 - 4*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 - 5*x^2 + 3*x + 8,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 5*x^2 + 2*x - 4[] 417,4,2,x^3 - 4*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 - 7*x + 26,7,x^3 - 5*x^2 + 3*x + 8,11,x^3 - 4*x^2 - x + 8,13,x^3 - 4*x^2 - 16*x + 56[] 417,5,2,x^7 + 3*x^6 - 6*x^5 - 19*x^4 + 9*x^3 + 30*x^2 - 8,3,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,5,x^7 + 4*x^6 - 13*x^5 - 55*x^4 + 45*x^3 + 208*x^2 - 9*x - 149,7,x^7 + 9*x^6 + 9*x^5 - 109*x^4 - 276*x^3 + 5*x^2 + 300*x + 125,11,x^7 + 4*x^6 - 45*x^5 - 207*x^4 + 347*x^3 + 2494*x^2 + 2881*x + 829,13,x^7 + 4*x^6 - 62*x^5 - 251*x^4 + 905*x^3 + 3849*x^2 + 350*x - 3868[] 417,6,2,x^7 - 14*x^5 + 2*x^4 + 57*x^3 - 14*x^2 - 56*x + 8,3,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,5,x^7 + 4*x^6 - 8*x^5 - 31*x^4 + 5*x^3 + 41*x^2 + 24*x + 4,7,x^7 - 6*x^6 - 24*x^5 + 165*x^4 + 121*x^3 - 1193*x^2 + 280*x + 784,11,x^7 + 4*x^6 - 41*x^5 - 135*x^4 + 555*x^3 + 1390*x^2 - 2275*x - 4907,13,x^7 - 4*x^6 - 41*x^5 + 147*x^4 + 219*x^3 - 466*x^2 - 475*x + 107[] 418,1,2,x - 1,3,x + 1,5,x + 2,7,x + 3,11,x + 1,13,x - 1[] 418,2,2,x - 1,3,x,5,x - 2,7,x - 2,11,x - 1,13,x + 2[] 418,3,2,x - 1,3,x - 3,5,x + 2,7,x - 1,11,x - 1,13,x + 7[] 418,4,2,x^2 + 2*x + 1,3,x^2 - x - 4,5,x^2 - 4*x + 4,7,x^2 - 3*x - 2,11,x^2 - 2*x + 1,13,x^2 + 3*x - 2[] 418,5,2,x^2 + 2*x + 1,3,x^2 + 3*x - 1,5,x^2 + x - 3,7,x^2 + x - 3,11,x^2 - 2*x + 1,13,x^2 + 3*x - 1[] 418,6,2,x^2 - 2*x + 1,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 + 5*x + 1,11,x^2 - 2*x + 1,13,x^2 - 7*x + 7[] 418,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 6*x - 3,5,x^3 + 3*x^2 - 9*x - 18,7,x^3 + 6*x^2 - 6*x - 57,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 18*x - 29[] 418,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 5*x + 4,5,x^3 - 5*x^2 + 3*x + 2,7,x^3 - x^2 - 7*x - 4,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 5*x^2 + x + 14[] 419,1,2,x^9 + 2*x^8 - 7*x^7 - 13*x^6 + 15*x^5 + 25*x^4 - 9*x^3 - 15*x^2 - x + 1,3,x^9 + 4*x^8 - 4*x^7 - 28*x^6 - 9*x^5 + 47*x^4 + 29*x^3 - 15*x^2 - 9*x + 1,5,x^9 + 5*x^8 - 4*x^7 - 35*x^6 + 2*x^5 + 54*x^4 - 8*x^3 - 17*x^2 + 1,7,x^9 + 7*x^8 - 101*x^6 - 215*x^5 + 118*x^4 + 666*x^3 + 271*x^2 - 483*x - 307,11,x^9 + 6*x^8 - 3*x^7 - 60*x^6 - 50*x^5 + 144*x^4 + 200*x^3 + 28*x^2 - 8*x - 1,13,x^9 + 19*x^8 + 135*x^7 + 408*x^6 + 214*x^5 - 1651*x^4 - 3652*x^3 - 1917*x^2 + 1271*x + 1093[] 419,2,2,x^26 - 2*x^25 - 43*x^24 + 85*x^23 + 807*x^22 - 1571*x^21 - 8689*x^20 + 16575*x^19 + 59362*x^18 - 110217*x^17 - 268789*x^16 + 481513*x^15 + 817911*x^14 - 1398615*x^13 - 1658267*x^12 + 2674771*x^11 + 2166607*x^10 - 3262315*x^9 - 1701132*x^8 + 2384864*x^7 + 697992*x^6 - 932912*x^5 - 104448*x^4 + 158080*x^3 - 4736*x^2 - 6656*x + 512,3,x^26 - 2*x^25 - 56*x^24 + 112*x^23 + 1360*x^22 - 2697*x^21 - 18861*x^20 + 36655*x^19 + 165783*x^18 - 310509*x^17 - 970565*x^16 + 1709870*x^15 + 3873246*x^14 - 6194080*x^13 - 10579146*x^12 + 14580799*x^11 + 19436188*x^10 - 21403195*x^9 - 22833853*x^8 + 17959682*x^7 + 15322485*x^6 - 7282611*x^5 - 4620027*x^4 + 1147264*x^3 + 536568*x^2 - 50646*x - 19573,5,x^26 - 5*x^25 - 76*x^24 + 408*x^23 + 2350*x^22 - 14020*x^21 - 37353*x^20 + 263933*x^19 + 308436*x^18 - 2970100*x^17 - 978578*x^16 + 20527286*x^15 - 3301588*x^14 - 86879933*x^13 + 37204504*x^12 + 221113241*x^11 - 119074256*x^10 - 327914224*x^9 + 180330624*x^8 + 261570439*x^7 - 138751056*x^6 - 93983582*x^5 + 50686447*x^4 + 7883301*x^3 - 6367075*x^2 + 703704*x + 3636,7,x^26 - 7*x^25 - 94*x^24 + 755*x^23 + 3376*x^22 - 34335*x^21 - 50704*x^20 + 855286*x^19 - 38855*x^18 - 12649727*x^17 + 12756501*x^16 + 111894539*x^15 - 196143244*x^14 - 557701291*x^13 + 1414715108*x^12 + 1277746296*x^11 - 5200868214*x^10 - 218735889*x^9 + 9073283331*x^8 - 2545605634*x^7 - 7481074932*x^6 + 2325109394*x^5 + 2658406017*x^4 - 250096947*x^3 - 240212414*x^2 + 7413162*x + 6287437,11,x^26 - 4*x^25 - 177*x^24 + 656*x^23 + 13862*x^22 - 46540*x^21 - 636334*x^20 + 1880028*x^19 + 19069370*x^18 - 47726569*x^17 - 392271834*x^16 + 789666148*x^15 + 5655617024*x^14 - 8493715936*x^13 - 57153539904*x^12 + 56629921664*x^11 + 396922638976*x^10 - 200663798272*x^9 - 1812408616960*x^8 + 132693870592*x^7 + 5016124092416*x^6 + 1392906018816*x^5 - 7264942759936*x^4 - 3756369494016*x^3 + 4146471239680*x^2 + 2654302830592*x - 147968098304,13,x^26 - 27*x^25 + 163*x^24 + 1928*x^23 - 27449*x^22 + 23700*x^21 + 1267187*x^20 - 5766791*x^19 - 21347328*x^18 + 211203676*x^17 - 82055796*x^16 - 3557303755*x^15 + 8511540838*x^14 + 27889892344*x^13 - 134521938974*x^12 - 27055321906*x^11 + 981401106854*x^10 - 1155399404446*x^9 - 3089614789233*x^8 + 7805633569236*x^7 + 101494956628*x^6 - 16093016897986*x^5 + 15461823929882*x^4 - 1041139154045*x^3 - 3230579452834*x^2 + 384994835418*x + 100306912571[] Total time: 16.789 seconds, Total memory usage: 5.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:29:33 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [419..425] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 03:29:10 on modular [Seed = 167746571] ------------------------------------- 419,1,2,$.1^9 + 2*$.1^8 - 7*$.1^7 - 13*$.1^6 + 15*$.1^5 + 25*$.1^4 - 9*$.1^3 - 15*$.1^2 - $.1 + 1,3,$.1^9 + 4*$.1^8 - 4*$.1^7 - 28*$.1^6 - 9*$.1^5 + 47*$.1^4 + 29*$.1^3 - 15*$.1^2 - 9*$.1 + 1,5,$.1^9 + 5*$.1^8 - 4*$.1^7 - 35*$.1^6 + 2*$.1^5 + 54*$.1^4 - 8*$.1^3 - 17*$.1^2 + 1,7,$.1^9 + 7*$.1^8 - 101*$.1^6 - 215*$.1^5 + 118*$.1^4 + 666*$.1^3 + 271*$.1^2 - 483*$.1 - 307,11,$.1^9 + 6*$.1^8 - 3*$.1^7 - 60*$.1^6 - 50*$.1^5 + 144*$.1^4 + 200*$.1^3 + 28*$.1^2 - 8*$.1 - 1,13,$.1^9 + 19*$.1^8 + 135*$.1^7 + 408*$.1^6 + 214*$.1^5 - 1651*$.1^4 - 3652*$.1^3 - 1917*$.1^2 + 1271*$.1 + 1093[] 419,2,2,$.1^26 - 2*$.1^25 - 43*$.1^24 + 85*$.1^23 + 807*$.1^22 - 1571*$.1^21 - 8689*$.1^20 + 16575*$.1^19 + 59362*$.1^18 - 110217*$.1^17 - 268789*$.1^16 + 481513*$.1^15 + 817911*$.1^14 - 1398615*$.1^13 - 1658267*$.1^12 + 2674771*$.1^11 + 2166607*$.1^10 - 3262315*$.1^9 - 1701132*$.1^8 + 2384864*$.1^7 + 697992*$.1^6 - 932912*$.1^5 - 104448*$.1^4 + 158080*$.1^3 - 4736*$.1^2 - 6656*$.1 + 512,3,$.1^26 - 2*$.1^25 - 56*$.1^24 + 112*$.1^23 + 1360*$.1^22 - 2697*$.1^21 - 18861*$.1^20 + 36655*$.1^19 + 165783*$.1^18 - 310509*$.1^17 - 970565*$.1^16 + 1709870*$.1^15 + 3873246*$.1^14 - 6194080*$.1^13 - 10579146*$.1^12 + 14580799*$.1^11 + 19436188*$.1^10 - 21403195*$.1^9 - 22833853*$.1^8 + 17959682*$.1^7 + 15322485*$.1^6 - 7282611*$.1^5 - 4620027*$.1^4 + 1147264*$.1^3 + 536568*$.1^2 - 50646*$.1 - 19573,5,$.1^26 - 5*$.1^25 - 76*$.1^24 + 408*$.1^23 + 2350*$.1^22 - 14020*$.1^21 - 37353*$.1^20 + 263933*$.1^19 + 308436*$.1^18 - 2970100*$.1^17 - 978578*$.1^16 + 20527286*$.1^15 - 3301588*$.1^14 - 86879933*$.1^13 + 37204504*$.1^12 + 221113241*$.1^11 - 119074256*$.1^10 - 327914224*$.1^9 + 180330624*$.1^8 + 261570439*$.1^7 - 138751056*$.1^6 - 93983582*$.1^5 + 50686447*$.1^4 + 7883301*$.1^3 - 6367075*$.1^2 + 703704*$.1 + 3636,7,$.1^26 - 7*$.1^25 - 94*$.1^24 + 755*$.1^23 + 3376*$.1^22 - 34335*$.1^21 - 50704*$.1^20 + 855286*$.1^19 - 38855*$.1^18 - 12649727*$.1^17 + 12756501*$.1^16 + 111894539*$.1^15 - 196143244*$.1^14 - 557701291*$.1^13 + 1414715108*$.1^12 + 1277746296*$.1^11 - 5200868214*$.1^10 - 218735889*$.1^9 + 9073283331*$.1^8 - 2545605634*$.1^7 - 7481074932*$.1^6 + 2325109394*$.1^5 + 2658406017*$.1^4 - 250096947*$.1^3 - 240212414*$.1^2 + 7413162*$.1 + 6287437,11,$.1^26 - 4*$.1^25 - 177*$.1^24 + 656*$.1^23 + 13862*$.1^22 - 46540*$.1^21 - 636334*$.1^20 + 1880028*$.1^19 + 19069370*$.1^18 - 47726569*$.1^17 - 392271834*$.1^16 + 789666148*$.1^15 + 5655617024*$.1^14 - 8493715936*$.1^13 - 57153539904*$.1^12 + 56629921664*$.1^11 + 396922638976*$.1^10 - 200663798272*$.1^9 - 1812408616960*$.1^8 + 132693870592*$.1^7 + 5016124092416*$.1^6 + 1392906018816*$.1^5 - 7264942759936*$.1^4 - 3756369494016*$.1^3 + 4146471239680*$.1^2 + 2654302830592*$.1 - 147968098304,13,$.1^26 - 27*$.1^25 + 163*$.1^24 + 1928*$.1^23 - 27449*$.1^22 + 23700*$.1^21 + 1267187*$.1^20 - 5766791*$.1^19 - 21347328*$.1^18 + 211203676*$.1^17 - 82055796*$.1^16 - 3557303755*$.1^15 + 8511540838*$.1^14 + 27889892344*$.1^13 - 134521938974*$.1^12 - 27055321906*$.1^11 + 981401106854*$.1^10 - 1155399404446*$.1^9 - 3089614789233*$.1^8 + 7805633569236*$.1^7 + 101494956628*$.1^6 - 16093016897986*$.1^5 + 15461823929882*$.1^4 - 1041139154045*$.1^3 - 3230579452834*$.1^2 + 384994835418*$.1 + 100306912571[] 420,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 2,13,x - 4[] 420,2,2,x,3,x + 1,5,x - 1,7,x - 1,11,x + 2,13,x - 4[] 420,3,2,x,3,x - 1,5,x + 1,7,x - 1,11,x - 6,13,x + 4[] 420,4,2,x,3,x - 1,5,x - 1,7,x + 1,11,x - 2,13,x - 4[] 421,1,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 74*x^11 + 296*x^10 + 488*x^9 - 494*x^8 - 1157*x^7 + 205*x^6 + 1137*x^5 + 203*x^4 - 374*x^3 - 127*x^2 + 3*x + 3,3,x^15 + 9*x^14 + 14*x^13 - 91*x^12 - 305*x^11 + 132*x^10 + 1479*x^9 + 921*x^8 - 2331*x^7 - 2352*x^6 + 977*x^5 + 898*x^4 - 420*x^3 + 17*x^2 + 11*x - 1,5,x^15 + 11*x^14 + 16*x^13 - 230*x^12 - 930*x^11 + 436*x^10 + 7576*x^9 + 7865*x^8 - 19233*x^7 - 37504*x^6 + 6032*x^5 + 47371*x^4 + 18885*x^3 - 11778*x^2 - 5830*x + 349,7,x^15 + 5*x^14 - 50*x^13 - 242*x^12 + 936*x^11 + 4262*x^10 - 8233*x^9 - 33810*x^8 + 36283*x^7 + 126356*x^6 - 89105*x^5 - 218711*x^4 + 124893*x^3 + 148397*x^2 - 75624*x - 13779,11,x^15 + 33*x^14 + 439*x^13 + 2752*x^12 + 4484*x^11 - 47895*x^10 - 329709*x^9 - 710805*x^8 + 700910*x^7 + 6176673*x^6 + 8607514*x^5 - 6970844*x^4 - 27108950*x^3 - 13911998*x^2 + 13470597*x + 10339781,13,x^15 + 8*x^14 - 74*x^13 - 663*x^12 + 1843*x^11 + 19456*x^10 - 24399*x^9 - 279096*x^8 + 231495*x^7 + 2108724*x^6 - 1675809*x^5 - 7940159*x^4 + 7233336*x^3 + 11299279*x^2 - 12659976*x + 1817397[] 421,2,2,x^19 - 4*x^18 - 20*x^17 + 93*x^16 + 145*x^15 - 874*x^14 - 402*x^13 + 4263*x^12 - 159*x^11 - 11551*x^10 + 3133*x^9 + 17375*x^8 - 5935*x^7 - 14018*x^6 + 4016*x^5 + 5896*x^4 - 1088*x^3 - 1185*x^2 + 101*x + 89,3,x^19 - 7*x^18 - 14*x^17 + 193*x^16 - 93*x^15 - 2088*x^14 + 2959*x^13 + 11085*x^12 - 23111*x^11 - 28776*x^10 + 86085*x^9 + 26346*x^8 - 164972*x^7 + 24505*x^6 + 152723*x^5 - 58753*x^4 - 51424*x^3 + 25848*x^2 - 1440*x - 64,5,x^19 - 7*x^18 - 27*x^17 + 273*x^16 + 101*x^15 - 4023*x^14 + 3046*x^13 + 28479*x^12 - 37573*x^11 - 101239*x^10 + 172591*x^9 + 170130*x^8 - 365278*x^7 - 99967*x^6 + 341999*x^5 - 20468*x^4 - 116495*x^3 + 26317*x^2 + 6952*x - 1367,7,x^19 - 3*x^18 - 66*x^17 + 238*x^16 + 1480*x^15 - 6706*x^14 - 10957*x^13 + 79510*x^12 - 24177*x^11 - 352324*x^10 + 430239*x^9 + 415669*x^8 - 872771*x^7 - 38067*x^6 + 613432*x^5 - 128311*x^4 - 154668*x^3 + 42700*x^2 + 12144*x - 3632,11,x^19 - 31*x^18 + 367*x^17 - 1800*x^16 - 484*x^15 + 43833*x^14 - 166849*x^13 + 49087*x^12 + 1209170*x^11 - 3296987*x^10 + 2907210*x^9 + 1405296*x^8 - 4451506*x^7 + 2474298*x^6 + 577657*x^5 - 1121663*x^4 + 425536*x^3 - 53776*x^2 - 976*x + 368,13,x^19 + 2*x^18 - 116*x^17 - 333*x^16 + 4635*x^15 + 18244*x^14 - 69879*x^13 - 402476*x^12 + 153875*x^11 + 3524646*x^10 + 3806553*x^9 - 10139483*x^8 - 20373936*x^7 + 6415283*x^6 + 34491570*x^5 + 8830049*x^4 - 21836432*x^3 - 9430500*x^2 + 3945040*x + 1163344[] Errors: /home/mfd/gomagma: line 2: 27485 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:30:32 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [419..421] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 03:30:11 on modular [Seed = 986492925] ------------------------------------- 419,1,2,$.1^9 + 2*$.1^8 - 7*$.1^7 - 13*$.1^6 + 15*$.1^5 + 25*$.1^4 - 9*$.1^3 - 15*$.1^2 - $.1 + 1,3,$.1^9 + 4*$.1^8 - 4*$.1^7 - 28*$.1^6 - 9*$.1^5 + 47*$.1^4 + 29*$.1^3 - 15*$.1^2 - 9*$.1 + 1,5,$.1^9 + 5*$.1^8 - 4*$.1^7 - 35*$.1^6 + 2*$.1^5 + 54*$.1^4 - 8*$.1^3 - 17*$.1^2 + 1,7,$.1^9 + 7*$.1^8 - 101*$.1^6 - 215*$.1^5 + 118*$.1^4 + 666*$.1^3 + 271*$.1^2 - 483*$.1 - 307,11,$.1^9 + 6*$.1^8 - 3*$.1^7 - 60*$.1^6 - 50*$.1^5 + 144*$.1^4 + 200*$.1^3 + 28*$.1^2 - 8*$.1 - 1,13,$.1^9 + 19*$.1^8 + 135*$.1^7 + 408*$.1^6 + 214*$.1^5 - 1651*$.1^4 - 3652*$.1^3 - 1917*$.1^2 + 1271*$.1 + 1093[] 419,2,2,$.1^26 - 2*$.1^25 - 43*$.1^24 + 85*$.1^23 + 807*$.1^22 - 1571*$.1^21 - 8689*$.1^20 + 16575*$.1^19 + 59362*$.1^18 - 110217*$.1^17 - 268789*$.1^16 + 481513*$.1^15 + 817911*$.1^14 - 1398615*$.1^13 - 1658267*$.1^12 + 2674771*$.1^11 + 2166607*$.1^10 - 3262315*$.1^9 - 1701132*$.1^8 + 2384864*$.1^7 + 697992*$.1^6 - 932912*$.1^5 - 104448*$.1^4 + 158080*$.1^3 - 4736*$.1^2 - 6656*$.1 + 512,3,$.1^26 - 2*$.1^25 - 56*$.1^24 + 112*$.1^23 + 1360*$.1^22 - 2697*$.1^21 - 18861*$.1^20 + 36655*$.1^19 + 165783*$.1^18 - 310509*$.1^17 - 970565*$.1^16 + 1709870*$.1^15 + 3873246*$.1^14 - 6194080*$.1^13 - 10579146*$.1^12 + 14580799*$.1^11 + 19436188*$.1^10 - 21403195*$.1^9 - 22833853*$.1^8 + 17959682*$.1^7 + 15322485*$.1^6 - 7282611*$.1^5 - 4620027*$.1^4 + 1147264*$.1^3 + 536568*$.1^2 - 50646*$.1 - 19573,5,$.1^26 - 5*$.1^25 - 76*$.1^24 + 408*$.1^23 + 2350*$.1^22 - 14020*$.1^21 - 37353*$.1^20 + 263933*$.1^19 + 308436*$.1^18 - 2970100*$.1^17 - 978578*$.1^16 + 20527286*$.1^15 - 3301588*$.1^14 - 86879933*$.1^13 + 37204504*$.1^12 + 221113241*$.1^11 - 119074256*$.1^10 - 327914224*$.1^9 + 180330624*$.1^8 + 261570439*$.1^7 - 138751056*$.1^6 - 93983582*$.1^5 + 50686447*$.1^4 + 7883301*$.1^3 - 6367075*$.1^2 + 703704*$.1 + 3636,7,$.1^26 - 7*$.1^25 - 94*$.1^24 + 755*$.1^23 + 3376*$.1^22 - 34335*$.1^21 - 50704*$.1^20 + 855286*$.1^19 - 38855*$.1^18 - 12649727*$.1^17 + 12756501*$.1^16 + 111894539*$.1^15 - 196143244*$.1^14 - 557701291*$.1^13 + 1414715108*$.1^12 + 1277746296*$.1^11 - 5200868214*$.1^10 - 218735889*$.1^9 + 9073283331*$.1^8 - 2545605634*$.1^7 - 7481074932*$.1^6 + 2325109394*$.1^5 + 2658406017*$.1^4 - 250096947*$.1^3 - 240212414*$.1^2 + 7413162*$.1 + 6287437,11,$.1^26 - 4*$.1^25 - 177*$.1^24 + 656*$.1^23 + 13862*$.1^22 - 46540*$.1^21 - 636334*$.1^20 + 1880028*$.1^19 + 19069370*$.1^18 - 47726569*$.1^17 - 392271834*$.1^16 + 789666148*$.1^15 + 5655617024*$.1^14 - 8493715936*$.1^13 - 57153539904*$.1^12 + 56629921664*$.1^11 + 396922638976*$.1^10 - 200663798272*$.1^9 - 1812408616960*$.1^8 + 132693870592*$.1^7 + 5016124092416*$.1^6 + 1392906018816*$.1^5 - 7264942759936*$.1^4 - 3756369494016*$.1^3 + 4146471239680*$.1^2 + 2654302830592*$.1 - 147968098304,13,$.1^26 - 27*$.1^25 + 163*$.1^24 + 1928*$.1^23 - 27449*$.1^22 + 23700*$.1^21 + 1267187*$.1^20 - 5766791*$.1^19 - 21347328*$.1^18 + 211203676*$.1^17 - 82055796*$.1^16 - 3557303755*$.1^15 + 8511540838*$.1^14 + 27889892344*$.1^13 - 134521938974*$.1^12 - 27055321906*$.1^11 + 981401106854*$.1^10 - 1155399404446*$.1^9 - 3089614789233*$.1^8 + 7805633569236*$.1^7 + 101494956628*$.1^6 - 16093016897986*$.1^5 + 15461823929882*$.1^4 - 1041139154045*$.1^3 - 3230579452834*$.1^2 + 384994835418*$.1 + 100306912571[] 420,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 2,13,x - 4[] 420,2,2,x,3,x + 1,5,x - 1,7,x - 1,11,x + 2,13,x - 4[] 420,3,2,x,3,x - 1,5,x + 1,7,x - 1,11,x - 6,13,x + 4[] 420,4,2,x,3,x - 1,5,x - 1,7,x + 1,11,x - 2,13,x - 4[] 421,1,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 74*x^11 + 296*x^10 + 488*x^9 - 494*x^8 - 1157*x^7 + 205*x^6 + 1137*x^5 + 203*x^4 - 374*x^3 - 127*x^2 + 3*x + 3,3,x^15 + 9*x^14 + 14*x^13 - 91*x^12 - 305*x^11 + 132*x^10 + 1479*x^9 + 921*x^8 - 2331*x^7 - 2352*x^6 + 977*x^5 + 898*x^4 - 420*x^3 + 17*x^2 + 11*x - 1,5,x^15 + 11*x^14 + 16*x^13 - 230*x^12 - 930*x^11 + 436*x^10 + 7576*x^9 + 7865*x^8 - 19233*x^7 - 37504*x^6 + 6032*x^5 + 47371*x^4 + 18885*x^3 - 11778*x^2 - 5830*x + 349,7,x^15 + 5*x^14 - 50*x^13 - 242*x^12 + 936*x^11 + 4262*x^10 - 8233*x^9 - 33810*x^8 + 36283*x^7 + 126356*x^6 - 89105*x^5 - 218711*x^4 + 124893*x^3 + 148397*x^2 - 75624*x - 13779,11,x^15 + 33*x^14 + 439*x^13 + 2752*x^12 + 4484*x^11 - 47895*x^10 - 329709*x^9 - 710805*x^8 + 700910*x^7 + 6176673*x^6 + 8607514*x^5 - 6970844*x^4 - 27108950*x^3 - 13911998*x^2 + 13470597*x + 10339781,13,x^15 + 8*x^14 - 74*x^13 - 663*x^12 + 1843*x^11 + 19456*x^10 - 24399*x^9 - 279096*x^8 + 231495*x^7 + 2108724*x^6 - 1675809*x^5 - 7940159*x^4 + 7233336*x^3 + 11299279*x^2 - 12659976*x + 1817397[] 421,2,2,x^19 - 4*x^18 - 20*x^17 + 93*x^16 + 145*x^15 - 874*x^14 - 402*x^13 + 4263*x^12 - 159*x^11 - 11551*x^10 + 3133*x^9 + 17375*x^8 - 5935*x^7 - 14018*x^6 + 4016*x^5 + 5896*x^4 - 1088*x^3 - 1185*x^2 + 101*x + 89,3,x^19 - 7*x^18 - 14*x^17 + 193*x^16 - 93*x^15 - 2088*x^14 + 2959*x^13 + 11085*x^12 - 23111*x^11 - 28776*x^10 + 86085*x^9 + 26346*x^8 - 164972*x^7 + 24505*x^6 + 152723*x^5 - 58753*x^4 - 51424*x^3 + 25848*x^2 - 1440*x - 64,5,x^19 - 7*x^18 - 27*x^17 + 273*x^16 + 101*x^15 - 4023*x^14 + 3046*x^13 + 28479*x^12 - 37573*x^11 - 101239*x^10 + 172591*x^9 + 170130*x^8 - 365278*x^7 - 99967*x^6 + 341999*x^5 - 20468*x^4 - 116495*x^3 + 26317*x^2 + 6952*x - 1367,7,x^19 - 3*x^18 - 66*x^17 + 238*x^16 + 1480*x^15 - 6706*x^14 - 10957*x^13 + 79510*x^12 - 24177*x^11 - 352324*x^10 + 430239*x^9 + 415669*x^8 - 872771*x^7 - 38067*x^6 + 613432*x^5 - 128311*x^4 - 154668*x^3 + 42700*x^2 + 12144*x - 3632,11,x^19 - 31*x^18 + 367*x^17 - 1800*x^16 - 484*x^15 + 43833*x^14 - 166849*x^13 + 49087*x^12 + 1209170*x^11 - 3296987*x^10 + 2907210*x^9 + 1405296*x^8 - 4451506*x^7 + 2474298*x^6 + 577657*x^5 - 1121663*x^4 + 425536*x^3 - 53776*x^2 - 976*x + 368,13,x^19 + 2*x^18 - 116*x^17 - 333*x^16 + 4635*x^15 + 18244*x^14 - 69879*x^13 - 402476*x^12 + 153875*x^11 + 3524646*x^10 + 3806553*x^9 - 10139483*x^8 - 20373936*x^7 + 6415283*x^6 + 34491570*x^5 + 8830049*x^4 - 21836432*x^3 - 9430500*x^2 + 3945040*x + 1163344[] Total time: 19.100 seconds, Total memory usage: 6.25MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:36:08 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [421..425] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 03:35:49 on modular [Seed = 702528920] ------------------------------------- 421,1,2,$.1^15 + 6*$.1^14 - 2*$.1^13 - 71*$.1^12 - 74*$.1^11 + 296*$.1^10 + 488*$.1^9 - 494*$.1^8 - 1157*$.1^7 + 205*$.1^6 + 1137*$.1^5 + 203*$.1^4 - 374*$.1^3 - 127*$.1^2 + 3*$.1 + 3,3,$.1^15 + 9*$.1^14 + 14*$.1^13 - 91*$.1^12 - 305*$.1^11 + 132*$.1^10 + 1479*$.1^9 + 921*$.1^8 - 2331*$.1^7 - 2352*$.1^6 + 977*$.1^5 + 898*$.1^4 - 420*$.1^3 + 17*$.1^2 + 11*$.1 - 1,5,$.1^15 + 11*$.1^14 + 16*$.1^13 - 230*$.1^12 - 930*$.1^11 + 436*$.1^10 + 7576*$.1^9 + 7865*$.1^8 - 19233*$.1^7 - 37504*$.1^6 + 6032*$.1^5 + 47371*$.1^4 + 18885*$.1^3 - 11778*$.1^2 - 5830*$.1 + 349,7,$.1^15 + 5*$.1^14 - 50*$.1^13 - 242*$.1^12 + 936*$.1^11 + 4262*$.1^10 - 8233*$.1^9 - 33810*$.1^8 + 36283*$.1^7 + 126356*$.1^6 - 89105*$.1^5 - 218711*$.1^4 + 124893*$.1^3 + 148397*$.1^2 - 75624*$.1 - 13779,11,$.1^15 + 33*$.1^14 + 439*$.1^13 + 2752*$.1^12 + 4484*$.1^11 - 47895*$.1^10 - 329709*$.1^9 - 710805*$.1^8 + 700910*$.1^7 + 6176673*$.1^6 + 8607514*$.1^5 - 6970844*$.1^4 - 27108950*$.1^3 - 13911998*$.1^2 + 13470597*$.1 + 10339781,13,$.1^15 + 8*$.1^14 - 74*$.1^13 - 663*$.1^12 + 1843*$.1^11 + 19456*$.1^10 - 24399*$.1^9 - 279096*$.1^8 + 231495*$.1^7 + 2108724*$.1^6 - 1675809*$.1^5 - 7940159*$.1^4 + 7233336*$.1^3 + 11299279*$.1^2 - 12659976*$.1 + 1817397[] 421,2,2,$.1^19 - 4*$.1^18 - 20*$.1^17 + 93*$.1^16 + 145*$.1^15 - 874*$.1^14 - 402*$.1^13 + 4263*$.1^12 - 159*$.1^11 - 11551*$.1^10 + 3133*$.1^9 + 17375*$.1^8 - 5935*$.1^7 - 14018*$.1^6 + 4016*$.1^5 + 5896*$.1^4 - 1088*$.1^3 - 1185*$.1^2 + 101*$.1 + 89,3,$.1^19 - 7*$.1^18 - 14*$.1^17 + 193*$.1^16 - 93*$.1^15 - 2088*$.1^14 + 2959*$.1^13 + 11085*$.1^12 - 23111*$.1^11 - 28776*$.1^10 + 86085*$.1^9 + 26346*$.1^8 - 164972*$.1^7 + 24505*$.1^6 + 152723*$.1^5 - 58753*$.1^4 - 51424*$.1^3 + 25848*$.1^2 - 1440*$.1 - 64,5,$.1^19 - 7*$.1^18 - 27*$.1^17 + 273*$.1^16 + 101*$.1^15 - 4023*$.1^14 + 3046*$.1^13 + 28479*$.1^12 - 37573*$.1^11 - 101239*$.1^10 + 172591*$.1^9 + 170130*$.1^8 - 365278*$.1^7 - 99967*$.1^6 + 341999*$.1^5 - 20468*$.1^4 - 116495*$.1^3 + 26317*$.1^2 + 6952*$.1 - 1367,7,$.1^19 - 3*$.1^18 - 66*$.1^17 + 238*$.1^16 + 1480*$.1^15 - 6706*$.1^14 - 10957*$.1^13 + 79510*$.1^12 - 24177*$.1^11 - 352324*$.1^10 + 430239*$.1^9 + 415669*$.1^8 - 872771*$.1^7 - 38067*$.1^6 + 613432*$.1^5 - 128311*$.1^4 - 154668*$.1^3 + 42700*$.1^2 + 12144*$.1 - 3632,11,$.1^19 - 31*$.1^18 + 367*$.1^17 - 1800*$.1^16 - 484*$.1^15 + 43833*$.1^14 - 166849*$.1^13 + 49087*$.1^12 + 1209170*$.1^11 - 3296987*$.1^10 + 2907210*$.1^9 + 1405296*$.1^8 - 4451506*$.1^7 + 2474298*$.1^6 + 577657*$.1^5 - 1121663*$.1^4 + 425536*$.1^3 - 53776*$.1^2 - 976*$.1 + 368,13,$.1^19 + 2*$.1^18 - 116*$.1^17 - 333*$.1^16 + 4635*$.1^15 + 18244*$.1^14 - 69879*$.1^13 - 402476*$.1^12 + 153875*$.1^11 + 3524646*$.1^10 + 3806553*$.1^9 - 10139483*$.1^8 - 20373936*$.1^7 + 6415283*$.1^6 + 34491570*$.1^5 + 8830049*$.1^4 - 21836432*$.1^3 - 9430500*$.1^2 + 3945040*$.1 + 1163344[] 422,1,2,x + 1,3,x,5,x - 1,7,x + 2,11,x + 3,13,x + 7[] 422,2,2,x^2 + 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 8*x + 16,11,x^2 - 2*x - 4,13,x^2[] 422,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 8*x - 3,5,x^3 + 5*x^2 + 4*x - 1,7,x^3 + 5*x^2 - 9,11,x^3 - 9*x^2 + 22*x - 15,13,x^3 + 11*x^2 + 30*x - 1[] 422,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 6*x - 5,5,x^3 - x^2 - 10*x + 15,7,x^3 - x^2 - 6*x + 5,11,x^3 + 5*x^2 - 8*x - 3,13,x^3 - 11*x^2 + 34*x - 29[] 422,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 5*x^2 + 6*x + 1,5,x^3 + 3*x^2 - 4*x - 13,7,x^3 + 9*x^2 + 20*x - 1,11,x^3 + 5*x^2 - 8*x - 41,13,x^3 + 7*x^2 - 49[] 422,6,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 4*x^5 - 4*x^4 + 28*x^3 - 15*x^2 - 33*x + 28,5,x^6 + 2*x^5 - 11*x^4 - 9*x^3 + 35*x^2 + 6*x - 28,7,x^6 - 7*x^5 + 4*x^4 + 45*x^3 - 30*x^2 - 88*x - 32,11,x^6 - 4*x^5 - 25*x^4 + 103*x^3 + 11*x^2 - 182*x - 68,13,x^6 - 8*x^5 - 17*x^4 + 127*x^3 + 293*x^2 + 56*x - 64[] 423,1,2,x + 2,3,x,5,x + 3,7,x - 1,11,x - 3,13,x[] 423,2,2,x - 2,3,x,5,x - 3,7,x - 1,11,x + 3,13,x[] 423,3,2,x - 1,3,x,5,x,7,x - 4,11,x,13,x - 6[] 423,4,2,x - 2,3,x,5,x - 3,7,x + 3,11,x - 5,13,x - 2[] 423,5,2,x,3,x,5,x - 1,7,x + 3,11,x - 3,13,x + 4[] 423,6,2,x - 1,3,x,5,x + 2,7,x,11,x + 4,13,x + 2[] 423,7,2,x + 2,3,x,5,x - 1,7,x + 3,11,x + 1,13,x + 2[] 423,8,2,x^2 - x - 4,3,x^2,5,x^2 + x - 4,7,x^2 - x - 4,11,x^2 + 7*x + 8,13,x^2 + 6*x - 8[] 423,9,2,x^3 + 2*x^2 - 3*x - 2,3,x^3,5,x^3 + x^2 - 4*x - 2,7,x^3 + 3*x^2 - 4*x - 8,11,x^3 + 9*x^2 + 20*x + 8,13,x^3 + 4*x^2 - 12*x - 16[] 423,10,2,x^3 - 2*x^2 - 3*x + 2,3,x^3,5,x^3 - x^2 - 4*x + 2,7,x^3 + 3*x^2 - 4*x - 8,11,x^3 - 9*x^2 + 20*x - 8,13,x^3 + 4*x^2 - 12*x - 16[] 423,11,2,x^4 + x^3 - 5*x^2 - 5*x - 1,3,x^4,5,x^4 - 2*x^3 - 16*x^2 + 16*x + 48,7,x^4 - 4*x^3 - 7*x^2 + 44*x - 43,11,x^4 - 6*x^3 - 4*x^2 + 56*x - 48,13,x^4 - 8*x^3 + 56*x + 48[] 424,1,2,x^2,3,x^2 + 2*x - 1,5,x^2 + 4*x + 4,7,x^2 - 4*x - 4,11,x^2 + 4*x - 4,13,x^2 + 6*x + 1[] 424,2,2,x^3,3,x^3 - 2*x^2 - 3*x + 2,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 5*x^2 - 8*x + 44,13,x^3 + 6*x^2 + 5*x - 4[] 424,3,2,x^3,3,x^3 + x^2 - 3*x - 1,5,x^3 + 2*x^2 - 8*x + 4,7,x^3 + 8*x^2 + 16*x + 4,11,x^3 + 4*x^2 - 4*x - 20,13,x^3 + x^2 - 21*x - 13[] 424,4,2,x^5,3,x^5 - x^4 - 13*x^3 + 9*x^2 + 42*x - 16,5,x^5 - 5*x^4 - 8*x^3 + 56*x^2 + 4*x - 136,7,x^5 + 6*x^4 - 8*x^3 - 60*x^2 + 40*x + 64,11,x^5 - 5*x^4 - 8*x^3 + 32*x^2 + 52*x + 16,13,x^5 - 9*x^4 + 17*x^3 + 29*x^2 - 78*x + 8[] 425,1,2,x - 1,3,x,5,x,7,x + 4,11,x,13,x - 2[] 425,2,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 4,13,x - 1[] 425,3,2,x + 1,3,x + 2,5,x,7,x - 2,11,x - 2,13,x + 2[] 425,4,2,x - 1,3,x + 1,5,x,7,x - 1,11,x + 4,13,x + 1[] 425,5,2,x^2 - 3,3,x^2 + 2*x - 2,5,x^2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2 - 8*x + 16[] 425,6,2,x^2 - 2*x - 1,3,x^2 - 4*x + 2,5,x^2,7,x^2 - 4*x + 2,11,x^2 + 8*x + 14,13,x^2 - 8[] 425,7,2,x^4 - 2*x^3 - 4*x^2 + 8*x - 1,3,x^4 - 4*x^3 + 10*x - 2,5,x^4,7,x^4 - 10*x^3 + 32*x^2 - 38*x + 14,11,x^4 + 2*x^3 - 14*x^2 - 26*x + 2,13,x^4 - 6*x^3 - 28*x^2 + 192*x - 164[] 425,8,2,x^4 + 2*x^3 - 4*x^2 - 8*x - 1,3,x^4 + 4*x^3 - 10*x - 2,5,x^4,7,x^4 + 10*x^3 + 32*x^2 + 38*x + 14,11,x^4 + 2*x^3 - 14*x^2 - 26*x + 2,13,x^4 + 6*x^3 - 28*x^2 - 192*x - 164[] 425,9,2,x^5 + x^4 - 10*x^3 - 6*x^2 + 21*x - 3,3,x^5 - x^4 - 10*x^3 + 10*x^2 + 23*x - 25,5,x^5,7,x^5 - x^4 - 22*x^3 + 2*x^2 + 109*x + 97,11,x^5 - 4*x^4 - 22*x^3 + 120*x^2 - 156*x + 60,13,x^5 + 3*x^4 - 26*x^3 - 58*x^2 + 177*x + 227[] 425,10,2,x^5 - x^4 - 10*x^3 + 6*x^2 + 21*x + 3,3,x^5 + x^4 - 10*x^3 - 10*x^2 + 23*x + 25,5,x^5,7,x^5 + x^4 - 22*x^3 - 2*x^2 + 109*x - 97,11,x^5 - 4*x^4 - 22*x^3 + 120*x^2 - 156*x + 60,13,x^5 - 3*x^4 - 26*x^3 + 58*x^2 + 177*x - 227[] Total time: 17.309 seconds, Total memory usage: 5.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:11:26 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [425..430] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 04:10:39 on modular [Seed = 1904736817] ------------------------------------- 425,1,2,$.1 - 1,3,$.1,5,$.1,7,$.1 + 4,11,$.1,13,$.1 - 2[] 425,2,2,$.1 + 1,3,$.1 - 1,5,$.1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[] 425,3,2,$.1 + 1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1 - 2,13,$.1 + 2[] 425,4,2,$.1 - 1,3,$.1 + 1,5,$.1,7,$.1 - 1,11,$.1 + 4,13,$.1 + 1[] 425,5,2,$.1^2 - 3,3,$.1^2 + 2*$.1 - 2,5,$.1^2,7,$.1^2 - 2*$.1 - 2,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 8*$.1 + 16[] 425,6,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2,7,$.1^2 - 4*$.1 + 2,11,$.1^2 + 8*$.1 + 14,13,$.1^2 - 8[] 425,7,2,$.1^4 - 2*$.1^3 - 4*$.1^2 + 8*$.1 - 1,3,$.1^4 - 4*$.1^3 + 10*$.1 - 2,5,$.1^4,7,$.1^4 - 10*$.1^3 + 32*$.1^2 - 38*$.1 + 14,11,$.1^4 + 2*$.1^3 - 14*$.1^2 - 26*$.1 + 2,13,$.1^4 - 6*$.1^3 - 28*$.1^2 + 192*$.1 - 164[] 425,8,2,$.1^4 + 2*$.1^3 - 4*$.1^2 - 8*$.1 - 1,3,$.1^4 + 4*$.1^3 - 10*$.1 - 2,5,$.1^4,7,$.1^4 + 10*$.1^3 + 32*$.1^2 + 38*$.1 + 14,11,$.1^4 + 2*$.1^3 - 14*$.1^2 - 26*$.1 + 2,13,$.1^4 + 6*$.1^3 - 28*$.1^2 - 192*$.1 - 164[] 425,9,2,$.1^5 + $.1^4 - 10*$.1^3 - 6*$.1^2 + 21*$.1 - 3,3,$.1^5 - $.1^4 - 10*$.1^3 + 10*$.1^2 + 23*$.1 - 25,5,$.1^5,7,$.1^5 - $.1^4 - 22*$.1^3 + 2*$.1^2 + 109*$.1 + 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 + 3*$.1^4 - 26*$.1^3 - 58*$.1^2 + 177*$.1 + 227[] 425,10,2,$.1^5 - $.1^4 - 10*$.1^3 + 6*$.1^2 + 21*$.1 + 3,3,$.1^5 + $.1^4 - 10*$.1^3 - 10*$.1^2 + 23*$.1 + 25,5,$.1^5,7,$.1^5 + $.1^4 - 22*$.1^3 - 2*$.1^2 + 109*$.1 - 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 - 3*$.1^4 - 26*$.1^3 + 58*$.1^2 + 177*$.1 - 227[] 426,1,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x + 2,13,x[] 426,2,2,x + 1,3,x - 1,5,x - 3,7,x + 1,11,x - 3,13,x - 2[] 426,3,2,x - 1,3,x - 1,5,x - 1,7,x - 3,11,x + 3,13,x + 6[] 426,4,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 7,7,x^2 + 2*x - 17,11,x^2 - 10*x + 23,13,x^2 + 8*x + 8[] 426,5,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 - 5*x + 2,11,x^2 + x - 4,13,x^2 - 4*x + 4[] 426,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 3*x + 10,7,x^3 - 2*x^2 - 5*x + 8,11,x^3 - 2*x^2 - 29*x + 80,13,x^3 - 2*x^2 - 24*x - 16[] 426,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - x^2 - 12*x + 4,7,x^3 + x^2 - 12*x - 4,11,x^3 - 3*x^2 - 10*x + 28,13,x^3 - 8*x^2 + 56[] 427,1,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 5,13,x - 4[] 427,2,2,x,3,x - 2,5,x - 4,7,x - 1,11,x + 2,13,x - 2[] 427,3,2,x - 1,3,x - 1,5,x + 4,7,x - 1,11,x + 3,13,x + 4[] 427,4,2,x^6 + 5*x^5 + 2*x^4 - 18*x^3 - 12*x^2 + 18*x + 5,3,x^6 - 10*x^4 - 5*x^3 + 16*x^2 + 12*x + 1,5,x^6 + 5*x^5 - 3*x^4 - 36*x^3 - 19*x^2 + 32*x + 21,7,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 6*x^5 + 5*x^4 - 15*x^3 - 14*x^2 + x + 1,13,x^6 + 13*x^5 + 15*x^4 - 368*x^3 - 1050*x^2 + 2495*x + 8275[] 427,5,2,x^6 + 5*x^5 + 2*x^4 - 22*x^3 - 30*x^2 + 9,3,x^6 + 8*x^5 + 18*x^4 - 3*x^3 - 44*x^2 - 18*x + 17,5,x^6 + 9*x^5 + 21*x^4 - 10*x^3 - 57*x^2 + 9,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 43*x^4 + 7*x^3 + 534*x^2 - 141*x - 1635,13,x^6 + 5*x^5 - 13*x^4 + 8*x^2 - x - 1[] 427,6,2,x^7 - 4*x^6 - 3*x^5 + 26*x^4 - 12*x^3 - 38*x^2 + 23*x + 11,3,x^7 - x^6 - 12*x^5 + 9*x^4 + 37*x^3 - 18*x^2 - 19*x + 1,5,x^7 - 7*x^6 + 11*x^5 + 18*x^4 - 47*x^3 - 8*x^2 + 41*x + 4,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,11,x^7 - x^6 - 27*x^5 + 82*x^4 - 47*x^3 - 59*x^2 + 60*x - 13,13,x^7 - 5*x^6 - 49*x^5 + 258*x^4 + 284*x^3 - 2365*x^2 + 1135*x + 2792[] 427,7,2,x^9 - 5*x^8 - 3*x^7 + 45*x^6 - 32*x^5 - 108*x^4 + 123*x^3 + 30*x^2 - 43*x + 4,3,x^9 + x^8 - 18*x^7 - 13*x^6 + 105*x^5 + 42*x^4 - 205*x^3 - 9*x^2 + 50*x + 8,5,x^9 - 9*x^8 + 13*x^7 + 78*x^6 - 193*x^5 - 190*x^4 + 693*x^3 - 14*x^2 - 768*x + 384,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,11,x^9 - 3*x^8 - 39*x^7 + 88*x^6 + 261*x^5 - 779*x^4 + 470*x^3 + 65*x^2 - 62*x - 8,13,x^9 - 13*x^8 + 39*x^7 + 142*x^6 - 906*x^5 + 595*x^4 + 3819*x^3 - 6580*x^2 + 804*x + 2432[] 428,1,2,x,3,x - 1,5,x - 2,7,x - 4,11,x + 3,13,x - 5[] 428,2,2,x,3,x + 1,5,x - 2,7,x + 4,11,x + 5,13,x - 1[] 428,3,2,x^2,3,x^2 + 3*x - 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + 4*x + 4[] 428,4,2,x^5,3,x^5 - 5*x^4 - 2*x^3 + 32*x^2 - 10*x - 43,5,x^5 + x^4 - 21*x^3 - 12*x^2 + 108*x + 24,7,x^5 - 6*x^4 - x^3 + 34*x^2 - 40,11,x^5 - 6*x^4 + 33*x^2 - 3*x - 9,13,x^5 + 8*x^4 - 23*x^3 - 185*x^2 + 236*x + 436[] Errors: /home/mfd/gomagma: line 2: 28192 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:12:32 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [425..428] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 04:11:45 on modular [Seed = 2039476857] ------------------------------------- 425,1,2,$.1 - 1,3,$.1,5,$.1,7,$.1 + 4,11,$.1,13,$.1 - 2[] 425,2,2,$.1 + 1,3,$.1 - 1,5,$.1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[] 425,3,2,$.1 + 1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1 - 2,13,$.1 + 2[] 425,4,2,$.1 - 1,3,$.1 + 1,5,$.1,7,$.1 - 1,11,$.1 + 4,13,$.1 + 1[] 425,5,2,$.1^2 - 3,3,$.1^2 + 2*$.1 - 2,5,$.1^2,7,$.1^2 - 2*$.1 - 2,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 8*$.1 + 16[] 425,6,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2,7,$.1^2 - 4*$.1 + 2,11,$.1^2 + 8*$.1 + 14,13,$.1^2 - 8[] 425,7,2,$.1^4 - 2*$.1^3 - 4*$.1^2 + 8*$.1 - 1,3,$.1^4 - 4*$.1^3 + 10*$.1 - 2,5,$.1^4,7,$.1^4 - 10*$.1^3 + 32*$.1^2 - 38*$.1 + 14,11,$.1^4 + 2*$.1^3 - 14*$.1^2 - 26*$.1 + 2,13,$.1^4 - 6*$.1^3 - 28*$.1^2 + 192*$.1 - 164[] 425,8,2,$.1^4 + 2*$.1^3 - 4*$.1^2 - 8*$.1 - 1,3,$.1^4 + 4*$.1^3 - 10*$.1 - 2,5,$.1^4,7,$.1^4 + 10*$.1^3 + 32*$.1^2 + 38*$.1 + 14,11,$.1^4 + 2*$.1^3 - 14*$.1^2 - 26*$.1 + 2,13,$.1^4 + 6*$.1^3 - 28*$.1^2 - 192*$.1 - 164[] 425,9,2,$.1^5 + $.1^4 - 10*$.1^3 - 6*$.1^2 + 21*$.1 - 3,3,$.1^5 - $.1^4 - 10*$.1^3 + 10*$.1^2 + 23*$.1 - 25,5,$.1^5,7,$.1^5 - $.1^4 - 22*$.1^3 + 2*$.1^2 + 109*$.1 + 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 + 3*$.1^4 - 26*$.1^3 - 58*$.1^2 + 177*$.1 + 227[] 425,10,2,$.1^5 - $.1^4 - 10*$.1^3 + 6*$.1^2 + 21*$.1 + 3,3,$.1^5 + $.1^4 - 10*$.1^3 - 10*$.1^2 + 23*$.1 + 25,5,$.1^5,7,$.1^5 + $.1^4 - 22*$.1^3 - 2*$.1^2 + 109*$.1 - 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 - 3*$.1^4 - 26*$.1^3 + 58*$.1^2 + 177*$.1 - 227[] 426,1,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x + 2,13,x[] 426,2,2,x + 1,3,x - 1,5,x - 3,7,x + 1,11,x - 3,13,x - 2[] 426,3,2,x - 1,3,x - 1,5,x - 1,7,x - 3,11,x + 3,13,x + 6[] 426,4,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 7,7,x^2 + 2*x - 17,11,x^2 - 10*x + 23,13,x^2 + 8*x + 8[] 426,5,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 - 5*x + 2,11,x^2 + x - 4,13,x^2 - 4*x + 4[] 426,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 3*x + 10,7,x^3 - 2*x^2 - 5*x + 8,11,x^3 - 2*x^2 - 29*x + 80,13,x^3 - 2*x^2 - 24*x - 16[] 426,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - x^2 - 12*x + 4,7,x^3 + x^2 - 12*x - 4,11,x^3 - 3*x^2 - 10*x + 28,13,x^3 - 8*x^2 + 56[] 427,1,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 5,13,x - 4[] 427,2,2,x,3,x - 2,5,x - 4,7,x - 1,11,x + 2,13,x - 2[] 427,3,2,x - 1,3,x - 1,5,x + 4,7,x - 1,11,x + 3,13,x + 4[] 427,4,2,x^6 + 5*x^5 + 2*x^4 - 18*x^3 - 12*x^2 + 18*x + 5,3,x^6 - 10*x^4 - 5*x^3 + 16*x^2 + 12*x + 1,5,x^6 + 5*x^5 - 3*x^4 - 36*x^3 - 19*x^2 + 32*x + 21,7,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 6*x^5 + 5*x^4 - 15*x^3 - 14*x^2 + x + 1,13,x^6 + 13*x^5 + 15*x^4 - 368*x^3 - 1050*x^2 + 2495*x + 8275[] 427,5,2,x^6 + 5*x^5 + 2*x^4 - 22*x^3 - 30*x^2 + 9,3,x^6 + 8*x^5 + 18*x^4 - 3*x^3 - 44*x^2 - 18*x + 17,5,x^6 + 9*x^5 + 21*x^4 - 10*x^3 - 57*x^2 + 9,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 43*x^4 + 7*x^3 + 534*x^2 - 141*x - 1635,13,x^6 + 5*x^5 - 13*x^4 + 8*x^2 - x - 1[] 427,6,2,x^7 - 4*x^6 - 3*x^5 + 26*x^4 - 12*x^3 - 38*x^2 + 23*x + 11,3,x^7 - x^6 - 12*x^5 + 9*x^4 + 37*x^3 - 18*x^2 - 19*x + 1,5,x^7 - 7*x^6 + 11*x^5 + 18*x^4 - 47*x^3 - 8*x^2 + 41*x + 4,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,11,x^7 - x^6 - 27*x^5 + 82*x^4 - 47*x^3 - 59*x^2 + 60*x - 13,13,x^7 - 5*x^6 - 49*x^5 + 258*x^4 + 284*x^3 - 2365*x^2 + 1135*x + 2792[] 427,7,2,x^9 - 5*x^8 - 3*x^7 + 45*x^6 - 32*x^5 - 108*x^4 + 123*x^3 + 30*x^2 - 43*x + 4,3,x^9 + x^8 - 18*x^7 - 13*x^6 + 105*x^5 + 42*x^4 - 205*x^3 - 9*x^2 + 50*x + 8,5,x^9 - 9*x^8 + 13*x^7 + 78*x^6 - 193*x^5 - 190*x^4 + 693*x^3 - 14*x^2 - 768*x + 384,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,11,x^9 - 3*x^8 - 39*x^7 + 88*x^6 + 261*x^5 - 779*x^4 + 470*x^3 + 65*x^2 - 62*x - 8,13,x^9 - 13*x^8 + 39*x^7 + 142*x^6 - 906*x^5 + 595*x^4 + 3819*x^3 - 6580*x^2 + 804*x + 2432[] 428,1,2,x,3,x - 1,5,x - 2,7,x - 4,11,x + 3,13,x - 5[] 428,2,2,x,3,x + 1,5,x - 2,7,x + 4,11,x + 5,13,x - 1[] 428,3,2,x^2,3,x^2 + 3*x - 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + 4*x + 4[] 428,4,2,x^5,3,x^5 - 5*x^4 - 2*x^3 + 32*x^2 - 10*x - 43,5,x^5 + x^4 - 21*x^3 - 12*x^2 + 108*x + 24,7,x^5 - 6*x^4 - x^3 + 34*x^2 - 40,11,x^5 - 6*x^4 + 33*x^2 - 3*x - 9,13,x^5 + 8*x^4 - 23*x^3 - 185*x^2 + 236*x + 436[] Total time: 17.730 seconds, Total memory usage: 5.83MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:18:13 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [428..432] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 04:17:48 on modular [Seed = 1805508998] ------------------------------------- 428,1,2,$.1,3,$.1 - 1,5,$.1 - 2,7,$.1 - 4,11,$.1 + 3,13,$.1 - 5[] 428,2,2,$.1,3,$.1 + 1,5,$.1 - 2,7,$.1 + 4,11,$.1 + 5,13,$.1 - 1[] 428,3,2,$.1^2,3,$.1^2 + 3*$.1 - 1,5,$.1^2 + $.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 + 4*$.1 + 4[] 428,4,2,$.1^5,3,$.1^5 - 5*$.1^4 - 2*$.1^3 + 32*$.1^2 - 10*$.1 - 43,5,$.1^5 + $.1^4 - 21*$.1^3 - 12*$.1^2 + 108*$.1 + 24,7,$.1^5 - 6*$.1^4 - $.1^3 + 34*$.1^2 - 40,11,$.1^5 - 6*$.1^4 + 33*$.1^2 - 3*$.1 - 9,13,$.1^5 + 8*$.1^4 - 23*$.1^3 - 185*$.1^2 + 236*$.1 + 436[] 429,1,2,x + 1,3,x + 1,5,x,7,x,11,x - 1,13,x - 1[] 429,2,2,x + 1,3,x - 1,5,x + 2,7,x,11,x + 1,13,x - 1[] 429,3,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 + 4*x + 4,11,x^2 + 2*x + 1,13,x^2 + 2*x + 1[] 429,4,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 4*x + 2,7,x^2 + 4*x - 4,11,x^2 - 2*x + 1,13,x^2 + 2*x + 1[] 429,5,2,x^3 + x^2 - 5*x - 3,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 10*x - 2,7,x^3 - 2*x^2 - 8*x + 12,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 + 3*x + 1[] 429,6,2,x^3 - 3*x^2 - x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 2*x + 2,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 + 3*x + 1[] 429,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x - 2,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 3*x^2 + 3*x - 1[] 429,8,2,x^4 + 2*x^3 - 6*x^2 - 12*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 12*x^2 - 14*x - 4,7,x^4 - 2*x^3 - 16*x^2 + 44*x - 16,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 430,1,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 4,13,x + 1[] 430,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x,13,x + 3[] 430,3,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x + 6,13,x - 5[] 430,4,2,x - 1,3,x + 2,5,x - 1,7,x + 5,11,x + 2,13,x + 5[] 430,5,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 11,11,x^2 - 2*x - 2,13,x^2 - 2*x - 11[] 430,6,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x - 2,13,x^2 + 2*x + 1[] 430,7,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x + 2,13,x^2 - 2*x - 7[] 430,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 6*x^2 + 5*x - 8,11,x^3 - 6*x^2 - 22*x + 136,13,x^3 + 4*x^2 - 27*x - 106[] 431,1,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x + 5,13,x + 2[] 431,2,2,x + 1,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x + 2[] 431,3,2,x^3 - x^2 - 4*x + 3,3,x^3 + x^2 - 4*x - 3,5,x^3 + 3*x^2 - 2*x - 7,7,x^3 + 6*x^2 + 12*x + 8,11,x^3,13,x^3 + 6*x^2 + 12*x + 8[] 431,4,2,x^3 - 5*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - x^2 - 10*x + 1,7,x^3 - 20*x - 8,11,x^3 + 12*x^2 + 48*x + 64,13,x^3 - 8*x^2 - 12*x + 136[] 431,5,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 3*x^3 - 4*x - 1,5,x^4 + 5*x^3 + 6*x^2 - 1,7,x^4 - 2*x^3 - 2*x^2 + 3*x + 1,11,x^4 - x^3 - 13*x^2 + 31*x - 19,13,x^4 + 5*x^3 - x^2 - 5*x - 1[] 431,6,2,x^24 - x^23 - 40*x^22 + 40*x^21 + 692*x^20 - 687*x^19 - 6790*x^18 + 6631*x^17 + 41657*x^16 - 39533*x^15 - 166175*x^14 + 150668*x^13 + 434546*x^12 - 367120*x^11 - 733353*x^10 + 555013*x^9 + 766426*x^8 - 486022*x^7 - 458392*x^6 + 216189*x^5 + 133642*x^4 - 39443*x^3 - 11021*x^2 + 2767*x + 13,3,x^24 - x^23 - 51*x^22 + 45*x^21 + 1118*x^20 - 853*x^19 - 13827*x^18 + 8872*x^17 + 106601*x^16 - 55088*x^15 - 535427*x^14 + 206199*x^13 + 1783081*x^12 - 432309*x^11 - 3938181*x^10 + 336862*x^9 + 5666150*x^8 + 485071*x^7 - 5053047*x^6 - 1363051*x^5 + 2461452*x^4 + 1177097*x^3 - 415667*x^2 - 363322*x - 62521,5,x^24 - 13*x^23 - x^22 + 693*x^21 - 2212*x^20 - 13027*x^19 + 73409*x^18 + 78062*x^17 - 1062921*x^16 + 636806*x^15 + 8076267*x^14 - 12881903*x^13 - 31663301*x^12 + 83663785*x^11 + 45711505*x^10 - 263035378*x^9 + 70497032*x^8 + 381236683*x^7 - 274310749*x^6 - 178921611*x^5 + 181598490*x^4 + 23883539*x^3 - 30789701*x^2 - 3434398*x + 738223,7,x^24 - 8*x^23 - 94*x^22 + 889*x^21 + 3211*x^20 - 41262*x^19 - 35920*x^18 + 1032968*x^17 - 571044*x^16 - 14958832*x^15 + 22590168*x^14 + 123054224*x^13 - 294152000*x^12 - 491861440*x^11 + 1902252288*x^10 + 168622848*x^9 - 5847215104*x^8 + 5061049344*x^7 + 5009858560*x^6 - 11097280512*x^5 + 7305969664*x^4 - 1900675072*x^3 - 24051712*x^2 + 100335616*x - 13238272,11,x^24 - 15*x^23 - 56*x^22 + 1718*x^21 - 967*x^20 - 85552*x^19 + 159131*x^18 + 2463154*x^17 - 5654857*x^16 - 45863834*x^15 + 103729723*x^14 + 580573026*x^13 - 1102854601*x^12 - 5039630656*x^11 + 6745640649*x^10 + 29106429742*x^9 - 21209517228*x^8 - 104340033191*x^7 + 20867246361*x^6 + 207698272456*x^5 + 35856946884*x^4 - 197939406720*x^3 - 78321571072*x^2 + 69887651200*x + 37007196736,13,x^24 - 11*x^23 - 153*x^22 + 2073*x^21 + 7799*x^20 - 162648*x^19 - 38534*x^18 + 6816228*x^17 - 11860956*x^16 - 160653936*x^15 + 537013864*x^14 + 1953872960*x^13 - 10978265728*x^12 - 5739512960*x^11 + 114862520832*x^10 - 130647495936*x^9 - 520848457216*x^8 + 1411147104256*x^7 - 56486131712*x^6 - 3959960002560*x^5 + 5582947106816*x^4 - 2083243065344*x^3 - 1377562722304*x^2 + 1279575916544*x - 244822704128[] Errors: /home/mfd/gomagma: line 2: 28218 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:19:09 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [428..431] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 04:18:51 on modular [Seed = 367239103] ------------------------------------- 428,1,2,$.1,3,$.1 - 1,5,$.1 - 2,7,$.1 - 4,11,$.1 + 3,13,$.1 - 5[] 428,2,2,$.1,3,$.1 + 1,5,$.1 - 2,7,$.1 + 4,11,$.1 + 5,13,$.1 - 1[] 428,3,2,$.1^2,3,$.1^2 + 3*$.1 - 1,5,$.1^2 + $.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 + 4*$.1 + 4[] 428,4,2,$.1^5,3,$.1^5 - 5*$.1^4 - 2*$.1^3 + 32*$.1^2 - 10*$.1 - 43,5,$.1^5 + $.1^4 - 21*$.1^3 - 12*$.1^2 + 108*$.1 + 24,7,$.1^5 - 6*$.1^4 - $.1^3 + 34*$.1^2 - 40,11,$.1^5 - 6*$.1^4 + 33*$.1^2 - 3*$.1 - 9,13,$.1^5 + 8*$.1^4 - 23*$.1^3 - 185*$.1^2 + 236*$.1 + 436[] 429,1,2,x + 1,3,x + 1,5,x,7,x,11,x - 1,13,x - 1[] 429,2,2,x + 1,3,x - 1,5,x + 2,7,x,11,x + 1,13,x - 1[] 429,3,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 + 4*x + 4,11,x^2 + 2*x + 1,13,x^2 + 2*x + 1[] 429,4,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 4*x + 2,7,x^2 + 4*x - 4,11,x^2 - 2*x + 1,13,x^2 + 2*x + 1[] 429,5,2,x^3 + x^2 - 5*x - 3,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 10*x - 2,7,x^3 - 2*x^2 - 8*x + 12,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 + 3*x + 1[] 429,6,2,x^3 - 3*x^2 - x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 2*x + 2,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 + 3*x + 1[] 429,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x - 2,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 3*x^2 + 3*x - 1[] 429,8,2,x^4 + 2*x^3 - 6*x^2 - 12*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 12*x^2 - 14*x - 4,7,x^4 - 2*x^3 - 16*x^2 + 44*x - 16,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 430,1,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 4,13,x + 1[] 430,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x,13,x + 3[] 430,3,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x + 6,13,x - 5[] 430,4,2,x - 1,3,x + 2,5,x - 1,7,x + 5,11,x + 2,13,x + 5[] 430,5,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 11,11,x^2 - 2*x - 2,13,x^2 - 2*x - 11[] 430,6,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x - 2,13,x^2 + 2*x + 1[] 430,7,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x + 2,13,x^2 - 2*x - 7[] 430,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 6*x^2 + 5*x - 8,11,x^3 - 6*x^2 - 22*x + 136,13,x^3 + 4*x^2 - 27*x - 106[] 431,1,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x + 5,13,x + 2[] 431,2,2,x + 1,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x + 2[] 431,3,2,x^3 - x^2 - 4*x + 3,3,x^3 + x^2 - 4*x - 3,5,x^3 + 3*x^2 - 2*x - 7,7,x^3 + 6*x^2 + 12*x + 8,11,x^3,13,x^3 + 6*x^2 + 12*x + 8[] 431,4,2,x^3 - 5*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - x^2 - 10*x + 1,7,x^3 - 20*x - 8,11,x^3 + 12*x^2 + 48*x + 64,13,x^3 - 8*x^2 - 12*x + 136[] 431,5,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 3*x^3 - 4*x - 1,5,x^4 + 5*x^3 + 6*x^2 - 1,7,x^4 - 2*x^3 - 2*x^2 + 3*x + 1,11,x^4 - x^3 - 13*x^2 + 31*x - 19,13,x^4 + 5*x^3 - x^2 - 5*x - 1[] 431,6,2,x^24 - x^23 - 40*x^22 + 40*x^21 + 692*x^20 - 687*x^19 - 6790*x^18 + 6631*x^17 + 41657*x^16 - 39533*x^15 - 166175*x^14 + 150668*x^13 + 434546*x^12 - 367120*x^11 - 733353*x^10 + 555013*x^9 + 766426*x^8 - 486022*x^7 - 458392*x^6 + 216189*x^5 + 133642*x^4 - 39443*x^3 - 11021*x^2 + 2767*x + 13,3,x^24 - x^23 - 51*x^22 + 45*x^21 + 1118*x^20 - 853*x^19 - 13827*x^18 + 8872*x^17 + 106601*x^16 - 55088*x^15 - 535427*x^14 + 206199*x^13 + 1783081*x^12 - 432309*x^11 - 3938181*x^10 + 336862*x^9 + 5666150*x^8 + 485071*x^7 - 5053047*x^6 - 1363051*x^5 + 2461452*x^4 + 1177097*x^3 - 415667*x^2 - 363322*x - 62521,5,x^24 - 13*x^23 - x^22 + 693*x^21 - 2212*x^20 - 13027*x^19 + 73409*x^18 + 78062*x^17 - 1062921*x^16 + 636806*x^15 + 8076267*x^14 - 12881903*x^13 - 31663301*x^12 + 83663785*x^11 + 45711505*x^10 - 263035378*x^9 + 70497032*x^8 + 381236683*x^7 - 274310749*x^6 - 178921611*x^5 + 181598490*x^4 + 23883539*x^3 - 30789701*x^2 - 3434398*x + 738223,7,x^24 - 8*x^23 - 94*x^22 + 889*x^21 + 3211*x^20 - 41262*x^19 - 35920*x^18 + 1032968*x^17 - 571044*x^16 - 14958832*x^15 + 22590168*x^14 + 123054224*x^13 - 294152000*x^12 - 491861440*x^11 + 1902252288*x^10 + 168622848*x^9 - 5847215104*x^8 + 5061049344*x^7 + 5009858560*x^6 - 11097280512*x^5 + 7305969664*x^4 - 1900675072*x^3 - 24051712*x^2 + 100335616*x - 13238272,11,x^24 - 15*x^23 - 56*x^22 + 1718*x^21 - 967*x^20 - 85552*x^19 + 159131*x^18 + 2463154*x^17 - 5654857*x^16 - 45863834*x^15 + 103729723*x^14 + 580573026*x^13 - 1102854601*x^12 - 5039630656*x^11 + 6745640649*x^10 + 29106429742*x^9 - 21209517228*x^8 - 104340033191*x^7 + 20867246361*x^6 + 207698272456*x^5 + 35856946884*x^4 - 197939406720*x^3 - 78321571072*x^2 + 69887651200*x + 37007196736,13,x^24 - 11*x^23 - 153*x^22 + 2073*x^21 + 7799*x^20 - 162648*x^19 - 38534*x^18 + 6816228*x^17 - 11860956*x^16 - 160653936*x^15 + 537013864*x^14 + 1953872960*x^13 - 10978265728*x^12 - 5739512960*x^11 + 114862520832*x^10 - 130647495936*x^9 - 520848457216*x^8 + 1411147104256*x^7 - 56486131712*x^6 - 3959960002560*x^5 + 5582947106816*x^4 - 2083243065344*x^3 - 1377562722304*x^2 + 1279575916544*x - 244822704128[] Total time: 16.840 seconds, Total memory usage: 5.71MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:26:27 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [431..434] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 04:26:08 on modular [Seed = 1369954808] ------------------------------------- 431,1,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 2,11,$.1 + 5,13,$.1 + 2[] 431,2,2,$.1 + 1,3,$.1 - 3,5,$.1 + 3,7,$.1 - 2,11,$.1 - 1,13,$.1 + 2[] 431,3,2,$.1^3 - $.1^2 - 4*$.1 + 3,3,$.1^3 + $.1^2 - 4*$.1 - 3,5,$.1^3 + 3*$.1^2 - 2*$.1 - 7,7,$.1^3 + 6*$.1^2 + 12*$.1 + 8,11,$.1^3,13,$.1^3 + 6*$.1^2 + 12*$.1 + 8[] 431,4,2,$.1^3 - 5*$.1 + 1,3,$.1^3 - $.1^2 - 8*$.1 + 11,5,$.1^3 - $.1^2 - 10*$.1 + 1,7,$.1^3 - 20*$.1 - 8,11,$.1^3 + 12*$.1^2 + 48*$.1 + 64,13,$.1^3 - 8*$.1^2 - 12*$.1 + 136[] 431,5,2,$.1^4 + $.1^3 - 3*$.1^2 - $.1 + 1,3,$.1^4 + 3*$.1^3 - 4*$.1 - 1,5,$.1^4 + 5*$.1^3 + 6*$.1^2 - 1,7,$.1^4 - 2*$.1^3 - 2*$.1^2 + 3*$.1 + 1,11,$.1^4 - $.1^3 - 13*$.1^2 + 31*$.1 - 19,13,$.1^4 + 5*$.1^3 - $.1^2 - 5*$.1 - 1[] 431,6,2,$.1^24 - $.1^23 - 40*$.1^22 + 40*$.1^21 + 692*$.1^20 - 687*$.1^19 - 6790*$.1^18 + 6631*$.1^17 + 41657*$.1^16 - 39533*$.1^15 - 166175*$.1^14 + 150668*$.1^13 + 434546*$.1^12 - 367120*$.1^11 - 733353*$.1^10 + 555013*$.1^9 + 766426*$.1^8 - 486022*$.1^7 - 458392*$.1^6 + 216189*$.1^5 + 133642*$.1^4 - 39443*$.1^3 - 11021*$.1^2 + 2767*$.1 + 13,3,$.1^24 - $.1^23 - 51*$.1^22 + 45*$.1^21 + 1118*$.1^20 - 853*$.1^19 - 13827*$.1^18 + 8872*$.1^17 + 106601*$.1^16 - 55088*$.1^15 - 535427*$.1^14 + 206199*$.1^13 + 1783081*$.1^12 - 432309*$.1^11 - 3938181*$.1^10 + 336862*$.1^9 + 5666150*$.1^8 + 485071*$.1^7 - 5053047*$.1^6 - 1363051*$.1^5 + 2461452*$.1^4 + 1177097*$.1^3 - 415667*$.1^2 - 363322*$.1 - 62521,5,$.1^24 - 13*$.1^23 - $.1^22 + 693*$.1^21 - 2212*$.1^20 - 13027*$.1^19 + 73409*$.1^18 + 78062*$.1^17 - 1062921*$.1^16 + 636806*$.1^15 + 8076267*$.1^14 - 12881903*$.1^13 - 31663301*$.1^12 + 83663785*$.1^11 + 45711505*$.1^10 - 263035378*$.1^9 + 70497032*$.1^8 + 381236683*$.1^7 - 274310749*$.1^6 - 178921611*$.1^5 + 181598490*$.1^4 + 23883539*$.1^3 - 30789701*$.1^2 - 3434398*$.1 + 738223,7,$.1^24 - 8*$.1^23 - 94*$.1^22 + 889*$.1^21 + 3211*$.1^20 - 41262*$.1^19 - 35920*$.1^18 + 1032968*$.1^17 - 571044*$.1^16 - 14958832*$.1^15 + 22590168*$.1^14 + 123054224*$.1^13 - 294152000*$.1^12 - 491861440*$.1^11 + 1902252288*$.1^10 + 168622848*$.1^9 - 5847215104*$.1^8 + 5061049344*$.1^7 + 5009858560*$.1^6 - 11097280512*$.1^5 + 7305969664*$.1^4 - 1900675072*$.1^3 - 24051712*$.1^2 + 100335616*$.1 - 13238272,11,$.1^24 - 15*$.1^23 - 56*$.1^22 + 1718*$.1^21 - 967*$.1^20 - 85552*$.1^19 + 159131*$.1^18 + 2463154*$.1^17 - 5654857*$.1^16 - 45863834*$.1^15 + 103729723*$.1^14 + 580573026*$.1^13 - 1102854601*$.1^12 - 5039630656*$.1^11 + 6745640649*$.1^10 + 29106429742*$.1^9 - 21209517228*$.1^8 - 104340033191*$.1^7 + 20867246361*$.1^6 + 207698272456*$.1^5 + 35856946884*$.1^4 - 197939406720*$.1^3 - 78321571072*$.1^2 + 69887651200*$.1 + 37007196736,13,$.1^24 - 11*$.1^23 - 153*$.1^22 + 2073*$.1^21 + 7799*$.1^20 - 162648*$.1^19 - 38534*$.1^18 + 6816228*$.1^17 - 11860956*$.1^16 - 160653936*$.1^15 + 537013864*$.1^14 + 1953872960*$.1^13 - 10978265728*$.1^12 - 5739512960*$.1^11 + 114862520832*$.1^10 - 130647495936*$.1^9 - 520848457216*$.1^8 + 1411147104256*$.1^7 - 56486131712*$.1^6 - 3959960002560*$.1^5 + 5582947106816*$.1^4 - 2083243065344*$.1^3 - 1377562722304*$.1^2 + 1279575916544*$.1 - 244822704128[] 432,1,2,x,3,x,5,x + 1,7,x + 3,11,x + 5,13,x - 4[] 432,2,2,x,3,x,5,x - 1,7,x + 3,11,x - 5,13,x - 4[] 432,3,2,x,3,x,5,x - 4,7,x - 3,11,x + 4,13,x - 1[] 432,4,2,x,3,x,5,x + 4,7,x - 3,11,x - 4,13,x - 1[] 432,5,2,x,3,x,5,x,7,x - 1,11,x,13,x - 5[] 432,6,2,x,3,x,5,x - 3,7,x - 1,11,x - 3,13,x + 4[] 432,7,2,x,3,x,5,x,7,x + 5,11,x,13,x + 7[] 432,8,2,x,3,x,5,x + 3,7,x - 1,11,x + 3,13,x + 4[] 433,1,2,x + 1,3,x + 2,5,x + 4,7,x + 3,11,x + 4,13,x + 5[] 433,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 8*x + 4,5,x^3 - 8*x + 4,7,x^3 - 7*x^2 + 11*x - 3,11,x^3 - 6*x^2 + 4*x + 4,13,x^3 - 5*x^2 - 21*x + 97[] 433,3,2,x^15 + 10*x^14 + 29*x^13 - 22*x^12 - 251*x^11 - 272*x^10 + 583*x^9 + 1252*x^8 - 186*x^7 - 1821*x^6 - 675*x^5 + 899*x^4 + 482*x^3 - 93*x^2 - 27*x - 1,3,x^15 + 8*x^14 + 7*x^13 - 92*x^12 - 221*x^11 + 232*x^10 + 1030*x^9 + 63*x^8 - 1719*x^7 - 429*x^6 + 1308*x^5 + 127*x^4 - 452*x^3 + 88*x^2 + 16*x - 4,5,x^15 + 5*x^14 - 27*x^13 - 170*x^12 + 160*x^11 + 1914*x^10 + 388*x^9 - 9870*x^8 - 5872*x^7 + 26083*x^6 + 16736*x^5 - 37759*x^4 - 18244*x^3 + 28460*x^2 + 6744*x - 8548,7,x^15 + 15*x^14 + 51*x^13 - 272*x^12 - 1975*x^11 - 212*x^10 + 22207*x^9 + 30408*x^8 - 109207*x^7 - 212799*x^6 + 274259*x^5 + 575247*x^4 - 419271*x^3 - 554748*x^2 + 403547*x - 59063,11,x^15 + 14*x^14 + 7*x^13 - 707*x^12 - 2663*x^11 + 9425*x^10 + 64024*x^9 - 718*x^8 - 553393*x^7 - 681386*x^6 + 1691664*x^5 + 3572557*x^4 - 430092*x^3 - 4182740*x^2 - 1450688*x + 655796,13,x^15 + 9*x^14 - 54*x^13 - 600*x^12 + 885*x^11 + 14731*x^10 - 3850*x^9 - 172818*x^8 - 19607*x^7 + 1039066*x^6 + 134513*x^5 - 3101189*x^4 + 184903*x^3 + 3670090*x^2 - 1421967*x - 30529[] 433,4,2,x^16 - 7*x^15 - 5*x^14 + 129*x^13 - 125*x^12 - 929*x^11 + 1471*x^10 + 3333*x^9 - 6394*x^8 - 6443*x^7 + 13118*x^6 + 7162*x^5 - 12217*x^4 - 4691*x^3 + 3598*x^2 + 1114*x - 3,3,x^16 - 6*x^15 - 13*x^14 + 134*x^13 - 33*x^12 - 1074*x^11 + 1074*x^10 + 4051*x^9 - 5657*x^8 - 7571*x^7 + 12986*x^6 + 6355*x^5 - 13826*x^4 - 1264*x^3 + 5720*x^2 - 680*x - 224,5,x^16 - 7*x^15 - 17*x^14 + 202*x^13 - 46*x^12 - 2060*x^11 + 2036*x^10 + 9692*x^9 - 12248*x^8 - 22667*x^7 + 29036*x^6 + 26041*x^5 - 26932*x^4 - 13736*x^3 + 7016*x^2 + 2216*x - 48,7,x^16 - 7*x^15 - 29*x^14 + 310*x^13 - 97*x^12 - 4172*x^11 + 7759*x^10 + 16632*x^9 - 54399*x^8 + 985*x^7 + 117147*x^6 - 88479*x^5 - 49471*x^4 + 73286*x^3 - 18921*x^2 - 1887*x + 636,11,x^16 - 12*x^15 - 13*x^14 + 627*x^13 - 1269*x^12 - 10221*x^11 + 29458*x^10 + 79946*x^9 - 239097*x^8 - 375776*x^7 + 817112*x^6 + 1070885*x^5 - 938542*x^4 - 1080712*x^3 + 448064*x^2 + 319336*x - 111648,13,x^16 + 3*x^15 - 76*x^14 - 252*x^13 + 2185*x^12 + 8069*x^11 - 29472*x^10 - 125818*x^9 + 183833*x^8 + 1020236*x^7 - 354339*x^6 - 4257291*x^5 - 1094143*x^4 + 8359796*x^3 + 4913205*x^2 - 5697071*x - 4141634[] 434,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 2,13,x + 2[] 434,2,2,x - 1,3,x - 2,5,x - 2,7,x + 1,11,x + 6,13,x - 4[] 434,3,2,x - 1,3,x + 3,5,x + 3,7,x + 1,11,x - 4,13,x - 4[] 434,4,2,x - 1,3,x + 2,5,x + 2,7,x - 1,11,x + 2,13,x + 4[] 434,5,2,x - 1,3,x - 1,5,x - 3,7,x - 1,11,x,13,x + 4[] 434,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 1,5,x^2 + 2*x - 7,7,x^2 - 2*x + 1,11,x^2,13,x^2 - 8*x + 8[] 434,7,2,x^2 - 2*x + 1,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2 + 2*x + 1,11,x^2 - 8*x + 16,13,x^2 + 6*x - 8[] 434,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 5*x - 8,5,x^3 + 2*x^2 - 7*x - 4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 2*x^2 - 32*x + 32,13,x^3 - 2*x^2 - 24*x - 16[] 434,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 8*x + 4,5,x^3 + x^2 - 8*x - 4,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 4*x^2 - 20*x - 64,13,x^3 - 12*x^2 + 48*x - 64[] Total time: 15.919 seconds, Total memory usage: 5.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:32:16 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [434..437] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 04:31:56 on modular [Seed = 1135986007] ------------------------------------- 434,1,2,$.1 + 1,3,$.1,5,$.1,7,$.1 + 1,11,$.1 + 2,13,$.1 + 2[] 434,2,2,$.1 - 1,3,$.1 - 2,5,$.1 - 2,7,$.1 + 1,11,$.1 + 6,13,$.1 - 4[] 434,3,2,$.1 - 1,3,$.1 + 3,5,$.1 + 3,7,$.1 + 1,11,$.1 - 4,13,$.1 - 4[] 434,4,2,$.1 - 1,3,$.1 + 2,5,$.1 + 2,7,$.1 - 1,11,$.1 + 2,13,$.1 + 4[] 434,5,2,$.1 - 1,3,$.1 - 1,5,$.1 - 3,7,$.1 - 1,11,$.1,13,$.1 + 4[] 434,6,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2*$.1 - 1,5,$.1^2 + 2*$.1 - 7,7,$.1^2 - 2*$.1 + 1,11,$.1^2,13,$.1^2 - 8*$.1 + 8[] 434,7,2,$.1^2 - 2*$.1 + 1,3,$.1^2 - $.1 - 4,5,$.1^2 - 3*$.1 - 2,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 16,13,$.1^2 + 6*$.1 - 8[] 434,8,2,$.1^3 + 3*$.1^2 + 3*$.1 + 1,3,$.1^3 + 2*$.1^2 - 5*$.1 - 8,5,$.1^3 + 2*$.1^2 - 7*$.1 - 4,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 - 2*$.1^2 - 32*$.1 + 32,13,$.1^3 - 2*$.1^2 - 24*$.1 - 16[] 434,9,2,$.1^3 - 3*$.1^2 + 3*$.1 - 1,3,$.1^3 - $.1^2 - 8*$.1 + 4,5,$.1^3 + $.1^2 - 8*$.1 - 4,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 + 4*$.1^2 - 20*$.1 - 64,13,$.1^3 - 12*$.1^2 + 48*$.1 - 64[] 435,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x - 1,13,x - 6[] 435,2,2,x,3,x - 1,5,x + 1,7,x - 2,11,x - 3,13,x - 2[] 435,3,2,x - 1,3,x - 1,5,x - 1,7,x - 4,11,x + 4,13,x - 6[] 435,4,2,x + 1,3,x - 1,5,x - 1,7,x + 4,11,x,13,x - 6[] 435,5,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 4*x + 4,13,x^2 - 4*x + 4[] 435,6,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + 2*x - 19,13,x^2 + 8*x + 11[] 435,7,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 + 7*x + 8,13,x^2 + 4*x + 4[] 435,8,2,x^2 + x - 5,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 10*x + 25,13,x^2 - 21[] 435,9,2,x^3 - x^2 - 5*x + 4,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 4*x^2 - 7*x - 14,11,x^3 - 9*x^2 + 27*x - 27,13,x^3 - 6*x^2 - x + 2[] 435,10,2,x^4 + 3*x^3 - 2*x^2 - 7*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 2*x^3 - 15*x^2 - 4*x + 4,11,x^4 + 2*x^3 - 15*x^2 + 4*x + 4,13,x^4 + 8*x^3 + 3*x^2 - 92*x - 164[] 436,1,2,x^2,3,x^2 - 8,5,x^2 - 2*x - 7,7,x^2 + 4*x + 4,11,x^2 + 6*x + 7,13,x^2[] 436,2,2,x^3,3,x^3 - 3*x - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 + 3*x^2 - 18*x - 3,13,x^3 + 3*x^2 - 6*x - 17[] 436,3,2,x^4,3,x^4 - 7*x^2 - x + 8,5,x^4 - 8*x^3 + 17*x^2 - 3*x - 6,7,x^4 - 5*x^3 - 10*x^2 + 45*x + 12,11,x^4 - 3*x^3 - 16*x^2 + 67*x - 58,13,x^4 - 5*x^3 - 14*x^2 + 57*x + 62[] 437,1,2,x - 2,3,x - 2,5,x - 1,7,x + 3,11,x - 5,13,x + 2[] 437,2,2,x,3,x - 2,5,x + 1,7,x + 5,11,x + 1,13,x[] 437,3,2,x^2 + 2*x + 1,3,x^2 + 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - x - 11,11,x^2 + 5*x - 5,13,x^2 - 20[] 437,4,2,x^2 - 5,3,x^2 + x - 1,5,x^2 + 2*x - 4,7,x^2 + 5*x + 5,11,x^2 + 7*x + 11,13,x^2 - 20[] 437,5,2,x^2 - 2,3,x^2 + 4*x + 2,5,x^2 + 2*x - 1,7,x^2 + 2*x - 1,11,x^2 - 2*x - 1,13,x^2 - 32[] 437,6,2,x^5 + x^4 - 7*x^3 - 2*x^2 + 12*x - 4,3,x^5 + 4*x^4 - x^3 - 12*x^2 + 4,5,x^5 + x^4 - 7*x^3 - 5*x^2 + 10*x + 4,7,x^5 + 9*x^4 + 25*x^3 + 19*x^2 - 6*x - 4,11,x^5 + x^4 - 39*x^3 - 41*x^2 + 174*x + 172,13,x^5 + 10*x^4 + 29*x^3 + 16*x^2 - 24*x - 16[] 437,7,2,x^8 - 13*x^6 + 47*x^4 - 2*x^3 - 37*x^2 - 2*x + 2,3,x^8 - 5*x^7 - 4*x^6 + 45*x^5 - 16*x^4 - 121*x^3 + 71*x^2 + 96*x - 62,5,x^8 - 2*x^7 - 19*x^6 + 18*x^5 + 116*x^4 - 12*x^3 - 240*x^2 - 128*x + 16,7,x^8 - 9*x^7 + 11*x^6 + 110*x^5 - 376*x^4 + 194*x^3 + 723*x^2 - 1105*x + 449,11,x^8 - 7*x^7 - 23*x^6 + 202*x^5 + 48*x^4 - 1550*x^3 + 1315*x^2 + 2045*x - 2225,13,x^8 - 8*x^7 - 16*x^6 + 180*x^5 + 64*x^4 - 1200*x^3 - 112*x^2 + 2112*x + 1152[] 437,8,2,x^12 - 2*x^11 - 19*x^10 + 35*x^9 + 137*x^8 - 219*x^7 - 483*x^6 + 605*x^5 + 866*x^4 - 707*x^3 - 682*x^2 + 236*x + 96,3,x^12 - 7*x^11 - x^10 + 100*x^9 - 146*x^8 - 386*x^7 + 819*x^6 + 495*x^5 - 1465*x^4 - 178*x^3 + 812*x^2 + 128*x - 64,5,x^12 + x^11 - 43*x^10 - 29*x^9 + 690*x^8 + 304*x^7 - 5116*x^6 - 1600*x^5 + 17904*x^4 + 4400*x^3 - 26240*x^2 - 4736*x + 10368,7,x^12 - 14*x^11 + 44*x^10 + 199*x^9 - 1254*x^8 - 56*x^7 + 10263*x^6 - 9726*x^5 - 33184*x^4 + 43045*x^3 + 38206*x^2 - 49124*x - 5344,11,x^12 - 4*x^11 - 60*x^10 + 245*x^9 + 1130*x^8 - 5248*x^7 - 6329*x^6 + 44008*x^5 - 10772*x^4 - 119905*x^3 + 103210*x^2 + 26396*x - 16944,13,x^12 - 2*x^11 - 103*x^10 + 240*x^9 + 3836*x^8 - 10756*x^7 - 62400*x^6 + 214944*x^5 + 388784*x^4 - 1876288*x^3 - 16320*x^2 + 5750784*x - 5141504[] Total time: 18.369 seconds, Total memory usage: 5.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:37:47 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [437..440] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 04:37:26 on modular [Seed = 1887892799] ------------------------------------- 437,1,2,$.1 - 2,3,$.1 - 2,5,$.1 - 1,7,$.1 + 3,11,$.1 - 5,13,$.1 + 2[] 437,2,2,$.1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 5,11,$.1 + 1,13,$.1[] 437,3,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - $.1 - 11,11,$.1^2 + 5*$.1 - 5,13,$.1^2 - 20[] 437,4,2,$.1^2 - 5,3,$.1^2 + $.1 - 1,5,$.1^2 + 2*$.1 - 4,7,$.1^2 + 5*$.1 + 5,11,$.1^2 + 7*$.1 + 11,13,$.1^2 - 20[] 437,5,2,$.1^2 - 2,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 - 1,7,$.1^2 + 2*$.1 - 1,11,$.1^2 - 2*$.1 - 1,13,$.1^2 - 32[] 437,6,2,$.1^5 + $.1^4 - 7*$.1^3 - 2*$.1^2 + 12*$.1 - 4,3,$.1^5 + 4*$.1^4 - $.1^3 - 12*$.1^2 + 4,5,$.1^5 + $.1^4 - 7*$.1^3 - 5*$.1^2 + 10*$.1 + 4,7,$.1^5 + 9*$.1^4 + 25*$.1^3 + 19*$.1^2 - 6*$.1 - 4,11,$.1^5 + $.1^4 - 39*$.1^3 - 41*$.1^2 + 174*$.1 + 172,13,$.1^5 + 10*$.1^4 + 29*$.1^3 + 16*$.1^2 - 24*$.1 - 16[] 437,7,2,$.1^8 - 13*$.1^6 + 47*$.1^4 - 2*$.1^3 - 37*$.1^2 - 2*$.1 + 2,3,$.1^8 - 5*$.1^7 - 4*$.1^6 + 45*$.1^5 - 16*$.1^4 - 121*$.1^3 + 71*$.1^2 + 96*$.1 - 62,5,$.1^8 - 2*$.1^7 - 19*$.1^6 + 18*$.1^5 + 116*$.1^4 - 12*$.1^3 - 240*$.1^2 - 128*$.1 + 16,7,$.1^8 - 9*$.1^7 + 11*$.1^6 + 110*$.1^5 - 376*$.1^4 + 194*$.1^3 + 723*$.1^2 - 1105*$.1 + 449,11,$.1^8 - 7*$.1^7 - 23*$.1^6 + 202*$.1^5 + 48*$.1^4 - 1550*$.1^3 + 1315*$.1^2 + 2045*$.1 - 2225,13,$.1^8 - 8*$.1^7 - 16*$.1^6 + 180*$.1^5 + 64*$.1^4 - 1200*$.1^3 - 112*$.1^2 + 2112*$.1 + 1152[] 437,8,2,$.1^12 - 2*$.1^11 - 19*$.1^10 + 35*$.1^9 + 137*$.1^8 - 219*$.1^7 - 483*$.1^6 + 605*$.1^5 + 866*$.1^4 - 707*$.1^3 - 682*$.1^2 + 236*$.1 + 96,3,$.1^12 - 7*$.1^11 - $.1^10 + 100*$.1^9 - 146*$.1^8 - 386*$.1^7 + 819*$.1^6 + 495*$.1^5 - 1465*$.1^4 - 178*$.1^3 + 812*$.1^2 + 128*$.1 - 64,5,$.1^12 + $.1^11 - 43*$.1^10 - 29*$.1^9 + 690*$.1^8 + 304*$.1^7 - 5116*$.1^6 - 1600*$.1^5 + 17904*$.1^4 + 4400*$.1^3 - 26240*$.1^2 - 4736*$.1 + 10368,7,$.1^12 - 14*$.1^11 + 44*$.1^10 + 199*$.1^9 - 1254*$.1^8 - 56*$.1^7 + 10263*$.1^6 - 9726*$.1^5 - 33184*$.1^4 + 43045*$.1^3 + 38206*$.1^2 - 49124*$.1 - 5344,11,$.1^12 - 4*$.1^11 - 60*$.1^10 + 245*$.1^9 + 1130*$.1^8 - 5248*$.1^7 - 6329*$.1^6 + 44008*$.1^5 - 10772*$.1^4 - 119905*$.1^3 + 103210*$.1^2 + 26396*$.1 - 16944,13,$.1^12 - 2*$.1^11 - 103*$.1^10 + 240*$.1^9 + 3836*$.1^8 - 10756*$.1^7 - 62400*$.1^6 + 214944*$.1^5 + 388784*$.1^4 - 1876288*$.1^3 - 16320*$.1^2 + 5750784*$.1 - 5141504[] 438,1,2,x + 1,3,x + 1,5,x,7,x + 2,11,x - 4,13,x + 6[] 438,2,2,x + 1,3,x - 1,5,x - 2,7,x + 2,11,x - 2,13,x - 4[] 438,3,2,x + 1,3,x - 1,5,x,7,x + 4,11,x + 6,13,x + 4[] 438,4,2,x + 1,3,x - 1,5,x + 4,7,x,11,x - 2,13,x[] 438,5,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x + 2[] 438,6,2,x - 1,3,x - 1,5,x,7,x - 2,11,x,13,x + 4[] 438,7,2,x - 1,3,x - 1,5,x,7,x + 2,11,x - 4,13,x - 4[] 438,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 + 4*x + 4,13,x^2 - 8*x + 8[] 438,9,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 4*x + 4,11,x^2 - 2*x - 4,13,x^2 - 6*x + 4[] 439,1,2,x^2 + 2*x + 1,3,x^2 - x - 1,5,x^2 - x - 1,7,x^2 + 4*x + 4,11,x^2 - 2*x - 4,13,x^2 + 3*x - 9[] 439,2,2,x^9 + x^8 - 12*x^7 - 6*x^6 + 49*x^5 - x^4 - 72*x^3 + 30*x^2 + 18*x - 9,3,x^9 + 4*x^8 - 2*x^7 - 22*x^6 - 10*x^5 + 32*x^4 + 20*x^3 - 10*x^2 - 3*x + 1,5,x^9 + 12*x^8 + 48*x^7 + 41*x^6 - 184*x^5 - 370*x^4 + 161*x^3 + 676*x^2 + 17*x - 389,7,x^9 - 28*x^7 + 5*x^6 + 231*x^5 - 151*x^4 - 594*x^3 + 645*x^2 - 27*x - 9,11,x^9 + 18*x^8 + 121*x^7 + 364*x^6 + 398*x^5 - 237*x^4 - 718*x^3 - 267*x^2 + 84*x + 37,13,x^9 - 2*x^8 - 42*x^7 + 100*x^6 + 442*x^5 - 997*x^4 - 1276*x^3 + 1828*x^2 + 868*x - 823[] 439,3,2,x^25 - 4*x^24 - 31*x^23 + 138*x^22 + 389*x^21 - 2034*x^20 - 2453*x^19 + 16766*x^18 + 7126*x^17 - 84887*x^16 + 1717*x^15 + 272618*x^14 - 79978*x^13 - 552928*x^12 + 255108*x^11 + 682589*x^10 - 376568*x^9 - 476301*x^8 + 270078*x^7 + 167567*x^6 - 81530*x^5 - 24739*x^4 + 6834*x^3 + 740*x^2 - 187*x + 5,3,x^25 - 3*x^24 - 59*x^23 + 180*x^22 + 1494*x^21 - 4658*x^20 - 21258*x^19 + 68240*x^18 + 186855*x^17 - 624866*x^16 - 1049494*x^15 + 3727909*x^14 + 3753610*x^13 - 14662056*x^12 - 8177104*x^11 + 37658528*x^10 + 9484576*x^9 - 61320448*x^8 - 2806912*x^7 + 59945728*x^6 - 5250560*x^5 - 31844352*x^4 + 5380096*x^3 + 7204864*x^2 - 1499136*x - 147456,5,x^25 - 15*x^24 + 30*x^23 + 604*x^22 - 3172*x^21 - 6786*x^20 + 78027*x^19 - 41625*x^18 - 905630*x^17 + 1695144*x^16 + 5338268*x^15 - 17310085*x^14 - 12108693*x^13 + 88929934*x^12 - 29524632*x^11 - 241700856*x^10 + 243645796*x^9 + 292676933*x^8 - 544530625*x^7 + 6259017*x^6 + 436474070*x^5 - 248916049*x^4 - 12779742*x^3 + 41632573*x^2 - 9162616*x + 377804,7,x^25 - 105*x^23 + 45*x^22 + 4725*x^21 - 3988*x^20 - 119042*x^19 + 147722*x^18 + 1837131*x^17 - 2989605*x^16 - 17816646*x^15 + 36211344*x^14 + 106565798*x^13 - 270164455*x^12 - 362278764*x^11 + 1231717441*x^10 + 517244602*x^9 - 3296794753*x^8 + 439878167*x^7 + 4783749693*x^6 - 2280863566*x^5 - 3210917657*x^4 + 2290198335*x^3 + 650761693*x^2 - 705120364*x + 87118028,11,x^25 - 24*x^24 + 124*x^23 + 1490*x^22 - 18593*x^21 + 17289*x^20 + 689967*x^19 - 3299178*x^18 - 5932965*x^17 + 87626128*x^16 - 168743742*x^15 - 695091746*x^14 + 3712353144*x^13 - 3530958885*x^12 - 16822456635*x^11 + 58054450667*x^10 - 60404970235*x^9 - 41347391882*x^8 + 176320147638*x^7 - 184928168301*x^6 + 65262520376*x^5 + 24682368471*x^4 - 23786089638*x^3 + 2069636251*x^2 + 1553679254*x - 50693164,13,x^25 - x^24 - 178*x^23 + 107*x^22 + 13573*x^21 - 2481*x^20 - 579935*x^19 - 147942*x^18 + 15220868*x^17 + 10829523*x^16 - 252158087*x^15 - 299172875*x^14 + 2590040022*x^13 + 4386472844*x^12 - 15273730089*x^11 - 35295225048*x^10 + 41401147127*x^9 + 145015590316*x^8 - 7591949171*x^7 - 255305231378*x^6 - 105555649063*x^5 + 177347525591*x^4 + 111323734500*x^3 - 34356348688*x^2 - 28624753632*x - 2786136752[] 440,1,2,x,3,x,5,x + 1,7,x + 2,11,x + 1,13,x[] 440,2,2,x,3,x,5,x - 1,7,x - 4,11,x + 1,13,x - 6[] 440,3,2,x,3,x - 3,5,x - 1,7,x - 1,11,x + 1,13,x + 6[] 440,4,2,x,3,x,5,x + 1,7,x + 2,11,x - 1,13,x + 4[] 440,5,2,x^2,3,x^2 - x - 4,5,x^2 + 2*x + 1,7,x^2 - 3*x - 2,11,x^2 - 2*x + 1,13,x^2 - 2*x - 16[] 440,6,2,x^2,3,x^2 - x - 4,5,x^2 + 2*x + 1,7,x^2 - 5*x + 2,11,x^2 + 2*x + 1,13,x^2 - 6*x - 8[] 440,7,2,x^2,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + x - 4,11,x^2 - 2*x + 1,13,x^2 - 4*x + 4[] Total time: 19.090 seconds, Total memory usage: 6.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:22:12 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [440..443] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:21:53 on modular [Seed = 3443063242] ------------------------------------- 440,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 + 1,13,$.1[] 440,2,2,$.1,3,$.1,5,$.1 - 1,7,$.1 - 4,11,$.1 + 1,13,$.1 - 6[] 440,3,2,$.1,3,$.1 - 3,5,$.1 - 1,7,$.1 - 1,11,$.1 + 1,13,$.1 + 6[] 440,4,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 - 1,13,$.1 + 4[] 440,5,2,$.1^2,3,$.1^2 - $.1 - 4,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 3*$.1 - 2,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 2*$.1 - 16[] 440,6,2,$.1^2,3,$.1^2 - $.1 - 4,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 5*$.1 + 2,11,$.1^2 + 2*$.1 + 1,13,$.1^2 - 6*$.1 - 8[] 440,7,2,$.1^2,3,$.1^2 + $.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 + $.1 - 4,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 + 4[] 441,1,2,x,3,x,5,x,7,x,11,x,13,x + 7[] 441,2,2,x,3,x,5,x,7,x,11,x,13,x - 7[] 441,3,2,x + 2,3,x,5,x - 2,7,x,11,x - 2,13,x - 1[] 441,4,2,x - 1,3,x,5,x + 2,7,x,11,x + 4,13,x - 2[] 441,5,2,x + 1,3,x,5,x,7,x,11,x + 4,13,x[] 441,6,2,x + 2,3,x,5,x + 2,7,x,11,x - 2,13,x + 1[] 441,7,2,x^2 - 7,3,x^2,5,x^2,7,x^2,11,x^2 - 28,13,x^2[] 441,8,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2,11,x^2 - 12,13,x^2 + 4*x + 4[] 441,9,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 4*x + 2,7,x^2,11,x^2 - 4*x + 4,13,x^2 + 8*x + 14[] 441,10,2,x^2 - 2*x - 1,3,x^2,5,x^2 + 4*x + 2,7,x^2,11,x^2 - 4*x + 4,13,x^2 - 8*x + 14[] 442,1,2,x + 1,3,x - 2,5,x - 2,7,x - 2,11,x - 2,13,x + 1[] 442,2,2,x - 1,3,x,5,x - 2,7,x - 4,11,x + 2,13,x + 1[] 442,3,2,x - 1,3,x - 2,5,x + 2,7,x - 2,11,x - 4,13,x + 1[] 442,4,2,x - 1,3,x - 2,5,x - 4,7,x + 4,11,x + 2,13,x + 1[] 442,5,2,x - 1,3,x,5,x + 4,7,x + 2,11,x + 2,13,x + 1[] 442,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 4,5,x^2 - 4*x + 4,7,x^2 + 2*x - 4,11,x^2 - 2*x - 4,13,x^2 - 2*x + 1[] 442,7,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 - 2,7,x^2 - 8,11,x^2 + 4*x - 4,13,x^2 - 2*x + 1[] 442,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 4*x^2 - 4*x - 20,7,x^3 - 16*x - 16,11,x^3 + 2*x^2 - 20*x - 8,13,x^3 + 3*x^2 + 3*x + 1[] 442,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 6*x + 8,5,x^3 - 4*x^2 - 2*x + 4,7,x^3,11,x^3 + 4*x^2 - 12*x - 16,13,x^3 - 3*x^2 + 3*x - 1[] 443,1,2,x,3,x - 1,5,x + 2,7,x - 2,11,x + 2,13,x + 3[] 443,2,2,x + 1,3,x + 2,5,x,7,x - 1,11,x - 3,13,x - 3[] 443,3,2,x - 1,3,x + 2,5,x - 4,7,x + 1,11,x - 5,13,x - 3[] 443,4,2,x^12 + 3*x^11 - 13*x^10 - 39*x^9 + 64*x^8 + 181*x^7 - 159*x^6 - 357*x^5 + 226*x^4 + 264*x^3 - 156*x^2 - 20*x + 6,3,x^12 + 7*x^11 + 2*x^10 - 78*x^9 - 124*x^8 + 233*x^7 + 550*x^6 - 102*x^5 - 652*x^4 - 190*x^3 + 90*x^2 + 34*x + 1,5,x^12 + 7*x^11 - 6*x^10 - 125*x^9 - 112*x^8 + 748*x^7 + 1161*x^6 - 1633*x^5 - 3454*x^4 + 648*x^3 + 3100*x^2 + 872*x + 56,7,x^12 + 16*x^11 + 82*x^10 + x^9 - 1576*x^8 - 6340*x^7 - 9454*x^6 + 1337*x^5 + 21270*x^4 + 20898*x^3 - 2376*x^2 - 13390*x - 5422,11,x^12 + 2*x^11 - 74*x^10 - 87*x^9 + 1927*x^8 + 1329*x^7 - 21068*x^6 - 13751*x^5 + 99640*x^4 + 84998*x^3 - 158154*x^2 - 203154*x - 59638,13,x^12 + 42*x^11 + 762*x^10 + 7742*x^9 + 47304*x^8 + 168507*x^7 + 264154*x^6 - 337744*x^5 - 2278142*x^4 - 3598919*x^3 - 1085318*x^2 + 1942180*x + 773943[] 443,5,2,x^22 - x^21 - 35*x^20 + 33*x^19 + 523*x^18 - 456*x^17 - 4360*x^16 + 3428*x^15 + 22226*x^14 - 15227*x^13 - 71363*x^12 + 40569*x^11 + 143034*x^10 - 62774*x^9 - 170342*x^8 + 51992*x^7 + 107186*x^6 - 20952*x^5 - 26926*x^4 + 5536*x^3 + 1736*x^2 - 512*x + 32,3,x^22 - 8*x^21 - 13*x^20 + 258*x^19 - 277*x^18 - 3152*x^17 + 7158*x^16 + 17518*x^15 - 62601*x^14 - 35125*x^13 + 273049*x^12 - 60648*x^11 - 639542*x^10 + 402011*x^9 + 820812*x^8 - 728657*x^7 - 555145*x^6 + 619866*x^5 + 160811*x^4 - 249823*x^3 + 3908*x^2 + 38492*x - 7505,5,x^22 - 3*x^21 - 62*x^20 + 193*x^19 + 1562*x^18 - 5048*x^17 - 20653*x^16 + 69697*x^15 + 154300*x^14 - 552410*x^13 - 648452*x^12 + 2567944*x^11 + 1370328*x^10 - 6881208*x^9 - 614072*x^8 + 9965872*x^7 - 2725408*x^6 - 6560320*x^5 + 4087552*x^4 + 727808*x^3 - 1277440*x^2 + 390144*x - 38912,7,x^22 - 12*x^21 - 24*x^20 + 825*x^19 - 1772*x^18 - 19756*x^17 + 88784*x^16 + 142763*x^15 - 1495800*x^14 + 1469332*x^13 + 9596562*x^12 - 27509624*x^11 + 1698414*x^10 + 104417834*x^9 - 189450790*x^8 + 104780356*x^7 + 88456536*x^6 - 180546416*x^5 + 124019648*x^4 - 41346880*x^3 + 5686400*x^2 + 61696*x - 48640,11,x^22 + 8*x^21 - 96*x^20 - 933*x^19 + 3101*x^18 + 44511*x^17 - 16118*x^16 - 1104161*x^15 - 1373092*x^14 + 14729830*x^13 + 36493070*x^12 - 92480016*x^11 - 387038572*x^10 + 69217042*x^9 + 1754528290*x^8 + 1648843156*x^7 - 2136261664*x^6 - 3633649248*x^5 + 105667456*x^4 + 1839810752*x^3 + 38525440*x^2 - 367278080*x + 62244352,13,x^22 - 49*x^21 + 1016*x^20 - 11182*x^19 + 62717*x^18 - 56731*x^17 - 1542348*x^16 + 9370609*x^15 - 12788700*x^14 - 82568456*x^13 + 374413256*x^12 - 228088937*x^11 - 1905863180*x^10 + 4362711726*x^9 + 406458928*x^8 - 11366848236*x^7 + 11182610208*x^6 + 483761322*x^5 - 3479002043*x^4 + 150563134*x^3 + 271225542*x^2 + 19429200*x - 1076517[] Total time: 18.000 seconds, Total memory usage: 5.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:28:46 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [443..446] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:28:30 on modular [Seed = 4245212789] ------------------------------------- 443,1,2,$.1,3,$.1 - 1,5,$.1 + 2,7,$.1 - 2,11,$.1 + 2,13,$.1 + 3[] 443,2,2,$.1 + 1,3,$.1 + 2,5,$.1,7,$.1 - 1,11,$.1 - 3,13,$.1 - 3[] 443,3,2,$.1 - 1,3,$.1 + 2,5,$.1 - 4,7,$.1 + 1,11,$.1 - 5,13,$.1 - 3[] 443,4,2,$.1^12 + 3*$.1^11 - 13*$.1^10 - 39*$.1^9 + 64*$.1^8 + 181*$.1^7 - 159*$.1^6 - 357*$.1^5 + 226*$.1^4 + 264*$.1^3 - 156*$.1^2 - 20*$.1 + 6,3,$.1^12 + 7*$.1^11 + 2*$.1^10 - 78*$.1^9 - 124*$.1^8 + 233*$.1^7 + 550*$.1^6 - 102*$.1^5 - 652*$.1^4 - 190*$.1^3 + 90*$.1^2 + 34*$.1 + 1,5,$.1^12 + 7*$.1^11 - 6*$.1^10 - 125*$.1^9 - 112*$.1^8 + 748*$.1^7 + 1161*$.1^6 - 1633*$.1^5 - 3454*$.1^4 + 648*$.1^3 + 3100*$.1^2 + 872*$.1 + 56,7,$.1^12 + 16*$.1^11 + 82*$.1^10 + $.1^9 - 1576*$.1^8 - 6340*$.1^7 - 9454*$.1^6 + 1337*$.1^5 + 21270*$.1^4 + 20898*$.1^3 - 2376*$.1^2 - 13390*$.1 - 5422,11,$.1^12 + 2*$.1^11 - 74*$.1^10 - 87*$.1^9 + 1927*$.1^8 + 1329*$.1^7 - 21068*$.1^6 - 13751*$.1^5 + 99640*$.1^4 + 84998*$.1^3 - 158154*$.1^2 - 203154*$.1 - 59638,13,$.1^12 + 42*$.1^11 + 762*$.1^10 + 7742*$.1^9 + 47304*$.1^8 + 168507*$.1^7 + 264154*$.1^6 - 337744*$.1^5 - 2278142*$.1^4 - 3598919*$.1^3 - 1085318*$.1^2 + 1942180*$.1 + 773943[] 443,5,2,$.1^22 - $.1^21 - 35*$.1^20 + 33*$.1^19 + 523*$.1^18 - 456*$.1^17 - 4360*$.1^16 + 3428*$.1^15 + 22226*$.1^14 - 15227*$.1^13 - 71363*$.1^12 + 40569*$.1^11 + 143034*$.1^10 - 62774*$.1^9 - 170342*$.1^8 + 51992*$.1^7 + 107186*$.1^6 - 20952*$.1^5 - 26926*$.1^4 + 5536*$.1^3 + 1736*$.1^2 - 512*$.1 + 32,3,$.1^22 - 8*$.1^21 - 13*$.1^20 + 258*$.1^19 - 277*$.1^18 - 3152*$.1^17 + 7158*$.1^16 + 17518*$.1^15 - 62601*$.1^14 - 35125*$.1^13 + 273049*$.1^12 - 60648*$.1^11 - 639542*$.1^10 + 402011*$.1^9 + 820812*$.1^8 - 728657*$.1^7 - 555145*$.1^6 + 619866*$.1^5 + 160811*$.1^4 - 249823*$.1^3 + 3908*$.1^2 + 38492*$.1 - 7505,5,$.1^22 - 3*$.1^21 - 62*$.1^20 + 193*$.1^19 + 1562*$.1^18 - 5048*$.1^17 - 20653*$.1^16 + 69697*$.1^15 + 154300*$.1^14 - 552410*$.1^13 - 648452*$.1^12 + 2567944*$.1^11 + 1370328*$.1^10 - 6881208*$.1^9 - 614072*$.1^8 + 9965872*$.1^7 - 2725408*$.1^6 - 6560320*$.1^5 + 4087552*$.1^4 + 727808*$.1^3 - 1277440*$.1^2 + 390144*$.1 - 38912,7,$.1^22 - 12*$.1^21 - 24*$.1^20 + 825*$.1^19 - 1772*$.1^18 - 19756*$.1^17 + 88784*$.1^16 + 142763*$.1^15 - 1495800*$.1^14 + 1469332*$.1^13 + 9596562*$.1^12 - 27509624*$.1^11 + 1698414*$.1^10 + 104417834*$.1^9 - 189450790*$.1^8 + 104780356*$.1^7 + 88456536*$.1^6 - 180546416*$.1^5 + 124019648*$.1^4 - 41346880*$.1^3 + 5686400*$.1^2 + 61696*$.1 - 48640,11,$.1^22 + 8*$.1^21 - 96*$.1^20 - 933*$.1^19 + 3101*$.1^18 + 44511*$.1^17 - 16118*$.1^16 - 1104161*$.1^15 - 1373092*$.1^14 + 14729830*$.1^13 + 36493070*$.1^12 - 92480016*$.1^11 - 387038572*$.1^10 + 69217042*$.1^9 + 1754528290*$.1^8 + 1648843156*$.1^7 - 2136261664*$.1^6 - 3633649248*$.1^5 + 105667456*$.1^4 + 1839810752*$.1^3 + 38525440*$.1^2 - 367278080*$.1 + 62244352,13,$.1^22 - 49*$.1^21 + 1016*$.1^20 - 11182*$.1^19 + 62717*$.1^18 - 56731*$.1^17 - 1542348*$.1^16 + 9370609*$.1^15 - 12788700*$.1^14 - 82568456*$.1^13 + 374413256*$.1^12 - 228088937*$.1^11 - 1905863180*$.1^10 + 4362711726*$.1^9 + 406458928*$.1^8 - 11366848236*$.1^7 + 11182610208*$.1^6 + 483761322*$.1^5 - 3479002043*$.1^4 + 150563134*$.1^3 + 271225542*$.1^2 + 19429200*$.1 - 1076517[] 444,1,2,x,3,x + 1,5,x,7,x,11,x - 4,13,x + 2[] 444,2,2,x,3,x - 1,5,x + 2,7,x + 4,11,x + 4,13,x + 6[] 444,3,2,x^2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 - 12,11,x^2 + 8*x + 16,13,x^2 - 12[] 444,4,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 6,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 4*x - 20[] 445,1,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x + 1,7,x^2 - 2*x - 4,11,x^2 + 4*x - 16,13,x^2 - 4*x - 16[] 445,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 + 2*x - 2,11,x^2,13,x^2 - 4*x + 4[] 445,3,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 2,11,x^2 - 8*x + 16,13,x^2 - 4*x - 4[] 445,4,2,x^4 - x^3 - 5*x^2 + 7*x - 1,3,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 2*x^3 - 12*x^2 + 18*x + 11,11,x^4 + 14*x^3 + 70*x^2 + 147*x + 109,13,x^4 + 5*x^3 - 14*x^2 - 10*x + 19[] 445,5,2,x^4 - x^3 - 5*x^2 + 5*x + 1,3,x^4 - 4*x^3 - 2*x^2 + 21*x - 17,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 12*x^3 + 54*x^2 - 108*x + 81,11,x^4 - 2*x^3 - 14*x^2 + 19*x + 13,13,x^4 + 7*x^3 - 58*x - 47[] 445,6,2,x^7 + 4*x^6 - 3*x^5 - 24*x^4 - 8*x^3 + 29*x^2 + 6*x - 9,3,x^7 + 8*x^6 + 16*x^5 - 19*x^4 - 89*x^3 - 72*x^2 - 8*x + 4,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 16*x^6 + 94*x^5 + 236*x^4 + 189*x^3 - 96*x^2 - 76*x + 4,11,x^7 + 10*x^6 + 14*x^5 - 149*x^4 - 639*x^3 - 968*x^2 - 608*x - 128,13,x^7 + 7*x^6 - 44*x^5 - 378*x^4 - 67*x^3 + 4078*x^2 + 9196*x + 5816[] 445,7,2,x^8 - x^7 - 11*x^6 + 9*x^5 + 34*x^4 - 19*x^3 - 27*x^2 + 11*x - 1,3,x^8 - 6*x^7 + 53*x^5 - 63*x^4 - 100*x^3 + 172*x^2 - 12*x - 44,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 6*x^7 - 12*x^6 - 102*x^5 + 11*x^4 + 536*x^3 + 244*x^2 - 856*x - 676,11,x^8 - 14*x^7 + 50*x^6 + 75*x^5 - 599*x^4 + 112*x^3 + 2192*x^2 - 704*x - 2752,13,x^8 + 7*x^7 - 40*x^6 - 270*x^5 + 475*x^4 + 2144*x^3 - 3408*x^2 + 1024*x - 64[] 446,1,2,x + 1,3,x + 1,5,x,7,x,11,x - 1,13,x + 2[] 446,2,2,x + 1,3,x + 3,5,x + 4,7,x + 4,11,x + 5,13,x + 6[] 446,3,2,x - 1,3,x - 2,5,x,7,x,11,x + 2,13,x - 4[] 446,4,2,x - 1,3,x + 1,5,x + 2,7,x + 2,11,x + 3,13,x[] 446,5,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - x^6 - 14*x^5 + 12*x^4 + 50*x^3 - 36*x^2 - 38*x + 18,5,x^7 - 2*x^6 - 22*x^5 + 42*x^4 + 92*x^3 - 256*x^2 + 174*x - 36,7,x^7 - 6*x^6 - 8*x^5 + 88*x^4 - 48*x^3 - 224*x^2 + 80*x + 96,11,x^7 - 9*x^6 - 14*x^5 + 254*x^4 - 58*x^3 - 2028*x^2 + 394*x + 3494,13,x^7 + 2*x^6 - 64*x^5 - 78*x^4 + 1360*x^3 + 416*x^2 - 9602*x + 7056[] 446,6,2,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,3,x^8 - 4*x^7 - 12*x^6 + 54*x^5 + 34*x^4 - 204*x^3 + 6*x^2 + 160*x + 34,5,x^8 - 4*x^7 - 24*x^6 + 106*x^5 + 130*x^4 - 788*x^3 + 98*x^2 + 1596*x - 942,7,x^8 - 4*x^7 - 40*x^6 + 176*x^5 + 456*x^4 - 2512*x^3 - 496*x^2 + 11712*x - 11312,11,x^8 - 2*x^7 - 50*x^6 + 122*x^5 + 650*x^4 - 1932*x^3 - 666*x^2 + 3600*x - 126,13,x^8 - 10*x^7 - 10*x^6 + 298*x^5 - 342*x^4 - 2048*x^3 + 3682*x^2 - 612*x - 942[] Total time: 16.010 seconds, Total memory usage: 5.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:33:47 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [446..449] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:33:32 on modular [Seed = 367011788] ------------------------------------- 446,1,2,$.1 + 1,3,$.1 + 1,5,$.1,7,$.1,11,$.1 - 1,13,$.1 + 2[] 446,2,2,$.1 + 1,3,$.1 + 3,5,$.1 + 4,7,$.1 + 4,11,$.1 + 5,13,$.1 + 6[] 446,3,2,$.1 - 1,3,$.1 - 2,5,$.1,7,$.1,11,$.1 + 2,13,$.1 - 4[] 446,4,2,$.1 - 1,3,$.1 + 1,5,$.1 + 2,7,$.1 + 2,11,$.1 + 3,13,$.1[] 446,5,2,$.1^7 - 7*$.1^6 + 21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1,3,$.1^7 - $.1^6 - 14*$.1^5 + 12*$.1^4 + 50*$.1^3 - 36*$.1^2 - 38*$.1 + 18,5,$.1^7 - 2*$.1^6 - 22*$.1^5 + 42*$.1^4 + 92*$.1^3 - 256*$.1^2 + 174*$.1 - 36,7,$.1^7 - 6*$.1^6 - 8*$.1^5 + 88*$.1^4 - 48*$.1^3 - 224*$.1^2 + 80*$.1 + 96,11,$.1^7 - 9*$.1^6 - 14*$.1^5 + 254*$.1^4 - 58*$.1^3 - 2028*$.1^2 + 394*$.1 + 3494,13,$.1^7 + 2*$.1^6 - 64*$.1^5 - 78*$.1^4 + 1360*$.1^3 + 416*$.1^2 - 9602*$.1 + 7056[] 446,6,2,$.1^8 + 8*$.1^7 + 28*$.1^6 + 56*$.1^5 + 70*$.1^4 + 56*$.1^3 + 28*$.1^2 + 8*$.1 + 1,3,$.1^8 - 4*$.1^7 - 12*$.1^6 + 54*$.1^5 + 34*$.1^4 - 204*$.1^3 + 6*$.1^2 + 160*$.1 + 34,5,$.1^8 - 4*$.1^7 - 24*$.1^6 + 106*$.1^5 + 130*$.1^4 - 788*$.1^3 + 98*$.1^2 + 1596*$.1 - 942,7,$.1^8 - 4*$.1^7 - 40*$.1^6 + 176*$.1^5 + 456*$.1^4 - 2512*$.1^3 - 496*$.1^2 + 11712*$.1 - 11312,11,$.1^8 - 2*$.1^7 - 50*$.1^6 + 122*$.1^5 + 650*$.1^4 - 1932*$.1^3 - 666*$.1^2 + 3600*$.1 - 126,13,$.1^8 - 10*$.1^7 - 10*$.1^6 + 298*$.1^5 - 342*$.1^4 - 2048*$.1^3 + 3682*$.1^2 - 612*$.1 - 942[] 447,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3,7,x^3 + 3*x^2 - 4*x - 13,11,x^3 - 3*x^2 - 4*x - 1,13,x^3 + 8*x^2 + 12*x - 8[] 447,2,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 12*x + 8,7,x^3 + 3*x^2 - 1,11,x^3 + 9*x^2 + 18*x + 9,13,x^3 - 12*x + 8[] 447,3,2,x^9 - 4*x^8 - 6*x^7 + 37*x^6 - 3*x^5 - 101*x^4 + 49*x^3 + 72*x^2 - 21*x - 13,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 - 8*x^8 + 2*x^7 + 120*x^6 - 256*x^5 - 224*x^4 + 1160*x^3 - 1216*x^2 + 480*x - 64,7,x^9 - x^8 - 29*x^7 + 32*x^6 + 222*x^5 - 293*x^4 - 313*x^3 + 435*x^2 - 144*x + 13,11,x^9 - 13*x^8 + 25*x^7 + 278*x^6 - 1046*x^5 - 1341*x^4 + 8767*x^3 - 3407*x^2 - 18734*x + 17707,13,x^9 + 2*x^8 - 68*x^7 - 72*x^6 + 1756*x^5 + 216*x^4 - 20008*x^3 + 14000*x^2 + 81472*x - 106688[] 447,4,2,x^10 - 3*x^9 - 12*x^8 + 37*x^7 + 44*x^6 - 142*x^5 - 50*x^4 + 181*x^3 - 5*x^2 - 30*x + 1,3,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1,5,x^10 - 4*x^9 - 34*x^8 + 132*x^7 + 392*x^6 - 1440*x^5 - 1848*x^4 + 5904*x^3 + 3488*x^2 - 6784*x - 2944,7,x^10 - 9*x^9 - 9*x^8 + 252*x^7 - 246*x^6 - 2289*x^5 + 3135*x^4 + 7363*x^3 - 8580*x^2 - 3231*x - 88,11,x^10 + 7*x^9 - 53*x^8 - 392*x^7 + 884*x^6 + 7133*x^5 - 3941*x^4 - 44019*x^3 - 15004*x^2 + 41021*x - 8900,13,x^10 - 4*x^9 - 80*x^8 + 248*x^7 + 2372*x^6 - 4632*x^5 - 31608*x^4 + 19680*x^3 + 164960*x^2 + 110144*x - 25216[] 448,1,2,x,3,x,5,x + 2,7,x + 1,11,x - 4,13,x + 2[] 448,2,2,x,3,x - 2,5,x,7,x - 1,11,x,13,x - 4[] 448,3,2,x,3,x + 2,5,x - 4,7,x - 1,11,x,13,x[] 448,4,2,x,3,x - 2,5,x,7,x + 1,11,x - 4,13,x - 4[] 448,5,2,x,3,x - 2,5,x - 4,7,x + 1,11,x,13,x[] 448,6,2,x,3,x + 2,5,x,7,x + 1,11,x,13,x - 4[] 448,7,2,x,3,x,5,x + 2,7,x - 1,11,x + 4,13,x + 2[] 448,8,2,x,3,x + 2,5,x,7,x - 1,11,x + 4,13,x - 4[] 448,9,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 2*x - 4,7,x^2 + 2*x + 1,11,x^2 + 4*x - 16,13,x^2 + 6*x + 4[] 448,10,2,x^2,3,x^2 - 2*x - 4,5,x^2 + 2*x - 4,7,x^2 - 2*x + 1,11,x^2 - 4*x - 16,13,x^2 + 6*x + 4[] 449,1,2,x^14 + 3*x^13 - 13*x^12 - 42*x^11 + 59*x^10 + 214*x^9 - 117*x^8 - 503*x^7 + 109*x^6 + 576*x^5 - 50*x^4 - 309*x^3 + 14*x^2 + 62*x - 3,3,x^14 + 5*x^13 - 11*x^12 - 84*x^11 - 4*x^10 + 452*x^9 + 260*x^8 - 1048*x^7 - 678*x^6 + 1119*x^5 + 457*x^4 - 559*x^3 - 10*x^2 + 50*x + 1,5,x^14 + 7*x^13 - 15*x^12 - 199*x^11 - 140*x^10 + 1792*x^9 + 2873*x^8 - 6770*x^7 - 15213*x^6 + 10156*x^5 + 33742*x^4 - 2190*x^3 - 30267*x^2 - 4139*x + 7679,7,x^14 + 22*x^13 + 190*x^12 + 754*x^11 + 811*x^10 - 4195*x^9 - 16603*x^8 - 20095*x^7 + 4151*x^6 + 30082*x^5 + 20539*x^4 - 3927*x^3 - 10087*x^2 - 4177*x - 567,11,x^14 + 14*x^13 + 12*x^12 - 640*x^11 - 2652*x^10 + 5733*x^9 + 48358*x^8 + 26988*x^7 - 280328*x^6 - 445385*x^5 + 389247*x^4 + 1164767*x^3 + 534702*x^2 - 79232*x - 4776,13,x^14 + 10*x^13 - 49*x^12 - 672*x^11 + 439*x^10 + 15890*x^9 + 11209*x^8 - 152535*x^7 - 224092*x^6 + 471926*x^5 + 1088176*x^4 + 371725*x^3 - 257324*x^2 - 76496*x - 1399[] 449,2,2,x^23 - 38*x^21 + x^20 + 623*x^19 - 31*x^18 - 5771*x^17 + 398*x^16 + 33229*x^15 - 2753*x^14 - 123306*x^13 + 11230*x^12 + 296022*x^11 - 28009*x^10 - 450008*x^9 + 43215*x^8 + 412760*x^7 - 40559*x^6 - 210040*x^5 + 21311*x^4 + 50781*x^3 - 5664*x^2 - 3789*x + 621,3,x^23 - 3*x^22 - 41*x^21 + 126*x^20 + 705*x^19 - 2239*x^18 - 6615*x^17 + 22000*x^16 + 36931*x^15 - 131324*x^14 - 125454*x^13 + 493823*x^12 + 253204*x^11 - 1176829*x^10 - 273386*x^9 + 1744851*x^8 + 89282*x^7 - 1530487*x^6 + 107122*x^5 + 709889*x^4 - 113406*x^3 - 130568*x^2 + 31357*x + 1052,5,x^23 - 3*x^22 - 67*x^21 + 205*x^20 + 1879*x^19 - 5847*x^18 - 28864*x^17 + 91095*x^16 + 266930*x^15 - 851395*x^14 - 1536438*x^13 + 4922437*x^12 + 5489362*x^11 - 17444495*x^10 - 11750004*x^9 + 36024274*x^8 + 13897552*x^7 - 38572189*x^6 - 7484349*x^5 + 16283982*x^4 + 563783*x^3 - 818077*x^2 - 71243*x + 46,7,x^23 - 26*x^22 + 238*x^21 - 482*x^20 - 6545*x^19 + 45377*x^18 - 30911*x^17 - 679327*x^16 + 2251007*x^15 + 2157766*x^14 - 23780381*x^13 + 25589713*x^12 + 96090845*x^11 - 241472873*x^10 - 73211795*x^9 + 769282916*x^8 - 517269912*x^7 - 912322192*x^6 + 1264824144*x^5 + 64165888*x^4 - 708731776*x^3 + 190621184*x^2 + 60660480*x + 1075200,11,x^23 - 6*x^22 - 124*x^21 + 740*x^20 + 6220*x^19 - 37467*x^18 - 161494*x^17 + 1008144*x^16 + 2308464*x^15 - 15603673*x^14 - 17920509*x^13 + 141260947*x^12 + 71700954*x^11 - 739015112*x^10 - 162391640*x^9 + 2185091808*x^8 + 465394048*x^7 - 3543357440*x^6 - 1399362304*x^5 + 2656435200*x^4 + 1817577472*x^3 - 264945664*x^2 - 439738368*x - 84639744,13,x^23 - 10*x^22 - 121*x^21 + 1584*x^20 + 4123*x^19 - 101054*x^18 + 62483*x^17 + 3334451*x^16 - 8140454*x^15 - 59666520*x^14 + 242531480*x^13 + 517488489*x^12 - 3599321598*x^11 - 494951422*x^10 + 28586733037*x^9 - 27400835882*x^8 - 111312873480*x^7 + 201107004784*x^6 + 134231844320*x^5 - 471865931584*x^4 + 162002751872*x^3 + 143643216128*x^2 - 22367896320*x - 6983520768[] Total time: 14.289 seconds, Total memory usage: 5.54MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:41:51 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [449..452] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:41:31 on modular [Seed = 234372531] ------------------------------------- 449,1,2,$.1^14 + 3*$.1^13 - 13*$.1^12 - 42*$.1^11 + 59*$.1^10 + 214*$.1^9 - 117*$.1^8 - 503*$.1^7 + 109*$.1^6 + 576*$.1^5 - 50*$.1^4 - 309*$.1^3 + 14*$.1^2 + 62*$.1 - 3,3,$.1^14 + 5*$.1^13 - 11*$.1^12 - 84*$.1^11 - 4*$.1^10 + 452*$.1^9 + 260*$.1^8 - 1048*$.1^7 - 678*$.1^6 + 1119*$.1^5 + 457*$.1^4 - 559*$.1^3 - 10*$.1^2 + 50*$.1 + 1,5,$.1^14 + 7*$.1^13 - 15*$.1^12 - 199*$.1^11 - 140*$.1^10 + 1792*$.1^9 + 2873*$.1^8 - 6770*$.1^7 - 15213*$.1^6 + 10156*$.1^5 + 33742*$.1^4 - 2190*$.1^3 - 30267*$.1^2 - 4139*$.1 + 7679,7,$.1^14 + 22*$.1^13 + 190*$.1^12 + 754*$.1^11 + 811*$.1^10 - 4195*$.1^9 - 16603*$.1^8 - 20095*$.1^7 + 4151*$.1^6 + 30082*$.1^5 + 20539*$.1^4 - 3927*$.1^3 - 10087*$.1^2 - 4177*$.1 - 567,11,$.1^14 + 14*$.1^13 + 12*$.1^12 - 640*$.1^11 - 2652*$.1^10 + 5733*$.1^9 + 48358*$.1^8 + 26988*$.1^7 - 280328*$.1^6 - 445385*$.1^5 + 389247*$.1^4 + 1164767*$.1^3 + 534702*$.1^2 - 79232*$.1 - 4776,13,$.1^14 + 10*$.1^13 - 49*$.1^12 - 672*$.1^11 + 439*$.1^10 + 15890*$.1^9 + 11209*$.1^8 - 152535*$.1^7 - 224092*$.1^6 + 471926*$.1^5 + 1088176*$.1^4 + 371725*$.1^3 - 257324*$.1^2 - 76496*$.1 - 1399[] 449,2,2,$.1^23 - 38*$.1^21 + $.1^20 + 623*$.1^19 - 31*$.1^18 - 5771*$.1^17 + 398*$.1^16 + 33229*$.1^15 - 2753*$.1^14 - 123306*$.1^13 + 11230*$.1^12 + 296022*$.1^11 - 28009*$.1^10 - 450008*$.1^9 + 43215*$.1^8 + 412760*$.1^7 - 40559*$.1^6 - 210040*$.1^5 + 21311*$.1^4 + 50781*$.1^3 - 5664*$.1^2 - 3789*$.1 + 621,3,$.1^23 - 3*$.1^22 - 41*$.1^21 + 126*$.1^20 + 705*$.1^19 - 2239*$.1^18 - 6615*$.1^17 + 22000*$.1^16 + 36931*$.1^15 - 131324*$.1^14 - 125454*$.1^13 + 493823*$.1^12 + 253204*$.1^11 - 1176829*$.1^10 - 273386*$.1^9 + 1744851*$.1^8 + 89282*$.1^7 - 1530487*$.1^6 + 107122*$.1^5 + 709889*$.1^4 - 113406*$.1^3 - 130568*$.1^2 + 31357*$.1 + 1052,5,$.1^23 - 3*$.1^22 - 67*$.1^21 + 205*$.1^20 + 1879*$.1^19 - 5847*$.1^18 - 28864*$.1^17 + 91095*$.1^16 + 266930*$.1^15 - 851395*$.1^14 - 1536438*$.1^13 + 4922437*$.1^12 + 5489362*$.1^11 - 17444495*$.1^10 - 11750004*$.1^9 + 36024274*$.1^8 + 13897552*$.1^7 - 38572189*$.1^6 - 7484349*$.1^5 + 16283982*$.1^4 + 563783*$.1^3 - 818077*$.1^2 - 71243*$.1 + 46,7,$.1^23 - 26*$.1^22 + 238*$.1^21 - 482*$.1^20 - 6545*$.1^19 + 45377*$.1^18 - 30911*$.1^17 - 679327*$.1^16 + 2251007*$.1^15 + 2157766*$.1^14 - 23780381*$.1^13 + 25589713*$.1^12 + 96090845*$.1^11 - 241472873*$.1^10 - 73211795*$.1^9 + 769282916*$.1^8 - 517269912*$.1^7 - 912322192*$.1^6 + 1264824144*$.1^5 + 64165888*$.1^4 - 708731776*$.1^3 + 190621184*$.1^2 + 60660480*$.1 + 1075200,11,$.1^23 - 6*$.1^22 - 124*$.1^21 + 740*$.1^20 + 6220*$.1^19 - 37467*$.1^18 - 161494*$.1^17 + 1008144*$.1^16 + 2308464*$.1^15 - 15603673*$.1^14 - 17920509*$.1^13 + 141260947*$.1^12 + 71700954*$.1^11 - 739015112*$.1^10 - 162391640*$.1^9 + 2185091808*$.1^8 + 465394048*$.1^7 - 3543357440*$.1^6 - 1399362304*$.1^5 + 2656435200*$.1^4 + 1817577472*$.1^3 - 264945664*$.1^2 - 439738368*$.1 - 84639744,13,$.1^23 - 10*$.1^22 - 121*$.1^21 + 1584*$.1^20 + 4123*$.1^19 - 101054*$.1^18 + 62483*$.1^17 + 3334451*$.1^16 - 8140454*$.1^15 - 59666520*$.1^14 + 242531480*$.1^13 + 517488489*$.1^12 - 3599321598*$.1^11 - 494951422*$.1^10 + 28586733037*$.1^9 - 27400835882*$.1^8 - 111312873480*$.1^7 + 201107004784*$.1^6 + 134231844320*$.1^5 - 471865931584*$.1^4 + 162002751872*$.1^3 + 143643216128*$.1^2 - 22367896320*$.1 - 6983520768[] 450,1,2,x + 1,3,x,5,x,7,x + 2,11,x + 6,13,x - 4[] 450,2,2,x + 1,3,x,5,x,7,x + 2,11,x - 3,13,x - 4[] 450,3,2,x + 1,3,x,5,x,7,x - 4,11,x,13,x + 2[] 450,4,2,x + 1,3,x,5,x,7,x + 2,11,x + 2,13,x + 6[] 450,5,2,x - 1,3,x,5,x,7,x + 2,11,x - 6,13,x - 4[] 450,6,2,x - 1,3,x,5,x,7,x - 2,11,x + 2,13,x - 6[] 450,7,2,x - 1,3,x,5,x,7,x - 2,11,x - 3,13,x + 4[] 451,1,2,x,3,x - 1,5,x + 3,7,x - 4,11,x + 1,13,x + 6[] 451,2,2,x^5 + 2*x^4 - 5*x^3 - 10*x^2 + 4*x + 9,3,x^5 + 4*x^4 + x^3 - 8*x^2 - 6*x - 1,5,x^5 + 4*x^4 - 15*x^2 - 16*x - 3,7,x^5 + 3*x^4 - 7*x^3 - 18*x^2 + 5*x + 13,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 - x^4 - 17*x^3 + 29*x^2 + 40*x - 75[] 451,3,2,x^5 + 2*x^4 - 3*x^3 - 4*x^2 + 2*x + 1,3,x^5 - 7*x^3 - 2*x^2 + 8*x - 1,5,x^5 + 8*x^4 + 12*x^3 - 27*x^2 - 36*x + 37,7,x^5 + 5*x^4 - 9*x^3 - 52*x^2 + 17*x + 97,11,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,13,x^5 + 5*x^4 - 3*x^3 - 9*x^2 + 4*x + 1[] 451,4,2,x^10 - 4*x^9 - 6*x^8 + 38*x^7 - 7*x^6 - 105*x^5 + 74*x^4 + 77*x^3 - 74*x^2 + 8,3,x^10 - 23*x^8 + 6*x^7 + 174*x^6 - 97*x^5 - 490*x^4 + 368*x^3 + 408*x^2 - 288*x - 64,5,x^10 - 6*x^9 - 14*x^8 + 118*x^7 + 49*x^6 - 774*x^5 - 141*x^4 + 2025*x^3 + 792*x^2 - 1485*x - 837,7,x^10 - 7*x^9 - 13*x^8 + 197*x^7 - 349*x^6 - 686*x^5 + 2520*x^4 - 1520*x^3 - 1308*x^2 + 838*x + 355,11,x^10 - 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1,13,x^10 - 4*x^9 - 77*x^8 + 232*x^7 + 2019*x^6 - 3811*x^5 - 22684*x^4 + 15743*x^3 + 104057*x^2 + 26432*x - 79324[] 451,5,2,x^12 - 3*x^11 - 16*x^10 + 48*x^9 + 93*x^8 - 270*x^7 - 251*x^6 + 633*x^5 + 359*x^4 - 582*x^3 - 248*x^2 + 136*x + 32,3,x^12 - x^11 - 31*x^10 + 27*x^9 + 360*x^8 - 241*x^7 - 1941*x^6 + 746*x^5 + 4752*x^4 + 8*x^3 - 3968*x^2 - 1984*x - 256,5,x^12 - 13*x^11 + 42*x^10 + 132*x^9 - 1041*x^8 + 1195*x^7 + 4687*x^6 - 13332*x^5 + 6395*x^4 + 11677*x^3 - 11562*x^2 + 833*x + 922,7,x^12 + 7*x^11 - 31*x^10 - 287*x^9 + 159*x^8 + 3946*x^7 + 2388*x^6 - 21684*x^5 - 25156*x^4 + 36136*x^3 + 62521*x^2 + 28448*x + 4096,11,x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1,13,x^12 - 99*x^10 + 78*x^9 + 3589*x^8 - 5381*x^7 - 56370*x^6 + 116503*x^5 + 339367*x^4 - 827784*x^3 - 563400*x^2 + 1526320*x + 135344[] 452,1,2,x^3,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 9*x + 9,11,x^3 - 21*x - 17,13,x^3 + 12*x^2 + 45*x + 53[] 452,2,2,x^7,3,x^7 - 3*x^6 - 12*x^5 + 33*x^4 + 40*x^3 - 98*x^2 - 16*x + 58,5,x^7 - 3*x^6 - 21*x^5 + 67*x^4 + 76*x^3 - 272*x^2 - 32*x + 240,7,x^7 - 29*x^5 + 5*x^4 + 232*x^3 - 96*x^2 - 512*x + 320,11,x^7 - 4*x^6 - 49*x^5 + 203*x^4 + 444*x^3 - 1856*x^2 - 1120*x + 4704,13,x^7 - 16*x^6 + 69*x^5 + 85*x^4 - 1124*x^3 + 1620*x^2 + 852*x - 892[] Total time: 19.920 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:46:52 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [452..455] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:46:35 on modular [Seed = 2022528950] ------------------------------------- 452,1,2,$.1^3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 - 9*$.1 + 9,11,$.1^3 - 21*$.1 - 17,13,$.1^3 + 12*$.1^2 + 45*$.1 + 53[] 452,2,2,$.1^7,3,$.1^7 - 3*$.1^6 - 12*$.1^5 + 33*$.1^4 + 40*$.1^3 - 98*$.1^2 - 16*$.1 + 58,5,$.1^7 - 3*$.1^6 - 21*$.1^5 + 67*$.1^4 + 76*$.1^3 - 272*$.1^2 - 32*$.1 + 240,7,$.1^7 - 29*$.1^5 + 5*$.1^4 + 232*$.1^3 - 96*$.1^2 - 512*$.1 + 320,11,$.1^7 - 4*$.1^6 - 49*$.1^5 + 203*$.1^4 + 444*$.1^3 - 1856*$.1^2 - 1120*$.1 + 4704,13,$.1^7 - 16*$.1^6 + 69*$.1^5 + 85*$.1^4 - 1124*$.1^3 + 1620*$.1^2 + 852*$.1 - 892[] 453,1,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 2*x + 1,11,x^2 - 4*x + 1,13,x^2 - 12[] 453,2,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 2*x + 1,11,x^2 - 6*x + 4,13,x^2 + 2*x + 1[] 453,3,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 - 3*x + 1,7,x^2 + 4*x - 1,11,x^2 - 6*x + 4,13,x^2 - 8*x + 11[] 453,4,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + x - 1,7,x^2 + 6*x + 9,11,x^2 + 6*x + 4,13,x^2 + 2*x + 1[] 453,5,2,x^3 + x^2 - 2*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 4*x - 13,7,x^3 - 2*x^2 - 8*x + 8,11,x^3 - x^2 - 16*x + 29,13,x^3 + 4*x^2 - 4*x - 8[] 453,6,2,x^5 + 3*x^4 - 6*x^3 - 18*x^2 + 8*x + 19,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 4*x^4 - 8*x^3 - 32*x^2 + 11*x + 49,7,x^5 + 6*x^4 - 9*x^3 - 90*x^2 - 40*x + 200,11,x^5 + 17*x^4 + 98*x^3 + 183*x^2 - 150*x - 580,13,x^5 - 4*x^4 - 45*x^3 + 164*x^2 + 480*x - 1600[] 453,7,2,x^9 - 6*x^8 + 3*x^7 + 42*x^6 - 68*x^5 - 62*x^4 + 168*x^3 - 15*x^2 - 98*x + 31,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 + 2*x^8 - 31*x^7 - 54*x^6 + 264*x^5 + 382*x^4 - 363*x^3 - 354*x^2 - 36*x + 8,7,x^9 - 14*x^8 + 53*x^7 + 96*x^6 - 1140*x^5 + 2688*x^4 - 1696*x^3 - 1664*x^2 + 2240*x - 512,11,x^9 - 2*x^8 - 46*x^7 + 86*x^6 + 193*x^5 - 124*x^4 - 193*x^3 + 36*x^2 + 43*x + 4,13,x^9 + 2*x^8 - 64*x^7 - 24*x^6 + 1376*x^5 - 1472*x^4 - 8768*x^3 + 21248*x^2 - 16384*x + 4096[] 454,1,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 2*x - 4,7,x^2 + 5*x + 5,11,x^2 + 9*x + 19,13,x^2 - 2*x - 4[] 454,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 3*x^2 - 2*x + 1,5,x^4 + 4*x^3 - 2*x^2 - 16*x - 4,7,x^4 - 2*x^3 - 13*x^2 + 14*x - 1,11,x^4 + 10*x^3 + 33*x^2 + 42*x + 17,13,x^4 + 4*x^3 - 24*x^2 - 24*x - 4[] 454,3,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + x^4 - 11*x^3 - 8*x^2 + 28*x + 8,5,x^5 - 3*x^4 - 8*x^3 + 23*x^2 + 4*x - 4,7,x^5 + 6*x^4 - 4*x^3 - 48*x^2 - 3*x + 19,11,x^5 - 7*x^4 + x^3 + 30*x^2 + 12*x - 8,13,x^5 - 3*x^4 - 32*x^3 + 11*x^2 + 54*x - 4[] 454,4,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - 4*x^6 - 9*x^5 + 48*x^4 - 11*x^3 - 92*x^2 + 28*x + 56,5,x^7 + x^6 - 20*x^5 - 9*x^4 + 86*x^3 - 10*x^2 - 52*x - 4,7,x^7 - 5*x^6 - 5*x^5 + 54*x^4 - 57*x^3 - 30*x^2 + 36*x - 7,11,x^7 - 10*x^6 - x^5 + 266*x^4 - 663*x^3 - 798*x^2 + 4076*x - 3304,13,x^7 + 5*x^6 - 30*x^5 - 231*x^4 - 480*x^3 - 352*x^2 - 72*x - 4[] 455,1,2,x - 1,3,x,5,x + 1,7,x + 1,11,x,13,x + 1[] 455,2,2,x + 1,3,x,5,x - 1,7,x + 1,11,x,13,x - 1[] 455,3,2,x^4 + x^3 - 5*x^2 - 3*x + 1,3,x^4 - 9*x^2 + 2*x + 11,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 - 2*x^3 - 32*x^2 + 112*x - 80,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 455,4,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 4*x^3 - x^2 + 14*x - 9,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 + 2*x^3 - 32*x^2 - 80*x - 48,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 455,5,2,x^6 - 3*x^5 - 6*x^4 + 20*x^3 + 6*x^2 - 31*x + 9,3,x^6 - 13*x^4 + 2*x^3 + 35*x^2 + 4*x - 8,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 + 2*x^5 - 40*x^4 - 80*x^3 + 368*x^2 + 448*x - 1152,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 455,6,2,x^7 - 15*x^5 + 2*x^4 + 66*x^3 - 17*x^2 - 72*x + 19,3,x^7 - 21*x^5 + 2*x^4 + 127*x^3 - 16*x^2 - 184*x - 80,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,11,x^7 - 6*x^6 - 48*x^5 + 320*x^4 + 368*x^3 - 3712*x^2 + 2432*x + 256,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] Total time: 16.750 seconds, Total memory usage: 5.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:52:29 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [455..458] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:52:10 on modular [Seed = 1788823381] ------------------------------------- 455,1,2,$.1 - 1,3,$.1,5,$.1 + 1,7,$.1 + 1,11,$.1,13,$.1 + 1[] 455,2,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1,13,$.1 - 1[] 455,3,2,$.1^4 + $.1^3 - 5*$.1^2 - 3*$.1 + 1,3,$.1^4 - 9*$.1^2 + 2*$.1 + 11,5,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,11,$.1^4 - 2*$.1^3 - 32*$.1^2 + 112*$.1 - 80,13,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1[] 455,4,2,$.1^4 - 3*$.1^3 - $.1^2 + 5*$.1 + 1,3,$.1^4 - 4*$.1^3 - $.1^2 + 14*$.1 - 9,5,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,11,$.1^4 + 2*$.1^3 - 32*$.1^2 - 80*$.1 - 48,13,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1[] 455,5,2,$.1^6 - 3*$.1^5 - 6*$.1^4 + 20*$.1^3 + 6*$.1^2 - 31*$.1 + 9,3,$.1^6 - 13*$.1^4 + 2*$.1^3 + 35*$.1^2 + 4*$.1 - 8,5,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1,7,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1,11,$.1^6 + 2*$.1^5 - 40*$.1^4 - 80*$.1^3 + 368*$.1^2 + 448*$.1 - 1152,13,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1[] 455,6,2,$.1^7 - 15*$.1^5 + 2*$.1^4 + 66*$.1^3 - 17*$.1^2 - 72*$.1 + 19,3,$.1^7 - 21*$.1^5 + 2*$.1^4 + 127*$.1^3 - 16*$.1^2 - 184*$.1 - 80,5,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,7,$.1^7 - 7*$.1^6 + 21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1,11,$.1^7 - 6*$.1^6 - 48*$.1^5 + 320*$.1^4 + 368*$.1^3 - 3712*$.1^2 + 2432*$.1 + 256,13,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1[] 456,1,2,x,3,x + 1,5,x - 4,7,x - 4,11,x + 4,13,x + 4[] 456,2,2,x,3,x - 1,5,x - 2,7,x,11,x,13,x - 2[] 456,3,2,x,3,x - 1,5,x + 3,7,x + 3,11,x + 1,13,x + 2[] 456,4,2,x,3,x + 1,5,x - 1,7,x + 3,11,x + 5,13,x + 2[] 456,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 10,7,x^2 + 3*x - 8,11,x^2 - 3*x - 8,13,x^2 - 12*x + 36[] 456,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x + 8,13,x^2 + 2*x - 16[] 457,1,2,x^2 - x - 1,3,x^2 - x - 1,5,x^2 + 4*x + 4,7,x^2 + x - 1,11,x^2 + 10*x + 25,13,x^2 - 9*x + 19[] 457,2,2,x^15 + 10*x^14 + 27*x^13 - 43*x^12 - 324*x^11 - 310*x^10 + 917*x^9 + 1910*x^8 - 330*x^7 - 3170*x^6 - 1281*x^5 + 1917*x^4 + 1110*x^3 - 506*x^2 - 232*x + 79,3,x^15 + 12*x^14 + 41*x^13 - 53*x^12 - 629*x^11 - 1007*x^10 + 1640*x^9 + 6449*x^8 + 3861*x^7 - 7351*x^6 - 10000*x^5 - 498*x^4 + 3853*x^3 + 938*x^2 - 275*x - 7,5,x^15 + 9*x^14 - 3*x^13 - 220*x^12 - 306*x^11 + 2107*x^10 + 4204*x^9 - 9949*x^8 - 22795*x^7 + 23452*x^6 + 56696*x^5 - 22253*x^4 - 55753*x^3 - 1526*x^2 + 9110*x + 1561,7,x^15 + 15*x^14 + 44*x^13 - 384*x^12 - 2576*x^11 - 615*x^10 + 30656*x^9 + 62493*x^8 - 94313*x^7 - 359632*x^6 + 26522*x^5 + 792762*x^4 + 205877*x^3 - 757233*x^2 - 155241*x + 243999,11,x^15 - 3*x^14 - 81*x^13 + 184*x^12 + 2489*x^11 - 2926*x^10 - 38009*x^9 - 2039*x^8 + 274479*x^7 + 326299*x^6 - 543677*x^5 - 1424824*x^4 - 1022219*x^3 - 129316*x^2 + 137450*x + 42709,13,x^15 + 22*x^14 + 134*x^13 - 480*x^12 - 9388*x^11 - 35576*x^10 + 42716*x^9 + 724698*x^8 + 2107635*x^7 + 1206799*x^6 - 6877134*x^5 - 18724263*x^4 - 21377048*x^3 - 12207240*x^2 - 3224610*x - 288757[] 457,3,2,x^20 - 6*x^19 - 12*x^18 + 130*x^17 - 25*x^16 - 1135*x^15 + 1068*x^14 + 5145*x^13 - 6910*x^12 - 12965*x^11 + 21043*x^10 + 17930*x^9 - 33307*x^8 - 12486*x^7 + 25549*x^6 + 3888*x^5 - 7077*x^4 - 927*x^3 + 255*x^2 + 6*x - 1,3,x^20 - 9*x^19 + 214*x^17 - 417*x^16 - 1941*x^15 + 6028*x^14 + 7936*x^13 - 39328*x^12 - 8993*x^11 + 141030*x^10 - 42579*x^9 - 287729*x^8 + 177855*x^7 + 317230*x^6 - 269642*x^5 - 156890*x^4 + 177939*x^3 + 12672*x^2 - 42176*x + 8336,5,x^20 - 11*x^19 + 7*x^18 + 328*x^17 - 1046*x^16 - 2665*x^15 + 15558*x^14 + 1385*x^13 - 95561*x^12 + 71734*x^11 + 286142*x^10 - 331613*x^9 - 433461*x^8 + 597630*x^7 + 325064*x^6 - 466163*x^5 - 111002*x^4 + 140752*x^3 + 11056*x^2 - 9232*x - 32,7,x^20 - 8*x^19 - 38*x^18 + 437*x^17 + 128*x^16 - 8783*x^15 + 12109*x^14 + 76044*x^13 - 202104*x^12 - 201942*x^11 + 1199771*x^10 - 750096*x^9 - 2289999*x^8 + 4040094*x^7 - 1174475*x^6 - 2581213*x^5 + 2947740*x^4 - 1324351*x^3 + 281816*x^2 - 25808*x + 736,11,x^20 - 9*x^19 - 66*x^18 + 819*x^17 + 680*x^16 - 26518*x^15 + 29864*x^14 + 408361*x^13 - 867122*x^12 - 3196750*x^11 + 9189590*x^10 + 12207587*x^9 - 45833068*x^8 - 20554064*x^7 + 106973755*x^6 + 24030413*x^5 - 117010702*x^4 - 31879529*x^3 + 48557012*x^2 + 18575440*x - 923198,13,x^20 - 3*x^19 - 115*x^18 + 294*x^17 + 5278*x^16 - 11782*x^15 - 122582*x^14 + 252976*x^13 + 1518121*x^12 - 3112978*x^11 - 9712412*x^10 + 20968864*x^9 + 28564321*x^8 - 67741911*x^7 - 34086000*x^6 + 97762415*x^5 + 8431877*x^4 - 52934837*x^3 + 5096834*x^2 + 8376084*x - 1627048[] 458,1,2,x + 1,3,x + 3,5,x - 1,7,x + 2,11,x - 1,13,x - 2[] 458,2,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 1,13,x + 2[] 458,3,2,x^2 + 2*x + 1,3,x^2,5,x^2 - x - 3,7,x^2 + 3*x - 1,11,x^2 + 2*x - 12,13,x^2 + 8*x + 16[] 458,4,2,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,3,x^7 - 4*x^6 - 6*x^5 + 31*x^4 + 12*x^3 - 77*x^2 - 10*x + 59,5,x^7 - x^6 - 30*x^5 + 40*x^4 + 216*x^3 - 400*x^2 + 192,7,x^7 - 7*x^6 - 11*x^5 + 156*x^4 - 176*x^3 - 497*x^2 + 551*x + 524,11,x^7 - 6*x^6 - 12*x^5 + 57*x^4 + 76*x^3 - 107*x^2 - 144*x - 27,13,x^7 - 9*x^6 - 27*x^5 + 344*x^4 + 96*x^3 - 3199*x^2 - 535*x + 1742[] 458,5,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 - 2*x^8 - 20*x^7 + 41*x^6 + 112*x^5 - 241*x^4 - 160*x^3 + 385*x^2 + 28*x - 112,5,x^9 - 4*x^8 - 26*x^7 + 107*x^6 + 214*x^5 - 944*x^4 - 456*x^3 + 2736*x^2 - 832*x + 64,7,x^9 - 6*x^8 - 21*x^7 + 164*x^6 - 121*x^5 - 277*x^4 + 74*x^3 + 82*x^2 - 15*x - 2,11,x^9 + 6*x^8 - 50*x^7 - 317*x^6 + 678*x^5 + 4981*x^4 - 944*x^3 - 22589*x^2 - 22614*x - 4436,13,x^9 - 11*x^8 - 19*x^7 + 544*x^6 - 1144*x^5 - 5361*x^4 + 24641*x^3 - 32662*x^2 + 12432*x + 896[] Total time: 18.440 seconds, Total memory usage: 6.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:59:54 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [458..461] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:59:38 on modular [Seed = 2238753146] ------------------------------------- 458,1,2,$.1 + 1,3,$.1 + 3,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 2[] 458,2,2,$.1 - 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 4,11,$.1 + 1,13,$.1 + 2[] 458,3,2,$.1^2 + 2*$.1 + 1,3,$.1^2,5,$.1^2 - $.1 - 3,7,$.1^2 + 3*$.1 - 1,11,$.1^2 + 2*$.1 - 12,13,$.1^2 + 8*$.1 + 16[] 458,4,2,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,3,$.1^7 - 4*$.1^6 - 6*$.1^5 + 31*$.1^4 + 12*$.1^3 - 77*$.1^2 - 10*$.1 + 59,5,$.1^7 - $.1^6 - 30*$.1^5 + 40*$.1^4 + 216*$.1^3 - 400*$.1^2 + 192,7,$.1^7 - 7*$.1^6 - 11*$.1^5 + 156*$.1^4 - 176*$.1^3 - 497*$.1^2 + 551*$.1 + 524,11,$.1^7 - 6*$.1^6 - 12*$.1^5 + 57*$.1^4 + 76*$.1^3 - 107*$.1^2 - 144*$.1 - 27,13,$.1^7 - 9*$.1^6 - 27*$.1^5 + 344*$.1^4 + 96*$.1^3 - 3199*$.1^2 - 535*$.1 + 1742[] 458,5,2,$.1^9 - 9*$.1^8 + 36*$.1^7 - 84*$.1^6 + 126*$.1^5 - 126*$.1^4 + 84*$.1^3 - 36*$.1^2 + 9*$.1 - 1,3,$.1^9 - 2*$.1^8 - 20*$.1^7 + 41*$.1^6 + 112*$.1^5 - 241*$.1^4 - 160*$.1^3 + 385*$.1^2 + 28*$.1 - 112,5,$.1^9 - 4*$.1^8 - 26*$.1^7 + 107*$.1^6 + 214*$.1^5 - 944*$.1^4 - 456*$.1^3 + 2736*$.1^2 - 832*$.1 + 64,7,$.1^9 - 6*$.1^8 - 21*$.1^7 + 164*$.1^6 - 121*$.1^5 - 277*$.1^4 + 74*$.1^3 + 82*$.1^2 - 15*$.1 - 2,11,$.1^9 + 6*$.1^8 - 50*$.1^7 - 317*$.1^6 + 678*$.1^5 + 4981*$.1^4 - 944*$.1^3 - 22589*$.1^2 - 22614*$.1 - 4436,13,$.1^9 - 11*$.1^8 - 19*$.1^7 + 544*$.1^6 - 1144*$.1^5 - 5361*$.1^4 + 24641*$.1^3 - 32662*$.1^2 + 12432*$.1 + 896[] 459,1,2,x - 1,3,x,5,x + 1,7,x + 2,11,x,13,x + 5[] 459,2,2,x + 2,3,x,5,x + 4,7,x - 1,11,x - 6,13,x - 1[] 459,3,2,x,3,x,5,x - 3,7,x - 2,11,x + 3,13,x - 2[] 459,4,2,x - 2,3,x,5,x + 2,7,x - 4,11,x - 3,13,x - 7[] 459,5,2,x - 2,3,x,5,x - 4,7,x - 1,11,x + 6,13,x - 1[] 459,6,2,x,3,x,5,x + 3,7,x - 2,11,x - 3,13,x - 2[] 459,7,2,x + 2,3,x,5,x - 2,7,x - 4,11,x + 3,13,x - 7[] 459,8,2,x + 1,3,x,5,x - 1,7,x + 2,11,x,13,x + 5[] 459,9,2,x^2 - x - 1,3,x^2,5,x^2 + 3*x + 1,7,x^2 + 3*x - 9,11,x^2 + 8*x + 11,13,x^2 - 2*x - 4[] 459,10,2,x^2 + x - 1,3,x^2,5,x^2 - 3*x + 1,7,x^2 + 3*x - 9,11,x^2 - 8*x + 11,13,x^2 - 2*x - 4[] 459,11,2,x^2 - x - 3,3,x^2,5,x^2 - 5*x + 3,7,x^2 - 3*x - 1,11,x^2 - 6*x + 9,13,x^2 + 6*x - 4[] 459,12,2,x^2 + x - 3,3,x^2,5,x^2 + 5*x + 3,7,x^2 - 3*x - 1,11,x^2 + 6*x + 9,13,x^2 + 6*x - 4[] 459,13,2,x^3 + x^2 - 7*x - 9,3,x^3,5,x^3 + 3*x^2 - 5*x - 3,7,x^3 + 4*x^2 - 12*x - 36,11,x^3 + 4*x^2 - 16*x - 48,13,x^3 - x^2 - 21*x + 29[] 459,14,2,x^3 - x^2 - 7*x + 9,3,x^3,5,x^3 - 3*x^2 - 5*x + 3,7,x^3 + 4*x^2 - 12*x - 36,11,x^3 - 4*x^2 - 16*x + 48,13,x^3 - x^2 - 21*x + 29[] 460,1,2,x,3,x,5,x + 1,7,x + 1,11,x - 6,13,x - 6[] 460,2,2,x,3,x - 3,5,x + 1,7,x - 2,11,x,13,x + 3[] 460,3,2,x,3,x - 1,5,x + 1,7,x + 4,11,x + 6,13,x + 1[] 460,4,2,x,3,x + 1,5,x - 1,7,x + 2,11,x + 4,13,x - 1[] 460,5,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - x - 4,11,x^2 - 4*x + 4,13,x^2 + 3*x - 2[] 461,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x - 4,11,x^2 - 5,13,x^2 + 2*x + 1[] 461,2,2,x^3 + 2*x^2 - x - 1,3,x^3 - 7*x + 7,5,x^3 + x^2 - 9*x - 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 9*x^2 + 20*x + 13,13,x^3 + 4*x^2 - 11*x - 1[] 461,3,2,x^7 - 8*x^5 + x^4 + 18*x^3 - 2*x^2 - 12*x + 1,3,x^7 + 3*x^6 - 5*x^5 - 19*x^4 - 8*x^3 + 8*x^2 + 2*x - 1,5,x^7 + 4*x^6 - 2*x^5 - 26*x^4 - 33*x^3 - 9*x^2 + 3*x + 1,7,x^7 + 5*x^6 - 17*x^5 - 104*x^4 + 17*x^3 + 445*x^2 + 153*x - 289,11,x^7 + 7*x^6 - 10*x^5 - 119*x^4 - 170*x^3 - 48*x^2 + 17*x - 1,13,x^7 - 2*x^6 - 46*x^5 + 72*x^4 + 457*x^3 - 180*x^2 - 242*x - 43[] 461,4,2,x^26 - 3*x^25 - 41*x^24 + 126*x^23 + 726*x^22 - 2303*x^21 - 7266*x^20 + 24054*x^19 + 45144*x^18 - 158550*x^17 - 179824*x^16 + 687620*x^15 + 456511*x^14 - 1985932*x^13 - 703693*x^12 + 3785104*x^11 + 571532*x^10 - 4624305*x^9 - 111938*x^8 + 3430214*x^7 - 156745*x^6 - 1399829*x^5 + 108715*x^4 + 249906*x^3 - 21297*x^2 - 6102*x + 223,3,x^26 - 8*x^25 - 25*x^24 + 350*x^23 - 67*x^22 - 6375*x^21 + 9131*x^20 + 62591*x^19 - 142101*x^18 - 354222*x^17 + 1131262*x^16 + 1100229*x^15 - 5439111*x^14 - 1179040*x^13 + 16616042*x^12 - 3766381*x^11 - 32549826*x^10 + 16848027*x^9 + 40027314*x^8 - 29339246*x^7 - 28984472*x^6 + 26997218*x^5 + 10382911*x^4 - 12846388*x^3 - 637663*x^2 + 2482812*x - 412364,5,x^26 - x^25 - 81*x^24 + 89*x^23 + 2834*x^22 - 3337*x^21 - 56369*x^20 + 69650*x^19 + 706674*x^18 - 899724*x^17 - 5857374*x^16 + 7559751*x^15 + 32782433*x^14 - 42250384*x^13 - 124348564*x^12 + 157850099*x^11 + 315862226*x^10 - 390387594*x^9 - 520297841*x^8 + 621732909*x^7 + 519864632*x^6 - 602181344*x^5 - 272562048*x^4 + 314042258*x^3 + 48441044*x^2 - 63929748*x + 3703649,7,x^26 - 10*x^25 - 60*x^24 + 871*x^23 + 794*x^22 - 31920*x^21 + 24932*x^20 + 646295*x^19 - 1052609*x^18 - 8001190*x^17 + 17074484*x^16 + 63570421*x^15 - 155447227*x^14 - 333095634*x^13 + 860725592*x^12 + 1174538237*x^11 - 2928391388*x^10 - 2824918032*x^9 + 5914395816*x^8 + 4532213984*x^7 - 6445957683*x^6 - 4306115742*x^5 + 3059587300*x^4 + 1793364464*x^3 - 439165584*x^2 - 254287328*x - 21295936,11,x^26 - 22*x^25 + 83*x^24 + 1560*x^23 - 14351*x^22 - 13740*x^21 + 588900*x^20 - 1405048*x^19 - 9844007*x^18 + 47950725*x^17 + 50344062*x^16 - 653138686*x^15 + 502380513*x^14 + 4333954341*x^13 - 8056737769*x^12 - 12971428871*x^11 + 41885314760*x^10 + 7218265149*x^9 - 97024228874*x^8 + 35476022484*x^7 + 96414098848*x^6 - 43009973890*x^5 - 50612978091*x^4 + 12228864075*x^3 + 12784976002*x^2 + 796292595*x - 328816693,13,x^26 - 6*x^25 - 182*x^24 + 1159*x^23 + 13772*x^22 - 95371*x^21 - 560750*x^20 + 4411668*x^19 + 13010037*x^18 - 126932023*x^17 - 155796755*x^16 + 2365313943*x^15 + 222285283*x^14 - 28723004920*x^13 + 20894083248*x^12 + 221761328032*x^11 - 311581537600*x^10 - 1012055432256*x^9 + 2157421019008*x^8 + 2184332068096*x^7 - 7839979669504*x^6 + 412493474816*x^5 + 13389378247680*x^4 - 9398097330176*x^3 - 6029370896384*x^2 + 8993424179200*x - 2762166648832[] Total time: 16.299 seconds, Total memory usage: 5.93MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:21:10 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [461..464] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:20:52 on modular [Seed = 3460032831] ------------------------------------- 461,1,2,$.1^2 + $.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 5,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 5,13,$.1^2 + 2*$.1 + 1[] 461,2,2,$.1^3 + 2*$.1^2 - $.1 - 1,3,$.1^3 - 7*$.1 + 7,5,$.1^3 + $.1^2 - 9*$.1 - 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 9*$.1^2 + 20*$.1 + 13,13,$.1^3 + 4*$.1^2 - 11*$.1 - 1[] 461,3,2,$.1^7 - 8*$.1^5 + $.1^4 + 18*$.1^3 - 2*$.1^2 - 12*$.1 + 1,3,$.1^7 + 3*$.1^6 - 5*$.1^5 - 19*$.1^4 - 8*$.1^3 + 8*$.1^2 + 2*$.1 - 1,5,$.1^7 + 4*$.1^6 - 2*$.1^5 - 26*$.1^4 - 33*$.1^3 - 9*$.1^2 + 3*$.1 + 1,7,$.1^7 + 5*$.1^6 - 17*$.1^5 - 104*$.1^4 + 17*$.1^3 + 445*$.1^2 + 153*$.1 - 289,11,$.1^7 + 7*$.1^6 - 10*$.1^5 - 119*$.1^4 - 170*$.1^3 - 48*$.1^2 + 17*$.1 - 1,13,$.1^7 - 2*$.1^6 - 46*$.1^5 + 72*$.1^4 + 457*$.1^3 - 180*$.1^2 - 242*$.1 - 43[] 461,4,2,$.1^26 - 3*$.1^25 - 41*$.1^24 + 126*$.1^23 + 726*$.1^22 - 2303*$.1^21 - 7266*$.1^20 + 24054*$.1^19 + 45144*$.1^18 - 158550*$.1^17 - 179824*$.1^16 + 687620*$.1^15 + 456511*$.1^14 - 1985932*$.1^13 - 703693*$.1^12 + 3785104*$.1^11 + 571532*$.1^10 - 4624305*$.1^9 - 111938*$.1^8 + 3430214*$.1^7 - 156745*$.1^6 - 1399829*$.1^5 + 108715*$.1^4 + 249906*$.1^3 - 21297*$.1^2 - 6102*$.1 + 223,3,$.1^26 - 8*$.1^25 - 25*$.1^24 + 350*$.1^23 - 67*$.1^22 - 6375*$.1^21 + 9131*$.1^20 + 62591*$.1^19 - 142101*$.1^18 - 354222*$.1^17 + 1131262*$.1^16 + 1100229*$.1^15 - 5439111*$.1^14 - 1179040*$.1^13 + 16616042*$.1^12 - 3766381*$.1^11 - 32549826*$.1^10 + 16848027*$.1^9 + 40027314*$.1^8 - 29339246*$.1^7 - 28984472*$.1^6 + 26997218*$.1^5 + 10382911*$.1^4 - 12846388*$.1^3 - 637663*$.1^2 + 2482812*$.1 - 412364,5,$.1^26 - $.1^25 - 81*$.1^24 + 89*$.1^23 + 2834*$.1^22 - 3337*$.1^21 - 56369*$.1^20 + 69650*$.1^19 + 706674*$.1^18 - 899724*$.1^17 - 5857374*$.1^16 + 7559751*$.1^15 + 32782433*$.1^14 - 42250384*$.1^13 - 124348564*$.1^12 + 157850099*$.1^11 + 315862226*$.1^10 - 390387594*$.1^9 - 520297841*$.1^8 + 621732909*$.1^7 + 519864632*$.1^6 - 602181344*$.1^5 - 272562048*$.1^4 + 314042258*$.1^3 + 48441044*$.1^2 - 63929748*$.1 + 3703649,7,$.1^26 - 10*$.1^25 - 60*$.1^24 + 871*$.1^23 + 794*$.1^22 - 31920*$.1^21 + 24932*$.1^20 + 646295*$.1^19 - 1052609*$.1^18 - 8001190*$.1^17 + 17074484*$.1^16 + 63570421*$.1^15 - 155447227*$.1^14 - 333095634*$.1^13 + 860725592*$.1^12 + 1174538237*$.1^11 - 2928391388*$.1^10 - 2824918032*$.1^9 + 5914395816*$.1^8 + 4532213984*$.1^7 - 6445957683*$.1^6 - 4306115742*$.1^5 + 3059587300*$.1^4 + 1793364464*$.1^3 - 439165584*$.1^2 - 254287328*$.1 - 21295936,11,$.1^26 - 22*$.1^25 + 83*$.1^24 + 1560*$.1^23 - 14351*$.1^22 - 13740*$.1^21 + 588900*$.1^20 - 1405048*$.1^19 - 9844007*$.1^18 + 47950725*$.1^17 + 50344062*$.1^16 - 653138686*$.1^15 + 502380513*$.1^14 + 4333954341*$.1^13 - 8056737769*$.1^12 - 12971428871*$.1^11 + 41885314760*$.1^10 + 7218265149*$.1^9 - 97024228874*$.1^8 + 35476022484*$.1^7 + 96414098848*$.1^6 - 43009973890*$.1^5 - 50612978091*$.1^4 + 12228864075*$.1^3 + 12784976002*$.1^2 + 796292595*$.1 - 328816693,13,$.1^26 - 6*$.1^25 - 182*$.1^24 + 1159*$.1^23 + 13772*$.1^22 - 95371*$.1^21 - 560750*$.1^20 + 4411668*$.1^19 + 13010037*$.1^18 - 126932023*$.1^17 - 155796755*$.1^16 + 2365313943*$.1^15 + 222285283*$.1^14 - 28723004920*$.1^13 + 20894083248*$.1^12 + 221761328032*$.1^11 - 311581537600*$.1^10 - 1012055432256*$.1^9 + 2157421019008*$.1^8 + 2184332068096*$.1^7 - 7839979669504*$.1^6 + 412493474816*$.1^5 + 13389378247680*$.1^4 - 9398097330176*$.1^3 - 6029370896384*$.1^2 + 8993424179200*$.1 - 2762166648832[] 462,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x + 1,13,x + 2[] 462,2,2,x + 1,3,x + 1,5,x - 2,7,x + 1,11,x - 1,13,x - 2[] 462,3,2,x + 1,3,x + 1,5,x + 2,7,x - 1,11,x - 1,13,x - 2[] 462,4,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 1,13,x - 6[] 462,5,2,x - 1,3,x + 1,5,x + 4,7,x - 1,11,x + 1,13,x + 6[] 462,6,2,x - 1,3,x - 1,5,x - 2,7,x + 1,11,x - 1,13,x + 2[] 462,7,2,x - 1,3,x - 1,5,x,7,x - 1,11,x + 1,13,x - 2[] 462,8,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 12,7,x^2 - 2*x + 1,11,x^2 - 2*x + 1,13,x^2 - 4*x + 4[] 463,1,2,x^16 + 9*x^15 + 17*x^14 - 70*x^13 - 282*x^12 + 7*x^11 + 1223*x^10 + 1073*x^9 - 2045*x^8 - 2946*x^7 + 1137*x^6 + 2847*x^5 + 88*x^4 - 954*x^3 - 47*x^2 + 118*x - 9,3,x^16 + 6*x^15 - 10*x^14 - 113*x^13 - 38*x^12 + 756*x^11 + 674*x^10 - 2299*x^9 - 2327*x^8 + 3496*x^7 + 2916*x^6 - 2854*x^5 - 1321*x^4 + 1115*x^3 + 125*x^2 - 151*x + 17,5,x^16 + 16*x^15 + 84*x^14 + 39*x^13 - 1210*x^12 - 4138*x^11 - 1410*x^10 + 16780*x^9 + 27638*x^8 - 8560*x^7 - 49341*x^6 - 20011*x^5 + 23715*x^4 + 12698*x^3 - 3322*x^2 - 355*x + 75,7,x^16 + 10*x^15 - 4*x^14 - 305*x^13 - 525*x^12 + 3091*x^11 + 7597*x^10 - 12200*x^9 - 33924*x^8 + 20827*x^7 + 52761*x^6 - 11881*x^5 - 27051*x^4 + 1806*x^3 + 3512*x^2 - 395*x + 9,11,x^16 + 7*x^15 - 69*x^14 - 471*x^13 + 2127*x^12 + 12574*x^11 - 39019*x^10 - 165746*x^9 + 448793*x^8 + 1057645*x^7 - 2970725*x^6 - 2325341*x^5 + 8806405*x^4 - 2477609*x^3 - 3318103*x^2 + 735353*x + 419003,13,x^16 + 17*x^15 + 29*x^14 - 948*x^13 - 4829*x^12 + 13057*x^11 + 126050*x^10 + 49398*x^9 - 1183509*x^8 - 1969668*x^7 + 3199115*x^6 + 10003714*x^5 + 5302860*x^4 - 4889311*x^3 - 6512429*x^2 - 2575705*x - 350517[] 463,2,2,x^22 - 8*x^21 - x^20 + 161*x^19 - 281*x^18 - 1216*x^17 + 3523*x^16 + 3859*x^15 - 19383*x^14 - 1030*x^13 + 56835*x^12 - 26406*x^11 - 90387*x^10 + 71356*x^9 + 71796*x^8 - 76057*x^7 - 22452*x^6 + 32959*x^5 + 1404*x^4 - 4772*x^3 - 174*x^2 + 237*x + 25,3,x^22 - 4*x^21 - 40*x^20 + 175*x^19 + 634*x^18 - 3196*x^17 - 4882*x^16 + 31685*x^15 + 15943*x^14 - 185800*x^13 + 17462*x^12 + 658774*x^11 - 317425*x^10 - 1385913*x^9 + 1058217*x^8 + 1616727*x^7 - 1650803*x^6 - 853772*x^5 + 1229264*x^4 + 27760*x^3 - 336304*x^2 + 87744*x - 6080,5,x^22 - 14*x^21 + 30*x^20 + 429*x^19 - 2232*x^18 - 2804*x^17 + 39278*x^16 - 37660*x^15 - 291072*x^14 + 650216*x^13 + 804651*x^12 - 3585845*x^11 + 758887*x^10 + 8250140*x^9 - 7478252*x^8 - 6369965*x^7 + 10268643*x^6 + 264580*x^5 - 4629944*x^4 + 762336*x^3 + 677968*x^2 - 51776*x - 27584,7,x^22 - 2*x^21 - 76*x^20 + 181*x^19 + 2301*x^18 - 6343*x^17 - 35541*x^16 + 113608*x^15 + 295698*x^14 - 1144665*x^13 - 1238901*x^12 + 6708483*x^11 + 1472515*x^10 - 22688648*x^9 + 7199360*x^8 + 41794201*x^7 - 29091175*x^6 - 35510916*x^5 + 38151008*x^4 + 6047480*x^3 - 16528576*x^2 + 4477728*x - 17728,11,x^22 - 3*x^21 - 113*x^20 + 343*x^19 + 5117*x^18 - 15366*x^17 - 121755*x^16 + 349548*x^15 + 1699863*x^14 - 4397687*x^13 - 14931055*x^12 + 31550965*x^11 + 85507127*x^10 - 126103999*x^9 - 314041293*x^8 + 247288771*x^7 + 673005607*x^6 - 136356452*x^5 - 675381584*x^4 - 101740656*x^3 + 217744368*x^2 + 59584960*x - 5641024,13,x^22 - 13*x^21 - 75*x^20 + 1644*x^19 - 881*x^18 - 77769*x^17 + 225146*x^16 + 1714666*x^15 - 8239929*x^14 - 15611588*x^13 + 137556583*x^12 - 31493298*x^11 - 1124303704*x^10 + 1647535345*x^9 + 3696411261*x^8 - 10524859959*x^7 + 1100329357*x^6 + 19814686542*x^5 - 21136903324*x^4 + 4162677720*x^3 + 3672221712*x^2 - 1509576416*x + 54642112[] 464,1,2,x,3,x - 1,5,x + 3,7,x + 2,11,x - 3,13,x + 5[] 464,2,2,x,3,x + 1,5,x - 1,7,x + 2,11,x + 3,13,x + 1[] 464,3,2,x,3,x - 1,5,x - 1,7,x - 2,11,x - 3,13,x + 1[] 464,4,2,x,3,x + 1,5,x - 3,7,x - 4,11,x + 3,13,x - 5[] 464,5,2,x,3,x + 2,5,x + 2,7,x + 4,11,x - 6,13,x - 2[] 464,6,2,x,3,x - 3,5,x - 3,7,x + 4,11,x - 1,13,x + 3[] 464,7,2,x,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x - 3[] 464,8,2,x^2,3,x^2 - 2*x - 1,5,x^2 + 2*x - 7,7,x^2 - 8*x + 16,11,x^2 - 2*x - 1,13,x^2 + 2*x - 31[] 464,9,2,x^2,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2 - 8,11,x^2 + 2*x - 1,13,x^2 + 2*x - 7[] 464,10,2,x^3,3,x^3 + 2*x^2 - 5*x - 8,5,x^3 - 4*x^2 - 3*x + 10,7,x^3,11,x^3 + 2*x^2 - 29*x - 80,13,x^3 - 4*x^2 - 19*x + 2[] Total time: 18.170 seconds, Total memory usage: 6.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:28:23 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [464..467] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:28:07 on modular [Seed = 468598424] ------------------------------------- 464,1,2,$.1,3,$.1 - 1,5,$.1 + 3,7,$.1 + 2,11,$.1 - 3,13,$.1 + 5[] 464,2,2,$.1,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 + 3,13,$.1 + 1[] 464,3,2,$.1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 2,11,$.1 - 3,13,$.1 + 1[] 464,4,2,$.1,3,$.1 + 1,5,$.1 - 3,7,$.1 - 4,11,$.1 + 3,13,$.1 - 5[] 464,5,2,$.1,3,$.1 + 2,5,$.1 + 2,7,$.1 + 4,11,$.1 - 6,13,$.1 - 2[] 464,6,2,$.1,3,$.1 - 3,5,$.1 - 3,7,$.1 + 4,11,$.1 - 1,13,$.1 + 3[] 464,7,2,$.1,3,$.1 - 3,5,$.1 + 3,7,$.1 - 2,11,$.1 - 1,13,$.1 - 3[] 464,8,2,$.1^2,3,$.1^2 - 2*$.1 - 1,5,$.1^2 + 2*$.1 - 7,7,$.1^2 - 8*$.1 + 16,11,$.1^2 - 2*$.1 - 1,13,$.1^2 + 2*$.1 - 31[] 464,9,2,$.1^2,3,$.1^2 + 2*$.1 - 1,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 8,11,$.1^2 + 2*$.1 - 1,13,$.1^2 + 2*$.1 - 7[] 464,10,2,$.1^3,3,$.1^3 + 2*$.1^2 - 5*$.1 - 8,5,$.1^3 - 4*$.1^2 - 3*$.1 + 10,7,$.1^3,11,$.1^3 + 2*$.1^2 - 29*$.1 - 80,13,$.1^3 - 4*$.1^2 - 19*$.1 + 2[] 465,1,2,x - 1,3,x + 1,5,x - 1,7,x + 2,11,x + 4,13,x[] 465,2,2,x + 1,3,x - 1,5,x - 1,7,x + 4,11,x + 4,13,x - 2[] 465,3,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 4*x - 8,13,x^2 + 6*x + 6[] 465,4,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 4*x + 2,11,x^2 - 8,13,x^2 + 8*x + 14[] 465,5,2,x^3 - x^2 - 5*x + 3,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 8*x^2 + 16*x - 6,11,x^3 - 2*x^2 - 20*x + 24,13,x^3 - 4*x^2 + 6[] 465,6,2,x^3 - 3*x^2 - x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 2*x^2 - 12*x - 10,11,x^3 - 2*x^2 - 12*x + 8,13,x^3 + 6*x^2 + 8*x - 2[] 465,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 2*x^2 - 2*x + 2,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 2*x^2 - 22*x + 2[] 465,8,2,x^4 - 2*x^3 - 6*x^2 + 12*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 4*x^3 - 10*x^2 + 46*x - 32,11,x^4 - 6*x^3 - 12*x^2 + 56*x + 32,13,x^4 - 2*x^3 - 50*x^2 + 94*x + 4[] 466,1,2,x + 1,3,x - 2,5,x,7,x,11,x - 2,13,x - 2[] 466,2,2,x - 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 5[] 466,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 3*x - 5,5,x^3 - 5*x^2 + 4*x + 5,7,x^3 - 3*x^2 - 10*x + 25,11,x^3 - 8*x^2 + 17*x - 5,13,x^3 + 5*x^2 - 9*x - 5[] 466,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 7*x^2 + 14*x + 7,7,x^3 + x^2 - 16*x - 29,11,x^3 + 10*x^2 + 17*x - 41,13,x^3 + 7*x^2 + 7*x - 7[] 466,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 8*x^3 + x^2 + 5*x - 1,5,x^5 + 5*x^4 - 4*x^3 - 37*x^2 - 24*x + 16,7,x^5 + 5*x^4 - 10*x^3 - 47*x^2 + 36*x - 4,11,x^5 + 12*x^4 + 33*x^3 - 71*x^2 - 320*x - 76,13,x^5 - 5*x^4 - 26*x^3 + 74*x^2 + 73*x + 11[] 466,6,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - x^5 - 13*x^4 + 10*x^3 + 43*x^2 - 12*x - 36,5,x^6 - 7*x^5 + 4*x^4 + 47*x^3 - 52*x^2 - 66*x + 64,7,x^6 + 3*x^5 - 18*x^4 - 33*x^3 + 42*x^2 + 72*x + 16,11,x^6 - 6*x^5 - 31*x^4 + 221*x^3 - 56*x^2 - 796*x + 64,13,x^6 - 2*x^5 - 24*x^4 + 6*x^3 + 171*x^2 + 212*x + 52[] 467,1,2,x,3,x + 3,5,x - 2,7,x - 1,11,x - 4,13,x + 6[] 467,2,2,x^12 + 5*x^11 - 3*x^10 - 46*x^9 - 28*x^8 + 144*x^7 + 140*x^6 - 182*x^5 - 197*x^4 + 102*x^3 + 104*x^2 - 22*x - 17,3,x^12 + 3*x^11 - 11*x^10 - 35*x^9 + 39*x^8 + 137*x^7 - 48*x^6 - 212*x^5 + 5*x^4 + 121*x^3 + 16*x^2 - 12*x + 1,5,x^12 + 7*x^11 - 92*x^9 - 169*x^8 + 187*x^7 + 773*x^6 + 653*x^5 + 21*x^4 - 197*x^3 - 74*x^2 - 4*x + 1,7,x^12 + 12*x^11 + 30*x^10 - 183*x^9 - 1201*x^8 - 2087*x^7 + 1097*x^6 + 7291*x^5 + 5601*x^4 - 4034*x^3 - 6862*x^2 - 2643*x - 269,11,x^12 + 6*x^11 - 38*x^10 - 240*x^9 + 409*x^8 + 3134*x^7 - 159*x^6 - 14588*x^5 - 13297*x^4 + 16338*x^3 + 33221*x^2 + 19331*x + 3845,13,x^12 + 29*x^11 + 339*x^10 + 1964*x^9 + 4955*x^8 - 3998*x^7 - 61729*x^6 - 174010*x^5 - 239727*x^4 - 170293*x^3 - 55755*x^2 - 6048*x + 27[] 467,3,2,x^26 - 5*x^25 - 30*x^24 + 181*x^23 + 338*x^22 - 2813*x^21 - 1420*x^20 + 24571*x^19 - 4052*x^18 - 132574*x^17 + 73889*x^16 + 457016*x^15 - 370842*x^14 - 1004824*x^13 + 992642*x^12 + 1361654*x^11 - 1526411*x^10 - 1049992*x^9 + 1309411*x^8 + 383566*x^7 - 569750*x^6 - 29300*x^5 + 105328*x^4 - 5888*x^3 - 6944*x^2 + 448*x + 128,3,x^26 - 4*x^25 - 46*x^24 + 196*x^23 + 893*x^22 - 4154*x^21 - 9443*x^20 + 49915*x^19 + 57965*x^18 - 374373*x^17 - 196608*x^16 + 1818054*x^15 + 249133*x^14 - 5741255*x^13 + 547597*x^12 + 11551260*x^11 - 2428841*x^10 - 14158547*x^9 + 3083763*x^8 + 9839699*x^7 - 1135144*x^6 - 3499562*x^5 - 199898*x^4 + 469317*x^3 + 73469*x^2 - 16172*x - 3151,5,x^26 - 3*x^25 - 88*x^24 + 282*x^23 + 3293*x^22 - 11295*x^21 - 68205*x^20 + 252251*x^19 + 852605*x^18 - 3451561*x^17 - 6582044*x^16 + 29965190*x^15 + 30905167*x^14 - 165685764*x^13 - 84525874*x^12 + 573092728*x^11 + 130984024*x^10 - 1193054512*x^9 - 146599680*x^8 + 1387791296*x^7 + 202913280*x^6 - 773243904*x^5 - 172236288*x^4 + 142046208*x^3 + 31006720*x^2 - 7929856*x - 1220608,7,x^26 - 11*x^25 - 48*x^24 + 911*x^23 - 237*x^22 - 30439*x^21 + 58280*x^20 + 530524*x^19 - 1552763*x^18 - 5213022*x^17 + 20094626*x^16 + 29129121*x^15 - 147617188*x^14 - 90880344*x^13 + 638793969*x^12 + 182147970*x^11 - 1621148858*x^10 - 456119623*x^9 + 2307815904*x^8 + 1136598134*x^7 - 1394567530*x^6 - 1251108627*x^5 - 186732226*x^4 + 107562639*x^3 + 42029309*x^2 + 4788605*x + 153911,11,x^26 - 170*x^24 + 60*x^23 + 12429*x^22 - 8628*x^21 - 511399*x^20 + 522410*x^19 + 13007513*x^18 - 17371744*x^17 - 211346041*x^16 + 346903909*x^15 + 2184972859*x^14 - 4270849060*x^13 - 13785736442*x^12 + 31948079796*x^11 + 47565552664*x^10 - 136506612320*x^9 - 63934259328*x^8 + 286039610304*x^7 - 23226979712*x^6 - 193807726848*x^5 + 1930760192*x^4 + 44769953792*x^3 + 10725629952*x^2 + 465903616*x - 33923072,13,x^26 - 47*x^25 + 901*x^24 - 8210*x^23 + 18582*x^22 + 334227*x^21 - 3290814*x^20 + 7720356*x^19 + 56998590*x^18 - 443724985*x^17 + 655975590*x^16 + 4770587780*x^15 - 23477796337*x^14 + 14328650996*x^13 + 169189717890*x^12 - 475812982626*x^11 - 27477167834*x^10 + 2218007529808*x^9 - 3372965479433*x^8 - 1428631387058*x^7 + 8642602458407*x^6 - 7173300791221*x^5 - 1144500659319*x^4 + 3299643594404*x^3 - 114001961373*x^2 - 484815751724*x - 51049532452[] Total time: 16.090 seconds, Total memory usage: 5.97MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:36:42 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [467..470] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:36:22 on modular [Seed = 1070210221] ------------------------------------- 467,1,2,$.1,3,$.1 + 3,5,$.1 - 2,7,$.1 - 1,11,$.1 - 4,13,$.1 + 6[] 467,2,2,$.1^12 + 5*$.1^11 - 3*$.1^10 - 46*$.1^9 - 28*$.1^8 + 144*$.1^7 + 140*$.1^6 - 182*$.1^5 - 197*$.1^4 + 102*$.1^3 + 104*$.1^2 - 22*$.1 - 17,3,$.1^12 + 3*$.1^11 - 11*$.1^10 - 35*$.1^9 + 39*$.1^8 + 137*$.1^7 - 48*$.1^6 - 212*$.1^5 + 5*$.1^4 + 121*$.1^3 + 16*$.1^2 - 12*$.1 + 1,5,$.1^12 + 7*$.1^11 - 92*$.1^9 - 169*$.1^8 + 187*$.1^7 + 773*$.1^6 + 653*$.1^5 + 21*$.1^4 - 197*$.1^3 - 74*$.1^2 - 4*$.1 + 1,7,$.1^12 + 12*$.1^11 + 30*$.1^10 - 183*$.1^9 - 1201*$.1^8 - 2087*$.1^7 + 1097*$.1^6 + 7291*$.1^5 + 5601*$.1^4 - 4034*$.1^3 - 6862*$.1^2 - 2643*$.1 - 269,11,$.1^12 + 6*$.1^11 - 38*$.1^10 - 240*$.1^9 + 409*$.1^8 + 3134*$.1^7 - 159*$.1^6 - 14588*$.1^5 - 13297*$.1^4 + 16338*$.1^3 + 33221*$.1^2 + 19331*$.1 + 3845,13,$.1^12 + 29*$.1^11 + 339*$.1^10 + 1964*$.1^9 + 4955*$.1^8 - 3998*$.1^7 - 61729*$.1^6 - 174010*$.1^5 - 239727*$.1^4 - 170293*$.1^3 - 55755*$.1^2 - 6048*$.1 + 27[] 467,3,2,$.1^26 - 5*$.1^25 - 30*$.1^24 + 181*$.1^23 + 338*$.1^22 - 2813*$.1^21 - 1420*$.1^20 + 24571*$.1^19 - 4052*$.1^18 - 132574*$.1^17 + 73889*$.1^16 + 457016*$.1^15 - 370842*$.1^14 - 1004824*$.1^13 + 992642*$.1^12 + 1361654*$.1^11 - 1526411*$.1^10 - 1049992*$.1^9 + 1309411*$.1^8 + 383566*$.1^7 - 569750*$.1^6 - 29300*$.1^5 + 105328*$.1^4 - 5888*$.1^3 - 6944*$.1^2 + 448*$.1 + 128,3,$.1^26 - 4*$.1^25 - 46*$.1^24 + 196*$.1^23 + 893*$.1^22 - 4154*$.1^21 - 9443*$.1^20 + 49915*$.1^19 + 57965*$.1^18 - 374373*$.1^17 - 196608*$.1^16 + 1818054*$.1^15 + 249133*$.1^14 - 5741255*$.1^13 + 547597*$.1^12 + 11551260*$.1^11 - 2428841*$.1^10 - 14158547*$.1^9 + 3083763*$.1^8 + 9839699*$.1^7 - 1135144*$.1^6 - 3499562*$.1^5 - 199898*$.1^4 + 469317*$.1^3 + 73469*$.1^2 - 16172*$.1 - 3151,5,$.1^26 - 3*$.1^25 - 88*$.1^24 + 282*$.1^23 + 3293*$.1^22 - 11295*$.1^21 - 68205*$.1^20 + 252251*$.1^19 + 852605*$.1^18 - 3451561*$.1^17 - 6582044*$.1^16 + 29965190*$.1^15 + 30905167*$.1^14 - 165685764*$.1^13 - 84525874*$.1^12 + 573092728*$.1^11 + 130984024*$.1^10 - 1193054512*$.1^9 - 146599680*$.1^8 + 1387791296*$.1^7 + 202913280*$.1^6 - 773243904*$.1^5 - 172236288*$.1^4 + 142046208*$.1^3 + 31006720*$.1^2 - 7929856*$.1 - 1220608,7,$.1^26 - 11*$.1^25 - 48*$.1^24 + 911*$.1^23 - 237*$.1^22 - 30439*$.1^21 + 58280*$.1^20 + 530524*$.1^19 - 1552763*$.1^18 - 5213022*$.1^17 + 20094626*$.1^16 + 29129121*$.1^15 - 147617188*$.1^14 - 90880344*$.1^13 + 638793969*$.1^12 + 182147970*$.1^11 - 1621148858*$.1^10 - 456119623*$.1^9 + 2307815904*$.1^8 + 1136598134*$.1^7 - 1394567530*$.1^6 - 1251108627*$.1^5 - 186732226*$.1^4 + 107562639*$.1^3 + 42029309*$.1^2 + 4788605*$.1 + 153911,11,$.1^26 - 170*$.1^24 + 60*$.1^23 + 12429*$.1^22 - 8628*$.1^21 - 511399*$.1^20 + 522410*$.1^19 + 13007513*$.1^18 - 17371744*$.1^17 - 211346041*$.1^16 + 346903909*$.1^15 + 2184972859*$.1^14 - 4270849060*$.1^13 - 13785736442*$.1^12 + 31948079796*$.1^11 + 47565552664*$.1^10 - 136506612320*$.1^9 - 63934259328*$.1^8 + 286039610304*$.1^7 - 23226979712*$.1^6 - 193807726848*$.1^5 + 1930760192*$.1^4 + 44769953792*$.1^3 + 10725629952*$.1^2 + 465903616*$.1 - 33923072,13,$.1^26 - 47*$.1^25 + 901*$.1^24 - 8210*$.1^23 + 18582*$.1^22 + 334227*$.1^21 - 3290814*$.1^20 + 7720356*$.1^19 + 56998590*$.1^18 - 443724985*$.1^17 + 655975590*$.1^16 + 4770587780*$.1^15 - 23477796337*$.1^14 + 14328650996*$.1^13 + 169189717890*$.1^12 - 475812982626*$.1^11 - 27477167834*$.1^10 + 2218007529808*$.1^9 - 3372965479433*$.1^8 - 1428631387058*$.1^7 + 8642602458407*$.1^6 - 7173300791221*$.1^5 - 1144500659319*$.1^4 + 3299643594404*$.1^3 - 114001961373*$.1^2 - 484815751724*$.1 - 51049532452[] 468,1,2,x,3,x,5,x - 4,7,x - 4,11,x + 4,13,x + 1[] 468,2,2,x,3,x,5,x + 4,7,x - 4,11,x - 4,13,x + 1[] 468,3,2,x,3,x,5,x + 2,7,x + 2,11,x - 2,13,x + 1[] 468,4,2,x,3,x,5,x,7,x - 2,11,x,13,x - 1[] 468,5,2,x,3,x,5,x - 4,7,x + 2,11,x - 4,13,x - 1[] 469,1,2,x - 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 1[] 469,2,2,x + 1,3,x + 3,5,x - 1,7,x + 1,11,x,13,x - 3[] 469,3,2,x^2 - x - 4,3,x^2 + x - 4,5,x^2 + 3*x - 2,7,x^2 - 2*x + 1,11,x^2 - 8*x + 16,13,x^2 + 7*x + 8[] 469,4,2,x^2 - 2*x + 1,3,x^2 + x - 4,5,x^2 + x - 4,7,x^2 - 2*x + 1,11,x^2 - 8*x + 16,13,x^2 - 9*x + 16[] 469,5,2,x^3 + x^2 - 3*x - 1,3,x^3 + x^2 - 5*x - 1,5,x^3 + 9*x^2 + 27*x + 27,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 12*x^2 + 48*x + 64,13,x^3 - 5*x^2 - 5*x + 17[] 469,6,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 - 3*x^2 + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 6*x^2 - 9*x - 51,13,x^3 + 3*x^2 - 6*x - 17[] 469,7,2,x^5 - 2*x^4 - 5*x^3 + 9*x^2 + 3*x - 4,3,x^5 + 2*x^4 - 5*x^3 - 9*x^2 + 3*x + 4,5,x^5 + 4*x^4 - 5*x^3 - 19*x^2 + 9*x + 18,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 + 16*x^4 + 77*x^3 + 27*x^2 - 620*x - 1024,13,x^5 + 4*x^4 - 41*x^3 - 99*x^2 + 477*x + 216[] 469,8,2,x^7 - x^6 - 12*x^5 + 9*x^4 + 43*x^3 - 17*x^2 - 44*x - 11,3,x^7 - 6*x^6 + x^5 + 51*x^4 - 85*x^3 - 12*x^2 + 80*x - 32,5,x^7 - 6*x^6 - 3*x^5 + 73*x^4 - 95*x^3 - 144*x^2 + 350*x - 178,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,11,x^7 - 8*x^6 - 7*x^5 + 83*x^4 + 164*x^3 + 72*x^2 - 28*x - 16,13,x^7 + 8*x^6 + x^5 - 113*x^4 - 151*x^3 + 362*x^2 + 374*x - 394[] 469,9,2,x^9 + x^8 - 13*x^7 - 10*x^6 + 53*x^5 + 28*x^4 - 69*x^3 - 12*x^2 + 12*x + 1,3,x^9 - 8*x^8 + 12*x^7 + 47*x^6 - 122*x^5 - 67*x^4 + 297*x^3 - 12*x^2 - 192*x + 32,5,x^9 - 8*x^8 + 6*x^7 + 87*x^6 - 176*x^5 - 177*x^4 + 507*x^3 + 88*x^2 - 334*x - 82,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,11,x^9 - 18*x^8 + 107*x^7 - 147*x^6 - 712*x^5 + 1952*x^4 + 1140*x^3 - 4896*x^2 - 256*x + 2048,13,x^9 - 4*x^8 - 68*x^7 + 157*x^6 + 1678*x^5 - 781*x^4 - 15613*x^3 - 12902*x^2 + 30374*x + 36406[] 470,1,2,x + 1,3,x - 1,5,x + 1,7,x + 1,11,x + 3,13,x + 5[] 470,2,2,x + 1,3,x - 1,5,x - 1,7,x + 1,11,x - 3,13,x - 5[] 470,3,2,x + 1,3,x + 1,5,x - 1,7,x + 1,11,x - 1,13,x + 5[] 470,4,2,x - 1,3,x - 1,5,x + 1,7,x - 5,11,x + 3,13,x - 5[] 470,5,2,x - 1,3,x + 1,5,x + 1,7,x + 3,11,x + 5,13,x + 1[] 470,6,2,x - 1,3,x + 3,5,x - 1,7,x + 3,11,x + 1,13,x + 1[] 470,7,2,x^2 + 2*x + 1,3,x^2 - x - 5,5,x^2 - 2*x + 1,7,x^2 - 8*x + 16,11,x^2 + 5*x + 1,13,x^2 - 2*x - 20[] 470,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 6*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 3*x^2 - 12*x + 16,11,x^3 - 12*x - 15,13,x^3 - 3*x^2 - 18*x + 4[] 470,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 5*x + 12,5,x^3 + 3*x^2 + 3*x + 1,7,x^3,11,x^3 - 5*x^2 - 15*x + 72,13,x^3 - 32*x - 40[] 470,10,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 4*x + 7,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - x^2 - 12*x + 16,11,x^3 - 4*x - 1,13,x^3 + x^2 - 6*x - 4[] Total time: 19.350 seconds, Total memory usage: 6.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:40:31 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [470..473] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:40:13 on modular [Seed = 685574737] ------------------------------------- 470,1,2,$.1 + 1,3,$.1 - 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 3,13,$.1 + 5[] 470,2,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 3,13,$.1 - 5[] 470,3,2,$.1 + 1,3,$.1 + 1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 1,13,$.1 + 5[] 470,4,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 5,11,$.1 + 3,13,$.1 - 5[] 470,5,2,$.1 - 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 3,11,$.1 + 5,13,$.1 + 1[] 470,6,2,$.1 - 1,3,$.1 + 3,5,$.1 - 1,7,$.1 + 3,11,$.1 + 1,13,$.1 + 1[] 470,7,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - $.1 - 5,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 8*$.1 + 16,11,$.1^2 + 5*$.1 + 1,13,$.1^2 - 2*$.1 - 20[] 470,8,2,$.1^3 + 3*$.1^2 + 3*$.1 + 1,3,$.1^3 - 6*$.1 - 1,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 - 3*$.1^2 - 12*$.1 + 16,11,$.1^3 - 12*$.1 - 15,13,$.1^3 - 3*$.1^2 - 18*$.1 + 4[] 470,9,2,$.1^3 - 3*$.1^2 + 3*$.1 - 1,3,$.1^3 - 3*$.1^2 - 5*$.1 + 12,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3,11,$.1^3 - 5*$.1^2 - 15*$.1 + 72,13,$.1^3 - 32*$.1 - 40[] 470,10,2,$.1^3 - 3*$.1^2 + 3*$.1 - 1,3,$.1^3 - 2*$.1^2 - 4*$.1 + 7,5,$.1^3 - 3*$.1^2 + 3*$.1 - 1,7,$.1^3 - $.1^2 - 12*$.1 + 16,11,$.1^3 - 4*$.1 - 1,13,$.1^3 + $.1^2 - 6*$.1 - 4[] 471,1,2,x + 1,3,x + 1,5,x + 2,7,x - 3,11,x,13,x - 1[] 471,2,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + x - 11,13,x^2 + 3*x + 1[] 471,3,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 5*x^2 + 3*x - 8,13,x^3 + 2*x^2 - 30*x - 29[] 471,4,2,x^9 - 2*x^8 - 11*x^7 + 19*x^6 + 39*x^5 - 53*x^4 - 49*x^3 + 45*x^2 + 14*x - 1,3,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,5,x^9 - 8*x^8 + x^7 + 122*x^6 - 214*x^5 - 330*x^4 + 728*x^3 + 380*x^2 - 648*x - 324,7,x^9 + 2*x^8 - 43*x^7 - 88*x^6 + 528*x^5 + 1152*x^4 - 1472*x^3 - 3264*x^2 - 384*x + 256,11,x^9 - 7*x^8 - 37*x^7 + 328*x^6 + 64*x^5 - 3696*x^4 + 4160*x^3 + 8320*x^2 - 14592*x + 5632,13,x^9 + x^8 - 77*x^7 - 30*x^6 + 2012*x^5 - 104*x^4 - 19440*x^3 + 5088*x^2 + 40512*x + 17536[] 471,5,2,x^12 + x^11 - 20*x^10 - 17*x^9 + 149*x^8 + 106*x^7 - 500*x^6 - 294*x^5 + 711*x^4 + 349*x^3 - 290*x^2 - 173*x - 15,3,x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1,5,x^12 - 4*x^11 - 33*x^10 + 140*x^9 + 334*x^8 - 1590*x^7 - 1164*x^6 + 7376*x^5 + 8*x^4 - 12456*x^3 + 4748*x^2 + 2096*x - 400,7,x^12 - 8*x^11 - 34*x^10 + 404*x^9 + 9*x^8 - 6916*x^7 + 9824*x^6 + 43904*x^5 - 100224*x^4 - 60608*x^3 + 249728*x^2 - 92928*x - 37376,11,x^12 + x^11 - 87*x^10 - 116*x^9 + 2752*x^8 + 4304*x^7 - 38464*x^6 - 65664*x^5 + 224512*x^4 + 385024*x^3 - 418816*x^2 - 499712*x + 393216,13,x^12 - 15*x^11 + 12*x^10 + 753*x^9 - 3031*x^8 - 6440*x^7 + 46816*x^6 - 17968*x^5 - 195232*x^4 + 233984*x^3 + 145152*x^2 - 297216*x + 80384[] 472,1,2,x,3,x + 3,5,x + 1,7,x - 3,11,x + 4,13,x - 6[] 472,2,2,x,3,x + 1,5,x + 1,7,x - 1,11,x - 4,13,x - 2[] 472,3,2,x,3,x - 2,5,x - 2,7,x - 1,11,x - 1,13,x + 1[] 472,4,2,x,3,x - 3,5,x + 3,7,x - 3,11,x - 6,13,x + 6[] 472,5,2,x,3,x + 1,5,x + 1,7,x - 1,11,x,13,x + 2[] 472,6,2,x^4,3,x^4 + x^3 - 5*x^2 + 1,5,x^4 + 3*x^3 - 11*x^2 - 20*x + 43,7,x^4 + 9*x^3 + 11*x^2 - 78*x - 169,11,x^4 + 4*x^3 - 36*x^2 - 72*x + 368,13,x^4 + 10*x^3 + 12*x^2 - 64*x + 16[] 472,7,2,x^6,3,x^6 + x^5 - 15*x^4 - 16*x^3 + 51*x^2 + 30*x - 56,5,x^6 - 7*x^5 - 3*x^4 + 118*x^3 - 279*x^2 + 180*x + 4,7,x^6 + 4*x^5 - 18*x^4 - 93*x^3 - 51*x^2 + 157*x + 128,11,x^6 + 3*x^5 - 30*x^4 - 56*x^3 + 264*x^2 + 224*x - 512,13,x^6 - 9*x^5 + 144*x^3 - 120*x^2 - 496*x + 32[] 473,1,2,x + 2,3,x - 1,5,x + 1,7,x,11,x + 1,13,x + 2[] 473,2,2,x^2 - x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x - 4,7,x^2 - 5,11,x^2 + 2*x + 1,13,x^2 - 20[] 473,3,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 4*x - 1,11,x^2 - 2*x + 1,13,x^2 + 12*x + 36[] 473,4,2,x^5 - x^4 - 6*x^3 + 5*x^2 + x - 1,3,x^5 + 3*x^4 - 7*x^3 - 19*x^2 + 4*x + 1,5,x^5 + 6*x^4 + 3*x^3 - 19*x^2 + x + 1,7,x^5 + 15*x^4 + 71*x^3 + 53*x^2 - 420*x - 799,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 + x^4 - 15*x^3 - 14*x^2 + 19*x + 7[] 473,5,2,x^5 + 3*x^4 - 4*x^3 - 13*x^2 + 3*x + 9,3,x^5 + x^4 - 9*x^3 - 7*x^2 + 2*x + 1,5,x^5 + 4*x^4 - 7*x^3 - 41*x^2 - 43*x - 11,7,x^5 + 9*x^4 + 23*x^3 + 9*x^2 - 30*x - 25,11,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,13,x^5 + 9*x^4 - x^3 - 132*x^2 - 117*x + 193[] 473,6,2,x^9 - 4*x^8 - 5*x^7 + 36*x^6 - 20*x^5 - 65*x^4 + 66*x^3 + 4*x^2 - 8*x + 1,3,x^9 - 5*x^8 - 4*x^7 + 52*x^6 - 47*x^5 - 108*x^4 + 148*x^3 + 43*x^2 - 82*x - 4,5,x^9 - 25*x^7 + 13*x^6 + 179*x^5 - 143*x^4 - 374*x^3 + 424*x^2 - 40*x - 16,7,x^9 - 19*x^8 + 140*x^7 - 482*x^6 + 627*x^5 + 570*x^4 - 2324*x^3 + 1223*x^2 + 1580*x - 1368,11,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,13,x^9 - 11*x^8 - 5*x^7 + 436*x^6 - 1613*x^5 + 957*x^4 + 3732*x^3 - 4212*x^2 - 1360*x + 992[] 473,7,2,x^11 + x^10 - 17*x^9 - 15*x^8 + 102*x^7 + 77*x^6 - 255*x^5 - 150*x^4 + 248*x^3 + 59*x^2 - 93*x + 18,3,x^11 - 6*x^10 - 7*x^9 + 94*x^8 - 53*x^7 - 483*x^6 + 524*x^5 + 873*x^4 - 1135*x^3 - 260*x^2 + 364*x + 64,5,x^11 - 3*x^10 - 31*x^9 + 82*x^8 + 354*x^7 - 824*x^6 - 1773*x^5 + 3616*x^4 + 3412*x^3 - 5976*x^2 - 768*x + 864,7,x^11 - 17*x^10 + 96*x^9 - 92*x^8 - 1043*x^7 + 3448*x^6 - 142*x^5 - 12971*x^4 + 13700*x^3 + 4760*x^2 - 6848*x + 1024,11,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,13,x^11 - 11*x^10 - 15*x^9 + 478*x^8 - 649*x^7 - 5829*x^6 + 10608*x^5 + 21112*x^4 - 20096*x^3 - 31984*x^2 - 5312*x + 384[] Total time: 17.389 seconds, Total memory usage: 5.87MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:47:27 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [473..476] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:47:07 on modular [Seed = 1605009216] ------------------------------------- 473,1,2,$.1 + 2,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 + 1,13,$.1 + 2[] 473,2,2,$.1^2 - $.1 - 1,3,$.1^2 + 4*$.1 + 4,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 5,11,$.1^2 + 2*$.1 + 1,13,$.1^2 - 20[] 473,3,2,$.1^2 - $.1 - 1,3,$.1^2 + 2*$.1 - 4,5,$.1^2 - 2*$.1 - 4,7,$.1^2 + 4*$.1 - 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 + 12*$.1 + 36[] 473,4,2,$.1^5 - $.1^4 - 6*$.1^3 + 5*$.1^2 + $.1 - 1,3,$.1^5 + 3*$.1^4 - 7*$.1^3 - 19*$.1^2 + 4*$.1 + 1,5,$.1^5 + 6*$.1^4 + 3*$.1^3 - 19*$.1^2 + $.1 + 1,7,$.1^5 + 15*$.1^4 + 71*$.1^3 + 53*$.1^2 - 420*$.1 - 799,11,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,13,$.1^5 + $.1^4 - 15*$.1^3 - 14*$.1^2 + 19*$.1 + 7[] 473,5,2,$.1^5 + 3*$.1^4 - 4*$.1^3 - 13*$.1^2 + 3*$.1 + 9,3,$.1^5 + $.1^4 - 9*$.1^3 - 7*$.1^2 + 2*$.1 + 1,5,$.1^5 + 4*$.1^4 - 7*$.1^3 - 41*$.1^2 - 43*$.1 - 11,7,$.1^5 + 9*$.1^4 + 23*$.1^3 + 9*$.1^2 - 30*$.1 - 25,11,$.1^5 - 5*$.1^4 + 10*$.1^3 - 10*$.1^2 + 5*$.1 - 1,13,$.1^5 + 9*$.1^4 - $.1^3 - 132*$.1^2 - 117*$.1 + 193[] 473,6,2,$.1^9 - 4*$.1^8 - 5*$.1^7 + 36*$.1^6 - 20*$.1^5 - 65*$.1^4 + 66*$.1^3 + 4*$.1^2 - 8*$.1 + 1,3,$.1^9 - 5*$.1^8 - 4*$.1^7 + 52*$.1^6 - 47*$.1^5 - 108*$.1^4 + 148*$.1^3 + 43*$.1^2 - 82*$.1 - 4,5,$.1^9 - 25*$.1^7 + 13*$.1^6 + 179*$.1^5 - 143*$.1^4 - 374*$.1^3 + 424*$.1^2 - 40*$.1 - 16,7,$.1^9 - 19*$.1^8 + 140*$.1^7 - 482*$.1^6 + 627*$.1^5 + 570*$.1^4 - 2324*$.1^3 + 1223*$.1^2 + 1580*$.1 - 1368,11,$.1^9 - 9*$.1^8 + 36*$.1^7 - 84*$.1^6 + 126*$.1^5 - 126*$.1^4 + 84*$.1^3 - 36*$.1^2 + 9*$.1 - 1,13,$.1^9 - 11*$.1^8 - 5*$.1^7 + 436*$.1^6 - 1613*$.1^5 + 957*$.1^4 + 3732*$.1^3 - 4212*$.1^2 - 1360*$.1 + 992[] 473,7,2,$.1^11 + $.1^10 - 17*$.1^9 - 15*$.1^8 + 102*$.1^7 + 77*$.1^6 - 255*$.1^5 - 150*$.1^4 + 248*$.1^3 + 59*$.1^2 - 93*$.1 + 18,3,$.1^11 - 6*$.1^10 - 7*$.1^9 + 94*$.1^8 - 53*$.1^7 - 483*$.1^6 + 524*$.1^5 + 873*$.1^4 - 1135*$.1^3 - 260*$.1^2 + 364*$.1 + 64,5,$.1^11 - 3*$.1^10 - 31*$.1^9 + 82*$.1^8 + 354*$.1^7 - 824*$.1^6 - 1773*$.1^5 + 3616*$.1^4 + 3412*$.1^3 - 5976*$.1^2 - 768*$.1 + 864,7,$.1^11 - 17*$.1^10 + 96*$.1^9 - 92*$.1^8 - 1043*$.1^7 + 3448*$.1^6 - 142*$.1^5 - 12971*$.1^4 + 13700*$.1^3 + 4760*$.1^2 - 6848*$.1 + 1024,11,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3 + 55*$.1^2 + 11*$.1 + 1,13,$.1^11 - 11*$.1^10 - 15*$.1^9 + 478*$.1^8 - 649*$.1^7 - 5829*$.1^6 + 10608*$.1^5 + 21112*$.1^4 - 20096*$.1^3 - 31984*$.1^2 - 5312*$.1 + 384[] 474,1,2,x + 1,3,x + 1,5,x - 2,7,x + 3,11,x + 5,13,x + 1[] 474,2,2,x + 1,3,x - 1,5,x + 2,7,x + 1,11,x + 5,13,x + 1[] 474,3,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + x - 7,7,x^2 - x - 7,11,x^2,13,x^2[] 474,4,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 3*x + 1,7,x^2 + x - 11,11,x^2 - 8*x + 16,13,x^2 + 4*x - 16[] 474,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - x + 2,7,x^3 - 4*x + 1,11,x^3 - x^2 - 12*x + 16,13,x^3 + x^2 - 12*x - 16[] 474,6,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - x^3 - 19*x^2 + 20*x - 4,7,x^4 - 4*x^3 - 12*x^2 + 55*x - 24,11,x^4 - 5*x^3 - 40*x^2 + 192*x + 64,13,x^4 - 9*x^3 + 2*x^2 + 112*x - 128[] 475,1,2,x,3,x - 2,5,x,7,x - 1,11,x - 3,13,x - 4[] 475,2,2,x - 1,3,x,5,x,7,x + 2,11,x + 4,13,x - 2[] 475,3,2,x + 1,3,x,5,x,7,x - 2,11,x + 4,13,x + 2[] 475,4,2,x^3 + x^2 - 3*x - 1,3,x^3 + 2*x^2 - 4*x - 4,5,x^3,7,x^3 - 16*x - 16,11,x^3 + 8*x^2 + 8*x - 16,13,x^3 + 8*x^2 + 12*x + 4[] 475,5,2,x^3 + 4*x^2 + 3*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3,7,x^3 - 7*x - 7,11,x^3 - x^2 - 16*x - 13,13,x^3 + 5*x^2 + 6*x + 1[] 475,6,2,x^3 - 2*x^2 - 3*x + 5,3,x^3 - 2*x^2 - 3*x + 5,5,x^3,7,x^3 - 4*x^2 + x + 1,11,x^3 - x^2 - 4*x - 1,13,x^3 - 3*x^2 - 36*x + 103[] 475,7,2,x^3 - 4*x^2 + 3*x + 1,3,x^3 - 2*x^2 - x + 1,5,x^3,7,x^3 - 7*x + 7,11,x^3 - x^2 - 16*x - 13,13,x^3 - 5*x^2 + 6*x - 1[] 475,8,2,x^3 + 2*x^2 - 3*x - 5,3,x^3 + 2*x^2 - 3*x - 5,5,x^3,7,x^3 + 4*x^2 + x - 1,11,x^3 - x^2 - 4*x - 1,13,x^3 + 3*x^2 - 36*x - 103[] 475,9,2,x^4 - 2*x^3 - 6*x^2 + 8*x + 9,3,x^4 + 2*x^3 - 8*x^2 - 16*x - 4,5,x^4,7,x^4 + 4*x^3 - 16*x^2 - 48*x + 32,11,x^4 - 4*x^3 - 16*x^2 + 32*x + 48,13,x^4 + 2*x^3 - 24*x^2 - 32*x + 20[] 475,10,2,x^6 - 10*x^4 + 27*x^2 - 16,3,x^6 - 16*x^4 + 60*x^2 - 16,5,x^6,7,x^6 - 19*x^4 + 104*x^2 - 144,11,x^6 - 2*x^5 - 31*x^4 + 56*x^3 + 232*x^2 - 384*x + 144,13,x^6 - 28*x^4 + 236*x^2 - 576[] 476,1,2,x^2,3,x^2 + x - 3,5,x^2 - x - 3,7,x^2 + 2*x + 1,11,x^2 - 8*x + 16,13,x^2 + 2*x - 12[] 476,2,2,x^2,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 + 2*x + 1,11,x^2 + 6*x + 4,13,x^2 + 2*x - 4[] 476,3,2,x^2,3,x^2 + 3*x - 1,5,x^2 + 3*x - 1,7,x^2 - 2*x + 1,11,x^2 - 2*x - 12,13,x^2 + 6*x - 4[] 476,4,2,x^2,3,x^2 - x - 3,5,x^2 + x - 3,7,x^2 - 2*x + 1,11,x^2,13,x^2 - 6*x - 4[] Total time: 19.250 seconds, Total memory usage: 6.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:51:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [476..479] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:50:46 on modular [Seed = 1220372666] ------------------------------------- 476,1,2,$.1^2,3,$.1^2 + $.1 - 3,5,$.1^2 - $.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 16,13,$.1^2 + 2*$.1 - 12[] 476,2,2,$.1^2,3,$.1^2 + $.1 - 1,5,$.1^2 + $.1 - 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 + 6*$.1 + 4,13,$.1^2 + 2*$.1 - 4[] 476,3,2,$.1^2,3,$.1^2 + 3*$.1 - 1,5,$.1^2 + 3*$.1 - 1,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 2*$.1 - 12,13,$.1^2 + 6*$.1 - 4[] 476,4,2,$.1^2,3,$.1^2 - $.1 - 3,5,$.1^2 + $.1 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2,13,$.1^2 - 6*$.1 - 4[] 477,1,2,x - 1,3,x,5,x,7,x + 4,11,x,13,x + 3[] 477,2,2,x^3 - x^2 - 3*x + 1,3,x^3,5,x^3 - 2*x^2 - 4*x + 4,7,x^3 - 4*x^2 + 4,11,x^3 - 4*x^2 - 4*x + 20,13,x^3 - 3*x^2 + 3*x - 1[] 477,3,2,x^4 + 3*x^3 - x^2 - 5*x + 1,3,x^4,5,x^4 + 4*x^3 - x^2 - 14*x - 9,7,x^4 - 7*x^2 + 4*x + 1,11,x^4 + 8*x^3 + 8*x^2 - 40*x - 48,13,x^4 + 6*x^3 - 21*x^2 - 106*x + 93[] 477,4,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4,5,x^4 - 4*x^3 - x^2 + 14*x - 9,7,x^4 - 7*x^2 + 4*x + 1,11,x^4 - 8*x^3 + 8*x^2 + 40*x - 48,13,x^4 + 6*x^3 - 21*x^2 - 106*x + 93[] 477,5,2,x^4 + 3*x^3 - x^2 - 7*x - 3,3,x^4,5,x^4 + 2*x^3 - 11*x^2 - 32*x - 21,7,x^4 + 4*x^3 - 7*x^2 - 44*x - 43,11,x^4 + 6*x^3 - 28*x^2 - 232*x - 336,13,x^4 + 6*x^3 - 9*x^2 - 70*x + 1[] 477,6,2,x^5 - 10*x^3 + 22*x - 5,3,x^5,5,x^5 - 19*x^3 - 6*x^2 + 67*x + 2,7,x^5 - 4*x^4 - 23*x^3 + 92*x^2 + 117*x - 472,11,x^5 + 2*x^4 - 28*x^3 - 72*x^2 + 16*x + 64,13,x^5 - 8*x^4 - 13*x^3 + 136*x^2 + 101*x - 110[] 478,1,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 4*x^2 - 5*x - 1,5,x^4 + 3*x^3 - 2*x^2 - 10*x - 5,7,x^4 + 2*x^3 - 8*x^2 - 9*x + 13,11,x^4 + 3*x^3 - 26*x^2 - 46*x + 103,13,x^4 + 3*x^3 - 17*x^2 + 11*x + 7[] 478,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 6*x^3 + 10*x^2 + 3*x - 1,5,x^4 + 7*x^3 + 10*x^2 - 16*x - 31,7,x^4 + 6*x^3 - 8*x^2 - 101*x - 149,11,x^4 + 3*x^3 - 30*x^2 - 44*x + 179,13,x^4 + 9*x^3 - 5*x^2 - 213*x - 451[] 478,3,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 2*x^4 - 6*x^3 + 11*x^2 + 7*x - 12,5,x^5 - 3*x^4 - 4*x^3 + 12*x^2 + 5*x - 6,7,x^5 - 4*x^4 - 2*x^3 + 21*x^2 - 15*x - 4,11,x^5 - 5*x^4 - 6*x^3 + 28*x^2 + 15*x - 16,13,x^5 - x^4 - 23*x^3 + 69*x^2 - 57*x + 8[] 478,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 2*x^5 - 12*x^4 + 19*x^3 + 35*x^2 - 32*x - 32,5,x^6 - 5*x^5 - 6*x^4 + 50*x^3 - 33*x^2 - 44*x + 28,7,x^6 - 26*x^4 + 5*x^3 + 71*x^2 - 48*x + 8,11,x^6 - 5*x^5 - 18*x^4 + 130*x^3 - 133*x^2 - 200*x + 232,13,x^6 - 3*x^5 - 53*x^4 + 131*x^3 + 563*x^2 - 334*x - 1186[] 479,1,2,x^8 + 2*x^7 - 6*x^6 - 11*x^5 + 10*x^4 + 17*x^3 - 4*x^2 - 7*x - 1,3,x^8 + 3*x^7 - 4*x^6 - 15*x^5 + x^4 + 16*x^3 + 2*x^2 - 4*x - 1,5,x^8 + 4*x^7 - 2*x^6 - 24*x^5 - 21*x^4 + 17*x^3 + 27*x^2 + 10*x + 1,7,x^8 + 4*x^7 - 6*x^6 - 44*x^5 - 49*x^4 + 19*x^3 + 49*x^2 + 14*x - 1,11,x^8 + 5*x^7 - 11*x^6 - 84*x^5 - 112*x^4 - 43*x^3 + 7*x^2 + 7*x + 1,13,x^8 + 9*x^7 + 23*x^6 - 10*x^5 - 116*x^4 - 107*x^3 + 99*x^2 + 177*x + 61[] 479,2,2,x^32 - 3*x^31 - 49*x^30 + 150*x^29 + 1068*x^28 - 3349*x^27 - 13663*x^26 + 44102*x^25 + 114017*x^24 - 381227*x^23 - 652363*x^22 + 2278423*x^21 + 2617329*x^20 - 9659993*x^19 - 7391907*x^18 + 29333039*x^17 + 14485613*x^16 - 63589225*x^15 - 18892591*x^14 + 96842403*x^13 + 14744217*x^12 - 100301909*x^11 - 4507611*x^10 + 66698107*x^9 - 2210691*x^8 - 25684834*x^7 + 2153748*x^6 + 4689118*x^5 - 470371*x^4 - 268239*x^3 + 38414*x^2 - 242*x - 7,3,x^32 - 5*x^31 - 63*x^30 + 344*x^29 + 1704*x^28 - 10494*x^27 - 25595*x^26 + 187357*x^25 + 227445*x^24 - 2177843*x^23 - 1114189*x^22 + 17365061*x^21 + 1360454*x^20 - 97608556*x^19 + 18763008*x^18 + 392002532*x^17 - 137548311*x^16 - 1129433662*x^15 + 478309511*x^14 + 2325377139*x^13 - 985918389*x^12 - 3375402978*x^11 + 1221010481*x^10 + 3357623855*x^9 - 830495510*x^8 - 2164167195*x^7 + 208967933*x^6 + 805018305*x^5 + 56962584*x^4 - 128835824*x^3 - 31102484*x^2 - 398028*x + 139187,5,x^32 - 6*x^31 - 99*x^30 + 650*x^29 + 4176*x^28 - 31187*x^27 - 95978*x^26 + 874153*x^25 + 1230170*x^24 - 15896279*x^23 - 6371926*x^22 + 196883940*x^21 - 55851768*x^20 - 1695138243*x^19 + 1356000015*x^18 + 10151496640*x^17 - 12573160105*x^16 - 41443199854*x^15 + 69699610005*x^14 + 109264004022*x^13 - 248513470559*x^12 - 160056140840*x^11 + 570181911365*x^10 + 46587939531*x^9 - 809089270013*x^8 + 237355977983*x^7 + 650249928390*x^6 - 376623575384*x^5 - 241458556798*x^4 + 219821395723*x^3 + 12651006597*x^2 - 45139203778*x + 9151995329,7,x^32 - 8*x^31 - 125*x^30 + 1172*x^29 + 6124*x^28 - 74777*x^27 - 127164*x^26 + 2715765*x^25 - 396922*x^24 - 61390141*x^23 + 85340794*x^22 + 880387964*x^21 - 2177495446*x^20 - 7632833373*x^19 + 29456135743*x^18 + 31292238770*x^17 - 236954544803*x^16 + 58898064532*x^15 + 1100884700503*x^14 - 1315047166956*x^13 - 2445524896771*x^12 + 5854903619054*x^11 + 191611506123*x^10 - 10294527175039*x^9 + 7720989332953*x^8 + 4916583932917*x^7 - 8596797576802*x^6 + 1645938589520*x^5 + 2700693624016*x^4 - 1440448082017*x^3 - 49317177497*x^2 + 159770207746*x - 23508342337,11,x^32 - 11*x^31 - 170*x^30 + 2265*x^29 + 10788*x^28 - 202568*x^27 - 225464*x^26 + 10290626*x^25 - 8512681*x^24 - 325230593*x^23 + 705680039*x^22 + 6543689371*x^21 - 22177538499*x^20 - 80731840869*x^19 + 404699138729*x^18 + 502086529171*x^17 - 4606709368897*x^16 + 545099209698*x^15 + 32350430642653*x^14 - 34722746983061*x^13 - 128353862486880*x^12 + 258847478402279*x^11 + 203773531088353*x^10 - 868283210528113*x^9 + 261837256912342*x^8 + 1229973469625787*x^7 - 1201747716097153*x^6 - 291619684645047*x^5 + 859061505759179*x^4 - 253385721770497*x^3 - 141315750945463*x^2 + 88787782173691*x - 12184098128923,13,x^32 - 13*x^31 - 207*x^30 + 3306*x^29 + 16128*x^28 - 368777*x^27 - 429085*x^26 + 23712447*x^25 - 17477467*x^24 - 971341690*x^23 + 1881302792*x^22 + 26443688640*x^21 - 74652373648*x^20 - 484433337312*x^19 + 1739050092352*x^18 + 5919946586624*x^17 - 25974846256640*x^16 - 46921286472704*x^15 + 254028258181120*x^14 + 229645967859712*x^13 - 1621563037339648*x^12 - 642474047692800*x^11 + 6660436956053504*x^10 + 877802533945344*x^9 - 17084262354649088*x^8 - 307470387642368*x^7 + 25775286115368960*x^6 - 470173925507072*x^5 - 20398713754091520*x^4 + 1055820137627648*x^3 + 6892854760701952*x^2 - 698012942729216*x - 415848749596672[] Total time: 16.219 seconds, Total memory usage: 5.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:01:59 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [479..482] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 12:01:36 on modular [Seed = 2640871673] ------------------------------------- 479,1,2,$.1^8 + 2*$.1^7 - 6*$.1^6 - 11*$.1^5 + 10*$.1^4 + 17*$.1^3 - 4*$.1^2 - 7*$.1 - 1,3,$.1^8 + 3*$.1^7 - 4*$.1^6 - 15*$.1^5 + $.1^4 + 16*$.1^3 + 2*$.1^2 - 4*$.1 - 1,5,$.1^8 + 4*$.1^7 - 2*$.1^6 - 24*$.1^5 - 21*$.1^4 + 17*$.1^3 + 27*$.1^2 + 10*$.1 + 1,7,$.1^8 + 4*$.1^7 - 6*$.1^6 - 44*$.1^5 - 49*$.1^4 + 19*$.1^3 + 49*$.1^2 + 14*$.1 - 1,11,$.1^8 + 5*$.1^7 - 11*$.1^6 - 84*$.1^5 - 112*$.1^4 - 43*$.1^3 + 7*$.1^2 + 7*$.1 + 1,13,$.1^8 + 9*$.1^7 + 23*$.1^6 - 10*$.1^5 - 116*$.1^4 - 107*$.1^3 + 99*$.1^2 + 177*$.1 + 61[] 479,2,2,$.1^32 - 3*$.1^31 - 49*$.1^30 + 150*$.1^29 + 1068*$.1^28 - 3349*$.1^27 - 13663*$.1^26 + 44102*$.1^25 + 114017*$.1^24 - 381227*$.1^23 - 652363*$.1^22 + 2278423*$.1^21 + 2617329*$.1^20 - 9659993*$.1^19 - 7391907*$.1^18 + 29333039*$.1^17 + 14485613*$.1^16 - 63589225*$.1^15 - 18892591*$.1^14 + 96842403*$.1^13 + 14744217*$.1^12 - 100301909*$.1^11 - 4507611*$.1^10 + 66698107*$.1^9 - 2210691*$.1^8 - 25684834*$.1^7 + 2153748*$.1^6 + 4689118*$.1^5 - 470371*$.1^4 - 268239*$.1^3 + 38414*$.1^2 - 242*$.1 - 7,3,$.1^32 - 5*$.1^31 - 63*$.1^30 + 344*$.1^29 + 1704*$.1^28 - 10494*$.1^27 - 25595*$.1^26 + 187357*$.1^25 + 227445*$.1^24 - 2177843*$.1^23 - 1114189*$.1^22 + 17365061*$.1^21 + 1360454*$.1^20 - 97608556*$.1^19 + 18763008*$.1^18 + 392002532*$.1^17 - 137548311*$.1^16 - 1129433662*$.1^15 + 478309511*$.1^14 + 2325377139*$.1^13 - 985918389*$.1^12 - 3375402978*$.1^11 + 1221010481*$.1^10 + 3357623855*$.1^9 - 830495510*$.1^8 - 2164167195*$.1^7 + 208967933*$.1^6 + 805018305*$.1^5 + 56962584*$.1^4 - 128835824*$.1^3 - 31102484*$.1^2 - 398028*$.1 + 139187,5,$.1^32 - 6*$.1^31 - 99*$.1^30 + 650*$.1^29 + 4176*$.1^28 - 31187*$.1^27 - 95978*$.1^26 + 874153*$.1^25 + 1230170*$.1^24 - 15896279*$.1^23 - 6371926*$.1^22 + 196883940*$.1^21 - 55851768*$.1^20 - 1695138243*$.1^19 + 1356000015*$.1^18 + 10151496640*$.1^17 - 12573160105*$.1^16 - 41443199854*$.1^15 + 69699610005*$.1^14 + 109264004022*$.1^13 - 248513470559*$.1^12 - 160056140840*$.1^11 + 570181911365*$.1^10 + 46587939531*$.1^9 - 809089270013*$.1^8 + 237355977983*$.1^7 + 650249928390*$.1^6 - 376623575384*$.1^5 - 241458556798*$.1^4 + 219821395723*$.1^3 + 12651006597*$.1^2 - 45139203778*$.1 + 9151995329,7,$.1^32 - 8*$.1^31 - 125*$.1^30 + 1172*$.1^29 + 6124*$.1^28 - 74777*$.1^27 - 127164*$.1^26 + 2715765*$.1^25 - 396922*$.1^24 - 61390141*$.1^23 + 85340794*$.1^22 + 880387964*$.1^21 - 2177495446*$.1^20 - 7632833373*$.1^19 + 29456135743*$.1^18 + 31292238770*$.1^17 - 236954544803*$.1^16 + 58898064532*$.1^15 + 1100884700503*$.1^14 - 1315047166956*$.1^13 - 2445524896771*$.1^12 + 5854903619054*$.1^11 + 191611506123*$.1^10 - 10294527175039*$.1^9 + 7720989332953*$.1^8 + 4916583932917*$.1^7 - 8596797576802*$.1^6 + 1645938589520*$.1^5 + 2700693624016*$.1^4 - 1440448082017*$.1^3 - 49317177497*$.1^2 + 159770207746*$.1 - 23508342337,11,$.1^32 - 11*$.1^31 - 170*$.1^30 + 2265*$.1^29 + 10788*$.1^28 - 202568*$.1^27 - 225464*$.1^26 + 10290626*$.1^25 - 8512681*$.1^24 - 325230593*$.1^23 + 705680039*$.1^22 + 6543689371*$.1^21 - 22177538499*$.1^20 - 80731840869*$.1^19 + 404699138729*$.1^18 + 502086529171*$.1^17 - 4606709368897*$.1^16 + 545099209698*$.1^15 + 32350430642653*$.1^14 - 34722746983061*$.1^13 - 128353862486880*$.1^12 + 258847478402279*$.1^11 + 203773531088353*$.1^10 - 868283210528113*$.1^9 + 261837256912342*$.1^8 + 1229973469625787*$.1^7 - 1201747716097153*$.1^6 - 291619684645047*$.1^5 + 859061505759179*$.1^4 - 253385721770497*$.1^3 - 141315750945463*$.1^2 + 88787782173691*$.1 - 12184098128923,13,$.1^32 - 13*$.1^31 - 207*$.1^30 + 3306*$.1^29 + 16128*$.1^28 - 368777*$.1^27 - 429085*$.1^26 + 23712447*$.1^25 - 17477467*$.1^24 - 971341690*$.1^23 + 1881302792*$.1^22 + 26443688640*$.1^21 - 74652373648*$.1^20 - 484433337312*$.1^19 + 1739050092352*$.1^18 + 5919946586624*$.1^17 - 25974846256640*$.1^16 - 46921286472704*$.1^15 + 254028258181120*$.1^14 + 229645967859712*$.1^13 - 1621563037339648*$.1^12 - 642474047692800*$.1^11 + 6660436956053504*$.1^10 + 877802533945344*$.1^9 - 17084262354649088*$.1^8 - 307470387642368*$.1^7 + 25775286115368960*$.1^6 - 470173925507072*$.1^5 - 20398713754091520*$.1^4 + 1055820137627648*$.1^3 + 6892854760701952*$.1^2 - 698012942729216*$.1 - 415848749596672[] 480,1,2,x,3,x + 1,5,x + 1,7,x,11,x + 4,13,x - 2[] 480,2,2,x,3,x + 1,5,x - 1,7,x,11,x,13,x - 2[] 480,3,2,x,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[] 480,4,2,x,3,x - 1,5,x + 1,7,x - 4,11,x + 4,13,x - 6[] 480,5,2,x,3,x + 1,5,x + 1,7,x + 4,11,x - 4,13,x - 6[] 480,6,2,x,3,x + 1,5,x - 1,7,x + 4,11,x,13,x + 2[] 480,7,2,x,3,x - 1,5,x - 1,7,x,11,x,13,x - 2[] 480,8,2,x,3,x - 1,5,x - 1,7,x - 4,11,x,13,x + 2[] 481,1,2,x - 1,3,x,5,x + 2,7,x - 2,11,x + 2,13,x + 1[] 481,2,2,x^7 + 5*x^6 + 2*x^5 - 21*x^4 - 25*x^3 + 8*x^2 + 13*x - 2,3,x^7 - x^6 - 11*x^5 + 7*x^4 + 39*x^3 - 6*x^2 - 46*x - 19,5,x^7 + 4*x^6 - 13*x^5 - 42*x^4 + 83*x^3 + 99*x^2 - 227*x + 94,7,x^7 + 8*x^6 - 5*x^5 - 147*x^4 - 126*x^3 + 621*x^2 + 405*x - 243,11,x^7 + 13*x^6 + 38*x^5 - 83*x^4 - 427*x^3 - 434*x^2 - 71*x + 37,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 481,3,2,x^7 + x^6 - 8*x^5 - 7*x^4 + 17*x^3 + 12*x^2 - 9*x - 6,3,x^7 + 7*x^6 + 13*x^5 - 5*x^4 - 29*x^3 - 10*x^2 + 10*x + 1,5,x^7 + 2*x^6 - 19*x^5 - 38*x^4 + 73*x^3 + 195*x^2 + 105*x + 12,7,x^7 + 2*x^6 - 15*x^5 - 11*x^4 + 64*x^3 - 27*x^2 - 21*x + 11,11,x^7 + 13*x^6 + 40*x^5 - 87*x^4 - 461*x^3 + 60*x^2 + 1035*x + 423,13,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1[] 481,4,2,x^11 - 3*x^10 - 14*x^9 + 45*x^8 + 64*x^7 - 237*x^6 - 99*x^5 + 529*x^4 - 7*x^3 - 460*x^2 + 67*x + 110,3,x^11 - x^10 - 23*x^9 + 19*x^8 + 191*x^7 - 106*x^6 - 702*x^5 + 153*x^4 + 1016*x^3 + 144*x^2 - 160*x - 32,5,x^11 - 4*x^10 - 29*x^9 + 128*x^8 + 223*x^7 - 1259*x^6 - 243*x^5 + 4516*x^4 - 2112*x^3 - 4300*x^2 + 3492*x - 640,7,x^11 - 4*x^10 - 27*x^9 + 115*x^8 + 174*x^7 - 923*x^6 - 157*x^5 + 2419*x^4 - 704*x^3 - 1246*x^2 + 126*x + 2,11,x^11 - 21*x^10 + 138*x^9 + 5*x^8 - 3767*x^7 + 13336*x^6 + 5591*x^5 - 102581*x^4 + 126638*x^3 + 89244*x^2 - 150718*x + 21938,13,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1[] 481,5,2,x^11 - 3*x^10 - 12*x^9 + 39*x^8 + 38*x^7 - 149*x^6 - 23*x^5 + 175*x^4 - 5*x^3 - 48*x^2 + 5*x + 2,3,x^11 - 5*x^10 - 11*x^9 + 83*x^8 - 9*x^7 - 418*x^6 + 314*x^5 + 709*x^4 - 692*x^3 - 192*x^2 + 128*x + 32,5,x^11 - 2*x^10 - 27*x^9 + 64*x^8 + 177*x^7 - 491*x^6 - 127*x^5 + 706*x^4 + 40*x^3 - 268*x^2 - 92*x - 8,7,x^11 - 45*x^9 + 13*x^8 + 694*x^7 - 379*x^6 - 4269*x^5 + 3371*x^4 + 8922*x^3 - 9110*x^2 + 486*x + 262,11,x^11 - 11*x^10 + 30*x^9 + 77*x^8 - 503*x^7 + 440*x^6 + 1621*x^5 - 3413*x^4 + 848*x^3 + 2084*x^2 - 1058*x + 102,13,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1[] 482,1,2,x + 1,3,x + 2,5,x + 1,7,x - 1,11,x - 4,13,x + 2[] 482,2,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 + 6*x + 9,13,x^2 + 7*x + 11[] 482,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 5*x - 2,5,x^3 - 2*x^2 - 4*x + 7,7,x^3 + 9*x^2 + 27*x + 27,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 + 5*x^2 - 11*x - 2[] 482,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 2*x^5 - 10*x^4 + 16*x^3 + 26*x^2 - 30*x - 13,5,x^6 + 5*x^5 - 9*x^4 - 56*x^3 + 20*x^2 + 128*x - 48,7,x^6 - 10*x^5 + 22*x^4 + 44*x^3 - 172*x^2 + 118*x - 23,11,x^6 + 4*x^5 - 17*x^4 - 48*x^3 + 104*x^2 + 128*x - 192,13,x^6 - 9*x^5 + 16*x^4 + 49*x^3 - 178*x^2 + 165*x - 45[] Errors: /home/mfd/gomagma: line 2: 11145 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:02:53 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [479..481] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:02:33 on modular [Seed = 2238748728] ------------------------------------- 479,1,2,$.1^8 + 2*$.1^7 - 6*$.1^6 - 11*$.1^5 + 10*$.1^4 + 17*$.1^3 - 4*$.1^2 - 7*$.1 - 1,3,$.1^8 + 3*$.1^7 - 4*$.1^6 - 15*$.1^5 + $.1^4 + 16*$.1^3 + 2*$.1^2 - 4*$.1 - 1,5,$.1^8 + 4*$.1^7 - 2*$.1^6 - 24*$.1^5 - 21*$.1^4 + 17*$.1^3 + 27*$.1^2 + 10*$.1 + 1,7,$.1^8 + 4*$.1^7 - 6*$.1^6 - 44*$.1^5 - 49*$.1^4 + 19*$.1^3 + 49*$.1^2 + 14*$.1 - 1,11,$.1^8 + 5*$.1^7 - 11*$.1^6 - 84*$.1^5 - 112*$.1^4 - 43*$.1^3 + 7*$.1^2 + 7*$.1 + 1,13,$.1^8 + 9*$.1^7 + 23*$.1^6 - 10*$.1^5 - 116*$.1^4 - 107*$.1^3 + 99*$.1^2 + 177*$.1 + 61[] 479,2,2,$.1^32 - 3*$.1^31 - 49*$.1^30 + 150*$.1^29 + 1068*$.1^28 - 3349*$.1^27 - 13663*$.1^26 + 44102*$.1^25 + 114017*$.1^24 - 381227*$.1^23 - 652363*$.1^22 + 2278423*$.1^21 + 2617329*$.1^20 - 9659993*$.1^19 - 7391907*$.1^18 + 29333039*$.1^17 + 14485613*$.1^16 - 63589225*$.1^15 - 18892591*$.1^14 + 96842403*$.1^13 + 14744217*$.1^12 - 100301909*$.1^11 - 4507611*$.1^10 + 66698107*$.1^9 - 2210691*$.1^8 - 25684834*$.1^7 + 2153748*$.1^6 + 4689118*$.1^5 - 470371*$.1^4 - 268239*$.1^3 + 38414*$.1^2 - 242*$.1 - 7,3,$.1^32 - 5*$.1^31 - 63*$.1^30 + 344*$.1^29 + 1704*$.1^28 - 10494*$.1^27 - 25595*$.1^26 + 187357*$.1^25 + 227445*$.1^24 - 2177843*$.1^23 - 1114189*$.1^22 + 17365061*$.1^21 + 1360454*$.1^20 - 97608556*$.1^19 + 18763008*$.1^18 + 392002532*$.1^17 - 137548311*$.1^16 - 1129433662*$.1^15 + 478309511*$.1^14 + 2325377139*$.1^13 - 985918389*$.1^12 - 3375402978*$.1^11 + 1221010481*$.1^10 + 3357623855*$.1^9 - 830495510*$.1^8 - 2164167195*$.1^7 + 208967933*$.1^6 + 805018305*$.1^5 + 56962584*$.1^4 - 128835824*$.1^3 - 31102484*$.1^2 - 398028*$.1 + 139187,5,$.1^32 - 6*$.1^31 - 99*$.1^30 + 650*$.1^29 + 4176*$.1^28 - 31187*$.1^27 - 95978*$.1^26 + 874153*$.1^25 + 1230170*$.1^24 - 15896279*$.1^23 - 6371926*$.1^22 + 196883940*$.1^21 - 55851768*$.1^20 - 1695138243*$.1^19 + 1356000015*$.1^18 + 10151496640*$.1^17 - 12573160105*$.1^16 - 41443199854*$.1^15 + 69699610005*$.1^14 + 109264004022*$.1^13 - 248513470559*$.1^12 - 160056140840*$.1^11 + 570181911365*$.1^10 + 46587939531*$.1^9 - 809089270013*$.1^8 + 237355977983*$.1^7 + 650249928390*$.1^6 - 376623575384*$.1^5 - 241458556798*$.1^4 + 219821395723*$.1^3 + 12651006597*$.1^2 - 45139203778*$.1 + 9151995329,7,$.1^32 - 8*$.1^31 - 125*$.1^30 + 1172*$.1^29 + 6124*$.1^28 - 74777*$.1^27 - 127164*$.1^26 + 2715765*$.1^25 - 396922*$.1^24 - 61390141*$.1^23 + 85340794*$.1^22 + 880387964*$.1^21 - 2177495446*$.1^20 - 7632833373*$.1^19 + 29456135743*$.1^18 + 31292238770*$.1^17 - 236954544803*$.1^16 + 58898064532*$.1^15 + 1100884700503*$.1^14 - 1315047166956*$.1^13 - 2445524896771*$.1^12 + 5854903619054*$.1^11 + 191611506123*$.1^10 - 10294527175039*$.1^9 + 7720989332953*$.1^8 + 4916583932917*$.1^7 - 8596797576802*$.1^6 + 1645938589520*$.1^5 + 2700693624016*$.1^4 - 1440448082017*$.1^3 - 49317177497*$.1^2 + 159770207746*$.1 - 23508342337,11,$.1^32 - 11*$.1^31 - 170*$.1^30 + 2265*$.1^29 + 10788*$.1^28 - 202568*$.1^27 - 225464*$.1^26 + 10290626*$.1^25 - 8512681*$.1^24 - 325230593*$.1^23 + 705680039*$.1^22 + 6543689371*$.1^21 - 22177538499*$.1^20 - 80731840869*$.1^19 + 404699138729*$.1^18 + 502086529171*$.1^17 - 4606709368897*$.1^16 + 545099209698*$.1^15 + 32350430642653*$.1^14 - 34722746983061*$.1^13 - 128353862486880*$.1^12 + 258847478402279*$.1^11 + 203773531088353*$.1^10 - 868283210528113*$.1^9 + 261837256912342*$.1^8 + 1229973469625787*$.1^7 - 1201747716097153*$.1^6 - 291619684645047*$.1^5 + 859061505759179*$.1^4 - 253385721770497*$.1^3 - 141315750945463*$.1^2 + 88787782173691*$.1 - 12184098128923,13,$.1^32 - 13*$.1^31 - 207*$.1^30 + 3306*$.1^29 + 16128*$.1^28 - 368777*$.1^27 - 429085*$.1^26 + 23712447*$.1^25 - 17477467*$.1^24 - 971341690*$.1^23 + 1881302792*$.1^22 + 26443688640*$.1^21 - 74652373648*$.1^20 - 484433337312*$.1^19 + 1739050092352*$.1^18 + 5919946586624*$.1^17 - 25974846256640*$.1^16 - 46921286472704*$.1^15 + 254028258181120*$.1^14 + 229645967859712*$.1^13 - 1621563037339648*$.1^12 - 642474047692800*$.1^11 + 6660436956053504*$.1^10 + 877802533945344*$.1^9 - 17084262354649088*$.1^8 - 307470387642368*$.1^7 + 25775286115368960*$.1^6 - 470173925507072*$.1^5 - 20398713754091520*$.1^4 + 1055820137627648*$.1^3 + 6892854760701952*$.1^2 - 698012942729216*$.1 - 415848749596672[] 480,1,2,x,3,x + 1,5,x + 1,7,x,11,x + 4,13,x - 2[] 480,2,2,x,3,x + 1,5,x - 1,7,x,11,x,13,x - 2[] 480,3,2,x,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[] 480,4,2,x,3,x - 1,5,x + 1,7,x - 4,11,x + 4,13,x - 6[] 480,5,2,x,3,x + 1,5,x + 1,7,x + 4,11,x - 4,13,x - 6[] 480,6,2,x,3,x + 1,5,x - 1,7,x + 4,11,x,13,x + 2[] 480,7,2,x,3,x - 1,5,x - 1,7,x,11,x,13,x - 2[] 480,8,2,x,3,x - 1,5,x - 1,7,x - 4,11,x,13,x + 2[] 481,1,2,x - 1,3,x,5,x + 2,7,x - 2,11,x + 2,13,x + 1[] 481,2,2,x^7 + 5*x^6 + 2*x^5 - 21*x^4 - 25*x^3 + 8*x^2 + 13*x - 2,3,x^7 - x^6 - 11*x^5 + 7*x^4 + 39*x^3 - 6*x^2 - 46*x - 19,5,x^7 + 4*x^6 - 13*x^5 - 42*x^4 + 83*x^3 + 99*x^2 - 227*x + 94,7,x^7 + 8*x^6 - 5*x^5 - 147*x^4 - 126*x^3 + 621*x^2 + 405*x - 243,11,x^7 + 13*x^6 + 38*x^5 - 83*x^4 - 427*x^3 - 434*x^2 - 71*x + 37,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 481,3,2,x^7 + x^6 - 8*x^5 - 7*x^4 + 17*x^3 + 12*x^2 - 9*x - 6,3,x^7 + 7*x^6 + 13*x^5 - 5*x^4 - 29*x^3 - 10*x^2 + 10*x + 1,5,x^7 + 2*x^6 - 19*x^5 - 38*x^4 + 73*x^3 + 195*x^2 + 105*x + 12,7,x^7 + 2*x^6 - 15*x^5 - 11*x^4 + 64*x^3 - 27*x^2 - 21*x + 11,11,x^7 + 13*x^6 + 40*x^5 - 87*x^4 - 461*x^3 + 60*x^2 + 1035*x + 423,13,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1[] 481,4,2,x^11 - 3*x^10 - 14*x^9 + 45*x^8 + 64*x^7 - 237*x^6 - 99*x^5 + 529*x^4 - 7*x^3 - 460*x^2 + 67*x + 110,3,x^11 - x^10 - 23*x^9 + 19*x^8 + 191*x^7 - 106*x^6 - 702*x^5 + 153*x^4 + 1016*x^3 + 144*x^2 - 160*x - 32,5,x^11 - 4*x^10 - 29*x^9 + 128*x^8 + 223*x^7 - 1259*x^6 - 243*x^5 + 4516*x^4 - 2112*x^3 - 4300*x^2 + 3492*x - 640,7,x^11 - 4*x^10 - 27*x^9 + 115*x^8 + 174*x^7 - 923*x^6 - 157*x^5 + 2419*x^4 - 704*x^3 - 1246*x^2 + 126*x + 2,11,x^11 - 21*x^10 + 138*x^9 + 5*x^8 - 3767*x^7 + 13336*x^6 + 5591*x^5 - 102581*x^4 + 126638*x^3 + 89244*x^2 - 150718*x + 21938,13,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1[] 481,5,2,x^11 - 3*x^10 - 12*x^9 + 39*x^8 + 38*x^7 - 149*x^6 - 23*x^5 + 175*x^4 - 5*x^3 - 48*x^2 + 5*x + 2,3,x^11 - 5*x^10 - 11*x^9 + 83*x^8 - 9*x^7 - 418*x^6 + 314*x^5 + 709*x^4 - 692*x^3 - 192*x^2 + 128*x + 32,5,x^11 - 2*x^10 - 27*x^9 + 64*x^8 + 177*x^7 - 491*x^6 - 127*x^5 + 706*x^4 + 40*x^3 - 268*x^2 - 92*x - 8,7,x^11 - 45*x^9 + 13*x^8 + 694*x^7 - 379*x^6 - 4269*x^5 + 3371*x^4 + 8922*x^3 - 9110*x^2 + 486*x + 262,11,x^11 - 11*x^10 + 30*x^9 + 77*x^8 - 503*x^7 + 440*x^6 + 1621*x^5 - 3413*x^4 + 848*x^3 + 2084*x^2 - 1058*x + 102,13,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1[] Total time: 19.090 seconds, Total memory usage: 6.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:07:03 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [481..484] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:06:46 on modular [Seed = 2340329273] ------------------------------------- 481,1,2,$.1 - 1,3,$.1,5,$.1 + 2,7,$.1 - 2,11,$.1 + 2,13,$.1 + 1[] 481,2,2,$.1^7 + 5*$.1^6 + 2*$.1^5 - 21*$.1^4 - 25*$.1^3 + 8*$.1^2 + 13*$.1 - 2,3,$.1^7 - $.1^6 - 11*$.1^5 + 7*$.1^4 + 39*$.1^3 - 6*$.1^2 - 46*$.1 - 19,5,$.1^7 + 4*$.1^6 - 13*$.1^5 - 42*$.1^4 + 83*$.1^3 + 99*$.1^2 - 227*$.1 + 94,7,$.1^7 + 8*$.1^6 - 5*$.1^5 - 147*$.1^4 - 126*$.1^3 + 621*$.1^2 + 405*$.1 - 243,11,$.1^7 + 13*$.1^6 + 38*$.1^5 - 83*$.1^4 - 427*$.1^3 - 434*$.1^2 - 71*$.1 + 37,13,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1[] 481,3,2,$.1^7 + $.1^6 - 8*$.1^5 - 7*$.1^4 + 17*$.1^3 + 12*$.1^2 - 9*$.1 - 6,3,$.1^7 + 7*$.1^6 + 13*$.1^5 - 5*$.1^4 - 29*$.1^3 - 10*$.1^2 + 10*$.1 + 1,5,$.1^7 + 2*$.1^6 - 19*$.1^5 - 38*$.1^4 + 73*$.1^3 + 195*$.1^2 + 105*$.1 + 12,7,$.1^7 + 2*$.1^6 - 15*$.1^5 - 11*$.1^4 + 64*$.1^3 - 27*$.1^2 - 21*$.1 + 11,11,$.1^7 + 13*$.1^6 + 40*$.1^5 - 87*$.1^4 - 461*$.1^3 + 60*$.1^2 + 1035*$.1 + 423,13,$.1^7 - 7*$.1^6 + 21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1[] 481,4,2,$.1^11 - 3*$.1^10 - 14*$.1^9 + 45*$.1^8 + 64*$.1^7 - 237*$.1^6 - 99*$.1^5 + 529*$.1^4 - 7*$.1^3 - 460*$.1^2 + 67*$.1 + 110,3,$.1^11 - $.1^10 - 23*$.1^9 + 19*$.1^8 + 191*$.1^7 - 106*$.1^6 - 702*$.1^5 + 153*$.1^4 + 1016*$.1^3 + 144*$.1^2 - 160*$.1 - 32,5,$.1^11 - 4*$.1^10 - 29*$.1^9 + 128*$.1^8 + 223*$.1^7 - 1259*$.1^6 - 243*$.1^5 + 4516*$.1^4 - 2112*$.1^3 - 4300*$.1^2 + 3492*$.1 - 640,7,$.1^11 - 4*$.1^10 - 27*$.1^9 + 115*$.1^8 + 174*$.1^7 - 923*$.1^6 - 157*$.1^5 + 2419*$.1^4 - 704*$.1^3 - 1246*$.1^2 + 126*$.1 + 2,11,$.1^11 - 21*$.1^10 + 138*$.1^9 + 5*$.1^8 - 3767*$.1^7 + 13336*$.1^6 + 5591*$.1^5 - 102581*$.1^4 + 126638*$.1^3 + 89244*$.1^2 - 150718*$.1 + 21938,13,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3 + 55*$.1^2 + 11*$.1 + 1[] 481,5,2,$.1^11 - 3*$.1^10 - 12*$.1^9 + 39*$.1^8 + 38*$.1^7 - 149*$.1^6 - 23*$.1^5 + 175*$.1^4 - 5*$.1^3 - 48*$.1^2 + 5*$.1 + 2,3,$.1^11 - 5*$.1^10 - 11*$.1^9 + 83*$.1^8 - 9*$.1^7 - 418*$.1^6 + 314*$.1^5 + 709*$.1^4 - 692*$.1^3 - 192*$.1^2 + 128*$.1 + 32,5,$.1^11 - 2*$.1^10 - 27*$.1^9 + 64*$.1^8 + 177*$.1^7 - 491*$.1^6 - 127*$.1^5 + 706*$.1^4 + 40*$.1^3 - 268*$.1^2 - 92*$.1 - 8,7,$.1^11 - 45*$.1^9 + 13*$.1^8 + 694*$.1^7 - 379*$.1^6 - 4269*$.1^5 + 3371*$.1^4 + 8922*$.1^3 - 9110*$.1^2 + 486*$.1 + 262,11,$.1^11 - 11*$.1^10 + 30*$.1^9 + 77*$.1^8 - 503*$.1^7 + 440*$.1^6 + 1621*$.1^5 - 3413*$.1^4 + 848*$.1^3 + 2084*$.1^2 - 1058*$.1 + 102,13,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 + 330*$.1^7 - 462*$.1^6 + 462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1[] 482,1,2,x + 1,3,x + 2,5,x + 1,7,x - 1,11,x - 4,13,x + 2[] 482,2,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 + 6*x + 9,13,x^2 + 7*x + 11[] 482,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 5*x - 2,5,x^3 - 2*x^2 - 4*x + 7,7,x^3 + 9*x^2 + 27*x + 27,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 + 5*x^2 - 11*x - 2[] 482,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 2*x^5 - 10*x^4 + 16*x^3 + 26*x^2 - 30*x - 13,5,x^6 + 5*x^5 - 9*x^4 - 56*x^3 + 20*x^2 + 128*x - 48,7,x^6 - 10*x^5 + 22*x^4 + 44*x^3 - 172*x^2 + 118*x - 23,11,x^6 + 4*x^5 - 17*x^4 - 48*x^3 + 104*x^2 + 128*x - 192,13,x^6 - 9*x^5 + 16*x^4 + 49*x^3 - 178*x^2 + 165*x - 45[] 482,5,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 - 4*x^8 - 12*x^7 + 58*x^6 + 24*x^5 - 252*x^4 + 97*x^3 + 336*x^2 - 244*x - 16,5,x^9 - 5*x^8 - 18*x^7 + 113*x^6 + 23*x^5 - 662*x^4 + 628*x^3 + 296*x^2 - 272*x - 32,7,x^9 - 6*x^8 - 15*x^7 + 126*x^6 + 42*x^5 - 854*x^4 + 19*x^3 + 2278*x^2 + 117*x - 1732,11,x^9 - 2*x^8 - 57*x^7 + 74*x^6 + 1020*x^5 - 984*x^4 - 6048*x^3 + 6208*x^2 + 6400*x - 6656,13,x^9 - 5*x^8 - 66*x^7 + 275*x^6 + 1352*x^5 - 3351*x^4 - 13353*x^3 + 7280*x^2 + 49580*x + 35936[] 483,1,2,x - 2,3,x - 1,5,x - 4,7,x + 1,11,x + 5,13,x + 2[] 483,2,2,x - 2,3,x - 1,5,x,7,x - 1,11,x - 1,13,x - 2[] 483,3,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x + 1,11,x^2 - 5,13,x^2 + 7*x + 11[] 483,4,2,x^2 - x - 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 2*x + 1,11,x^2 - 5,13,x^2 + 7*x + 1[] 483,5,2,x^2 + x - 3,3,x^2 - 2*x + 1,5,x^2 + 5*x + 3,7,x^2 + 2*x + 1,11,x^2 + 10*x + 25,13,x^2 - x - 3[] 483,6,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 5*x + 5,7,x^2 - 2*x + 1,11,x^2 + 2*x - 19,13,x^2 + 7*x + 11[] 483,7,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 - 5*x + 5,7,x^2 - 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + x - 1[] 483,8,2,x^3 - 6*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 3*x + 6,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 6*x^2 - 3*x + 20,13,x^3 - 9*x^2 + 15*x - 6[] 483,9,2,x^4 - 2*x^3 - 4*x^2 + 5*x + 2,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 5*x^3 - 3*x^2 + 38*x - 32,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 - x^3 - 17*x^2 - 19*x + 4,13,x^4 - 7*x^3 - 17*x^2 + 164*x - 188[] 483,10,2,x^4 - 6*x^2 + x + 2,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 5*x^3 - x^2 + 14*x + 8,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 + 5*x^3 - 9*x^2 - 65*x - 68,13,x^4 - 7*x^3 - 11*x^2 + 152*x - 236[] 484,1,2,x,3,x - 1,5,x + 3,7,x + 2,11,x,13,x - 4[] 484,2,2,x^2,3,x^2 - x - 8,5,x^2 - 3*x - 6,7,x^2,11,x^2,13,x^2[] 484,3,2,x^2,3,x^2 + 3*x + 1,5,x^2 + x - 1,7,x^2 + x - 11,11,x^2,13,x^2 - 7*x + 11[] 484,4,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 27[] 484,5,2,x^2,3,x^2 + 3*x + 1,5,x^2 + x - 1,7,x^2 - x - 11,11,x^2,13,x^2 + 7*x + 11[] Total time: 17.229 seconds, Total memory usage: 6.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:11:08 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [484..487] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:10:52 on modular [Seed = 2773532205] ------------------------------------- 484,1,2,$.1,3,$.1 - 1,5,$.1 + 3,7,$.1 + 2,11,$.1,13,$.1 - 4[] 484,2,2,$.1^2,3,$.1^2 - $.1 - 8,5,$.1^2 - 3*$.1 - 6,7,$.1^2,11,$.1^2,13,$.1^2[] 484,3,2,$.1^2,3,$.1^2 + 3*$.1 + 1,5,$.1^2 + $.1 - 1,7,$.1^2 + $.1 - 11,11,$.1^2,13,$.1^2 - 7*$.1 + 11[] 484,4,2,$.1^2,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - 6*$.1 + 9,7,$.1^2 - 12,11,$.1^2,13,$.1^2 - 27[] 484,5,2,$.1^2,3,$.1^2 + 3*$.1 + 1,5,$.1^2 + $.1 - 1,7,$.1^2 - $.1 - 11,11,$.1^2,13,$.1^2 + 7*$.1 + 11[] 485,1,2,x,3,x + 2,5,x + 1,7,x + 1,11,x + 3,13,x - 5[] 485,2,2,x,3,x,5,x - 1,7,x + 1,11,x - 1,13,x - 1[] 485,3,2,x^2 - 5,3,x^2 - x - 1,5,x^2 + 2*x + 1,7,x^2 - 8*x + 16,11,x^2 + 6*x + 4,13,x^2 - 5*x + 5[] 485,4,2,x^2 - 2*x + 1,3,x^2 - x - 7,5,x^2 - 2*x + 1,7,x^2,11,x^2 - 2*x - 28,13,x^2 - 7*x + 5[] 485,5,2,x^3 + 2*x^2 - 5*x - 8,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 2*x + 10,11,x^3 - 5*x^2 + 8,13,x^3 + x^2 - 24*x + 20[] 485,6,2,x^4 + x^3 - 4*x^2 - 2*x + 3,3,x^4 + 4*x^3 - 7*x + 3,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 3*x^3 - 5*x^2 - 5*x - 1,11,x^4 + 16*x^3 + 92*x^2 + 225*x + 197,13,x^4 + 4*x^3 - 22*x^2 - 84*x - 43[] 485,7,2,x^6 + x^5 - 9*x^4 - 9*x^3 + 17*x^2 + 14*x + 1,3,x^6 + x^5 - 9*x^4 - 9*x^3 + 8*x^2 + 8*x + 1,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 3*x^5 - 35*x^4 + 115*x^3 + 241*x^2 - 928*x + 448,11,x^6 - 6*x^5 - 12*x^4 + 113*x^3 - 141*x^2 + 42*x + 4,13,x^6 - x^5 - 17*x^4 + 4*x^3 + 73*x^2 + 45*x + 7[] 485,8,2,x^7 + x^6 - 9*x^5 - 7*x^4 + 23*x^3 + 12*x^2 - 15*x - 8,3,x^7 + 6*x^6 + 2*x^5 - 41*x^4 - 51*x^3 + 48*x^2 + 68*x + 16,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 10*x^6 + 14*x^5 - 142*x^4 - 504*x^3 - 191*x^2 + 1022*x + 982,11,x^7 - 5*x^6 - 24*x^5 + 165*x^4 - 156*x^3 - 481*x^2 + 996*x - 504,13,x^7 + 9*x^6 - 14*x^5 - 234*x^4 + 61*x^3 + 1837*x^2 - 736*x - 2428[] 485,9,2,x^7 - 2*x^6 - 10*x^5 + 18*x^4 + 26*x^3 - 35*x^2 - 21*x + 7,3,x^7 - 9*x^6 + 21*x^5 + 29*x^4 - 182*x^3 + 218*x^2 - 19*x - 68,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 3*x^6 - 23*x^5 + 45*x^4 + 191*x^3 - 106*x^2 - 592*x - 352,11,x^7 - 6*x^6 - 12*x^5 + 145*x^4 - 297*x^3 + 106*x^2 + 148*x - 32,13,x^7 - 5*x^6 - 47*x^5 + 226*x^4 + 441*x^3 - 1327*x^2 - 2955*x - 1438[] 486,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 6,13,x + 1[] 486,2,2,x + 1,3,x,5,x + 3,7,x - 2,11,x,13,x + 4[] 486,3,2,x + 1,3,x,5,x - 3,7,x + 4,11,x - 6,13,x - 2[] 486,4,2,x - 1,3,x,5,x,7,x + 1,11,x - 6,13,x + 1[] 486,5,2,x - 1,3,x,5,x - 3,7,x - 2,11,x,13,x + 4[] 486,6,2,x - 1,3,x,5,x + 3,7,x + 4,11,x + 6,13,x - 2[] 486,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3,5,x^3 - 9*x - 9,7,x^3 - 6*x^2 + 3*x + 19,11,x^3 - 9*x - 9,13,x^3 - 6*x^2 - 24*x + 136[] 486,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3,5,x^3 - 9*x + 9,7,x^3 - 6*x^2 + 3*x + 19,11,x^3 - 9*x + 9,13,x^3 - 6*x^2 - 24*x + 136[] 487,1,2,x^2,3,x^2 + x - 3,5,x^2 - 3*x - 1,7,x^2 - 13,11,x^2 + 2*x + 1,13,x^2 - 9*x + 17[] 487,2,2,x^2,3,x^2 - 3*x - 1,5,x^2 - x - 3,7,x^2 + 2*x + 1,11,x^2 - 4*x - 9,13,x^2 - 3*x - 1[] 487,3,2,x^3 - 5*x + 3,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 6*x^2 + 12*x - 8,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 4*x^2 - 36*x + 152,13,x^3 + 6*x^2 + 12*x + 8[] 487,4,2,x^16 - 7*x^15 - 5*x^14 + 131*x^13 - 132*x^12 - 977*x^11 + 1666*x^10 + 3671*x^9 - 8191*x^8 - 7212*x^7 + 20571*x^6 + 6937*x^5 - 27100*x^4 - 2748*x^3 + 17207*x^2 + 360*x - 3825,3,x^16 + 4*x^15 - 27*x^14 - 120*x^13 + 254*x^12 + 1398*x^11 - 784*x^10 - 7896*x^9 - 1793*x^8 + 21749*x^7 + 15439*x^6 - 24655*x^5 - 26442*x^4 + 5641*x^3 + 10500*x^2 - 148*x - 1224,5,x^16 - 9*x^15 - 17*x^14 + 326*x^13 - 155*x^12 - 4490*x^11 + 4421*x^10 + 30506*x^9 - 25817*x^8 - 110435*x^7 + 40289*x^6 + 185308*x^5 + 24592*x^4 - 73975*x^3 - 14792*x^2 - 108*x + 72,7,x^16 - x^15 - 65*x^14 + 62*x^13 + 1599*x^12 - 1579*x^11 - 18837*x^10 + 19796*x^9 + 108749*x^8 - 122733*x^7 - 268709*x^6 + 330038*x^5 + 155861*x^4 - 236191*x^3 + 20622*x^2 + 20672*x - 632,11,x^16 - x^15 - 60*x^14 + 115*x^13 + 1231*x^12 - 3266*x^11 - 9620*x^10 + 32513*x^9 + 30643*x^8 - 148399*x^7 - 20214*x^6 + 327721*x^5 - 86790*x^4 - 317637*x^3 + 153178*x^2 + 89832*x - 50616,13,x^16 - 4*x^15 - 106*x^14 + 364*x^13 + 4612*x^12 - 13192*x^11 - 105021*x^10 + 245349*x^9 + 1320155*x^8 - 2540046*x^7 - 8851982*x^6 + 15030336*x^5 + 27662566*x^4 - 49136445*x^3 - 24458970*x^2 + 67586632*x - 26544200[] 487,5,2,x^17 + 8*x^16 + 7*x^15 - 97*x^14 - 239*x^13 + 327*x^12 + 1500*x^11 + 70*x^10 - 3964*x^9 - 2280*x^8 + 4849*x^7 + 4192*x^6 - 2492*x^5 - 2765*x^4 + 364*x^3 + 588*x^2 - 16,3,x^17 + 6*x^16 - 12*x^15 - 126*x^14 - 28*x^13 + 966*x^12 + 843*x^11 - 3526*x^10 - 3777*x^9 + 7023*x^8 + 6916*x^7 - 8306*x^6 - 5364*x^5 + 5495*x^4 + 1085*x^3 - 1358*x^2 + 162*x - 1,5,x^17 + 19*x^16 + 132*x^15 + 297*x^14 - 1001*x^13 - 7281*x^12 - 13237*x^11 + 8658*x^10 + 62929*x^9 + 64801*x^8 - 33491*x^7 - 87085*x^6 - 12860*x^5 + 37682*x^4 + 10983*x^3 - 4959*x^2 - 1836*x - 81,7,x^17 + 11*x^16 - x^15 - 412*x^14 - 1166*x^13 + 4148*x^12 + 20568*x^11 - 8760*x^10 - 144166*x^9 - 81902*x^8 + 488378*x^7 + 521494*x^6 - 803370*x^5 - 1136782*x^4 + 581809*x^3 + 1043038*x^2 - 135633*x - 337347,11,x^17 + 11*x^16 - 50*x^15 - 939*x^14 - 446*x^13 + 29897*x^12 + 69242*x^11 - 440580*x^10 - 1628456*x^9 + 2744029*x^8 + 16876622*x^7 + 39618*x^6 - 80051629*x^5 - 69160750*x^4 + 130895976*x^3 + 190034733*x^2 + 24632784*x - 17408851,13,x^17 + 12*x^16 - 45*x^15 - 1078*x^14 - 1845*x^13 + 29816*x^12 + 126839*x^11 - 175735*x^10 - 1911940*x^9 - 2693463*x^8 + 5037822*x^7 + 17181885*x^6 + 11294537*x^5 - 13465343*x^4 - 25963998*x^3 - 16440181*x^2 - 4592586*x - 454771[] Total time: 16.039 seconds, Total memory usage: 5.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:18:29 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [487..490] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:18:11 on modular [Seed = 3609382544] ------------------------------------- 487,1,2,$.1^2,3,$.1^2 + $.1 - 3,5,$.1^2 - 3*$.1 - 1,7,$.1^2 - 13,11,$.1^2 + 2*$.1 + 1,13,$.1^2 - 9*$.1 + 17[] 487,2,2,$.1^2,3,$.1^2 - 3*$.1 - 1,5,$.1^2 - $.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 4*$.1 - 9,13,$.1^2 - 3*$.1 - 1[] 487,3,2,$.1^3 - 5*$.1 + 3,3,$.1^3 - 6*$.1^2 + 12*$.1 - 8,5,$.1^3 - 6*$.1^2 + 12*$.1 - 8,7,$.1^3 - 6*$.1^2 + 12*$.1 - 8,11,$.1^3 - 4*$.1^2 - 36*$.1 + 152,13,$.1^3 + 6*$.1^2 + 12*$.1 + 8[] 487,4,2,$.1^16 - 7*$.1^15 - 5*$.1^14 + 131*$.1^13 - 132*$.1^12 - 977*$.1^11 + 1666*$.1^10 + 3671*$.1^9 - 8191*$.1^8 - 7212*$.1^7 + 20571*$.1^6 + 6937*$.1^5 - 27100*$.1^4 - 2748*$.1^3 + 17207*$.1^2 + 360*$.1 - 3825,3,$.1^16 + 4*$.1^15 - 27*$.1^14 - 120*$.1^13 + 254*$.1^12 + 1398*$.1^11 - 784*$.1^10 - 7896*$.1^9 - 1793*$.1^8 + 21749*$.1^7 + 15439*$.1^6 - 24655*$.1^5 - 26442*$.1^4 + 5641*$.1^3 + 10500*$.1^2 - 148*$.1 - 1224,5,$.1^16 - 9*$.1^15 - 17*$.1^14 + 326*$.1^13 - 155*$.1^12 - 4490*$.1^11 + 4421*$.1^10 + 30506*$.1^9 - 25817*$.1^8 - 110435*$.1^7 + 40289*$.1^6 + 185308*$.1^5 + 24592*$.1^4 - 73975*$.1^3 - 14792*$.1^2 - 108*$.1 + 72,7,$.1^16 - $.1^15 - 65*$.1^14 + 62*$.1^13 + 1599*$.1^12 - 1579*$.1^11 - 18837*$.1^10 + 19796*$.1^9 + 108749*$.1^8 - 122733*$.1^7 - 268709*$.1^6 + 330038*$.1^5 + 155861*$.1^4 - 236191*$.1^3 + 20622*$.1^2 + 20672*$.1 - 632,11,$.1^16 - $.1^15 - 60*$.1^14 + 115*$.1^13 + 1231*$.1^12 - 3266*$.1^11 - 9620*$.1^10 + 32513*$.1^9 + 30643*$.1^8 - 148399*$.1^7 - 20214*$.1^6 + 327721*$.1^5 - 86790*$.1^4 - 317637*$.1^3 + 153178*$.1^2 + 89832*$.1 - 50616,13,$.1^16 - 4*$.1^15 - 106*$.1^14 + 364*$.1^13 + 4612*$.1^12 - 13192*$.1^11 - 105021*$.1^10 + 245349*$.1^9 + 1320155*$.1^8 - 2540046*$.1^7 - 8851982*$.1^6 + 15030336*$.1^5 + 27662566*$.1^4 - 49136445*$.1^3 - 24458970*$.1^2 + 67586632*$.1 - 26544200[] 487,5,2,$.1^17 + 8*$.1^16 + 7*$.1^15 - 97*$.1^14 - 239*$.1^13 + 327*$.1^12 + 1500*$.1^11 + 70*$.1^10 - 3964*$.1^9 - 2280*$.1^8 + 4849*$.1^7 + 4192*$.1^6 - 2492*$.1^5 - 2765*$.1^4 + 364*$.1^3 + 588*$.1^2 - 16,3,$.1^17 + 6*$.1^16 - 12*$.1^15 - 126*$.1^14 - 28*$.1^13 + 966*$.1^12 + 843*$.1^11 - 3526*$.1^10 - 3777*$.1^9 + 7023*$.1^8 + 6916*$.1^7 - 8306*$.1^6 - 5364*$.1^5 + 5495*$.1^4 + 1085*$.1^3 - 1358*$.1^2 + 162*$.1 - 1,5,$.1^17 + 19*$.1^16 + 132*$.1^15 + 297*$.1^14 - 1001*$.1^13 - 7281*$.1^12 - 13237*$.1^11 + 8658*$.1^10 + 62929*$.1^9 + 64801*$.1^8 - 33491*$.1^7 - 87085*$.1^6 - 12860*$.1^5 + 37682*$.1^4 + 10983*$.1^3 - 4959*$.1^2 - 1836*$.1 - 81,7,$.1^17 + 11*$.1^16 - $.1^15 - 412*$.1^14 - 1166*$.1^13 + 4148*$.1^12 + 20568*$.1^11 - 8760*$.1^10 - 144166*$.1^9 - 81902*$.1^8 + 488378*$.1^7 + 521494*$.1^6 - 803370*$.1^5 - 1136782*$.1^4 + 581809*$.1^3 + 1043038*$.1^2 - 135633*$.1 - 337347,11,$.1^17 + 11*$.1^16 - 50*$.1^15 - 939*$.1^14 - 446*$.1^13 + 29897*$.1^12 + 69242*$.1^11 - 440580*$.1^10 - 1628456*$.1^9 + 2744029*$.1^8 + 16876622*$.1^7 + 39618*$.1^6 - 80051629*$.1^5 - 69160750*$.1^4 + 130895976*$.1^3 + 190034733*$.1^2 + 24632784*$.1 - 17408851,13,$.1^17 + 12*$.1^16 - 45*$.1^15 - 1078*$.1^14 - 1845*$.1^13 + 29816*$.1^12 + 126839*$.1^11 - 175735*$.1^10 - 1911940*$.1^9 - 2693463*$.1^8 + 5037822*$.1^7 + 17181885*$.1^6 + 11294537*$.1^5 - 13465343*$.1^4 - 25963998*$.1^3 - 16440181*$.1^2 - 4592586*$.1 - 454771[] 488,1,2,x^2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 2*x - 1,11,x^2 + 2*x - 17,13,x^2 + 6*x + 1[] 488,2,2,x^3,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + x^2 - 5*x - 1,7,x^3 + 7*x^2 + 13*x + 5,11,x^3 + 3*x^2 - x - 5,13,x^3 + 5*x^2 - 5*x - 17[] 488,3,2,x^4,3,x^4 - x^3 - 7*x^2 + 4*x + 8,5,x^4 + 2*x^3 - 11*x^2 - 4*x + 16,7,x^4 - 7*x^3 + 12*x^2 - 3*x - 1,11,x^4 - 2*x^3 - 11*x^2 + 14*x - 4,13,x^4 - 4*x^3 - 19*x^2 + 10*x + 4[] 488,4,2,x^6,3,x^6 - 3*x^5 - 9*x^4 + 26*x^3 + 16*x^2 - 52*x + 16,5,x^6 - 5*x^5 - 11*x^4 + 77*x^3 - 26*x^2 - 192*x + 128,7,x^6 - 6*x^5 - 7*x^4 + 69*x^3 - 22*x^2 - 117*x - 36,11,x^6 - 3*x^5 - 31*x^4 + 109*x^3 + 182*x^2 - 932*x + 736,13,x^6 - 7*x^5 - 41*x^4 + 355*x^3 - 116*x^2 - 2584*x + 3688[] 489,1,2,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 3*x^3 - 5*x^2 - 19*x - 11,7,x^4 + 10*x^3 + 35*x^2 + 50*x + 25,11,x^4 + 8*x^3 + 3*x^2 - 62*x - 89,13,x^4 + 14*x^3 + 60*x^2 + 82*x + 19[] 489,2,2,x^5 + 2*x^4 - 4*x^3 - 7*x^2 + 3*x + 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 3*x^4 - 5*x^3 - 21*x^2 - 17*x - 4,7,x^5 + 4*x^4 - 9*x^3 - 20*x^2 + 37*x - 14,11,x^5 + 10*x^4 + 21*x^3 - 78*x^2 - 355*x - 362,13,x^5 - 10*x^4 + 24*x^3 + 2*x^2 - 25*x - 8[] 489,3,2,x^8 - 4*x^7 - 6*x^6 + 35*x^5 - 86*x^3 + 36*x^2 + 39*x - 19,3,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 - 5*x^7 - 10*x^6 + 66*x^5 - x^4 - 174*x^3 + 32*x^2 + 105*x - 19,7,x^8 - 4*x^7 - 22*x^6 + 84*x^5 + 155*x^4 - 516*x^3 - 382*x^2 + 768*x + 305,11,x^8 - 14*x^7 + 45*x^6 + 244*x^5 - 2181*x^4 + 6108*x^3 - 6696*x^2 + 320*x + 3008,13,x^8 + 14*x^7 + 32*x^6 - 290*x^5 - 1225*x^4 + 676*x^3 + 7720*x^2 + 9728*x + 3392[] 489,4,2,x^10 - x^9 - 16*x^8 + 15*x^7 + 87*x^6 - 72*x^5 - 188*x^4 + 125*x^3 + 132*x^2 - 55*x + 4,3,x^10 - 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1,5,x^10 + x^9 - 28*x^8 - 16*x^7 + 277*x^6 + 26*x^5 - 1134*x^4 + 371*x^3 + 1509*x^2 - 850*x - 56,7,x^10 - 14*x^9 + 58*x^8 + 36*x^7 - 829*x^6 + 1558*x^5 + 1442*x^4 - 5932*x^3 + 1305*x^2 + 5666*x - 2384,11,x^10 - 4*x^9 - 45*x^8 + 108*x^7 + 669*x^6 - 306*x^5 - 2712*x^4 - 624*x^3 + 2432*x^2 + 640*x - 512,13,x^10 - 16*x^9 + 64*x^8 + 182*x^7 - 1761*x^6 + 2746*x^5 + 4384*x^4 - 11696*x^3 - 2624*x^2 + 12160*x + 2048[] 490,1,2,x + 1,3,x - 1,5,x + 1,7,x,11,x + 6,13,x + 4[] 490,2,2,x + 1,3,x - 2,5,x + 1,7,x,11,x - 3,13,x - 1[] 490,3,2,x + 1,3,x + 2,5,x - 1,7,x,11,x - 3,13,x + 1[] 490,4,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 6,13,x - 4[] 490,5,2,x - 1,3,x + 2,5,x + 1,7,x,11,x - 3,13,x - 5[] 490,6,2,x - 1,3,x - 3,5,x + 1,7,x,11,x + 2,13,x[] 490,7,2,x - 1,3,x + 2,5,x + 1,7,x,11,x + 4,13,x + 2[] 490,8,2,x - 1,3,x,5,x - 1,7,x,11,x - 4,13,x - 6[] 490,9,2,x - 1,3,x - 2,5,x - 1,7,x,11,x - 3,13,x + 5[] 490,10,2,x - 1,3,x - 2,5,x - 1,7,x,11,x + 4,13,x - 2[] 490,11,2,x - 1,3,x + 3,5,x - 1,7,x,11,x + 2,13,x[] 490,12,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2,11,x^2 - 4*x - 4,13,x^2 - 4*x - 4[] 490,13,2,x^2 + 2*x + 1,3,x^2 - 4*x + 2,5,x^2 - 2*x + 1,7,x^2,11,x^2 - 4*x - 4,13,x^2 + 4*x - 4[] Total time: 17.270 seconds, Total memory usage: 6.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:23:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [490..493] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:22:41 on modular [Seed = 3275152310] ------------------------------------- 490,1,2,$.1 + 1,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 + 6,13,$.1 + 4[] 490,2,2,$.1 + 1,3,$.1 - 2,5,$.1 + 1,7,$.1,11,$.1 - 3,13,$.1 - 1[] 490,3,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1,11,$.1 - 3,13,$.1 + 1[] 490,4,2,$.1 + 1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 + 6,13,$.1 - 4[] 490,5,2,$.1 - 1,3,$.1 + 2,5,$.1 + 1,7,$.1,11,$.1 - 3,13,$.1 - 5[] 490,6,2,$.1 - 1,3,$.1 - 3,5,$.1 + 1,7,$.1,11,$.1 + 2,13,$.1[] 490,7,2,$.1 - 1,3,$.1 + 2,5,$.1 + 1,7,$.1,11,$.1 + 4,13,$.1 + 2[] 490,8,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1 - 4,13,$.1 - 6[] 490,9,2,$.1 - 1,3,$.1 - 2,5,$.1 - 1,7,$.1,11,$.1 - 3,13,$.1 + 5[] 490,10,2,$.1 - 1,3,$.1 - 2,5,$.1 - 1,7,$.1,11,$.1 + 4,13,$.1 - 2[] 490,11,2,$.1 - 1,3,$.1 + 3,5,$.1 - 1,7,$.1,11,$.1 + 2,13,$.1[] 490,12,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2,11,$.1^2 - 4*$.1 - 4,13,$.1^2 - 4*$.1 - 4[] 490,13,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2 - 2*$.1 + 1,7,$.1^2,11,$.1^2 - 4*$.1 - 4,13,$.1^2 + 4*$.1 - 4[] 491,1,2,x^2 - x - 1,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 - x - 11,11,x^2 + 3*x + 1,13,x^2 + 8*x + 11[] 491,2,2,x^10 + 3*x^9 - 7*x^8 - 25*x^7 + 10*x^6 + 60*x^5 + 3*x^4 - 45*x^3 - 2*x^2 + 7*x - 1,3,x^10 + 4*x^9 - 8*x^8 - 41*x^7 + 8*x^6 + 115*x^5 + 37*x^4 - 52*x^3 - 7*x^2 + 8*x - 1,5,x^10 + 9*x^9 + 17*x^8 - 54*x^7 - 191*x^6 - 8*x^5 + 389*x^4 + 169*x^3 - 139*x^2 - 16*x + 4,7,x^10 + 6*x^9 + x^8 - 47*x^7 - 55*x^6 + 94*x^5 + 163*x^4 - 19*x^3 - 121*x^2 - 48*x - 4,11,x^10 + 3*x^9 - 40*x^8 - 120*x^7 + 416*x^6 + 1119*x^5 - 1621*x^4 - 2979*x^3 + 2233*x^2 - 149*x + 1,13,x^10 + 15*x^9 + 72*x^8 + 73*x^7 - 299*x^6 - 570*x^5 + 106*x^4 + 547*x^3 + 63*x^2 - 95*x + 11[] 491,3,2,x^29 - 49*x^27 + x^26 + 1068*x^25 - 39*x^24 - 13655*x^23 + 658*x^22 + 113723*x^21 - 6306*x^20 - 647801*x^19 + 37953*x^18 + 2578721*x^17 - 150115*x^16 - 7201417*x^15 + 398246*x^14 + 13959112*x^13 - 711934*x^12 - 18310154*x^11 + 839798*x^10 + 15574775*x^9 - 585854*x^8 - 8065060*x^7 + 132680*x^6 + 2339280*x^5 + 83968*x^4 - 350400*x^3 - 36608*x^2 + 20992*x + 3584,3,x^29 - 5*x^28 - 51*x^27 + 285*x^26 + 1074*x^25 - 7083*x^24 - 11671*x^23 + 101035*x^22 + 61012*x^21 - 916051*x^20 + 9358*x^19 + 5521492*x^18 - 2268766*x^17 - 22476158*x^16 + 15564692*x^15 + 61480703*x^14 - 55671561*x^13 - 110117294*x^12 + 119536861*x^11 + 122122439*x^10 - 155573079*x^9 - 74561960*x^8 + 116894326*x^7 + 18045557*x^6 - 45284459*x^5 + 1071678*x^4 + 7240653*x^3 - 382097*x^2 - 378798*x - 20629,5,x^29 - 12*x^28 - 25*x^27 + 827*x^26 - 1385*x^25 - 23115*x^24 + 79578*x^23 + 322515*x^22 - 1736444*x^21 - 1973332*x^20 + 20894215*x^19 - 4080535*x^18 - 149899042*x^17 + 153502827*x^16 + 634768721*x^15 - 1098785934*x^14 - 1416285283*x^13 + 3910213899*x^12 + 857385707*x^11 - 7264915276*x^10 + 2451049126*x^9 + 6205475492*x^8 - 4251009756*x^7 - 1575152001*x^6 + 1562591587*x^5 + 181201045*x^4 - 196190120*x^3 - 21924992*x^2 + 3942016*x + 447296,7,x^29 - 3*x^28 - 136*x^27 + 412*x^26 + 8115*x^25 - 24880*x^24 - 279700*x^23 + 870828*x^22 + 6168083*x^21 - 19594692*x^20 - 91046243*x^19 + 297033872*x^18 + 914234208*x^17 - 3089629912*x^16 - 6223062620*x^15 + 22032007040*x^14 + 28147738144*x^13 - 105800264928*x^12 - 81947049408*x^11 + 329785114368*x^10 + 150613360384*x^9 - 626925014528*x^8 - 190515703808*x^7 + 653954707456*x^6 + 202447900672*x^5 - 298738786304*x^4 - 127617892352*x^3 + 7909670912*x^2 + 3912368128*x + 142475264,11,x^29 - 174*x^27 + 3*x^26 + 13387*x^25 - 5*x^24 - 600700*x^23 - 31244*x^22 + 17457958*x^21 + 2480297*x^20 - 345012431*x^19 - 93873749*x^18 + 4734024421*x^17 + 2100989175*x^16 - 45173732357*x^15 - 29743014907*x^14 + 294544324496*x^13 + 270822348921*x^12 - 1252941801030*x^11 - 1561412678711*x^10 + 3116139977050*x^9 + 5404743012046*x^8 - 3123372493282*x^7 - 9890918895463*x^6 - 2551461338584*x^5 + 6416553573185*x^4 + 5849603936438*x^3 + 1895405070433*x^2 + 209949016511*x - 2521936469,13,x^29 - 35*x^28 + 375*x^27 + 738*x^26 - 43178*x^25 + 223154*x^24 + 1278098*x^23 - 15300869*x^22 + 8339177*x^21 + 416021113*x^20 - 1204667595*x^19 - 5693819640*x^18 + 28847903406*x^17 + 38959400842*x^16 - 368828569445*x^15 - 73831634315*x^14 + 3009910729081*x^13 - 745404787749*x^12 - 16858747455882*x^11 + 5330362373840*x^10 + 66058381678064*x^9 - 8825110202864*x^8 - 173388274625185*x^7 - 32275281536103*x^6 + 264595714433913*x^5 + 138838988426446*x^4 - 164090391440550*x^3 - 127318042428327*x^2 + 19583693385928*x + 23545612672057[] 492,1,2,x,3,x + 1,5,x,7,x + 2,11,x + 1,13,x + 2[] 492,2,2,x,3,x - 1,5,x + 2,7,x + 4,11,x + 5,13,x - 4[] 492,3,2,x^2,3,x^2 + 2*x + 1,5,x^2 + 4*x - 2,7,x^2 - 4*x - 2,11,x^2 + 2*x - 5,13,x^2 - 4*x - 2[] 492,4,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 2*x - 2,7,x^2 - 2*x - 2,11,x^2 - 4*x + 1,13,x^2 + 2*x - 2[] 493,1,2,x + 1,3,x,5,x + 2,7,x + 5,11,x,13,x - 7[] 493,2,2,x + 1,3,x + 3,5,x - 1,7,x + 2,11,x - 3,13,x - 1[] 493,3,2,x^2 - 2*x + 1,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 - 5*x + 2,11,x^2 - x - 4,13,x^2 - 17[] 493,4,2,x^4 - 2*x^3 - 6*x^2 + 12*x - 1,3,x^4 - 3*x^3 - 7*x^2 + 27*x - 16,5,x^4 - 3*x^3 - 3*x^2 + 7*x + 2,7,x^4 - x^3 - 6*x^2 + 4*x + 4,11,x^4 - 15*x^3 + 79*x^2 - 171*x + 128,13,x^4 + 2*x^3 - 20*x^2 + 10*x - 1[] 493,5,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 3,3,x^5 + 2*x^4 - 5*x^3 - 10*x^2 + 1,5,x^5 + x^4 - 18*x^3 - 31*x^2 + 21*x + 41,7,x^5 + 4*x^4 - 16*x^3 - 65*x^2 + 14*x + 83,11,x^5 + 14*x^4 + 52*x^3 - 69*x^2 - 738*x - 1081,13,x^5 + 8*x^4 + 18*x^3 + x^2 - 26*x - 7[] 493,6,2,x^6 - 5*x^5 + 3*x^4 + 16*x^3 - 20*x^2 + 1,3,x^6 - 2*x^5 - 11*x^4 + 14*x^3 + 38*x^2 - 15*x - 26,5,x^6 - x^5 - 24*x^4 + 37*x^3 + 133*x^2 - 293*x + 142,7,x^6 - 2*x^5 - 18*x^4 + 47*x^3 + 8*x^2 - 93*x + 58,11,x^6 - 32*x^4 - 19*x^3 + 180*x^2 + 203*x - 26,13,x^6 + 6*x^5 - 6*x^4 - 87*x^3 - 96*x^2 + 177*x + 262[] 493,7,2,x^8 - 3*x^7 - 10*x^6 + 29*x^5 + 37*x^4 - 88*x^3 - 65*x^2 + 80*x + 51,3,x^8 - 6*x^7 + x^6 + 44*x^5 - 42*x^4 - 85*x^3 + 80*x^2 + 42*x - 8,5,x^8 - x^7 - 26*x^6 + 31*x^5 + 203*x^4 - 251*x^3 - 514*x^2 + 580*x + 168,7,x^8 - 3*x^7 - 20*x^6 + 41*x^5 + 121*x^4 - 101*x^3 - 109*x^2 + 106*x - 22,11,x^8 - 10*x^7 + 4*x^6 + 195*x^5 - 438*x^4 - 477*x^3 + 1604*x^2 - 386*x + 24,13,x^8 - 3*x^7 - 38*x^6 + 179*x^5 + 43*x^4 - 1333*x^3 + 2205*x^2 - 1088*x + 128[] 493,8,2,x^10 + 5*x^9 - 3*x^8 - 44*x^7 - 25*x^6 + 119*x^5 + 98*x^4 - 116*x^3 - 94*x^2 + 28*x + 11,3,x^10 + 9*x^9 + 22*x^8 - 16*x^7 - 115*x^6 - 54*x^5 + 155*x^4 + 95*x^3 - 65*x^2 - 24*x + 2,5,x^10 + 4*x^9 - 22*x^8 - 85*x^7 + 173*x^6 + 565*x^5 - 707*x^4 - 1316*x^3 + 1435*x^2 + 456*x - 484,7,x^10 + 4*x^9 - 30*x^8 - 123*x^7 + 264*x^6 + 1127*x^5 - 752*x^4 - 3078*x^3 + 1496*x^2 + 1880*x - 1000,11,x^10 + 19*x^9 + 115*x^8 + 32*x^7 - 2393*x^6 - 9046*x^5 - 5030*x^4 + 37325*x^3 + 87481*x^2 + 70032*x + 16258,13,x^10 + x^9 - 87*x^8 - 82*x^7 + 2761*x^6 + 2132*x^5 - 39298*x^4 - 20799*x^3 + 238099*x^2 + 57204*x - 413528[] Total time: 20.809 seconds, Total memory usage: 7.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:34:05 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [493..496] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:33:45 on modular [Seed = 4212059414] ------------------------------------- 493,1,2,$.1 + 1,3,$.1,5,$.1 + 2,7,$.1 + 5,11,$.1,13,$.1 - 7[] 493,2,2,$.1 + 1,3,$.1 + 3,5,$.1 - 1,7,$.1 + 2,11,$.1 - 3,13,$.1 - 1[] 493,3,2,$.1^2 - 2*$.1 + 1,3,$.1^2 + $.1 - 4,5,$.1^2 - 3*$.1 - 2,7,$.1^2 - 5*$.1 + 2,11,$.1^2 - $.1 - 4,13,$.1^2 - 17[] 493,4,2,$.1^4 - 2*$.1^3 - 6*$.1^2 + 12*$.1 - 1,3,$.1^4 - 3*$.1^3 - 7*$.1^2 + 27*$.1 - 16,5,$.1^4 - 3*$.1^3 - 3*$.1^2 + 7*$.1 + 2,7,$.1^4 - $.1^3 - 6*$.1^2 + 4*$.1 + 4,11,$.1^4 - 15*$.1^3 + 79*$.1^2 - 171*$.1 + 128,13,$.1^4 + 2*$.1^3 - 20*$.1^2 + 10*$.1 - 1[] 493,5,2,$.1^5 + 2*$.1^4 - 5*$.1^3 - 7*$.1^2 + 7*$.1 + 3,3,$.1^5 + 2*$.1^4 - 5*$.1^3 - 10*$.1^2 + 1,5,$.1^5 + $.1^4 - 18*$.1^3 - 31*$.1^2 + 21*$.1 + 41,7,$.1^5 + 4*$.1^4 - 16*$.1^3 - 65*$.1^2 + 14*$.1 + 83,11,$.1^5 + 14*$.1^4 + 52*$.1^3 - 69*$.1^2 - 738*$.1 - 1081,13,$.1^5 + 8*$.1^4 + 18*$.1^3 + $.1^2 - 26*$.1 - 7[] 493,6,2,$.1^6 - 5*$.1^5 + 3*$.1^4 + 16*$.1^3 - 20*$.1^2 + 1,3,$.1^6 - 2*$.1^5 - 11*$.1^4 + 14*$.1^3 + 38*$.1^2 - 15*$.1 - 26,5,$.1^6 - $.1^5 - 24*$.1^4 + 37*$.1^3 + 133*$.1^2 - 293*$.1 + 142,7,$.1^6 - 2*$.1^5 - 18*$.1^4 + 47*$.1^3 + 8*$.1^2 - 93*$.1 + 58,11,$.1^6 - 32*$.1^4 - 19*$.1^3 + 180*$.1^2 + 203*$.1 - 26,13,$.1^6 + 6*$.1^5 - 6*$.1^4 - 87*$.1^3 - 96*$.1^2 + 177*$.1 + 262[] 493,7,2,$.1^8 - 3*$.1^7 - 10*$.1^6 + 29*$.1^5 + 37*$.1^4 - 88*$.1^3 - 65*$.1^2 + 80*$.1 + 51,3,$.1^8 - 6*$.1^7 + $.1^6 + 44*$.1^5 - 42*$.1^4 - 85*$.1^3 + 80*$.1^2 + 42*$.1 - 8,5,$.1^8 - $.1^7 - 26*$.1^6 + 31*$.1^5 + 203*$.1^4 - 251*$.1^3 - 514*$.1^2 + 580*$.1 + 168,7,$.1^8 - 3*$.1^7 - 20*$.1^6 + 41*$.1^5 + 121*$.1^4 - 101*$.1^3 - 109*$.1^2 + 106*$.1 - 22,11,$.1^8 - 10*$.1^7 + 4*$.1^6 + 195*$.1^5 - 438*$.1^4 - 477*$.1^3 + 1604*$.1^2 - 386*$.1 + 24,13,$.1^8 - 3*$.1^7 - 38*$.1^6 + 179*$.1^5 + 43*$.1^4 - 1333*$.1^3 + 2205*$.1^2 - 1088*$.1 + 128[] 493,8,2,$.1^10 + 5*$.1^9 - 3*$.1^8 - 44*$.1^7 - 25*$.1^6 + 119*$.1^5 + 98*$.1^4 - 116*$.1^3 - 94*$.1^2 + 28*$.1 + 11,3,$.1^10 + 9*$.1^9 + 22*$.1^8 - 16*$.1^7 - 115*$.1^6 - 54*$.1^5 + 155*$.1^4 + 95*$.1^3 - 65*$.1^2 - 24*$.1 + 2,5,$.1^10 + 4*$.1^9 - 22*$.1^8 - 85*$.1^7 + 173*$.1^6 + 565*$.1^5 - 707*$.1^4 - 1316*$.1^3 + 1435*$.1^2 + 456*$.1 - 484,7,$.1^10 + 4*$.1^9 - 30*$.1^8 - 123*$.1^7 + 264*$.1^6 + 1127*$.1^5 - 752*$.1^4 - 3078*$.1^3 + 1496*$.1^2 + 1880*$.1 - 1000,11,$.1^10 + 19*$.1^9 + 115*$.1^8 + 32*$.1^7 - 2393*$.1^6 - 9046*$.1^5 - 5030*$.1^4 + 37325*$.1^3 + 87481*$.1^2 + 70032*$.1 + 16258,13,$.1^10 + $.1^9 - 87*$.1^8 - 82*$.1^7 + 2761*$.1^6 + 2132*$.1^5 - 39298*$.1^4 - 20799*$.1^3 + 238099*$.1^2 + 57204*$.1 - 413528[] 494,1,2,x + 1,3,x + 1,5,x - 1,7,x + 1,11,x,13,x + 1[] 494,2,2,x + 1,3,x,5,x - 2,7,x - 4,11,x - 4,13,x + 1[] 494,3,2,x + 1,3,x - 3,5,x + 3,7,x - 3,11,x,13,x + 1[] 494,4,2,x - 1,3,x + 1,5,x + 1,7,x + 3,11,x + 4,13,x - 1[] 494,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 3*x^2 - 6*x - 17,5,x^3 - 3*x^2 - 18*x + 57,7,x^3 + 6*x^2 - 24,11,x^3 + 3*x^2 - 18*x - 57,13,x^3 + 3*x^2 + 3*x + 1[] 494,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 6*x - 7,5,x^3 - x^2 - 6*x + 7,7,x^3 - 2*x^2 - 24*x + 56,11,x^3 + x^2 - 6*x - 7,13,x^3 - 3*x^2 + 3*x - 1[] 494,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 5*x^2 + 6*x - 1,5,x^3 - 5*x^2 + 6*x - 1,7,x^3 + 2*x^2 - 8*x - 8,11,x^3 + x^2 - 30*x - 43,13,x^3 + 3*x^2 + 3*x + 1[] 494,8,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 5*x^2 + 7*x + 5,5,x^4 - 2*x^3 - 9*x^2 + 11*x - 3,7,x^4 - 7*x^3 + 6*x^2 + 24*x - 8,11,x^4 - x^3 - 22*x^2 + 35*x + 12,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 495,1,2,x + 1,3,x,5,x + 1,7,x,11,x - 1,13,x - 2[] 495,2,2,x^2 + 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 + 2*x + 1,13,x^2 + 8*x + 8[] 495,3,2,x^2 - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 4*x + 4,11,x^2 - 2*x + 1,13,x^2 - 4*x - 8[] 495,4,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 - 2*x + 1,13,x^2 - 32[] 495,5,2,x^3 - x^2 - 5*x + 1,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 16*x + 16,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 2*x^2 - 12*x - 8[] 495,6,2,x^4 + 2*x^3 - 6*x^2 - 10*x + 3,3,x^4,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 4*x^3 - 16*x^2 + 64*x - 36,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 - 8*x^3 - 8*x^2 + 168*x - 292[] 495,7,2,x^4 - 2*x^3 - 6*x^2 + 10*x + 3,3,x^4,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 4*x^3 - 16*x^2 + 64*x - 36,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 - 8*x^3 - 8*x^2 + 168*x - 292[] 496,1,2,x,3,x,5,x + 3,7,x - 3,11,x + 2,13,x + 4[] 496,2,2,x,3,x - 2,5,x - 1,7,x - 3,11,x - 2,13,x + 2[] 496,3,2,x,3,x - 2,5,x - 2,7,x,11,x + 2,13,x - 4[] 496,4,2,x,3,x - 2,5,x + 3,7,x - 1,11,x - 6,13,x - 2[] 496,5,2,x,3,x,5,x - 1,7,x + 3,11,x + 6,13,x + 4[] 496,6,2,x,3,x,5,x + 2,7,x,11,x,13,x - 2[] 496,7,2,x^2,3,x^2 + 4*x + 4,5,x^2 - 3*x - 6,7,x^2 + x - 8,11,x^2 - 4*x + 4,13,x^2 - 2*x - 32[] 496,8,2,x^2,3,x^2 - 2*x - 4,5,x^2 - 2*x + 1,7,x^2 - 4*x - 1,11,x^2 + 4*x + 4,13,x^2 + 2*x - 4[] 496,9,2,x^2,3,x^2 + 2*x - 2,5,x^2 - 12,7,x^2 + 4*x + 4,11,x^2 - 6*x + 6,13,x^2 + 2*x - 26[] 496,10,2,x^3,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 + 3*x^2 - 4*x - 4,7,x^3 + 5*x^2 - 8*x - 44,11,x^3 + 8*x^2 + 6*x - 44,13,x^3 - 2*x^2 - 14*x + 32[] Total time: 19.719 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:37:24 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [496..499] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:37:08 on modular [Seed = 3910990905] ------------------------------------- 496,1,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 3,11,$.1 + 2,13,$.1 + 4[] 496,2,2,$.1,3,$.1 - 2,5,$.1 - 1,7,$.1 - 3,11,$.1 - 2,13,$.1 + 2[] 496,3,2,$.1,3,$.1 - 2,5,$.1 - 2,7,$.1,11,$.1 + 2,13,$.1 - 4[] 496,4,2,$.1,3,$.1 - 2,5,$.1 + 3,7,$.1 - 1,11,$.1 - 6,13,$.1 - 2[] 496,5,2,$.1,3,$.1,5,$.1 - 1,7,$.1 + 3,11,$.1 + 6,13,$.1 + 4[] 496,6,2,$.1,3,$.1,5,$.1 + 2,7,$.1,11,$.1,13,$.1 - 2[] 496,7,2,$.1^2,3,$.1^2 + 4*$.1 + 4,5,$.1^2 - 3*$.1 - 6,7,$.1^2 + $.1 - 8,11,$.1^2 - 4*$.1 + 4,13,$.1^2 - 2*$.1 - 32[] 496,8,2,$.1^2,3,$.1^2 - 2*$.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 4*$.1 - 1,11,$.1^2 + 4*$.1 + 4,13,$.1^2 + 2*$.1 - 4[] 496,9,2,$.1^2,3,$.1^2 + 2*$.1 - 2,5,$.1^2 - 12,7,$.1^2 + 4*$.1 + 4,11,$.1^2 - 6*$.1 + 6,13,$.1^2 + 2*$.1 - 26[] 496,10,2,$.1^3,3,$.1^3 + 2*$.1^2 - 6*$.1 - 8,5,$.1^3 + 3*$.1^2 - 4*$.1 - 4,7,$.1^3 + 5*$.1^2 - 8*$.1 - 44,11,$.1^3 + 8*$.1^2 + 6*$.1 - 44,13,$.1^3 - 2*$.1^2 - 14*$.1 + 32[] 497,1,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 1,13,x + 3[] 497,2,2,x^2 + 2*x + 1,3,x^2 + 2*x - 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 2*x + 1,13,x^2 + 2*x - 17[] 497,3,2,x^8 - 12*x^6 + 42*x^4 + 4*x^3 - 44*x^2 - 8*x + 1,3,x^8 - 5*x^7 - x^6 + 33*x^5 - 25*x^4 - 53*x^3 + 57*x^2 - 3*x - 2,5,x^8 - 2*x^7 - 20*x^6 + 32*x^5 + 112*x^4 - 152*x^3 - 160*x^2 + 176*x + 32,7,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,11,x^8 + x^7 - 31*x^6 - 43*x^5 + 227*x^4 + 431*x^3 - 105*x^2 - 537*x - 236,13,x^8 - 9*x^7 + 3*x^6 + 125*x^5 - 151*x^4 - 307*x^3 + 347*x^2 + x - 8[] 497,4,2,x^9 + 2*x^8 - 9*x^7 - 16*x^6 + 26*x^5 + 36*x^4 - 28*x^3 - 19*x^2 + 10*x + 1,3,x^9 + 7*x^8 + 8*x^7 - 36*x^6 - 75*x^5 + 19*x^4 + 99*x^3 + 49*x^2 + 3*x - 1,5,x^9 + 4*x^8 - 17*x^7 - 82*x^6 + 52*x^5 + 524*x^4 + 329*x^3 - 928*x^2 - 1344*x - 496,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,11,x^9 - x^8 - 69*x^7 - 3*x^6 + 1580*x^5 + 1536*x^4 - 12656*x^3 - 21296*x^2 + 16832*x + 35648,13,x^9 + 15*x^8 + 61*x^7 - 115*x^6 - 1516*x^5 - 4144*x^4 - 4392*x^3 - 1376*x^2 + 288*x + 64[] 497,5,2,x^15 - 2*x^14 - 24*x^13 + 46*x^12 + 224*x^11 - 406*x^10 - 1026*x^9 + 1731*x^8 + 2373*x^7 - 3662*x^6 - 2504*x^5 + 3488*x^4 + 818*x^3 - 1062*x^2 - 54*x + 27,3,x^15 - 5*x^14 - 22*x^13 + 134*x^12 + 150*x^11 - 1360*x^10 - 207*x^9 + 6723*x^8 - 1448*x^7 - 17210*x^6 + 5407*x^5 + 21721*x^4 - 4821*x^3 - 10775*x^2 - 942*x + 656,5,x^15 - 57*x^13 + 22*x^12 + 1268*x^11 - 1004*x^10 - 13807*x^9 + 16352*x^8 + 73900*x^7 - 115416*x^6 - 161608*x^5 + 327976*x^4 + 44080*x^3 - 219888*x^2 + 10368*x + 15552,7,x^15 - 15*x^14 + 105*x^13 - 455*x^12 + 1365*x^11 - 3003*x^10 + 5005*x^9 - 6435*x^8 + 6435*x^7 - 5005*x^6 + 3003*x^5 - 1365*x^4 + 455*x^3 - 105*x^2 + 15*x - 1,11,x^15 - 5*x^14 - 87*x^13 + 483*x^12 + 2427*x^11 - 16499*x^10 - 17121*x^9 + 227697*x^8 - 187868*x^7 - 995056*x^6 + 1794832*x^5 + 587792*x^4 - 3364544*x^3 + 2528064*x^2 - 539136*x - 27648,13,x^15 - 5*x^14 - 111*x^13 + 551*x^12 + 4623*x^11 - 22427*x^10 - 92267*x^9 + 419999*x^8 + 958290*x^7 - 3691576*x^6 - 5251560*x^5 + 13177968*x^4 + 13337824*x^3 - 10126080*x^2 - 2121344*x - 83968[] 498,1,2,x + 1,3,x - 1,5,x - 2,7,x - 4,11,x,13,x[] 498,2,2,x + 1,3,x - 1,5,x + 1,7,x + 4,11,x - 3,13,x + 6[] 498,3,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 3*x - 3,7,x^2 - x - 5,11,x^2,13,x^2 - 7*x + 7[] 498,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2,11,x^2 - x - 4,13,x^2 - 4*x + 4[] 498,5,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 3*x - 9,11,x^2 + 4*x - 16,13,x^2 + 7*x + 11[] 498,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 12*x - 7,7,x^3 + 3*x^2 - 9*x - 4,11,x^3 + 3*x^2 - 24*x - 64,13,x^3 + 3*x^2 - 15*x - 46[] 498,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 8*x^2 + 11*x + 14,7,x^4 - x^3 - 21*x^2 + 52*x - 32,11,x^4 + x^3 - 28*x^2 - 16*x + 128,13,x^4 - 7*x^3 - 31*x^2 + 202*x + 112[] 499,1,2,x^2 + x - 1,3,x^2 - 5,5,x^2 + 5*x + 5,7,x^2 + 2*x + 1,11,x^2 + 2*x - 19,13,x^2 - 45[] 499,2,2,x^16 + 5*x^15 - 11*x^14 - 85*x^13 + 9*x^12 + 548*x^11 + 293*x^10 - 1718*x^9 - 1408*x^8 + 2735*x^7 + 2662*x^6 - 2058*x^5 - 2241*x^4 + 585*x^3 + 738*x^2 - 54*x - 81,3,x^16 + 5*x^15 - 14*x^14 - 98*x^13 + 18*x^12 + 617*x^11 + 258*x^10 - 1767*x^9 - 985*x^8 + 2671*x^7 + 1338*x^6 - 2241*x^5 - 719*x^4 + 1008*x^3 + 68*x^2 - 194*x + 35,5,x^16 + 20*x^15 + 149*x^14 + 408*x^13 - 651*x^12 - 6586*x^11 - 11148*x^10 + 15067*x^9 + 66330*x^8 + 32190*x^7 - 110780*x^6 - 126154*x^5 + 51365*x^4 + 119462*x^3 + 17428*x^2 - 33621*x - 11849,7,x^16 + 4*x^15 - 63*x^14 - 248*x^13 + 1575*x^12 + 6076*x^11 - 19859*x^10 - 74491*x^9 + 132137*x^8 + 473816*x^7 - 440367*x^6 - 1450597*x^5 + 618118*x^4 + 1720867*x^3 - 165914*x^2 - 583503*x - 27953,11,x^16 + 18*x^15 + 61*x^14 - 734*x^13 - 5949*x^12 - 1787*x^11 + 112530*x^10 + 308694*x^9 - 502294*x^8 - 2986329*x^7 - 822966*x^6 + 11116513*x^5 + 10278876*x^4 - 17684787*x^3 - 22277034*x^2 + 9519653*x + 14162251,13,x^16 + 14*x^15 - 2*x^14 - 819*x^13 - 2570*x^12 + 15509*x^11 + 81665*x^10 - 79401*x^9 - 977484*x^8 - 677266*x^7 + 4767550*x^6 + 8109124*x^5 - 5223609*x^4 - 21003732*x^3 - 14674885*x^2 - 1340222*x + 1007372[] 499,3,2,x^23 - 4*x^22 - 26*x^21 + 117*x^20 + 268*x^19 - 1447*x^18 - 1325*x^17 + 9859*x^16 + 2497*x^15 - 40388*x^14 + 4836*x^13 + 101760*x^12 - 34790*x^11 - 154579*x^10 + 72287*x^9 + 132753*x^8 - 68227*x^7 - 57242*x^6 + 26996*x^5 + 11011*x^4 - 4109*x^3 - 660*x^2 + 172*x - 8,3,x^23 - x^22 - 47*x^21 + 49*x^20 + 938*x^19 - 1009*x^18 - 10386*x^17 + 11358*x^16 + 70051*x^15 - 76320*x^14 - 298353*x^13 + 315080*x^12 + 809095*x^11 - 799217*x^10 - 1383405*x^9 + 1226888*x^8 + 1441343*x^7 - 1105750*x^6 - 847011*x^5 + 553800*x^4 + 237620*x^3 - 138504*x^2 - 21632*x + 11776,5,x^23 - 25*x^22 + 242*x^21 - 958*x^20 - 774*x^19 + 21179*x^18 - 62625*x^17 - 51232*x^16 + 653345*x^15 - 982565*x^14 - 1702705*x^13 + 6480859*x^12 - 2790244*x^11 - 12328951*x^10 + 15243330*x^9 + 5901074*x^8 - 17613142*x^7 + 3290507*x^6 + 6617092*x^5 - 1954498*x^4 - 959061*x^3 + 184141*x^2 + 60531*x + 2043,7,x^23 - 2*x^22 - 86*x^21 + 184*x^20 + 3066*x^19 - 7094*x^18 - 58500*x^17 + 149025*x^16 + 639920*x^15 - 1857955*x^14 - 3908486*x^13 + 14016231*x^12 + 10726921*x^11 - 61960310*x^10 + 7490888*x^9 + 142825764*x^8 - 113008621*x^7 - 110238725*x^6 + 187850257*x^5 - 72076130*x^4 - 8718240*x^3 + 8461496*x^2 - 99136*x - 226112,11,x^23 - 10*x^22 - 72*x^21 + 886*x^20 + 1948*x^19 - 32143*x^18 - 23119*x^17 + 609371*x^16 + 72764*x^15 - 6373481*x^14 + 989180*x^13 + 35884388*x^12 - 11126828*x^11 - 102770942*x^10 + 41074754*x^9 + 151249934*x^8 - 69690257*x^7 - 109156833*x^6 + 56283273*x^5 + 30315234*x^4 - 18273116*x^3 + 309656*x^2 + 689184*x - 35136,13,x^23 - 14*x^22 - 53*x^21 + 1501*x^20 - 1370*x^19 - 65954*x^18 + 176723*x^17 + 1526698*x^16 - 5948323*x^15 - 19654349*x^14 + 104348794*x^13 + 128901988*x^12 - 1074468215*x^11 - 162469082*x^10 + 6631301500*x^9 - 3526175718*x^8 - 23451765391*x^7 + 24981860880*x^6 + 39771509500*x^5 - 68805809440*x^4 - 7449698960*x^3 + 67995404512*x^2 - 44128976704*x + 8912473984[] Total time: 16.670 seconds, Total memory usage: 6.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:47:39 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [499..452] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:47:36 on modular [Seed = 99620654] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:48:27 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [499..502] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:48:11 on modular [Seed = 234364741] ------------------------------------- 499,1,2,$.1^2 + $.1 - 1,3,$.1^2 - 5,5,$.1^2 + 5*$.1 + 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 + 2*$.1 - 19,13,$.1^2 - 45[] 499,2,2,$.1^16 + 5*$.1^15 - 11*$.1^14 - 85*$.1^13 + 9*$.1^12 + 548*$.1^11 + 293*$.1^10 - 1718*$.1^9 - 1408*$.1^8 + 2735*$.1^7 + 2662*$.1^6 - 2058*$.1^5 - 2241*$.1^4 + 585*$.1^3 + 738*$.1^2 - 54*$.1 - 81,3,$.1^16 + 5*$.1^15 - 14*$.1^14 - 98*$.1^13 + 18*$.1^12 + 617*$.1^11 + 258*$.1^10 - 1767*$.1^9 - 985*$.1^8 + 2671*$.1^7 + 1338*$.1^6 - 2241*$.1^5 - 719*$.1^4 + 1008*$.1^3 + 68*$.1^2 - 194*$.1 + 35,5,$.1^16 + 20*$.1^15 + 149*$.1^14 + 408*$.1^13 - 651*$.1^12 - 6586*$.1^11 - 11148*$.1^10 + 15067*$.1^9 + 66330*$.1^8 + 32190*$.1^7 - 110780*$.1^6 - 126154*$.1^5 + 51365*$.1^4 + 119462*$.1^3 + 17428*$.1^2 - 33621*$.1 - 11849,7,$.1^16 + 4*$.1^15 - 63*$.1^14 - 248*$.1^13 + 1575*$.1^12 + 6076*$.1^11 - 19859*$.1^10 - 74491*$.1^9 + 132137*$.1^8 + 473816*$.1^7 - 440367*$.1^6 - 1450597*$.1^5 + 618118*$.1^4 + 1720867*$.1^3 - 165914*$.1^2 - 583503*$.1 - 27953,11,$.1^16 + 18*$.1^15 + 61*$.1^14 - 734*$.1^13 - 5949*$.1^12 - 1787*$.1^11 + 112530*$.1^10 + 308694*$.1^9 - 502294*$.1^8 - 2986329*$.1^7 - 822966*$.1^6 + 11116513*$.1^5 + 10278876*$.1^4 - 17684787*$.1^3 - 22277034*$.1^2 + 9519653*$.1 + 14162251,13,$.1^16 + 14*$.1^15 - 2*$.1^14 - 819*$.1^13 - 2570*$.1^12 + 15509*$.1^11 + 81665*$.1^10 - 79401*$.1^9 - 977484*$.1^8 - 677266*$.1^7 + 4767550*$.1^6 + 8109124*$.1^5 - 5223609*$.1^4 - 21003732*$.1^3 - 14674885*$.1^2 - 1340222*$.1 + 1007372[] 499,3,2,$.1^23 - 4*$.1^22 - 26*$.1^21 + 117*$.1^20 + 268*$.1^19 - 1447*$.1^18 - 1325*$.1^17 + 9859*$.1^16 + 2497*$.1^15 - 40388*$.1^14 + 4836*$.1^13 + 101760*$.1^12 - 34790*$.1^11 - 154579*$.1^10 + 72287*$.1^9 + 132753*$.1^8 - 68227*$.1^7 - 57242*$.1^6 + 26996*$.1^5 + 11011*$.1^4 - 4109*$.1^3 - 660*$.1^2 + 172*$.1 - 8,3,$.1^23 - $.1^22 - 47*$.1^21 + 49*$.1^20 + 938*$.1^19 - 1009*$.1^18 - 10386*$.1^17 + 11358*$.1^16 + 70051*$.1^15 - 76320*$.1^14 - 298353*$.1^13 + 315080*$.1^12 + 809095*$.1^11 - 799217*$.1^10 - 1383405*$.1^9 + 1226888*$.1^8 + 1441343*$.1^7 - 1105750*$.1^6 - 847011*$.1^5 + 553800*$.1^4 + 237620*$.1^3 - 138504*$.1^2 - 21632*$.1 + 11776,5,$.1^23 - 25*$.1^22 + 242*$.1^21 - 958*$.1^20 - 774*$.1^19 + 21179*$.1^18 - 62625*$.1^17 - 51232*$.1^16 + 653345*$.1^15 - 982565*$.1^14 - 1702705*$.1^13 + 6480859*$.1^12 - 2790244*$.1^11 - 12328951*$.1^10 + 15243330*$.1^9 + 5901074*$.1^8 - 17613142*$.1^7 + 3290507*$.1^6 + 6617092*$.1^5 - 1954498*$.1^4 - 959061*$.1^3 + 184141*$.1^2 + 60531*$.1 + 2043,7,$.1^23 - 2*$.1^22 - 86*$.1^21 + 184*$.1^20 + 3066*$.1^19 - 7094*$.1^18 - 58500*$.1^17 + 149025*$.1^16 + 639920*$.1^15 - 1857955*$.1^14 - 3908486*$.1^13 + 14016231*$.1^12 + 10726921*$.1^11 - 61960310*$.1^10 + 7490888*$.1^9 + 142825764*$.1^8 - 113008621*$.1^7 - 110238725*$.1^6 + 187850257*$.1^5 - 72076130*$.1^4 - 8718240*$.1^3 + 8461496*$.1^2 - 99136*$.1 - 226112,11,$.1^23 - 10*$.1^22 - 72*$.1^21 + 886*$.1^20 + 1948*$.1^19 - 32143*$.1^18 - 23119*$.1^17 + 609371*$.1^16 + 72764*$.1^15 - 6373481*$.1^14 + 989180*$.1^13 + 35884388*$.1^12 - 11126828*$.1^11 - 102770942*$.1^10 + 41074754*$.1^9 + 151249934*$.1^8 - 69690257*$.1^7 - 109156833*$.1^6 + 56283273*$.1^5 + 30315234*$.1^4 - 18273116*$.1^3 + 309656*$.1^2 + 689184*$.1 - 35136,13,$.1^23 - 14*$.1^22 - 53*$.1^21 + 1501*$.1^20 - 1370*$.1^19 - 65954*$.1^18 + 176723*$.1^17 + 1526698*$.1^16 - 5948323*$.1^15 - 19654349*$.1^14 + 104348794*$.1^13 + 128901988*$.1^12 - 1074468215*$.1^11 - 162469082*$.1^10 + 6631301500*$.1^9 - 3526175718*$.1^8 - 23451765391*$.1^7 + 24981860880*$.1^6 + 39771509500*$.1^5 - 68805809440*$.1^4 - 7449698960*$.1^3 + 67995404512*$.1^2 - 44128976704*$.1 + 8912473984[] 500,1,2,x^2,3,x^2 - x - 1,5,x^2,7,x^2 - 4*x - 1,11,x^2 - 5,13,x^2 - 9*x + 19[] 500,2,2,x^2,3,x^2 + x - 1,5,x^2,7,x^2 + 4*x - 1,11,x^2 - 5,13,x^2 + 9*x + 19[] 500,3,2,x^4,3,x^4 - 13*x^2 + 31,5,x^4,7,x^4 - 23*x^2 + 31,11,x^4 - 40*x^2 + 400,13,x^4 - 48*x^2 + 496[] 501,1,2,x - 1,3,x + 1,5,x + 4,7,x - 4,11,x - 4,13,x - 6[] 501,2,2,x^5 - 5*x^3 + 4*x + 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + x^4 - 9*x^3 - 2*x^2 + 17*x - 1,7,x^5 + 4*x^4 - 3*x^3 - 29*x^2 - 37*x - 13,11,x^5 + 7*x^4 - 3*x^3 - 92*x^2 - 101*x + 121,13,x^5 + 8*x^4 - x^3 - 66*x^2 - 48*x + 17[] 501,3,2,x^5 + 4*x^4 + x^3 - 8*x^2 - 2*x + 3,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 + 9*x^4 + 25*x^3 + 12*x^2 - 39*x - 37,7,x^5 + 4*x^4 - 15*x^3 - 49*x^2 + 55*x + 83,11,x^5 + 15*x^4 + 69*x^3 + 36*x^2 - 447*x - 761,13,x^5 - 41*x^3 - 32*x^2 + 412*x + 687[] 501,4,2,x^8 + 3*x^7 - 10*x^6 - 34*x^5 + 17*x^4 + 100*x^3 + 43*x^2 - 21*x - 7,3,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 - x^7 - 21*x^6 + 18*x^5 + 91*x^4 - 117*x^3 - 18*x^2 + 48*x - 2,7,x^8 - 31*x^6 + 7*x^5 + 175*x^4 + 59*x^3 - 224*x^2 - 160*x - 16,11,x^8 - 5*x^7 - 23*x^6 + 104*x^5 + 151*x^4 - 547*x^3 - 460*x^2 + 700*x + 500,13,x^8 - 61*x^6 - 10*x^5 + 1088*x^4 - 237*x^3 - 6922*x^2 + 3828*x + 9224[] 501,5,2,x^8 - 3*x^7 - 8*x^6 + 28*x^5 + 9*x^4 - 64*x^3 + 17*x^2 + 23*x + 1,3,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,5,x^8 - 7*x^7 + 7*x^6 + 50*x^5 - 125*x^4 + 9*x^3 + 196*x^2 - 124*x - 18,7,x^8 + 4*x^7 - 19*x^6 - 65*x^5 + 63*x^4 + 255*x^3 + 84*x^2 - 48*x - 16,11,x^8 - 13*x^7 + 41*x^6 + 104*x^5 - 691*x^4 + 435*x^3 + 1804*x^2 - 1316*x - 1596,13,x^8 - 37*x^6 - 52*x^5 + 320*x^4 + 973*x^3 + 994*x^2 + 412*x + 56[] 502,1,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 5*x + 3,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 - 13[] 502,2,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 + 6*x + 9,13,x^2 + 2*x + 1[] 502,3,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + x^4 - 7*x^3 - 4*x^2 + 6*x - 1,5,x^5 + 6*x^4 + 6*x^3 - 18*x^2 - 25*x + 7,7,x^5 + x^4 - 19*x^3 - 18*x^2 + 78*x + 73,11,x^5 + 4*x^4 - 29*x^3 - 76*x^2 + 160*x - 64,13,x^5 + 7*x^4 - 7*x^3 - 100*x^2 - 6*x + 373[] 502,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 2*x^4 - 9*x^3 + 14*x^2 + 16*x - 8,5,x^5 - 7*x^4 + 9*x^3 + 24*x^2 - 52*x + 24,7,x^5 - x^4 - 19*x^3 + 28*x^2 + 80*x - 137,11,x^5 - 7*x^4 + 13*x^3 - 10*x - 1,13,x^5 - 4*x^4 - 23*x^3 + 138*x^2 - 200*x + 72[] 502,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - x^5 - 16*x^4 + 9*x^3 + 74*x^2 - 8*x - 88,5,x^6 + x^5 - 14*x^4 - 3*x^3 + 44*x^2 - 36*x + 8,7,x^6 - 6*x^5 - 7*x^4 + 90*x^3 - 146*x^2 + 72*x - 11,11,x^6 - x^5 - 30*x^4 + 23*x^3 + 280*x^2 - 112*x - 832,13,x^6 + 5*x^5 - 24*x^4 - 141*x^3 - 78*x^2 + 360*x + 392[] Total time: 15.839 seconds, Total memory usage: 6.14MB ************** MAGMA ***************** Host c-67-160-217-111.client.comcast.net. (67.160.217.111) Time: Sun Nov 30 14:09:33 2003 Input: 2+2 Output: Magma V2.10-6 Sun Nov 30 2003 14:09:30 on modular [Seed = 451896674] ------------------------------------- 4 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-67-160-217-111.client.comcast.net. (67.160.217.111) Time: Sun Nov 30 14:09:36 2003 Input: 2+2 Output: Magma V2.10-6 Sun Nov 30 2003 14:09:33 on modular [Seed = 434923110] ------------------------------------- 4 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-67-160-217-111.client.comcast.net. (67.160.217.111) Time: Sun Nov 30 14:09:56 2003 Input: 2+2+2 Output: Magma V2.10-6 Sun Nov 30 2003 14:09:53 on modular [Seed = 201225368] ------------------------------------- 6 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-67-160-217-111.client.comcast.net. (67.160.217.111) Time: Sun Nov 30 14:12:07 2003 Input: 2+2+2 Output: Magma V2.10-6 Sun Nov 30 2003 14:12:04 on modular [Seed = 719279164] ------------------------------------- 6 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:23:09 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=14; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; Output: Magma V2.10-6 Sun Nov 30 2003 14:23:06 on modular [Seed = 2824721440] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 14,1,2,x + 1,3,x + 2,5,x,7,x - 1,11,x,13,x + 4[] Total time: 3.319 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:25:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [503..507] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 14:24:37 on modular [Seed = 3609373488] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 503,1,2,x - 1,3,x - 1,5,x + 2,7,x + 3,11,x - 1,13,x - 1[] 503,2,2,x - 1,3,x - 3,5,x + 2,7,x - 3,11,x - 3,13,x - 5[] 503,3,2,x + 1,3,x - 1,5,x + 4,7,x + 3,11,x - 5,13,x - 1[] 503,4,2,x^3 - 5*x + 3,3,x^3 - x^2 - 4*x + 3,5,x^3,7,x^3 - x^2 - 8*x + 3,11,x^3 - 11*x^2 + 36*x - 35,13,x^3 - 5*x^2 - 2*x + 25[] 503,5,2,x^10 + 4*x^9 - 4*x^8 - 31*x^7 - 13*x^6 + 66*x^5 + 56*x^4 - 37*x^3 - 46*x^2 - 8*x + 1,3,x^10 + 8*x^9 + 18*x^8 - 10*x^7 - 85*x^6 - 75*x^5 + 54*x^4 + 86*x^3 + 5*x^2 - 14*x + 1,5,x^10 + x^9 - 11*x^8 - 7*x^7 + 41*x^6 + 7*x^5 - 59*x^4 + 16*x^3 + 18*x^2 - 9*x + 1,7,x^10 + 5*x^9 - 9*x^8 - 64*x^7 + 8*x^6 + 228*x^5 + 23*x^4 - 214*x^3 + 86*x^2 - 4*x - 1,11,x^10 + 3*x^9 - 41*x^8 - 80*x^7 + 515*x^6 + 537*x^5 - 1961*x^4 - 1781*x^3 + 1973*x^2 + 1920*x + 311,13,x^10 + 18*x^9 + 120*x^8 + 307*x^7 - 212*x^6 - 2777*x^5 - 4882*x^4 - 481*x^3 + 5985*x^2 + 4107*x - 19[] 503,6,2,x^26 - 4*x^25 - 36*x^24 + 154*x^23 + 554*x^22 - 2577*x^21 - 4772*x^20 + 24652*x^19 + 25321*x^18 - 149131*x^17 - 86017*x^16 + 595540*x^15 + 189834*x^14 - 1589003*x^13 - 278156*x^12 + 2799707*x^11 + 297701*x^10 - 3137915*x^9 - 283355*x^8 + 2081504*x^7 + 236065*x^6 - 725019*x^5 - 120174*x^4 + 115872*x^3 + 24760*x^2 - 6437*x - 1583,3,x^26 - 4*x^25 - 52*x^24 + 211*x^23 + 1175*x^22 - 4814*x^21 - 15259*x^20 + 62449*x^19 + 127340*x^18 - 509651*x^17 - 726005*x^16 + 2735786*x^15 + 2939963*x^14 - 9813106*x^13 - 8635730*x^12 + 23403122*x^11 + 18323065*x^10 - 36123133*x^9 - 27001213*x^8 + 34013592*x^7 + 25434027*x^6 - 17328663*x^5 - 13187700*x^4 + 3683025*x^3 + 2752584*x^2 - 219997*x - 113513,5,x^26 - 9*x^25 - 71*x^24 + 873*x^23 + 1333*x^22 - 35769*x^21 + 27305*x^20 + 795330*x^19 - 1730386*x^18 - 10082887*x^17 + 35969747*x^16 + 64971026*x^15 - 407126924*x^14 - 30144880*x^13 + 2659470320*x^12 - 2703014464*x^11 - 9170377216*x^10 + 19446722944*x^9 + 9083193856*x^8 - 57597089792*x^7 + 35068894208*x^6 + 60235479040*x^5 - 94082748416*x^4 + 22315384832*x^3 + 39809548288*x^2 - 32069681152*x + 7351042048,7,x^26 - 11*x^25 - 63*x^24 + 1107*x^23 + 43*x^22 - 44446*x^21 + 93217*x^20 + 898238*x^19 - 3273637*x^18 - 9066021*x^17 + 53508259*x^16 + 26089563*x^15 - 476783660*x^14 + 340019836*x^13 + 2258493746*x^12 - 3638899633*x^11 - 4488923464*x^10 + 13313053218*x^9 - 1189588910*x^8 - 17825595396*x^7 + 10116673017*x^6 + 8032872453*x^5 - 6538139464*x^4 - 992741156*x^3 + 848600087*x^2 + 172525027*x + 5803441,11,x^26 + 17*x^25 - 19*x^24 - 1993*x^23 - 9318*x^22 + 69343*x^21 + 684361*x^20 + 171574*x^19 - 17790495*x^18 - 58741228*x^17 + 140418152*x^16 + 1195749823*x^15 + 1337713907*x^14 - 7963423904*x^13 - 26524346571*x^12 - 2437492147*x^11 + 127147119393*x^10 + 220655004639*x^9 - 72117070449*x^8 - 683061933795*x^7 - 791478601478*x^6 + 76774743603*x^5 + 1080817421692*x^4 + 1209958900604*x^3 + 658913392984*x^2 + 184269684053*x + 21107618035,13,x^26 - 14*x^25 - 120*x^24 + 2386*x^23 + 3454*x^22 - 168492*x^21 + 136722*x^20 + 6506843*x^19 - 11822453*x^18 - 153132460*x^17 + 344794423*x^16 + 2326590816*x^15 - 5339743095*x^14 - 23621117551*x^13 + 47008122323*x^12 + 162052333548*x^11 - 225426275374*x^10 - 725968713666*x^9 + 471071882753*x^8 + 1883475205603*x^7 + 51373051032*x^6 - 2118085970313*x^5 - 982189476223*x^4 + 528503780175*x^3 + 396000550123*x^2 + 39464838428*x - 4565810269[] 504,1,2,x,3,x,5,x + 2,7,x + 1,11,x + 2,13,x - 2[] 504,2,2,x,3,x,5,x - 2,7,x - 1,11,x - 6,13,x + 6[] 504,3,2,x,3,x,5,x + 2,7,x + 1,11,x - 4,13,x - 2[] 504,4,2,x,3,x,5,x - 2,7,x + 1,11,x - 2,13,x - 2[] 504,5,2,x,3,x,5,x + 2,7,x - 1,11,x + 6,13,x + 6[] 504,6,2,x,3,x,5,x + 2,7,x + 1,11,x,13,x + 2[] 504,7,2,x,3,x,5,x + 2,7,x - 1,11,x,13,x - 6[] 504,8,2,x,3,x,5,x - 4,7,x - 1,11,x,13,x[] 505,1,2,x - 1,3,x,5,x + 1,7,x,11,x + 2,13,x - 2[] 505,2,2,x^6 + 3*x^5 - 4*x^4 - 17*x^3 - 5*x^2 + 13*x + 5,3,x^6 + x^5 - 9*x^4 - 8*x^3 + 15*x^2 + 7*x - 8,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,7,x^6 + 2*x^5 - 25*x^4 - 39*x^3 + 133*x^2 + 111*x - 232,11,x^6 + 11*x^5 + 17*x^4 - 192*x^3 - 799*x^2 - 737*x + 362,13,x^6 + 3*x^5 - 39*x^4 - 33*x^3 + 480*x^2 - 479*x - 298[] 505,3,2,x^8 + 5*x^7 + x^6 - 26*x^5 - 27*x^4 + 30*x^3 + 46*x^2 + 9*x - 1,3,x^8 + 11*x^7 + 43*x^6 + 62*x^5 - 11*x^4 - 91*x^3 - 34*x^2 + 16*x + 4,5,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,7,x^8 + 12*x^7 + 37*x^6 - 65*x^5 - 553*x^4 - 979*x^3 - 418*x^2 + 384*x + 284,11,x^8 + 9*x^7 - 27*x^6 - 400*x^5 - 219*x^4 + 4817*x^3 + 7176*x^2 - 12232*x - 16784,13,x^8 + 7*x^7 - 43*x^6 - 215*x^5 + 790*x^4 + 925*x^3 - 3070*x^2 - 1092*x + 3064[] 505,4,2,x^9 - 2*x^8 - 12*x^7 + 21*x^6 + 47*x^5 - 61*x^4 - 72*x^3 + 43*x^2 + 34*x - 1,3,x^9 - x^8 - 17*x^7 + 14*x^6 + 91*x^5 - 57*x^4 - 180*x^3 + 88*x^2 + 108*x - 52,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,7,x^9 - 39*x^7 + 13*x^6 + 521*x^5 - 329*x^4 - 2644*x^3 + 2292*x^2 + 3636*x - 3620,11,x^9 - 11*x^8 + 13*x^7 + 224*x^6 - 711*x^5 - 787*x^4 + 5064*x^3 - 3288*x^2 - 3632*x + 1040,13,x^9 + x^8 - 65*x^7 - 131*x^6 + 1286*x^5 + 3317*x^4 - 8768*x^3 - 25672*x^2 + 18784*x + 60880[] 505,5,2,x^9 - 2*x^8 - 10*x^7 + 19*x^6 + 31*x^5 - 57*x^4 - 28*x^3 + 57*x^2 - 6*x - 7,3,x^9 - 7*x^8 + 7*x^7 + 44*x^6 - 87*x^5 - 63*x^4 + 210*x^3 - 28*x^2 - 116*x + 28,5,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,7,x^9 - 6*x^8 - 5*x^7 + 67*x^6 - 37*x^5 - 119*x^4 + 62*x^3 + 48*x^2 - 12*x - 4,11,x^9 - 3*x^8 - 33*x^7 + 98*x^6 + 233*x^5 - 567*x^4 - 504*x^3 + 888*x^2 + 80*x - 224,13,x^9 - 3*x^8 - 41*x^7 + 35*x^6 + 556*x^5 + 561*x^4 - 836*x^3 - 832*x^2 + 400*x - 16[] 506,1,2,x + 1,3,x + 2,5,x - 1,7,x + 1,11,x + 1,13,x - 3[] 506,2,2,x + 1,3,x,5,x + 3,7,x - 3,11,x + 1,13,x - 5[] 506,3,2,x + 1,3,x + 2,5,x - 3,7,x - 5,11,x - 1,13,x + 1[] 506,4,2,x + 1,3,x,5,x + 1,7,x - 1,11,x - 1,13,x + 7[] 506,5,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 1,13,x + 1[] 506,6,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x - 1,13,x + 3[] Errors: /home/mfd/gomagma: line 2: 11717 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:26:05 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [503..506] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 14:25:42 on modular [Seed = 3241458405] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 503,1,2,x - 1,3,x - 1,5,x + 2,7,x + 3,11,x - 1,13,x - 1[] 503,2,2,x - 1,3,x - 3,5,x + 2,7,x - 3,11,x - 3,13,x - 5[] 503,3,2,x + 1,3,x - 1,5,x + 4,7,x + 3,11,x - 5,13,x - 1[] 503,4,2,x^3 - 5*x + 3,3,x^3 - x^2 - 4*x + 3,5,x^3,7,x^3 - x^2 - 8*x + 3,11,x^3 - 11*x^2 + 36*x - 35,13,x^3 - 5*x^2 - 2*x + 25[] 503,5,2,x^10 + 4*x^9 - 4*x^8 - 31*x^7 - 13*x^6 + 66*x^5 + 56*x^4 - 37*x^3 - 46*x^2 - 8*x + 1,3,x^10 + 8*x^9 + 18*x^8 - 10*x^7 - 85*x^6 - 75*x^5 + 54*x^4 + 86*x^3 + 5*x^2 - 14*x + 1,5,x^10 + x^9 - 11*x^8 - 7*x^7 + 41*x^6 + 7*x^5 - 59*x^4 + 16*x^3 + 18*x^2 - 9*x + 1,7,x^10 + 5*x^9 - 9*x^8 - 64*x^7 + 8*x^6 + 228*x^5 + 23*x^4 - 214*x^3 + 86*x^2 - 4*x - 1,11,x^10 + 3*x^9 - 41*x^8 - 80*x^7 + 515*x^6 + 537*x^5 - 1961*x^4 - 1781*x^3 + 1973*x^2 + 1920*x + 311,13,x^10 + 18*x^9 + 120*x^8 + 307*x^7 - 212*x^6 - 2777*x^5 - 4882*x^4 - 481*x^3 + 5985*x^2 + 4107*x - 19[] 503,6,2,x^26 - 4*x^25 - 36*x^24 + 154*x^23 + 554*x^22 - 2577*x^21 - 4772*x^20 + 24652*x^19 + 25321*x^18 - 149131*x^17 - 86017*x^16 + 595540*x^15 + 189834*x^14 - 1589003*x^13 - 278156*x^12 + 2799707*x^11 + 297701*x^10 - 3137915*x^9 - 283355*x^8 + 2081504*x^7 + 236065*x^6 - 725019*x^5 - 120174*x^4 + 115872*x^3 + 24760*x^2 - 6437*x - 1583,3,x^26 - 4*x^25 - 52*x^24 + 211*x^23 + 1175*x^22 - 4814*x^21 - 15259*x^20 + 62449*x^19 + 127340*x^18 - 509651*x^17 - 726005*x^16 + 2735786*x^15 + 2939963*x^14 - 9813106*x^13 - 8635730*x^12 + 23403122*x^11 + 18323065*x^10 - 36123133*x^9 - 27001213*x^8 + 34013592*x^7 + 25434027*x^6 - 17328663*x^5 - 13187700*x^4 + 3683025*x^3 + 2752584*x^2 - 219997*x - 113513,5,x^26 - 9*x^25 - 71*x^24 + 873*x^23 + 1333*x^22 - 35769*x^21 + 27305*x^20 + 795330*x^19 - 1730386*x^18 - 10082887*x^17 + 35969747*x^16 + 64971026*x^15 - 407126924*x^14 - 30144880*x^13 + 2659470320*x^12 - 2703014464*x^11 - 9170377216*x^10 + 19446722944*x^9 + 9083193856*x^8 - 57597089792*x^7 + 35068894208*x^6 + 60235479040*x^5 - 94082748416*x^4 + 22315384832*x^3 + 39809548288*x^2 - 32069681152*x + 7351042048,7,x^26 - 11*x^25 - 63*x^24 + 1107*x^23 + 43*x^22 - 44446*x^21 + 93217*x^20 + 898238*x^19 - 3273637*x^18 - 9066021*x^17 + 53508259*x^16 + 26089563*x^15 - 476783660*x^14 + 340019836*x^13 + 2258493746*x^12 - 3638899633*x^11 - 4488923464*x^10 + 13313053218*x^9 - 1189588910*x^8 - 17825595396*x^7 + 10116673017*x^6 + 8032872453*x^5 - 6538139464*x^4 - 992741156*x^3 + 848600087*x^2 + 172525027*x + 5803441,11,x^26 + 17*x^25 - 19*x^24 - 1993*x^23 - 9318*x^22 + 69343*x^21 + 684361*x^20 + 171574*x^19 - 17790495*x^18 - 58741228*x^17 + 140418152*x^16 + 1195749823*x^15 + 1337713907*x^14 - 7963423904*x^13 - 26524346571*x^12 - 2437492147*x^11 + 127147119393*x^10 + 220655004639*x^9 - 72117070449*x^8 - 683061933795*x^7 - 791478601478*x^6 + 76774743603*x^5 + 1080817421692*x^4 + 1209958900604*x^3 + 658913392984*x^2 + 184269684053*x + 21107618035,13,x^26 - 14*x^25 - 120*x^24 + 2386*x^23 + 3454*x^22 - 168492*x^21 + 136722*x^20 + 6506843*x^19 - 11822453*x^18 - 153132460*x^17 + 344794423*x^16 + 2326590816*x^15 - 5339743095*x^14 - 23621117551*x^13 + 47008122323*x^12 + 162052333548*x^11 - 225426275374*x^10 - 725968713666*x^9 + 471071882753*x^8 + 1883475205603*x^7 + 51373051032*x^6 - 2118085970313*x^5 - 982189476223*x^4 + 528503780175*x^3 + 396000550123*x^2 + 39464838428*x - 4565810269[] 504,1,2,x,3,x,5,x + 2,7,x + 1,11,x + 2,13,x - 2[] 504,2,2,x,3,x,5,x - 2,7,x - 1,11,x - 6,13,x + 6[] 504,3,2,x,3,x,5,x + 2,7,x + 1,11,x - 4,13,x - 2[] 504,4,2,x,3,x,5,x - 2,7,x + 1,11,x - 2,13,x - 2[] 504,5,2,x,3,x,5,x + 2,7,x - 1,11,x + 6,13,x + 6[] 504,6,2,x,3,x,5,x + 2,7,x + 1,11,x,13,x + 2[] 504,7,2,x,3,x,5,x + 2,7,x - 1,11,x,13,x - 6[] 504,8,2,x,3,x,5,x - 4,7,x - 1,11,x,13,x[] 505,1,2,x - 1,3,x,5,x + 1,7,x,11,x + 2,13,x - 2[] 505,2,2,x^6 + 3*x^5 - 4*x^4 - 17*x^3 - 5*x^2 + 13*x + 5,3,x^6 + x^5 - 9*x^4 - 8*x^3 + 15*x^2 + 7*x - 8,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,7,x^6 + 2*x^5 - 25*x^4 - 39*x^3 + 133*x^2 + 111*x - 232,11,x^6 + 11*x^5 + 17*x^4 - 192*x^3 - 799*x^2 - 737*x + 362,13,x^6 + 3*x^5 - 39*x^4 - 33*x^3 + 480*x^2 - 479*x - 298[] 505,3,2,x^8 + 5*x^7 + x^6 - 26*x^5 - 27*x^4 + 30*x^3 + 46*x^2 + 9*x - 1,3,x^8 + 11*x^7 + 43*x^6 + 62*x^5 - 11*x^4 - 91*x^3 - 34*x^2 + 16*x + 4,5,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,7,x^8 + 12*x^7 + 37*x^6 - 65*x^5 - 553*x^4 - 979*x^3 - 418*x^2 + 384*x + 284,11,x^8 + 9*x^7 - 27*x^6 - 400*x^5 - 219*x^4 + 4817*x^3 + 7176*x^2 - 12232*x - 16784,13,x^8 + 7*x^7 - 43*x^6 - 215*x^5 + 790*x^4 + 925*x^3 - 3070*x^2 - 1092*x + 3064[] 505,4,2,x^9 - 2*x^8 - 12*x^7 + 21*x^6 + 47*x^5 - 61*x^4 - 72*x^3 + 43*x^2 + 34*x - 1,3,x^9 - x^8 - 17*x^7 + 14*x^6 + 91*x^5 - 57*x^4 - 180*x^3 + 88*x^2 + 108*x - 52,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,7,x^9 - 39*x^7 + 13*x^6 + 521*x^5 - 329*x^4 - 2644*x^3 + 2292*x^2 + 3636*x - 3620,11,x^9 - 11*x^8 + 13*x^7 + 224*x^6 - 711*x^5 - 787*x^4 + 5064*x^3 - 3288*x^2 - 3632*x + 1040,13,x^9 + x^8 - 65*x^7 - 131*x^6 + 1286*x^5 + 3317*x^4 - 8768*x^3 - 25672*x^2 + 18784*x + 60880[] 505,5,2,x^9 - 2*x^8 - 10*x^7 + 19*x^6 + 31*x^5 - 57*x^4 - 28*x^3 + 57*x^2 - 6*x - 7,3,x^9 - 7*x^8 + 7*x^7 + 44*x^6 - 87*x^5 - 63*x^4 + 210*x^3 - 28*x^2 - 116*x + 28,5,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,7,x^9 - 6*x^8 - 5*x^7 + 67*x^6 - 37*x^5 - 119*x^4 + 62*x^3 + 48*x^2 - 12*x - 4,11,x^9 - 3*x^8 - 33*x^7 + 98*x^6 + 233*x^5 - 567*x^4 - 504*x^3 + 888*x^2 + 80*x - 224,13,x^9 - 3*x^8 - 41*x^7 + 35*x^6 + 556*x^5 + 561*x^4 - 836*x^3 - 832*x^2 + 400*x - 16[] 506,1,2,x + 1,3,x + 2,5,x - 1,7,x + 1,11,x + 1,13,x - 3[] 506,2,2,x + 1,3,x,5,x + 3,7,x - 3,11,x + 1,13,x - 5[] 506,3,2,x + 1,3,x + 2,5,x - 3,7,x - 5,11,x - 1,13,x + 1[] 506,4,2,x + 1,3,x,5,x + 1,7,x - 1,11,x - 1,13,x + 7[] 506,5,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 1,13,x + 1[] 506,6,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x - 1,13,x + 3[] 506,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 6*x + 17,5,x^3 - 3*x^2 + 3,7,x^3 - 12*x - 8,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 - 6*x - 17[] 506,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 2*x + 5,5,x^3 + 7*x^2 + 8*x - 15,7,x^3 - 20*x + 8,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 5*x^2 - 2*x + 15[] 506,9,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + x^3 - 6*x^2 - 3*x + 8,5,x^4 - 2*x^3 - 11*x^2 + 23*x - 1,7,x^4 - 3*x^3 - 8*x^2 + 20*x - 8,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 - 6*x^3 - 21*x^2 + 103*x + 137[] 506,10,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 12*x^3 + 13*x^2 + 22*x - 8,5,x^5 - 4*x^4 - 7*x^3 + 31*x^2 + x - 18,7,x^5 - x^4 - 24*x^3 + 4*x^2 + 88*x - 64,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 - 10*x^4 - 23*x^3 + 377*x^2 + 33*x - 3578[] Total time: 22.860 seconds, Total memory usage: 7.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:37:08 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [507..510] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 14:36:45 on modular [Seed = 4262168353] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 507,1,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x + 2,13,x[] 507,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 2,13,x[] 507,3,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x[] 507,4,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 3,11,x^2 - 12,13,x^2[] 507,5,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 12,11,x^2 - 12,13,x^2[] 507,6,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 + 3*x - 2,11,x^2 + 4*x + 4,13,x^2[] 507,7,2,x^2 + x - 4,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 - 3*x - 2,11,x^2 - 4*x + 4,13,x^2[] 507,8,2,x^2 - 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 - 4*x + 4,13,x^2[] 507,9,2,x^3 + 3*x^2 - 4*x - 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 6*x^2 + 5*x - 13,7,x^3 + 2*x^2 - x - 1,11,x^3 + 5*x^2 - 8*x - 41,13,x^3[] 507,10,2,x^3 - 3*x^2 - 4*x + 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 6*x^2 + 5*x + 13,7,x^3 - 2*x^2 - x + 1,11,x^3 - 5*x^2 - 8*x + 41,13,x^3[] 507,11,2,x^3 - x^2 - 2*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 3*x + 1,7,x^3 - 10*x^2 + 31*x - 29,11,x^3 + x^2 - 30*x - 43,13,x^3[] 507,12,2,x^3 + x^2 - 2*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3 + 10*x^2 + 31*x + 29,11,x^3 - x^2 - 30*x + 43,13,x^3[] 508,1,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 5*x + 5,13,x^2 - 7*x + 11[] 508,2,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 4*x + 4,7,x^2 - 20,11,x^2 - x - 11,13,x^2 + 5*x - 5[] 508,3,2,x^3,3,x^3 - x^2 - 6*x - 3,5,x^3 - 4*x^2 + x + 3,7,x^3 - 7*x^2 + 12*x - 3,11,x^3 - 2*x^2 - 5*x + 9,13,x^3 + 7*x^2 + 10*x + 3[] 508,4,2,x^3,3,x^3 + 3*x^2 - 1,5,x^3 - 9*x + 9,7,x^3 + 3*x^2 - 6*x - 17,11,x^3 + 6*x^2 - 9*x - 51,13,x^3 + 3*x^2 - 6*x - 17[] 509,1,2,x^14 + 3*x^13 - 11*x^12 - 36*x^11 + 43*x^10 + 161*x^9 - 70*x^8 - 337*x^7 + 29*x^6 + 336*x^5 + 40*x^4 - 139*x^3 - 36*x^2 + 12*x + 3,3,x^14 + 5*x^13 - 11*x^12 - 81*x^11 + 8*x^10 + 438*x^9 + 183*x^8 - 1032*x^7 - 579*x^6 + 1074*x^5 + 579*x^4 - 417*x^3 - 172*x^2 + 29*x + 11,5,x^14 + 5*x^13 - 17*x^12 - 121*x^11 - 3*x^10 + 866*x^9 + 897*x^8 - 2207*x^7 - 3776*x^6 + 1189*x^5 + 4603*x^4 + 984*x^3 - 1708*x^2 - 736*x - 16,7,x^14 + 17*x^13 + 96*x^12 + 61*x^11 - 1535*x^10 - 6288*x^9 - 6227*x^8 + 16783*x^7 + 47959*x^6 + 26599*x^5 - 43785*x^4 - 69420*x^3 - 33088*x^2 - 4384*x - 64,11,x^14 + 20*x^13 + 129*x^12 + 28*x^11 - 3389*x^10 - 14314*x^9 - 2747*x^8 + 135745*x^7 + 385001*x^6 + 194812*x^5 - 1097552*x^4 - 2779576*x^3 - 3033711*x^2 - 1660621*x - 371677,13,x^14 + 6*x^13 - 70*x^12 - 566*x^11 + 780*x^10 + 15417*x^9 + 23838*x^8 - 122059*x^7 - 422348*x^6 - 172234*x^5 + 768087*x^4 + 624287*x^3 - 531991*x^2 - 344123*x + 199459[] 509,2,2,x^28 - 3*x^27 - 44*x^26 + 135*x^25 + 847*x^24 - 2674*x^23 - 9369*x^22 + 30699*x^21 + 65714*x^20 - 226429*x^19 - 303558*x^18 + 1123948*x^17 + 922806*x^16 - 3822074*x^15 - 1752519*x^14 + 8879314*x^13 + 1675588*x^12 - 13751763*x^11 + 382971*x^10 + 13397267*x^9 - 2958134*x^8 - 7169500*x^7 + 3056380*x^6 + 1305763*x^5 - 1072947*x^4 + 245723*x^3 - 24485*x^2 + 1114*x - 19,3,x^28 - 5*x^27 - 48*x^26 + 272*x^25 + 931*x^24 - 6405*x^23 - 8850*x^22 + 85759*x^21 + 31965*x^20 - 721317*x^19 + 164032*x^18 + 3972999*x^17 - 2503752*x^16 - 14475994*x^15 + 13508475*x^14 + 34330526*x^13 - 41204799*x^12 - 50312318*x^11 + 75928604*x^10 + 39824769*x^9 - 82931046*x^8 - 9371818*x^7 + 49394521*x^6 - 6602510*x^5 - 13320545*x^4 + 3321297*x^3 + 1196222*x^2 - 267183*x - 31583,5,x^28 - x^27 - 86*x^26 + 100*x^25 + 3226*x^24 - 4251*x^23 - 69315*x^22 + 101474*x^21 + 941574*x^20 - 1508877*x^19 - 8418071*x^18 + 14621274*x^17 + 49979838*x^16 - 93690681*x^15 - 194106206*x^14 + 394225378*x^13 + 473294393*x^12 - 1060961763*x^11 - 669570897*x^10 + 1744938012*x^9 + 465995781*x^8 - 1643052709*x^7 - 73313109*x^6 + 799280568*x^5 - 66191620*x^4 - 163204400*x^3 + 24714384*x^2 + 6775680*x - 395200,7,x^28 - 19*x^27 + 59*x^26 + 1046*x^25 - 7773*x^24 - 12799*x^23 + 266239*x^22 - 328866*x^21 - 4320998*x^20 + 12180077*x^19 + 36055653*x^18 - 165902683*x^17 - 133267136*x^16 + 1240417261*x^15 - 83325840*x^14 - 5674708476*x^13 + 2619605547*x^12 + 16832782791*x^11 - 10032388939*x^10 - 33338640274*x^9 + 18249500769*x^8 + 43742965431*x^7 - 16307228095*x^6 - 35600041583*x^5 + 5188671857*x^4 + 15282505552*x^3 + 865161736*x^2 - 2359400544*x - 427287872,11,x^28 - 24*x^27 + 109*x^26 + 1716*x^25 - 17505*x^24 - 16702*x^23 + 774057*x^22 - 1728287*x^21 - 15056563*x^20 + 66368896*x^19 + 114572412*x^18 - 1020245916*x^17 + 300125641*x^16 + 7751456251*x^15 - 10332794825*x^14 - 29149056508*x^13 + 66040834520*x^12 + 42954791184*x^11 - 195283700736*x^10 + 32381865088*x^9 + 287532490752*x^8 - 180086084096*x^7 - 188919045888*x^6 + 200298798080*x^5 + 28612415488*x^4 - 81634443264*x^3 + 12479713280*x^2 + 11091165184*x - 3179560960,13,x^28 - 8*x^27 - 186*x^26 + 1570*x^25 + 14590*x^24 - 133651*x^23 - 620848*x^22 + 6506217*x^21 + 14924456*x^20 - 200543250*x^19 - 167804839*x^18 + 4081257155*x^17 - 801119881*x^16 - 55212568969*x^15 + 56352951195*x^14 + 482890261616*x^13 - 864977589548*x^12 - 2496581876256*x^11 + 6925120183312*x^10 + 5504434047296*x^9 - 30250690896192*x^8 + 8697521814528*x^7 + 63084344508672*x^6 - 63829683296256*x^5 - 35153013180416*x^4 + 78367682740224*x^3 - 20830072713216*x^2 - 18202017693696*x + 8555162042368[] Errors: /home/mfd/gomagma: line 2: 11756 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:38:01 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [507..509] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 14:37:49 on modular [Seed = 3927937781] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 507,1,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x + 2,13,x[] 507,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 2,13,x[] 507,3,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x[] 507,4,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 3,11,x^2 - 12,13,x^2[] 507,5,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 12,11,x^2 - 12,13,x^2[] 507,6,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 + 3*x - 2,11,x^2 + 4*x + 4,13,x^2[] 507,7,2,x^2 + x - 4,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 - 3*x - 2,11,x^2 - 4*x + 4,13,x^2[] 507,8,2,x^2 - 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 - 4*x + 4,13,x^2[] 507,9,2,x^3 + 3*x^2 - 4*x - 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 6*x^2 + 5*x - 13,7,x^3 + 2*x^2 - x - 1,11,x^3 + 5*x^2 - 8*x - 41,13,x^3[] 507,10,2,x^3 - 3*x^2 - 4*x + 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 6*x^2 + 5*x + 13,7,x^3 - 2*x^2 - x + 1,11,x^3 - 5*x^2 - 8*x + 41,13,x^3[] 507,11,2,x^3 - x^2 - 2*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 3*x + 1,7,x^3 - 10*x^2 + 31*x - 29,11,x^3 + x^2 - 30*x - 43,13,x^3[] 507,12,2,x^3 + x^2 - 2*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3 + 10*x^2 + 31*x + 29,11,x^3 - x^2 - 30*x + 43,13,x^3[] 508,1,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 5*x + 5,13,x^2 - 7*x + 11[] 508,2,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 4*x + 4,7,x^2 - 20,11,x^2 - x - 11,13,x^2 + 5*x - 5[] 508,3,2,x^3,3,x^3 - x^2 - 6*x - 3,5,x^3 - 4*x^2 + x + 3,7,x^3 - 7*x^2 + 12*x - 3,11,x^3 - 2*x^2 - 5*x + 9,13,x^3 + 7*x^2 + 10*x + 3[] 508,4,2,x^3,3,x^3 + 3*x^2 - 1,5,x^3 - 9*x + 9,7,x^3 + 3*x^2 - 6*x - 17,11,x^3 + 6*x^2 - 9*x - 51,13,x^3 + 3*x^2 - 6*x - 17[] 509,1,2,x^14 + 3*x^13 - 11*x^12 - 36*x^11 + 43*x^10 + 161*x^9 - 70*x^8 - 337*x^7 + 29*x^6 + 336*x^5 + 40*x^4 - 139*x^3 - 36*x^2 + 12*x + 3,3,x^14 + 5*x^13 - 11*x^12 - 81*x^11 + 8*x^10 + 438*x^9 + 183*x^8 - 1032*x^7 - 579*x^6 + 1074*x^5 + 579*x^4 - 417*x^3 - 172*x^2 + 29*x + 11,5,x^14 + 5*x^13 - 17*x^12 - 121*x^11 - 3*x^10 + 866*x^9 + 897*x^8 - 2207*x^7 - 3776*x^6 + 1189*x^5 + 4603*x^4 + 984*x^3 - 1708*x^2 - 736*x - 16,7,x^14 + 17*x^13 + 96*x^12 + 61*x^11 - 1535*x^10 - 6288*x^9 - 6227*x^8 + 16783*x^7 + 47959*x^6 + 26599*x^5 - 43785*x^4 - 69420*x^3 - 33088*x^2 - 4384*x - 64,11,x^14 + 20*x^13 + 129*x^12 + 28*x^11 - 3389*x^10 - 14314*x^9 - 2747*x^8 + 135745*x^7 + 385001*x^6 + 194812*x^5 - 1097552*x^4 - 2779576*x^3 - 3033711*x^2 - 1660621*x - 371677,13,x^14 + 6*x^13 - 70*x^12 - 566*x^11 + 780*x^10 + 15417*x^9 + 23838*x^8 - 122059*x^7 - 422348*x^6 - 172234*x^5 + 768087*x^4 + 624287*x^3 - 531991*x^2 - 344123*x + 199459[] 509,2,2,x^28 - 3*x^27 - 44*x^26 + 135*x^25 + 847*x^24 - 2674*x^23 - 9369*x^22 + 30699*x^21 + 65714*x^20 - 226429*x^19 - 303558*x^18 + 1123948*x^17 + 922806*x^16 - 3822074*x^15 - 1752519*x^14 + 8879314*x^13 + 1675588*x^12 - 13751763*x^11 + 382971*x^10 + 13397267*x^9 - 2958134*x^8 - 7169500*x^7 + 3056380*x^6 + 1305763*x^5 - 1072947*x^4 + 245723*x^3 - 24485*x^2 + 1114*x - 19,3,x^28 - 5*x^27 - 48*x^26 + 272*x^25 + 931*x^24 - 6405*x^23 - 8850*x^22 + 85759*x^21 + 31965*x^20 - 721317*x^19 + 164032*x^18 + 3972999*x^17 - 2503752*x^16 - 14475994*x^15 + 13508475*x^14 + 34330526*x^13 - 41204799*x^12 - 50312318*x^11 + 75928604*x^10 + 39824769*x^9 - 82931046*x^8 - 9371818*x^7 + 49394521*x^6 - 6602510*x^5 - 13320545*x^4 + 3321297*x^3 + 1196222*x^2 - 267183*x - 31583,5,x^28 - x^27 - 86*x^26 + 100*x^25 + 3226*x^24 - 4251*x^23 - 69315*x^22 + 101474*x^21 + 941574*x^20 - 1508877*x^19 - 8418071*x^18 + 14621274*x^17 + 49979838*x^16 - 93690681*x^15 - 194106206*x^14 + 394225378*x^13 + 473294393*x^12 - 1060961763*x^11 - 669570897*x^10 + 1744938012*x^9 + 465995781*x^8 - 1643052709*x^7 - 73313109*x^6 + 799280568*x^5 - 66191620*x^4 - 163204400*x^3 + 24714384*x^2 + 6775680*x - 395200,7,x^28 - 19*x^27 + 59*x^26 + 1046*x^25 - 7773*x^24 - 12799*x^23 + 266239*x^22 - 328866*x^21 - 4320998*x^20 + 12180077*x^19 + 36055653*x^18 - 165902683*x^17 - 133267136*x^16 + 1240417261*x^15 - 83325840*x^14 - 5674708476*x^13 + 2619605547*x^12 + 16832782791*x^11 - 10032388939*x^10 - 33338640274*x^9 + 18249500769*x^8 + 43742965431*x^7 - 16307228095*x^6 - 35600041583*x^5 + 5188671857*x^4 + 15282505552*x^3 + 865161736*x^2 - 2359400544*x - 427287872,11,x^28 - 24*x^27 + 109*x^26 + 1716*x^25 - 17505*x^24 - 16702*x^23 + 774057*x^22 - 1728287*x^21 - 15056563*x^20 + 66368896*x^19 + 114572412*x^18 - 1020245916*x^17 + 300125641*x^16 + 7751456251*x^15 - 10332794825*x^14 - 29149056508*x^13 + 66040834520*x^12 + 42954791184*x^11 - 195283700736*x^10 + 32381865088*x^9 + 287532490752*x^8 - 180086084096*x^7 - 188919045888*x^6 + 200298798080*x^5 + 28612415488*x^4 - 81634443264*x^3 + 12479713280*x^2 + 11091165184*x - 3179560960,13,x^28 - 8*x^27 - 186*x^26 + 1570*x^25 + 14590*x^24 - 133651*x^23 - 620848*x^22 + 6506217*x^21 + 14924456*x^20 - 200543250*x^19 - 167804839*x^18 + 4081257155*x^17 - 801119881*x^16 - 55212568969*x^15 + 56352951195*x^14 + 482890261616*x^13 - 864977589548*x^12 - 2496581876256*x^11 + 6925120183312*x^10 + 5504434047296*x^9 - 30250690896192*x^8 + 8697521814528*x^7 + 63084344508672*x^6 - 63829683296256*x^5 - 35153013180416*x^4 + 78367682740224*x^3 - 20830072713216*x^2 - 18202017693696*x + 8555162042368[] Total time: 11.839 seconds, Total memory usage: 5.01MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:47:52 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [510..513] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 14:47:28 on modular [Seed = 217676365] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 510,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x - 4[] 510,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 4,13,x[] 510,3,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x,13,x - 4[] 510,4,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 4,13,x + 2[] 510,5,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x + 2[] 510,6,2,x - 1,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[] 510,7,2,x - 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x + 4[] 510,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 24,11,x^2,13,x^2 - 4*x - 20[] 511,1,2,x^3 - x^2 - 4*x - 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 3*x^2 - 36*x + 103[] 511,2,2,x^3 - 5*x + 1,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 3*x^2 - 2*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 - 5*x^2 - 14*x + 73[] 511,3,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 7*x - 1,3,x^6 - x^5 - 6*x^4 + 4*x^3 + 8*x^2 - 1,5,x^6 + 2*x^5 - 15*x^4 - 29*x^3 + 46*x^2 + 59*x - 59,7,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 9*x^5 - 135*x^3 + 729*x - 729,13,x^6 + 4*x^5 - 27*x^4 - 104*x^3 + 35*x^2 + 301*x + 131[] 511,4,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 11*x + 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 10*x^2 + 4*x + 3,5,x^6 + 6*x^5 + 5*x^4 - 15*x^3 - 4*x^2 + 11*x - 3,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 + 5*x^5 - 12*x^4 - 59*x^3 + 52*x^2 + 109*x - 93,13,x^6 - 35*x^4 - 6*x^3 + 285*x^2 + 59*x + 3[] 511,5,2,x^9 - 2*x^8 - 10*x^7 + 18*x^6 + 33*x^5 - 50*x^4 - 40*x^3 + 45*x^2 + 17*x - 11,3,x^9 + x^8 - 22*x^7 - 30*x^6 + 138*x^5 + 250*x^4 - 167*x^3 - 480*x^2 - 144*x + 64,5,x^9 - 7*x^8 - 7*x^7 + 139*x^6 - 203*x^5 - 448*x^4 + 1101*x^3 - 283*x^2 - 401*x + 59,7,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,11,x^9 + 5*x^8 - 82*x^7 - 463*x^6 + 1854*x^5 + 13253*x^4 - 3763*x^3 - 114484*x^2 - 137676*x + 35704,13,x^9 + x^8 - 47*x^7 - 32*x^6 + 685*x^5 + 215*x^4 - 3440*x^3 + 406*x^2 + 4081*x - 341[] 511,6,2,x^10 - 4*x^9 - 9*x^8 + 50*x^7 + 4*x^6 - 194*x^5 + 123*x^4 + 224*x^3 - 231*x^2 + 11*x + 27,3,x^10 + x^9 - 34*x^8 - 28*x^7 + 440*x^6 + 278*x^5 - 2679*x^4 - 1138*x^3 + 7540*x^2 + 1576*x - 7520,5,x^10 - x^9 - 39*x^8 + 45*x^7 + 509*x^6 - 680*x^5 - 2299*x^4 + 3603*x^3 + 925*x^2 - 2281*x + 554,7,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1,11,x^10 - 5*x^9 - 28*x^8 + 125*x^7 + 328*x^6 - 943*x^5 - 1957*x^4 + 1574*x^3 + 4044*x^2 + 2008*x + 288,13,x^10 + x^9 - 71*x^8 - 4*x^7 + 1351*x^6 - 1271*x^5 - 3902*x^4 + 2902*x^3 + 3459*x^2 - 1357*x - 1094[] 512,1,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 + 8*x + 16,11,x^2 - 2,13,x^2 - 8[] 512,2,2,x^2,3,x^2 - 2,5,x^2 + 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 + 12*x + 36[] 512,3,2,x^2,3,x^2 + 4*x + 2,5,x^2,7,x^2,11,x^2 + 4*x - 14,13,x^2[] 512,4,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2,13,x^2 - 8[] 512,5,2,x^2,3,x^2 - 2,5,x^2 - 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 - 12*x + 36[] 512,6,2,x^2,3,x^2 - 4*x + 2,5,x^2,7,x^2,11,x^2 - 4*x - 14,13,x^2[] 512,7,2,x^4,3,x^4 - 12*x^2 + 36,5,x^4 - 24*x^2 + 144,7,x^4 - 16*x^2 + 64,11,x^4 - 12*x^2 + 36,13,x^4 - 24*x^2 + 144[] Errors: /home/mfd/gomagma: line 2: 11805 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:48:31 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [510..512] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 14:48:11 on modular [Seed = 885080670] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 510,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x - 4[] 510,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 4,13,x[] 510,3,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x,13,x - 4[] 510,4,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 4,13,x + 2[] 510,5,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x + 2[] 510,6,2,x - 1,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[] 510,7,2,x - 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x + 4[] 510,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 24,11,x^2,13,x^2 - 4*x - 20[] 511,1,2,x^3 - x^2 - 4*x - 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 3*x^2 - 36*x + 103[] 511,2,2,x^3 - 5*x + 1,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 3*x^2 - 2*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 - 5*x^2 - 14*x + 73[] 511,3,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 7*x - 1,3,x^6 - x^5 - 6*x^4 + 4*x^3 + 8*x^2 - 1,5,x^6 + 2*x^5 - 15*x^4 - 29*x^3 + 46*x^2 + 59*x - 59,7,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 9*x^5 - 135*x^3 + 729*x - 729,13,x^6 + 4*x^5 - 27*x^4 - 104*x^3 + 35*x^2 + 301*x + 131[] 511,4,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 11*x + 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 10*x^2 + 4*x + 3,5,x^6 + 6*x^5 + 5*x^4 - 15*x^3 - 4*x^2 + 11*x - 3,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 + 5*x^5 - 12*x^4 - 59*x^3 + 52*x^2 + 109*x - 93,13,x^6 - 35*x^4 - 6*x^3 + 285*x^2 + 59*x + 3[] 511,5,2,x^9 - 2*x^8 - 10*x^7 + 18*x^6 + 33*x^5 - 50*x^4 - 40*x^3 + 45*x^2 + 17*x - 11,3,x^9 + x^8 - 22*x^7 - 30*x^6 + 138*x^5 + 250*x^4 - 167*x^3 - 480*x^2 - 144*x + 64,5,x^9 - 7*x^8 - 7*x^7 + 139*x^6 - 203*x^5 - 448*x^4 + 1101*x^3 - 283*x^2 - 401*x + 59,7,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,11,x^9 + 5*x^8 - 82*x^7 - 463*x^6 + 1854*x^5 + 13253*x^4 - 3763*x^3 - 114484*x^2 - 137676*x + 35704,13,x^9 + x^8 - 47*x^7 - 32*x^6 + 685*x^5 + 215*x^4 - 3440*x^3 + 406*x^2 + 4081*x - 341[] 511,6,2,x^10 - 4*x^9 - 9*x^8 + 50*x^7 + 4*x^6 - 194*x^5 + 123*x^4 + 224*x^3 - 231*x^2 + 11*x + 27,3,x^10 + x^9 - 34*x^8 - 28*x^7 + 440*x^6 + 278*x^5 - 2679*x^4 - 1138*x^3 + 7540*x^2 + 1576*x - 7520,5,x^10 - x^9 - 39*x^8 + 45*x^7 + 509*x^6 - 680*x^5 - 2299*x^4 + 3603*x^3 + 925*x^2 - 2281*x + 554,7,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1,11,x^10 - 5*x^9 - 28*x^8 + 125*x^7 + 328*x^6 - 943*x^5 - 1957*x^4 + 1574*x^3 + 4044*x^2 + 2008*x + 288,13,x^10 + x^9 - 71*x^8 - 4*x^7 + 1351*x^6 - 1271*x^5 - 3902*x^4 + 2902*x^3 + 3459*x^2 - 1357*x - 1094[] 512,1,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 + 8*x + 16,11,x^2 - 2,13,x^2 - 8[] 512,2,2,x^2,3,x^2 - 2,5,x^2 + 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 + 12*x + 36[] 512,3,2,x^2,3,x^2 + 4*x + 2,5,x^2,7,x^2,11,x^2 + 4*x - 14,13,x^2[] 512,4,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2,13,x^2 - 8[] 512,5,2,x^2,3,x^2 - 2,5,x^2 - 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 - 12*x + 36[] 512,6,2,x^2,3,x^2 - 4*x + 2,5,x^2,7,x^2,11,x^2 - 4*x - 14,13,x^2[] 512,7,2,x^4,3,x^4 - 12*x^2 + 36,5,x^4 - 24*x^2 + 144,7,x^4 - 16*x^2 + 64,11,x^4 - 12*x^2 + 36,13,x^4 - 24*x^2 + 144[] Total time: 19.739 seconds, Total memory usage: 7.03MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 14:52:43 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [513..515] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 14:52:29 on modular [Seed = 668095051] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 513,1,2,x - 1,3,x,5,x,7,x + 2,11,x + 5,13,x + 4[] 513,2,2,x + 1,3,x,5,x,7,x + 2,11,x - 5,13,x + 4[] 513,3,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2 + 8*x + 16,11,x^2 - 27,13,x^2 + 8*x + 16[] 513,4,2,x^3 + x^2 - 4*x - 1,3,x^3,5,x^3 + 5*x^2 + 4*x - 3,7,x^3 - x^2 - 6*x - 3,11,x^3 + 8*x^2 + 15*x - 3,13,x^3 + x^2 - 6*x + 3[] 513,5,2,x^3 - 3*x^2 + 3,3,x^3,5,x^3 - 3*x^2 + 3,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 - 27*x + 27,13,x^3 + 3*x^2 - 24*x + 1[] 513,6,2,x^3 - x^2 - 4*x + 1,3,x^3,5,x^3 - 5*x^2 + 4*x + 3,7,x^3 - x^2 - 6*x - 3,11,x^3 - 8*x^2 + 15*x + 3,13,x^3 + x^2 - 6*x + 3[] 513,7,2,x^3 + 3*x^2 - 3,3,x^3,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 - 27*x - 27,13,x^3 + 3*x^2 - 24*x + 1[] 513,8,2,x^4 - 6*x^2 + 3,3,x^4,5,x^4 - 12*x^2 + 12,7,x^4 - 8*x^3 + 12*x^2 + 16*x + 4,11,x^4 - 18*x^2 + 27,13,x^4 - 8*x^3 + 24*x^2 - 32*x + 16[] 513,9,2,x^4 - 8*x^2 + 13,3,x^4,5,x^4 - 20*x^2 + 52,7,x^4 - 12*x^3 + 48*x^2 - 72*x + 36,11,x^4 - 24*x^2 + 117,13,x^4 - 24*x^2 + 144[] 514,1,2,x - 1,3,x,5,x + 2,7,x + 4,11,x + 4,13,x + 2[] 514,2,2,x - 1,3,x + 2,5,x + 2,7,x - 2,11,x + 4,13,x + 2[] 514,3,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2 - 6,7,x^2 + 4*x + 4,11,x^2,13,x^2 + 4*x - 20[] 514,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 4*x^2 + 2*x + 2,7,x^3 - 6*x^2 + 8*x - 2,11,x^3 - 10*x^2 + 28*x - 20,13,x^3 + 6*x^2 - 4*x - 8[] 514,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 8*x^3 + 6*x - 2,5,x^5 + 4*x^4 - 8*x^3 - 48*x^2 - 48*x - 8,7,x^5 + 4*x^4 - 6*x^3 - 20*x^2 + 18*x + 2,11,x^5 + 14*x^4 + 52*x^3 - 56*x^2 - 592*x - 688,13,x^5 - 2*x^4 - 28*x^3 - 16*x^2 + 64*x - 16[] 514,6,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 - 2*x^8 - 20*x^7 + 40*x^6 + 116*x^5 - 226*x^4 - 204*x^3 + 376*x^2 + 96*x - 176,5,x^9 - 4*x^8 - 22*x^7 + 86*x^6 + 174*x^5 - 612*x^4 - 576*x^3 + 1440*x^2 + 640*x - 16,7,x^9 + 4*x^8 - 26*x^7 - 74*x^6 + 282*x^5 + 350*x^4 - 1220*x^3 - 68*x^2 + 820*x + 244,11,x^9 - 12*x^8 + 16*x^7 + 252*x^6 - 604*x^5 - 2176*x^4 + 4976*x^3 + 10144*x^2 - 13248*x - 22208,13,x^9 - 6*x^8 - 52*x^7 + 264*x^6 + 976*x^5 - 3280*x^4 - 6976*x^3 + 8960*x^2 + 3840*x - 2816[] 515,1,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + x^3 - 3*x^2 - x + 1,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 3*x^3 - 7*x^2 - 27*x - 19,11,x^4 + 9*x^3 + 22*x^2 + 6*x - 19,13,x^4 + 11*x^3 + 35*x^2 + 13*x - 61[] 515,2,2,x^8 + 2*x^7 - 9*x^6 - 16*x^5 + 25*x^4 + 36*x^3 - 21*x^2 - 18*x + 9,3,x^8 + 3*x^7 - 13*x^6 - 37*x^5 + 43*x^4 + 98*x^3 - 68*x^2 - 72*x + 48,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 11*x^7 + 28*x^6 - 58*x^5 - 247*x^4 + 30*x^3 + 406*x^2 + 189*x + 3,11,x^8 - 5*x^7 - 30*x^6 + 116*x^5 + 363*x^4 - 662*x^3 - 1940*x^2 - 72*x + 1296,13,x^8 + 23*x^7 + 204*x^6 + 860*x^5 + 1657*x^4 + 900*x^3 - 720*x^2 - 243*x + 81[] 515,3,2,x^9 - x^8 - 14*x^7 + 12*x^6 + 64*x^5 - 45*x^4 - 107*x^3 + 64*x^2 + 52*x - 24,3,x^9 - 3*x^8 - 11*x^7 + 34*x^6 + 37*x^5 - 113*x^4 - 57*x^3 + 121*x^2 + 44*x - 5,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,7,x^9 - 9*x^8 - 5*x^7 + 267*x^6 - 745*x^5 - 432*x^4 + 3620*x^3 - 1696*x^2 - 4544*x + 2816,11,x^9 - x^8 - 34*x^7 + 42*x^6 + 325*x^5 - 374*x^4 - 1072*x^3 + 1176*x^2 + 1088*x - 1152,13,x^9 - 23*x^8 + 197*x^7 - 691*x^6 + 115*x^5 + 5478*x^4 - 10800*x^3 - 4680*x^2 + 27840*x - 17600[] 515,4,2,x^14 + x^13 - 22*x^12 - 18*x^11 + 188*x^10 + 120*x^9 - 778*x^8 - 354*x^7 + 1574*x^6 + 400*x^5 - 1345*x^4 - 43*x^3 + 284*x^2 + 20*x - 8,3,x^14 - x^13 - 33*x^12 + 36*x^11 + 411*x^10 - 499*x^9 - 2353*x^8 + 3237*x^7 + 5790*x^6 - 9331*x^5 - 3658*x^4 + 8340*x^3 - 856*x^2 - 784*x - 64,5,x^14 - 14*x^13 + 91*x^12 - 364*x^11 + 1001*x^10 - 2002*x^9 + 3003*x^8 - 3432*x^7 + 3003*x^6 - 2002*x^5 + 1001*x^4 - 364*x^3 + 91*x^2 - 14*x + 1,7,x^14 - 9*x^13 - 22*x^12 + 384*x^11 - 227*x^10 - 6064*x^9 + 10238*x^8 + 41915*x^7 - 103699*x^6 - 102808*x^5 + 416876*x^4 - 89376*x^3 - 556032*x^2 + 516096*x - 131072,11,x^14 - 3*x^13 - 94*x^12 + 248*x^11 + 3407*x^10 - 8104*x^9 - 60376*x^8 + 131624*x^7 + 543632*x^6 - 1088576*x^5 - 2309824*x^4 + 4184960*x^3 + 3551744*x^2 - 5865472*x + 524288,13,x^14 - 21*x^13 + 108*x^12 + 518*x^11 - 5725*x^10 + 1638*x^9 + 101086*x^8 - 159853*x^7 - 827345*x^6 + 1778544*x^5 + 3078652*x^4 - 7484472*x^3 - 3309040*x^2 + 9757248*x - 3492224[] Total time: 13.389 seconds, Total memory usage: 4.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 15:38:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [516..518] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 15:38:17 on modular [Seed = 2340348323] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 516,1,2,x,3,x + 1,5,x - 3,7,x + 1,11,x + 1,13,x - 7[] 516,2,2,x,3,x + 1,5,x + 2,7,x - 2,11,x + 3,13,x + 1[] 516,3,2,x,3,x - 1,5,x,7,x,11,x + 2,13,x - 6[] 516,4,2,x,3,x - 1,5,x - 3,7,x - 5,11,x + 3,13,x + 1[] 516,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 8,7,x^2 + x - 8,11,x^2 - 5*x - 2,13,x^2 + 3*x - 6[] 516,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 - x - 14,7,x^2 + x - 14,11,x^2 - 10*x + 25,13,x^2 + 2*x + 1[] 517,1,2,x - 2,3,x + 1,5,x - 3,7,x - 4,11,x + 1,13,x[] 517,2,2,x,3,x - 3,5,x - 3,7,x + 2,11,x - 1,13,x + 2[] 517,3,2,x - 2,3,x + 1,5,x + 3,7,x + 2,11,x - 1,13,x[] 517,4,2,x^2 - 2,3,x^2 - 6*x + 9,5,x^2 + 2*x - 1,7,x^2 - 2,11,x^2 + 2*x + 1,13,x^2 - 2[] 517,5,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 - 2,7,x^2 + 6*x + 9,11,x^2 + 2*x + 1,13,x^2 + 2*x - 1[] 517,6,2,x^2 - 2*x - 1,3,x^2 - 4*x + 2,5,x^2 + 4*x + 2,7,x^2 + 2*x - 7,11,x^2 - 2*x + 1,13,x^2 - 2*x - 1[] 517,7,2,x^2 + 2*x - 2,3,x^2 + 2*x + 1,5,x^2 - 3,7,x^2 - 2*x - 2,11,x^2 - 2*x + 1,13,x^2 + 6*x + 6[] 517,8,2,x^3 - x^2 - 5*x + 1,3,x^3 - 4*x + 2,5,x^3 - 2*x^2 - 2*x + 2,7,x^3 - 5*x^2 + 5*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 5*x^2 - 13*x + 25[] 517,9,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 4*x^2 - 2*x - 14,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 + x^2 - 19*x - 37,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 - 5*x - 3[] 517,10,2,x^10 + 6*x^9 + 3*x^8 - 40*x^7 - 56*x^6 + 79*x^5 + 148*x^4 - 41*x^3 - 112*x^2 - 8*x + 4,3,x^10 + 7*x^9 + 6*x^8 - 48*x^7 - 78*x^6 + 92*x^5 + 139*x^4 - 99*x^3 - 30*x^2 + 20*x - 2,5,x^10 + 3*x^9 - 27*x^8 - 85*x^7 + 212*x^6 + 734*x^5 - 490*x^4 - 2096*x^3 + 384*x^2 + 1776*x - 416,7,x^10 + 9*x^9 - 182*x^7 - 262*x^6 + 1254*x^5 + 2215*x^4 - 3393*x^3 - 5552*x^2 + 3216*x + 4036,11,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1,13,x^10 + 5*x^9 - 71*x^8 - 353*x^7 + 1646*x^6 + 8676*x^5 - 12964*x^4 - 85184*x^3 + 4096*x^2 + 284672*x + 212992[] 517,11,2,x^10 - 3*x^9 - 13*x^8 + 41*x^7 + 54*x^6 - 189*x^5 - 75*x^4 + 345*x^3 + x^2 - 206*x + 36,3,x^10 - 2*x^9 - 18*x^8 + 32*x^7 + 114*x^6 - 182*x^5 - 295*x^4 + 420*x^3 + 256*x^2 - 298*x - 24,5,x^10 - 4*x^9 - 31*x^8 + 134*x^7 + 242*x^6 - 1374*x^5 + 204*x^4 + 3840*x^3 - 3792*x^2 + 704*x + 192,7,x^10 - 7*x^9 - 14*x^8 + 150*x^7 + 26*x^6 - 970*x^5 - 21*x^4 + 2351*x^3 + 370*x^2 - 1900*x - 736,11,x^10 - 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1,13,x^10 + 11*x^9 - 13*x^8 - 487*x^7 - 936*x^6 + 5120*x^5 + 13272*x^4 - 18944*x^3 - 47104*x^2 + 28672*x + 32768[] 518,1,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 - 8,7,x^2 + 2*x + 1,11,x^2 - 8,13,x^2 - 8*x + 16[] 518,2,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x - 8,13,x^2 - 4*x - 8[] 518,3,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 + 3*x + 1,13,x^2 + 7*x + 1[] 518,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 5*x + 2,5,x^3 + 3*x^2 - x - 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 5*x^2 - 31*x + 148,13,x^3 + 11*x^2 + 35*x + 26[] 518,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 7*x + 8,5,x^3 - 3*x^2 - 7*x + 20,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 3*x^2 - 7*x - 20,13,x^3 - 11*x^2 + 33*x - 28[] 518,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 11*x^3 + 12*x^2 + 24*x - 28,5,x^5 + 3*x^4 - 15*x^3 - 20*x^2 + 80*x - 48,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - 5*x^4 - 23*x^3 + 104*x^2 + 32*x - 96,13,x^5 - 5*x^4 - 31*x^3 + 164*x^2 - 104*x + 16[] Total time: 19.549 seconds, Total memory usage: 6.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 15:43:29 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [519..521] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 15:43:14 on modular [Seed = 2740374224] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 519,1,2,x^3 - 3*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 - 3,11,x^3 - 3*x^2 - 9*x + 3,13,x^3 + 3*x^2 - 3[] 519,2,2,x^3 + 2*x^2 - x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3 + x^2 - 2*x - 1,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + 3*x^2 - 4*x + 1[] 519,3,2,x^11 - 3*x^10 - 12*x^9 + 39*x^8 + 43*x^7 - 165*x^6 - 45*x^5 + 271*x^4 - 29*x^3 - 134*x^2 + 60*x - 7,3,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,5,x^11 - 9*x^10 + 7*x^9 + 150*x^8 - 451*x^7 - 80*x^6 + 1582*x^5 - 1057*x^4 - 951*x^3 + 439*x^2 + 44*x + 1,7,x^11 + 3*x^10 - 48*x^9 - 95*x^8 + 850*x^7 + 712*x^6 - 6576*x^5 + 672*x^4 + 19328*x^3 - 14208*x^2 - 7680*x + 6400,11,x^11 - 13*x^10 + 26*x^9 + 254*x^8 - 882*x^7 - 1402*x^6 + 5473*x^5 + 5337*x^4 - 9513*x^3 - 11475*x^2 - 2673*x + 243,13,x^11 + x^10 - 75*x^9 + 38*x^8 + 1873*x^7 - 2994*x^6 - 16349*x^5 + 39962*x^4 + 25166*x^3 - 114923*x^2 + 44392*x + 30524[] 519,4,2,x^12 + 2*x^11 - 19*x^10 - 37*x^9 + 128*x^8 + 244*x^7 - 352*x^6 - 664*x^5 + 316*x^4 + 597*x^3 - 24*x^2 - 27*x + 1,3,x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1,5,x^12 - x^11 - 49*x^10 + 42*x^9 + 919*x^8 - 688*x^7 - 8144*x^6 + 5699*x^5 + 33691*x^4 - 25057*x^3 - 52812*x^2 + 45721*x + 3682,7,x^12 - 3*x^11 - 62*x^10 + 191*x^9 + 1330*x^8 - 4400*x^7 - 10800*x^6 + 43744*x^5 + 11904*x^4 - 160512*x^3 + 147968*x^2 + 14592*x - 45056,11,x^12 + 7*x^11 - 70*x^10 - 518*x^9 + 1690*x^8 + 13518*x^7 - 17063*x^6 - 148531*x^5 + 86035*x^4 + 654861*x^3 - 379109*x^2 - 944217*x + 699092,13,x^12 - 13*x^11 - 29*x^10 + 956*x^9 - 1391*x^8 - 25788*x^7 + 70723*x^6 + 317924*x^5 - 1116722*x^4 - 1779475*x^3 + 7471394*x^2 + 3542620*x - 17962376[] 520,1,2,x,3,x,5,x + 1,7,x,11,x + 4,13,x + 1[] 520,2,2,x,3,x - 2,5,x - 1,7,x,11,x - 2,13,x - 1[] 520,3,2,x^2,3,x^2 + 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 12,11,x^2 - 2*x - 2,13,x^2 - 2*x + 1[] 520,4,2,x^2,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 4*x - 2,13,x^2 + 2*x + 1[] 520,5,2,x^2,3,x^2 - 2*x - 4,5,x^2 + 2*x + 1,7,x^2,11,x^2 - 6*x + 4,13,x^2 + 2*x + 1[] 520,6,2,x^2,3,x^2 + 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 12,11,x^2 + 6*x + 6,13,x^2 - 2*x + 1[] 520,7,2,x^2,3,x^2 + 4*x + 2,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 18,13,x^2 + 2*x + 1[] 521,1,2,x^14 + 2*x^13 - 13*x^12 - 25*x^11 + 63*x^10 + 115*x^9 - 142*x^8 - 242*x^7 + 151*x^6 + 238*x^5 - 65*x^4 - 104*x^3 + 2*x^2 + 17*x + 3,3,x^14 + 5*x^13 - 9*x^12 - 73*x^11 - 8*x^10 + 358*x^9 + 250*x^8 - 654*x^7 - 659*x^6 + 261*x^5 + 453*x^4 + 76*x^3 - 67*x^2 - 28*x - 3,5,x^14 + 3*x^13 - 27*x^12 - 92*x^11 + 203*x^10 + 917*x^9 - 126*x^8 - 3265*x^7 - 2489*x^6 + 3061*x^5 + 4750*x^4 + 1154*x^3 - 1150*x^2 - 742*x - 125,7,x^14 + 20*x^13 + 150*x^12 + 433*x^11 - 468*x^10 - 6502*x^9 - 16175*x^8 - 10267*x^7 + 20750*x^6 + 34650*x^5 + 2014*x^4 - 23989*x^3 - 9725*x^2 + 4904*x + 2705,11,x^14 + 14*x^13 + 27*x^12 - 415*x^11 - 1800*x^10 + 3153*x^9 + 25012*x^8 + 4014*x^7 - 128407*x^6 - 89151*x^5 + 268529*x^4 + 194251*x^3 - 252739*x^2 - 114889*x + 91151,13,x^14 + 12*x^13 - 6*x^12 - 482*x^11 - 596*x^10 + 8095*x^9 + 11752*x^8 - 73271*x^7 - 83440*x^6 + 370837*x^5 + 224073*x^4 - 947320*x^3 - 71804*x^2 + 867673*x - 233169[] 521,2,2,x^29 - x^28 - 50*x^27 + 49*x^26 + 1112*x^25 - 1061*x^24 - 14511*x^23 + 13387*x^22 + 123412*x^21 - 109286*x^20 - 718385*x^19 + 606113*x^18 + 2924033*x^17 - 2333576*x^16 - 8348401*x^15 + 6263323*x^14 + 16508066*x^13 - 11605772*x^12 - 21923563*x^11 + 14498124*x^10 + 18478199*x^9 - 11710480*x^8 - 8913548*x^7 + 5683110*x^6 + 1973213*x^5 - 1428489*x^4 - 75206*x^3 + 126742*x^2 - 12580*x - 647,3,x^29 - 3*x^28 - 57*x^27 + 175*x^26 + 1416*x^25 - 4478*x^24 - 20174*x^23 + 66310*x^22 + 182503*x^21 - 631731*x^20 - 1095179*x^19 + 4074814*x^18 + 4405585*x^17 - 18242234*x^16 - 11594711*x^15 + 57146460*x^14 + 18034386*x^13 - 124534362*x^12 - 9245398*x^11 + 184711504*x^10 - 21908590*x^9 - 178114686*x^8 + 50841804*x^7 + 101705076*x^6 - 45772420*x^5 - 27285314*x^4 + 18445740*x^3 + 700184*x^2 - 2236414*x + 374662,5,x^29 + x^28 - 93*x^27 - 66*x^26 + 3823*x^25 + 1579*x^24 - 91624*x^23 - 10829*x^22 + 1420077*x^21 - 238337*x^20 - 14904844*x^19 + 6557662*x^18 + 107682638*x^17 - 74932098*x^16 - 532623473*x^15 + 498953610*x^14 + 1754721156*x^13 - 2051596488*x^12 - 3637268440*x^11 + 5122275040*x^10 + 4290498968*x^9 - 7224726888*x^8 - 2565373648*x^7 + 5076815504*x^6 + 1157607376*x^5 - 1770925392*x^4 - 462474672*x^3 + 226762208*x^2 + 79303760*x + 3136144,7,x^29 - 26*x^28 + 208*x^27 + 289*x^26 - 13280*x^25 + 53478*x^24 + 204431*x^23 - 2005201*x^22 + 1462262*x^21 + 29700020*x^20 - 81771174*x^19 - 191231711*x^18 + 1094992267*x^17 - 38121866*x^16 - 7383820445*x^15 + 8959022328*x^14 + 25477695022*x^13 - 61134642580*x^12 - 26202204398*x^11 + 187428285440*x^10 - 101854421698*x^9 - 241529892404*x^8 + 332867888996*x^7 - 13818864698*x^6 - 248812651082*x^5 + 209175022120*x^4 - 75571529386*x^3 + 12084102956*x^2 - 455251218*x - 47545450,11,x^29 - 14*x^28 - 93*x^27 + 2129*x^26 + 140*x^25 - 135155*x^24 + 331784*x^23 + 4556450*x^22 - 19422179*x^21 - 83302355*x^20 + 551616537*x^19 + 627686815*x^18 - 9017563715*x^17 + 4657820187*x^16 + 85585238423*x^15 - 145901558052*x^14 - 420994270592*x^13 + 1314952125184*x^12 + 514875597056*x^11 - 5466825958272*x^10 + 3891170455808*x^9 + 9141854047232*x^8 - 14919589138944*x^7 - 300972565504*x^6 + 14214404550656*x^5 - 7807168249856*x^4 - 2711152517120*x^3 + 3185594138624*x^2 - 485356765184*x - 86829105152,13,x^29 - 10*x^28 - 162*x^27 + 1922*x^26 + 10072*x^25 - 159569*x^24 - 252918*x^23 + 7516917*x^22 - 2038966*x^21 - 221821171*x^20 + 321260227*x^19 + 4264114414*x^18 - 10043549048*x^17 - 53506778471*x^16 + 173919337229*x^15 + 418988055918*x^14 - 1892913448712*x^13 - 1698838015528*x^12 + 13244949039648*x^11 - 587911453592*x^10 - 57787247954956*x^9 + 42542040694952*x^8 + 141091798290056*x^7 - 198684083332764*x^6 - 127811810086032*x^5 + 375712136581416*x^4 - 117523168109860*x^3 - 208034047032508*x^2 + 186714211552040*x - 45824749347532[] Total time: 14.729 seconds, Total memory usage: 5.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 18:54:53 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [522..525] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 18:54:30 on modular [Seed = 2957315209] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 522,1,2,x + 1,3,x,5,x - 3,7,x + 5,11,x + 4,13,x + 6[] 522,2,2,x + 1,3,x,5,x - 2,7,x - 4,11,x,13,x - 2[] 522,3,2,x + 1,3,x,5,x + 3,7,x + 1,11,x,13,x - 2[] 522,4,2,x + 1,3,x,5,x - 1,7,x - 1,11,x - 2,13,x[] 522,5,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 6,13,x + 4[] 522,6,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 3,13,x + 1[] 522,7,2,x - 1,3,x,5,x + 2,7,x - 4,11,x,13,x - 2[] 522,8,2,x - 1,3,x,5,x - 3,7,x + 1,11,x,13,x - 2[] 522,9,2,x - 1,3,x,5,x + 3,7,x + 5,11,x - 4,13,x + 6[] 522,10,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 6,13,x[] 522,11,2,x - 1,3,x,5,x + 2,7,x,11,x - 4,13,x - 6[] 522,12,2,x - 1,3,x,5,x - 3,7,x + 2,11,x - 1,13,x - 3[] 522,13,2,x - 1,3,x,5,x - 3,7,x - 5,11,x + 6,13,x + 4[] 523,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2,13,x^2 + x - 11[] 523,2,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 72*x^11 + 308*x^10 + 492*x^9 - 587*x^8 - 1283*x^7 + 418*x^6 + 1526*x^5 + 33*x^4 - 774*x^3 - 85*x^2 + 141*x + 8,3,x^15 + 3*x^14 - 17*x^13 - 50*x^12 + 111*x^11 + 312*x^10 - 349*x^9 - 897*x^8 + 543*x^7 + 1180*x^6 - 401*x^5 - 623*x^4 + 181*x^3 + 114*x^2 - 33*x - 2,5,x^15 + 19*x^14 + 140*x^13 + 442*x^12 + 24*x^11 - 4077*x^10 - 11810*x^9 - 10832*x^8 + 8722*x^7 + 23778*x^6 + 9378*x^5 - 9987*x^4 - 8231*x^3 - 341*x^2 + 1043*x + 218,7,x^15 + x^14 - 65*x^13 - 71*x^12 + 1622*x^11 + 2079*x^10 - 19593*x^9 - 29759*x^8 + 114951*x^7 + 207182*x^6 - 263534*x^5 - 598861*x^4 + 4063*x^3 + 322280*x^2 + 37779*x - 2744,11,x^15 + 7*x^14 - 85*x^13 - 719*x^12 + 2007*x^11 + 26554*x^10 + 7728*x^9 - 410286*x^8 - 784569*x^7 + 2121922*x^6 + 7495618*x^5 + 1560600*x^4 - 15953890*x^3 - 15090096*x^2 + 3265879*x + 6017216,13,x^15 + 15*x^14 + 10*x^13 - 909*x^12 - 4293*x^11 + 12207*x^10 + 129405*x^9 + 140948*x^8 - 1181467*x^7 - 3470111*x^6 + 1369276*x^5 + 16369458*x^4 + 13960211*x^3 - 18909210*x^2 - 29808448*x - 7023157[] 523,3,2,x^26 - 9*x^25 - x^24 + 231*x^23 - 464*x^22 - 2306*x^21 + 7763*x^20 + 10298*x^19 - 60057*x^18 - 8015*x^17 + 266789*x^16 - 125796*x^15 - 723565*x^14 + 622138*x^13 + 1202991*x^12 - 1407289*x^11 - 1178824*x^10 + 1766306*x^9 + 617378*x^8 - 1241966*x^7 - 135947*x^6 + 462396*x^5 + 400*x^4 - 78680*x^3 + 2576*x^2 + 4032*x - 384,3,x^26 - 4*x^25 - 49*x^24 + 208*x^23 + 1012*x^22 - 4663*x^21 - 11396*x^20 + 59094*x^19 + 75007*x^18 - 466388*x^17 - 280600*x^16 + 2381986*x^15 + 472857*x^14 - 7939604*x^13 + 309652*x^12 + 17086537*x^11 - 2646657*x^10 - 23178878*x^9 + 3952698*x^8 + 19159320*x^7 - 1998424*x^6 - 9145408*x^5 - 112256*x^4 + 2223616*x^3 + 295296*x^2 - 196608*x - 42496,5,x^26 - 21*x^25 + 133*x^24 + 189*x^23 - 5652*x^22 + 16091*x^21 + 67148*x^20 - 424783*x^19 + 1108*x^18 + 4494594*x^17 - 6685702*x^16 - 23809605*x^15 + 66301197*x^14 + 54241804*x^13 - 319227622*x^12 + 53568465*x^11 + 861747737*x^10 - 640623368*x^9 - 1250489090*x^8 + 1587993980*x^7 + 684118440*x^6 - 1736185744*x^5 + 365192256*x^4 + 648584256*x^3 - 446921856*x^2 + 106382592*x - 8750592,7,x^26 - 3*x^25 - 100*x^24 + 332*x^23 + 4188*x^22 - 15475*x^21 - 95119*x^20 + 398414*x^19 + 1260778*x^18 - 6247004*x^17 - 9578508*x^16 + 62051571*x^15 + 34312880*x^14 - 393739786*x^13 + 27090636*x^12 + 1572077681*x^11 - 741916832*x^10 - 3800557726*x^9 + 2763329261*x^8 + 5217039801*x^7 - 4505859008*x^6 - 3750173443*x^5 + 3257166390*x^4 + 1371874260*x^3 - 941636161*x^2 - 224401796*x + 68725316,11,x^26 - 11*x^25 - 87*x^24 + 1307*x^23 + 2074*x^22 - 65149*x^21 + 34467*x^20 + 1783337*x^19 - 2908355*x^18 - 29305733*x^17 + 69754523*x^16 + 294503313*x^15 - 899355720*x^14 - 1734222972*x^13 + 6832413781*x^12 + 5021134610*x^11 - 30319565127*x^10 - 1070558006*x^9 + 72749481441*x^8 - 27663976900*x^7 - 79359825114*x^6 + 46389402198*x^5 + 28335287243*x^4 - 17095836984*x^3 - 2526515156*x^2 + 1622311536*x - 135464256,13,x^26 - 14*x^25 - 96*x^24 + 2136*x^23 + 383*x^22 - 132080*x^21 + 301427*x^20 + 4199329*x^19 - 16468009*x^18 - 70566834*x^17 + 412698712*x^16 + 520810586*x^15 - 5699369592*x^14 + 968098975*x^13 + 45100198785*x^12 - 45073381925*x^11 - 203890014853*x^10 + 327499828693*x^9 + 499671005301*x^8 - 1128758701394*x^7 - 551108498487*x^6 + 1984720955197*x^5 + 55147303448*x^4 - 1628923185473*x^3 + 220929697737*x^2 + 473723308718*x - 30230457287[] 524,1,2,x,3,x - 1,5,x + 2,7,x + 3,11,x,13,x - 1[] 524,2,2,x^2,3,x^2 + 3*x + 1,5,x^2 - x - 1,7,x^2 + x - 1,11,x^2 + 5*x + 5,13,x^2 + 3*x - 9[] 524,3,2,x^4,3,x^4 - x^3 - 12*x^2 + 7*x + 29,5,x^4 + 3*x^3 - 9*x^2 - 16*x + 24,7,x^4 + x^3 - 18*x^2 - 11*x + 43,11,x^4 + 3*x^3 - 15*x^2 - 24*x + 36,13,x^4 + x^3 - 66*x^2 - 27*x + 1023[] 524,4,2,x^4,3,x^4 - 3*x^3 - 2*x^2 + 6*x + 3,5,x^4 - 2*x^3 - 13*x^2 + 30*x - 3,7,x^4 - 7*x^3 + 10*x^2 + 18*x - 37,11,x^4 - 12*x^3 + 41*x^2 - 16*x - 79,13,x^4 + x^3 - 8*x^2 + 9[] 525,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x,13,x - 6[] 525,2,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 4,13,x - 2[] 525,3,2,x - 1,3,x + 1,5,x,7,x - 1,11,x + 6,13,x - 2[] 525,4,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 6,13,x + 2[] 525,5,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 6*x + 9,13,x^2 + 2*x - 12[] 525,6,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 2*x - 19,13,x^2 + 6*x + 4[] 525,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x - 16,13,x^2 - 20[] 525,8,2,x^2 - 3*x + 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 2*x - 19,13,x^2 - 6*x + 4[] 525,9,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 6*x + 9,13,x^2 - 2*x - 12[] Errors: /home/mfd/gomagma: line 2: 12479 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 18:55:47 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [522..524] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 18:55:30 on modular [Seed = 3275128766] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 522,1,2,x + 1,3,x,5,x - 3,7,x + 5,11,x + 4,13,x + 6[] 522,2,2,x + 1,3,x,5,x - 2,7,x - 4,11,x,13,x - 2[] 522,3,2,x + 1,3,x,5,x + 3,7,x + 1,11,x,13,x - 2[] 522,4,2,x + 1,3,x,5,x - 1,7,x - 1,11,x - 2,13,x[] 522,5,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 6,13,x + 4[] 522,6,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 3,13,x + 1[] 522,7,2,x - 1,3,x,5,x + 2,7,x - 4,11,x,13,x - 2[] 522,8,2,x - 1,3,x,5,x - 3,7,x + 1,11,x,13,x - 2[] 522,9,2,x - 1,3,x,5,x + 3,7,x + 5,11,x - 4,13,x + 6[] 522,10,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 6,13,x[] 522,11,2,x - 1,3,x,5,x + 2,7,x,11,x - 4,13,x - 6[] 522,12,2,x - 1,3,x,5,x - 3,7,x + 2,11,x - 1,13,x - 3[] 522,13,2,x - 1,3,x,5,x - 3,7,x - 5,11,x + 6,13,x + 4[] 523,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2,13,x^2 + x - 11[] 523,2,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 72*x^11 + 308*x^10 + 492*x^9 - 587*x^8 - 1283*x^7 + 418*x^6 + 1526*x^5 + 33*x^4 - 774*x^3 - 85*x^2 + 141*x + 8,3,x^15 + 3*x^14 - 17*x^13 - 50*x^12 + 111*x^11 + 312*x^10 - 349*x^9 - 897*x^8 + 543*x^7 + 1180*x^6 - 401*x^5 - 623*x^4 + 181*x^3 + 114*x^2 - 33*x - 2,5,x^15 + 19*x^14 + 140*x^13 + 442*x^12 + 24*x^11 - 4077*x^10 - 11810*x^9 - 10832*x^8 + 8722*x^7 + 23778*x^6 + 9378*x^5 - 9987*x^4 - 8231*x^3 - 341*x^2 + 1043*x + 218,7,x^15 + x^14 - 65*x^13 - 71*x^12 + 1622*x^11 + 2079*x^10 - 19593*x^9 - 29759*x^8 + 114951*x^7 + 207182*x^6 - 263534*x^5 - 598861*x^4 + 4063*x^3 + 322280*x^2 + 37779*x - 2744,11,x^15 + 7*x^14 - 85*x^13 - 719*x^12 + 2007*x^11 + 26554*x^10 + 7728*x^9 - 410286*x^8 - 784569*x^7 + 2121922*x^6 + 7495618*x^5 + 1560600*x^4 - 15953890*x^3 - 15090096*x^2 + 3265879*x + 6017216,13,x^15 + 15*x^14 + 10*x^13 - 909*x^12 - 4293*x^11 + 12207*x^10 + 129405*x^9 + 140948*x^8 - 1181467*x^7 - 3470111*x^6 + 1369276*x^5 + 16369458*x^4 + 13960211*x^3 - 18909210*x^2 - 29808448*x - 7023157[] 523,3,2,x^26 - 9*x^25 - x^24 + 231*x^23 - 464*x^22 - 2306*x^21 + 7763*x^20 + 10298*x^19 - 60057*x^18 - 8015*x^17 + 266789*x^16 - 125796*x^15 - 723565*x^14 + 622138*x^13 + 1202991*x^12 - 1407289*x^11 - 1178824*x^10 + 1766306*x^9 + 617378*x^8 - 1241966*x^7 - 135947*x^6 + 462396*x^5 + 400*x^4 - 78680*x^3 + 2576*x^2 + 4032*x - 384,3,x^26 - 4*x^25 - 49*x^24 + 208*x^23 + 1012*x^22 - 4663*x^21 - 11396*x^20 + 59094*x^19 + 75007*x^18 - 466388*x^17 - 280600*x^16 + 2381986*x^15 + 472857*x^14 - 7939604*x^13 + 309652*x^12 + 17086537*x^11 - 2646657*x^10 - 23178878*x^9 + 3952698*x^8 + 19159320*x^7 - 1998424*x^6 - 9145408*x^5 - 112256*x^4 + 2223616*x^3 + 295296*x^2 - 196608*x - 42496,5,x^26 - 21*x^25 + 133*x^24 + 189*x^23 - 5652*x^22 + 16091*x^21 + 67148*x^20 - 424783*x^19 + 1108*x^18 + 4494594*x^17 - 6685702*x^16 - 23809605*x^15 + 66301197*x^14 + 54241804*x^13 - 319227622*x^12 + 53568465*x^11 + 861747737*x^10 - 640623368*x^9 - 1250489090*x^8 + 1587993980*x^7 + 684118440*x^6 - 1736185744*x^5 + 365192256*x^4 + 648584256*x^3 - 446921856*x^2 + 106382592*x - 8750592,7,x^26 - 3*x^25 - 100*x^24 + 332*x^23 + 4188*x^22 - 15475*x^21 - 95119*x^20 + 398414*x^19 + 1260778*x^18 - 6247004*x^17 - 9578508*x^16 + 62051571*x^15 + 34312880*x^14 - 393739786*x^13 + 27090636*x^12 + 1572077681*x^11 - 741916832*x^10 - 3800557726*x^9 + 2763329261*x^8 + 5217039801*x^7 - 4505859008*x^6 - 3750173443*x^5 + 3257166390*x^4 + 1371874260*x^3 - 941636161*x^2 - 224401796*x + 68725316,11,x^26 - 11*x^25 - 87*x^24 + 1307*x^23 + 2074*x^22 - 65149*x^21 + 34467*x^20 + 1783337*x^19 - 2908355*x^18 - 29305733*x^17 + 69754523*x^16 + 294503313*x^15 - 899355720*x^14 - 1734222972*x^13 + 6832413781*x^12 + 5021134610*x^11 - 30319565127*x^10 - 1070558006*x^9 + 72749481441*x^8 - 27663976900*x^7 - 79359825114*x^6 + 46389402198*x^5 + 28335287243*x^4 - 17095836984*x^3 - 2526515156*x^2 + 1622311536*x - 135464256,13,x^26 - 14*x^25 - 96*x^24 + 2136*x^23 + 383*x^22 - 132080*x^21 + 301427*x^20 + 4199329*x^19 - 16468009*x^18 - 70566834*x^17 + 412698712*x^16 + 520810586*x^15 - 5699369592*x^14 + 968098975*x^13 + 45100198785*x^12 - 45073381925*x^11 - 203890014853*x^10 + 327499828693*x^9 + 499671005301*x^8 - 1128758701394*x^7 - 551108498487*x^6 + 1984720955197*x^5 + 55147303448*x^4 - 1628923185473*x^3 + 220929697737*x^2 + 473723308718*x - 30230457287[] 524,1,2,x,3,x - 1,5,x + 2,7,x + 3,11,x,13,x - 1[] 524,2,2,x^2,3,x^2 + 3*x + 1,5,x^2 - x - 1,7,x^2 + x - 1,11,x^2 + 5*x + 5,13,x^2 + 3*x - 9[] 524,3,2,x^4,3,x^4 - x^3 - 12*x^2 + 7*x + 29,5,x^4 + 3*x^3 - 9*x^2 - 16*x + 24,7,x^4 + x^3 - 18*x^2 - 11*x + 43,11,x^4 + 3*x^3 - 15*x^2 - 24*x + 36,13,x^4 + x^3 - 66*x^2 - 27*x + 1023[] 524,4,2,x^4,3,x^4 - 3*x^3 - 2*x^2 + 6*x + 3,5,x^4 - 2*x^3 - 13*x^2 + 30*x - 3,7,x^4 - 7*x^3 + 10*x^2 + 18*x - 37,11,x^4 - 12*x^3 + 41*x^2 - 16*x - 79,13,x^4 + x^3 - 8*x^2 + 9[] Total time: 16.569 seconds, Total memory usage: 5.81MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 19:04:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [525..527] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:03:44 on modular [Seed = 1270804773] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 525,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x,13,x - 6[] 525,2,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 4,13,x - 2[] 525,3,2,x - 1,3,x + 1,5,x,7,x - 1,11,x + 6,13,x - 2[] 525,4,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 6,13,x + 2[] 525,5,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 6*x + 9,13,x^2 + 2*x - 12[] 525,6,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 2*x - 19,13,x^2 + 6*x + 4[] 525,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x - 16,13,x^2 - 20[] 525,8,2,x^2 - 3*x + 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 2*x - 19,13,x^2 - 6*x + 4[] 525,9,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 6*x + 9,13,x^2 - 2*x - 12[] 525,10,2,x^3 - x^2 - 5*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 6*x^2 - 4*x - 8[] 525,11,2,x^3 + x^2 - 5*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 - 6*x^2 - 4*x + 8[] 526,1,2,x^2 + 2*x + 1,3,x^2 - 8,5,x^2 - 6*x + 7,7,x^2 - 4*x - 4,11,x^2,13,x^2 + 4*x + 4[] 526,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - x^3 - 4*x^2 + 2*x + 3,5,x^4 + 5*x^3 + 4*x^2 - 8*x - 9,7,x^4 + x^3 - 12*x^2 + 12*x + 1,11,x^4 + 8*x^3 + 11*x^2 - 42*x - 89,13,x^4 - 6*x^2 - x + 7[] 526,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 5*x^3 + 6*x^2 - 1,5,x^4 + 7*x^3 + 10*x^2 - 16*x - 31,7,x^4 + 5*x^3 - 10*x^2 - 50*x - 25,11,x^4 + 8*x^3 - 5*x^2 - 154*x - 281,13,x^4 + 12*x^3 + 48*x^2 + 77*x + 41[] 526,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + 3*x^4 - 4*x^3 - 10*x^2 + 7*x + 4,5,x^5 - x^4 - 12*x^3 + 12*x^2 + 21*x - 8,7,x^5 + 7*x^4 - 90*x^2 - 181*x - 56,11,x^5 - 8*x^4 - 9*x^3 + 166*x^2 - 209*x - 92,13,x^5 - 2*x^4 - 54*x^3 + 67*x^2 + 561*x + 394[] 526,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 3*x^5 - 6*x^4 + 20*x^3 + 3*x^2 - 32*x + 16,5,x^6 - 5*x^5 + x^4 + 21*x^3 - 11*x^2 - 22*x - 1,7,x^6 - 5*x^5 - 2*x^4 + 24*x^3 - 19*x^2 - 4*x + 4,11,x^6 - 4*x^5 - 9*x^4 + 50*x^3 - 17*x^2 - 96*x + 64,13,x^6 - 36*x^4 - 27*x^3 + 309*x^2 + 376*x - 124[] 527,1,2,x^2 - x - 1,3,x^2 - 5,5,x^2,7,x^2 - 2*x - 4,11,x^2 + 8*x + 11,13,x^2 + 2*x - 4[] 527,2,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,3,x^5 + 3*x^4 - 3*x^3 - 11*x^2 + 2*x + 7,5,x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 18*x + 9,7,x^5 + 4*x^4 + x^3 - 9*x^2 - 7*x - 1,11,x^5 + 2*x^4 - 26*x^3 - x^2 + 118*x - 77,13,x^5 + 15*x^4 + 78*x^3 + 175*x^2 + 165*x + 53[] 527,3,2,x^7 + x^6 - 8*x^5 - 8*x^4 + 15*x^3 + 13*x^2 - 8*x - 5,3,x^7 + 3*x^6 - 7*x^5 - 23*x^4 + 2*x^3 + 33*x^2 + 22*x + 4,5,x^7 + 6*x^6 + 5*x^5 - 29*x^4 - 54*x^3 + 8*x^2 + 60*x + 23,7,x^7 + 10*x^6 + 30*x^5 + 11*x^4 - 80*x^3 - 98*x^2 - 5*x + 19,11,x^7 - 38*x^5 - 25*x^4 + 408*x^3 + 549*x^2 - 898*x - 1412,13,x^7 + 9*x^6 + 10*x^5 - 97*x^4 - 277*x^3 - 123*x^2 + 218*x + 164[] 527,4,2,x^11 + 2*x^10 - 17*x^9 - 34*x^8 + 101*x^7 + 202*x^6 - 238*x^5 - 469*x^4 + 182*x^3 + 295*x^2 - 83*x - 3,3,x^11 - 7*x^10 + 3*x^9 + 71*x^8 - 105*x^7 - 252*x^6 + 472*x^5 + 388*x^4 - 741*x^3 - 302*x^2 + 330*x + 139,5,x^11 - 6*x^10 - 30*x^9 + 217*x^8 + 276*x^7 - 2917*x^6 - 404*x^5 + 17936*x^4 - 5320*x^3 - 49088*x^2 + 17152*x + 46272,7,x^11 - 8*x^10 - 21*x^9 + 305*x^8 - 237*x^7 - 3483*x^6 + 6828*x^5 + 11052*x^4 - 32712*x^3 + 1504*x^2 + 28576*x - 4928,11,x^11 - 12*x^10 + 411*x^8 - 609*x^7 - 5455*x^6 + 8507*x^5 + 32317*x^4 - 39900*x^3 - 63546*x^2 + 71648*x - 6729,13,x^11 - 17*x^10 + 58*x^9 + 491*x^8 - 3815*x^7 + 4485*x^6 + 24590*x^5 - 57012*x^4 - 30624*x^3 + 98976*x^2 + 43488*x - 15424[] 527,5,2,x^16 - 3*x^15 - 22*x^14 + 70*x^13 + 179*x^12 - 631*x^11 - 642*x^10 + 2789*x^9 + 792*x^8 - 6335*x^7 + 903*x^6 + 6928*x^5 - 3096*x^4 - 2631*x^3 + 2063*x^2 - 344*x - 11,3,x^16 - 3*x^15 - 34*x^14 + 102*x^13 + 444*x^12 - 1341*x^11 - 2785*x^10 + 8642*x^9 + 8401*x^8 - 28364*x^7 - 10183*x^6 + 44605*x^5 + 2730*x^4 - 29441*x^3 - 966*x^2 + 7148*x + 1008,5,x^16 - 4*x^15 - 57*x^14 + 249*x^13 + 1172*x^12 - 5894*x^11 - 9730*x^10 + 65513*x^9 + 14914*x^8 - 336400*x^7 + 164680*x^6 + 663056*x^5 - 440640*x^4 - 529088*x^3 + 302976*x^2 + 133120*x - 67584,7,x^16 - 8*x^15 - 48*x^14 + 477*x^13 + 722*x^12 - 10702*x^11 - 3811*x^10 + 118555*x^9 + 15646*x^8 - 721168*x^7 - 217504*x^6 + 2353408*x^5 + 1536384*x^4 - 3198336*x^3 - 3539200*x^2 - 278272*x + 456704,11,x^16 + 6*x^15 - 81*x^14 - 519*x^13 + 2237*x^12 + 16810*x^11 - 21684*x^10 - 252558*x^9 - 35799*x^8 + 1779801*x^7 + 1694694*x^6 - 5021831*x^5 - 7678550*x^4 + 2811663*x^3 + 9030698*x^2 + 3399132*x - 259632,13,x^16 - 19*x^15 + 34*x^14 + 1419*x^13 - 8221*x^12 - 28219*x^11 + 306840*x^10 - 46964*x^9 - 4570200*x^8 + 6126032*x^7 + 30425472*x^6 - 50967168*x^5 - 96196224*x^4 + 114630656*x^3 + 159542272*x^2 + 17356800*x - 14366720[] Total time: 15.479 seconds, Total memory usage: 5.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 19:11:39 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [527..529] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:11:20 on modular [Seed = 1855706696] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 527,1,2,x^2 - x - 1,3,x^2 - 5,5,x^2,7,x^2 - 2*x - 4,11,x^2 + 8*x + 11,13,x^2 + 2*x - 4[] 527,2,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,3,x^5 + 3*x^4 - 3*x^3 - 11*x^2 + 2*x + 7,5,x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 18*x + 9,7,x^5 + 4*x^4 + x^3 - 9*x^2 - 7*x - 1,11,x^5 + 2*x^4 - 26*x^3 - x^2 + 118*x - 77,13,x^5 + 15*x^4 + 78*x^3 + 175*x^2 + 165*x + 53[] 527,3,2,x^7 + x^6 - 8*x^5 - 8*x^4 + 15*x^3 + 13*x^2 - 8*x - 5,3,x^7 + 3*x^6 - 7*x^5 - 23*x^4 + 2*x^3 + 33*x^2 + 22*x + 4,5,x^7 + 6*x^6 + 5*x^5 - 29*x^4 - 54*x^3 + 8*x^2 + 60*x + 23,7,x^7 + 10*x^6 + 30*x^5 + 11*x^4 - 80*x^3 - 98*x^2 - 5*x + 19,11,x^7 - 38*x^5 - 25*x^4 + 408*x^3 + 549*x^2 - 898*x - 1412,13,x^7 + 9*x^6 + 10*x^5 - 97*x^4 - 277*x^3 - 123*x^2 + 218*x + 164[] 527,4,2,x^11 + 2*x^10 - 17*x^9 - 34*x^8 + 101*x^7 + 202*x^6 - 238*x^5 - 469*x^4 + 182*x^3 + 295*x^2 - 83*x - 3,3,x^11 - 7*x^10 + 3*x^9 + 71*x^8 - 105*x^7 - 252*x^6 + 472*x^5 + 388*x^4 - 741*x^3 - 302*x^2 + 330*x + 139,5,x^11 - 6*x^10 - 30*x^9 + 217*x^8 + 276*x^7 - 2917*x^6 - 404*x^5 + 17936*x^4 - 5320*x^3 - 49088*x^2 + 17152*x + 46272,7,x^11 - 8*x^10 - 21*x^9 + 305*x^8 - 237*x^7 - 3483*x^6 + 6828*x^5 + 11052*x^4 - 32712*x^3 + 1504*x^2 + 28576*x - 4928,11,x^11 - 12*x^10 + 411*x^8 - 609*x^7 - 5455*x^6 + 8507*x^5 + 32317*x^4 - 39900*x^3 - 63546*x^2 + 71648*x - 6729,13,x^11 - 17*x^10 + 58*x^9 + 491*x^8 - 3815*x^7 + 4485*x^6 + 24590*x^5 - 57012*x^4 - 30624*x^3 + 98976*x^2 + 43488*x - 15424[] 527,5,2,x^16 - 3*x^15 - 22*x^14 + 70*x^13 + 179*x^12 - 631*x^11 - 642*x^10 + 2789*x^9 + 792*x^8 - 6335*x^7 + 903*x^6 + 6928*x^5 - 3096*x^4 - 2631*x^3 + 2063*x^2 - 344*x - 11,3,x^16 - 3*x^15 - 34*x^14 + 102*x^13 + 444*x^12 - 1341*x^11 - 2785*x^10 + 8642*x^9 + 8401*x^8 - 28364*x^7 - 10183*x^6 + 44605*x^5 + 2730*x^4 - 29441*x^3 - 966*x^2 + 7148*x + 1008,5,x^16 - 4*x^15 - 57*x^14 + 249*x^13 + 1172*x^12 - 5894*x^11 - 9730*x^10 + 65513*x^9 + 14914*x^8 - 336400*x^7 + 164680*x^6 + 663056*x^5 - 440640*x^4 - 529088*x^3 + 302976*x^2 + 133120*x - 67584,7,x^16 - 8*x^15 - 48*x^14 + 477*x^13 + 722*x^12 - 10702*x^11 - 3811*x^10 + 118555*x^9 + 15646*x^8 - 721168*x^7 - 217504*x^6 + 2353408*x^5 + 1536384*x^4 - 3198336*x^3 - 3539200*x^2 - 278272*x + 456704,11,x^16 + 6*x^15 - 81*x^14 - 519*x^13 + 2237*x^12 + 16810*x^11 - 21684*x^10 - 252558*x^9 - 35799*x^8 + 1779801*x^7 + 1694694*x^6 - 5021831*x^5 - 7678550*x^4 + 2811663*x^3 + 9030698*x^2 + 3399132*x - 259632,13,x^16 - 19*x^15 + 34*x^14 + 1419*x^13 - 8221*x^12 - 28219*x^11 + 306840*x^10 - 46964*x^9 - 4570200*x^8 + 6126032*x^7 + 30425472*x^6 - 50967168*x^5 - 96196224*x^4 + 114630656*x^3 + 159542272*x^2 + 17356800*x - 14366720[] 528,1,2,x,3,x + 1,5,x,7,x + 2,11,x + 1,13,x[] 528,2,2,x,3,x + 1,5,x + 2,7,x + 4,11,x - 1,13,x - 6[] 528,3,2,x,3,x + 1,5,x - 4,7,x - 2,11,x - 1,13,x[] 528,4,2,x,3,x - 1,5,x - 2,7,x,11,x + 1,13,x - 2[] 528,5,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x + 2[] 528,6,2,x,3,x + 1,5,x + 4,7,x - 2,11,x + 1,13,x - 4[] 528,7,2,x,3,x + 1,5,x,7,x + 2,11,x - 1,13,x + 4[] 528,8,2,x,3,x - 1,5,x + 2,7,x + 4,11,x + 1,13,x + 2[] 528,9,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x - 6[] 528,10,2,x,3,x - 1,5,x - 2,7,x - 4,11,x - 1,13,x + 6[] 529,1,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2 - 6*x + 6,13,x^2 - 2*x + 1[] 529,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 + 6*x + 6,11,x^2 + 6*x + 6,13,x^2 - 2*x + 1[] 529,3,2,x^2 + x - 1,3,x^2 - 5,5,x^2 - 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 6*x + 4,13,x^2 - 6*x + 9[] 529,4,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 - 2*x - 7,7,x^2 - 4*x + 2,11,x^2 - 2,13,x^2 + 6*x + 9[] 529,5,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 + 2*x - 7,7,x^2 + 4*x + 2,11,x^2 - 2,13,x^2 + 6*x + 9[] 529,6,2,x^3 - 6*x - 3,3,x^3 - 9*x - 4,5,x^3,7,x^3,11,x^3,13,x^3 - 39*x + 74[] 529,7,2,x^4 + 2*x^3 - 5*x^2 - 6*x + 9,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 14*x^2 + 36,7,x^4 - 14*x^2 + 36,11,x^4 - 14*x^2 + 36,13,x^4 + 8*x^3 - 2*x^2 - 72*x + 81[] 529,8,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 4*x^3 - 8*x + 4,5,x^4 - 4*x^2 + 1,7,x^4 - 12*x^2 + 36,11,x^4 - 28*x^2 + 4,13,x^4 + 4*x^3 - 18*x^2 - 44*x + 121[] 529,9,2,x^5 - 2*x^4 - 5*x^3 + 13*x^2 - 7*x + 1,3,x^5 - 2*x^4 - 5*x^3 + 13*x^2 - 7*x + 1,5,x^5 + 7*x^4 + 13*x^3 - 6*x^2 - 35*x - 23,7,x^5 + 8*x^4 + 19*x^3 + 4*x^2 - 32*x - 23,11,x^5 + 13*x^4 + 61*x^3 + 119*x^2 + 70*x - 23,13,x^5 - 4*x^4 - 9*x^3 + 38*x^2 - 2*x - 1[] 529,10,2,x^5 - 2*x^4 - 5*x^3 + 13*x^2 - 7*x + 1,3,x^5 - 2*x^4 - 5*x^3 + 13*x^2 - 7*x + 1,5,x^5 - 7*x^4 + 13*x^3 + 6*x^2 - 35*x + 23,7,x^5 - 8*x^4 + 19*x^3 - 4*x^2 - 32*x + 23,11,x^5 - 13*x^4 + 61*x^3 - 119*x^2 + 70*x + 23,13,x^5 - 4*x^4 - 9*x^3 + 38*x^2 - 2*x - 1[] Total time: 18.709 seconds, Total memory usage: 5.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 19:15:43 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [530..532] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:15:24 on modular [Seed = 1637144179] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 530,1,2,x + 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x - 5[] 530,2,2,x + 1,3,x,5,x - 1,7,x + 2,11,x,13,x + 2[] 530,3,2,x + 1,3,x + 3,5,x - 1,7,x + 2,11,x,13,x - 1[] 530,4,2,x - 1,3,x + 1,5,x + 1,7,x + 2,11,x + 4,13,x + 3[] 530,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 10*x - 13,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 3*x^2 - 18*x + 47,11,x^3 + x^2 - 16*x - 7,13,x^3 + 7*x^2 - 27[] 530,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 2*x + 7,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 - 2*x + 25,11,x^3 + x^2 - 4*x - 3,13,x^3 - 7*x^2 + 12*x - 1[] 530,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 9*x + 16,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 3*x^3 - 12*x^2 + 5*x + 10,11,x^4 - 7*x^3 - 4*x^2 + 65*x + 24,13,x^4 - x^3 - 22*x^2 + 3*x + 98[] 530,8,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 4*x^4 - 3*x^3 + 23*x^2 - 19*x + 4,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - x^4 - 16*x^3 + 19*x^2 + 30*x + 8,11,x^5 + x^4 - 40*x^3 - 11*x^2 + 192*x + 176,13,x^5 - 51*x^3 - 29*x^2 + 265*x - 82[] 531,1,2,x^2 - 3*x + 1,3,x^2,5,x^2 - 6*x + 9,7,x^2 + 7*x + 11,11,x^2 - 2*x - 19,13,x^2 - 45[] 531,2,2,x^2 - x - 1,3,x^2,5,x^2 - 5,7,x^2 + 7*x + 11,11,x^2 - 5,13,x^2 + 8*x + 11[] 531,3,2,x^2 + x - 1,3,x^2,5,x^2 + 2*x + 1,7,x^2 - x - 1,11,x^2 + 4*x - 1,13,x^2 + 2*x + 1[] 531,4,2,x^3 - 4*x + 1,3,x^3,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 - 9*x^2 + 23*x - 16,11,x^3 - 2*x^2 - 11*x - 4,13,x^3 - 4*x^2 - 7*x + 26[] 531,5,2,x^5 + 3*x^4 - 3*x^3 - 11*x^2 + x + 5,3,x^5,5,x^5 + 8*x^4 + 16*x^3 - 8*x^2 - 29*x + 8,7,x^5 - 2*x^4 - 13*x^3 - 2*x^2 + 13*x + 4,11,x^5 + 10*x^4 + 12*x^3 - 66*x^2 + 35*x + 4,13,x^5 + 4*x^4 - 30*x^3 - 170*x^2 - 243*x - 86[] 531,6,2,x^5 - 3*x^4 - 3*x^3 + 11*x^2 + x - 5,3,x^5,5,x^5 - 8*x^4 + 16*x^3 + 8*x^2 - 29*x - 8,7,x^5 - 2*x^4 - 13*x^3 - 2*x^2 + 13*x + 4,11,x^5 - 10*x^4 + 12*x^3 + 66*x^2 + 35*x - 4,13,x^5 + 4*x^4 - 30*x^3 - 170*x^2 - 243*x - 86[] 531,7,2,x^5 - 9*x^3 - 2*x^2 + 16*x + 8,3,x^5,5,x^5 + 2*x^4 - 14*x^3 - 23*x^2 + 19*x - 1,7,x^5 - 2*x^4 - 16*x^3 + 43*x^2 + 13*x - 71,11,x^5 - 2*x^4 - 24*x^3 + 24*x^2 + 128*x + 64,13,x^5 - 8*x^4 + 88*x^2 - 48*x - 224[] 532,1,2,x,3,x,5,x + 2,7,x - 1,11,x - 4,13,x - 4[] 532,2,2,x^2,3,x^2 - x - 1,5,x^2 + 4*x - 1,7,x^2 + 2*x + 1,11,x^2 + 3*x + 1,13,x^2 + 2*x - 19[] 532,3,2,x^2,3,x^2 + 3*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - x - 31,13,x^2 - 5[] 532,4,2,x^2,3,x^2 + x - 5,5,x^2 - 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 3*x - 3,13,x^2 + 2*x + 1[] 532,5,2,x^3,3,x^3 + x^2 - 7*x - 8,5,x^3 - 2*x^2 - 9*x + 14,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 3*x^2 - 7*x - 20,13,x^3 - 8*x^2 + 11*x + 16[] Total time: 18.319 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 19:18:50 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [533..535] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:18:35 on modular [Seed = 1954661281] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 533,1,2,x^2 - 2*x - 1,3,x^2 - 2*x - 1,5,x^2 - 8,7,x^2 - 4*x - 4,11,x^2 - 8,13,x^2 + 2*x + 1[] 533,2,2,x^7 + 2*x^6 - 6*x^5 - 12*x^4 + 9*x^3 + 19*x^2 - x - 5,3,x^7 + 8*x^6 + 19*x^5 + 2*x^4 - 45*x^3 - 50*x^2 - 17*x - 1,5,x^7 + 2*x^6 - 17*x^5 - 34*x^4 + 63*x^3 + 150*x^2 + 19*x - 59,7,x^7 + 10*x^6 + 25*x^5 - 45*x^4 - 267*x^3 - 245*x^2 + 245*x + 343,11,x^7 + 2*x^6 - 50*x^5 - 54*x^4 + 548*x^3 - 268*x^2 - 203*x - 25,13,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1[] 533,3,2,x^8 - x^7 - 10*x^6 + 8*x^5 + 31*x^4 - 22*x^3 - 28*x^2 + 22*x - 3,3,x^8 - 4*x^7 - 11*x^6 + 52*x^5 + 31*x^4 - 220*x^3 + 27*x^2 + 299*x - 162,5,x^8 - 4*x^7 - 13*x^6 + 68*x^5 + x^4 - 236*x^3 + 83*x^2 + 237*x - 14,7,x^8 - 6*x^7 - 9*x^6 + 75*x^5 + 49*x^4 - 301*x^3 - 191*x^2 + 389*x + 294,11,x^8 - 2*x^7 - 38*x^6 + 98*x^5 + 378*x^4 - 1246*x^3 - 533*x^2 + 4217*x - 3138,13,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[] 533,4,2,x^11 + 2*x^10 - 14*x^9 - 26*x^8 + 64*x^7 + 103*x^6 - 117*x^5 - 149*x^4 + 65*x^3 + 71*x^2 + 5*x - 1,3,x^11 + 8*x^10 + 7*x^9 - 86*x^8 - 189*x^7 + 214*x^6 + 773*x^5 + 113*x^4 - 724*x^3 - 400*x^2 - 58*x - 2,5,x^11 + 4*x^10 - 23*x^9 - 96*x^8 + 121*x^7 + 664*x^6 + 243*x^5 - 1291*x^4 - 1888*x^3 - 1084*x^2 - 284*x - 28,7,x^11 + 18*x^10 + 111*x^9 + 143*x^8 - 1367*x^7 - 6565*x^6 - 9777*x^5 + 1275*x^4 + 13932*x^3 + 5098*x^2 - 3270*x - 1466,11,x^11 + 10*x^10 - 16*x^9 - 438*x^8 - 814*x^7 + 4636*x^6 + 14709*x^5 - 8983*x^4 - 56906*x^3 - 12200*x^2 + 45646*x - 5402,13,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1[] 533,5,2,x^13 - 21*x^11 + 166*x^9 + x^8 - 613*x^7 - 16*x^6 + 1074*x^5 + 72*x^4 - 822*x^3 - 76*x^2 + 215*x + 27,3,x^13 - 10*x^12 + 24*x^11 + 62*x^10 - 330*x^9 + 154*x^8 + 1082*x^7 - 1389*x^6 - 889*x^5 + 2087*x^4 - 332*x^3 - 634*x^2 + 170*x - 2,5,x^13 - 39*x^11 + 12*x^10 + 539*x^9 - 356*x^8 - 3093*x^7 + 3139*x^6 + 6168*x^5 - 8492*x^4 - 2420*x^3 + 7004*x^2 - 2560*x + 96,7,x^13 - 10*x^12 - 3*x^11 + 303*x^10 - 595*x^9 - 2829*x^8 + 8439*x^7 + 8049*x^6 - 35878*x^5 - 1806*x^4 + 47502*x^3 - 6426*x^2 - 15552*x - 1944,11,x^13 - 2*x^12 - 68*x^11 + 122*x^10 + 1732*x^9 - 2470*x^8 - 20989*x^7 + 18027*x^6 + 129028*x^5 - 26852*x^4 - 353854*x^3 - 123922*x^2 + 221632*x + 98352,13,x^13 - 13*x^12 + 78*x^11 - 286*x^10 + 715*x^9 - 1287*x^8 + 1716*x^7 - 1716*x^6 + 1287*x^5 - 715*x^4 + 286*x^3 - 78*x^2 + 13*x - 1[] 534,1,2,x - 1,3,x + 1,5,x + 2,7,x + 2,11,x + 4,13,x[] 534,2,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 4,7,x^2 - 4*x + 2,11,x^2 + 4*x - 4,13,x^2 - 18[] 534,3,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 3*x - 1,7,x^2 + 2*x - 12,11,x^2 - 5*x + 3,13,x^2 + x - 3[] 534,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x - 4,11,x^2 - 3*x - 9,13,x^2 + x - 11[] 534,5,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 3*x^3 - 13*x^2 + 32*x + 12,7,x^4 - 2*x^3 - 22*x^2 + 60*x - 8,11,x^4 - x^3 - 13*x^2 + 8*x + 36,13,x^4 - 13*x^3 + 43*x^2 + 38*x - 262[] 534,6,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - x^3 - 13*x^2 + 16*x - 4,7,x^4 - 4*x^3 - 4*x^2 + 16*x + 16,11,x^4 - 3*x^3 - 17*x^2 + 72*x - 64,13,x^4 + x^3 - 33*x^2 + 74*x - 44[] 535,1,2,x^3 + 2*x^2 - x - 1,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + x^2 - 2*x - 1,11,x^3 + 7*x^2 - 49,13,x^3 + 2*x^2 - 8*x - 8[] 535,2,2,x^8 + 4*x^7 - 4*x^6 - 27*x^5 - 3*x^4 + 49*x^3 + 14*x^2 - 24*x - 8,3,x^8 + 2*x^7 - 10*x^6 - 17*x^5 + 31*x^4 + 37*x^3 - 36*x^2 - 20*x + 8,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 3*x^7 - 24*x^6 - 73*x^5 + 166*x^4 + 556*x^3 - 224*x^2 - 1344*x - 736,11,x^8 + 9*x^7 + 6*x^6 - 110*x^5 - 216*x^4 + 136*x^3 + 340*x^2 - 53*x - 1,13,x^8 + 8*x^7 - 2*x^6 - 93*x^5 - x^4 + 211*x^3 + 20*x^2 - 108*x - 8[] 535,3,2,x^9 - 5*x^8 + 31*x^6 - 29*x^5 - 47*x^4 + 59*x^3 + 2*x^2 - 8*x - 1,3,x^9 - 2*x^8 - 20*x^7 + 36*x^6 + 124*x^5 - 168*x^4 - 296*x^3 + 208*x^2 + 192*x - 64,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,7,x^9 - 3*x^8 - 19*x^7 + 48*x^6 + 66*x^5 - 151*x^4 - 63*x^3 + 111*x^2 - 8*x - 1,11,x^9 - 9*x^8 + 3*x^7 + 188*x^6 - 562*x^5 - 277*x^4 + 3847*x^3 - 7105*x^2 + 5524*x - 1611,13,x^9 - 4*x^8 - 54*x^7 + 168*x^6 + 1048*x^5 - 2184*x^4 - 8760*x^3 + 7936*x^2 + 27552*x + 6208[] 535,4,2,x^15 - 4*x^14 - 18*x^13 + 85*x^12 + 103*x^11 - 685*x^10 - 108*x^9 + 2595*x^8 - 846*x^7 - 4594*x^6 + 2565*x^5 + 3187*x^4 - 1951*x^3 - 470*x^2 + 136*x + 24,3,x^15 - 38*x^13 + 7*x^12 + 565*x^11 - 209*x^10 - 4158*x^9 + 2268*x^8 + 15708*x^7 - 11036*x^6 - 28200*x^5 + 23544*x^4 + 18192*x^3 - 16512*x^2 - 1472*x + 1280,5,x^15 - 15*x^14 + 105*x^13 - 455*x^12 + 1365*x^11 - 3003*x^10 + 5005*x^9 - 6435*x^8 + 6435*x^7 - 5005*x^6 + 3003*x^5 - 1365*x^4 + 455*x^3 - 105*x^2 + 15*x - 1,7,x^15 + 3*x^14 - 69*x^13 - 202*x^12 + 1846*x^11 + 5081*x^10 - 24969*x^9 - 61451*x^8 + 185062*x^7 + 379539*x^6 - 740046*x^5 - 1147436*x^4 + 1379008*x^3 + 1421664*x^2 - 695328*x - 407552,11,x^15 - 11*x^14 - 43*x^13 + 785*x^12 - 108*x^11 - 20672*x^10 + 28631*x^9 + 247214*x^8 - 473963*x^7 - 1323229*x^6 + 2902537*x^5 + 2521814*x^4 - 6646278*x^3 - 494379*x^2 + 4818017*x - 1525884,13,x^15 + 4*x^14 - 112*x^13 - 365*x^12 + 4707*x^11 + 11137*x^10 - 91822*x^9 - 127346*x^8 + 810968*x^7 + 421400*x^6 - 2458304*x^5 - 562392*x^4 + 1665872*x^3 + 52704*x^2 - 185472*x - 24704[] Total time: 14.989 seconds, Total memory usage: 5.70MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sun Nov 30 19:27:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [536..538] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:26:59 on modular [Seed = 2624137537] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 536,1,2,x^2,3,x^2 + x - 1,5,x^2 + 2*x + 1,7,x^2 + x - 1,11,x^2 - 2*x - 19,13,x^2 + 5*x + 5[] 536,2,2,x^3,3,x^3 + 3*x^2 - x - 2,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 + x^2 - 5*x + 2,11,x^3 + 4*x^2 - x - 8,13,x^3 + 5*x^2 - 7*x + 2[] 536,3,2,x^3,3,x^3 - 3*x^2 - 7*x + 20,5,x^3 - 2*x^2 - 9*x + 14,7,x^3 - x^2 - 7*x + 8,11,x^3 - 4*x^2 - 5*x + 4,13,x^3 + 5*x^2 + x - 2[] 536,4,2,x^4,3,x^4 + 3*x^3 - 2*x^2 - 7*x - 2,5,x^4 + x^3 - 16*x^2 - 7*x + 58,7,x^4 + 2*x^3 - 28*x^2 - 32*x + 176,11,x^4 + 3*x^3 - 24*x^2 - 109*x - 112,13,x^4 - 11*x^3 + 24*x^2 + 77*x - 242[] 536,5,2,x^5,3,x^5 - 4*x^4 - 2*x^3 + 16*x^2 - x - 15,5,x^5 - x^4 - 15*x^3 + 16*x^2 + 16*x + 3,7,x^5 - 7*x^4 + 7*x^3 + 20*x^2 - 4*x - 8,11,x^5 - 5*x^4 - 13*x^3 + 74*x^2 - 86*x + 25,13,x^5 - 6*x^4 - 24*x^3 + 106*x^2 + 249*x - 125[] 537,1,2,x - 1,3,x + 1,5,x,7,x + 1,11,x - 6,13,x - 7[] 537,2,2,x,3,x - 1,5,x - 1,7,x,11,x,13,x - 3[] 537,3,2,x,3,x - 1,5,x + 3,7,x - 2,11,x - 6,13,x + 1[] 537,4,2,x - 1,3,x - 1,5,x - 4,7,x - 1,11,x - 2,13,x + 1[] 537,5,2,x + 2,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x + 1[] 537,6,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 - x - 4,7,x^2 - 3*x - 2,11,x^2 - 4*x + 4,13,x^2 + 2*x + 1[] 537,7,2,x^2 - 4*x + 4,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 4*x - 4,11,x^2 + 4*x - 4,13,x^2 + 2*x - 31[] 537,8,2,x^6 + 2*x^5 - 6*x^4 - 10*x^3 + 8*x^2 + 8*x - 4,3,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,5,x^6 - 4*x^5 - 7*x^4 + 28*x^3 + 7*x^2 - 8*x - 1,7,x^6 + 12*x^5 + 46*x^4 + 34*x^3 - 156*x^2 - 300*x - 116,11,x^6 + 4*x^5 - 22*x^4 - 66*x^3 + 96*x^2 + 92*x + 4,13,x^6 + 10*x^5 + 3*x^4 - 136*x^3 - 69*x^2 + 126*x + 49[] 537,9,2,x^6 + 4*x^5 - 12*x^3 - 4*x^2 + 8*x + 4,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 + 10*x^5 + 31*x^4 + 20*x^3 - 41*x^2 - 30*x + 25,7,x^6 + 10*x^5 + 22*x^4 - 28*x^3 - 72*x^2 - 36*x - 4,11,x^6 + 4*x^5 - 50*x^4 - 184*x^3 + 540*x^2 + 1164*x - 2404,13,x^6 + 6*x^5 - 41*x^4 - 204*x^3 + 463*x^2 + 1350*x + 137[] 537,10,2,x^8 - 2*x^7 - 13*x^6 + 22*x^5 + 54*x^4 - 66*x^3 - 72*x^2 + 32*x + 12,3,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 + 6*x^7 - 15*x^6 - 114*x^5 + 79*x^4 + 646*x^3 - 401*x^2 - 1050*x + 800,7,x^8 - 15*x^7 + 72*x^6 - 42*x^5 - 642*x^4 + 1636*x^3 + 8*x^2 - 3812*x + 3152,11,x^8 + 4*x^7 - 24*x^6 - 74*x^5 + 136*x^4 + 292*x^3 - 20*x^2 - 136*x - 32,13,x^8 + x^7 - 45*x^6 - 55*x^5 + 657*x^4 + 971*x^3 - 3199*x^2 - 5349*x + 842[] 538,1,2,x^2 - 2*x + 1,3,x^2 - x - 3,5,x^2 - x - 3,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 - 10*x + 25[] 538,2,2,x^2 - 2*x + 1,3,x^2 + x - 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 + 4*x - 1,13,x^2 + 2*x + 1[] 538,3,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 3*x^3 - 3*x^2 + 10*x - 4,5,x^4 - 5*x^3 + 3*x^2 + 6*x - 4,7,x^4 + x^3 - 6*x^2 - x + 1,11,x^4 - 7*x^3 + 12*x^2 + 3*x - 13,13,x^4 - 4*x^3 - 11*x^2 + 30*x + 52[] 538,4,2,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,3,x^7 + 4*x^6 - 6*x^5 - 30*x^4 + 31*x^2 + 2*x - 3,5,x^7 + 6*x^6 - 4*x^5 - 82*x^4 - 102*x^3 + 229*x^2 + 520*x + 233,7,x^7 + 3*x^6 - 23*x^5 - 70*x^4 + 127*x^3 + 392*x^2 - 187*x - 563,11,x^7 + 12*x^6 + 5*x^5 - 370*x^4 - 980*x^3 + 1576*x^2 + 4864*x - 480,13,x^7 - 3*x^6 - 51*x^5 + 88*x^4 + 635*x^3 - 54*x^2 - 607*x - 89[] 538,5,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - x^6 - 16*x^5 + 19*x^4 + 63*x^3 - 87*x^2 - 10*x + 12,5,x^7 - 7*x^6 - 4*x^5 + 109*x^4 - 161*x^3 - 109*x^2 + 130*x - 4,7,x^7 - 6*x^6 - 14*x^5 + 142*x^4 - 258*x^3 + 137*x^2 + 18*x - 19,11,x^7 + 3*x^6 - 33*x^5 - 130*x^4 + 100*x^3 + 856*x^2 + 992*x + 288,13,x^7 + 9*x^6 + 8*x^5 - 71*x^4 - 79*x^3 + 117*x^2 + 54*x + 4[] Total time: 16.369 seconds, Total memory usage: 5.55MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sun Nov 30 19:32:26 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [539..541] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:32:03 on modular [Seed = 2908233383] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 539,1,2,x,3,x + 1,5,x + 3,7,x,11,x + 1,13,x - 4[] 539,2,2,x,3,x - 3,5,x - 1,7,x,11,x + 1,13,x - 4[] 539,3,2,x - 1,3,x + 2,5,x - 2,7,x,11,x - 1,13,x + 4[] 539,4,2,x + 2,3,x - 1,5,x + 1,7,x,11,x - 1,13,x + 4[] 539,5,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 - 2,7,x^2,11,x^2 + 2*x + 1,13,x^2[] 539,6,2,x^2 - 5,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2,11,x^2 + 2*x + 1,13,x^2 + 2*x - 4[] 539,7,2,x^3 - 5*x + 3,3,x^3 + x^2 - 4*x - 3,5,x^3 + 2*x^2 - 7*x - 5,7,x^3,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 11*x^2 + 36*x + 35[] 539,8,2,x^3 - 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 - 6*x^2 + 9*x - 1,7,x^3,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 3*x^2 - 6*x - 1[] 539,9,2,x^3 - 5*x + 3,3,x^3 - x^2 - 4*x + 3,5,x^3 - 2*x^2 - 7*x + 5,7,x^3,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 11*x^2 + 36*x - 35[] 539,10,2,x^3 - 3*x - 1,3,x^3 + 3*x^2 - 1,5,x^3 + 6*x^2 + 9*x + 1,7,x^3,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 - 6*x + 1[] 539,11,2,x^4 - 2*x^3 - 7*x^2 + 8*x + 16,3,x^4 - 7*x^2 + 8,5,x^4 - 23*x^2 + 128,7,x^4,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 - 56*x^2 + 512[] 539,12,2,x^10 - 2*x^9 - 17*x^8 + 36*x^7 + 87*x^6 - 202*x^5 - 119*x^4 + 360*x^3 - 192*x + 64,3,x^10 - 26*x^8 + 245*x^6 - 1038*x^4 + 1884*x^2 - 968,5,x^10 - 34*x^8 + 365*x^6 - 1214*x^4 + 204*x^2 - 8,7,x^10,11,x^10 - 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1,13,x^10 - 72*x^8 + 1696*x^6 - 16672*x^4 + 69120*x^2 - 100352[] 540,1,2,x,3,x,5,x + 1,7,x - 2,11,x,13,x - 2[] 540,2,2,x,3,x,5,x - 1,7,x + 4,11,x + 6,13,x + 4[] 540,3,2,x,3,x,5,x + 1,7,x + 1,11,x + 6,13,x + 1[] 540,4,2,x,3,x,5,x + 1,7,x + 4,11,x - 6,13,x + 4[] 540,5,2,x,3,x,5,x - 1,7,x + 1,11,x - 6,13,x + 1[] 540,6,2,x,3,x,5,x - 1,7,x - 2,11,x,13,x - 2[] 541,1,2,x^20 + 5*x^19 - 15*x^18 - 105*x^17 + 53*x^16 + 888*x^15 + 248*x^14 - 3950*x^13 - 2525*x^12 + 10014*x^11 + 8292*x^10 - 14513*x^9 - 13426*x^8 + 11322*x^7 + 10779*x^6 - 4166*x^5 - 3649*x^4 + 669*x^3 + 389*x^2 - 45*x - 9,3,x^20 + 12*x^19 + 35*x^18 - 120*x^17 - 818*x^16 - 503*x^15 + 5196*x^14 + 9925*x^13 - 10141*x^12 - 40746*x^11 - 9933*x^10 + 61918*x^9 + 46584*x^8 - 29769*x^7 - 31815*x^6 + 7628*x^5 + 8524*x^4 - 1815*x^3 - 808*x^2 + 263*x - 19,5,x^20 + 17*x^19 + 83*x^18 - 160*x^17 - 2704*x^16 - 5758*x^15 + 21317*x^14 + 106677*x^13 + 35612*x^12 - 597190*x^11 - 1068980*x^10 + 739500*x^9 + 3863028*x^8 + 2706594*x^7 - 3110844*x^6 - 5424167*x^5 - 1630358*x^4 + 1640521*x^3 + 1393701*x^2 + 366210*x + 31369,7,x^20 + 6*x^19 - 63*x^18 - 424*x^17 + 1388*x^16 + 11650*x^15 - 10625*x^14 - 157713*x^13 - 39378*x^12 + 1086458*x^11 + 1033532*x^10 - 3437110*x^9 - 5033789*x^8 + 3390483*x^7 + 7142396*x^6 - 568725*x^5 - 3050148*x^4 + 134703*x^3 + 337508*x^2 - 2990*x - 7943,11,x^20 + 40*x^19 + 654*x^18 + 5168*x^17 + 12370*x^16 - 120631*x^15 - 1142633*x^14 - 3208037*x^13 + 6005022*x^12 + 67537660*x^11 + 168761948*x^10 - 5915323*x^9 - 844155774*x^8 - 1364248341*x^7 + 615302043*x^6 + 3549597747*x^5 + 1885966284*x^4 - 2836376965*x^3 - 2724916829*x^2 + 461761032*x + 726492771,13,x^20 + 5*x^19 - 127*x^18 - 631*x^17 + 6439*x^16 + 32187*x^15 - 167332*x^14 - 859067*x^13 + 2369765*x^12 + 12999623*x^11 - 17717297*x^10 - 113532837*x^9 + 56650003*x^8 + 559512234*x^7 + 41271202*x^6 - 1422693506*x^5 - 694255401*x^4 + 1382830503*x^3 + 1185975823*x^2 + 192015993*x - 12374199[] 541,2,2,x^24 - 3*x^23 - 31*x^22 + 97*x^21 + 402*x^20 - 1333*x^19 - 2825*x^18 + 10187*x^17 + 11576*x^16 - 47520*x^15 - 27272*x^14 + 139733*x^13 + 31933*x^12 - 258608*x^11 - 4817*x^10 + 293651*x^9 - 26127*x^8 - 196645*x^7 + 21140*x^6 + 74903*x^5 - 4562*x^4 - 14861*x^3 - 379*x^2 + 1179*x + 153,3,x^24 - 12*x^23 + 23*x^22 + 264*x^21 - 1202*x^20 - 1359*x^19 + 16144*x^18 - 11151*x^17 - 101433*x^16 + 169382*x^15 + 316059*x^14 - 879646*x^13 - 352728*x^12 + 2350767*x^11 - 566655*x^10 - 3332320*x^9 + 2073100*x^8 + 2202693*x^7 - 2071804*x^6 - 371069*x^5 + 648245*x^4 - 62600*x^3 - 27760*x^2 + 2960*x - 16,5,x^24 - 13*x^23 + 16*x^22 + 471*x^21 - 1896*x^20 - 5343*x^19 + 39712*x^18 + 8885*x^17 - 408527*x^16 + 324485*x^15 + 2485859*x^14 - 3477513*x^13 - 9557728*x^12 + 17929032*x^11 + 23513024*x^10 - 55616625*x^9 - 35612272*x^8 + 108441058*x^7 + 28373219*x^6 - 129873224*x^5 - 2688364*x^4 + 86826119*x^3 - 13479964*x^2 - 24511980*x + 7776873,7,x^24 - 2*x^23 - 87*x^22 + 192*x^21 + 3132*x^20 - 7646*x^19 - 60269*x^18 + 164371*x^17 + 664490*x^16 - 2077806*x^15 - 4115052*x^14 + 15762462*x^13 + 12202559*x^12 - 70260609*x^11 - 2852624*x^10 + 173225463*x^9 - 69692264*x^8 - 212783853*x^7 + 138052360*x^6 + 115329438*x^5 - 88029127*x^4 - 24541960*x^3 + 17114400*x^2 + 2046176*x - 11152,11,x^24 - 38*x^23 + 593*x^22 - 4588*x^21 + 13589*x^20 + 51937*x^19 - 565855*x^18 + 1360874*x^17 + 3383657*x^16 - 24858652*x^15 + 29524911*x^14 + 119539590*x^13 - 389706424*x^12 + 50644662*x^11 + 1409318191*x^10 - 1892090669*x^9 - 1290184109*x^8 + 4815555739*x^7 - 2466416816*x^6 - 3172675484*x^5 + 4274432912*x^4 - 1163442301*x^3 - 719976526*x^2 + 498835026*x - 82710567,13,x^24 + 3*x^23 - 155*x^22 - 429*x^21 + 10213*x^20 + 26473*x^19 - 373202*x^18 - 929109*x^17 + 8265861*x^16 + 20477029*x^15 - 113584445*x^14 - 292969719*x^13 + 943671573*x^12 + 2693354440*x^11 - 4261879806*x^10 - 15062333404*x^9 + 6721329171*x^8 + 45156864567*x^7 + 14102878627*x^6 - 53248950673*x^5 - 40969305993*x^4 + 8026474040*x^3 + 11935366248*x^2 + 819040384*x - 350893376[] Total time: 22.529 seconds, Total memory usage: 6.78MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sun Nov 30 19:40:54 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [542..544] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:40:38 on modular [Seed = 3040871613] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 542,1,2,x - 1,3,x - 2,5,x - 2,7,x,11,x + 4,13,x[] 542,2,2,x - 1,3,x + 1,5,x,7,x + 5,11,x,13,x + 1[] 542,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 1,5,x^2 + 4*x + 2,7,x^2 + 2*x - 1,11,x^2 + 8*x + 14,13,x^2 + 6*x + 1[] 542,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 3*x - 1,5,x^3 - 4*x - 2,7,x^3 + 5*x^2 + 5*x - 1,11,x^3 - 4*x^2 - 10*x + 38,13,x^3 + 7*x^2 + 7*x - 19[] 542,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 5*x - 1,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 - x^2 - 19*x + 37,11,x^3 + 10*x^2 + 26*x + 6,13,x^3 - 15*x^2 + 75*x - 125[] 542,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - x + 5,5,x^3 - 4*x^2 - 4*x + 20,7,x^3 - 5*x^2 + 3*x + 5,11,x^3 - 4*x^2 + 4,13,x^3 + 5*x^2 - 5*x + 1[] 542,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 4*x^3 + 2*x^2 - 4*x + 1,5,x^4 + 4*x^3 - 2*x^2 - 8*x + 4,7,x^4 - 4*x^3 - 8*x^2 + 8*x + 7,11,x^4 - 8*x^3 + 10*x^2 + 40*x - 68,13,x^4 - 12*x^3 + 16*x^2 + 240*x - 721[] 542,8,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 16*x^4 + 2*x^3 + 69*x^2 - 8*x - 82,5,x^6 - 2*x^5 - 32*x^4 + 80*x^3 + 232*x^2 - 768*x + 416,7,x^6 - 10*x^5 + 20*x^4 + 74*x^3 - 285*x^2 + 224*x - 32,11,x^6 - 2*x^5 - 44*x^4 + 104*x^3 + 312*x^2 - 640*x + 256,13,x^6 - 26*x^4 + 6*x^3 + 171*x^2 - 108*x - 162[] 543,1,2,x^3 + 2*x^2 - x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + x^2 - 2*x - 1,7,x^3 + 7*x^2 + 14*x + 7,11,x^3 + 2*x^2 - x - 1,13,x^3 + 9*x^2 + 20*x - 1[] 543,2,2,x^5 + x^4 - 6*x^3 - 8*x^2 + 1,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 - 3*x^4 - 14*x^3 + 43*x^2 - 12*x - 16,7,x^5 - 9*x^4 - 2*x^3 + 211*x^2 - 562*x + 284,11,x^5 + 4*x^4 - 13*x^3 - 27*x^2 + 86*x - 52,13,x^5 - 9*x^4 + 23*x^3 - 8*x^2 - 18*x + 7[] 543,3,2,x^7 + 4*x^6 - 3*x^5 - 23*x^4 - 5*x^3 + 32*x^2 + 15*x - 1,3,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,5,x^7 + 3*x^6 - 11*x^5 - 30*x^4 + 17*x^3 + 28*x^2 - 6*x - 7,7,x^7 + x^6 - 19*x^5 + 43*x^3 - 26*x^2 + 1,11,x^7 + 4*x^6 - 27*x^5 - 111*x^4 + 136*x^3 + 556*x^2 - 272*x - 400,13,x^7 + 11*x^6 + 21*x^5 - 84*x^4 - 123*x^3 + 322*x^2 - 130*x + 7[] 543,4,2,x^8 - 3*x^7 - 6*x^6 + 21*x^5 + 5*x^4 - 35*x^3 + 10*x^2 + 4*x - 1,3,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 - 5*x^7 - 14*x^6 + 97*x^5 - 30*x^4 - 336*x^3 + 192*x^2 + 320*x - 128,7,x^8 + 3*x^7 - 26*x^6 - 57*x^5 + 216*x^4 + 268*x^3 - 576*x^2 - 272*x + 448,11,x^8 - 4*x^7 - 23*x^6 + 57*x^5 + 172*x^4 - 68*x^3 - 208*x^2 + 16*x + 64,13,x^8 - 13*x^7 + 24*x^6 + 289*x^5 - 1077*x^4 - 1095*x^3 + 6318*x^2 + 1067*x - 6298[] 543,5,2,x^8 - 3*x^7 - 12*x^6 + 43*x^5 + 24*x^4 - 169*x^3 + 84*x^2 + 113*x - 73,3,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,5,x^8 + 2*x^7 - 25*x^6 - 30*x^5 + 193*x^4 + 40*x^3 - 524*x^2 + 304*x + 64,7,x^8 + 2*x^7 - 19*x^6 - 2*x^5 + 87*x^4 - 58*x^3 - 92*x^2 + 112*x - 32,11,x^8 + 2*x^7 - 56*x^6 - 104*x^5 + 864*x^4 + 1824*x^3 - 3648*x^2 - 10240*x - 5120,13,x^8 - 8*x^7 - 40*x^6 + 430*x^5 - 84*x^4 - 4996*x^3 + 6205*x^2 + 7300*x + 500[] 544,1,2,x,3,x,5,x,7,x + 2,11,x + 4,13,x - 2[] 544,2,2,x,3,x - 2,5,x - 2,7,x - 2,11,x + 2,13,x - 2[] 544,3,2,x,3,x + 2,5,x - 2,7,x + 2,11,x - 2,13,x - 2[] 544,4,2,x,3,x,5,x,7,x - 2,11,x - 4,13,x - 2[] 544,5,2,x,3,x - 2,5,x - 4,7,x + 4,11,x - 2,13,x - 2[] 544,6,2,x,3,x + 2,5,x - 4,7,x - 4,11,x + 2,13,x - 2[] 544,7,2,x^2,3,x^2 - 2,5,x^2 + 4*x + 4,7,x^2 - 18,11,x^2 - 2,13,x^2 + 8*x + 16[] 544,8,2,x^2,3,x^2 - 10,5,x^2 + 4*x + 4,7,x^2 - 10,11,x^2 - 10,13,x^2 + 8*x + 16[] 544,9,2,x^3,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 + 2*x^2 - 12*x - 8,7,x^3 - 2*x^2 - 8*x - 4,11,x^3 - 10*x^2 + 28*x - 20,13,x^3 + 6*x^2 - 4*x - 40[] 544,10,2,x^3,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 2*x^2 - 12*x - 8,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 + 10*x^2 + 28*x + 20,13,x^3 + 6*x^2 - 4*x - 40[] Total time: 16.039 seconds, Total memory usage: 5.78MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 19:45:46 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [545..547] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:45:26 on modular [Seed = 3341973487] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 545,1,2,x - 1,3,x,5,x - 1,7,x + 4,11,x - 4,13,x + 6[] 545,2,2,x^2 - 2*x - 1,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 2,11,x^2 - 18,13,x^2 - 4*x + 4[] 545,3,2,x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1,3,x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 8*x^4 + 19*x^3 + 15*x^2 + x - 1,11,x^5 + 4*x^4 - 9*x^3 - 27*x^2 - 13*x + 1,13,x^5 - 33*x^3 - 22*x^2 + 220*x + 253[] 545,4,2,x^5 + 3*x^4 - 2*x^3 - 11*x^2 - 7*x - 1,3,x^5 + 7*x^4 + 12*x^3 - 11*x^2 - 39*x - 17,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 + 8*x^4 + 17*x^3 - 11*x^2 - 69*x - 53,11,x^5 + 8*x^4 + 9*x^3 - 43*x^2 - 73*x + 1,13,x^5 - 7*x^3 + 2*x^2 + 8*x + 1[] 545,5,2,x^11 + 3*x^10 - 17*x^9 - 52*x^8 + 98*x^7 + 305*x^6 - 228*x^5 - 681*x^4 + 257*x^3 + 460*x^2 - 215*x - 3,3,x^11 - x^10 - 22*x^9 + 21*x^8 + 171*x^7 - 159*x^6 - 558*x^5 + 522*x^4 + 672*x^3 - 616*x^2 - 100*x + 36,5,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,7,x^11 - 8*x^10 - 23*x^9 + 271*x^8 + 131*x^7 - 3211*x^6 - 694*x^5 + 16258*x^4 + 9132*x^3 - 27752*x^2 - 29036*x - 6668,11,x^11 - 12*x^10 + 11*x^9 + 325*x^8 - 975*x^7 - 1889*x^6 + 8558*x^5 + 2550*x^4 - 24700*x^3 + 176*x^2 + 21892*x + 5556,13,x^11 - 6*x^10 - 69*x^9 + 472*x^8 + 1224*x^7 - 11855*x^6 + 1988*x^5 + 101740*x^4 - 142056*x^3 - 128800*x^2 + 186464*x + 113328[] 545,6,2,x^13 - 3*x^12 - 18*x^11 + 57*x^10 + 113*x^9 - 391*x^8 - 300*x^7 + 1206*x^6 + 323*x^5 - 1685*x^4 - 114*x^3 + 921*x^2 - 5*x - 89,3,x^13 - 9*x^12 + 12*x^11 + 109*x^10 - 339*x^9 - 261*x^8 + 1992*x^7 - 988*x^6 - 4096*x^5 + 4120*x^4 + 2588*x^3 - 3680*x^2 - 180*x + 652,5,x^13 - 13*x^12 + 78*x^11 - 286*x^10 + 715*x^9 - 1287*x^8 + 1716*x^7 - 1716*x^6 + 1287*x^5 - 715*x^4 + 286*x^3 - 78*x^2 + 13*x - 1,7,x^13 - 16*x^12 + 73*x^11 + 101*x^10 - 1649*x^9 + 2759*x^8 + 9104*x^7 - 29636*x^6 - 6940*x^5 + 95220*x^4 - 47024*x^3 - 101440*x^2 + 64948*x + 24556,11,x^13 - 73*x^11 + 61*x^10 + 2007*x^9 - 3051*x^8 - 24732*x^7 + 51576*x^6 + 125860*x^5 - 335844*x^4 - 181096*x^3 + 781432*x^2 - 143596*x - 349292,13,x^13 - 6*x^12 - 75*x^11 + 544*x^10 + 1308*x^9 - 15931*x^8 + 12832*x^7 + 155056*x^6 - 411384*x^5 - 3464*x^4 + 1262416*x^3 - 1774384*x^2 + 908576*x - 143536[] 546,1,2,x + 1,3,x + 1,5,x + 1,7,x + 1,11,x + 1,13,x - 1[] 546,2,2,x + 1,3,x - 1,5,x - 1,7,x + 1,11,x - 3,13,x + 1[] 546,3,2,x + 1,3,x - 1,5,x + 2,7,x + 1,11,x + 4,13,x - 1[] 546,4,2,x + 1,3,x - 1,5,x - 3,7,x - 1,11,x - 3,13,x - 1[] 546,5,2,x - 1,3,x + 1,5,x - 3,7,x + 1,11,x - 1,13,x + 1[] 546,6,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x - 5,13,x + 1[] 546,7,2,x - 1,3,x - 1,5,x - 2,7,x - 1,11,x + 4,13,x + 1[] 546,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + x - 14,7,x^2 - 2*x + 1,11,x^2 - 3*x - 12,13,x^2 + 2*x + 1[] 546,9,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + x - 10,7,x^2 - 2*x + 1,11,x^2 - 5*x - 4,13,x^2 - 2*x + 1[] 546,10,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 + 2*x + 1,11,x^2 - x - 4,13,x^2 - 2*x + 1[] 547,1,2,x^2 + 2*x - 1,3,x^2 - 2,5,x^2 - 2,7,x^2 - 4*x + 4,11,x^2 + 10*x + 23,13,x^2 - 6*x + 9[] 547,2,2,x^18 + 4*x^17 - 18*x^16 - 84*x^15 + 116*x^14 + 708*x^13 - 282*x^12 - 3104*x^11 - 137*x^10 + 7703*x^9 + 2068*x^8 - 11068*x^7 - 4274*x^6 + 9021*x^5 + 4048*x^4 - 3834*x^3 - 1851*x^2 + 654*x + 328,3,x^18 + 10*x^17 + 16*x^16 - 141*x^15 - 499*x^14 + 485*x^13 + 3908*x^12 + 1561*x^11 - 12985*x^10 - 13361*x^9 + 17477*x^8 + 27279*x^7 - 4923*x^6 - 17035*x^5 - 529*x^4 + 4092*x^3 + 221*x^2 - 266*x - 32,5,x^18 + 27*x^17 + 304*x^16 + 1771*x^15 + 4872*x^14 - 1378*x^13 - 53562*x^12 - 157710*x^11 - 138777*x^10 + 238435*x^9 + 649756*x^8 + 308466*x^7 - 551465*x^6 - 657632*x^5 + 22692*x^4 + 316340*x^3 + 88161*x^2 - 42046*x - 15872,7,x^18 + 11*x^17 - 17*x^16 - 591*x^15 - 1324*x^14 + 9436*x^13 + 41987*x^12 - 23119*x^11 - 382155*x^10 - 455177*x^9 + 916701*x^8 + 2110064*x^7 - 191995*x^6 - 3024596*x^5 - 1344002*x^4 + 1335870*x^3 + 1038609*x^2 + 62202*x - 58576,11,x^18 - 2*x^17 - 113*x^16 + 224*x^15 + 4921*x^14 - 9574*x^13 - 104309*x^12 + 191844*x^11 + 1134032*x^10 - 1787123*x^9 - 6381183*x^8 + 6865320*x^7 + 18625653*x^6 - 7534045*x^5 - 23371203*x^4 - 5528150*x^3 + 3523832*x^2 + 843423*x - 82432,13,x^18 + 25*x^17 + 185*x^16 - 448*x^15 - 13499*x^14 - 57203*x^13 + 128151*x^12 + 1756201*x^11 + 3932642*x^10 - 10003709*x^9 - 62952777*x^8 - 74607411*x^7 + 173378296*x^6 + 573367312*x^5 + 388950788*x^4 - 562304121*x^3 - 1130971990*x^2 - 716121924*x - 160401143[] 547,3,2,x^25 - 4*x^24 - 30*x^23 + 134*x^22 + 365*x^21 - 1926*x^20 - 2226*x^19 + 15560*x^18 + 6033*x^17 - 77601*x^16 + 4782*x^15 + 246402*x^14 - 87059*x^13 - 493902*x^12 + 275826*x^11 + 594258*x^10 - 427359*x^9 - 378617*x^8 + 334926*x^7 + 87006*x^6 - 111411*x^5 + 8810*x^4 + 6600*x^3 - 872*x^2 - 68*x + 8,3,x^25 - 8*x^24 - 20*x^23 + 311*x^22 - 159*x^21 - 4979*x^20 + 8554*x^19 + 41509*x^18 - 110927*x^17 - 181277*x^16 + 746037*x^15 + 285827*x^14 - 2917461*x^13 + 845121*x^12 + 6693937*x^11 - 4939122*x^10 - 8518495*x^9 + 9727960*x^8 + 5007908*x^7 - 9161144*x^6 - 323960*x^5 + 4025440*x^4 - 733752*x^3 - 682336*x^2 + 165984*x + 25088,5,x^25 - 29*x^24 + 340*x^23 - 1865*x^22 + 2290*x^21 + 29052*x^20 - 157882*x^19 + 151052*x^18 + 1248513*x^17 - 4381041*x^16 + 564172*x^15 + 24220956*x^14 - 42611521*x^13 - 31283226*x^12 + 174636898*x^11 - 123240086*x^10 - 225721819*x^9 + 401447188*x^8 - 46423448*x^7 - 329851888*x^6 + 207596896*x^5 + 74345104*x^4 - 101463976*x^3 + 10062688*x^2 + 14644416*x - 3804416,7,x^25 - 5*x^24 - 85*x^23 + 465*x^22 + 2784*x^21 - 17422*x^20 - 43107*x^19 + 340033*x^18 + 289119*x^17 - 3774099*x^16 + 59601*x^15 + 24772864*x^14 - 13059041*x^13 - 96710450*x^12 + 83645960*x^11 + 217712200*x^10 - 246472963*x^9 - 258864260*x^8 + 371321974*x^7 + 128241888*x^6 - 273367336*x^5 - 31328*x^4 + 88279072*x^3 - 15330560*x^2 - 9703552*x + 2553344,11,x^25 - 10*x^24 - 86*x^23 + 1174*x^22 + 1669*x^21 - 54292*x^20 + 51648*x^19 + 1293656*x^18 - 2890661*x^17 - 17268413*x^16 + 56033375*x^15 + 130103461*x^14 - 581944349*x^13 - 510635922*x^12 + 3569100663*x^11 + 607783568*x^10 - 13299156853*x^9 + 2729170202*x^8 + 29712735620*x^7 - 12132769546*x^6 - 37413264447*x^5 + 19408199907*x^4 + 22917476944*x^3 - 13010797205*x^2 - 4446362004*x + 2284779388,13,x^25 - 19*x^24 + 32*x^23 + 1521*x^22 - 9375*x^21 - 29718*x^20 + 394046*x^19 - 344627*x^18 - 6307669*x^17 + 16538325*x^16 + 40622837*x^15 - 191250128*x^14 - 31072558*x^13 + 969686277*x^12 - 786046477*x^11 - 2107130475*x^10 + 3278287707*x^9 + 1043197692*x^8 - 4333912697*x^7 + 1663175229*x^6 + 1272531297*x^5 - 926066215*x^4 + 26976803*x^3 + 80134296*x^2 - 8499211*x - 1439326[] Total time: 19.819 seconds, Total memory usage: 7.13MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sun Nov 30 19:57:06 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [548..550] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 19:56:48 on modular [Seed = 3961078322] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 548,1,2,x^4,3,x^4 + 3*x^3 - 2*x^2 - 4*x - 1,5,x^4 + 4*x^3 + 2*x^2 - 5*x - 3,7,x^4 + x^3 - 8*x^2 - 10*x - 3,11,x^4 + x^3 - 20*x^2 + 14*x + 27,13,x^4 + 14*x^3 + 60*x^2 + 61*x - 69[] 548,2,2,x^8,3,x^8 - 3*x^7 - 14*x^6 + 42*x^5 + 55*x^4 - 170*x^3 - 46*x^2 + 198*x - 54,5,x^8 - 2*x^7 - 28*x^6 + 61*x^5 + 213*x^4 - 484*x^3 - 312*x^2 + 624*x + 144,7,x^8 + x^7 - 32*x^6 - 30*x^5 + 233*x^4 + 120*x^3 - 472*x^2 + 112*x + 32,11,x^8 - 3*x^7 - 48*x^6 + 214*x^5 + 339*x^4 - 3340*x^3 + 6784*x^2 - 5584*x + 1632,13,x^8 - 20*x^7 + 118*x^6 + 95*x^5 - 3497*x^4 + 12820*x^3 - 16232*x^2 + 3056*x + 4016[] 549,1,2,x - 1,3,x,5,x,7,x + 2,11,x + 4,13,x + 2[] 549,2,2,x + 1,3,x,5,x,7,x + 2,11,x - 4,13,x + 2[] 549,3,2,x - 1,3,x,5,x - 3,7,x - 1,11,x - 5,13,x - 1[] 549,4,2,x^2 - 3,3,x^2,5,x^2 - 3,7,x^2 + 2*x + 1,11,x^2 - 27,13,x^2 - 10*x + 25[] 549,5,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 2*x - 1,11,x^2 - 2*x - 1,13,x^2 + 6*x + 9[] 549,6,2,x^3 + x^2 - 3*x - 1,3,x^3,5,x^3 - x^2 - 9*x + 13,7,x^3 + 3*x^2 - x - 1,11,x^3 + 13*x^2 + 53*x + 67,13,x^3 + 9*x^2 + 11*x - 37[] 549,7,2,x^3 + x^2 - 3*x - 1,3,x^3,5,x^3 + 6*x^2 + 12*x + 8,7,x^3 - 16*x - 16,11,x^3 + 2*x^2 - 4*x - 4,13,x^3 - 6*x^2 - 4*x + 40[] 549,8,2,x^6 - 13*x^4 + 41*x^2 - 1,3,x^6,5,x^6 - 19*x^4 + 80*x^2 - 64,7,x^6 - 6*x^5 - 23*x^4 + 184*x^3 - 8*x^2 - 1408*x + 1936,11,x^6 - 15*x^4 + 56*x^2 - 4,13,x^6 + 6*x^5 - 23*x^4 - 80*x^3 + 304*x^2 - 256*x + 64[] 549,9,2,x^6 - 11*x^4 - 2*x^3 + 31*x^2 + 10*x - 17,3,x^6,5,x^6 + 2*x^5 - 23*x^4 - 28*x^3 + 144*x^2 + 80*x - 144,7,x^6 - 2*x^5 - 25*x^4 + 60*x^3 + 128*x^2 - 432*x + 288,11,x^6 - 8*x^5 - 5*x^4 + 110*x^3 - 68*x^2 - 8*x + 4,13,x^6 - 6*x^5 - 23*x^4 + 116*x^3 + 168*x^2 - 464*x - 608[] 550,1,2,x + 1,3,x + 1,5,x,7,x - 1,11,x + 1,13,x + 2[] 550,2,2,x + 1,3,x - 1,5,x,7,x + 3,11,x - 1,13,x - 6[] 550,3,2,x + 1,3,x + 2,5,x,7,x,11,x - 1,13,x + 3[] 550,4,2,x + 1,3,x + 2,5,x,7,x + 4,11,x + 1,13,x - 5[] 550,5,2,x + 1,3,x - 3,5,x,7,x - 1,11,x + 1,13,x[] 550,6,2,x + 1,3,x - 1,5,x,7,x + 3,11,x - 1,13,x + 4[] 550,7,2,x + 1,3,x + 2,5,x,7,x,11,x - 1,13,x - 2[] 550,8,2,x - 1,3,x - 2,5,x,7,x - 4,11,x + 1,13,x + 5[] 550,9,2,x - 1,3,x + 1,5,x,7,x + 5,11,x - 1,13,x + 2[] 550,10,2,x - 1,3,x + 3,5,x,7,x + 1,11,x + 1,13,x[] 550,11,2,x - 1,3,x + 1,5,x,7,x - 3,11,x - 1,13,x - 4[] 550,12,2,x - 1,3,x - 2,5,x,7,x,11,x - 1,13,x + 2[] 550,13,2,x - 1,3,x - 2,5,x,7,x,11,x - 1,13,x - 3[] 550,14,2,x^2 - 2*x + 1,3,x^2 - x - 8,5,x^2,7,x^2 + x - 8,11,x^2 + 2*x + 1,13,x^2 + 4*x + 4[] Total time: 18.119 seconds, Total memory usage: 6.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 20:33:09 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [551..553] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 20:32:51 on modular [Seed = 2574007511] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 551,1,2,x - 1,3,x - 1,5,x + 1,7,x + 4,11,x - 1,13,x + 1[] 551,2,2,x + 1,3,x - 1,5,x + 1,7,x - 2,11,x + 3,13,x + 5[] 551,3,2,x - 2,3,x + 2,5,x + 1,7,x + 1,11,x + 3,13,x + 2[] 551,4,2,x + 2,3,x + 2,5,x + 1,7,x + 1,11,x - 1,13,x - 2[] 551,5,2,x^2 + 2*x + 1,3,x^2 - 5,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 - 5,13,x^2 - 2*x + 1[] 551,6,2,x^3 - 4*x + 2,3,x^3,5,x^3 - x^2 - 9*x + 13,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 7*x^2 + 13*x + 5,13,x^3 + 4*x^2 + 2*x - 2[] 551,7,2,x^16 - 3*x^15 - 22*x^14 + 68*x^13 + 190*x^12 - 608*x^11 - 832*x^10 + 2760*x^9 + 1972*x^8 - 6728*x^7 - 2502*x^6 + 8420*x^5 + 1642*x^4 - 4511*x^3 - 577*x^2 + 572*x - 18,3,x^16 - 4*x^15 - 28*x^14 + 120*x^13 + 284*x^12 - 1372*x^11 - 1215*x^10 + 7450*x^9 + 1666*x^8 - 19442*x^7 + 1155*x^6 + 21898*x^5 - 1672*x^4 - 8702*x^3 + 5*x^2 + 704*x - 44,5,x^16 + 2*x^15 - 51*x^14 - 86*x^13 + 1000*x^12 + 1272*x^11 - 9667*x^10 - 7454*x^9 + 48303*x^8 + 11318*x^7 - 114963*x^6 + 30334*x^5 + 93501*x^4 - 67948*x^3 + 12083*x^2 + 290*x - 15,7,x^16 - 4*x^15 - 66*x^14 + 266*x^13 + 1682*x^12 - 6726*x^11 - 21539*x^10 + 82902*x^9 + 150434*x^8 - 518552*x^7 - 592907*x^6 + 1516972*x^5 + 1351768*x^4 - 1568050*x^3 - 1469107*x^2 + 71670*x + 181540,11,x^16 - 4*x^15 - 104*x^14 + 404*x^13 + 3867*x^12 - 14080*x^11 - 62900*x^10 + 198392*x^9 + 453696*x^8 - 974432*x^7 - 1614912*x^6 + 1469568*x^5 + 1840384*x^4 - 896512*x^3 - 576512*x^2 + 133120*x + 61440,13,x^16 - 8*x^15 - 89*x^14 + 894*x^13 + 1978*x^12 - 36384*x^11 + 29448*x^10 + 632752*x^9 - 1640672*x^8 - 3621440*x^7 + 18889472*x^6 - 11678720*x^5 - 52017152*x^4 + 102978560*x^3 - 61104128*x^2 + 188416*x + 7135232[] 551,8,2,x^18 - 2*x^17 - 29*x^16 + 56*x^15 + 342*x^14 - 632*x^13 - 2112*x^12 + 3692*x^11 + 7332*x^10 - 11948*x^9 - 14282*x^8 + 21322*x^7 + 14618*x^6 - 19599*x^5 - 6476*x^4 + 7481*x^3 + 560*x^2 - 346*x + 6,3,x^18 + 2*x^17 - 42*x^16 - 74*x^15 + 738*x^14 + 1102*x^13 - 7037*x^12 - 8474*x^11 + 39398*x^10 + 36022*x^9 - 130265*x^8 - 85036*x^7 + 240754*x^6 + 109972*x^5 - 215593*x^4 - 80360*x^3 + 66816*x^2 + 26928*x + 1472,5,x^18 - 7*x^17 - 47*x^16 + 417*x^15 + 656*x^14 - 9996*x^13 + 1989*x^12 + 121685*x^11 - 144781*x^10 - 764253*x^9 + 1543373*x^8 + 2012045*x^7 - 7000435*x^6 + 940819*x^5 + 12069681*x^4 - 11086865*x^3 - 951023*x^2 + 4806227*x - 1538766,7,x^18 - 11*x^17 - 34*x^16 + 732*x^15 - 556*x^14 - 18180*x^13 + 36623*x^12 + 215027*x^11 - 555132*x^10 - 1334394*x^9 + 3662293*x^8 + 4526337*x^7 - 10650664*x^6 - 7964510*x^5 + 10172147*x^4 + 3566067*x^3 - 2623386*x^2 - 553488*x + 86272,11,x^18 - 5*x^17 - 142*x^16 + 732*x^15 + 8121*x^14 - 43647*x^13 - 238272*x^12 + 1358396*x^11 + 3768136*x^10 - 23468128*x^9 - 30660192*x^8 + 220323264*x^7 + 110432384*x^6 - 1008092928*x^5 - 169786880*x^4 + 1619770368*x^3 + 674871296*x^2 - 84307968*x - 45400064,13,x^18 - 10*x^17 - 143*x^16 + 1646*x^15 + 7412*x^14 - 108898*x^13 - 152348*x^12 + 3748776*x^11 + 22496*x^10 - 72958208*x^9 + 48721024*x^8 + 816188032*x^7 - 764462080*x^6 - 5085597696*x^5 + 4716821504*x^4 + 15931901952*x^3 - 12106178560*x^2 - 17603731456*x + 13163282432[] 552,1,2,x,3,x + 1,5,x + 2,7,x - 2,11,x + 2,13,x + 2[] 552,2,2,x,3,x + 1,5,x,7,x + 2,11,x,13,x - 2[] 552,3,2,x,3,x + 1,5,x - 4,7,x - 2,11,x,13,x - 2[] 552,4,2,x,3,x + 1,5,x - 2,7,x + 4,11,x + 4,13,x + 2[] 552,5,2,x,3,x - 1,5,x + 2,7,x + 4,11,x,13,x + 2[] 552,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 2*x - 4,7,x^2 - 4*x + 4,11,x^2 - 2*x - 4,13,x^2 - 20[] 552,7,2,x^3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 16*x + 16,7,x^3 - 2*x^2 - 12*x + 8,11,x^3 - 4*x^2 - 16*x + 32,13,x^3 - 6*x^2 + 12*x - 8[] 553,1,2,x^7 + 6*x^6 + 7*x^5 - 17*x^4 - 35*x^3 - 3*x^2 + 15*x + 3,3,x^7 + 3*x^6 - 5*x^5 - 16*x^4 + 5*x^3 + 23*x^2 + 3*x - 5,5,x^7 + 4*x^6 - 9*x^5 - 57*x^4 - 49*x^3 + 78*x^2 + 126*x + 45,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,11,x^7 + 13*x^6 + 40*x^5 - 92*x^4 - 614*x^3 - 810*x^2 + 375,13,x^7 + x^6 - 49*x^5 - 87*x^4 + 533*x^3 + 845*x^2 - 1282*x - 125[] 553,2,2,x^8 - 3*x^7 - 7*x^6 + 24*x^5 + 6*x^4 - 40*x^3 + 6*x^2 + 8*x + 1,3,x^8 - 3*x^7 - 7*x^6 + 26*x^5 + 3*x^4 - 55*x^3 + 31*x^2 + 9*x - 4,5,x^8 - 4*x^7 - 9*x^6 + 49*x^5 - 11*x^4 - 96*x^3 + 14*x^2 + 63*x + 18,7,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,11,x^8 - 3*x^7 - 36*x^6 + 136*x^5 + 214*x^4 - 1430*x^3 + 1936*x^2 - 849*x + 32,13,x^8 - 3*x^7 - 45*x^6 + 155*x^5 + 483*x^4 - 1925*x^3 - 778*x^2 + 6281*x - 3566[] 553,3,2,x^11 + 5*x^10 - 4*x^9 - 49*x^8 - 24*x^7 + 154*x^6 + 125*x^5 - 183*x^4 - 154*x^3 + 67*x^2 + 32*x - 11,3,x^11 + 5*x^10 - 11*x^9 - 80*x^8 + 3*x^7 + 391*x^6 + 215*x^5 - 577*x^4 - 324*x^3 + 256*x^2 + 88*x - 16,5,x^11 + 10*x^10 + 18*x^9 - 107*x^8 - 365*x^7 + 257*x^6 + 1820*x^5 + 360*x^4 - 3191*x^3 - 1265*x^2 + 1640*x + 709,7,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,11,x^11 + 5*x^10 - 67*x^9 - 335*x^8 + 1343*x^7 + 6855*x^6 - 8554*x^5 - 49991*x^4 + 5762*x^3 + 111885*x^2 + 41180*x - 14797,13,x^11 + 11*x^10 - 22*x^9 - 596*x^8 - 999*x^7 + 8945*x^6 + 25960*x^5 - 40773*x^4 - 165481*x^3 + 35172*x^2 + 309446*x + 54547[] 553,4,2,x^13 - 7*x^12 + 3*x^11 + 78*x^10 - 144*x^9 - 249*x^8 + 769*x^7 + 79*x^6 - 1451*x^5 + 654*x^4 + 878*x^3 - 686*x^2 + 56*x + 27,3,x^13 - x^12 - 29*x^11 + 26*x^10 + 321*x^9 - 231*x^8 - 1741*x^7 + 857*x^6 + 4836*x^5 - 1136*x^4 - 6360*x^3 - 176*x^2 + 2944*x + 768,5,x^13 - 4*x^12 - 30*x^11 + 119*x^10 + 299*x^9 - 1121*x^8 - 1472*x^7 + 4586*x^6 + 3617*x^5 - 8619*x^4 - 3396*x^3 + 7075*x^2 + 400*x - 1500,7,x^13 - 13*x^12 + 78*x^11 - 286*x^10 + 715*x^9 - 1287*x^8 + 1716*x^7 - 1716*x^6 + 1287*x^5 - 715*x^4 + 286*x^3 - 78*x^2 + 13*x - 1,11,x^13 - 15*x^12 + 53*x^11 + 225*x^10 - 1725*x^9 + 859*x^8 + 14506*x^7 - 24231*x^6 - 42950*x^5 + 112769*x^4 + 20848*x^3 - 166973*x^2 + 58620*x + 27200,13,x^13 + x^12 - 80*x^11 + 14*x^10 + 2299*x^9 - 2341*x^8 - 27032*x^7 + 37029*x^6 + 134289*x^5 - 173902*x^4 - 286484*x^3 + 193213*x^2 + 281180*x + 61284[] Total time: 17.569 seconds, Total memory usage: 6.01MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Sun Nov 30 20:48:32 2003 Input: !ls Output: Magma V2.10-6 Sun Nov 30 2003 20:48:28 on modular [Seed = 3860022279] ------------------------------------- >> !ls; ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Sun Nov 30 20:49:49 2003 Input: !ls Output: Magma V2.10-6 Sun Nov 30 2003 20:49:46 on modular [Seed = 4026880455] ------------------------------------- >> !ls; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Sun Nov 30 20:50:03 2003 Input: %ls Output: Magma V2.10-6 Sun Nov 30 2003 20:50:00 on modular [Seed = 16097604] ------------------------------------- %: bad command Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Sun Nov 30 20:50:18 2003 ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 20:52:01 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [554..556] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 20:51:44 on modular [Seed = 617711000] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 554,1,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 7*x^2 + 14*x + 7,7,x^3 + 6*x^2 + 5*x + 1,11,x^3 + x^2 - 2*x - 1,13,x^3 + 6*x^2 - 9*x - 41[] 554,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 7*x - 2,5,x^4 - x^3 - 8*x^2 - 5*x + 2,7,x^4 + 6*x^3 + 9*x^2 - x - 4,11,x^4 + 8*x^3 - 5*x^2 - 151*x - 257,13,x^4 + 3*x^3 - 9*x^2 - 38*x - 31[] 554,3,2,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,3,x^8 - 3*x^7 - 13*x^6 + 37*x^5 + 54*x^4 - 146*x^3 - 60*x^2 + 182*x - 49,5,x^8 + 2*x^7 - 25*x^6 - 32*x^5 + 201*x^4 + 168*x^3 - 620*x^2 - 285*x + 609,7,x^8 - 8*x^7 - 9*x^6 + 207*x^5 - 430*x^4 - 204*x^3 + 1080*x^2 - 768*x + 160,11,x^8 - 5*x^7 - 20*x^6 + 121*x^5 - 10*x^4 - 604*x^3 + 848*x^2 - 240*x - 96,13,x^8 - 4*x^7 - 47*x^6 + 137*x^5 + 856*x^4 - 1500*x^3 - 6960*x^2 + 5088*x + 20320[] 554,4,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 + x^8 - 17*x^7 - 9*x^6 + 94*x^5 + 12*x^4 - 194*x^3 + 46*x^2 + 119*x - 54,5,x^9 - 8*x^8 + 3*x^7 + 112*x^6 - 197*x^5 - 434*x^4 + 1014*x^3 + 519*x^2 - 1447*x - 66,7,x^9 - 8*x^8 - 5*x^7 + 169*x^6 - 294*x^5 - 620*x^4 + 2392*x^3 - 2752*x^2 + 1376*x - 256,11,x^9 - 67*x^7 - 87*x^6 + 1409*x^5 + 3326*x^4 - 8052*x^3 - 31744*x^2 - 26384*x - 1056,13,x^9 - 7*x^8 - 49*x^7 + 434*x^6 + 283*x^5 - 7876*x^4 + 11764*x^3 + 31536*x^2 - 92832*x + 62048[] 555,1,2,x,3,x - 1,5,x + 1,7,x + 2,11,x - 4,13,x - 5[] 555,2,2,x,3,x - 1,5,x - 1,7,x - 2,11,x,13,x + 1[] 555,3,2,x^2 - x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 5,11,x^2 - x - 1,13,x^2 + 4*x - 1[] 555,4,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 6*x + 9,11,x^2 - 3*x - 1,13,x^2 + 10*x + 25[] 555,5,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - x - 3,13,x^2 - 13[] 555,6,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 + 9*x + 19,13,x^2 + 4*x - 1[] 555,7,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 + 3*x - 9,13,x^2 + 10*x + 25[] 555,8,2,x^3 - x^2 - 5*x + 4,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 4*x^2 - 7*x + 14,11,x^3 - x^2 - 7*x - 4,13,x^3 - 15*x^2 + 75*x - 125[] 555,9,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 4*x^2 - x - 8,11,x^3 + x^2 - 15*x - 28,13,x^3 - 4*x^2 - 7*x + 26[] 555,10,2,x^5 + 3*x^4 - 4*x^3 - 13*x^2 + x + 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 - 2*x^4 - 25*x^3 + 62*x^2 + 96*x - 256,11,x^5 + x^4 - 31*x^3 - 48*x^2 + 80*x + 128,13,x^5 - 7*x^4 + 3*x^3 + 39*x^2 - 40*x - 4[] 556,1,2,x,3,x,5,x + 1,7,x + 1,11,x - 1,13,x + 3[] 556,2,2,x^3,3,x^3 + 2*x^2 - 3*x - 3,5,x^3 - 9*x + 1,7,x^3 + 4*x^2 - x - 1,11,x^3 + 13*x^2 + 52*x + 63,13,x^3 - x^2 - 12*x - 9[] 556,3,2,x^7,3,x^7 - 4*x^6 - 9*x^5 + 43*x^4 + 14*x^3 - 120*x^2 + 24*x + 64,5,x^7 + x^6 - 24*x^5 - 2*x^4 + 161*x^3 - 117*x^2 - 91*x + 49,7,x^7 - x^6 - 22*x^5 + 18*x^4 + 125*x^3 - 85*x^2 - 209*x + 121,11,x^7 - 14*x^6 + 64*x^5 - 104*x^4 + 48*x^3 + 12*x^2 - 10*x + 1,13,x^7 + 2*x^6 - 54*x^5 - 132*x^4 + 588*x^3 + 846*x^2 - 2466*x + 919[] Total time: 17.279 seconds, Total memory usage: 6.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 20:56:33 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [557..559] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 20:56:17 on modular [Seed = 1136059278] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 557,1,2,x - 1,3,x + 1,5,x,7,x - 2,11,x + 3,13,x - 2[] 557,2,2,x - 2,3,x - 2,5,x,7,x - 5,11,x + 6,13,x + 4[] 557,3,2,x^18 + 6*x^17 - 6*x^16 - 98*x^15 - 83*x^14 + 588*x^13 + 978*x^12 - 1507*x^11 - 3913*x^10 + 1062*x^9 + 7268*x^8 + 2007*x^7 - 6225*x^6 - 3695*x^5 + 2078*x^4 + 1980*x^3 - 23*x^2 - 339*x - 72,3,x^18 + 15*x^17 + 75*x^16 + 49*x^15 - 814*x^14 - 2394*x^13 + 1044*x^12 + 13596*x^11 + 12477*x^10 - 25556*x^9 - 45888*x^8 + 6698*x^7 + 47848*x^6 + 15237*x^5 - 10287*x^4 - 2442*x^3 + 395*x^2 + 93*x + 4,5,x^18 + 6*x^17 - 32*x^16 - 254*x^15 + 188*x^14 + 3821*x^13 + 3078*x^12 - 23586*x^11 - 38270*x^10 + 49953*x^9 + 115450*x^8 - 32043*x^7 - 118597*x^6 + 6367*x^5 + 32117*x^4 - 219*x^3 - 1942*x^2 - 25*x + 28,7,x^18 + 23*x^17 + 195*x^16 + 518*x^15 - 2765*x^14 - 25160*x^13 - 65832*x^12 + 26918*x^11 + 542548*x^10 + 1102830*x^9 + 79979*x^8 - 2707932*x^7 - 3217980*x^6 + 804502*x^5 + 3679394*x^4 + 1446746*x^3 - 1010698*x^2 - 715740*x - 86551,11,x^18 + 3*x^17 - 117*x^16 - 397*x^15 + 5485*x^14 + 20912*x^13 - 130583*x^12 - 568746*x^11 + 1616882*x^10 + 8545534*x^9 - 8748519*x^8 - 69281842*x^7 - 1470968*x^6 + 266228143*x^5 + 148974278*x^4 - 337958309*x^3 - 118352665*x^2 + 206218677*x - 44939592,13,x^18 + 26*x^17 + 217*x^16 - 6*x^15 - 10471*x^14 - 52386*x^13 + 44764*x^12 + 1116943*x^11 + 2635070*x^10 - 4804436*x^9 - 29573582*x^8 - 26419680*x^7 + 68269706*x^6 + 126084225*x^5 - 33806500*x^4 - 151090139*x^3 - 1952582*x^2 + 58539389*x - 10679518[] 557,4,2,x^26 - x^25 - 40*x^24 + 36*x^23 + 701*x^22 - 557*x^21 - 7078*x^20 + 4855*x^19 + 45533*x^18 - 26248*x^17 - 194780*x^16 + 91281*x^15 + 561051*x^14 - 204613*x^13 - 1077249*x^12 + 286983*x^11 + 1332859*x^10 - 233167*x^9 - 994145*x^8 + 90493*x^7 + 396290*x^6 - 6446*x^5 - 68301*x^4 - 2616*x^3 + 3093*x^2 + 320*x + 1,3,x^26 - 16*x^25 + 73*x^24 + 144*x^23 - 2140*x^22 + 3536*x^21 + 19587*x^20 - 71418*x^19 - 52175*x^18 + 543571*x^17 - 309381*x^16 - 2168193*x^15 + 2929364*x^14 + 4627520*x^13 - 10350762*x^12 - 4071610*x^11 + 19645056*x^10 - 2652133*x^9 - 20674454*x^8 + 9142187*x^7 + 11093092*x^6 - 7524689*x^5 - 2244755*x^4 + 2413207*x^3 - 114917*x^2 - 214756*x + 37327,5,x^26 - 4*x^25 - 78*x^24 + 330*x^23 + 2574*x^22 - 11831*x^21 - 46244*x^20 + 241510*x^19 + 476450*x^18 - 3087203*x^17 - 2525590*x^16 + 25559573*x^15 + 1236433*x^14 - 136506775*x^13 + 70273939*x^12 + 449954679*x^11 - 442035918*x^10 - 811357321*x^9 + 1215128520*x^8 + 520294416*x^7 - 1490157376*x^6 + 316025488*x^5 + 533790848*x^4 - 242004160*x^3 - 36429056*x^2 + 34909184*x - 4845568,7,x^26 - 14*x^25 - x^24 + 839*x^23 - 2570*x^22 - 19872*x^21 + 98016*x^20 + 231198*x^19 - 1767490*x^18 - 1167484*x^17 + 18924615*x^16 - 1978915*x^15 - 130476091*x^14 + 60221791*x^13 + 599025825*x^12 - 339579585*x^11 - 1840646835*x^10 + 879823953*x^9 + 3680192806*x^8 - 878697236*x^7 - 4373680492*x^6 - 319188000*x^5 + 2453382528*x^4 + 798349056*x^3 - 415843776*x^2 - 245728000*x - 32370944,11,x^26 - 10*x^25 - 85*x^24 + 1104*x^23 + 1895*x^22 - 48219*x^21 + 29383*x^20 + 1064958*x^19 - 2045082*x^18 - 12448150*x^17 + 38032434*x^16 + 69320330*x^15 - 344799591*x^14 - 57739069*x^13 + 1598735561*x^12 - 1153437848*x^11 - 3364156911*x^10 + 4652056450*x^9 + 1926712089*x^8 - 5389461202*x^7 + 482086769*x^6 + 2377027167*x^5 - 518768014*x^4 - 396989189*x^3 + 91402908*x^2 + 14339718*x - 3048543,13,x^26 - 30*x^25 + 287*x^24 + 58*x^23 - 18219*x^22 + 86356*x^21 + 323848*x^20 - 3489483*x^19 + 1494832*x^18 + 63108978*x^17 - 139381884*x^16 - 603007232*x^15 + 2327856456*x^14 + 2708706105*x^13 - 20251437668*x^12 + 1287018421*x^11 + 102966116646*x^10 - 76820813555*x^9 - 303743144182*x^8 + 373689287684*x^7 + 471854852632*x^6 - 812789181216*x^5 - 280070965376*x^4 + 795666009856*x^3 - 44401380864*x^2 - 263816327168*x + 48157855744[] 558,1,2,x + 1,3,x,5,x + 1,7,x,11,x + 3,13,x + 1[] 558,2,2,x + 1,3,x,5,x - 3,7,x + 4,11,x - 3,13,x - 5[] 558,3,2,x + 1,3,x,5,x - 2,7,x,11,x,13,x - 2[] 558,4,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 3,13,x + 1[] 558,5,2,x - 1,3,x,5,x - 1,7,x,11,x - 3,13,x + 1[] 558,6,2,x - 1,3,x,5,x + 3,7,x + 4,11,x + 3,13,x - 5[] 558,7,2,x - 1,3,x,5,x + 3,7,x + 2,11,x + 5,13,x + 7[] 558,8,2,x - 1,3,x,5,x - 1,7,x - 2,11,x + 3,13,x - 3[] 558,9,2,x^2 + 2*x + 1,3,x^2,5,x^2 + 3*x - 2,7,x^2 - 2*x - 16,11,x^2 - x - 4,13,x^2 - 3*x - 2[] 558,10,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 - 6*x + 6,13,x^2 + 2*x - 26[] 559,1,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x - 1,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 - 6*x - 17,11,x^3 + 3*x^2 - 18*x - 57,13,x^3 - 3*x^2 + 3*x - 1[] 559,2,2,x^4 + x^3 - 5*x^2 - 3*x + 1,3,x^4 - x^3 - 5*x^2 + 3*x + 1,5,x^4 + 5*x^3 + x^2 - 23*x - 25,7,x^4 - 2*x^3 - 10*x^2 - 7*x - 1,11,x^4 + 11*x^3 + 37*x^2 + 47*x + 19,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 559,3,2,x^7 + 2*x^6 - 6*x^5 - 9*x^4 + 11*x^3 + 10*x^2 - 5*x - 1,3,x^7 + 3*x^6 - 4*x^5 - 13*x^4 + 5*x^3 + 12*x^2 - 1,5,x^7 - 12*x^5 + 5*x^4 + 13*x^3 - 4*x^2 - 3*x + 1,7,x^7 + x^6 - 26*x^5 - 6*x^4 + 122*x^3 - 97*x^2 - 23*x + 27,11,x^7 + 8*x^6 + 10*x^5 - 47*x^4 - 103*x^3 - 38*x^2 + 17*x + 3,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 559,4,2,x^14 - 7*x^13 + 3*x^12 + 78*x^11 - 145*x^10 - 243*x^9 + 758*x^8 + 83*x^7 - 1422*x^6 + 532*x^5 + 1004*x^4 - 525*x^3 - 224*x^2 + 82*x + 23,3,x^14 - x^13 - 32*x^12 + 35*x^11 + 389*x^10 - 460*x^9 - 2236*x^8 + 2831*x^7 + 6128*x^6 - 8232*x^5 - 6928*x^4 + 10048*x^3 + 1408*x^2 - 3072*x + 512,5,x^14 - 12*x^13 + 30*x^12 + 163*x^11 - 845*x^10 - 158*x^9 + 6609*x^8 - 6773*x^7 - 20072*x^6 + 36040*x^5 + 15142*x^4 - 58784*x^3 + 20516*x^2 + 15364*x - 7444,7,x^14 - x^13 - 50*x^12 + 68*x^11 + 890*x^10 - 1715*x^9 - 6445*x^8 + 18137*x^7 + 9558*x^6 - 70048*x^5 + 63234*x^4 + 15892*x^3 - 50380*x^2 + 24164*x - 3268,11,x^14 - 10*x^13 - 40*x^12 + 571*x^11 + 511*x^10 - 12470*x^9 - 4325*x^8 + 129449*x^7 + 70816*x^6 - 616632*x^5 - 605584*x^4 + 837216*x^3 + 1101504*x^2 + 81024*x - 104704,13,x^14 - 14*x^13 + 91*x^12 - 364*x^11 + 1001*x^10 - 2002*x^9 + 3003*x^8 - 3432*x^7 + 3003*x^6 - 2002*x^5 + 1001*x^4 - 364*x^3 + 91*x^2 - 14*x + 1[] 559,5,2,x^15 - 2*x^14 - 22*x^13 + 43*x^12 + 187*x^11 - 354*x^10 - 769*x^9 + 1395*x^8 + 1553*x^7 - 2684*x^6 - 1328*x^5 + 2265*x^4 + 241*x^3 - 606*x^2 + 33*x + 13,3,x^15 - x^14 - 40*x^13 + 37*x^12 + 629*x^11 - 504*x^10 - 4938*x^9 + 3055*x^8 + 20332*x^7 - 7704*x^6 - 41872*x^5 + 5056*x^4 + 34944*x^3 + 2304*x^2 - 6144*x - 1024,5,x^15 + 2*x^14 - 46*x^13 - 73*x^12 + 819*x^11 + 922*x^10 - 7211*x^9 - 4481*x^8 + 32674*x^7 + 3564*x^6 - 69062*x^5 + 23068*x^4 + 43608*x^3 - 25756*x^2 + 2716*x - 68,7,x^15 - x^14 - 78*x^13 + 96*x^12 + 2364*x^11 - 3329*x^10 - 35253*x^9 + 53543*x^8 + 269506*x^7 - 419404*x^6 - 985046*x^5 + 1486276*x^4 + 1324860*x^3 - 1759896*x^2 - 278100*x + 344412,11,x^15 - 16*x^14 + 30*x^13 + 781*x^12 - 4579*x^11 - 3330*x^10 + 85817*x^9 - 155409*x^8 - 400264*x^7 + 1487880*x^6 - 434288*x^5 - 3298656*x^4 + 4052928*x^3 - 796032*x^2 - 571648*x + 14848,13,x^15 + 15*x^14 + 105*x^13 + 455*x^12 + 1365*x^11 + 3003*x^10 + 5005*x^9 + 6435*x^8 + 6435*x^7 + 5005*x^6 + 3003*x^5 + 1365*x^4 + 455*x^3 + 105*x^2 + 15*x + 1[] Total time: 15.189 seconds, Total memory usage: 5.68MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Sun Nov 30 21:00:22 2003 Input: MinimumDistance(DoubleCirculantQRCode(43)); Output: Magma V2.10-6 Sun Nov 30 2003 21:00:19 on modular [Seed = 2674524192] ------------------------------------- >> MinimumDistance(DoubleCirculantQRCode(43));; ^ User error: Identifier 'DoubleCirculantQRCode' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Sun Nov 30 21:01:06 2003 Input: % Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Sun Nov 30 21:01:18 2003 Input: MinimumDistance(DoublyCirculantQRCode(43)); Output: Magma V2.10-6 Sun Nov 30 2003 21:01:03 on modular [Seed = 2723626353] ------------------------------------- 15 Total time: 14.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-68-91-194-244.dsl.austtx.swbell.net. (68.91.194.244) Time: Sun Nov 30 21:04:37 2003 Input: MinimumDistance(DoublyCirculantQRCode(59)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 21:04:14 on modular [Seed = 3275119953] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13263 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 21:08:23 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [560..562] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Sun Nov 30 21:09:56 2003 Input: EllipticCurve([1,2,3,4,5]); Output: Magma V2.10-6 Sun Nov 30 2003 21:09:52 on modular [Seed = 1588315045] ------------------------------------- Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Field Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 21:10:14 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [560..562] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Sun Nov 30 21:10:38 2003 Input: EllipticCurve([1,2,3,4,5]); % Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 21:10:57 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 21:11:43 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host 3(NXDOMAIN) (62.231.244.23) Time: Sun Nov 30 23:06:29 2003 Input: 1+1; Output: Magma V2.10-6 Sun Nov 30 2003 23:06:26 on modular [Seed = 736012896] ------------------------------------- 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (62.231.244.22) Time: Sun Nov 30 23:09:28 2003 Input: S:=CuspForms(4992); Newforms(S); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sun Nov 30 2003 23:09:17 on modular [Seed = 634430657] ------------------------------------- Current total memory usage: 78.6MB, failed memory request: 36.8MB System Error: User memory limit has been reached Total time: 10.689 seconds, Total memory usage: 82.41MB ************** MAGMA ***************** Host 130-127-119-141.generic.clemson.edu. (130.127.119.141) Time: Sun Nov 30 23:21:28 2003 Input: ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ................................................................................ Output: Magma V2.10-6 Sun Nov 30 2003 23:21:24 on modular [Seed = 2005043642] ------------------------------------- >> +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ^ User error: yacc stack overflow >> ........................................................................... ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Mon Dec 1 01:50:43 2003 Input: // Allan printf "%on", 1; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Mon Dec 1 01:50:52 2003 Input: // Allan printf "%on", 1; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Mon Dec 1 02:11:47 2003 Input: // Allan knows about this and has already fixed it: P := PolynomialRing(IntegerRing(), 2); ExactQuotient(P!1, P!2); Output: WARNING: MAGMA command contains unsafe command 'read', so it will not be executed. ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Mon Dec 1 02:12:13 2003 Input: // Allan knows about this and has fixed it: P := PolynomialRing(IntegerRing(), 2); ExactQuotient(P!1, P!2); Output: Magma V2.10-6 Mon Dec 1 2003 02:12:10 on modular [Seed = 3040895864] ------------------------------------- Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 3040895864 Time to this point: 2.96 Internal error in dpoly_exact_div() at dpoly/exact_div.c, line 937 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache-ntc-ad07.proxy.aol.com. (198.81.26.108) Time: Mon Dec 1 02:46:47 2003 Input: cos Pi 3x+9 Output: Magma V2.10-6 Mon Dec 1 2003 02:46:44 on modular [Seed = 251379948] ------------------------------------- >> cos Pi ^ User error: bad syntax >> 3x+9 ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache-ntc-ad07.proxy.aol.com. (198.81.26.108) Time: Mon Dec 1 02:47:11 2003 Input: cos Pi 3x+9 hhhh Output: Magma V2.10-6 Mon Dec 1 2003 02:47:08 on modular [Seed = 518770916] ------------------------------------- >> cos Pi ^ User error: bad syntax >> 3x+9 ^ User error: bad syntax >> hhhh; ^ User error: Identifier 'hhhh' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Mon Dec 1 06:13:28 2003 Input: > 2+2 Output: Magma V2.10-6 Mon Dec 1 2003 06:13:24 on modular [Seed = 4077383333] ------------------------------------- 4 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Mon Dec 1 09:46:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Dec 1 16:44:27 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(3*a-4)/(5*(a-4)),2*(a-3)/(5*(a-4)),2/(4-a),(a+2)*(3*a-4)/(5*(3-a)*(a-4)),2*(4*a- 7)/(5*(a-4)),(a+2)/((a-3)*(a-4)),2*(a-1)*(a+2)/(5*(a-4)),2*(1-a)*(a-3)/(5*(a-4)),(a+2)/(4-a )]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,0); Output: Magma V2.10-6 Mon Dec 1 2003 16:44:24 on modular [Seed = 3894174119] ------------------------------------- { <0, 1>, <1, 1>, <(1/5*a - 8/5)/(a - 4), 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*a + 6)/(a + 2) -2/(a - 1)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-a^2 + 3*a)/(a^2 - 4) (-3*a + 4)/(a^2 - 4)) Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host rescomp-03-43192.Stanford.EDU. (128.12.179.51) Time: Mon Dec 1 16:45:36 2003 Input: F:=FieldOfFractions(PolynomialRing(Rationals())); space:=MatrixAlgebra(F,3); M:=space![(3*a-4)/(5*(a-4)),2*(a-3)/(5*(a-4)),2/(4-a),(a+2)*(3*a-4)/(5*(3-a)*(a-4)),2*(4*a- 7)/(5*(a-4)),(a+2)/((a-3)*(a-4)),2*(a-1)*(a+2)/(5*(a-4)),2*(1-a)*(a-3)/(5*(a-4)),(a+2)/(4-a )]; Eigenvalues(M); Eigenspace(M,1); Eigenspace(M,(1/5*a - 8/5)/(a - 4)); Eigenspace(M,0); Output: Magma V2.10-6 Mon Dec 1 2003 16:45:32 on modular [Seed = 3677311696] ------------------------------------- { <0, 1>, <1, 1>, <(1/5*a - 8/5)/(a - 4), 1> } Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-2*a + 6)/(a + 2) -2/(a - 1)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-a + 3)/(a - 1/2) -5/2/(a - 1/2)) Vector space of degree 3, dimension 1 over Univariate rational function field over Rational Field Echelonized basis: ( 1 (-a^2 + 3*a)/(a^2 - 4) (-3*a + 4)/(a^2 - 4)) Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 19:31:20 2003 Input: >l:=Lattice("Kappa",13); >G:=AutomorphismGroup(L:Stabilizer:=2); >#G; Output: Magma V2.10-6 Mon Dec 1 2003 19:31:13 on modular [Seed = 1169270625] ------------------------------------- >> G:=AutomorphismGroup(L:Stabilizer:=2); ^ User error: Identifier 'L' has not been declared or assigned >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 19:31:20 2003 Input: >l:=Lattice("Kappa",13); >G:=AutomorphismGroup(L:Stabilizer:=2); >#G; Output: Magma V2.10-6 Mon Dec 1 2003 19:31:16 on modular [Seed = 1102422880] ------------------------------------- >> G:=AutomorphismGroup(L:Stabilizer:=2); ^ User error: Identifier 'L' has not been declared or assigned >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 19:31:39 2003 Input: >L:=Lattice("Kappa",13); >G:=AutomorphismGroup(L:Stabilizer:=2); >#G; Output: Magma V2.10-6 Mon Dec 1 2003 19:31:36 on modular [Seed = 918737963] ------------------------------------- 48 Total time: 3.459 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 19:47:02 2003 Input: >L:=Lattice("E",8); >G:=AutomorphismGroup(L); >#G;FactoredOrder(G); >M:=MatrixRing(Ratinals(),8); >B:=BasisMatrix(L); >A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; >A; Output: Magma V2.10-6 Mon Dec 1 2003 19:46:59 on modular [Seed = 468698477] ------------------------------------- 696729600 [ <2, 14>, <3, 5>, <5, 2>, <7, 1> ] >> M:=MatrixRing(Ratinals(),8); ^ User error: Identifier 'Ratinals' has not been declared or assigned >> A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; ^ User error: Identifier 'M' has not been declared or assigned >> A;; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.129 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 19:48:02 2003 Input: >L:=Lattice("E",8); >G:=AutomorphismGroup(L); >#G;FactoredOrder(G); >M:=MatrixRing(Rationals(),8); >B:=BasisMatrix(L); >A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; >A; Output: Magma V2.10-6 Mon Dec 1 2003 19:47:58 on modular [Seed = 49732681] ------------------------------------- 696729600 [ <2, 14>, <3, 5>, <5, 2>, <7, 1> ] MatrixGroup(8, Rational Field) Generators: [ 1/2 0 0 -1/2 0 1/2 0 1/2] [ 0 1/2 1/2 0 1/2 0 -1/2 0] [ 0 1/2 -1/2 0 -1/2 0 -1/2 0] [ 0 1/2 1/2 0 -1/2 0 1/2 0] [-1/2 0 0 -1/2 0 -1/2 0 1/2] [ 0 1/2 -1/2 0 1/2 0 1/2 0] [-1/2 0 0 1/2 0 1/2 0 1/2] [ 1/2 0 0 1/2 0 -1/2 0 1/2] [ 1/2 0 1/2 -1/2 0 0 -1/2 0] [ 0 1/2 0 0 1/2 1/2 0 1/2] [ 0 -1/2 0 0 1/2 -1/2 0 1/2] [ 0 1/2 0 0 1/2 -1/2 0 -1/2] [-1/2 0 -1/2 -1/2 0 0 -1/2 0] [ 1/2 0 -1/2 1/2 0 0 -1/2 0] [ 0 1/2 0 0 -1/2 -1/2 0 1/2] [ 1/2 0 -1/2 -1/2 0 0 1/2 0] Total time: 3.279 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 19:51:13 2003 Input: >L:=Lattice("E",8); >G:=AutomorphismGroup(L); >#G;FactoredOrder(G); >M:=MatrixRing(Rationals(),8); >B:=BasisMatrix(L); >A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; >A; Output: Magma V2.10-6 Mon Dec 1 2003 19:51:10 on modular [Seed = 3843111790] ------------------------------------- 696729600 [ <2, 14>, <3, 5>, <5, 2>, <7, 1> ] MatrixGroup(8, Rational Field) Generators: [ 1/2 0 0 -1/2 0 1/2 0 1/2] [ 0 1/2 1/2 0 1/2 0 -1/2 0] [ 0 1/2 -1/2 0 -1/2 0 -1/2 0] [ 0 1/2 1/2 0 -1/2 0 1/2 0] [-1/2 0 0 -1/2 0 -1/2 0 1/2] [ 0 1/2 -1/2 0 1/2 0 1/2 0] [-1/2 0 0 1/2 0 1/2 0 1/2] [ 1/2 0 0 1/2 0 -1/2 0 1/2] [ 1/2 0 1/2 -1/2 0 0 -1/2 0] [ 0 1/2 0 0 1/2 1/2 0 1/2] [ 0 -1/2 0 0 1/2 -1/2 0 1/2] [ 0 1/2 0 0 1/2 -1/2 0 -1/2] [-1/2 0 -1/2 -1/2 0 0 -1/2 0] [ 1/2 0 -1/2 1/2 0 0 -1/2 0] [ 0 1/2 0 0 -1/2 -1/2 0 1/2] [ 1/2 0 -1/2 -1/2 0 0 1/2 0] Total time: 3.279 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 20:23:59 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >G:=AutomorphismGroup(L); >#G;FactoredOrder(G); >M:=MatrixRing(Rationals(),8); >B:=BasisMatrix(L); >A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; >A; Output: Magma V2.10-6 Mon Dec 1 2003 20:23:55 on modular [Seed = 2557234758] ------------------------------------- 288 [ <2, 5>, <3, 2> ] >> A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; ^ Runtime error in '!': Arguments 1 and 2 have incompatible degrees >> A;; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 20:24:52 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >G:=AutomorphismGroup(L); >#G;FactoredOrder(G); >M:=MatrixRing(Rationals(),6); >B:=BasisMatrix(L); >A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; >A; Output: Magma V2.10-6 Mon Dec 1 2003 20:24:49 on modular [Seed = 2155107860] ------------------------------------- 288 [ <2, 5>, <3, 2> ] >> A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>; ^ Runtime error in '*': Arguments 1 and 2 have incompatible coefficient rings >> A;; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 20:28:09 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >G:=AutomorphismGroup(L); >#G;FactoredOrder(G); >M:=MatrixRing(Rationals(),6); >B:=BasisMatrix(L); >A:=MatrixGroup<8,Rationals()|[B^-1*g*B:g in Generators(G)]>; >A; Output: Magma V2.10-6 Mon Dec 1 2003 20:28:06 on modular [Seed = 1887741346] ------------------------------------- 288 [ <2, 5>, <3, 2> ] >> A:=MatrixGroup<8,Rationals()|[B^-1*g*B:g in Generators(G)]>; ^ Runtime error in MatrixGroup< ... >: Can not build a generator from the arguments given >> A;; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 1 20:29:16 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >G:=AutomorphismGroup(L); >#G;FactoredOrder(G); >M:=MatrixRing(Rationals(),6); >B:=BasisMatrix(L); >A:=MatrixGroup<8,Rationals()|G,[B^-1*g*B:g in Generators(G)]>; >A; Output: Magma V2.10-6 Mon Dec 1 2003 20:29:13 on modular [Seed = 2039327972] ------------------------------------- 288 [ <2, 5>, <3, 2> ] >> A:=MatrixGroup<8,Rationals()|G,[B^-1*g*B:g in Generators(G)]>; ^ Runtime error in MatrixGroup< ... >: Argument is not a subgroup >> A;; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (162.33.91.63) Time: Mon Dec 1 21:25:12 2003 Input: 2^6; Output: Magma V2.10-6 Mon Dec 1 2003 21:25:09 on modular [Seed = 2205631730] ------------------------------------- 64 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:45:51 2003 Input: // Allan knows about this and has fixed it: P := PolynomialRing(IntegerRing(), 2); ExactQuotient(P!1, P!2); Output: Magma V2.10-6 Tue Dec 2 2003 00:45:48 on modular [Seed = 2106483969] ------------------------------------- Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 2106483969 Time to this point: 3.1 Internal error in dpoly_exact_div() at dpoly/exact_div.c, line 937 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:47:11 2003 Input: // Allan time Factorization(2^512 + 1); Output: Magma V2.10-6 Tue Dec 2 2003 00:47:06 on modular [Seed = 1755017282] ------------------------------------- [ <2424833, 1>, <7455602825647884208337395736200454918783366342657, 1>, <741640062627530801524787141901937474059940781097519023905821316144415759504705\ 008092818711693940737, 1> ] Time: 1.830 Total time: 5.069 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:48:46 2003 Input: // Allan time Factorization(2^512 - 1); Output: Magma V2.10-6 Tue Dec 2 2003 00:48:42 on modular [Seed = 1352878234] ------------------------------------- [ <3, 1>, <5, 1>, <17, 1>, <257, 1>, <641, 1>, <65537, 1>, <274177, 1>, <6700417, 1>, <67280421310721, 1>, <1238926361552897, 1>, <59649589127497217, 1>, <5704689200685129054721, 1>, <934616397153579777691635581996068965840512375\ 41638188580280321, 1> ] Time: 0.510 Total time: 3.669 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:49:22 2003 Input: // Allan time Factorization(2^1024 - 1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 2 2003 00:48:58 on modular [Seed = 1487618274] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 20264 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:49:47 2003 Input: // Allan SetVerbose("Factorization", 1); time Factorization(2^768 - 1); Output: Magma V2.10-6 Tue Dec 2 2003 00:49:42 on modular [Seed = 1102207431] ------------------------------------- Integer main factorization (primality of factors will be proved) Seed: 1 Number: 18446744073709551617 Trial Division Number: 18446744073709551617 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 18446744073709551617 (20 digits) Factor: 274177 (6 digits) Cofactor: 67280421310721 (14 digits) Time: 0.020 Total time: 0.020 [ <3, 2>, <5, 1>, <7, 1>, <13, 1>, <17, 1>, <97, 1>, <193, 1>, <241, 1>, <257, 1>, <641, 1>, <673, 1>, <769, 1>, <65537, 1>, <274177, 1>, <6700417, 1>, <22253377, 1>, <67280421310721, 1>, <59649589127497217, 1>, <18446744069414584321, 1>, <5704689200685129054721, 1>, <349621839326921795694385454593, 1>, <442499826945303593556473164314770689, 1>, <331192380488114152600457428497953408512758882817, 1> ] Time: 0.500 Total time: 3.679 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:50:15 2003 Input: // Allan SetVerbose("Cunningham", 1); time Factorization(2^768 - 1); Output: Magma V2.10-6 Tue Dec 2 2003 00:50:12 on modular [Seed = 834807381] ------------------------------------- Cunningham Factorization: a = 2, e = 768, c = -1 Trial Division Found prime <3, 2> Found prime <5, 1> Found prime <7, 1> Found prime <13, 1> Found prime <17, 1> Found prime <97, 1> Found prime <193, 1> Found prime <241, 1> Found prime <257, 1> Found prime <641, 1> Found prime <673, 1> Found prime <769, 1> Database lookup Found prime <59649589127497217, 1> Found prime <349621839326921795694385454593, 1> Aurifeuillian factors Algebraic factors Found prime <65537, 1> Found prime <6700417, 1> Found prime <22253377, 1> Found composite 18446744073709551617 Found prime <18446744069414584321, 1> Found prime <5704689200685129054721, 1> Found prime <442499826945303593556473164314770689, 1> Primality testing 331192380488114152600457428497953408512758882817 Found prime <331192380488114152600457428497953408512758882817, 1> Factoring 18446744073709551617 [ <3, 2>, <5, 1>, <7, 1>, <13, 1>, <17, 1>, <97, 1>, <193, 1>, <241, 1>, <257, 1>, <641, 1>, <673, 1>, <769, 1>, <65537, 1>, <274177, 1>, <6700417, 1>, <22253377, 1>, <67280421310721, 1>, <59649589127497217, 1>, <18446744069414584321, 1>, <5704689200685129054721, 1>, <349621839326921795694385454593, 1>, <442499826945303593556473164314770689, 1>, <331192380488114152600457428497953408512758882817, 1> ] Time: 0.520 Total time: 3.559 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:50:39 2003 Input: // Allan SetVerbose("Cunningham", 1); SetVerbose("Factorization", 1); time Factorization(2^800 - 1); Output: Magma V2.10-6 Tue Dec 2 2003 00:50:35 on modular [Seed = 969551458] ------------------------------------- Cunningham Factorization: a = 2, e = 800, c = -1 Trial Division Found prime <3, 1> Found prime <5, 3> Found prime <11, 1> Found prime <17, 1> Found prime <31, 1> Found prime <41, 1> Found prime <101, 1> Found prime <251, 1> Found prime <257, 1> Found prime <401, 1> Found prime <601, 1> Found prime <1601, 1> Found prime <1801, 1> Found prime <4051, 1> Found prime <8101, 1> Database lookup Found prime <3399426377632056001, 1> Found prime <4850484222084371979240001, 1> Aurifeuillian factors Found prime <268501, 1> Algebraic factors Found prime <65537, 1> Found prime <61681, 1> Found prime <4278255361, 1> Found composite 18446462603027742721 Found composite 3014774729910783238001 Primality testing 912867980842956708437164975496064226186955201 Found composite 912867980842956708437164975496064226186955201 Primality testing 129541188208935646963818844716591986208974410651257601 Found prime <129541188208935646963818844716591986208974410651257601, 1> Factoring 18446462603027742721 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 18446462603027742721 Trial Division Number: 18446462603027742721 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 18446462603027742721 (20 digits) Factor: 414721 (6 digits) Cofactor: 44479210368001 (14 digits) Time: 0.009 Total time: 0.009 Factoring 3014774729910783238001 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 3014774729910783238001 Trial Division Number: 3014774729910783238001 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 3014774729910783238001 (22 digits) Factor: 340801 (6 digits) Cofactor: 8846144025137201 (16 digits) Time: 0.000 Pollard Rho Trials: 8191 Number: 8846144025137201 (16 digits) Factor: 2787601 (7 digits) Cofactor: 3173389601 (10 digits) Time: 0.010 Total time: 0.010 Factoring 912867980842956708437164975496064226186955201 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 912867980842956708437164975496064226186955201 Trial Division Number: 912867980842956708437164975496064226186955201 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 912867980842956708437164975496064226186955201 (45 digits) Factor: 25601 (5 digits) Cofactor: 35657512630090883498190108804189845169601 (41 digits) Time: 0.009 Pollard Rho Trials: 8191 Number: 35657512630090883498190108804189845169601 (41 digits) No factor found Time: 0.050 1 composite number remaining ECM x: 35657512630090883498190108804189845169601 (41 digits) Initial smoothness: 500, steps: 6, step size: 100 Step 1/6; smoothness: 500, digits: 41, elapsed time: 0.000 Factor: 82471201 (8 digits) Cofactor: 432363203127002885506543172618401 (33 digits) Time: 0.049 Total time: 0.199 [ <3, 1>, <5, 3>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <257, 1>, <401, 1>, <601, 1>, <1601, 1>, <1801, 1>, <4051, 1>, <8101, 1>, <25601, 1>, <61681, 1>, <65537, 1>, <268501, 1>, <340801, 1>, <414721, 1>, <2787601, 1>, <82471201, 1>, <3173389601, 1>, <4278255361, 1>, <44479210368001, 1>, <3399426377632056001, 1>, <4850484222084371979240001, 1>, <432363203127002885506543172618401, 1>, <12954118820893564696381884471659198620\ 8974410651257601, 1> ] Time: 0.590 Total time: 3.759 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:51:00 2003 Input: // Allan SetVerbose("Cunningham", 1); SetVerbose("Factorization", 1); time Factorization(2^900 - 1); Output: Magma V2.10-6 Tue Dec 2 2003 00:50:56 on modular [Seed = 567424529] ------------------------------------- Cunningham Factorization: a = 2, e = 900, c = -1 Trial Division Found prime <3, 3> Found prime <5, 3> Found prime <7, 1> Found prime <11, 1> Found prime <13, 1> Found prime <19, 1> Found prime <31, 1> Found prime <37, 1> Found prime <41, 1> Found prime <61, 1> Found prime <73, 1> Found prime <101, 1> Found prime <109, 1> Found prime <151, 1> Found prime <181, 1> Found prime <251, 1> Found prime <331, 1> Found prime <601, 1> Found prime <631, 1> Found prime <1201, 1> Found prime <1321, 1> Found prime <1801, 1> Found prime <4051, 1> Found prime <8101, 1> Database lookup Found prime <1348206751, 1> Found prime <4714696801, 1> Found prime <307116398490301, 1> Found prime <413150254353901, 1> Aurifeuillian factors Found prime <268501, 1> Found prime <54001, 1> Found prime <29247661, 1> Found composite 852100728601 Found prime <1182468601, 1> Found prime <3192261504216112476901, 1> Found composite 4362038237992319774101 Algebraic factors Found prime <23311, 1> Found prime <18837001, 1> Found composite 1065184428001 Found prime <1133836730401, 1> Found composite 985892875836627780943321951 Found prime <281941472953710177758647201, 1> Factoring 852100728601 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 852100728601 Trial Division Number: 852100728601 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 852100728601 (12 digits) Factor: 63901 (5 digits) Cofactor: 13334701 (8 digits) Time: 0.000 Total time: 0.000 Factoring 4362038237992319774101 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 4362038237992319774101 Trial Division Number: 4362038237992319774101 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 4362038237992319774101 (22 digits) Factor: 695701 (6 digits) Cofactor: 6269989892198401 (16 digits) Time: 0.010 Total time: 0.050 Factoring 1065184428001 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 1065184428001 Trial Division Number: 1065184428001 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 1065184428001 (13 digits) Factor: 100801 (6 digits) Cofactor: 10567201 (8 digits) Time: 0.000 Total time: 0.000 Factoring 985892875836627780943321951 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 985892875836627780943321951 Trial Division Number: 985892875836627780943321951 Minimum: 2 Maximum: 10000 No factors found Time: 0.009 Pollard Rho Trials: 8191 Number: 985892875836627780943321951 (27 digits) Factor: 71125212601 (11 digits) Cofactor: 13861369826299351 (17 digits) Time: 0.000 Pollard Rho Trials: 8191 Number: 71125212601 (11 digits) Factor: 115201 (6 digits) Cofactor: 617401 (6 digits) Time: 0.010 Total time: 0.049 [ <3, 3>, <5, 3>, <7, 1>, <11, 1>, <13, 1>, <19, 1>, <31, 1>, <37, 1>, <41, 1>, <61, 1>, <73, 1>, <101, 1>, <109, 1>, <151, 1>, <181, 1>, <251, 1>, <331, 1>, <601, 1>, <631, 1>, <1201, 1>, <1321, 1>, <1801, 1>, <4051, 1>, <8101, 1>, <23311, 1>, <54001, 1>, <63901, 1>, <100801, 1>, <115201, 1>, <268501, 1>, <617401, 1>, <695701, 1>, <10567201, 1>, <13334701, 1>, <18837001, 1>, <29247661, 1>, <1182468601, 1>, <1348206751, 1>, <4714696801, 1>, <1133836730401, 1>, <307116398490301, 1>, <413150254353901, 1>, <6269989892198401, 1>, <13861369826299351, 1>, <3192261504216112476901, 1>, <281941472953710177758647201, 1> ] Time: 0.280 Total time: 3.439 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:51:20 2003 Input: // Allan SetVerbose("Cunningham", 1); SetVerbose("Factorization", 1); time Factorization(2^1000 - 1); Output: Magma V2.10-6 Tue Dec 2 2003 00:51:15 on modular [Seed = 702168586] ------------------------------------- Cunningham Factorization: a = 2, e = 1000, c = -1 Trial Division Found prime <3, 1> Found prime <5, 4> Found prime <11, 1> Found prime <17, 1> Found prime <31, 1> Found prime <41, 1> Found prime <101, 1> Found prime <251, 1> Found prime <401, 1> Found prime <601, 1> Found prime <1801, 1> Found prime <4001, 1> Found prime <4051, 1> Found prime <7001, 1> Found prime <8101, 1> Database lookup Found prime <269089806001, 1> Found prime <1481124532001, 1> Aurifeuillian factors Found prime <268501, 1> Found composite 253468230599467758697053367501 Found composite 181111287389941648853409001 Algebraic factors Found prime <61681, 1> Found composite 3014774729910783238001 Found prime <4710883168879506001, 1> Found composite 1267650562449298664439414784001 Primality testing 4357507456648357759435539669451839600394175931174635840276981\ 76425409152335529484786678327261647827656001 Found composite 435750745664835775943553966945183960039417593117463584027698176\ 425409152335529484786678327261647827656001 Factoring 253468230599467758697053367501 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 253468230599467758697053367501 Trial Division Number: 253468230599467758697053367501 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 253468230599467758697053367501 (30 digits) Factor: 28001 (5 digits) Cofactor: 9052113517355371547339501 (25 digits) Time: 0.000 Pollard Rho Trials: 8191 Number: 9052113517355371547339501 (25 digits) Factor: 96001 (5 digits) Cofactor: 94291866932171243501 (20 digits) Time: 0.000 Total time: 0.039 Factoring 181111287389941648853409001 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 181111287389941648853409001 Trial Division Number: 181111287389941648853409001 Minimum: 2 Maximum: 10000 No factors found Time: 0.009 Pollard Rho Trials: 8191 Number: 181111287389941648853409001 (27 digits) Factor: 3775501 (7 digits) Cofactor: 47970133603445383501 (20 digits) Time: 0.030 Total time: 0.069 Factoring 3014774729910783238001 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 3014774729910783238001 Trial Division Number: 3014774729910783238001 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 3014774729910783238001 (22 digits) Factor: 340801 (6 digits) Cofactor: 8846144025137201 (16 digits) Time: 0.000 Pollard Rho Trials: 8191 Number: 8846144025137201 (16 digits) Factor: 2787601 (7 digits) Cofactor: 3173389601 (10 digits) Time: 0.010 Total time: 0.010 Factoring 1267650562449298664439414784001 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 1267650562449298664439414784001 Trial Division Number: 1267650562449298664439414784001 Minimum: 2 Maximum: 10000 No factors found Time: 0.000 Pollard Rho Trials: 8191 Number: 1267650562449298664439414784001 (31 digits) Factor: 229668251 (9 digits) Cofactor: 5519485418336288303251 (22 digits) Time: 0.039 Total time: 0.079 Factoring 435750745664835775943553966945183960039417593117463584027698176425409\ 152335529484786678327261647827656001 Integer main factorization (primality of factors will be proved) Seed: 1 Number: 4357507456648357759435539669451839600394175931174635840276981764254\ 09152335529484786678327261647827656001 Trial Division Number: 4357507456648357759435539669451839600394175931174635840276981764254\ 09152335529484786678327261647827656001 Minimum: 2 Maximum: 10000 No factors found Time: 0.009 Pollard Rho Trials: 8191 Number: 4357507456648357759435539669451839600394175931174635840276981764254\ 09152335529484786678327261647827656001 (105 digits) Factor: 1074001 (7 digits) Cofactor: 40572657349931310673225999505138632090604905686071389507802895567\ 6399884483840783003626930758582001 (99 digits) Time: 0.010 Pollard Rho Trials: 8191 Number: 4057265734993131067322599950513863209060490568607138950780289556763\ 99884483840783003626930758582001 (99 digits) Factor: 2020001 (7 digits) Cofactor: 20085463992310553644887304266254636552459580805193358571507091119\ 0835986954383083475516562001 (93 digits) Time: 0.059 Pollard Rho Trials: 8191 Number: 2008546399231055364488730426625463655245958080519335857150709111908\ 35986954383083475516562001 (93 digits) No factor found Time: 0.099 1 composite number remaining ECM x: 200854639923105536448873042662546365524595808051933585715070911190835986\ 954383083475516562001 (93 digits) Initial smoothness: 500, steps: 2000, step size: 7 Step 1/2000; smoothness: 500, digits: 93, elapsed time: 0.000 Factor: 22624001 (8 digits) Cofactor: 88779451487429450011460414390251470340986905035910131773363566944\ 16517527310181938001 (85 digits) Time: 0.569 Total time: 1.439 [ <3, 1>, <5, 4>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <401, 1>, <601, 1>, <1801, 1>, <4001, 1>, <4051, 1>, <7001, 1>, <8101, 1>, <28001, 1>, <61681, 1>, <96001, 1>, <268501, 1>, <340801, 1>, <1074001, 1>, <2020001, 1>, <2787601, 1>, <3775501, 1>, <22624001, 1>, <229668251, 1>, <3173389601, 1>, <269089806001, 1>, <1481124532001, 1>, <4710883168879506001, 1>, <47970133603445383501, 1>, <94291866932171243501, 1>, <5519485418336288303251, 1>, <88779451487429450011460414390251470340986905035910131773363566944165175273\ 10181938001, 1> ] Time: 1.740 Total time: 4.850 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:52:09 2003 Input: // Allan SetVerbose("Cunningham", 1); SetVerbose("Factorization", 1); time Factorization(2^1020 - 1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 2 2003 00:51:46 on modular [Seed = 316736784] ------------------------------------- Integer main factorization (primality of factors will be proved) Seed: 1 Number: 1123558209288947442330815744243140458511235611838941607958938007235\ 829223784381019579427983265047100132000711749196208485367436055090103890580\ 296441496713277361049333905409282976888872507788088246581768450531286055238\ 441764640393009211956940880170232270940691778664363999670287115498226905220\ 9770601514008575 Trial Division Number: 1123558209288947442330815744243140458511235611838941607958938007235\ 829223784381019579427983265047100132000711749196208485367436055090103890580\ 296441496713277361049333905409282976888872507788088246581768450531286055238\ 441764640393009211956940880170232270940691778664363999670287115498226905220\ 9770601514008575 Minimum: 2 Maximum: 10000 Factors found: <3, 2> <5, 2> <7, 1> <11, 1> <13, 1> <31, 1> <41, 1> <61, 1> <103, 1> <137, 1> <151, 1> <307, 1> <331, 1> <409, 1> <953, 1> <1021, 1> <1321, 1> <2143, 1> <2857, 1> <3061, 1> <4421, 1> <6529, 1> Time: 0.009 Pollard Rho Trials: 8191 Number: 1044948278467622800909065101703579308989613169559014911305410475219\ 298089905968556479519157552551238986426114626404414391694574968986333572485\ 611465254333992032293789721185161402252721828716586103197643087620402928477\ 8612010747889805683965422600249102265687 (257 digits) Factor: 51001 (5 digits) Cofactor: 20488780189949663749908141050245667908268723545793512113594056493\ 388327481931110301357211771387840218553089441901225748351886727103122165692\ 547429761266131880400262538404838363997818117854877082864995648862187073360\ 8725554611632905348600329848439228687 (252 digits) Time: 0.000 Pollard Rho Trials: 8191 Number: 2048878018994966374990814105024566790826872354579351211359405649338\ 832748193111030135721177138784021855308944190122574835188672710312216569254\ 742976126613188040026253840483836399781811785487708286499564886218707336087\ 25554611632905348600329848439228687 (252 digits) Factor: 11119 (5 digits) Cofactor: 18426819129372842656631118850837006842583616823269639458219315130\ 306976780224040202677589505700009190172757839644955255285445388167211229150\ 595763792846597608058514739099593815988684340187855996820753349098108708841\ 507829356204056601187186783743073 (248 digits) Time: 0.009 Pollard Rho Trials: 8191 Number: 1842681912937284265663111885083700684258361682326963945821931513030\ 697678022404020267758950570000919017275783964495525528544538816721122915059\ 576379284659760805851473909959381598868434018785599682075334909810870884150\ 7829356204056601187186783743073 (248 digits) Factor: 13669 (5 digits) Cofactor: 13480736798136544485061905663060214238483880915406861846674456895\ 388819065201580366286918944838692801355445050585233195760805756212752380679\ 344329353168920629203683326578091898448082771371611673729426694782433761680\ 81632113263885917125406890317 (244 digits) Time: 0.020 Pollard Rho Trials: 8191 Number: 1348073679813654448506190566306021423848388091540686184667445689538\ 881906520158036628691894483869280135544505058523319576080575621275238067934\ 432935316892062920368332657809189844808277137161167372942669478243376168081\ 632113263885917125406890317 (244 digits) Factor: 42224050401187 (14 digits) Cofactor: 31926678445224607850309617780953195990463213540972998416900116726\ 320065873311294608464928030296719486759193026819145646274765003102286274489\ 005894316061210138362369807695498982330546854527598997386058668316342397336\ 427338283622991 (230 digits) Time: 0.020 Pollard Rho Trials: 8191 Number: 42224050401187 (14 digits) Factor: 26317 (5 digits) Cofactor: 1604440111 (10 digits) Time: 0.000 Pollard Rho Trials: 8191 Number: 1604440111 (10 digits) Factor: 12241 (5 digits) Cofactor: 131071 (6 digits) Time: 0.009 Pollard Rho Trials: 8191 Number: 3192667844522460785030961778095319599046321354097299841690011672632\ 006587331129460846492803029671948675919302681914564627476500310228627448900\ 589431606121013836236980769549898233054685452759899738605866831634239733642\ 7338283622991 (230 digits) Factor: 2565117370522181 (16 digits) Cofactor: 12446478594749562360659035480275859729700120829737494476483531092\ 027737944850904962950969228296177115731069633024074829851789816687978225425\ 630616109032074968145372571686409884423637759183463565512356450267823259011 (215 digits) Time: 0.049 Pollard Rho Trials: 8191 Number: 2565117370522181 (16 digits) Factor: 106591 (6 digits) Cofactor: 24065046491 (11 digits) Time: 0.000 Pollard Rho Trials: 8191 Number: 24065046491 (11 digits) No factor found Time: 0.000 Pollard Rho Trials: 8191 Number: 1244647859474956236065903548027585972970012082973749447648353109202\ 773794485090496295096922829617711573106963302407482985178981668797822542563\ 0616109032074968145372571686409884423637759183463565512356450267823259011 (215 digits) Factor: 949111 (6 digits) Cofactor: 13113828197913165436560144683051676494846357095995615345816802346\ 646217296871393296412083758692267938872344365436787509418592574196251255570\ 350165690875013531763273812743093151826959922689193956778876707010901 (209 digits) Time: 0.169 Pollard Rho Trials: 8191 Number: 1311382819791316543656014468305167649484635709599561534581680234664\ 621729687139329641208375869226793887234436543678750941859257419625125557035\ 0165690875013531763273812743093151826959922689193956778876707010901 (209 digits) Factor: 23650061 (8 digits) Cofactor: 55449447669133561374578038860245123658862262959895178899609613466\ 308680120830949638616508256330788909476150465052870305148864411792642968533\ 3588175137265545816701014544659870087732962832070241035694441 (201 digits) Time: 0.309 Pollard Rho Trials: 8191 Number: 5544944766913356137457803886024512365886226295989517889960961346630\ 868012083094963861650825633078890947615046505287030514886441179264296853335\ 88175137265545816701014544659870087732962832070241035694441 (201 digits) No factor found Time: 0.290 2 composite numbers remaining ECM x: 24065046491 (11 digits) Initial smoothness: 500, steps: 2, step size: 100 Step 1/2; smoothness: 500, digits: 11, elapsed time: 0.000 Factor: 43691 (5 digits) Cofactor: 550801 (6 digits) Time: 0.000 ECM x: 554494476691335613745780388602451236588622629598951788996096134663086801\ 208309496386165082563307889094761504650528703051488644117926429685333588175\ 137265545816701014544659870087732962832070241035694441 (201 digits) Initial smoothness: 500, steps: 2000, step size: 23 Step 1/2000; smoothness: 500, digits: 201, elapsed time: 0.000 Factor: 15571321 (8 digits) Cofactor: 35609983038133734045157786458994149346007485787426242705811288243\ 501421697511052298399415345898263165646736371983385549080174001802829039702\ 770765250890759095949599558358592060861950173146532721 (194 digits) Time: 0.289 ECM x: 356099830381337340451577864589941493460074857874262427058112882435014216\ 975110522983994153458982631656467363719833855490801740018028290397027707652\ 50890759095949599558358592060861950173146532721 (194 digits) Initial smoothness: 500, steps: 2000, step size: 22 Step 1/2000; smoothness: 500, digits: 194, elapsed time: 0.000 Factor: 611787251461 (12 digits) Cofactor: 58206481016225927036648290820789410790816834809883414616064031228\ 882053478745057478646190108728449991062204933237010319552919621871841023408\ 073689099756654492562777901508038205697661 (182 digits) Time: 0.739 ECM x: 582064810162259270366482908207894107908168348098834146160640312288820534\ 787450574786461901087284499910622049332370103195529196218718410234080736890\ 99756654492562777901508038205697661 (182 digits) Initial smoothness: 500, steps: 2000, step size: 20 Step 1/2000; smoothness: 500, digits: 182, elapsed time: 0.000 Factor: 1326700741 (10 digits) Cofactor: 43873105077451620294714443685374719174003110630570918341006663558\ 411364058132426624344660789428510608680066255602558919165418346496454563605\ 368250186088238939607841751788121 (173 digits) Time: 1.699 ECM x: 438731050774516202947144436853747191740031106305709183410066635584113640\ 581324266243446607894285106086800662556025589191654183464964545636053682501\ 86088238939607841751788121 (173 digits) Initial smoothness: 500, steps: 2000, step size: 19 Step 1/2000; smoothness: 500, digits: 173, elapsed time: 0.000 Step 2/2000; smoothness: 519, digits: 173, elapsed time: 1.559 Step 3/2000; smoothness: 538, digits: 173, elapsed time: 3.159 Step 4/2000; smoothness: 557, digits: 173, elapsed time: 4.799 Step 5/2000; smoothness: 576, digits: 173, elapsed time: 6.459 Step 6/2000; smoothness: 595, digits: 173, elapsed time: 8.169 Factor: 2949879781 (10 digits) Cofactor: 14872845110514563133891470164076737056018728185103255345512218878\ 594145683977087683338597990623845904003660905665415969426388751703659534186\ 748693873666792300919141 (164 digits) Time: 9.929 ECM x: 148728451105145631338914701640767370560187281851032553455122188785941456\ 839770876833385979906238459040036609056654159694263887517036595341867486938\ 73666792300919141 (164 digits) Initial smoothness: 595, steps: 2000, step size: 17 Step 1/2000; smoothness: 595, digits: 164, elapsed time: 0.000 Step 2/2000; smoo ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 20322 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Tue Dec 2 00:52:46 2003 Input: // Allan SetVerbose("Cunningham", 1); SetVerbose("Factorization", 1); time Factorization(2^1024 - 1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 2 2003 00:52:23 on modular [Seed = 451481085] ------------------------------------- Integer main factorization (primality of factors will be proved) Seed: 1 Number: 1797693134862315907729305190789024733617976978942306572734300811577\ 326758055009631327084773224075360211201138798713933576587897688144166224928\ 474306394741243777678934248654852763022196012460941194530829520850057688381\ 506823424628814739131105408272371633505106845862982399472459384797163048353\ 56329624224137215 Trial Division Number: 1797693134862315907729305190789024733617976978942306572734300811577\ 326758055009631327084773224075360211201138798713933576587897688144166224928\ 474306394741243777678934248654852763022196012460941194530829520850057688381\ 506823424628814739131105408272371633505106845862982399472459384797163048353\ 56329624224137215 Minimum: 2 Maximum: 10000 Factors found: <3, 1> <5, 1> <17, 1> <257, 1> <641, 1> Time: 0.010 Pollard Rho Trials: 8191 Number: 4279413246241015912182555964222056460566264394910881891086293129089\ 365516431620910018749489171689492023831066199073897768571337029882964313595\ 691638721925378568784526658248858847791961238896749374923641261704622444263\ 225086938048287160821176780701959364356059982150949337244164429404023426415\ 898082689 (301 digits) Factor: 65537 (5 digits) Cofactor: 65297667672322747641523963016647946359556653415793855243393703237\ 703366288228342921078924716903268261040802389475775482072284923476554683821\ 287084222987402208962639831823990400045653008817870048597336485675337938023\ 761006560233887531635887769972717081409830477167873862661460921760288438995\ 008897 (296 digits) Time: 0.029 Pollard Rho Trials: 8191 Number: 6529766767232274764152396301664794635955665341579385524339370323770\ 336628822834292107892471690326826104080238947577548207228492347655468382128\ 708422298740220896263983182399040004565300881787004859733648567533793802376\ 100656023388753163588776997271708140983047716787386266146092176028843899500\ 8897 (296 digits) Factor: 274177 (6 digits) Cofactor: 23815880862480349424468122058614670945978930915355356300270884588\ 314616575507188028565096531402440124824767354473852833050286830578989004847\ 703156801258822661624658462170054526836916666539450810460883475154859064773\ 398573388808648257014953030331762723134993262442828487678200914650130550336\ 1 (291 digits) Time: 0.130 Pollard Rho Trials: 8191 Number: 2381588086248034942446812205861467094597893091535535630027088458831\ 461657550718802856509653140244012482476735447385283305028683057898900484770\ 315680125882266162465846217005452683691666653945081046088347515485906477339\ 85733888086482570149530303317627231349932624428284876782009146501305503361 (291 digits) Factor: 2424833 (7 digits) Cofactor: 98216581770704825546617528129214139472610818622789100528864810848\ 065069122315590511037653031785859582184700366886514795246876096535262448373\ 571115211888087392511807873655853936485179253744281814297658746622382097131\ 631635617003926691095646711883922410883525844636840919264134538956417 (284 digits) Time: 0.270 Pollard Rho Trials: 8191 Number: 9821658177070482554661752812921413947261081862278910052886481084806\ 506912231559051103765303178585958218470036688651479524687609653526244837357\ 111521188808739251180787365585393648517925374428181429765874662238209713163\ 1635617003926691095646711883922410883525844636840919264134538956417 (284 digits) No factor found Time: 0.500 1 composite number remaining ECM x: 982165817707048255466175281292141394726108186227891005288648108480650691\ 223155905110376530317858595821847003668865147952468760965352624483735711152\ 118880873925118078736558539364851792537442818142976587466223820971316316356\ 17003926691095646711883922410883525844636840919264134538956417 (284 digits) Initial smoothness: 500, steps: 2000, step size: 35 Step 1/2000; smoothness: 500, digits: 284, elapsed time: 0.000 Factor: 6700417 (7 digits) Cofactor: 14658278995278178290488118594591073879821333302507754447053789465\ 351942889870226063696879318374641396525723752251018823939894501571359282321\ 319869377068335805444916021444016683810153793971969478063478548666804185042\ 756538229934633425217512090946566819779056414643572320836768001 (278 digits) Time: 3.710 ECM x: 146582789952781782904881185945910738798213333025077544470537894653519428\ 898702260636968793183746413965257237522510188239398945015713592823213198693\ 770683358054449160214440166838101537939719694780634785486668041850427565382\ 29934633425217512090946566819779056414643572320836768001 (278 digits) Initial smoothness: 500, steps: 2000, step size: 34 Step 1/2000; smoothness: 500, digits: 278, elapsed time: 0.000 Step 2/2000; smoothness: 534, digits: 278, elapsed time: 3.479 Step 3/2000; smoothness: 568, digits: 278, elapsed time: 7.099 Step 4/2000; smoothness: 602, digits: 278, elapsed time: 10.869 Step 5/2000; smoothness: 636, digits: 278, elapsed time: 14.829 Errors: /home/mfd/gomagma: line 2: 20330 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 168ext7.cab.uniroma3.it. (193.204.163.2) Time: Tue Dec 2 04:24:23 2003 Input: d=prodeuler(p=2,436270000,1-(2*p)/(p^3-1)) Output: Magma V2.10-6 Tue Dec 2 2003 04:24:20 on modular [Seed = 3342115567] ------------------------------------- >> d=prodeuler(p=2,436270000,1-(2*p)/(p^3-1)); ^ User error: Identifier 'p' has not been declared or assigned Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host isgpc002.rhul.ac.uk. (134.219.148.41) Time: Tue Dec 2 09:20:33 2003 Input: F := GF( 103); g:= F.1; R := PolynomialRing(F); p := x^4 + g*x + 1; l := Factorization(p); print "Steven Galbraith tests! l = ", l; Output: Magma V2.10-6 Tue Dec 2 2003 09:19:55 on modular [Seed = 1003002834] ------------------------------------- Steven Galbraith tests! l = [ , ] Total time: 3.809 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host maximum.byu.edu. (128.187.91.72) Time: Tue Dec 2 14:48:23 2003 Input: GaloisGroup(x^5+5*x+1); Output: Magma V2.10-6 Tue Dec 2 2003 14:48:20 on modular [Seed = 15979482] ------------------------------------- >> GaloisGroup(x^5+5*x+1);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 2 23:41:12 2003 Input: printf "%o",5; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host pclecacheux.institut.math.jussieu.fr. (134.157.51.81) Time: Wed Dec 3 05:21:27 2003 Input: vecsort([6,8,1,2]) Output: Magma V2.10-6 Wed Dec 3 2003 05:21:22 on modular [Seed = 3192666317] ------------------------------------- >> vecsort([6,8,1,2]); ^ User error: Identifier 'vecsort' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ub084068.mat.ub.es. (161.116.84.68) Time: Wed Dec 3 09:38:01 2003 Input: A:=NewSubspace(ModularForms(6400,4)); pp:=HeckePolynomial(A,7); print pp; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 3 2003 09:37:37 on modular [Seed = 3125309633] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 30192 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ub084068.mat.ub.es. (161.116.84.68) Time: Wed Dec 3 09:38:28 2003 Input: A:=NewSubspace(ModularForms(64,4)); pp:=HeckePolynomial(A,7); print pp; Output: Magma V2.10-6 Wed Dec 3 2003 09:38:23 on modular [Seed = 3007412646] ------------------------------------- Computing Hecke polynomial on Eisenstein series not yet implemented. (Returning 1.) $.1^5 - 832*$.1^3 + 147456*$.1 Total time: 4.519 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:34:53 2003 Input: P4<[z]> := PolynomialRing(Rationals(), 4); Output: Magma V2.10-6 Wed Dec 3 2003 10:34:50 on modular [Seed = 834669795] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:35:41 2003 Input: Output: Magma V2.10-6 Wed Dec 3 2003 10:35:37 on modular [Seed = 3224501570] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:35:52 2003 Input: Output: Magma V2.10-6 Wed Dec 3 2003 10:35:49 on modular [Seed = 3626624325] ------------------------------------- Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:36:01 2003 Input: Output: Magma V2.10-6 Wed Dec 3 2003 10:35:58 on modular [Seed = 3491884358] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:36:05 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; Output: Magma V2.10-6 Wed Dec 3 2003 10:36:02 on modular [Seed = 3894007106] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:37:02 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; > D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; > Q2mat := func *MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>; > M1 := Q2mat(D1);> M2 := Q2mat(D2); > M1; [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] > M2; [ 1 0 1 -1] [ 0 1 1 0] [ 1 1 -1 -1] [-1 0 -1 0] > P1 := PolynomialRing(Rationals()); Output: Magma V2.10-6 Wed Dec 3 2003 10:36:59 on modular [Seed = 2239019478] ------------------------------------- >> M1 := Q2mat(D1);> M2 := Q2mat(D2); ^ User error: bad syntax [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] >> [ 1 1 0 0] ^ User error: bad syntax >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 2 0] ^ User error: bad syntax >> [ 0 -1 0 3] ^ User error: bad syntax >> M2; ^ User error: Identifier 'M2' has not been declared or assigned >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 1 0] ^ User error: bad syntax >> [ 1 1 -1 -1] ^ User error: bad syntax >> [-1 0 -1 0] ^ User error: bad syntax Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:37:46 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; > D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; > Q2mat := func *MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>; > M1 := Q2mat(D1);> M2 := Q2mat(D2); > M1; [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] > M2; [ 1 0 1 -1] [ 0 1 1 0] [ 1 1 -1 -1] [-1 0 -1 0] > P1 := PolynomialRing(Rationals()); Output: Magma V2.10-6 Wed Dec 3 2003 10:37:42 on modular [Seed = 2506402203] ------------------------------------- >> M1 := Q2mat(D1);> M2 := Q2mat(D2); ^ User error: bad syntax [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] >> [ 1 1 0 0] ^ User error: bad syntax >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 2 0] ^ User error: bad syntax >> [ 0 -1 0 3] ^ User error: bad syntax >> M2; ^ User error: Identifier 'M2' has not been declared or assigned >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 1 0] ^ User error: bad syntax >> [ 1 1 -1 -1] ^ User error: bad syntax >> [-1 0 -1 0] ^ User error: bad syntax Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:38:46 2003 Input: Q:=Rationals(); Output: Magma V2.10-6 Wed Dec 3 2003 10:38:43 on modular [Seed = 2773784942] ------------------------------------- Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:38:55 2003 Input: Q:=Rationals(); Q Output: Magma V2.10-6 Wed Dec 3 2003 10:38:52 on modular [Seed = 3175907705] ------------------------------------- Rational Field Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:40:30 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; > D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; > Q2mat := func *MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>; > M1 := Q2mat(D1);> M2 := Q2mat(D2); > M1; [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] > M2; [ 1 0 1 -1] [ 0 1 1 0] [ 1 1 -1 -1] [-1 0 -1 0] > P1 := PolynomialRing(Rationals()); > Determinant(x*ChangeRing(M1,P1) + ChangeRing(M2,P1)); -11*x^4 + 11*x^3 - 12*x + 3 > Reduce($1); 3*x^4 - 18*x^2 + 13*x - 9 [ 0 -1] [ 1 -1] > Determinant(ChangeRing(M1,P1) + x*ChangeRing(M2,P1)); 3*x^4 - 12*x^3 + 11*x - 11 > g := 27*Evaluate($1, x/3); g; x^4 - 12*x^3 + 99*x - 297 > K := NumberField(g); > Mlambda := ChangeRing(M1, K) + lambda/3*ChangeRing(M2, K); Mlambda; [ 1/3*(lambda + 3) 1 1/3*lambda -1/3*lambda] [ 1 1/3*lambda 1/3*(lambda + 3) -1] [ 1/3*lambda 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ -1/3*lambda -1 -1/3*lambda 3] > Determinant(Mlambda); 0 > Kernel(Mlambda); Vector space of degree 4, dimension 1 over K Echelonized basis: (1 1/1947*(17*lambda^3 - 110*lambda^2 - 990*lambda + 561) 1/5841*(-65*lambda^3 + 726*lambda^2 + 693*lambda - 6039) 1/531*(lambda^3 - 3*lambda^2 - 27*lambda - 144)) > node := Eltseq(Basis($1)[1]); > node := Eltseq(1947*Basis($1)[1]); > node; [ 1947, 17*lambda^3 - 110*lambda^2 - 990*lambda + 561, 1/3*(-65*lambda^3 + 726*lambda^2 + 693*lambda - 6039), 1/3*(11*lambda^3 - 33*lambda^2 - 297*lambda - 1584) ] > T := Matrix([node, [0,1,0,0], [0,0,1,0], [0,0,0,1]]); > T*Mlambda*Transpose(T); [ 0 0 0 0] [ 0 1/3*lambda 1/3*(lambda + 3) -1] [ 0 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ 0 -1 -1/3*lambda 3] > Rlambda := Submatrix($1, 2,2, 3,3); Rlambda; [ 1/3*lambda 1/3*(lambda + 3) -1] [ 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ -1 -1/3*lambda 3] > Determinant($1); 1/27*(-lambda^3 - 12*lambda^2 + 27*lambda - 135) > Norm($1); 421201/27 > Factorisation(Numerator($1)); [ <11, 2>, <59, 2> ] > Rlambda *:= 3; > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > Determinant($1); -lambda^3 - 12*lambda^2 + 27*lambda - 135 > Norm($1); 8290499283 > Factorisation(Integers()!($1)); [ <3, 9>, <11, 2>, <59, 2> ] > OK := Integers(K); > [K | b : b in Basis(OK)]; [ 1, lambda, 1/3*lambda^2, 1/9*lambda^3 ] > Decomposition(OK, 3); [ , ] > p31 := $1[1,1]; p32 := $1[2,1]; > Decomposition(OK, 11); [ , ] > p111 := $1[1,1]; p112 := $1[1,2]; > Decomposition(OK, 59); [ , , ] > p591 := $1[1,1]; p592 := $1[2,1]; p593 := $1[3,1]; > RlO := ChangeRing(Rlambda, OK); > RlO; [[0, 1, 0, 0] [3, 1, 0, 0] [-3, 0, 0, 0]] [[3, 1, 0, 0] [6, -1, 0, 0] [0, -1, 0, 0]] [[-3, 0, 0, 0] [0, -1, 0, 0] [9, 0, 0, 0]] > p31; Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] > p32; Prime Ideal of OK Basis: [1 0 0 2] [0 1 0 0] [0 0 1 0] [0 0 0 3] > p111; Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0] > p112; 3 > Decomposition(OK, 11); [ , ] > p111 := $1[1,1]; p112 := $1[2,1]; > pl := [p31, p32, p111, p112, p591, p592,p593]; > det := Determinant(RlO); > [Valuation(det, p) : p in pl]; [ 3, 6, 0, 2, 2, 0, 0 ] > pl1 := [pl[i] : i in [1..#pl] | $1[i] ne 0]; #pl1; 4 > pl1[4]; Prime Ideal of OK Two element generators: [59, 0, 0, 0] [50, 1, 0, 0] > F4, m4 := ResidueClassField(pl1[4]); > RlO4 := Matrix(3, [m4(c) : c in Eltseq(RlO)]); > RlO4; [ 9 12 56] [12 56 50] [56 50 9] > Kernel($1); Vector space of degree 3, dimension 1 over GF(59) Echelonized basis: ( 1 45 6) > T1 := Matrix([Eltseq(Basis($1)[1]), [0,1,0], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 56 50] [ 0 50 9] > PF := PolynomialRing(F4); > Factorisation($1[2,2]*u^2 + 2*$1[2,3]*u + $1[3,3]); [ , ] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 54 2] [ 0 2 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 39 39] [ 0 39 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]); > T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,0,1]])*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 54 2] [ 0 2 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,1,-40]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 54 24] [ 0 24 13] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,1,40]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 39 34] [ 0 34 48] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]); > T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,1,-40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 5 7] [ 0 7 30] > T2 := Matrix(F4, [[1,0,0], [0,1,25], [0,1,40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 5 52] [ 0 52 30] > T2 := Matrix(F4, [[1,0,0], [0,1,1], [0,25,40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 0 28] [ 0 28 0] > T2l := Matrix(3, [c @@ m4 : c in Eltseq(T2)]); > T2l; [[1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]] [[0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]] [[0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]] > T2b := Matrix(OK, [[1,0,0,0]] cat [[0] cat Eltseq(T2l[i]) : i in [1..3]]); > T2b; [[1, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0]] [[0, 0, 0, 0] [1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]] [[0, 0, 0, 0] [0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]] [[0, 0, 0, 0] [0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]] > Rnew1 := T2l*RlO*Transpose(T2l); > Rnew1; [[12708, -2474, 0, 0] [14271, -4575, 0, 0] [5118, -1080, 0, 0]] [[14271, -4575, 0, 0] [37809, -6384, 0, 0] [6516, -1914, 0, 0]] [[5118, -1080, 0, 0] [6516, -1914, 0, 0] [2088, -468, 0, 0]] > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > P1; Univariate Polynomial Ring in x over Rational Field > P1K := PolynomialRing(K); > P3K<[Z]> := PolynomialRing(K, 3); > Rpol := &+[Rlambda[i,j]*Z[i]*Z[j] : i,j in [1..3]]; > rand := func< | K!OK![Random(-5,5) : i in [1..4]]>; > rand(); 1/9*(2*lambda^3 - 9*lambda^2 + 45*lambda - 18) > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>; > try(); false > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>; > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>; > try(); false 1/9*(-4*lambda^3 - 15*lambda^2 + 27*lambda - 18) 1/3*(-lambda^3 - 2*lambda^2 + 6*lambda + 12) > repeat flag, r1, r2 := try(); until flag; [Interrupted] > rand := func< | K!OK![Random(-15,15) : i in [1..4]]>; > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>; > repeat flag, r1, r2 := try(); until flag; [Interrupted] > Rpol; lambda*Z[1]^2 + (2*lambda + 6)*Z[1]*Z[2] - 6*Z[1]*Z[3] + (-lambda + 6)*Z[2]^2 - 2*lambda*Z[2]*Z[3] + 9*Z[3]^2 > Rpol/lambda; Z[1]^2 + 1/99*(2*lambda^3 - 24*lambda^2 + 396)*Z[1]*Z[2] + 1/99*(-2*lambda^3 + 24*lambda^2 - 198)*Z[1]*Z[3] + 1/99*(2*lambda^3 - 24*lambda^2 + 99)*Z[2]^2 - 2*Z[2]*Z[3] + 1/33*(lambda^3 - 12*lambda^2 + 99)*Z[3]^2 > Rpol1 := Evaluate($1, [Z[1]-1/2*MonomialCoefficient($1,Z[1]*Z[2])*Z[2] > -1/2*MonomialCoefficient($1, Z[1]*Z[3])*Z[3], Z[2], Z[3]]); > Rpol1; Z[1]^2 + 1/99*(-lambda^3 + 9*lambda^2 + 36*lambda - 297)*Z[2]^2 + 1/99*(4*lambda^3 - 42*lambda^2 - 72*lambda + 198)*Z[2]*Z[3] + 1/99*(2*lambda^3 - 27*lambda^2 + 36*lambda + 198)*Z[3]^2 > Rpol1 := lambda*Rpol1; Rpol1; lambda*Z[1]^2 + 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99)*Z[2]^2 + 1/33*(2*lambda^3 - 24*lambda^2 - 66*lambda + 396)*Z[2]*Z[3] + 1/33*(-lambda^3 + 12*lambda^2 + 198)*Z[3]^2 > Rpol1 := lambda*Rpol1; Rpol1; lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + (-2*lambda^2 + 6*lambda + 18)*Z[2]*Z[3] + (9*lambda - 9)*Z[3]^2 > Rpol2 := Evaluate($1, [Z[1], Z[2] - 1/(2*MonomialCoefficient($1,Z[2]^2))* > MonomialCoefficient($1, Z[2]*Z[3])*Z[3], Z[3]]); > Rpol2; lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + 1/33*(4*lambda^3 - 33*lambda^2 + 198*lambda + 99)*Z[3]^2 > lambda*Rpol2; lambda^3*Z[1]^2 + (-2*lambda^3 - 9*lambda)*Z[2]^2 + 1/11*(5*lambda^3 + 66*lambda^2 - 99*lambda + 396)*Z[3]^2 > lambda^2*Rpol2; (12*lambda^3 - 99*lambda + 297)*Z[1]^2 + (-24*lambda^3 - 9*lambda^2 + 198*lambda - 594)*Z[2]^2 + 1/11*(126*lambda^3 - 99*lambda^2 - 99*lambda + 1485)*Z[3]^2 > (2*lambda^2+9)*Rpol2; (24*lambda^3 + 9*lambda^2 - 198*lambda + 594)*Z[1]^2 + (-48*lambda^3 - 36*lambda^2 + 396*lambda - 1269)*Z[2]^2 + (24*lambda^3 - 27*lambda^2 + 36*lambda + 297)*Z[3]^2 > Rpol3 := $1; > ideal; Ideal of OK Basis: [ 27 18 0 783] [ 0 27 0 54] [ 0 0 27 513] [ 0 0 0 3267] > Norm($1); 64304361 > Factorisation($1); [ <3, 12>, <11, 2> ] > ChangeUniverse(Coefficients(Rpol3), OK); [ [594, -198, 27, 216], [-1269, 396, -108, -432], [297, 36, -81, 216] ] > GCD(&cat[ChangeUniverse(Eltseq(c), Integers()) : c in $1]); 9 > Rpol3 := 1/9*Rpol3; > ideal; Ideal of OK Basis: [ 3 2 0 87] [ 0 3 0 6] [ 0 0 3 57] [ 0 0 0 363] > Norm($1); 9801 > Factorisation($1); [ <3, 4>, <11, 2> ] > ideal; Ideal of OK Basis: [ 3 2 0 87] [ 0 3 0 6] [ 0 0 3 57] [ 0 0 0 363] > flag, gen := IsPrincipal($1); flag; true > gen; [-48, 4, 12, -3] > Rpol3 := 1/gen*Rpol3; > Rpol3; 1/9*(5*lambda^3 - 60*lambda^2 + 198*lambda - 297)*Z[1]^2 + 1/9*(-13*lambda^3 + 165*lambda^2 - 549*lambda + 837)*Z[2]^2 + 1/9*(-10*lambda^3 + 171*lambda^2 - 603*lambda + 990)*Z[3]^2 > [Norm(c) : c in Coefficients(Rpol3)]; [ -3993, -131769, 38291 ] > [Factorisation(Integers()!n) : n in $1]; [ [ <3, 1>, <11, 3> ], [ <3, 2>, <11, 4> ], [ <11, 1>, <59, 2> ] ] > > > a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]); > ideal; Ideal of OK Two element generators: [-33, 22, -20, 5] [93, -61, 55, -13] > flag, gen := IsPrincipal($1); flag; true > a := a/gen; b := b/gen; c := c*gen; > ideal; Ideal of OK Two element generators: [77724, -48384, 41973, -8147] [-66, -3, 13, -1] > flag, gen := IsPrincipal($1); flag; true > b := b/gen; c := c/gen; a := a*gen; > ideal; Ideal of OK Two element generators: [-33, 22, -20, 5] [110, -67, 57, -10] > flag, gen := IsPrincipal($1); flag; true > a := a/gen; b := b*gen; c := c/gen; > ideal; Ideal of OK Two element generators: [126225, -78574, 68161, -13228] [-17468, 10844, -9385, 1795] > Norm($1); 121 > a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]); > ideal; Ideal of OK Basis: [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] > Factorisation(ideal); [ , , ] > flag, gen := IsPrincipal($1[2,1]); flag; true > a := a/gen^2; > IsIntegral(a); true > Factorisation(ideal); [ , ] > flag, rt := IsSquare(b); flag; false > Factorisation(ideal); [ , ] > flag, gen := IsPrincipal($1[1,1]*$1[2,1]^2); flag; true > b := b/gen^2; IsIntegral(b); true > IsUnit(b); true > b; 1/9*(-35203866485*lambda^3 + 544192313463*lambda^2 - 1881986216391*lambda + 3023310688146) > U, mU := UnitGroup(OK); > U; Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*U.1 = 0 > (OK!b) @@ mU; U.1 - U.2 + U.3 > Factorisation(ideal); [ , ] > flag, gen := IsPrincipal($1[2,1]); flag; true > c := c/gen^2; > IsIntegral(c); true > ideal; Ideal of OK Two element generators: [-435353142, 271003776, -235089137, 45623834] [97396574, -60628572, 52593801, -10206898] > flag, gen := IsPrincipal($1); flag; true > a := a*b; c := c*b; b := b/b; > a; 1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 + 4741581890375719065612*lambda - 7617098936772540178011) > c; 1/3*(-6614209165540654351*lambda^3 + 102244501724191609815*lambda^2 - 353593276101607037424*lambda + 568028778098368129917) > Factorisation(ideal); [ , ] > Norm(a); 33 > Norm(c); -11 > b; 1 > L := ext; > NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 202.77 Segmentation fault > DefiningPolynomial(K); x^4 - 12*x^3 + 99*x - 297 > lambda; lambda > MinimalPolynomial(lambda); x^4 - 12*x^3 + 99*x - 297 > OL := Integers(L); > NormEquation(OL, -OK!a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 202.98 Segmentation fault > SUnitGroup; Intrinsic 'SUnitGroup' Signatures: ( I) -> GrpAb, Map ( S) -> GrpAb, Map The group of s-units of the prime ideals given in the sequence S or the factorization of I ( S) -> GrpAb, Map The group of S-units as an Abelian group and the map into the function field > Labs := AbsoluteField(L); > OLabs := Integers(Labs); > ClassGroup(OLabs : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OLabs > ideal; Ideal of OK Two element generators: 88694600599454463649] -19842627496621963053] > I := ideal; > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..5]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1 ] > a; 1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 + 4741581890375719065612*lambda - 7617098936772540178011) > norms := $2; > Factorisation(ideal); [ , ] > p31 := $1[1,1]; p111 := $1[2,1]; > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > I; Principal Ideal of OLabs Generator: [1, 0, 0, 0, 0, 0, 0, 0] > ideal; Ideal of OK Two element generators: 88694600599454463649] -19842627496621963053] > flag, gen := IsPrincipal($1); flag; true > I := ideal; > I; Principal Ideal of OLabs Generator: [1, 0, 0, 0, 0, 0, 0, 0] > Norm($3); 1 > Factorisation(ideal); [ ] > I := ideal; > I; Principal Ideal of OLabs Generator: 97187721532932707077425300749268443936597, 0, 0, 0, 0] > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..8]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1, 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66), 1/3*(4*lambda^3 - 8*lambda^2 - 33*lambda + 147), 1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399) ] > norms := $1; > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > Tr1 := Matrix([[1, -(lambda+3)/lambda, 3/lambda], [0,1,0], [0,0,1]]); Tr1; [1 1/99*(-lambda^3 + 12*lambda^2 - 198) 1/99*(lambda^3 - 12*lambda^2 + 99)] [0 1 0] [0 0 1] > Tr1*Rlambda*Transpose(Tr1); [1/11*(2*lambda^3 - 19*lambda^2 - 82*lambda + 132) 1/33*(-2*lambda^3 + 24*lambda^2 + 66*lambda - 297) 1/11*(lambda^3 - 12*lambda^2 + 11*lambda + 99)] [1/33*(-2*lambda^3 + 24*lambda^2 + 66*lambda - 297) -lambda + 6 -lambda] [1/11*(lambda^3 - 12*lambda^2 + 11*lambda + 99) -lambda 9] > Transpose(Tr1)*Rlambda*Tr1; [lambda 0 0] [0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 1/33*(lambda^3 - 12*lambda^2 - 33*lambda + 198)] [0 1/33*(lambda^3 - 12*lambda^2 - 33*lambda + 198) 1/33*(-lambda^3 + 12*lambda^2 + 198)] > Tr2 := Matrix([[1,0,0], [0,1,-$1[2,3]/$1[2,2]], [0,0,1]]); Tr2; [1 0 0] [0 1 1/3267*(26*lambda^3 - 297*lambda^2 - 297*lambda + 2277)] [0 0 1] > Transpose(Tr2)*$2*Tr2; [lambda 0 0] [0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 0] [0 0 1/99*(lambda^3 - 99*lambda + 693)] > a,b,c := Explode([$1[i,i] : i in [1..3]]); > IsIntegral(b); false > IsIntegral(c); false > Denominator(b); 33 > Denominator(c); 99 > Factorisation(ideal); [ , , ] > flag, gen := IsPrincipal($1[1,1]*$1[3,1]); flag; true > c := c/gen; > flag, gen := IsPrincipal($2[2,1]); flag; true > flag, gen := IsPrincipal($3[1,1]*$3[3,1]); flag; true > c := c/gen; > Factorisation(ideal); [ ] > flag, gen := IsPrincipal($1[1,1]); flag; true > c := c*gen^2; > c; 1/9*(-25211*lambda^3 + 524037*lambda^2 - 1578888*lambda - 12770478) > Factorisation(ideal); [ , , , ] > flag, gen := IsPrincipal($1[1,1]*$1[2,1]*$1[4,1]); flag; true > b := b/gen^2; > Factorisation(ideal); [ , ] > flag, gen := IsPrincipal($1[1,1]); flag; true > b := b*gen^2; > Factorisation(ideal); [ , , ] > flag, gen := IsPrincipal($1[2,1]); flag; true > a := a/gen^2; > Factorisation(ideal); [ , ] > Factorisation(ideal); [ , ] > Factorisation(ideal); [ ] > flag, gen := IsPrincipal($1[1,1]); flag; true > c := c/gen; b := b/gen; a := a*gen; > c; 1/9*(-12910*lambda^3 + 73386*lambda^2 + 747855*lambda + 1174653) > IsUnit(c); true > a := a/c; b := b/c; c := c/c; > a; 1/9*(11768733070573612150898*lambda^3 - 6565975199446345850085*lambda^2 - 75128433793103508474861*lambda + 305478792168156995505975) > b; 1/3*(-lambda^3 + 9*lambda^2 + 24*lambda - 66) > L := ext; > NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 289.15 Segmentation fault > Factorisation(ideal); [ , , ] > Labs := AbsoluteField(L); > OLabs := Integers(Labs); > OL := Integers(L); > ClassGroup(OLabs : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OLabs > I := ideal; > I; Principal Ideal of OLabs Generator: 81061059655244371456034, -435877053076387089543350, 0, 0, 0, 0] > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..8]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666), 1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666), 1, 124*lambda^3 - 1075*lambda^2 - 4228*lambda + 3364, 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66), 1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399) ] > norms := $1; > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > ClassGroup(OK : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OK > ideal; Ideal of OK Two element generators: 11768733070573612150898] [-22, 8, 9, -3] > Factorisation($1); [ ] > flag, gen := IsPrincipal($2); flag; true > a := a/gen; b := b/gen; c := c*gen; > ideal; Ideal of OK Two element generators: [-1, 0, 0, 0] 317757210900264194558] > Norm($1); 1 > $2 eq ideal; true > ideal; Ideal of OK Two element generators: 317757210900264194558] [22, -8, -9, 3] > $1 eq ideal; true > ideal; Ideal of OK Two element generators: [-1, 0, 0, 0] [22, -8, -9, 3] > $1 eq ideal; true > c; 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66) > b; -1 > a; 1/9*(317757210900264194558*lambda^3 - 177282073464141075450*lambda^2 - 2028476957468286393567*lambda + 8247964555766062942857) > Factorisation(ideal); [ , ] > Factorisation(ideal); [ ] > p3 := $2[1,1]; p11a := $2[2,1]; p11b := $1[1,1]; > F3, mF3 := ResidueClassField(p3); > IsSquare(mF3(c)); true 1 > F11a, mF11a := ResidueClassField(p11a); > IsSquare(mF11a(c)); true 9 > F11b, mF11b := ResidueClassField(p11b); > IsSquare(mF11b(a)); true 1 > Conjugates(a); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:41:10 2003 Input: > Q:=Rationals(); R:=PolynomialRing(Q) P:= Output: Magma V2.10-6 Wed Dec 3 2003 10:41:07 on modular [Seed = 1220113180] ------------------------------------- >> P:=; ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:41:34 2003 Input: P4<[z]> := PolynomialRing(Rationals(), 4); D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; Q2mat := func; M1 := Q2mat(D1);> M2 := Q2mat(D2); M1; [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] > M2; [ 1 0 1 -1] [ 0 1 1 0] [ 1 1 -1 -1] [-1 0 -1 0] > P1 := PolynomialRing(Rationals()); > Determinant(x*ChangeRing(M1,P1) + ChangeRing(M2,P1)); -11*x^4 + 11*x^3 - 12*x + 3 > Reduce($1); 3*x^4 - 18*x^2 + 13*x - 9 [ 0 -1] [ 1 -1] > Determinant(ChangeRing(M1,P1) + x*ChangeRing(M2,P1)); 3*x^4 - 12*x^3 + 11*x - 11 > g := 27*Evaluate($1, x/3); g; x^4 - 12*x^3 + 99*x - 297 > K := NumberField(g); > Mlambda := ChangeRing(M1, K) + lambda/3*ChangeRing(M2, K); Mlambda; [ 1/3*(lambda + 3) 1 1/3*lambda -1/3*lambda] [ 1 1/3*lambda 1/3*(lambda + 3) -1] [ 1/3*lambda 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ -1/3*lambda -1 -1/3*lambda 3] > Determinant(Mlambda); 0 > Kernel(Mlambda); Vector space of degree 4, dimension 1 over K Echelonized basis: (1 1/1947*(17*lambda^3 - 110*lambda^2 - 990*lambda + 561) 1/5841*(-65*lambda^3 + 726*lambda^2 + 693*lambda - 6039) 1/531*(lambda^3 - 3*lambda^2 - 27*lambda - 144)) > node := Eltseq(Basis($1)[1]); > node := Eltseq(1947*Basis($1)[1]); > node; [ 1947, 17*lambda^3 - 110*lambda^2 - 990*lambda + 561, 1/3*(-65*lambda^3 + 726*lambda^2 + 693*lambda - 6039), 1/3*(11*lambda^3 - 33*lambda^2 - 297*lambda - 1584) ] > T := Matrix([node, [0,1,0,0], [0,0,1,0], [0,0,0,1]]); > T*Mlambda*Transpose(T); [ 0 0 0 0] [ 0 1/3*lambda 1/3*(lambda + 3) -1] [ 0 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ 0 -1 -1/3*lambda 3] > Rlambda := Submatrix($1, 2,2, 3,3); Rlambda; [ 1/3*lambda 1/3*(lambda + 3) -1] [ 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ -1 -1/3*lambda 3] > Determinant($1); 1/27*(-lambda^3 - 12*lambda^2 + 27*lambda - 135) > Norm($1); 421201/27 > Factorisation(Numerator($1)); [ <11, 2>, <59, 2> ] > Rlambda *:= 3; > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > Determinant($1); -lambda^3 - 12*lambda^2 + 27*lambda - 135 > Norm($1); 8290499283 > Factorisation(Integers()!($1)); [ <3, 9>, <11, 2>, <59, 2> ] > OK := Integers(K); > [K | b : b in Basis(OK)]; [ 1, lambda, 1/3*lambda^2, 1/9*lambda^3 ] > Decomposition(OK, 3); [ , ] > p31 := $1[1,1]; p32 := $1[2,1]; > Decomposition(OK, 11); [ , ] > p111 := $1[1,1]; p112 := $1[1,2]; > Decomposition(OK, 59); [ , , ] > p591 := $1[1,1]; p592 := $1[2,1]; p593 := $1[3,1]; > RlO := ChangeRing(Rlambda, OK); > RlO; [[0, 1, 0, 0] [3, 1, 0, 0] [-3, 0, 0, 0]] [[3, 1, 0, 0] [6, -1, 0, 0] [0, -1, 0, 0]] [[-3, 0, 0, 0] [0, -1, 0, 0] [9, 0, 0, 0]] > p31; Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] > p32; Prime Ideal of OK Basis: [1 0 0 2] [0 1 0 0] [0 0 1 0] [0 0 0 3] > p111; Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0] > p112; 3 > Decomposition(OK, 11); [ , ] > p111 := $1[1,1]; p112 := $1[2,1]; > pl := [p31, p32, p111, p112, p591, p592,p593]; > det := Determinant(RlO); > [Valuation(det, p) : p in pl]; [ 3, 6, 0, 2, 2, 0, 0 ] > pl1 := [pl[i] : i in [1..#pl] | $1[i] ne 0]; #pl1; 4 > pl1[4]; Prime Ideal of OK Two element generators: [59, 0, 0, 0] [50, 1, 0, 0] > F4, m4 := ResidueClassField(pl1[4]); > RlO4 := Matrix(3, [m4(c) : c in Eltseq(RlO)]); > RlO4; [ 9 12 56] [12 56 50] [56 50 9] > Kernel($1); Vector space of degree 3, dimension 1 over GF(59) Echelonized basis: ( 1 45 6) > T1 := Matrix([Eltseq(Basis($1)[1]), [0,1,0], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 56 50] [ 0 50 9] > PF := PolynomialRing(F4); > Factorisation($1[2,2]*u^2 + 2*$1[2,3]*u + $1[3,3]); [ , ] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 54 2] [ 0 2 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 39 39] [ 0 39 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]); > T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,0,1]])*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 54 2] [ 0 2 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,1,-40]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 54 24] [ 0 24 13] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,1,40]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 39 34] [ 0 34 48] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]); > T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,1,-40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 5 7] [ 0 7 30] > T2 := Matrix(F4, [[1,0,0], [0,1,25], [0,1,40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 5 52] [ 0 52 30] > T2 := Matrix(F4, [[1,0,0], [0,1,1], [0,25,40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 0 28] [ 0 28 0] > T2l := Matrix(3, [c @@ m4 : c in Eltseq(T2)]); > T2l; [[1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]] [[0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]] [[0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]] > T2b := Matrix(OK, [[1,0,0,0]] cat [[0] cat Eltseq(T2l[i]) : i in [1..3]]); > T2b; [[1, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0]] [[0, 0, 0, 0] [1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]] [[0, 0, 0, 0] [0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]] [[0, 0, 0, 0] [0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]] > Rnew1 := T2l*RlO*Transpose(T2l); > Rnew1; [[12708, -2474, 0, 0] [14271, -4575, 0, 0] [5118, -1080, 0, 0]] [[14271, -4575, 0, 0] [37809, -6384, 0, 0] [6516, -1914, 0, 0]] [[5118, -1080, 0, 0] [6516, -1914, 0, 0] [2088, -468, 0, 0]] > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > P1; Univariate Polynomial Ring in x over Rational Field > P1K := PolynomialRing(K); > P3K<[Z]> := PolynomialRing(K, 3); > Rpol := &+[Rlambda[i,j]*Z[i]*Z[j] : i,j in [1..3]]; > rand := func< | K!OK![Random(-5,5) : i in [1..4]]>; > rand(); 1/9*(2*lambda^3 - 9*lambda^2 + 45*lambda - 18) > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>; > try(); false > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>; > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>; > try(); false 1/9*(-4*lambda^3 - 15*lambda^2 + 27*lambda - 18) 1/3*(-lambda^3 - 2*lambda^2 + 6*lambda + 12) > repeat flag, r1, r2 := try(); until flag; [Interrupted] > rand := func< | K!OK![Random(-15,15) : i in [1..4]]>; > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>; > repeat flag, r1, r2 := try(); until flag; [Interrupted] > Rpol; lambda*Z[1]^2 + (2*lambda + 6)*Z[1]*Z[2] - 6*Z[1]*Z[3] + (-lambda + 6)*Z[2]^2 - 2*lambda*Z[2]*Z[3] + 9*Z[3]^2 > Rpol/lambda; Z[1]^2 + 1/99*(2*lambda^3 - 24*lambda^2 + 396)*Z[1]*Z[2] + 1/99*(-2*lambda^3 + 24*lambda^2 - 198)*Z[1]*Z[3] + 1/99*(2*lambda^3 - 24*lambda^2 + 99)*Z[2]^2 - 2*Z[2]*Z[3] + 1/33*(lambda^3 - 12*lambda^2 + 99)*Z[3]^2 > Rpol1 := Evaluate($1, [Z[1]-1/2*MonomialCoefficient($1,Z[1]*Z[2])*Z[2] > -1/2*MonomialCoefficient($1, Z[1]*Z[3])*Z[3], Z[2], Z[3]]); > Rpol1; Z[1]^2 + 1/99*(-lambda^3 + 9*lambda^2 + 36*lambda - 297)*Z[2]^2 + 1/99*(4*lambda^3 - 42*lambda^2 - 72*lambda + 198)*Z[2]*Z[3] + 1/99*(2*lambda^3 - 27*lambda^2 + 36*lambda + 198)*Z[3]^2 > Rpol1 := lambda*Rpol1; Rpol1; lambda*Z[1]^2 + 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99)*Z[2]^2 + 1/33*(2*lambda^3 - 24*lambda^2 - 66*lambda + 396)*Z[2]*Z[3] + 1/33*(-lambda^3 + 12*lambda^2 + 198)*Z[3]^2 > Rpol1 := lambda*Rpol1; Rpol1; lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + (-2*lambda^2 + 6*lambda + 18)*Z[2]*Z[3] + (9*lambda - 9)*Z[3]^2 > Rpol2 := Evaluate($1, [Z[1], Z[2] - 1/(2*MonomialCoefficient($1,Z[2]^2))* > MonomialCoefficient($1, Z[2]*Z[3])*Z[3], Z[3]]); > Rpol2; lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + 1/33*(4*lambda^3 - 33*lambda^2 + 198*lambda + 99)*Z[3]^2 > lambda*Rpol2; lambda^3*Z[1]^2 + (-2*lambda^3 - 9*lambda)*Z[2]^2 + 1/11*(5*lambda^3 + 66*lambda^2 - 99*lambda + 396)*Z[3]^2 > lambda^2*Rpol2; (12*lambda^3 - 99*lambda + 297)*Z[1]^2 + (-24*lambda^3 - 9*lambda^2 + 198*lambda - 594)*Z[2]^2 + 1/11*(126*lambda^3 - 99*lambda^2 - 99*lambda + 1485)*Z[3]^2 > (2*lambda^2+9)*Rpol2; (24*lambda^3 + 9*lambda^2 - 198*lambda + 594)*Z[1]^2 + (-48*lambda^3 - 36*lambda^2 + 396*lambda - 1269)*Z[2]^2 + (24*lambda^3 - 27*lambda^2 + 36*lambda + 297)*Z[3]^2 > Rpol3 := $1; > ideal; Ideal of OK Basis: [ 27 18 0 783] [ 0 27 0 54] [ 0 0 27 513] [ 0 0 0 3267] > Norm($1); 64304361 > Factorisation($1); [ <3, 12>, <11, 2> ] > ChangeUniverse(Coefficients(Rpol3), OK); [ [594, -198, 27, 216], [-1269, 396, -108, -432], [297, 36, -81, 216] ] > GCD(&cat[ChangeUniverse(Eltseq(c), Integers()) : c in $1]); 9 > Rpol3 := 1/9*Rpol3; > ideal; Ideal of OK Basis: [ 3 2 0 87] [ 0 3 0 6] [ 0 0 3 57] [ 0 0 0 363] > Norm($1); 9801 > Factorisation($1); [ <3, 4>, <11, 2> ] > ideal; Ideal of OK Basis: [ 3 2 0 87] [ 0 3 0 6] [ 0 0 3 57] [ 0 0 0 363] > flag, gen := IsPrincipal($1); flag; true > gen; [-48, 4, 12, -3] > Rpol3 := 1/gen*Rpol3; > Rpol3; 1/9*(5*lambda^3 - 60*lambda^2 + 198*lambda - 297)*Z[1]^2 + 1/9*(-13*lambda^3 + 165*lambda^2 - 549*lambda + 837)*Z[2]^2 + 1/9*(-10*lambda^3 + 171*lambda^2 - 603*lambda + 990)*Z[3]^2 > [Norm(c) : c in Coefficients(Rpol3)]; [ -3993, -131769, 38291 ] > [Factorisation(Integers()!n) : n in $1]; [ [ <3, 1>, <11, 3> ], [ <3, 2>, <11, 4> ], [ <11, 1>, <59, 2> ] ] > > > a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]); > ideal; Ideal of OK Two element generators: [-33, 22, -20, 5] [93, -61, 55, -13] > flag, gen := IsPrincipal($1); flag; true > a := a/gen; b := b/gen; c := c*gen; > ideal; Ideal of OK Two element generators: [77724, -48384, 41973, -8147] [-66, -3, 13, -1] > flag, gen := IsPrincipal($1); flag; true > b := b/gen; c := c/gen; a := a*gen; > ideal; Ideal of OK Two element generators: [-33, 22, -20, 5] [110, -67, 57, -10] > flag, gen := IsPrincipal($1); flag; true > a := a/gen; b := b*gen; c := c/gen; > ideal; Ideal of OK Two element generators: [126225, -78574, 68161, -13228] [-17468, 10844, -9385, 1795] > Norm($1); 121 > a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]); > ideal; Ideal of OK Basis: [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] > Factorisation(ideal); [ , , ] > flag, gen := IsPrincipal($1[2,1]); flag; true > a := a/gen^2; > IsIntegral(a); true > Factorisation(ideal); [ , ] > flag, rt := IsSquare(b); flag; false > Factorisation(ideal); [ , ] > flag, gen := IsPrincipal($1[1,1]*$1[2,1]^2); flag; true > b := b/gen^2; IsIntegral(b); true > IsUnit(b); true > b; 1/9*(-35203866485*lambda^3 + 544192313463*lambda^2 - 1881986216391*lambda + 3023310688146) > U, mU := UnitGroup(OK); > U; Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*U.1 = 0 > (OK!b) @@ mU; U.1 - U.2 + U.3 > Factorisation(ideal); [ , ] > flag, gen := IsPrincipal($1[2,1]); flag; true > c := c/gen^2; > IsIntegral(c); true > ideal; Ideal of OK Two element generators: [-435353142, 271003776, -235089137, 45623834] [97396574, -60628572, 52593801, -10206898] > flag, gen := IsPrincipal($1); flag; true > a := a*b; c := c*b; b := b/b; > a; 1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 + 4741581890375719065612*lambda - 7617098936772540178011) > c; 1/3*(-6614209165540654351*lambda^3 + 102244501724191609815*lambda^2 - 353593276101607037424*lambda + 568028778098368129917) > Factorisation(ideal); [ , ] > Norm(a); 33 > Norm(c); -11 > b; 1 > L := ext; > NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 202.77 Segmentation fault > DefiningPolynomial(K); x^4 - 12*x^3 + 99*x - 297 > lambda; lambda > MinimalPolynomial(lambda); x^4 - 12*x^3 + 99*x - 297 > OL := Integers(L); > NormEquation(OL, -OK!a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 202.98 Segmentation fault > SUnitGroup; Intrinsic 'SUnitGroup' Signatures: ( I) -> GrpAb, Map ( S) -> GrpAb, Map The group of s-units of the prime ideals given in the sequence S or the factorization of I ( S) -> GrpAb, Map The group of S-units as an Abelian group and the map into the function field > Labs := AbsoluteField(L); > OLabs := Integers(Labs); > ClassGroup(OLabs : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OLabs > ideal; Ideal of OK Two element generators: 88694600599454463649] -19842627496621963053] > I := ideal; > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..5]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1 ] > a; 1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 + 4741581890375719065612*lambda - 7617098936772540178011) > norms := $2; > Factorisation(ideal); [ , ] > p31 := $1[1,1]; p111 := $1[2,1]; > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > I; Principal Ideal of OLabs Generator: [1, 0, 0, 0, 0, 0, 0, 0] > ideal; Ideal of OK Two element generators: 88694600599454463649] -19842627496621963053] > flag, gen := IsPrincipal($1); flag; true > I := ideal; > I; Principal Ideal of OLabs Generator: [1, 0, 0, 0, 0, 0, 0, 0] > Norm($3); 1 > Factorisation(ideal); [ ] > I := ideal; > I; Principal Ideal of OLabs Generator: 97187721532932707077425300749268443936597, 0, 0, 0, 0] > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..8]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1, 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66), 1/3*(4*lambda^3 - 8*lambda^2 - 33*lambda + 147), 1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399) ] > norms := $1; > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > Tr1 := Matrix([[1, -(lambda+3)/lambda, 3/lambda], [0,1,0], [0,0,1]]); Tr1; [1 1/99*(-lambda^3 + 12*lambda^2 - 198) 1/99*(lambda^3 - 12*lambda^2 + 99)] [0 1 0] [0 0 1] > Tr1*Rlambda*Transpose(Tr1); [1/11*(2*lambda^3 - 19*lambda^2 - 82*lambda + 132) 1/33*(-2*lambda^3 + 24*lambda^2 + 66*lambda - 297) 1/11*(lambda^3 - 12*lambda^2 + 11*lambda + 99)] [1/33*(-2*lambda^3 + 24*lambda^2 + 66*lambda - 297) -lambda + 6 -lambda] [1/11*(lambda^3 - 12*lambda^2 + 11*lambda + 99) -lambda 9] > Transpose(Tr1)*Rlambda*Tr1; [lambda 0 0] [0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 1/33*(lambda^3 - 12*lambda^2 - 33*lambda + 198)] [0 1/33*(lambda^3 - 12*lambda^2 - 33*lambda + 198) 1/33*(-lambda^3 + 12*lambda^2 + 198)] > Tr2 := Matrix([[1,0,0], [0,1,-$1[2,3]/$1[2,2]], [0,0,1]]); Tr2; [1 0 0] [0 1 1/3267*(26*lambda^3 - 297*lambda^2 - 297*lambda + 2277)] [0 0 1] > Transpose(Tr2)*$2*Tr2; [lambda 0 0] [0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 0] [0 0 1/99*(lambda^3 - 99*lambda + 693)] > a,b,c := Explode([$1[i,i] : i in [1..3]]); > IsIntegral(b); false > IsIntegral(c); false > Denominator(b); 33 > Denominator(c); 99 > Factorisation(ideal); [ , , ] > flag, gen := IsPrincipal($1[1,1]*$1[3,1]); flag; true > c := c/gen; > flag, gen := IsPrincipal($2[2,1]); flag; true > flag, gen := IsPrincipal($3[1,1]*$3[3,1]); flag; true > c := c/gen; > Factorisation(ideal); [ ] > flag, gen := IsPrincipal($1[1,1]); flag; true > c := c*gen^2; > c; 1/9*(-25211*lambda^3 + 524037*lambda^2 - 1578888*lambda - 12770478) > Factorisation(ideal); [ , , , ] > flag, gen := IsPrincipal($1[1,1]*$1[2,1]*$1[4,1]); flag; true > b := b/gen^2; > Factorisation(ideal); [ , ] > flag, gen := IsPrincipal($1[1,1]); flag; true > b := b*gen^2; > Factorisation(ideal); [ , , ] > flag, gen := IsPrincipal($1[2,1]); flag; true > a := a/gen^2; > Factorisation(ideal); [ , ] > Factorisation(ideal); [ , ] > Factorisation(ideal); [ ] > flag, gen := IsPrincipal($1[1,1]); flag; true > c := c/gen; b := b/gen; a := a*gen; > c; 1/9*(-12910*lambda^3 + 73386*lambda^2 + 747855*lambda + 1174653) > IsUnit(c); true > a := a/c; b := b/c; c := c/c; > a; 1/9*(11768733070573612150898*lambda^3 - 6565975199446345850085*lambda^2 - 75128433793103508474861*lambda + 305478792168156995505975) > b; 1/3*(-lambda^3 + 9*lambda^2 + 24*lambda - 66) > L := ext; > NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 289.15 Segmentation fault > Factorisation(ideal); [ , , ] > Labs := AbsoluteField(L); > OLabs := Integers(Labs); > OL := Integers(L); > ClassGroup(OLabs : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OLabs > I := ideal; > I; Principal Ideal of OLabs Generator: 81061059655244371456034, -435877053076387089543350, 0, 0, 0, 0] > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..8]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666), 1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666), 1, 124*lambda^3 - 1075*lambda^2 - 4228*lambda + 3364, 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66), 1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399) ] > norms := $1; > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > Factorisation(ideal); [ ] > ClassGroup(OK : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OK > ideal; Ideal of OK Two element generators: 11768733070573612150898] [-22, 8, 9, -3] > Factorisation($1); [ ] > flag, gen := IsPrincipal($2); flag; true > a := a/gen; b := b/gen; c := c*gen; > ideal; Ideal of OK Two element generators: [-1, 0, 0, 0] 317757210900264194558] > Norm($1); 1 > $2 eq ideal; true > ideal; Ideal of OK Two element generators: 317757210900264194558] [22, -8, -9, 3] > $1 eq ideal; true > ideal; Ideal of OK Two element generators: [-1, 0, 0, 0] [22, -8, -9, 3] > $1 eq ideal; true > c; 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66) > b; -1 > a; 1/9*(317757210900264194558*lambda^3 - 177282073464141075450*lambda^2 - 2028476957468286393567*lambda + 8247964555766062942857) > Factorisation(ideal); [ , ] > Factorisation(ideal); [ ] > p3 := $2[1,1]; p11a := $2[2,1]; p11b := $1[1,1]; > F3, mF3 := ResidueClassField(p3); > IsSquare(mF3(c)); true 1 > F11a, mF11a := ResidueClassField(p11a); > IsSquare(mF11a(c)); true 9 > F11b, mF11b := ResidueClassField(p11b); > IsSquare(mF11b(a)); true 1 > Conjugates(a); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:41:40 2003 Input: > Q:=Rationals(); R:=PolynomialRing(Q) P:=x^2 Output: Magma V2.10-6 Wed Dec 3 2003 10:41:37 on modular [Seed = 1872647193] ------------------------------------- >> P:=x^2; ^ User error: bad syntax Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:41:56 2003 Input: P4<[z]> := PolynomialRing(Rationals(), 4); D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; Q2mat := func; M1 := Q2mat(D1);> M2 := Q2mat(D2); M1; Output: Magma V2.10-6 Wed Dec 3 2003 10:41:53 on modular [Seed = 2005290097] ------------------------------------- >> M1 := Q2mat(D1);> M2 := Q2mat(D2); ^ User error: bad syntax [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:42:03 2003 Input: > Q:=Rationals(); R:=PolynomialRing(Q); P:=x^2 Output: Magma V2.10-6 Wed Dec 3 2003 10:42:00 on modular [Seed = 2140030064] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:42:16 2003 Input: > Q:=Rationals(); R:=PolynomialRing(Q); P:=x^2; P Output: Magma V2.10-6 Wed Dec 3 2003 10:42:13 on modular [Seed = 133577749] ------------------------------------- x^2 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:42:31 2003 Input: > Q:=Rationals(); R:=PolynomialRing(Q); > P:=x^2; P Output: Magma V2.10-6 Wed Dec 3 2003 10:42:27 on modular [Seed = 251606314] ------------------------------------- x^2 Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:56:38 2003 Input: > SetVerbose("Factorization", true); > SetVerbose("MPQS", true); > n := 279227912220351686582028455516412641158896790659830288566001946957408; > time Factorization(n); Output: Magma V2.10-6 Wed Dec 3 2003 10:56:24 on modular [Seed = 719000261] ------------------------------------- Integer main factorization (primality of factors will be proved) Seed: 1 Number: 2792279122203516865820284555164126411588967906598302885660019469574\ 08 Trial Division Number: 2792279122203516865820284555164126411588967906598302885660019469574\ 08 Minimum: 2 Maximum: 10000 Factors found: <2, 5> <3, 2> <61, 1> Time: 0.000 Pollard Rho Trials: 8191 Number: 15894120686495428425661911174659189501303323694207097482126704631 (65 digits) Factor: 1234577 (7 digits) Cofactor: 12874142873628318384079657384399020475274789417109744861703 (59 digits) Time: 0.039 Pollard Rho Trials: 8191 Number: 12874142873628318384079657384399020475274789417109744861703 (59 digits) No factor found Time: 0.069 1 composite number remaining ECM x: 12874142873628318384079657384399020475274789417109744861703 (59 digits) Initial smoothness: 500, steps: 14, step size: 285 Step 1/14; smoothness: 500, digits: 59, elapsed time: 0.000 Step 2/14; smoothness: 785, digits: 59, elapsed time: 0.330 Factor: 51030885799 (11 digits) Cofactor: 252281391397689588517339571105707909275219700897 (48 digits) Time: 0.780 ECM x: 252281391397689588517339571105707909275219700897 (48 digits) Initial smoothness: 785, steps: 10, step size: 100 Step 1/10; smoothness: 785, digits: 48, elapsed time: 0.000 Step 2/10; smoothness: 885, digits: 48, elapsed time: 0.359 Step 3/10; smoothness: 985, digits: 48, elapsed time: 0.709 Step 4/10; smoothness: 1085, digits: 48, elapsed time: 1.089 Step 5/10; smoothness: 1185, digits: 48, elapsed time: 1.489 Step 6/10; smoothness: 1285, digits: 48, elapsed time: 1.909 Step 7/10; smoothness: 1385, digits: 48, elapsed time: 2.359 Step 8/10; smoothness: 1485, digits: 48, elapsed time: 2.839 Step 9/10; smoothness: 1585, digits: 48, elapsed time: 3.339 Step 10/10; smoothness: 1685, digits: 48, elapsed time: 3.869 No factor found Time: 4.409 MPQS MPQS: 252281391397689588517339571105707909275219700897 (48d) 1042 factor base elements created in 0.010 seconds master completed initialization for /tmp/mqs30829: multiplier=1 sievelength=62464, sievesize=124928 one large prime will be used initialized global data in -0.000 seconds master ready to sieve master made own task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 8 total 100 fulls, 8 cycles, rate 0.018, need 966 more fulls+cycles another 894 fulls and 3872 partials and double partials should suffice 533 relations: 100 fulls, 433 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 35 new, 43 total 200 fulls, 43 cycles, rate 0.094, need 831 more fulls+cycles another 602 fulls and 2433 partials and double partials should suffice 1007 relations: 200 fulls, 807 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 47 new, 90 total 302 fulls, 90 cycles, rate 0.118, need 682 more fulls+cycles another 463 fulls and 1852 partials and double partials should suffice 1508 relations: 302 fulls, 1206 partials, 0 double partials initialized global data in 0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 57 new, 147 total 402 fulls, 147 cycles, rate 0.148, need 525 more fulls+cycles another 330 fulls and 1310 partials and double partials should suffice 1993 relations: 402 fulls, 1591 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 104 new, 251 total 503 fulls, 251 cycles, rate 0.223, need 320 more fulls+cycles another 167 fulls and 684 partials and double partials should suffice 2560 relations: 503 fulls, 2057 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 78 new, 329 total 603 fulls, 329 cycles, rate 0.222, need 142 more fulls+cycles another 75 fulls and 300 partials and double partials should suffice 3012 relations: 603 fulls, 2409 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate cycles: 76 new, 405 total 663 fulls, 405 cycles, rate 0.256, need 6 more fulls+cycles another 2 fulls and 11 partials and double partials should suffice 3369 relations: 663 fulls, 2706 partials, 0 double partials initialized global data in -0.000 seconds master ready to resume sieving with task 0 interrupt sieving: collect, count, try to factor if appropriate no need to count cycles sent termination signal to slaves, start factoring attempt made 405 cycle descriptions making combinations: 405 made used partials: 405 combined relations formed collecting from /tmp/mqs30829/f777mas: accepted 405 Lanczos call with seed 12 first scan: 1074 rows, 1028 columns>16, weight 9326 second scan complete, matrix read into memory Removed 59 singletons Removed 3 singletons all 62 singletons removed Got 947 by 1012 matrix with 8779 nonzeros in 0.040 seconds average of 9 nonzero entries per column Lanczos iteration 0, sum = 32, 915 to go Lanczos iterations done at i=31, sum=946, after 0.030 seconds Lanczos complete in 0.030 seconds, 17 dependencies factoring attempt dependency 1 produced 21905534578936053246671913391051 (32d) dependency 2 produced 6756504442031587 (16d) dependency 3 produced 11516787708996547 (17d) dependency 4 failed to produce a factor dependency 5 produced 11516787708996547 (17d) dependency 6 failed to produce a factor dependency 7 produced 6756504442031587 (16d) dependency 8 produced 3242140187559673 (16d) dependency 9 produced 37339040262931001600391513449131 (32d) dependency 10 produced 3242140187559673 (16d) dependency 11 produced 37339040262931001600391513449131 (32d) dependency 12 produced 6756504442031587 (16d) dependency 13 failed to produce a factor dependency 14 produced 77813227313769953941525847930089 (32d) dependency 15 failed to produce a factor dependency 16 produced 77813227313769953941525847930089 (32d) dependency 17 produced 37339040262931001600391513449131 (32d) done at 1065: 3803(1074,2729,0)(3398(669,2729,0)), 4.69(2.98,1.71), 0.001s/r MPQS time: 5.439 Factor 1: 6756504442031587 (16 digits) Factor 2: 3242140187559673 (16 digits) Factor 3: 11516787708996547 (17 digits) Total MPQS Time: 5.559 Total time: 10.859 [ <2, 5>, <3, 2>, <61, 1>, <1234577, 1>, <51030885799, 1>, <3242140187559673, 1>, <6756504442031587, 1>, <11516787708996547, 1> ] Time: 10.860 Total time: 13.839 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 11:02:48 2003 Input: > SetVerbose("Factorization", true); > SetVerbose("MPQS", true); > n := 279227912220351686582028455516412641158896790659830288566001946957408; > time Factorization(n); > b := 10^20; > for n in [b .. b + 100] do > s, x, y := NormEquation(1, n); > if s then > printf "%o = %o^2 + %o^2n", n, x, y; > end if; > end for; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 11:03:46 2003 Input: > d := func< m | DivisorSigma(1, m) - m >; > for m := 2 to 10000 do > n := d(m); > if d(n) eq m then > print m, n; > end if; > end for; Output: Magma V2.10-6 Wed Dec 3 2003 11:03:42 on modular [Seed = 3643338688] ------------------------------------- 6 6 28 28 220 284 284 220 496 496 1184 1210 1210 1184 2620 2924 2924 2620 5020 5564 5564 5020 6232 6368 6368 6232 8128 8128 Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 11:04:33 2003 Input: > d := func< m | DivisorSigma(1, m) - m >; > for m := 2 to 10000 do > n := d(m); > if d(n) eq m then > print m, n; > end if; > end for; > k := GF(2, 100); > P := PolynomialRing(k); > time Factorization(x^100 + x + 1); Output: Magma V2.10-6 Wed Dec 3 2003 11:04:29 on modular [Seed = 3775977259] ------------------------------------- 6 6 28 28 220 284 284 220 496 496 1184 1210 1210 1184 2620 2924 2924 2620 5020 5564 5564 5020 6232 6368 6368 6232 8128 8128 [ , , , ] Time: 0.120 Total time: 3.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl3-63-249-104-22.cruzio.com. (63.249.104.22) Time: Wed Dec 3 19:46:32 2003 Input: 3+2 Output: Magma V2.10-6 Wed Dec 3 2003 19:46:29 on modular [Seed = 1036812697] ------------------------------------- 5 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Dec 3 20:30:15 2003 Input: printf "%o",1; Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Dec 3 20:30:30 2003 Input: printf "%o",1; Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Dec 3 20:36:30 2003 Input: 1+1 Output: Magma V2.10-6 Wed Dec 3 2003 20:36:27 on modular [Seed = 1771624882] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Dec 3 20:36:39 2003 Input: printf "%o",2; Output: Magma V2.10-6 Wed Dec 3 2003 20:36:36 on modular [Seed = 1904263573] ------------------------------------- 2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Wed Dec 3 20:36:46 2003 Input: %s Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed. ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:06:07 2003 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(2749936217096833768575); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 02:06:04 on modular [Seed = 1904251543] ------------------------------------- [ x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167, x*y + 317*x + 18988427413535611858*y + 7168823795450084621, 495*x + 18988427413535611680*y + 17880669574151734350, y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949, 495*y^2 + 1107757839383877825*y + 7099394057680662045, 18988427413535612175 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <35159, 1>, <2430902559671, 1> ] [ x^2 + 6*x + y^2 + 5*y + 3, x*y + 9*x + 2*y + 7, y^3 + 3*y^2 + 7*y + 10 ] Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:09:02 2003 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(18988427413535612175); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 02:08:59 on modular [Seed = 1636860880] ------------------------------------- [ x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167, x*y + 317*x + 18988427413535611858*y + 7168823795450084621, 495*x + 18988427413535611680*y + 17880669574151734350, y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949, 495*y^2 + 1107757839383877825*y + 7099394057680662045, 18988427413535612175 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1> ] [ x^2 + 6*x + y^2 + 5*y + 3, x*y + 9*x + 2*y + 7, y^3 + 3*y^2 + 7*y + 10 ] Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:11:10 2003 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(18988427413535612175); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(47))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(1693))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(390357049))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 02:11:07 on modular [Seed = 1470543462] ------------------------------------- [ x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167, x*y + 317*x + 18988427413535611858*y + 7168823795450084621, 495*x + 18988427413535611680*y + 17880669574151734350, y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949, 495*y^2 + 1107757839383877825*y + 7099394057680662045, 18988427413535612175 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1> ] [ x^2 + 6*x + y^2 + 5*y + 3, x*y + 9*x + 2*y + 7, y^3 + 3*y^2 + 7*y + 10 ] [ x + 12*y, y^2 + 9 ] [ x + 18*y + 2, y^2 + 17*y + 7 ] [ x + 46*y + 12, y^2 + 35*y + 18 ] [ x + 1692*y + 1205, y^2 + 488*y + 680 ] [ x + 390357048*y + 86547272, y^2 + 303809777*y + 387394951 ] Total time: 2.939 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:13:23 2003 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(18988427413535612175); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Factorization( y^3 + 3*y^2 + 7*y + 10) Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(47))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(1693))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(390357049))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 02:13:20 on modular [Seed = 1085383146] ------------------------------------- [ x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167, x*y + 317*x + 18988427413535611858*y + 7168823795450084621, 495*x + 18988427413535611680*y + 17880669574151734350, y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949, 495*y^2 + 1107757839383877825*y + 7099394057680662045, 18988427413535612175 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1> ] [ x^2 + 6*x + y^2 + 5*y + 3, x*y + 9*x + 2*y + 7, y^3 + 3*y^2 + 7*y + 10 ] >> Bn:=GroebnerBasis(ChangeRing(I,GF(13))); ^ User error: bad syntax [ x^2 + 6*x + y^2 + 5*y + 3, x*y + 9*x + 2*y + 7, y^3 + 3*y^2 + 7*y + 10 ] [ x + 18*y + 2, y^2 + 17*y + 7 ] [ x + 46*y + 12, y^2 + 35*y + 18 ] [ x + 1692*y + 1205, y^2 + 488*y + 680 ] [ x + 390357048*y + 86547272, y^2 + 303809777*y + 387394951 ] Total time: 2.909 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:13:49 2003 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(18988427413535612175); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Factorization( y^3 + 3*y^2 + 7*y + 10); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(47))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(1693))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(390357049))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 02:13:44 on modular [Seed = 3108526123] ------------------------------------- [ x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167, x*y + 317*x + 18988427413535611858*y + 7168823795450084621, 495*x + 18988427413535611680*y + 17880669574151734350, y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949, 495*y^2 + 1107757839383877825*y + 7099394057680662045, 18988427413535612175 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1> ] [ x^2 + 6*x + y^2 + 5*y + 3, x*y + 9*x + 2*y + 7, y^3 + 3*y^2 + 7*y + 10 ] [ , ] [ x + 12*y, y^2 + 9 ] [ x + 18*y + 2, y^2 + 17*y + 7 ] [ x + 46*y + 12, y^2 + 35*y + 18 ] [ x + 1692*y + 1205, y^2 + 488*y + 680 ] [ x + 390357048*y + 86547272, y^2 + 303809777*y + 387394951 ] Total time: 2.989 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:20:53 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(9*x^2-4)*(9*x^2-1)*3*x-6*(4*x^2-4)*(4*x^2-1)*2*x+15*(x^2-4)*(x^2-1)*x; Output: Magma V2.10-6 Thu Dec 4 2003 02:20:50 on modular [Seed = 2523351550] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:21:04 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(9*x^2-4)*(9*x^2-1)*3*x-6*(4*x^2-4)*(4*x^2-1)*2*x+15*(x^2-4)*(x^2-1)*x; c; Output: Magma V2.10-6 Thu Dec 4 2003 02:21:01 on modular [Seed = 2390708713] ------------------------------------- 66*x^5 + 30*x^3 + 24*x Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:22:02 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(9*x^2-4)*(9*x^2-1)*3*x-6*(4*x^2-4)*(4*x^2-1)*2*x+15*(x^2-4)*(x^2-1)*x; c/120; Output: Magma V2.10-6 Thu Dec 4 2003 02:21:59 on modular [Seed = 4195034455] ------------------------------------- >> c/120;; ^ Runtime error in '/': Coefficient ring of argument 1 is not a field Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:25:10 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(16*x^2-9)*(16*x^2-4)*(16*x^2-1)*4*x-8*(9*x^2-9)*(9*x^2-4)*(9*x^2-1)*3*x+28*(4*x^2-9)*(4*x^2-4)*(4*x^2-1)*2*x-56*(x^2-9)*(x^2-4)*(x^2-1)*x; c; Output: Magma V2.10-6 Thu Dec 4 2003 02:25:07 on modular [Seed = 4093979293] ------------------------------------- 2416*x^7 + 1120*x^5 + 784*x^3 + 720*x Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:25:29 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(16*x^2-9)*(16*x^2-4)*(16*x^2-1)*4*x-8*(9*x^2-9)*(9*x^2-4)*(9*x^2-1)*3*x+28*(4*x^2-9)*(4*x^2-4)*(4*x^2-1)*2*x-56*(x^2-9)*(x^2-4)*(x^2-1)*x; c/16; Output: Magma V2.10-6 Thu Dec 4 2003 02:25:26 on modular [Seed = 3961336496] ------------------------------------- >> c/16;; ^ Runtime error in '/': Coefficient ring of argument 1 is not a field Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:25:54 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(16*x^2-9)*(16*x^2-4)*(16*x^2-1)*4*x-8*(9*x^2-9)*(9*x^2-4)*(9*x^2-1)*3*x+28*(4*x^2-9)*(4*x^2-4)*(4*x^2-1)*2*x-56*(x^2-9)*(x^2-4)*(x^2-1)*x; Factorization(c); Output: Magma V2.10-6 Thu Dec 4 2003 02:25:51 on modular [Seed = 3826596513] ------------------------------------- [ <2, 4>, , <151*x^6 + 70*x^4 + 49*x^2 + 45, 1> ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:27:39 2003 Input: P:=PolynomialRing(GF(11),2); c:=y^3 + 3*y^2 + 7*y + 10; Factorization(c); Output: Magma V2.10-6 Thu Dec 4 2003 02:27:36 on modular [Seed = 3491827202] ------------------------------------- [ , , ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:28:43 2003 Input: P:=PolynomialRing(GF(19),2); c:=y^2 + 17*y + 7; Factorization(c); Output: Magma V2.10-6 Thu Dec 4 2003 02:28:39 on modular [Seed = 3460240339] ------------------------------------- [ ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:29:40 2003 Input: P:=PolynomialRing(GF(47),2); c:=y^2 + 35*y + 18; Factorization(c); Output: Magma V2.10-6 Thu Dec 4 2003 02:29:37 on modular [Seed = 1003152995] ------------------------------------- [ , ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:30:29 2003 Input: P:=PolynomialRing(GF(1693),2); c:=y^2 + 488*y + 680; Factorization(c); Output: Magma V2.10-6 Thu Dec 4 2003 02:30:26 on modular [Seed = 685372803] ------------------------------------- [ , ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:31:23 2003 Input: P:=PolynomialRing(GF(390357049),2); c:=y^2 +303809777*y + 387394951 ; Factorization(c); Output: Magma V2.10-6 Thu Dec 4 2003 02:31:20 on modular [Seed = 601030354] ------------------------------------- [ , ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:34:26 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(8*x+7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1); Factorization(c); Output: Magma V2.10-6 Thu Dec 4 2003 02:34:23 on modular [Seed = 268358473] ------------------------------------- [ <8*x - 5, 1>, <8*x - 3, 1>, <8*x - 1, 1>, <8*x + 1, 1>, <8*x + 3, 1>, <8*x + 5, 1>, <8*x + 7, 1> ] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:34:44 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(8*x+7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 02:34:41 on modular [Seed = 133618607] ------------------------------------- 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:38:09 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(8*x+7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1)-8*(6*x+7)*(36*x^2-25)*(36*x^2-9)*(36*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 02:38:06 on modular [Seed = 1838986762] ------------------------------------- -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:40:08 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(8*x-7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1)-8*(6*x-7)*(36*x^2-25)*(36*x^2-9)*(36*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 02:40:05 on modular [Seed = 1571587761] ------------------------------------- -142336*x^7 + 777728*x^6 + 1030400*x^5 - 1536640*x^4 - 314944*x^3 + 406112*x^2 + 9000*x - 11025 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:40:56 2003 Input: P:=PolynomialRing(IntegerRing(),2); c:=(8*x-7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 02:40:53 on modular [Seed = 1420136040] ------------------------------------- 2097152*x^7 - 1835008*x^6 - 1146880*x^5 + 1003520*x^4 + 132608*x^3 - 116032*x^2 - 1800*x + 1575 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:44:48 2003 Input: P:=PolynomialRing(RationalField(),2); c:=x^6+y^6+(11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y))/40+(144*(x^5-y^5)-40*(x^3-y^3)+x-y)*18/1280+(144*(x^4+y^4)-20*(x^2+y^2)+1)*15/1280-128; c; Output: Magma V2.10-6 Thu Dec 4 2003 02:44:45 on modular [Seed = 1321178266] ------------------------------------- x^6 + 23/10*x^5 + 27/16*x^4 - 7/16*x^3 - 15/64*x^2 + 73/640*x + y^6 - 23/10*y^5 + 27/16*y^4 + 7/16*y^3 - 15/64*y^2 - 73/640*y - 32765/256 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:46:11 2003 Input: P:=PolynomialRing(RationalField(),2); c:=x^6+y^6+(11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y))/40+(144*(x^5-y^5)-40*(x^3-y^3)+x-y)*18/1280+(144*(x^4+y^4)-40*(x^2+y^2)+2)*15/1280-128; c; Output: Magma V2.10-6 Thu Dec 4 2003 02:46:09 on modular [Seed = 3125502914] ------------------------------------- x^6 + 23/10*x^5 + 27/16*x^4 - 7/16*x^3 - 15/32*x^2 + 73/640*x + y^6 - 23/10*y^5 + 27/16*y^4 + 7/16*y^3 - 15/32*y^2 - 73/640*y - 16381/128 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:46:34 2003 Input: P:=PolynomialRing(RationalField(),2); c:=x^6+y^6+(11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y))/40+(144*(x^5-y^5)-40*(x^3-y^3)+x-y)*18/1280+(144*(x^4+y^4)-40*(x^2+y^2)+2)*15/1280-128; 640*c; Output: Magma V2.10-6 Thu Dec 4 2003 02:46:31 on modular [Seed = 2990762972] ------------------------------------- 640*x^6 + 1472*x^5 + 1080*x^4 - 280*x^3 - 300*x^2 + 73*x + 640*y^6 - 1472*y^5 + 1080*y^4 + 280*y^3 - 300*y^2 - 73*y - 81905 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:58:21 2003 Input: P:=PolynomialRing(RationalField(),2); c:=(6*x+5)*(36*x^2-9)*(36*x^2-1); 640*c; Output: Magma V2.10-6 Thu Dec 4 2003 02:58:18 on modular [Seed = 2373737390] ------------------------------------- 4976640*x^5 + 4147200*x^4 - 1382400*x^3 - 1152000*x^2 + 34560*x + 28800 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 02:58:44 2003 Input: P:=PolynomialRing(RationalField(),2); c:=(6*x+5)*(36*x^2-9)*(36*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 02:58:41 on modular [Seed = 2222281356] ------------------------------------- 7776*x^5 + 6480*x^4 - 2160*x^3 - 1800*x^2 + 54*x + 45 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:04:57 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >A:=AutomorphismGroup(L); >#A; Output: Magma V2.10-6 Thu Dec 4 2003 03:04:54 on modular [Seed = 3626569031] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] 288 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:05:24 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >A:=AutomorphismGroup(L); >#A; Output: Magma V2.10-6 Thu Dec 4 2003 03:05:21 on modular [Seed = 3609592367] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] 288 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:06:55 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >G:=AutomorphismGroup(L); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:06:52 on modular [Seed = 3460242155] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] 288 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:09:13 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >F:=latticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]); >G:=AutomorphismGroup(L,[F]); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:09:10 on modular [Seed = 952757414] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> F:=latticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]); ^ User error: Identifier 'latticeWithGram' has not been declared or assigned >> G:=AutomorphismGroup(L,[F]); ^ User error: Identifier 'F' has not been declared or assigned >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:09:32 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >F:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]); >G:=AutomorphismGroup(L,[F]); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:09:29 on modular [Seed = 834725296] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> G:=AutomorphismGroup(L,[F]); ^ Runtime error in 'AutomorphismGroup': Universe of argument 2 is not a matrix structure >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:09:59 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >F:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]); >G:=AutomorphismGroup(L,F); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:09:56 on modular [Seed = 702086597] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> G:=AutomorphismGroup(L,F); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: Lat, Lat >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 03:10:54 2003 Input: P:=PolynomialRing(RationalField(),2); c:=(6*x+5)*(36*x^2-9)*(36*x^2-1)-6*(4*x+5)*(16*x^2-9)*(16*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 03:10:51 on modular [Seed = 417975083] ------------------------------------- 1632*x^5 - 1200*x^4 + 1680*x^3 + 3000*x^2 - 162*x - 225 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:11:32 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >F:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]); >F; >G:=AutomorphismGroup(L,F); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:11:29 on modular [Seed = 283231001] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 3 2] [2 2 2 2 2 3] >> G:=AutomorphismGroup(L,F); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: Lat, Lat >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 03:11:53 2003 Input: P:=PolynomialRing(RationalField(),2); c:=(6*x-5)*(36*x^2-9)*(36*x^2-1)-6*(4*x-5)*(16*x^2-9)*(16*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 03:11:50 on modular [Seed = 150592374] ------------------------------------- 1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:12:35 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; >F:=Gram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]); >F; >G:=AutomorphismGroup(L,F); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:12:32 on modular [Seed = 32559689] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> F:=Gram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]); ^ User error: Identifier 'Gram' has not been declared or assigned >> F; ^ User error: Identifier 'F' has not been declared or assigned >> G:=AutomorphismGroup(L,F); ^ User error: Identifier 'F' has not been declared or assigned >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 03:12:56 2003 Input: P:=PolynomialRing(RationalField(),2); c:=(6*x-5)*(36*x^2-9)*(36*x^2-1); c; Output: Magma V2.10-6 Thu Dec 4 2003 03:12:53 on modular [Seed = 2038999748] ------------------------------------- 7776*x^5 - 6480*x^4 - 2160*x^3 + 1800*x^2 + 54*x - 45 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:27:06 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; > Q := RationalField(); > A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0, >0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>; >G:=AutomorphismGroup(L,A); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:27:03 on modular [Seed = 1537903540] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0, >0,1,0,0,0,0,0,0,1,0,0,0,0,0,0 ^ User error: bad syntax >> G:=AutomorphismGroup(L,A); ^ User error: Identifier 'A' has not been declared or assigned >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:27:30 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; > Q := RationalField(); > A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0, 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>; >G:=AutomorphismGroup(L,A); >#G; Output: Magma V2.10-6 Thu Dec 4 2003 03:27:27 on modular [Seed = 1403159428] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> G:=AutomorphismGroup(L,A); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: Lat, AlgMat >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:30:49 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; > Q := RationalField(); > A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0, 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>; >G:=AutomorphismGroup(L,A); >#G; >AlgMatElt?; Output: Magma V2.10-6 Thu Dec 4 2003 03:30:46 on modular [Seed = 1152748490] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> G:=AutomorphismGroup(L,A); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: Lat, AlgMat >> #G; ^ User error: Identifier 'G' has not been declared or assigned >> AlgMatElt?; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Thu Dec 4 03:31:27 2003 Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]); >L; > Q := RationalField(); > A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0, 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>; >G:=AutomorphismGroup(L,A); >#G; >?AlgMatElt Output: Magma V2.10-6 Thu Dec 4 2003 03:31:24 on modular [Seed = 3175903833] ------------------------------------- Standard Lattice of rank 6 and degree 6 Inner Product Matrix: [4 1 2 2 2 2] [1 4 2 2 2 2] [2 2 4 1 1 2] [2 2 1 4 1 2] [2 2 1 1 4 2] [2 2 2 2 2 4] >> G:=AutomorphismGroup(L,A); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: Lat, AlgMat >> #G; ^ User error: Identifier 'G' has not been declared or assigned No references for word "AlgMatElt" Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 03:59:42 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Dec 4 2003 03:59:39 on modular [Seed = 2390705869] ------------------------------------- [ x - y, 4*y^2 - 16 ] Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 04:07:43 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Thu Dec 4 2003 04:07:39 on modular [Seed = 3995019395] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] Total time: 3.729 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host ms0303.math.uni-bonn.de. (131.220.120.238) Time: Thu Dec 4 04:07:44 2003 Input: ClassicalModularPolynomial(1) Output: Magma V2.10-6 Thu Dec 4 2003 04:07:39 on modular [Seed = 3775932300] ------------------------------------- $.1 + $.2 Total time: 3.909 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host ms0303.math.uni-bonn.de. (131.220.120.238) Time: Thu Dec 4 04:08:17 2003 Input: ClassicalModularPolynomial(2) Output: Magma V2.10-6 Thu Dec 4 2003 04:08:13 on modular [Seed = 3542226328] ------------------------------------- $.1^3 - $.1^2*$.2^2 + 1488*$.1^2*$.2 - 162000*$.1^2 + 1488*$.1*$.2^2 + 40773375*$.1*$.2 + 8748000000*$.1 + $.2^3 - 162000*$.2^2 + 8748000000*$.2 - 157464000000000 Total time: 3.489 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host ms0303.math.uni-bonn.de. (131.220.120.238) Time: Thu Dec 4 04:08:49 2003 Input: ClassicalModularPolynomial(1) Output: Magma V2.10-6 Thu Dec 4 2003 04:08:46 on modular [Seed = 634708878] ------------------------------------- $.1 + $.2 Total time: 3.009 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 04:09:34 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Output: Magma V2.10-6 Thu Dec 4 2003 04:09:31 on modular [Seed = 316921068] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 3.029 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 04:10:22 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Output: Magma V2.10-6 Thu Dec 4 2003 04:10:19 on modular [Seed = 49530060] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host ms0303.math.uni-bonn.de. (131.220.120.238) Time: Thu Dec 4 04:11:17 2003 Input: ClassicalModularPolynomial(2) Output: Magma V2.10-6 Thu Dec 4 2003 04:11:14 on modular [Seed = 184274701] ------------------------------------- $.1^3 - $.1^2*$.2^2 + 1488*$.1^2*$.2 - 162000*$.1^2 + 1488*$.1*$.2^2 + 40773375*$.1*$.2 + 8748000000*$.1 + $.2^3 - 162000*$.2^2 + 8748000000*$.2 - 157464000000000 Total time: 2.999 seconds, Total memory usage: 2.78MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 04:12:17 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 04:12:14 on modular [Seed = 1921234729] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 3.059 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:18:36 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Output: Magma V2.10-6 Thu Dec 4 2003 07:18:31 on modular [Seed = 3491809779] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 3.099 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:21:04 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:21:01 on modular [Seed = 3241269336] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 2.999 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:27:03 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:27:00 on modular [Seed = 817899287] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ 1 ] [ 1 ] [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 3.089 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:27:54 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:27:50 on modular [Seed = 1070540874] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ 1 ] [ 1 ] [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 3.129 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:28:48 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:28:45 on modular [Seed = 651571560] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 3.069 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:33:52 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:33:49 on modular [Seed = 350487178] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 2.979 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:34:24 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:34:21 on modular [Seed = 485231330] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 3.009 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:39:55 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:39:52 on modular [Seed = 234690854] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 363738371, 15*x + 14549520*y + 363738375, y^3 + 9*y^2 + 14549531*y + 363738339, 15*y^2 + 3011753685, 14549535*y + 363738375, 3011753745 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] Total time: 3.059 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:40:31 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:40:28 on modular [Seed = 2106419570] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 363738371, 15*x + 14549520*y + 363738375, y^3 + 9*y^2 + 14549531*y + 363738339, 15*y^2 + 3011753685, 14549535*y + 363738375, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] Total time: 3.059 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:41:24 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:41:20 on modular [Seed = 1704292646] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 363738371, 15*x + 14549520*y + 363738375, y^3 + 9*y^2 + 14549531*y + 363738339, 15*y^2 + 3011753685, 14549535*y + 363738375, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 2, y + 2 ] Total time: 3.049 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:45:06 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:45:03 on modular [Seed = 1470579755] ------------------------------------- [ x^2 + 8*x + y^2 + 203693482*y + 203693482, x*y + 2*x + 15*y^2 + 203693488*y + 203693426, 15*x + 203693475*y, 2*y^3 + 18*y^2 + 203693482*y + 203693418, 30*y^2 + 203693370, 203693490 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ 1 ] Total time: 3.069 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:45:46 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(203693490); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:45:43 on modular [Seed = 1605323803] ------------------------------------- [ x^2 + 8*x + y^2 + 203693482*y + 203693482, x*y + 2*x + 15*y^2 + 203693488*y + 203693426, 15*x + 203693475*y, 2*y^3 + 18*y^2 + 203693482*y + 203693418, 30*y^2 + 203693370, 203693490 ] [ <2, 1>, <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ 1 ] Total time: 2.969 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:46:26 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(203693490); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:46:22 on modular [Seed = 1203197162] ------------------------------------- [ x^2 + 8*x + y^2 + 203693482*y + 203693482, x*y + 2*x + 15*y^2 + 203693488*y + 203693426, 15*x + 203693475*y, 2*y^3 + 18*y^2 + 203693482*y + 203693418, 30*y^2 + 203693370, 203693490 ] [ <2, 1>, <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] Total time: 3.039 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:48:36 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(203693490); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:48:33 on modular [Seed = 1321098332] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <2, 1>, <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ 1 ] Total time: 3.029 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:49:30 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B;Factorization(6435); Factorization(765765); Output: Magma V2.10-6 Thu Dec 4 2003 07:49:27 on modular [Seed = 3041241041] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 2.949 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:49:55 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B;Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:49:52 on modular [Seed = 3159142143] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 3.049 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Dec 4 07:52:16 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Dec 4 2003 07:52:13 on modular [Seed = 2908602211] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 643496, 495*x + 5940*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 3.039 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 4 11:50:12 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print [N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [560..562] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Dec 4 2003 11:49:49 on modular [Seed = 3910775659] ------------------------------------- [ 11, 1, 2, $.1 + 2, 3, $.1 + 1, 5, $.1 - 1, 7, $.1 + 2, 11, $.1 - 1, 13, $.1 - 4 ] 560,1,2,x,3,x - 1,5,x + 1,7,x - 1,11,x - 5,13,x - 1[] 560,2,2,x,3,x - 3,5,x - 1,7,x + 1,11,x - 5,13,x + 5[] 560,3,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 3,13,x - 5[] 560,4,2,x,3,x,5,x + 1,7,x - 1,11,x + 4,13,x + 6[] 560,5,2,x,3,x + 3,5,x + 1,7,x - 1,11,x - 5,13,x + 3[] 560,6,2,x,3,x + 1,5,x - 1,7,x + 1,11,x + 3,13,x + 1[] 560,7,2,x^2,3,x^2 - x - 8,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 7*x + 4,13,x^2 - 3*x - 6[] 560,8,2,x^2,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - x - 4,13,x^2 - x - 38[] 560,9,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 - 5*x + 2[] 561,1,2,x,3,x + 1,5,x + 2,7,x + 3,11,x - 1,13,x - 2[] 561,2,2,x,3,x - 1,5,x + 2,7,x - 1,11,x - 1,13,x + 6[] 561,3,2,x + 2,3,x - 1,5,x,7,x + 3,11,x - 1,13,x + 4[] 561,4,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 1,13,x + 2[] 561,5,2,x^2 - x - 4,3,x^2 + 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - 2*x + 1,13,x^2 + 4*x + 4[] 561,6,2,x^2 - 2,3,x^2 - 2*x + 1,5,x^2 + 4*x + 2,7,x^2 + 6*x + 9,11,x^2 + 2*x + 1,13,x^2 - 18[] 561,7,2,x^3 + 2*x^2 - 2*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 2*x - 2,7,x^3 + x^2 - 5*x - 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 4*x^2 - 16*x - 10[] 561,8,2,x^3 - x^2 - 4*x + 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 2*x + 4,7,x^3 - 2*x^2 - 15*x + 32,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 8*x^2 + 6*x - 44[] 561,9,2,x^3 - 4*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 4*x^2 - 8*x - 34,7,x^3 + 7*x^2 + 7*x - 19,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 2*x^2 - 2*x + 2[] 561,10,2,x^4 - x^3 - 6*x^2 + 6*x + 2,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 4*x^3 - 4*x^2 - 22*x - 4,7,x^4 - 9*x^3 + 19*x^2 + 9*x - 16,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 - 10*x^3 + 22*x^2 + 22*x - 76[] 561,11,2,x^6 + x^5 - 11*x^4 - 9*x^3 + 32*x^2 + 20*x - 18,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 2*x^5 - 18*x^4 + 38*x^3 + 44*x^2 - 56*x - 48,7,x^6 - 7*x^5 + 3*x^4 + 51*x^3 - 60*x^2 - 48*x + 64,11,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 8*x^5 - 24*x^4 + 358*x^3 - 780*x^2 - 696*x + 2608[] Errors: /home/mfd/gomagma: line 2: 4294 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 4 11:50:59 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print [N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [560..561] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Thu Dec 4 2003 11:50:41 on modular [Seed = 4178158391] ------------------------------------- [ 11, 1, 2, $.1 + 2, 3, $.1 + 1, 5, $.1 - 1, 7, $.1 + 2, 11, $.1 - 1, 13, $.1 - 4 ] 560,1,2,x,3,x - 1,5,x + 1,7,x - 1,11,x - 5,13,x - 1[] 560,2,2,x,3,x - 3,5,x - 1,7,x + 1,11,x - 5,13,x + 5[] 560,3,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 3,13,x - 5[] 560,4,2,x,3,x,5,x + 1,7,x - 1,11,x + 4,13,x + 6[] 560,5,2,x,3,x + 3,5,x + 1,7,x - 1,11,x - 5,13,x + 3[] 560,6,2,x,3,x + 1,5,x - 1,7,x + 1,11,x + 3,13,x + 1[] 560,7,2,x^2,3,x^2 - x - 8,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 7*x + 4,13,x^2 - 3*x - 6[] 560,8,2,x^2,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - x - 4,13,x^2 - x - 38[] 560,9,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 - 5*x + 2[] 561,1,2,x,3,x + 1,5,x + 2,7,x + 3,11,x - 1,13,x - 2[] 561,2,2,x,3,x - 1,5,x + 2,7,x - 1,11,x - 1,13,x + 6[] 561,3,2,x + 2,3,x - 1,5,x,7,x + 3,11,x - 1,13,x + 4[] 561,4,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 1,13,x + 2[] 561,5,2,x^2 - x - 4,3,x^2 + 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - 2*x + 1,13,x^2 + 4*x + 4[] 561,6,2,x^2 - 2,3,x^2 - 2*x + 1,5,x^2 + 4*x + 2,7,x^2 + 6*x + 9,11,x^2 + 2*x + 1,13,x^2 - 18[] 561,7,2,x^3 + 2*x^2 - 2*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 2*x - 2,7,x^3 + x^2 - 5*x - 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 4*x^2 - 16*x - 10[] 561,8,2,x^3 - x^2 - 4*x + 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 2*x + 4,7,x^3 - 2*x^2 - 15*x + 32,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 8*x^2 + 6*x - 44[] 561,9,2,x^3 - 4*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 4*x^2 - 8*x - 34,7,x^3 + 7*x^2 + 7*x - 19,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 2*x^2 - 2*x + 2[] 561,10,2,x^4 - x^3 - 6*x^2 + 6*x + 2,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 4*x^3 - 4*x^2 - 22*x - 4,7,x^4 - 9*x^3 + 19*x^2 + 9*x - 16,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 - 10*x^3 + 22*x^2 + 22*x - 76[] 561,11,2,x^6 + x^5 - 11*x^4 - 9*x^3 + 32*x^2 + 20*x - 18,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 2*x^5 - 18*x^4 + 38*x^3 + 44*x^2 - 56*x - 48,7,x^6 - 7*x^5 + 3*x^4 + 51*x^3 - 60*x^2 - 48*x + 64,11,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 8*x^5 - 24*x^4 + 358*x^3 - 780*x^2 - 696*x + 2608[] Total time: 17.739 seconds, Total memory usage: 5.87MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 4 11:54:33 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print [N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [562..563] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Thu Dec 4 2003 11:54:23 on modular [Seed = 4026575200] ------------------------------------- [ 11, 1, 2, $.1 + 2, 3, $.1 + 1, 5, $.1 - 1, 7, $.1 + 2, 11, $.1 - 1, 13, $.1 - 4 ] 562,1,2,x + 1,3,x - 2,5,x - 2,7,x - 4,11,x - 2,13,x + 2[] 562,2,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 4*x - 1,5,x^3 + x^2 - 4*x + 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 4*x^2 + x + 1,13,x^3 - 2*x^2 - 3*x + 5[] 562,3,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 5*x^2 + 6*x + 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3 + x^2 - 9*x - 1,11,x^3 + 2*x^2 - 15*x - 29,13,x^3 + 10*x^2 + 31*x + 29[] 562,4,2,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,3,x^7 + 5*x^6 - x^5 - 28*x^4 - 9*x^3 + 32*x^2 - 12*x + 1,5,x^7 + 3*x^6 - 15*x^5 - 50*x^4 + 49*x^3 + 220*x^2 + 22*x - 187,7,x^7 + 7*x^6 - 9*x^5 - 107*x^4 + 28*x^3 + 392*x^2 - 224*x + 16,11,x^7 - 56*x^5 + 5*x^4 + 1024*x^3 - 279*x^2 - 6079*x + 3583,13,x^7 + 4*x^6 - 63*x^5 - 177*x^4 + 1296*x^3 + 2068*x^2 - 7712*x - 8336[] 562,5,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 - 5*x^8 - 9*x^7 + 74*x^6 - 27*x^5 - 310*x^4 + 350*x^3 + 243*x^2 - 456*x + 140,5,x^9 - 5*x^8 - 13*x^7 + 86*x^6 + 19*x^5 - 412*x^4 + 96*x^3 + 597*x^2 - 120*x + 4,7,x^9 + x^8 - 33*x^7 - 17*x^6 + 312*x^5 - 832*x^3 + 112*x^2 + 576*x - 128,11,x^9 - 2*x^8 - 38*x^7 + 109*x^6 + 198*x^5 - 809*x^4 + 369*x^3 + 601*x^2 - 448*x + 20,13,x^9 - 10*x^8 - 11*x^7 + 321*x^6 - 512*x^5 - 1598*x^4 + 3736*x^3 - 2440*x^2 + 544*x - 32[] 563,1,2,x + 1,3,x + 1,5,x + 4,7,x + 5,11,x + 4,13,x - 2[] 563,2,2,x^3 + x^2 - 3*x - 1,3,x^3 - x^2 - 3*x + 1,5,x^3 - 2*x^2 - 2*x + 2,7,x^3 + 9*x^2 + 23*x + 13,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 8*x^2 + 12*x + 4[] 563,3,2,x^3 + x^2 - 3*x - 1,3,x^3 + x^2 - 5*x - 1,5,x^3 + 6*x^2 + 12*x + 8,7,x^3 + x^2 - 5*x - 1,11,x^3 + 4*x^2 - 16*x - 32,13,x^3 + 6*x^2 - 4*x - 8[] 563,4,2,x^9 + 2*x^8 - 8*x^7 - 15*x^6 + 18*x^5 + 31*x^4 - 15*x^3 - 22*x^2 + 4*x + 5,3,x^9 + 7*x^8 + 11*x^7 - 21*x^6 - 66*x^5 - 26*x^4 + 35*x^3 + 12*x^2 - 5*x - 1,5,x^9 + 3*x^8 - 14*x^7 - 33*x^6 + 70*x^5 + 70*x^4 - 157*x^3 + 59*x^2 + x - 1,7,x^9 - 27*x^7 - 11*x^6 + 218*x^5 + 153*x^4 - 523*x^3 - 590*x^2 - 53*x + 65,11,x^9 + 2*x^8 - 49*x^7 - 104*x^6 + 664*x^5 + 1499*x^4 - 2312*x^3 - 5107*x^2 + 2348*x + 5021,13,x^9 + 18*x^8 + 114*x^7 + 226*x^6 - 526*x^5 - 2544*x^4 - 838*x^3 + 6462*x^2 + 3433*x - 6077[] 563,5,2,x^31 - 5*x^30 - 40*x^29 + 233*x^28 + 650*x^27 - 4804*x^26 - 5046*x^25 + 57710*x^24 + 10034*x^23 - 447489*x^22 + 163153*x^21 + 2342476*x^20 - 1745428*x^19 - 8396607*x^18 + 8854751*x^17 + 20387988*x^16 - 27682203*x^15 - 32062270*x^14 + 56150683*x^13 + 28712111*x^12 - 73374682*x^11 - 7360185*x^10 + 58781075*x^9 - 10788006*x^8 - 25769684*x^7 + 10398304*x^6 + 4640992*x^5 - 3106816*x^4 + 10432*x^3 + 288640*x^2 - 60160*x + 3584,3,x^31 - 8*x^30 - 36*x^29 + 438*x^28 + 229*x^27 - 10386*x^26 + 9349*x^25 + 139463*x^24 - 243265*x^23 - 1159135*x^22 + 2851453*x^21 + 6057717*x^20 - 20207187*x^19 - 18643013*x^18 + 93374168*x^17 + 22641515*x^16 - 286762553*x^15 + 54965386*x^14 + 578900608*x^13 - 285946450*x^12 - 739516991*x^11 + 536988337*x^10 + 554432663*x^9 - 521875426*x^8 - 209275676*x^7 + 259828126*x^6 + 26338408*x^5 - 57891892*x^4 + 335898*x^3 + 4701225*x^2 + 63363*x - 68089,5,x^31 - 13*x^30 - 26*x^29 + 1025*x^28 - 2102*x^27 - 32770*x^26 + 134661*x^25 + 514351*x^24 - 3461109*x^23 - 3048685*x^22 + 50336186*x^21 - 26854136*x^20 - 448679606*x^19 + 668750172*x^18 + 2448826664*x^17 - 5939789760*x^16 - 7455513992*x^15 + 29871172864*x^14 + 7135503584*x^13 - 91648676288*x^12 + 29193504768*x^11 + 172431682560*x^10 - 116278431744*x^9 - 193646750720*x^8 + 181886720000*x^7 + 121650561024*x^6 - 144319168512*x^5 - 36176625664*x^4 + 55909974016*x^3 + 1518731264*x^2 - 8008761344*x + 1232863232,7,x^31 - 17*x^30 + 13*x^29 + 1328*x^28 - 6397*x^27 - 35629*x^26 + 313036*x^25 + 202715*x^24 - 7099189*x^23 + 9101485*x^22 + 87487282*x^21 - 229554480*x^20 - 574461178*x^19 + 2512784249*x^18 + 1356800852*x^17 - 15316612926*x^16 + 6550245011*x^15 + 53002656084*x^14 - 58251890718*x^13 - 93065574450*x^12 + 175381630972*x^11 + 40560504830*x^10 - 237782527740*x^9 + 91841655157*x^8 + 116370729448*x^7 - 98304084009*x^6 + 846085118*x^5 + 20517963379*x^4 - 5135652928*x^3 - 612079241*x^2 + 243535921*x - 2256971,11,x^31 - 6*x^30 - 181*x^29 + 989*x^28 + 15111*x^27 - 71131*x^26 - 774054*x^25 + 2908028*x^24 + 27102043*x^23 - 72967583*x^22 - 678267911*x^21 + 1095446837*x^20 + 12253624411*x^19 - 7412153693*x^18 - 157311865686*x^17 - 48681305231*x^16 + 1373125407486*x^15 + 1601659948979*x^14 - 7378293633701*x^13 - 15796421835088*x^12 + 17838816236677*x^11 + 77004478755908*x^10 + 23845434839929*x^9 - 164027921942707*x^8 - 212029592832857*x^7 + 31525674378114*x^6 + 268850695721036*x^5 + 240334292631624*x^4 + 89281483293488*x^3 + 9124329793824*x^2 - 2401789898304*x - 478894639744,13,x^31 - 40*x^30 + 548*x^29 - 1005*x^28 - 50031*x^27 + 469667*x^26 + 194555*x^25 - 25000942*x^24 + 109063970*x^23 + 400996320*x^22 - 4523338832*x^21 + 5393121569*x^20 + 71759905967*x^19 - 276321720544*x^18 - 291953710267*x^17 + 3640841116386*x^16 - 4499242718225*x^15 - 17987242882760*x^14 + 52649670072965*x^13 + 7331792052332*x^12 - 175174679577777*x^11 + 127249824533077*x^10 + 231602352580555*x^9 - 276690468843700*x^8 - 119024923899873*x^7 + 209864721881820*x^6 + 14555659971244*x^5 - 62525703110692*x^4 + 3218373849616*x^3 + 5670063405760*x^2 - 78984241664*x - 124605421696[] Total time: 10.219 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 4 12:05:03 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print [N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [563..565] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Thu Dec 4 2003 12:04:46 on modular [Seed = 651587622] ------------------------------------- [ 11, 1, 2, $.1 + 2, 3, $.1 + 1, 5, $.1 - 1, 7, $.1 + 2, 11, $.1 - 1, 13, $.1 - 4 ] 563,1,2,x + 1,3,x + 1,5,x + 4,7,x + 5,11,x + 4,13,x - 2[] 563,2,2,x^3 + x^2 - 3*x - 1,3,x^3 - x^2 - 3*x + 1,5,x^3 - 2*x^2 - 2*x + 2,7,x^3 + 9*x^2 + 23*x + 13,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 8*x^2 + 12*x + 4[] 563,3,2,x^3 + x^2 - 3*x - 1,3,x^3 + x^2 - 5*x - 1,5,x^3 + 6*x^2 + 12*x + 8,7,x^3 + x^2 - 5*x - 1,11,x^3 + 4*x^2 - 16*x - 32,13,x^3 + 6*x^2 - 4*x - 8[] 563,4,2,x^9 + 2*x^8 - 8*x^7 - 15*x^6 + 18*x^5 + 31*x^4 - 15*x^3 - 22*x^2 + 4*x + 5,3,x^9 + 7*x^8 + 11*x^7 - 21*x^6 - 66*x^5 - 26*x^4 + 35*x^3 + 12*x^2 - 5*x - 1,5,x^9 + 3*x^8 - 14*x^7 - 33*x^6 + 70*x^5 + 70*x^4 - 157*x^3 + 59*x^2 + x - 1,7,x^9 - 27*x^7 - 11*x^6 + 218*x^5 + 153*x^4 - 523*x^3 - 590*x^2 - 53*x + 65,11,x^9 + 2*x^8 - 49*x^7 - 104*x^6 + 664*x^5 + 1499*x^4 - 2312*x^3 - 5107*x^2 + 2348*x + 5021,13,x^9 + 18*x^8 + 114*x^7 + 226*x^6 - 526*x^5 - 2544*x^4 - 838*x^3 + 6462*x^2 + 3433*x - 6077[] 563,5,2,x^31 - 5*x^30 - 40*x^29 + 233*x^28 + 650*x^27 - 4804*x^26 - 5046*x^25 + 57710*x^24 + 10034*x^23 - 447489*x^22 + 163153*x^21 + 2342476*x^20 - 1745428*x^19 - 8396607*x^18 + 8854751*x^17 + 20387988*x^16 - 27682203*x^15 - 32062270*x^14 + 56150683*x^13 + 28712111*x^12 - 73374682*x^11 - 7360185*x^10 + 58781075*x^9 - 10788006*x^8 - 25769684*x^7 + 10398304*x^6 + 4640992*x^5 - 3106816*x^4 + 10432*x^3 + 288640*x^2 - 60160*x + 3584,3,x^31 - 8*x^30 - 36*x^29 + 438*x^28 + 229*x^27 - 10386*x^26 + 9349*x^25 + 139463*x^24 - 243265*x^23 - 1159135*x^22 + 2851453*x^21 + 6057717*x^20 - 20207187*x^19 - 18643013*x^18 + 93374168*x^17 + 22641515*x^16 - 286762553*x^15 + 54965386*x^14 + 578900608*x^13 - 285946450*x^12 - 739516991*x^11 + 536988337*x^10 + 554432663*x^9 - 521875426*x^8 - 209275676*x^7 + 259828126*x^6 + 26338408*x^5 - 57891892*x^4 + 335898*x^3 + 4701225*x^2 + 63363*x - 68089,5,x^31 - 13*x^30 - 26*x^29 + 1025*x^28 - 2102*x^27 - 32770*x^26 + 134661*x^25 + 514351*x^24 - 3461109*x^23 - 3048685*x^22 + 50336186*x^21 - 26854136*x^20 - 448679606*x^19 + 668750172*x^18 + 2448826664*x^17 - 5939789760*x^16 - 7455513992*x^15 + 29871172864*x^14 + 7135503584*x^13 - 91648676288*x^12 + 29193504768*x^11 + 172431682560*x^10 - 116278431744*x^9 - 193646750720*x^8 + 181886720000*x^7 + 121650561024*x^6 - 144319168512*x^5 - 36176625664*x^4 + 55909974016*x^3 + 1518731264*x^2 - 8008761344*x + 1232863232,7,x^31 - 17*x^30 + 13*x^29 + 1328*x^28 - 6397*x^27 - 35629*x^26 + 313036*x^25 + 202715*x^24 - 7099189*x^23 + 9101485*x^22 + 87487282*x^21 - 229554480*x^20 - 574461178*x^19 + 2512784249*x^18 + 1356800852*x^17 - 15316612926*x^16 + 6550245011*x^15 + 53002656084*x^14 - 58251890718*x^13 - 93065574450*x^12 + 175381630972*x^11 + 40560504830*x^10 - 237782527740*x^9 + 91841655157*x^8 + 116370729448*x^7 - 98304084009*x^6 + 846085118*x^5 + 20517963379*x^4 - 5135652928*x^3 - 612079241*x^2 + 243535921*x - 2256971,11,x^31 - 6*x^30 - 181*x^29 + 989*x^28 + 15111*x^27 - 71131*x^26 - 774054*x^25 + 2908028*x^24 + 27102043*x^23 - 72967583*x^22 - 678267911*x^21 + 1095446837*x^20 + 12253624411*x^19 - 7412153693*x^18 - 157311865686*x^17 - 48681305231*x^16 + 1373125407486*x^15 + 1601659948979*x^14 - 7378293633701*x^13 - 15796421835088*x^12 + 17838816236677*x^11 + 77004478755908*x^10 + 23845434839929*x^9 - 164027921942707*x^8 - 212029592832857*x^7 + 31525674378114*x^6 + 268850695721036*x^5 + 240334292631624*x^4 + 89281483293488*x^3 + 9124329793824*x^2 - 2401789898304*x - 478894639744,13,x^31 - 40*x^30 + 548*x^29 - 1005*x^28 - 50031*x^27 + 469667*x^26 + 194555*x^25 - 25000942*x^24 + 109063970*x^23 + 400996320*x^22 - 4523338832*x^21 + 5393121569*x^20 + 71759905967*x^19 - 276321720544*x^18 - 291953710267*x^17 + 3640841116386*x^16 - 4499242718225*x^15 - 17987242882760*x^14 + 52649670072965*x^13 + 7331792052332*x^12 - 175174679577777*x^11 + 127249824533077*x^10 + 231602352580555*x^9 - 276690468843700*x^8 - 119024923899873*x^7 + 209864721881820*x^6 + 14555659971244*x^5 - 62525703110692*x^4 + 3218373849616*x^3 + 5670063405760*x^2 - 78984241664*x - 124605421696[] 564,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 3,13,x + 2[] 564,2,2,x,3,x - 1,5,x + 3,7,x + 1,11,x + 3,13,x + 4[] 564,3,2,x^3,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 3*x^2 - 12*x + 34,7,x^3 - 3*x^2 - 12*x + 24,11,x^3 + 3*x^2 - 12*x - 24,13,x^3 - 6*x^2 + 12*x - 8[] 564,4,2,x^3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 5*x^2 + 4*x + 2,7,x^3 - 3*x^2 - 4*x + 8,11,x^3 - 3*x^2 - 4*x + 8,13,x^3 - 28*x - 16[] 565,1,2,x - 1,3,x + 2,5,x + 1,7,x - 1,11,x - 4,13,x - 4[] 565,2,2,x^6 + 3*x^5 - 2*x^4 - 9*x^3 - x^2 + 4*x + 1,3,x^6 + 3*x^5 - 4*x^4 - 13*x^3 - x^2 + 6*x - 1,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 + 4*x^5 - 13*x^4 - 49*x^3 + 6*x^2 + 77*x + 37,11,x^6 + 21*x^5 + 166*x^4 + 610*x^3 + 1021*x^2 + 543*x - 163,13,x^6 + 2*x^5 - 29*x^4 - 130*x^3 - 175*x^2 - 45*x + 37[] 565,3,2,x^8 - 5*x^7 - x^6 + 34*x^5 - 23*x^4 - 67*x^3 + 52*x^2 + 30*x - 5,3,x^8 - 7*x^7 + 6*x^6 + 53*x^5 - 113*x^4 - 42*x^3 + 253*x^2 - 172*x + 20,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 - 5*x^7 - 15*x^6 + 76*x^5 + 89*x^4 - 335*x^3 - 178*x^2 + 407*x - 80,11,x^8 - 15*x^7 + 74*x^6 - 102*x^5 - 179*x^4 + 495*x^3 - 251*x^2 - 60*x + 32,13,x^8 - 49*x^6 - 30*x^5 + 753*x^4 + 789*x^3 - 3461*x^2 - 3398*x + 3272[] 565,4,2,x^10 + 5*x^9 - 4*x^8 - 49*x^7 - 24*x^6 + 153*x^5 + 127*x^4 - 165*x^3 - 145*x^2 + 56*x + 41,3,x^10 + 5*x^9 - 8*x^8 - 65*x^7 - 11*x^6 + 236*x^5 + 101*x^4 - 308*x^3 - 128*x^2 + 110*x + 50,5,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1,7,x^10 + 6*x^9 - 21*x^8 - 173*x^7 + 38*x^6 + 1581*x^5 + 1235*x^4 - 4864*x^3 - 5320*x^2 + 4704*x + 5488,11,x^10 + 21*x^9 + 146*x^8 + 182*x^7 - 2243*x^6 - 9201*x^5 - 1823*x^4 + 47732*x^3 + 76424*x^2 + 9328*x - 30304,13,x^10 + 4*x^9 - 71*x^8 - 252*x^7 + 1653*x^6 + 5439*x^5 - 12205*x^4 - 45080*x^3 - 580*x^2 + 59952*x + 12172[] 565,5,2,x^12 - 5*x^11 - 7*x^10 + 66*x^9 - 26*x^8 - 280*x^7 + 269*x^6 + 398*x^5 - 472*x^4 - 115*x^3 + 146*x^2 - 24*x + 1,3,x^12 - 3*x^11 - 20*x^10 + 65*x^9 + 119*x^8 - 466*x^7 - 165*x^6 + 1270*x^5 - 304*x^4 - 1118*x^3 + 402*x^2 + 304*x - 88,5,x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1,7,x^12 - 42*x^10 + 37*x^9 + 513*x^8 - 792*x^7 - 1189*x^6 + 1837*x^5 + 767*x^4 - 1232*x^3 - 104*x^2 + 224*x - 16,11,x^12 - 23*x^11 + 182*x^10 - 354*x^9 - 2691*x^8 + 15159*x^7 - 14351*x^6 - 67624*x^5 + 165768*x^4 - 23376*x^3 - 258720*x^2 + 253952*x - 69632,13,x^12 + 8*x^11 - 31*x^10 - 366*x^9 - 15*x^8 + 5319*x^7 + 7107*x^6 - 23864*x^5 - 48636*x^4 + 1176*x^3 + 25644*x^2 - 1184*x - 2368[] Total time: 16.239 seconds, Total memory usage: 5.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 4 12:09:58 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print [N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [566..568] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Thu Dec 4 2003 12:09:41 on modular [Seed = 1003187776] ------------------------------------- [ 11, 1, 2, $.1 + 2, 3, $.1 + 1, 5, $.1 - 1, 7, $.1 + 2, 11, $.1 - 1, 13, $.1 - 4 ] 566,1,2,x + 1,3,x,5,x,7,x - 1,11,x + 3,13,x + 5[] 566,2,2,x - 1,3,x - 1,5,x + 2,7,x - 3,11,x,13,x - 4[] 566,3,2,x^2 + 2*x + 1,3,x^2 - x - 3,5,x^2 + x - 3,7,x^2 + 5*x + 3,11,x^2,13,x^2 + 4*x + 4[] 566,4,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + x - 1,7,x^2 + 5*x + 5,11,x^2 + 6*x + 4,13,x^2[] 566,5,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - x^3 - 8*x^2 + 6*x - 1,5,x^4 + 2*x^3 - 7*x^2 - 12*x + 3,7,x^4 + 5*x^3 - 14*x^2 - 54*x + 81,11,x^4 - 4*x^3 - 16*x^2 + 24*x + 48,13,x^4 - 8*x^3 + 24*x^2 - 32*x + 16[] 566,6,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + 3*x^4 - 7*x^3 - 21*x^2 + 7*x + 27,5,x^5 - 6*x^4 - 5*x^3 + 90*x^2 - 169*x + 74,7,x^5 - 11*x^4 + 35*x^3 - 19*x^2 - 29*x - 3,11,x^5 - 34*x^3 - 12*x^2 + 220*x + 48,13,x^5 + 2*x^4 - 48*x^3 - 84*x^2 + 468*x + 576[] 566,7,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 - 3*x^8 - 19*x^7 + 57*x^6 + 116*x^5 - 351*x^4 - 265*x^3 + 828*x^2 + 197*x - 652,5,x^9 - 28*x^7 + 28*x^6 + 235*x^5 - 436*x^4 - 338*x^3 + 1184*x^2 - 645*x - 8,7,x^9 - 4*x^8 - 26*x^7 + 76*x^6 + 259*x^5 - 353*x^4 - 934*x^3 + 239*x^2 + 601*x + 61,11,x^9 - 11*x^8 - 8*x^7 + 342*x^6 - 76*x^5 - 3876*x^4 - 1648*x^3 + 14784*x^2 + 18912*x + 5824,13,x^9 + 3*x^8 - 82*x^7 - 276*x^6 + 1896*x^5 + 7044*x^4 - 9360*x^3 - 38336*x^2 + 14144*x + 54464[] 567,1,2,x - 1,3,x,5,x + 1,7,x + 1,11,x - 2,13,x + 5[] 567,2,2,x + 1,3,x,5,x - 1,7,x + 1,11,x + 2,13,x + 5[] 567,3,2,x^3 + x^2 - 4*x - 1,3,x^3,5,x^3 + 5*x^2 + 2*x - 11,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 2*x^2 - 19*x - 47,13,x^3 - 3*x^2 + 3*x - 1[] 567,4,2,x^3 - 6*x + 3,3,x^3,5,x^3 - 3*x^2 - 6*x + 12,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 3*x + 6,13,x^3 - 3*x^2 - 36*x + 112[] 567,5,2,x^3 - 6*x - 3,3,x^3,5,x^3 + 3*x^2 - 6*x - 12,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 6*x^2 + 3*x - 6,13,x^3 - 3*x^2 - 36*x + 112[] 567,6,2,x^3 - 3*x^2 + 3,3,x^3,5,x^3 - 3*x^2 + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 9*x - 3,13,x^3 + 3*x^2 - 33*x - 107[] 567,7,2,x^3 - x^2 - 4*x + 1,3,x^3,5,x^3 - 5*x^2 + 2*x + 11,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 2*x^2 - 19*x + 47,13,x^3 - 3*x^2 + 3*x - 1[] 567,8,2,x^3 + 3*x^2 - 3,3,x^3,5,x^3 + 3*x^2 - 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 6*x^2 + 9*x + 3,13,x^3 + 3*x^2 - 33*x - 107[] 567,9,2,x^4 - 5*x^2 + 1,3,x^4,5,x^4 - 20*x^2 + 16,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 - 14*x^2 + 49,13,x^4 - 16*x^3 + 96*x^2 - 256*x + 256[] 568,1,2,x,3,x + 1,5,x - 2,7,x - 5,11,x - 2,13,x + 1[] 568,2,2,x^4,3,x^4 + 4*x^3 + x^2 - 5*x + 1,5,x^4 + x^3 - 8*x^2 + 5*x + 2,7,x^4 + 5*x^3 - 20*x - 8,11,x^4 + 2*x^3 - 32*x^2 - 32*x + 128,13,x^4 - 3*x^3 - 6*x^2 + 8*x + 8[] 568,3,2,x^4,3,x^4 - 5*x^3 + 2*x^2 + 17*x - 16,5,x^4 + x^3 - 12*x^2 - 15*x + 14,7,x^4,11,x^4 - 8*x^3 + 24*x^2 - 32*x + 16,13,x^4 + 4*x^3 - 28*x^2 - 88*x + 128[] 568,4,2,x^4,3,x^4 + 2*x^3 - 5*x^2 - 5*x - 1,5,x^4 + 7*x^3 + 14*x^2 + 5*x - 4,7,x^4 - x^3 - 20*x^2 + 64,11,x^4 + 2*x^3 - 36*x^2 - 72*x + 128,13,x^4 + 11*x^3 + 36*x^2 + 36*x + 8[] 568,5,2,x^5,3,x^5 - 2*x^4 - 9*x^3 + 15*x^2 + 19*x - 28,5,x^5 - 7*x^4 + 8*x^3 + 29*x^2 - 54*x + 16,7,x^5 + x^4 - 20*x^3 - 4*x^2 + 88*x - 64,11,x^5,13,x^5 - 11*x^4 + 28*x^3 + 20*x^2 - 56*x + 16[] Total time: 17.409 seconds, Total memory usage: 5.93MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 4 12:14:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print [N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [569..571] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Dec 4 2003 12:14:14 on modular [Seed = 133649231] ------------------------------------- [ 11, 1, 2, $.1 + 2, 3, $.1 + 1, 5, $.1 - 1, 7, $.1 + 2, 11, $.1 - 1, 13, $.1 - 4 ] 569,1,2,x^16 + 3*x^15 - 13*x^14 - 43*x^13 + 60*x^12 + 236*x^11 - 110*x^10 - 630*x^9 + 22*x^8 + 846*x^7 + 159*x^6 - 522*x^5 - 144*x^4 + 113*x^3 + 23*x^2 - 7*x - 1,3,x^16 + 8*x^15 + 7*x^14 - 93*x^13 - 218*x^12 + 302*x^11 + 1219*x^10 - 98*x^9 - 2820*x^8 - 1045*x^7 + 2916*x^6 + 1691*x^5 - 1080*x^4 - 783*x^3 - 31*x^2 + 22*x + 1,5,x^16 + 6*x^15 - 23*x^14 - 211*x^13 - 47*x^12 + 2324*x^11 + 3633*x^10 - 9584*x^9 - 26129*x^8 + 8154*x^7 + 70810*x^6 + 33333*x^5 - 75339*x^4 - 72290*x^3 + 16500*x^2 + 39420*x + 11753,7,x^16 + 16*x^15 + 80*x^14 - 6*x^13 - 1304*x^12 - 3266*x^11 + 4251*x^10 + 27607*x^9 + 18925*x^8 - 76553*x^7 - 133447*x^6 + 29864*x^5 + 223302*x^4 + 136688*x^3 - 59585*x^2 - 82615*x - 20489,11,x^16 + 7*x^15 - 65*x^14 - 573*x^13 + 1001*x^12 + 16173*x^11 + 8217*x^10 - 197003*x^9 - 303703*x^8 + 1022837*x^7 + 2192591*x^6 - 2034974*x^5 - 5418338*x^4 + 1096023*x^3 + 2880925*x^2 - 1325489*x + 154303,13,x^16 + 11*x^15 - 37*x^14 - 773*x^13 - 924*x^12 + 16660*x^11 + 46701*x^10 - 118440*x^9 - 496552*x^8 + 223545*x^7 + 2010571*x^6 + 376568*x^5 - 3141432*x^4 - 992439*x^3 + 1252736*x^2 - 277950*x + 18207[] 569,2,2,x^31 - 53*x^29 + 1260*x^27 + 4*x^26 - 17750*x^25 - 160*x^24 + 164884*x^23 + 2756*x^22 - 1063367*x^21 - 26739*x^20 + 4881497*x^19 + 160306*x^18 - 16085855*x^17 - 611602*x^16 + 37872670*x^15 + 1464757*x^14 - 62581486*x^13 - 2043005*x^12 + 70114271*x^11 + 1238201*x^10 - 50129555*x^9 + 450969*x^8 + 20481249*x^7 - 1061301*x^6 - 3789930*x^5 + 449436*x^4 + 156552*x^3 - 18419*x^2 - 1828*x + 173,3,x^31 - 8*x^30 - 33*x^29 + 411*x^28 + 166*x^27 - 9166*x^26 + 8381*x^25 + 116624*x^24 - 196146*x^23 - 931703*x^22 + 2151180*x^21 + 4804145*x^20 - 14532484*x^19 - 15436049*x^18 + 65252937*x^17 + 24997462*x^16 - 199068733*x^15 + 13804668*x^14 + 408585020*x^13 - 168236600*x^12 - 538629038*x^11 + 389186762*x^10 + 402026716*x^9 - 455117126*x^8 - 98319742*x^7 + 267431596*x^6 - 61574476*x^5 - 53800648*x^4 + 33668690*x^3 - 6363020*x^2 + 167982*x + 46054,5,x^31 - 4*x^30 - 95*x^29 + 387*x^28 + 3979*x^27 - 16670*x^26 - 96623*x^25 + 422090*x^24 + 1502883*x^23 - 6986904*x^22 - 15567578*x^21 + 79561621*x^20 + 107389479*x^19 - 638694476*x^18 - 467981904*x^17 + 3643738596*x^16 + 1019837325*x^15 - 14698754866*x^14 + 938334788*x^13 + 41151579456*x^12 - 13736838832*x^11 - 77010928996*x^10 + 42936413228*x^9 + 89578074828*x^8 - 68722779052*x^7 - 54791545628*x^6 + 57203753328*x^5 + 8335311516*x^4 - 19466322868*x^3 + 4655636784*x^2 - 63564924*x - 1779772,7,x^31 - 20*x^30 + 56*x^29 + 1430*x^28 - 10544*x^27 - 27822*x^26 + 485139*x^25 - 472057*x^24 - 10890515*x^23 + 32016391*x^22 + 128411733*x^21 - 670763356*x^20 - 584958518*x^19 + 7707428244*x^18 - 4102028185*x^17 - 52867070411*x^16 + 78011584239*x^15 + 211146765188*x^14 - 519487202864*x^13 - 408508308656*x^12 + 1875850973664*x^11 - 59087908096*x^10 - 3843913217024*x^9 + 1858051694080*x^8 + 4227999904256*x^7 - 3292489034752*x^6 - 2084919975936*x^5 + 2153320865792*x^4 + 255033925632*x^3 - 419009773568*x^2 + 6834225152*x + 18389598208,11,x^31 - x^30 - 193*x^29 + 283*x^28 + 16207*x^27 - 31461*x^26 - 774635*x^25 + 1887565*x^24 + 23102625*x^23 - 68950775*x^22 - 441591321*x^21 + 1618073620*x^20 + 5289842938*x^19 - 24881756667*x^18 - 35469993759*x^17 + 249941454073*x^16 + 65388582051*x^15 - 1601784497790*x^14 + 850485678026*x^13 + 6235051904112*x^12 - 7168389745198*x^11 - 13356973056950*x^10 + 24420881818582*x^9 + 11780846338966*x^8 - 41600126176960*x^7 + 4089498866596*x^6 + 35349569730086*x^5 - 13538299074340*x^4 - 14313466929762*x^3 + 7848288515852*x^2 + 2199828169256*x - 1457337952058,13,x^31 - 11*x^30 - 159*x^29 + 2097*x^28 + 9110*x^27 - 166996*x^26 - 172527*x^25 + 7280958*x^24 - 4362416*x^23 - 191615667*x^22 + 306281613*x^21 + 3159934858*x^20 - 7419008900*x^19 - 32636067087*x^18 + 100849816246*x^17 + 200950614874*x^16 - 842616832413*x^15 - 604358435438*x^14 + 4405797197180*x^13 - 276396209376*x^12 - 14148664151280*x^11 + 8559070873288*x^10 + 26276879666600*x^9 - 28332918761592*x^8 - 23872929744192*x^7 + 43064246148192*x^6 + 2666771010816*x^5 - 30896880598848*x^4 + 11006099408576*x^3 + 7331400699344*x^2 - 5610019376592*x + 1009169454448[] 570,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x + 6,13,x[] 570,2,2,x + 1,3,x + 1,5,x + 1,7,x + 2,11,x - 4,13,x + 6[] 570,3,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x + 2,13,x[] 570,4,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x,13,x - 2[] 570,5,2,x + 1,3,x - 1,5,x - 1,7,x + 4,11,x + 4,13,x + 6[] 570,6,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 2[] 570,7,2,x - 1,3,x + 1,5,x + 1,7,x,11,x - 4,13,x - 2[] 570,8,2,x - 1,3,x + 1,5,x - 1,7,x + 2,11,x,13,x - 6[] 570,9,2,x - 1,3,x + 1,5,x - 1,7,x - 4,11,x,13,x + 6[] 570,10,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x + 4,13,x - 6[] 570,11,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x - 6,13,x + 4[] 570,12,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x - 4[] 570,13,2,x - 1,3,x - 1,5,x - 1,7,x - 4,11,x + 4,13,x + 2[] Errors: /home/mfd/gomagma: line 2: 4393 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 4 12:16:13 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); print [N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; end for; CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [569..570] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Thu Dec 4 2003 12:15:52 on modular [Seed = 468406269] ------------------------------------- [ 11, 1, 2, $.1 + 2, 3, $.1 + 1, 5, $.1 - 1, 7, $.1 + 2, 11, $.1 - 1, 13, $.1 - 4 ] 569,1,2,x^16 + 3*x^15 - 13*x^14 - 43*x^13 + 60*x^12 + 236*x^11 - 110*x^10 - 630*x^9 + 22*x^8 + 846*x^7 + 159*x^6 - 522*x^5 - 144*x^4 + 113*x^3 + 23*x^2 - 7*x - 1,3,x^16 + 8*x^15 + 7*x^14 - 93*x^13 - 218*x^12 + 302*x^11 + 1219*x^10 - 98*x^9 - 2820*x^8 - 1045*x^7 + 2916*x^6 + 1691*x^5 - 1080*x^4 - 783*x^3 - 31*x^2 + 22*x + 1,5,x^16 + 6*x^15 - 23*x^14 - 211*x^13 - 47*x^12 + 2324*x^11 + 3633*x^10 - 9584*x^9 - 26129*x^8 + 8154*x^7 + 70810*x^6 + 33333*x^5 - 75339*x^4 - 72290*x^3 + 16500*x^2 + 39420*x + 11753,7,x^16 + 16*x^15 + 80*x^14 - 6*x^13 - 1304*x^12 - 3266*x^11 + 4251*x^10 + 27607*x^9 + 18925*x^8 - 76553*x^7 - 133447*x^6 + 29864*x^5 + 223302*x^4 + 136688*x^3 - 59585*x^2 - 82615*x - 20489,11,x^16 + 7*x^15 - 65*x^14 - 573*x^13 + 1001*x^12 + 16173*x^11 + 8217*x^10 - 197003*x^9 - 303703*x^8 + 1022837*x^7 + 2192591*x^6 - 2034974*x^5 - 5418338*x^4 + 1096023*x^3 + 2880925*x^2 - 1325489*x + 154303,13,x^16 + 11*x^15 - 37*x^14 - 773*x^13 - 924*x^12 + 16660*x^11 + 46701*x^10 - 118440*x^9 - 496552*x^8 + 223545*x^7 + 2010571*x^6 + 376568*x^5 - 3141432*x^4 - 992439*x^3 + 1252736*x^2 - 277950*x + 18207[] 569,2,2,x^31 - 53*x^29 + 1260*x^27 + 4*x^26 - 17750*x^25 - 160*x^24 + 164884*x^23 + 2756*x^22 - 1063367*x^21 - 26739*x^20 + 4881497*x^19 + 160306*x^18 - 16085855*x^17 - 611602*x^16 + 37872670*x^15 + 1464757*x^14 - 62581486*x^13 - 2043005*x^12 + 70114271*x^11 + 1238201*x^10 - 50129555*x^9 + 450969*x^8 + 20481249*x^7 - 1061301*x^6 - 3789930*x^5 + 449436*x^4 + 156552*x^3 - 18419*x^2 - 1828*x + 173,3,x^31 - 8*x^30 - 33*x^29 + 411*x^28 + 166*x^27 - 9166*x^26 + 8381*x^25 + 116624*x^24 - 196146*x^23 - 931703*x^22 + 2151180*x^21 + 4804145*x^20 - 14532484*x^19 - 15436049*x^18 + 65252937*x^17 + 24997462*x^16 - 199068733*x^15 + 13804668*x^14 + 408585020*x^13 - 168236600*x^12 - 538629038*x^11 + 389186762*x^10 + 402026716*x^9 - 455117126*x^8 - 98319742*x^7 + 267431596*x^6 - 61574476*x^5 - 53800648*x^4 + 33668690*x^3 - 6363020*x^2 + 167982*x + 46054,5,x^31 - 4*x^30 - 95*x^29 + 387*x^28 + 3979*x^27 - 16670*x^26 - 96623*x^25 + 422090*x^24 + 1502883*x^23 - 6986904*x^22 - 15567578*x^21 + 79561621*x^20 + 107389479*x^19 - 638694476*x^18 - 467981904*x^17 + 3643738596*x^16 + 1019837325*x^15 - 14698754866*x^14 + 938334788*x^13 + 41151579456*x^12 - 13736838832*x^11 - 77010928996*x^10 + 42936413228*x^9 + 89578074828*x^8 - 68722779052*x^7 - 54791545628*x^6 + 57203753328*x^5 + 8335311516*x^4 - 19466322868*x^3 + 4655636784*x^2 - 63564924*x - 1779772,7,x^31 - 20*x^30 + 56*x^29 + 1430*x^28 - 10544*x^27 - 27822*x^26 + 485139*x^25 - 472057*x^24 - 10890515*x^23 + 32016391*x^22 + 128411733*x^21 - 670763356*x^20 - 584958518*x^19 + 7707428244*x^18 - 4102028185*x^17 - 52867070411*x^16 + 78011584239*x^15 + 211146765188*x^14 - 519487202864*x^13 - 408508308656*x^12 + 1875850973664*x^11 - 59087908096*x^10 - 3843913217024*x^9 + 1858051694080*x^8 + 4227999904256*x^7 - 3292489034752*x^6 - 2084919975936*x^5 + 2153320865792*x^4 + 255033925632*x^3 - 419009773568*x^2 + 6834225152*x + 18389598208,11,x^31 - x^30 - 193*x^29 + 283*x^28 + 16207*x^27 - 31461*x^26 - 774635*x^25 + 1887565*x^24 + 23102625*x^23 - 68950775*x^22 - 441591321*x^21 + 1618073620*x^20 + 5289842938*x^19 - 24881756667*x^18 - 35469993759*x^17 + 249941454073*x^16 + 65388582051*x^15 - 1601784497790*x^14 + 850485678026*x^13 + 6235051904112*x^12 - 7168389745198*x^11 - 13356973056950*x^10 + 24420881818582*x^9 + 11780846338966*x^8 - 41600126176960*x^7 + 4089498866596*x^6 + 35349569730086*x^5 - 13538299074340*x^4 - 14313466929762*x^3 + 7848288515852*x^2 + 2199828169256*x - 1457337952058,13,x^31 - 11*x^30 - 159*x^29 + 2097*x^28 + 9110*x^27 - 166996*x^26 - 172527*x^25 + 7280958*x^24 - 4362416*x^23 - 191615667*x^22 + 306281613*x^21 + 3159934858*x^20 - 7419008900*x^19 - 32636067087*x^18 + 100849816246*x^17 + 200950614874*x^16 - 842616832413*x^15 - 604358435438*x^14 + 4405797197180*x^13 - 276396209376*x^12 - 14148664151280*x^11 + 8559070873288*x^10 + 26276879666600*x^9 - 28332918761592*x^8 - 23872929744192*x^7 + 43064246148192*x^6 + 2666771010816*x^5 - 30896880598848*x^4 + 11006099408576*x^3 + 7331400699344*x^2 - 5610019376592*x + 1009169454448[] 570,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x + 6,13,x[] 570,2,2,x + 1,3,x + 1,5,x + 1,7,x + 2,11,x - 4,13,x + 6[] 570,3,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x + 2,13,x[] 570,4,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x,13,x - 2[] 570,5,2,x + 1,3,x - 1,5,x - 1,7,x + 4,11,x + 4,13,x + 6[] 570,6,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 2[] 570,7,2,x - 1,3,x + 1,5,x + 1,7,x,11,x - 4,13,x - 2[] 570,8,2,x - 1,3,x + 1,5,x - 1,7,x + 2,11,x,13,x - 6[] 570,9,2,x - 1,3,x + 1,5,x - 1,7,x - 4,11,x,13,x + 6[] 570,10,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x + 4,13,x - 6[] 570,11,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x - 6,13,x + 4[] 570,12,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x - 4[] 570,13,2,x - 1,3,x - 1,5,x - 1,7,x - 4,11,x + 4,13,x + 2[] Total time: 21.469 seconds, Total memory usage: 7.53MB ************** MAGMA ***************** Host pD950B027.dip.t-dialin.net. (217.80.176.39) Time: Thu Dec 4 12:29:16 2003 Input: 20 Output: Magma V2.10-6 Thu Dec 4 2003 12:29:13 on modular [Seed = 1636905126] ------------------------------------- 20 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD950B027.dip.t-dialin.net. (217.80.176.39) Time: Thu Dec 4 12:31:47 2003 Input: [74, 37] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1] 12 Output: Magma V2.10-6 Thu Dec 4 2003 12:31:44 on modular [Seed = 1887445214] ------------------------------------- >> [74, 37] Linear Code over GF(2) ^ User error: bad syntax >> Generator matrix: ^ User error: bad syntax >> [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1] ^ User error: bad syntax >> [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0] ^ User error: bad syntax >> [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1] ^ User error: bad syntax >> [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1] ^ User error: bad syntax >> [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ^ User error: bad syntax >> 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ^ User error: bad syntax >> 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ^ User error: bad syntax >> 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ^ User error: bad syntax >> 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ^ User error: bad syntax >> 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1] ^ User error: bad syntax 12 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD950B027.dip.t-dialin.net. (217.80.176.39) Time: Thu Dec 4 12:32:29 2003 Input: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 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0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1] 12 Output: Magma V2.10-6 Thu Dec 4 2003 12:32:25 on modular [Seed = 1220024527] ------------------------------------- >> [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1] ^ User error: bad syntax >> [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0] ^ User error: bad syntax >> [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1] ^ User error: bad syntax >> [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1] ^ User error: bad syntax >> [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ^ User error: bad syntax >> 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ^ User error: bad syntax >> 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ^ User error: bad syntax >> 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ^ User error: bad syntax >> 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ^ User error: bad syntax >> 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1] ^ User error: bad syntax >> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ^ User error: bad syntax >> 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1] ^ User error: bad syntax 12 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD950B027.dip.t-dialin.net. (217.80.176.39) Time: Thu Dec 4 12:38:12 2003 Input: kronecker(5,3) Output: Magma V2.10-6 Thu Dec 4 2003 12:38:09 on modular [Seed = 3091789463] ------------------------------------- >> kronecker(5,3); ^ User error: Identifier 'kronecker' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-108.fas.harvard.edu. (140.247.240.108) Time: Thu Dec 4 15:41:25 2003 Input: -1728 mod 89 Output: Magma V2.10-6 Thu Dec 4 2003 15:41:22 on modular [Seed = 417905862] ------------------------------------- 52 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:07:48 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L; >M:=MatrixRing(Rationals(),2); >H:=elt; >L; >H; Output: Magma V2.10-6 Fri Dec 5 2003 02:07:44 on modular [Seed = 485690873] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:09:29 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L; >M:=MatrixRing(Rationals(),2); >H:=elt; >L; >H; >G:=AutomorphismGroup(L,H); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 02:09:26 on modular [Seed = 1736996708] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] >> G:=AutomorphismGroup(L,H); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: Lat, AlgMatElt >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:10:03 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L; >M:=MatrixRing(Rationals(),2); >H:=elt; >L; >H; >G:=AutomorphismGroup(L,[H]); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 02:10:00 on modular [Seed = 1870692098] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] >> G:=AutomorphismGroup(L,[H]); ^ Runtime error in 'AutomorphismGroup': Matrices of argument 2 are not over Z >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:10:45 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >L; >H; >G:=AutomorphismGroup(L,[H]); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 02:10:42 on modular [Seed = 2090036267] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] 4 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:11:10 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >L; >H; >G:=AutomorphismGroup(L,H); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 02:11:07 on modular [Seed = 1152079082] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] >> G:=AutomorphismGroup(L,H); ^ Runtime error in 'AutomorphismGroup': Bad argument types Argument types given: Lat, AlgMatElt >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:11:32 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >L; >H; >G:=AutomorphismGroup(L,[H]); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 02:11:28 on modular [Seed = 1285774537] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] 4 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:12:49 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >J:=elt; >L; >H; >J; >G:=AutomorphismGroup(L,[H,J]); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 02:12:46 on modular [Seed = 1471694748] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] [ 1 0] [ 0 -1] 2 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:18:44 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L1:=LatticeWithGram(2,[2,3,8]); >L1; >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >H1:=elt; >J:=elt; >J1:=eltL; >H; >J; >G:=AutomorphismGroup(L,[H,J]); >#G; >Islsometric(L,[H,J],L1,[H1,J1]); Output: Magma V2.10-6 Fri Dec 5 2003 02:18:41 on modular [Seed = 2756422352] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 3] [3 8] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] >> J1:=elt> Islsometric(L,[H,J],L1,[H1,J1]); ^ User error: Identifier 'J1' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:19:49 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L1:=LatticeWithGram(2,[2,3,8]); >L1; >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >H1:=elt; >J:=elt; >J1:=elt; >L; >H; >J; >G:=AutomorphismGroup(L,[H,J]); >#G; >Islsometric(L,[H,J],L1,[H1,J1]); Output: Magma V2.10-6 Fri Dec 5 2003 02:19:46 on modular [Seed = 2823267871] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 3] [3 8] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] [ 1 0] [ 0 -1] 2 >> Islsometric(L,[H,J],L1,[H1,J1]); ^ User error: Identifier 'Islsometric' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:20:21 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L1:=LatticeWithGram(2,[2,3,8]); >L1; >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >H1:=elt; >J:=elt; >J1:=elt; >L; >H; >J; >G:=AutomorphismGroup(L,[H,J]); >#G; >Isisometric(L,[H,J],L1,[H1,J1]); Output: Magma V2.10-6 Fri Dec 5 2003 02:20:18 on modular [Seed = 3109467950] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 3] [3 8] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] [ 1 0] [ 0 -1] 2 >> Isisometric(L,[H,J],L1,[H1,J1]); ^ User error: Identifier 'Isisometric' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:21:31 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L1:=LatticeWithGram(2,[2,3,8]); >L1; >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >H1:=elt; >J:=elt; >J1:=elt; >L; >H; >J; >G:=AutomorphismGroup(L,[H,J]); >#G; >IsIsometric(L,[H,J],L1,[H1,J1]); Output: Magma V2.10-6 Fri Dec 5 2003 02:21:28 on modular [Seed = 2154794589] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 3] [3 8] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] [ 1 0] [ 0 -1] 2 false Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:24:48 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L1:=LatticeWithGram(2,[2,3,8]); >L1; >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >H1:=elt; >J:=elt; >J1:=elt; >L; >H; >J; >G:=AutomorphismGroup(L,[H,J]); >#G; >IsIsometric(L,[H,J],L1,[H1,J1]); Output: Magma V2.10-6 Fri Dec 5 2003 02:24:45 on modular [Seed = 2338620947] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 3] [3 8] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] [ 1 0] [ 0 -1] 2 false Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:25:19 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L1:=LatticeWithGram(2,[2,1,2]); >L1; >L; >M:=MatrixRing(IntegerRing(),2); >H:=elt; >H1:=elt; >J:=elt; >J1:=elt; >L; >H; >J; >G:=AutomorphismGroup(L,[H,J]); >#G; >IsIsometric(L,[H,J],L1,[H1,J1]); Output: Magma V2.10-6 Fri Dec 5 2003 02:25:16 on modular [Seed = 2674954854] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [2 1] [1 2] [3 2] [2 3] [ 1 0] [ 0 -1] 2 true [1 0] [0 1] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 02:26:05 2003 Input: >L:=LatticeWithGram(2,[2,1,2]); >L1:=LatticeWithGram(2,[2,1,2]); >M:=MatrixRing(IntegerRing(),2); >H:=elt; >H1:=elt; >J:=elt; >J1:=elt; >G:=AutomorphismGroup(L,[H,J]); >#G; >IsIsometric(L,[H,J],L1,[H1,J1]); Output: Magma V2.10-6 Fri Dec 5 2003 02:26:02 on modular [Seed = 3876121544] ------------------------------------- 2 true [1 0] [0 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:46:05 2003 Input: ?div Output: Magma V2.10-6 Fri Dec 5 2003 06:46:02 on modular [Seed = 3059345005] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:47:49 2003 Input: ?div ?1 Output: Magma V2.10-6 Fri Dec 5 2003 06:47:46 on modular [Seed = 3193041405] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra KIND: Overview =============================================================================== Magma supports the following categories of rings, fields and algebras: RngInt integer ring RngIntRes residue rings of integers (i.e. modulo n) RngUPol univariate polynomial rings RngUPolRes residue rings of univariate polynomials RngMPol distributed multivariate polynomial rings RngInvar invariant rings of finite groups RngPow power, Laurent and Puiseux series rings RngLaz lazy series rings RngVal valuation rings RngPad p-adic rings and fields AlgChtr algebras of characters of finite groups AlgFP finitely presented algebras FldRat rational field FldPr, FldRe, FldCom real and complex fields FldFin finite (Galois) fields FldFunRat rational function fields FldFun function fields FldNum number fields FldQuad quadratic fields FldCyc cyclotomic fields FldAb abelian extensions (of number fields) AlgMat matrix algebras + Structure Constant Algebras + Associative Algebras + Basic Algebras + Lie Algebras + Group Algebras They are created by the functions: + IntegerRing or Integers + ResidueClassRing + PolynomialRing or PolynomialAlgebra + InvariantRing + PowerSeriesRing or PowerSeriesAlgebra, LaurentSeriesRing or LaurentSeriesAlgebra + ValuationRing + pAdicRing, pAdicField + CharacterRing + FreeAlgebra + RationalField + RealField, ComplexField + FiniteField or GaloisField or GF + FieldOfFractions + NumberField + QuadraticField + CyclotomicField + Local Ring + MatrixRing or MatrixAlgebra + Algebra + AssociativeAlgebra + BasicAlgebra + LieAlgebra + GroupAlgebra One may create any ring by creating one of these magmas and then taking the required subring or quotient ring, as appropriate, with the sub or quo constructor. The characteristic of ring R is Characteristic(R). Its cardinality is #R. The operators for arithmetic on ring elements are: r + s, r - s, -r, r * s, and r ^ n. In fields the division operator is / and in other rings division-with-remainder is performed with div and mod . The additive identity is Zero(R) or R!0, and the multiplicative identity is One(R) or R!1 . Functions testing properties of a ring element include IsZero, IsOne, IsMinusOne, IsUnit. For rings in which an ordering is defined on the elements, the comparison operations are gt, ge, lt, le, and also Max and Min. EXAMPLE: > GF81 := GF(3, 4); > print GF81; Finite field of size 3^4 > e := 2 * w^5; print e; w^45 > P := PolynomialRing(GF81); > print P; Univariate Polynomial Ring in x over GF(3^4) > p := 2*x^6 - w*x^2 + 1; print p; 2*x^6 + w^41*x^2 + 1 > FF := FieldOfFractions(P); print FF; Rational function field of rank 1 over GF(3^4) Variables: $.1 > print (p^2 - FF!1) / (p + 1) eq (p - 1); true =============================================================================== Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:49:48 2003 Input: ?div ?1 ?4 Output: Magma V2.10-6 Fri Dec 5 2003 06:49:45 on modular [Seed = 2305214065] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra KIND: Overview =============================================================================== Magma supports the following categories of rings, fields and algebras: RngInt integer ring RngIntRes residue rings of integers (i.e. modulo n) RngUPol univariate polynomial rings RngUPolRes residue rings of univariate polynomials RngMPol distributed multivariate polynomial rings RngInvar invariant rings of finite groups RngPow power, Laurent and Puiseux series rings RngLaz lazy series rings RngVal valuation rings RngPad p-adic rings and fields AlgChtr algebras of characters of finite groups AlgFP finitely presented algebras FldRat rational field FldPr, FldRe, FldCom real and complex fields FldFin finite (Galois) fields FldFunRat rational function fields FldFun function fields FldNum number fields FldQuad quadratic fields FldCyc cyclotomic fields FldAb abelian extensions (of number fields) AlgMat matrix algebras + Structure Constant Algebras + Associative Algebras + Basic Algebras + Lie Algebras + Group Algebras They are created by the functions: + IntegerRing or Integers + ResidueClassRing + PolynomialRing or PolynomialAlgebra + InvariantRing + PowerSeriesRing or PowerSeriesAlgebra, LaurentSeriesRing or LaurentSeriesAlgebra + ValuationRing + pAdicRing, pAdicField + CharacterRing + FreeAlgebra + RationalField + RealField, ComplexField + FiniteField or GaloisField or GF + FieldOfFractions + NumberField + QuadraticField + CyclotomicField + Local Ring + MatrixRing or MatrixAlgebra + Algebra + AssociativeAlgebra + BasicAlgebra + LieAlgebra + GroupAlgebra One may create any ring by creating one of these magmas and then taking the required subring or quotient ring, as appropriate, with the sub or quo constructor. The characteristic of ring R is Characteristic(R). Its cardinality is #R. The operators for arithmetic on ring elements are: r + s, r - s, -r, r * s, and r ^ n. In fields the division operator is / and in other rings division-with-remainder is performed with div and mod . The additive identity is Zero(R) or R!0, and the multiplicative identity is One(R) or R!1 . Functions testing properties of a ring element include IsZero, IsOne, IsMinusOne, IsUnit. For rings in which an ordering is defined on the elements, the comparison operations are gt, ge, lt, le, and also Max and Min. EXAMPLE: > GF81 := GF(3, 4); > print GF81; Finite field of size 3^4 > e := 2 * w^5; print e; w^45 > P := PolynomialRing(GF81); > print P; Univariate Polynomial Ring in x over GF(3^4) > p := 2*x^6 - w*x^2 + 1; print p; 2*x^6 + w^41*x^2 + 1 > FF := FieldOfFractions(P); print FF; Rational function field of rank 1 over GF(3^4) Variables: $.1 > print (p^2 - FF!1) / (p + 1) eq (p - 1); true =============================================================================== =============================================================================== PATH: /magma/ring-field-algebra/algebraic-field/divisors/div-create-s KIND: Section =============================================================================== Creation of Structures. Intrinsics: [+1] Places =============================================================================== Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:50:22 2003 Input: ?div ?4 Output: Magma V2.10-6 Fri Dec 5 2003 06:50:19 on modular [Seed = 2524567884] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/algebraic-field/divisors/div-create-s KIND: Section =============================================================================== Creation of Structures. Intrinsics: [+1] Places =============================================================================== Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:50:33 2003 Input: ?div ?4 Output: Magma V2.10-6 Fri Dec 5 2003 06:50:30 on modular [Seed = 2658259129] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/algebraic-field/divisors/div-create-s KIND: Section =============================================================================== Creation of Structures. Intrinsics: [+1] Places =============================================================================== Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:51:03 2003 Input: ?div ?4 Output: Magma V2.10-6 Fri Dec 5 2003 06:51:00 on modular [Seed = 3859392739] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/algebraic-field/divisors/div-create-s KIND: Section =============================================================================== Creation of Structures. Intrinsics: [+1] Places =============================================================================== Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:51:45 2003 Input: ? Output: Magma V2.10-6 Fri Dec 5 2003 06:51:42 on modular [Seed = 3993084033] ------------------------------------- =============================================================================== PATH: /language/statement KIND: Overview =============================================================================== A statement is a complete command to Magma. Every statement must end with a semicolon ( ; ). If you press the key before typing ; then Magma may give you a special prompt symbol such as print> or if> to remind you that the statement is not yet finished. EXAMPLE: > print 5+8; > DivBy3 := func< n | IsZero(n mod 3) >; =============================================================================== Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:53:47 2003 Input: 23 div 4; Output: Magma V2.10-6 Fri Dec 5 2003 06:53:44 on modular [Seed = 4128880671] ------------------------------------- 5 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 06:54:12 2003 Input: 23 div 4, 23 mod 4; Output: Magma V2.10-6 Fri Dec 5 2003 06:54:09 on modular [Seed = 3241053953] ------------------------------------- 5 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 07:00:18 2003 Input: alp1:=5; alp1:=alp1 + alp1; ShowIdentifiers(); ShowValues(); Output: Magma V2.10-6 Fri Dec 5 2003 07:00:14 on modular [Seed = 3627521206] ------------------------------------- alp1 alp1: 10 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 07:00:48 2003 Input: alp1:=5; alp1:=alp1 + alp1; ShowValues(); Output: Magma V2.10-6 Fri Dec 5 2003 07:00:45 on modular [Seed = 567176556] ------------------------------------- alp1: 10 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 07:01:06 2003 Input: alp1:=5; alp1:=alp1 + alp1; Output: Magma V2.10-6 Fri Dec 5 2003 07:01:03 on modular [Seed = 1003779940] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 07:01:23 2003 Input: alp1:=5; alp1:=alp1 + alp1; ShowValues(); Output: Magma V2.10-6 Fri Dec 5 2003 07:01:20 on modular [Seed = 82528436] ------------------------------------- alp1: 10 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 07:01:33 2003 Input: alp1:=5; alp1:=alp1 + alp1; Output: Magma V2.10-6 Fri Dec 5 2003 07:01:30 on modular [Seed = 216219830] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 07:01:49 2003 Input: ShowValues(); Output: Magma V2.10-6 Fri Dec 5 2003 07:01:46 on modular [Seed = 352016542] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.46.235) Time: Fri Dec 5 07:04:10 2003 Input: ShowValues(); Output: Magma V2.10-6 Fri Dec 5 2003 07:04:07 on modular [Seed = 1653418357] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:16:24 2003 Input: procedure>? Output: Magma V2.10-6 Fri Dec 5 2003 07:16:21 on modular [Seed = 1152060529] ------------------------------------- >> procedure>? ^ User error: bad syntax Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:16:40 2003 Input: procedure? Output: Magma V2.10-6 Fri Dec 5 2003 07:16:37 on modular [Seed = 1285751881] ------------------------------------- >> procedure? ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:17:25 2003 Input: ?procedure Output: Magma V2.10-6 Fri Dec 5 2003 07:17:22 on modular [Seed = 1421548582] ------------------------------------- 7 matches: 1 O /language/function-procedure-mapping 2 O /language/function-procedure-mapping/procedure 3 S /language/function-procedure-package 4 S /language/function-procedure-package/function-procedure 5 S /language/function-procedure-package/function-procedure/procedure 6 S /language/semantics/procedure-expression 7 I /language/function-procedure-package/function-procedure/\ procedure/procedure To view an entry, type ? followed by the number next to it Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:17:48 2003 Input: ?procedure> Output: Magma V2.10-6 Fri Dec 5 2003 07:17:45 on modular [Seed = 1588663831] ------------------------------------- No references for word "procedure>" Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:17:58 2003 Input: ?procedure Output: Magma V2.10-6 Fri Dec 5 2003 07:17:54 on modular [Seed = 2789863156] ------------------------------------- 7 matches: 1 O /language/function-procedure-mapping 2 O /language/function-procedure-mapping/procedure 3 S /language/function-procedure-package 4 S /language/function-procedure-package/function-procedure 5 S /language/function-procedure-package/function-procedure/procedure 6 S /language/semantics/procedure-expression 7 I /language/function-procedure-package/function-procedure/\ procedure/procedure To view an entry, type ? followed by the number next to it Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:18:08 2003 Input: ?procedure ?1 Output: Magma V2.10-6 Fri Dec 5 2003 07:18:04 on modular [Seed = 2959079660] ------------------------------------- 7 matches: 1 O /language/function-procedure-mapping 2 O /language/function-procedure-mapping/procedure 3 S /language/function-procedure-package 4 S /language/function-procedure-package/function-procedure 5 S /language/function-procedure-package/function-procedure/procedure 6 S /language/semantics/procedure-expression 7 I /language/function-procedure-package/function-procedure/\ procedure/procedure To view an entry, type ? followed by the number next to it =============================================================================== PATH: /language/function-procedure-mapping KIND: Overview =============================================================================== This section provides a very brief overview of the ideas behind functions, procedures and mappings. The Magma language has a number of ways of writing routines that collect a quantity of programming steps together as one idea. They are functions and procedures, which are familiar from many programming languages, and mappings (including homomorphisms and partial mappings), which are familiar from mathematics. Most Magma intrinsics, such as Abs(x), are functions. A few are procedures, such as ExtractRep(~S, ~x). Moreover, many standard Magma intrinsics return mappings, such as OrbitAction(G, T), and several constructors, such as quo, return mappings as one of their return values. Functions, procedures and mappings can all be defined by the user too. An important difference between mappings and the other two sorts of routines is that a mapping is specified as being from one algebraic structure to another, with a rule for calculating the image of any given element of the domain, whereas for functions and procedures there is no explicit declaration when they are being defined of the structures to which the arguments must belong. When the routine has been defined, as an intrinsic or by the user, it can be invoked, or called. This involves matching up the formal arguments used in the definition with the inputs, known as the actual arguments. For functions and mappings, the arguments are value arguments, that is, they are fully evaluated before the routine starts computing with them. For procedures, if the arguments are preceded with a ~ symbol, as they are above, they are reference arguments, otherwise they are value arguments. Actual reference arguments must be given as identifiers, and these identifiers may change, according to how their formal parallels change. Procedures are different from functions and mappings in that they do not return values when they are called, except in the sense that if the reference arguments change the context will alter. A mapping must return a single value, an element of the codomain (though the domain may be a Cartesian product, with tuples as elements), but a function may return several values. EXAMPLE: A call to an intrinsic function: > print Gcd(474, 255); 3 A procedure definition and invocation: > SelectIntegers := procedure(~Q, b) procedure> if b then procedure|if> Q := [Q[i]: i in [1..#Q] | IsIntegral(Q[i])]; procedure|if> return; procedure|if> end if; procedure> Q:=[Q[i]: i in [1..#Q] | not IsIntegral(Q[i])]; procedure> end procedure; > > r := [6/8, 3, -8/4, 7, 36/5]; > SelectIntegers(~r, true); > print r; [ 3, -2, 7 ] The natural homomorphism from S6 to S6/A6: > S6 := Sym(6); A6 := Alt(6); > Q, natural := quo< S6 | A6 >; > print natural; Mapping from: GrpPerm: S6 to GrpPerm: Q > print natural(S6!(5, 4)); (1, 2) SEE ALSO: +1 /language/function-procedure-mapping/function +2 /language/function-procedure-mapping/procedure +3 /magma/mapping +4 /system/intrinsic =============================================================================== Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:23:50 2003 Input: G := AbelianGroup< a,b | 6*a, 14*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:23:47 on modular [Seed = 2441008738] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/42 Defined on 2 generators Relations: 2*a = 0 42*b = 0 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:24:05 2003 Input: G := AbelianGroup< a,b | 7*a, 14*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:24:02 on modular [Seed = 2574704219] ------------------------------------- Abelian Group isomorphic to Z/7 + Z/14 Defined on 2 generators Relations: 7*a = 0 14*b = 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:24:28 2003 Input: G := AbelianGroup< a,b | 6*a, 14*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:24:24 on modular [Seed = 3792545082] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/42 Defined on 2 generators Relations: 2*a = 0 42*b = 0 Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:24:54 2003 Input: G := AbelianGroup< a,b | 2*a, 3*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:24:51 on modular [Seed = 3942952408] ------------------------------------- >> G := AbelianGroup< a,b | 2*a, 3*b >; G;; ^ Runtime error in 'AssignNames': Too many names given for this object Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*G.1 = 0 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:25:30 2003 Input: G := AbelianGroup< a,b | 6*a, 3*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:25:27 on modular [Seed = 4145590752] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/6 Defined on 2 generators Relations: 3*a = 0 6*b = 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:25:43 2003 Input: G := AbelianGroup< a,b | 6*a, 6*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:25:40 on modular [Seed = 4279286171] ------------------------------------- Abelian Group isomorphic to Z/6 + Z/6 Defined on 2 generators Relations: 6*a = 0 6*b = 0 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:25:53 2003 Input: G := AbelianGroup< a,b | 2*a, 6*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:25:50 on modular [Seed = 3341320617] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/6 Defined on 2 generators Relations: 2*a = 0 6*b = 0 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:26:10 2003 Input: G := AbelianGroup< a,b | 2*a, 7*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:26:07 on modular [Seed = 3475016112] ------------------------------------- >> G := AbelianGroup< a,b | 2*a, 7*b >; G;; ^ Runtime error in 'AssignNames': Too many names given for this object Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*G.1 = 0 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:27:06 2003 Input: G := AbelianGroup< a,b | 2*a, 7*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:27:03 on modular [Seed = 3610808672] ------------------------------------- Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*a = 0 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:27:25 2003 Input: G := AbelianGroup< a,b,c | 2*a, 7*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:27:22 on modular [Seed = 3744504149] ------------------------------------- Abelian Group isomorphic to Z/14 + Z Defined on 2 generators Relations: 14*a = 0 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:27:39 2003 Input: G := AbelianGroup< a,b,c | 2*a, 7*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:27:36 on modular [Seed = 418864831] ------------------------------------- Abelian Group isomorphic to Z/14 + Z Defined on 2 generators Relations: 14*a = 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:27:53 2003 Input: G := AbelianGroup< a,b,c | 2*a, 7*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:27:50 on modular [Seed = 266357206] ------------------------------------- Abelian Group isomorphic to Z/14 + Z Defined on 2 generators Relations: 14*c = 0 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:28:05 2003 Input: G := AbelianGroup< a,b,c | 2*a, 7*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:28:02 on modular [Seed = 132661706] ------------------------------------- Abelian Group isomorphic to Z/14 + Z Defined on 2 generators Relations: 14*f = 0 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:28:34 2003 Input: G := AbelianGroup< a,b,c | 2*a = 7*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:28:31 on modular [Seed = 1070627279] ------------------------------------- Abelian Group isomorphic to Z + Z Defined on 2 generators (free) Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:28:49 2003 Input: G := AbelianGroup< a,b,c | 2*a = 6*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:28:46 on modular [Seed = 936931798] ------------------------------------- Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*x = 0 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:29:04 2003 Input: G := AbelianGroup< a,b | 2*a = 6*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:29:01 on modular [Seed = 801139261] ------------------------------------- Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*x = 0 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:29:35 2003 Input: G := AbelianGroup< a,b | 2*a = 6*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:29:32 on modular [Seed = 650732309] ------------------------------------- Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*x = 0 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:30:03 2003 Input: G := AbelianGroup< a,b | 2*a , 6*b >; G; Output: Magma V2.10-6 Fri Dec 5 2003 07:29:59 on modular [Seed = 1588665094] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/6 Defined on 2 generators Relations: 2*x = 0 6*G.2 = 0 Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:37:19 2003 Input: ?PolynomialRing Output: Magma V2.10-6 Fri Dec 5 2003 07:37:16 on modular [Seed = 1085211811] ------------------------------------- 7 matches: 1 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 2 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 3 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 4 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 5 I /magma/ring-field-algebra/ideal-groebner/graded-weight/creation/\ PolynomialRing 6 I /magma/ring-field-algebra/invariant-ring/access/PolynomialRing 7 I /magma/ring-field-algebra/univariate-polynomial/creation/magma/\ PolynomialAlgebra To view an entry, type ? followed by the number next to it Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:38:25 2003 Input: ?PolynomialRing ?1 Output: Magma V2.10-6 Fri Dec 5 2003 07:38:21 on modular [Seed = 2023177050] ------------------------------------- 7 matches: 1 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 2 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 3 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 4 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 5 I /magma/ring-field-algebra/ideal-groebner/graded-weight/creation/\ PolynomialRing 6 I /magma/ring-field-algebra/invariant-ring/access/PolynomialRing 7 I /magma/ring-field-algebra/univariate-polynomial/creation/magma/\ PolynomialAlgebra To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/distributive-multivariate-polynomial/rings/\ creation/PolynomialRing KIND: Intrinsic =============================================================================== PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol PolynomialAlgebra(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol Create a multivariate polynomial ring in n>0 indeterminates over the ring R with the given order order on the monomials. See Section H46E24 for details. =============================================================================== Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:39:48 2003 Input: ?PolynomialRing ?1 ?FieldOfRationals Output: Magma V2.10-6 Fri Dec 5 2003 07:39:44 on modular [Seed = 1870671072] ------------------------------------- 7 matches: 1 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 2 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 3 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 4 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 5 I /magma/ring-field-algebra/ideal-groebner/graded-weight/creation/\ PolynomialRing 6 I /magma/ring-field-algebra/invariant-ring/access/PolynomialRing 7 I /magma/ring-field-algebra/univariate-polynomial/creation/magma/\ PolynomialAlgebra To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/distributive-multivariate-polynomial/rings/\ creation/PolynomialRing KIND: Intrinsic =============================================================================== PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol PolynomialAlgebra(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol Create a multivariate polynomial ring in n>0 indeterminates over the ring R with the given order order on the monomials. See Section H46E24 for details. =============================================================================== No references for word "FieldOfRationals" Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:40:32 2003 Input: ?PolynomialRing ?1 ?RationalField Output: Magma V2.10-6 Fri Dec 5 2003 07:40:29 on modular [Seed = 2674973757] ------------------------------------- 7 matches: 1 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 2 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 3 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 4 I /magma/ring-field-algebra/ideal-groebner/creation/rings/\ PolynomialRing 5 I /magma/ring-field-algebra/ideal-groebner/graded-weight/creation/\ PolynomialRing 6 I /magma/ring-field-algebra/invariant-ring/access/PolynomialRing 7 I /magma/ring-field-algebra/univariate-polynomial/creation/magma/\ PolynomialAlgebra To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/distributive-multivariate-polynomial/rings/\ creation/PolynomialRing KIND: Intrinsic =============================================================================== PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol PolynomialAlgebra(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol Create a multivariate polynomial ring in n>0 indeterminates over the ring R with the given order order on the monomials. See Section H46E24 for details. =============================================================================== =============================================================================== PATH: /magma/ring-field-algebra/rational/creation/magma/Rationals KIND: Intrinsic =============================================================================== Rationals() : Null -> FldRat RationalField() : Null -> FldRat Create the field Q of rational numbers. =============================================================================== Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:40:59 2003 Input: ?RationalField Output: Magma V2.10-6 Fri Dec 5 2003 07:40:56 on modular [Seed = 2541278288] ------------------------------------- =============================================================================== PATH: /magma/ring-field-algebra/rational/creation/magma/Rationals KIND: Intrinsic =============================================================================== Rationals() : Null -> FldRat RationalField() : Null -> FldRat Create the field Q of rational numbers. =============================================================================== Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:42:53 2003 Input: R:=PolynomialRing(RationalField());R; Output: Magma V2.10-6 Fri Dec 5 2003 07:42:50 on modular [Seed = 2388774107] ------------------------------------- Univariate Polynomial Ring over Rational Field Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:43:22 2003 Input: R:=PolynomialRing(RationalField());R; Output: Magma V2.10-6 Fri Dec 5 2003 07:43:18 on modular [Seed = 2255078655] ------------------------------------- >> R:=PolynomialRing(RationalField());R; ^ User error: Bad print expression Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:43:38 2003 Input: R:=PolynomialRing(RationalField());R; Output: Magma V2.10-6 Fri Dec 5 2003 07:43:34 on modular [Seed = 3193044182] ------------------------------------- Univariate Polynomial Ring in x over Rational Field Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:44:12 2003 Input: R:=PolynomialRing(RationalField(),n); Output: Magma V2.10-6 Fri Dec 5 2003 07:44:09 on modular [Seed = 3042637619] ------------------------------------- >> R:=PolynomialRing(RationalField(),n); ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:44:31 2003 Input: R:=PolynomialRing(RationalField(),2); Output: Magma V2.10-6 Fri Dec 5 2003 07:44:28 on modular [Seed = 2906844958] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:44:49 2003 Input: R:=PolynomialRing(RationalField(),2); Output: Magma V2.10-6 Fri Dec 5 2003 07:44:46 on modular [Seed = 2773149444] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:45:03 2003 Input: R:=PolynomialRing(RationalField(),2);R; Output: Magma V2.10-6 Fri Dec 5 2003 07:45:00 on modular [Seed = 3644234506] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, $.2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:45:25 2003 Input: R:=PolynomialRing(RationalField(),2);R; Output: Magma V2.10-6 Fri Dec 5 2003 07:45:22 on modular [Seed = 3510539052] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:46:29 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R);A; Output: Magma V2.10-6 Fri Dec 5 2003 07:46:26 on modular [Seed = 3257762815] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Univariate Polynomial Ring over Polynomial ring of rank 2 over Rational Field Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:46:59 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; Output: Magma V2.10-6 Fri Dec 5 2003 07:46:56 on modular [Seed = 4195728293] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: $.1, $.2, $.3, $.4 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:47:15 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; Output: Magma V2.10-6 Fri Dec 5 2003 07:47:12 on modular [Seed = 535846481] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:49:04 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=x1; Output: Magma V2.10-6 Fri Dec 5 2003 07:49:01 on modular [Seed = 402151092] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:49:49 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=x1;f; Output: Magma V2.10-6 Fri Dec 5 2003 07:49:46 on modular [Seed = 232934649] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d x1 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:50:20 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=x1;f; ?quo Output: Magma V2.10-6 Fri Dec 5 2003 07:50:17 on modular [Seed = 1020492843] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d x1 34 matches: 1 O /language/expression/constructor 2 S /magma/module-lattice/complexes/complexes/sub-quo 3 S /magma/module-lattice/lattice/new-construction/sub-super-quo 4 S /magma/module-lattice/modules-affine-algebras/sub-quo 5 I /magma/combinatorial-geometrical-incidence/graph/operation/\ subgraph-supergraph-quotient/quo 6 I /magma/group/abelian/subgroup-quotient/quotient/quo 7 I /magma/group/finitely-presented/fp-group-construction/\ fp-group-quotient/quo 8 I /magma/group/group-overview/creation-general/quotient/quo 9 I /magma/group/matrix/quotient/construction-quotient/quo 10 I /magma/group/permutation/quotient/construction-quotient/quo 11 I /magma/group/polycyclic/polycyclic-groups/magma/quo 12 I /magma/group/polycyclic/subgroup-quotient-homomorphism-extension/\ quotient/quo 13 I /magma/group/soluble/definition/constructor/quo 14 I /magma/group/soluble/quotient/construction-quotient/quo 15 I /magma/module-lattice/complexes/complexes/sub-quo/quo 16 I /magma/module-lattice/dedekind-modules/creation/quo 17 I /magma/module-lattice/general/quotient/quo 18 I /magma/module-lattice/general/quotient/quotient/quo 19 I /magma/module-lattice/lattice/new-construction/sub-super-quo/quo 20 I /magma/module-lattice/modules-affine-algebras/sub-quo/quo 21 I /magma/module-lattice/vector-space-linear-transformation/\ subspace-quotient-homomorphism/quotient/quo 22 I /magma/ring-field-algebra/affine-algebra/creation/quo 23 I /magma/ring-field-algebra/alg_grp/subring-ideal-quotient/quo 24 I /magma/ring-field-algebra/algebraic-field/creation/magma/quo 25 I /magma/ring-field-algebra/algebraic-field/ideal/quotient-ring/\ orderq/quo 26 I /magma/ring-field-algebra/detail/ideal-quotient/creation/quo 27 I /magma/ring-field-algebra/finitely-presented/presentation/quo 28 I /magma/ring-field-algebra/grp_alg/subs-quos/quos/quo 29 I /magma/ring-field-algebra/integer/residue-class-rings/creation/quo 30 I /magma/ring-field-algebra/integer/residue-class-rings/creation/quo 31 I /magma/ring-field-algebra/lie_alg/sub-construct/quo 32 I /magma/ring-field-algebra/local/creation/elementary_padic/quo 33 I /magma/ring-field-algebra/univariate-polynomial/ideal-quotient/\ creation/quo 34 I /magma/semigroup/finitely-presented/subsemigroup-ideal-quotient/\ quotient/quo To view an entry, type ? followed by the number next to it Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:51:56 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=x1;f; R1:=R/(f);R1; Output: Magma V2.10-6 Fri Dec 5 2003 07:51:53 on modular [Seed = 886797379] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d x1 >> R1:=R/(f);R1;; ^ Runtime error in '/': Bad argument types Argument types given: RngMPol, RngMPolElt >> R1:=R/(f);R1;; ^ User error: Identifier 'R1' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:52:18 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=x1;f; R1:=R quo(f);R1; Output: Magma V2.10-6 Fri Dec 5 2003 07:52:15 on modular [Seed = 751004749] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d x1 >> R1:=R quo(f);R1;; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:52:43 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=x1;f; R1:= quo(R,f);R1; Output: Magma V2.10-6 Fri Dec 5 2003 07:52:40 on modular [Seed = 634021283] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d x1 >> R1:= quo(R,f);R1;; ^ User error: Identifier 'quo' has not been declared or assigned >> R1:= quo(R,f);R1;; ^ User error: Identifier 'R1' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:54:20 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=x1;f; R1:= quo;R1; Output: Magma V2.10-6 Fri Dec 5 2003 07:54:17 on modular [Seed = 1521818301] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d x1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x1, x2 Quotient relations: [ x1 ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:55:16 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; Output: Magma V2.10-6 Fri Dec 5 2003 07:55:13 on modular [Seed = 1319235937] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ -x^3 + y^2 - 1 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:56:30 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; x^3; Output: Magma V2.10-6 Fri Dec 5 2003 07:56:27 on modular [Seed = 1202255906] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ -x^3 + y^2 - 1 ] x^3 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:56:48 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; x^4; Output: Magma V2.10-6 Fri Dec 5 2003 07:56:45 on modular [Seed = 2090058735] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ -x^3 + y^2 - 1 ] x^4 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:57:57 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; a^4; Output: Magma V2.10-6 Fri Dec 5 2003 07:57:54 on modular [Seed = 1956367288] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: a, $.2 Quotient relations: [ a^3 - $.2^2 + 1 ] a*$.2^2 - a Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:58:25 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; a^4; Output: Magma V2.10-6 Fri Dec 5 2003 07:58:22 on modular [Seed = 1820578716] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: a, b Quotient relations: [ a^3 - b^2 + 1 ] a*b^2 - a Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:58:40 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; a^3; Output: Magma V2.10-6 Fri Dec 5 2003 07:58:37 on modular [Seed = 1686887303] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: a, b Quotient relations: [ a^3 - b^2 + 1 ] b^2 - 1 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:59:00 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; b^2; Output: Magma V2.10-6 Fri Dec 5 2003 07:58:57 on modular [Seed = 2624791187] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: a, b Quotient relations: [ a^3 - b^2 + 1 ] b^2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:59:27 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; y^2; Output: Magma V2.10-6 Fri Dec 5 2003 07:59:24 on modular [Seed = 2507811751] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ -x^3 + y^2 - 1 ] y^2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 07:59:47 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; y^2; Output: Magma V2.10-6 Fri Dec 5 2003 07:59:44 on modular [Seed = 2321888468] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] y^2 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:00:03 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; y^4; Output: Magma V2.10-6 Fri Dec 5 2003 08:00:00 on modular [Seed = 2188197068] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] y^4 Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:00:18 2003 Input: R:=PolynomialRing(RationalField(),2);R; A:=PolynomialRing(R,4);A; f:=y^2-x^3-1;f; R1:= quo;R1; x^4; Output: Magma V2.10-6 Fri Dec 5 2003 08:00:15 on modular [Seed = 3009154546] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y Polynomial ring of rank 4 over Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: a, b, c, d -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] x*y^2 - x Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:00:39 2003 Input: R:=PolynomialRing(RationalField(),2);R; f:=y^2-x^3-1;f; R1:= quo;R1; x^3; Output: Magma V2.10-6 Fri Dec 5 2003 08:00:36 on modular [Seed = 2873365953] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] y^2 - 1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:00:55 2003 Input: R:=PolynomialRing(RationalField(),2);R; f:=y^2-x^3-1;f; R1:= quo;R1; y^3; Output: Magma V2.10-6 Fri Dec 5 2003 08:00:52 on modular [Seed = 2739674425] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] y^3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:01:14 2003 Input: R:=PolynomialRing(RationalField(),2);R; f:=y^2-x^3-1;f; R1:= quo;R1; y^9; Output: Magma V2.10-6 Fri Dec 5 2003 08:01:11 on modular [Seed = 3374741312] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] y^9 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:02:27 2003 Input: R:=PolynomialRing(RationalField(),2);R; f:=y^2-x^3-1;f; R1:= quo;R1; x^4-xy^2+x; Output: Magma V2.10-6 Fri Dec 5 2003 08:02:24 on modular [Seed = 3241049919] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] >> x^4-xy^2+x;; ^ User error: Identifier 'xy' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:02:40 2003 Input: R:=PolynomialRing(RationalField(),2);R; f:=y^2-x^3-1;f; R1:= quo;R1; x^4-x*y^2+x; Output: Magma V2.10-6 Fri Dec 5 2003 08:02:37 on modular [Seed = 4178986762] ------------------------------------- Polynomial ring of rank 2 over Rational Field Lexicographical Order Variables: x, y -x^3 + y^2 - 1 Affine Algebra of rank 2 over Rational Field Lexicographical Order Variables: x, y Quotient relations: [ x^3 - y^2 + 1 ] 0 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:10:51 2003 Input: ?ellipt Output: Magma V2.10-6 Fri Dec 5 2003 08:10:48 on modular [Seed = 3775814951] ------------------------------------- No references for word "ellipt" Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:13:58 2003 Input: ?elliptic Output: Magma V2.10-6 Fri Dec 5 2003 08:13:55 on modular [Seed = 368750235] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:15:50 2003 Input: ?elliptic ?2 Output: Magma V2.10-6 Fri Dec 5 2003 08:15:47 on modular [Seed = 199536917] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:16:24 2003 Input: ?elliptic ?2 ?+1 Output: Magma V2.10-6 Fri Dec 5 2003 08:16:21 on modular [Seed = 65845563] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/introduction KIND: Section =============================================================================== Introduction. This chapter describes the features for working with elliptic curves in Magma. An elliptic curve E is the projective closure of the curve given by the generalized Weierstrass equation y^2 + a_1 xy + a_3 y = x^3 + a_2 x^2 + a_4 x + a_6, and is specified by the sequence [a_1, a_2, a_3, a_4, a_6] of coefficients, or by the two element sequence [a_4, a_6] when a_1 = a_2 = a_3 = 0. Elliptic curve functionality covers both elementary invariants of curves and arithmetic in the group of rational points, as well as higher level features for computing local invariants, heights, and Mordell--Weil groups for curves over Q, and for point counting and the determination of the group structure over F_q. The base ring of elliptic curves is currently restricted to fields. Curves over the rationals have special features to allow the construction of integral and minimal models, and for base change to finite fields, in acknowledgement of the integral structure over Z or Z_p. For curves over the rationals, there exist algorithms for determining minimal models, and we implement Tate's algorithm for determining Kodaira symbols and various local invariants. Algorithms for the computation of the Mordell--Weil group are heavily based on publications of John Cremona; see [Cre97] for details. Point counting on elliptic curves over finite fields is achieved with a high-performance implementation of the Schoof--Elkies--Atkin algorithm (see [Elk98]), with improvements of Lercier [Ler97] in characteristic 2. An implementation of the Weil pairing (see [Men93]) permits the rapid proof of Z/nZ-independence of n-torsion points and for the MOV reduction of discrete logarithm problem on supersingular elliptic curves to that in a finite field. Elliptic curves are specialised forms of the more general curve and scheme types, and as such all functions which apply to these general types work on elliptic curves. Some of these functions are described here, but not all of them --- refer to chapters H86E8 (Schemes) and H87E46 (Curves) for descriptions of these functions, as well as an explanation of the relationships between points, point sets, and schemes. In particular, note that the parent of a point is a point set, and not the curve. The category of elliptic curves is called CrvEll, with points of type PtEll lying in point sets of type SetPtEll. There is also the category SchGrpEll for subgroup schemes of elliptic curves, and a special category SymKod exists for the datatype of Kodaira symbols, classifying the local structure of the special fiber at p of the N'eron model of an elliptic curve E/Q. =============================================================================== Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:19:21 2003 Input: ?elliptic ?2 ?+2 Output: Magma V2.10-6 Fri Dec 5 2003 08:19:18 on modular [Seed = 936939004] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:19:53 2003 Input: ?elliptic ?2 ?+2 ?+1 Output: Magma V2.10-6 Fri Dec 5 2003 08:19:50 on modular [Seed = 801150404] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:21:22 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 Output: Magma V2.10-6 Fri Dec 5 2003 08:21:19 on modular [Seed = 1555293454] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:25:19 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; Output: Magma V2.10-6 Fri Dec 5 2003 08:25:16 on modular [Seed = 1302525292] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:26:04 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?descent Output: Magma V2.10-6 Fri Dec 5 2003 08:26:01 on modular [Seed = 1168833841] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 6 matches: 1 I /magma/group/fiurg/operations/LeftDescentSet 2 I /magma/group/fiurg/operations/RightDescentSet 3 I /magma/lie-theory/coxeter-groups/group-elt-op/LeftDescentSet 4 I /magma/lie-theory/coxeter-groups/group-elt-op/RightDescentSet 5 I /magma/lie-theory/finite-coxeter-groups/group-elt-op/\ LeftDescentSet 6 I /magma/lie-theory/finite-coxeter-groups/group-elt-op/\ RightDescentSet To view an entry, type ? followed by the number next to it Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:26:56 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?twodescent Output: Magma V2.10-6 Fri Dec 5 2003 08:26:53 on modular [Seed = 2106770941] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field No references for word "twodescent" Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:27:13 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?2descent Output: Magma V2.10-6 Fri Dec 5 2003 08:27:10 on modular [Seed = 1973079494] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field No references for word "2descent" Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:28:18 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; mwrank(E); Output: Magma V2.10-6 Fri Dec 5 2003 08:28:15 on modular [Seed = 1837290911] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field >> mwrank(E);; ^ User error: Identifier 'mwrank' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:28:45 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; MWrank(E); Output: Magma V2.10-6 Fri Dec 5 2003 08:28:42 on modular [Seed = 1686885235] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field >> MWrank(E);; ^ User error: Identifier 'MWrank' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:29:11 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?mwrank Output: Magma V2.10-6 Fri Dec 5 2003 08:29:08 on modular [Seed = 2624793509] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field No references for word "mwrank" Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:29:27 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank Output: Magma V2.10-6 Fri Dec 5 2003 08:29:24 on modular [Seed = 2541232318] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:30:25 2003 Input: ?elliptic ?2 ?+2 ?+1 ?+1 E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 Output: Magma V2.10-6 Fri Dec 5 2003 08:30:22 on modular [Seed = 2221618167] ------------------------------------- 34 matches: 1 O /magma/combinatorial-geometrical-incidence 2 S /magma/combinatorial-geometrical-incidence/elliptic-curve 3 S /magma/combinatorial-geometrical-incidence/modular-symbol/\ elliptic-curves 4 S /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points 5 S /magma/ring-field-algebra/real-complex/elliptic-modular 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 11 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurve 12 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 13 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/EllipticCurveFromjInvariant 14 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/SupersingularEllipticCurve 15 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 16 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 17 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/IsEllipticCurve 18 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/CremonaDatabase 19 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 20 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 21 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurve 22 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 23 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 24 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 25 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/EllipticCurves 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/EllipticLogarithm 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-elliptic_logs/\ pAdicEllipticLogarithm 29 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/quadratic-twists/IsEllipticCurve 30 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ EllipticCurve 31 I /magma/geometry/algebraic-curve/global-curvepl/global-special/\ IsEllipticWeierstrass 32 I /magma/geometry/modular-forms/abelian-varieties/EllipticCurve 33 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints 34 I /magma/group/GrpPSL2/structure-of-congruence-groups/\ cusps-and-elliptic-points/EllipticPoints To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve KIND: Section =============================================================================== ELLIPTIC CURVES. Subsections: [+1] introduction [+2] creation [+3] operations_curve [+4] subgroup_schemes [+5] pointset [+6] point [+7] function_field [+8] rational_curves [+9] integral_points [+10] database [+11] over_anf [+12] ff_curves [+13] morphism  
Acknowledgements<\ /I>







DETAILS

=============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation KIND: Section =============================================================================== Creation Functions. Subsections: [+1] creation-curve [+2] creation-predicates [+3] creation-change_ring [+4] creation-models [+5] creation-model-predicates [+6] twists =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve KIND: Section =============================================================================== Creation of an Elliptic Curve. An elliptic curve E may be created by specifying Weierstrass coordinates for the curve over a field K, where integer coordinates are interpreted as elements of Q. Note that the coordinate ring K defines the base point set of E, and points defined over an extension field of K must be created in the appropriate point set. Intrinsics: [+1] EllipticCurve [+2] EllipticCurve [+3] EllipticCurveFromjInvariant [+4] EllipticCurve [+5] EllipticCurve [+6] EllipticCurve [+7] SupersingularEllipticCurve Examples: [+8] Example-Creation [+9] Example-CreationFromCurve [+10] Example-CreationFromCurve2 =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/creation/\ creation-curve/EllipticCurve KIND: Intrinsic =============================================================================== EllipticCurve([a, b]) : [ RngElt ] -> CrvEll EllipticCurve([a1, a2, a3, a4, a6]) : [ RngElt ] -> CrvEll Given a sequence of elements of a ring K, creates the elliptic curve E over K defined by taking the elements of the sequence as Weierstrass coefficients. The length of the sequence must either be two, that is s=[a, b], in which case E is defined by y^2 = x^3 + ax + b, or five, that is s=[a_1, a_2, a_3, a_4, a_6], in which case E is given by y^2 + a_1xy + a_3y=x^3 + a_2x^2 + a_4x + a_6. Currently K must be field; if integers are given, they will be coerced into Q. The given coefficients must define a nonsingular curve; that is, the discriminant of the curve must be nonzero. =============================================================================== Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:30:47 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 Output: Magma V2.10-6 Fri Dec 5 2003 08:30:44 on modular [Seed = 3159558949] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:31:45 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 Rank(E); Output: Magma V2.10-6 Fri Dec 5 2003 08:31:42 on modular [Seed = 3075997716] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== Warning: rank computed (0) is only a lower bound (It may still be correct, though) Warning: rank computed (0) is only a lower bound (It may still be correct, though) 0 Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:32:32 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 RankBound(E); Output: Magma V2.10-6 Fri Dec 5 2003 08:32:29 on modular [Seed = 2940213343] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== >> RankBound(E); ^ Runtime error in 'RankBound': Bad argument types Argument types given: CrvEll Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:33:08 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 MordellWeilRank(E); Output: Magma V2.10-6 Fri Dec 5 2003 08:33:05 on modular [Seed = 2806518187] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== Warning: rank computed (0) is only a lower bound (It may still be correct, though) Warning: rank computed (0) is only a lower bound (It may still be correct, though) 0 Total time: 3.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:33:35 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup Output: Magma V2.10-6 Fri Dec 5 2003 08:33:32 on modular [Seed = 3744492014] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:35:40 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup Selmergroup(2); Output: Magma V2.10-6 Fri Dec 5 2003 08:35:37 on modular [Seed = 3441589113] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== >> Selmergroup(2);; ^ User error: Identifier 'Selmergroup' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:36:04 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup SelmerGroup(2); Output: Magma V2.10-6 Fri Dec 5 2003 08:36:01 on modular [Seed = 3307893529] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== >> SelmerGroup(2);; ^ Runtime error in 'SelmerGroup': Bad argument types Argument types given: RngIntElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:36:31 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup SelmerGroup(2:E->E); Output: Magma V2.10-6 Fri Dec 5 2003 08:36:28 on modular [Seed = 4245834556] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== >> SelmerGroup(2:E->E);; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:39:53 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup MordellWeilRankBounds(E); Output: Magma V2.10-6 Fri Dec 5 2003 08:39:50 on modular [Seed = 4145562188] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== 0 2 Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:41:02 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup MordellWeilRankBounds(E); Isogeny; Output: Magma V2.10-6 Fri Dec 5 2003 08:40:59 on modular [Seed = 3825946898] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== 0 2 Intrinsic 'Isogeny' Signatures: ( E, F, s, h, o) -> Map Returns the isogeny E -> F defined by the polynomials psi, phi, omega, taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be univariate (although elements of a multivariate polynomial ring) and the polynomials need not be coprime. ( E, P) -> Map Returns the isogeny E -> F corresponding to the point P on the modular curve X_0(N). Total time: 3.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:49:50 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup MordellWeilRankBounds(E); Isogeny; C := HyperellipticCurve(E); Output: Magma V2.10-6 Fri Dec 5 2003 08:49:47 on modular [Seed = 385459697] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== 0 2 Intrinsic 'Isogeny' Signatures: ( E, F, s, h, o) -> Map Returns the isogeny E -> F defined by the polynomials psi, phi, omega, taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be univariate (although elements of a multivariate polynomial ring) and the polynomials need not be coprime. ( E, P) -> Map Returns the isogeny E -> F corresponding to the point P on the modular curve X_0(N). Total time: 3.199 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:50:19 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup MordellWeilRankBounds(E); Isogeny; C := HyperellipticCurve(E); J := Jacobian(C); Output: Magma V2.10-6 Fri Dec 5 2003 08:50:15 on modular [Seed = 99268366] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== 0 2 Intrinsic 'Isogeny' Signatures: ( E, F, s, h, o) -> Map Returns the isogeny E -> F defined by the polynomials psi, phi, omega, taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be univariate (although elements of a multivariate polynomial ring) and the polynomials need not be coprime. ( E, P) -> Map Returns the isogeny E -> F corresponding to the point P on the modular curve X_0(N). Total time: 3.269 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 08:50:45 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; ?rank ?4 ?Selmergroup MordellWeilRankBounds(E); Isogeny; C := HyperellipticCurve(E); J := Jacobian(C); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Fri Dec 5 2003 08:50:40 on modular [Seed = 1037209361] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 45 matches: 1 S /magma/module-lattice/smat/non-trivial/rank 2 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/Dimension 3 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ over_anf/over_anf-selmer/over_anf-selmer-selmer/RankBound 4 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 5 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 6 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank 7 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 8 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 9 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 10 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/RankBounds 11 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 12 I /magma/combinatorial-geometrical-incidence/incidence-geometry/\ access/Rank 13 I /magma/geometry/grd-rng/gr-lists/gr-details/K3SingularRank 14 I /magma/group/abelian/invariant/TorsionFreeRank 15 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 16 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/NuclearRank 17 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 18 I /magma/group/finitely-presented-groups-advanced/p-Quotient/\ interactive/pMultiplicatorRank 19 I /magma/group/finitely-presented/quotient/abelian/TorsionFreeRank 20 I /magma/group/fiurg/operations/Rank 21 I /magma/group/groups-lie-type/operations/Rank 22 I /magma/group/groups-lie-type/operations/SemisimpleRank 23 I /magma/group/root-data/operators-root-dtm/Rank 24 I /magma/lie-theory/coxeter-groups/group-op/Rank 25 I /magma/lie-theory/finite-coxeter-groups/group-op/Rank 26 I /magma/lie-theory/root-systems/operators-root-sys/Rank 27 I /magma/module-lattice/general/basis/Rank 28 I /magma/module-lattice/general/homomorphisms/operation-element/Rank 29 I /magma/module-lattice/lattice/lattice-properties/\ lattice-attributes/Dimension 30 I /magma/module-lattice/mat/properties/Rank 31 I /magma/module-lattice/smat/non-trivial/rank/Rank 32 I /magma/module-lattice/vector-space-linear-transformation/\ linear-transformation/Rank 33 I /magma/ring-field-algebra/affine-algebra/operations/Rank 34 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 35 I /magma/ring-field-algebra/algebraic-field/operation/invariant/\ UnitRank 36 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 37 I /magma/ring-field-algebra/algebraic-field/unit-group/UnitRank 38 I /magma/ring-field-algebra/algebraically-closed-field/property/Rank 39 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/invariant/Rank 40 I /magma/ring-field-algebra/function-field/global/UnitRank 41 I /magma/ring-field-algebra/lazy/ring_ops/Rank 42 I /magma/ring-field-algebra/matrix/element/Boolean/other/Rank 43 I /magma/ring-field-algebra/rational-function-field/operation/\ magma/Rank 44 I /magma/ring-field-algebra/univariate-polynomial/operation/\ invariant/Rank 45 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Example-Rank To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/\ rational_curves/rational_curves-group/Rank KIND: Intrinsic =============================================================================== Rank(H: parameters) : SetPtEll -> RngIntElt Rank(E: parameters) : CrvEll -> RngIntElt MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt MordellWeilRank(E: parameters) : CrvEll -> RngIntElt Bound: RngIntElt Default: 150 Given an elliptic curve E defined over Q, this returns the rank of the Mordell--Weil group of E. The general procedure to calculate the rank involves searching for rational points on certain homogeneous spaces represented by equations of the form y^2 = a*x^4 + b*x^3 + c*x^2 + d*x + e. The parameter Bound is a bound on the numerator and denominator of x that will be used when searching for such points. =============================================================================== =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/elliptic-curve/over_anf/\ over_anf-selmer/over_anf-selmer-selmer/SelmerGroup KIND: Intrinsic =============================================================================== SelmerGroup(phi) : Map -> GrpAb, Map, SetEnum Hints: SetEnum Default: { } SetVerbose("EllSelmer", n): Maximum: 2 Given an isogeny phi:E'to E over a number field K, returns S, AtoS, where S =S^((phi))(E/K) as a finite abelian group and AtoS:A^ * to S^((phi))(E/K) the map such that mu*AtoS:E(K)to S^((phi))(E/K). Hints can be supplied to give the system a list of x-coordinates to try first when determining local images, to speed up computations. The third return value gives a set of suitable hints. The calculation of the Selmer group involves possibly expensive Class group and Unit group computations. If no such data is available, SelmerGroup will attempt to obtain this information unconditionally. However, if such data is already stored, it will be used and subsequent results will be conditional on whatever assumptions were made while computing this information. If conditional results are desired (for instance, if the user is willing to assume GRH), one should precompute class group information on the codomain of IsogenyMu(phi) prior to calling SelmerGroup(phi). =============================================================================== 0 2 Intrinsic 'Isogeny' Signatures: ( E, F, s, h, o) -> Map Returns the isogeny E -> F defined by the polynomials psi, phi, omega, taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be univariate (although elements of a multivariate polynomial ring) and the polynomials need not be coprime. ( E, P) -> Map Returns the isogeny E -> F corresponding to the point P on the modular curve X_0(N). m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 4*$.1 4*$.1*$.3 + 8*$.2 + 4*$.3^2 $.3 and inverse 1/4*$.1 -1/8*$.1*$.3 + 1/8*$.2 - 1/2*$.3^2 $.3 2 3 <[ 2*$.1^2 - 17488*$.1 - 306092513, 26405/162*$.1^2 - 76961773/54*$.1 - 2020593203587/81, -$.1^2 + 8744*$.1 + 153046258 ], [], []> { Number Field with defining polynomial $.1^2 - 410 over the Rational Field } Total time: 4.429 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 09:28:47 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; MordellWeilRankBounds(E); Isogeny; C := HyperellipticCurve(E); J := Jacobian(C); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Fri Dec 5 2003 09:28:43 on modular [Seed = 2658219929] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 0 2 Intrinsic 'Isogeny' Signatures: ( E, F, s, h, o) -> Map Returns the isogeny E -> F defined by the polynomials psi, phi, omega, taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be univariate (although elements of a multivariate polynomial ring) and the polynomials need not be coprime. ( E, P) -> Map Returns the isogeny E -> F corresponding to the point P on the modular curve X_0(N). m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 4*$.1 4*$.1*$.3 + 8*$.2 + 4*$.3^2 $.3 and inverse 1/4*$.1 -1/8*$.1*$.3 + 1/8*$.2 - 1/2*$.3^2 $.3 2 3 <[ 2*$.1^2 - 17488*$.1 - 306092513, 26405/162*$.1^2 - 76961773/54*$.1 - 2020593203587/81, -$.1^2 + 8744*$.1 + 153046258 ], [], []> { Number Field with defining polynomial $.1^2 - 410 over the Rational Field } Total time: 4.149 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 09:29:20 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; MordellWeilRankBounds(E); C := HyperellipticCurve(E); J := Jacobian(C); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Fri Dec 5 2003 09:29:16 on modular [Seed = 2541239991] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 0 2 m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 4*$.1 4*$.1*$.3 + 8*$.2 + 4*$.3^2 $.3 and inverse 1/4*$.1 -1/8*$.1*$.3 + 1/8*$.2 - 1/2*$.3^2 $.3 2 3 <[ 2*$.1^2 - 17488*$.1 - 306092513, 26405/162*$.1^2 - 76961773/54*$.1 - 2020593203587/81, -$.1^2 + 8744*$.1 + 153046258 ], [], []> { Number Field with defining polynomial $.1^2 - 410 over the Rational Field } Total time: 4.169 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Fri Dec 5 09:30:20 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; MordellWeilRankBounds(E); C := HyperellipticCurve(E); J := Jacobian(C); TwoSelmerGroupData(J : Bound := 300); ?TwoSelmerGroupData Output: Magma V2.10-6 Fri Dec 5 2003 09:30:15 on modular [Seed = 2255040493] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 0 2 m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 4*$.1 4*$.1*$.3 + 8*$.2 + 4*$.3^2 $.3 and inverse 1/4*$.1 -1/8*$.1*$.3 + 1/8*$.2 - 1/2*$.3^2 $.3 2 3 <[ 2*$.1^2 - 17488*$.1 - 306092513, 163/162*$.1^2 - 475091/54*$.1 - 12473274239/81, -$.1^2 + 8744*$.1 + 153046258 ], [], []> { Number Field with defining polynomial $.1^2 - 410 over the Rational Field } =============================================================================== PATH: /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ 2-selmer-group/TwoSelmerGroupData KIND: Intrinsic =============================================================================== TwoSelmerGroupData(J: parameters) : JacHyp -> RngIntElt, RngIntElt, Tup, List BoundType: MonStgElt Default: "Default" Bound: RngIntElt Default: 0 Points: {JacHyp} Default: {} UseUnits: BoolElt Default: true Fields: SetEnum Default: {} Returns defining data for the 2-Selmer group of the Jacobian J over Q. Three values are returned. The first value is the upper bound for the Mordell--Weil rank deduced from the computation, and the second is the dimension of the Selmer group. The third value, only defined when UseUnits is true, gives a presentation of the fake Selmer group. The form of the return value is a triple < B_1, B_2, B_3 >, where B_1 is a sequence of elements in L = Q[x]/(f(x)) representing a basis of some subgroup S_1 of L^ * /(L^ * )^2, and B_2 and B_3 are sequences of integers representing bases of subgroups S_2 and S_3 of Q^ * /(Q^ * )^2, respectively. The fake Selmer group S is then defined by the exact sequence 0 -> S_3 -> S_2 -> S_1 -> S -> 0. The parameters BoundType and Bound determine the bound parameter passed to ClassGroup. For each of the possible values for BoundType the following Bound parameter is passes to ClassGroup: "Default": no parameter; "Absolute": minimum of MinkowskiBound(K) and Bound; "Relative": minimum of MinkowskiBound(K) and Floor(Bound*Log(D_K)), where D_K is the absolute value of the discriminant of K; "Bach": minimum of MinkowskiBound(K) and BachBound(K); "Minkowski": MinkowskiBound(K)). If a positive Bound is specified, but no BoundType is given, then BoundType is taken to be "Absolute", and otherwise "Default" is used. If Points is set to be a sequence or indexed set of rational points on J, they will be used to find the local images, which speeds up this part of the computation. If UseUnits is false, the program does not attempt to compute the fundamental units of the number fields involved. This saves considerable time in many cases, but only leads to an upper bound for the dimension of the Selmer group, and the parity information is lost. †P‡ The parameter Fields can be used to pass a sequence or set of number fields to the algorithm. If one of the fields coming up in the computation is isomorphic to one of the given fields, the given field will be used. This can be useful if the class and unit groups of these fields are already known. =============================================================================== Total time: 4.139 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 12:52:20 2003 Input: A:=PolynomialRing(Rationals(),5); B:=PolynomialRing(A,1); f:=a*x^4+b*x^3+c*x^2+d*x+e; L:=QuotientField(quod); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 12:52:17 on modular [Seed = 3159574138] ------------------------------------- >> L:=QuotientField(quod); ^ User error: bad syntax >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 12:53:19 2003 Input: ?quod A:=PolynomialRing(Rationals(),5); B:=PolynomialRing(A,1); f:=a*x^4+b*x^3+c*x^2+d*x+e; L:=QuotientField(quod); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 12:53:16 on modular [Seed = 3993049077] ------------------------------------- No references for word "quod" >> L:=QuotientField(quod); ^ User error: bad syntax >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 12:53:35 2003 Input: ?quot A:=PolynomialRing(Rationals(),5); B:=PolynomialRing(A,1); f:=a*x^4+b*x^3+c*x^2+d*x+e; L:=QuotientField(quod); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 12:53:32 on modular [Seed = 402189853] ------------------------------------- No references for word "quot" >> L:=QuotientField(quod); ^ User error: bad syntax >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 12:54:02 2003 Input: ?ring A:=PolynomialRing(Rationals(),5); B:=PolynomialRing(A,1); f:=a*x^4+b*x^3+c*x^2+d*x+e; L:=QuotientField(quod); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 12:53:59 on modular [Seed = 535881278] ------------------------------------- 174 matches: 1 O /magma/ring-field-algebra 2 S /magma/group/character/creation/creation-class-function-ring 3 S /magma/group/character/ring 4 S /magma/group/matrix/creation-general-linear-group/change-ring 5 S /magma/module-lattice/general/homomorphisms/endomorphism-ring 6 S /magma/module-lattice/general/K[G]-module/polynomial-ring-action 7 S /magma/module-lattice/general/operation/changing-ring 8 S /magma/module-lattice/general/operation/changing-ring 9 S /magma/module-lattice/general/operation/changing-ring 10 S /magma/module-lattice/general/operation/\ modification-coefficient-ring 11 S /magma/module-lattice/lattice/lattice-properties/base-ring 12 S /magma/module-lattice/mat/change-ring 13 S /magma/module-lattice/smat/change-ring 14 S /magma/ring-field-algebra/algebraic-field/ideal/quotient-ring 15 S /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/change-ring 16 S /magma/ring-field-algebra/finitely-presented/creation/ring-monoid 17 S /magma/ring-field-algebra/galois-ring 18 S /magma/ring-field-algebra/grp_alg/ops/change-ring 19 S /magma/ring-field-algebra/ideal-groebner/change-ring 20 S /magma/ring-field-algebra/invariant-ring 21 S /magma/ring-field-algebra/invariant-ring/invariant-ring 22 S /magma/ring-field-algebra/lie_alg/operation/change-ring 23 S /magma/ring-field-algebra/matrix/change-ring 24 S /magma/ring-field-algebra/univariate-polynomial/operation/\ change-ring 25 I /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Elementary-Invariants/BaseRing 26 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-change_ring/ChangeRing 27 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ operations_curve/operations_curve-category/BaseRing 28 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ pointset/pointset-category/Ring 29 I /magma/combinatorial-geometrical-incidence/elliptic-curve/\ subgroup_schemes/subgroup_schemes-category/BaseRing 30 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ creation/base_change_curve/ChangeRing 31 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ jacobian/base_ring_jacobian/BaseField 32 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ kummer-surfaces/base_ring_kummer/BaseField 33 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ structure_operations/base_ring_curve/BaseField 34 I /magma/combinatorial-geometrical-incidence/modular-symbol/\ hecke-algebra/HeckeEigenvalueRing 35 I /magma/geometry/algebraic-curve/ambients/CoordinateRing 36 I /magma/geometry/algebraic-curve/curves/curves-attributes/BaseRing 37 I /magma/geometry/algebraic-curve/curves/curves-attributes/\ CoordinateRing 38 I /magma/geometry/modular-forms/predicates/IsRingOfAllModularForms 39 I /magma/geometry/schemes/schemes-ambient/\ schemes-ambient-functions/CoordinateRing 40 I /magma/geometry/schemes/schemes-basic/equations/CoordinateRing 41 I /magma/geometry/schemes/schemes-basic/schemes-basic-ambient/\ BaseRing 42 I /magma/geometry/schemes/schemes-basic/schemes-basic-ambient/\ CoefficientRing 43 I /magma/geometry/schemes/schemes-points/Ring 44 I /magma/geometry/schemes/schemes-points/RingMap 45 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/BaseRing 46 I /magma/group/character/creation/creation-class-function-ring/\ ClassFunctionSpace 47 I /magma/group/cohomology/structure-invar/Ring 48 I /magma/group/groups-lie-type/operations/BaseRing 49 I /magma/group/GrpPSL2/Congruence-subgroups/predicates-GrpPsl2/\ BaseRing 50 I /magma/group/matrix/creation-general-linear-group/change-ring/\ ChangeRing 51 I /magma/group/matrix/creation-general-linear-group/change-ring/\ ChangeRing 52 I /magma/group/matrix/properties/access/CoefficientRing 53 I /magma/group/root-data/operators-root-dtm/BaseRing 54 I /magma/lie-theory/root-systems/operators-root-sys/BaseField 55 I /magma/module-lattice/dedekind-modules/elementary-functions/\ BaseRing 56 I /magma/module-lattice/general/access/access-vector-space/\ CoefficientRing 57 I /magma/module-lattice/general/access/CoefficientRing 58 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 59 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 60 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 61 I /magma/module-lattice/general/operation/changing-ring/ChangeRing 62 I /magma/module-lattice/general/operation/\ modification-coefficient-ring/ChangeRing 63 I /magma/module-lattice/general/operation/\ modification-coefficient-ring/ChangeRing 64 I /magma/module-lattice/lattice/G-lattices/endo-hom/\ CentreOfEndomorphismRing 65 I /magma/module-lattice/lattice/G-lattices/endo-hom/\ DimensionOfCentreOfEndomorphismRing 66 I /magma/module-lattice/lattice/G-lattices/endo-hom/\ DimensionOfEndomorphismRing 67 I /magma/module-lattice/lattice/G-lattices/endo-hom/EndomorphismRing 68 I /magma/module-lattice/lattice/lattice-properties/base-ring/\ BaseRing 69 I /magma/module-lattice/lattice/lattice-properties/base-ring/\ ChangeRing 70 I /magma/module-lattice/lattice/lattice-properties/base-ring/\ CoordinateRing 71 I /magma/module-lattice/mat/access/BaseRing 72 I /magma/module-lattice/mat/change-ring/ChangeRing 73 I /magma/module-lattice/modules-affine-algebras/access/\ CoefficientRing 74 I /magma/module-lattice/smat/access/invariants/BaseRing 75 I /magma/module-lattice/smat/change-ring/ChangeRing 76 I /magma/ring-field-algebra/abelian-extension/creation/\ ray-class-group/RayResidueRing 77 I /magma/ring-field-algebra/abelian-extension/invariants/BaseRing 78 I /magma/ring-field-algebra/abelian-extension/invariants/BaseRing 79 I /magma/ring-field-algebra/affine-algebra/operations/\ CoefficientRing 80 I /magma/ring-field-algebra/affine-algebra/operations/OriginalRing 81 I /magma/ring-field-algebra/affine-algebra/operations/PreimageRing 82 I /magma/ring-field-algebra/alg_quat/algebra-attributes/BaseField 83 I /magma/ring-field-algebra/alg_quat/order-attributes/BaseRing 84 I /magma/ring-field-algebra/algebraic-field/creation/homomorphism/\ IsRingHomomorphism 85 I /magma/ring-field-algebra/algebraic-field/creation/order/\ MaximalOrder 86 I /magma/ring-field-algebra/algebraic-field/creation/orders_ideals/\ MultiplicatorRing 87 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 88 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 89 I /magma/ring-field-algebra/algebraic-field/operation/related/\ BaseRing 90 I /magma/ring-field-algebra/algebraic-field/operation/related/\ LocalRing 91 I /magma/ring-field-algebra/algebraically-closed-field/absolute/\ AbsoluteAffineAlgebra 92 I /magma/ring-field-algebra/algebraically-closed-field/property/\ AffineAlgebra 93 I /magma/ring-field-algebra/basic/algebras/access/BaseRing 94 I /magma/ring-field-algebra/basic/cohomology/\ CohomologyRingGenerators 95 I /magma/ring-field-algebra/detail/generic/predicate/IsDivisionRing 96 I /magma/ring-field-algebra/detail/generic/predicate/IsEuclideanRing 97 I /magma/ring-field-algebra/detail/generic/predicate/\ IsMagmaEuclideanRing 98 I /magma/ring-field-algebra/detail/generic/predicate/IsPIR 99 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 100 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/change-ring/ChangeRing 101 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation/generic/BaseRing 102 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 103 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ rings/creation/PolynomialRing 104 I /magma/ring-field-algebra/finitely-presented/creation/\ ring-monoid/CoefficientRing 105 I /magma/ring-field-algebra/function-field/class-fields/structures/\ RayResidueRing 106 I /magma/ring-field-algebra/function-field/class-fields/witt-rings/\ BaseRing 107 I /magma/ring-field-algebra/function-field/class-fields/witt-rings/\ LocalRing 108 I /magma/ring-field-algebra/function-field/class-fields/witt-rings/\ WittRing 109 I /magma/ring-field-algebra/function-field/creation/orders_ideals/\ MultiplicatorRing 110 I /magma/ring-field-algebra/function-field/hom/IsRingHomomorphism 111 I /magma/ring-f ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:03:29 2003 Input: A:=PolynomialRing(Rationals(),5); B:=PolynomialRing(A,1); f:=a*x^4+b*x^3+c*x^2+d*x+e; L:=QuotientField(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:03:26 on modular [Seed = 1922925834] ------------------------------------- >> L:=QuotientField(quo); ^ User error: Identifier 'R' has not been declared or assigned >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:03:57 2003 Input: A:=PolynomialRing(Rationals(),5); B:=PolynomialRing(A,1); f:=a*x^4+b*x^3+c*x^2+d*x+e; L:=QuotientField(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:03:54 on modular [Seed = 2056621542] ------------------------------------- >> L:=QuotientField(quo); ^ User error: Identifier 'QuotientField' has not been declared or assigned >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:04:33 2003 Input: A:=PolynomialRing(Rationals(),5); B:=PolynomialRing(A,1); f:=a*x^4+b*x^3+c*x^2+d*x+e; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:04:30 on modular [Seed = 1670157531] ------------------------------------- >> L:=FieldOfFractions(quo); ^ Runtime error in quo< ... >: Base ring must be a field or Euclidean ring >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:06:38 2003 Input: A:=PolynomialRing(Rationals(),5);A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:06:35 on modular [Seed = 2491114153] ------------------------------------- Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: a, b, c, d, e Polynomial ring of rank 1 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e >> L:=FieldOfFractions(quo); ^ Runtime error in quo< ... >: Base ring must be a field or Euclidean ring >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:08:11 2003 Input: ?ideal A:=PolynomialRing(Rationals(),5);A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:08:08 on modular [Seed = 2624809474] ------------------------------------- 90 matches: 1 O /language/expression/constructor 2 S /magma/ring-field-algebra/alg_grp/subring-ideal-quotient 3 S /magma/ring-field-algebra/alg_quat/ideal-theory 4 S /magma/ring-field-algebra/algebraic-field/ideal 5 S /magma/ring-field-algebra/algebraic-field/ideal-class-group 6 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic 7 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean 8 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-creation 9 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-other 10 S /magma/ring-field-algebra/detail/ideal-quotient 11 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 12 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-completion 13 S /magma/ring-field-algebra/function-field/ideals/ideal-ops-further 14 S /magma/ring-field-algebra/ideal-groebner 15 S /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal 16 S /magma/ring-field-algebra/ideal-groebner/elimination/\ univariate-elimination-ideal-generator 17 S /magma/ring-field-algebra/ideal-groebner/ideal-operation 18 S /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal 19 S /magma/ring-field-algebra/integer/residue-class-rings/ideal 20 S /magma/ring-field-algebra/matrix/subalgebra-ideal 21 S /magma/ring-field-algebra/matrix/subring-ideal-quotient 22 S /magma/ring-field-algebra/univariate-polynomial/ideal-quotient 23 S /magma/ring-field-algebra/univariate-polynomial/ideal-quotient/\ other-ideal 24 S /magma/semigroup/finitely-presented/subsemigroup-ideal-quotient 25 S /magma/semigroup/finitely-presented/subsemigroup-ideal-quotient/\ subsemigroup-ideal 26 I /magma/geometry/algebraic-curve/curves/curves-attributes/\ DefiningIdeal 27 I /magma/geometry/algebraic-curve/curves/curves-attributes/\ JacobianIdeal 28 I /magma/geometry/conic/crvgen0-sec:main/crvgen0-subsec:access/\ DefiningIdeal 29 I /magma/geometry/schemes/schemes-basic/equations/DefiningIdeal 30 I /magma/geometry/schemes/schemes-basic/equations/JacobianIdeal 31 I /magma/module-lattice/quadratic/form-operations/related/Ideal 32 I /magma/ring-field-algebra/affine-algebra/operations/DivisorIdeal 33 I /magma/ring-field-algebra/affine-algebra/operations/PreimageIdeal 34 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/grp-alg-ops/\ AugmentationIdeal 35 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/IsIdeal 36 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsLeftIdeal 37 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsLeftIdeal 38 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsRightIdeal 39 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsRightIdeal 40 I /magma/ring-field-algebra/alg_grp/subring-ideal-quotient/ideal 41 I /magma/ring-field-algebra/alg_quat/ideal-theory/classes/\ LeftIdealClasses 42 I /magma/ring-field-algebra/alg_quat/ideal-theory/classes/\ RightIdealClasses 43 I /magma/ring-field-algebra/alg_quat/ideal-theory/classes/\ TwoSidedIdealClasses 44 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ CommutatorIdeal 45 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ ideal 46 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ LeftIdeal 47 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 48 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ RightIdeal 49 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ ColonIdeal 50 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ ColonIdeal 51 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-creation/\ ideal 52 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 53 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 54 I /magma/ring-field-algebra/algebraically-closed-field/property/\ Ideal 55 I /magma/ring-field-algebra/detail/generic/predicate/IsPID 56 I /magma/ring-field-algebra/detail/generic/predicate/IsPIR 57 I /magma/ring-field-algebra/detail/ideal-quotient/creation/ideal 58 I /magma/ring-field-algebra/detail/ideal-quotient/creation/\ PowerIdeal 59 I /magma/ring-field-algebra/finitely-presented/subalgebra/ideal 60 I /magma/ring-field-algebra/function-field/global/PrincipalIdealMap 61 I /magma/ring-field-algebra/function-field/ideals/arithmetic/\ ColonIdeal 62 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ Ideal 63 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ ideal 64 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ ideal 65 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ ideal 66 I /magma/ring-field-algebra/function-field/Places/\ operation-element/element-ops-other/Ideal 67 I /magma/ring-field-algebra/grp_alg/ops/alg-ops/CommutatorIdeal 68 I /magma/ring-field-algebra/grp_alg/subs-quos/subs/ideal 69 I /magma/ring-field-algebra/ideal-groebner/creation/ideals/ideal 70 I /magma/ring-field-algebra/ideal-groebner/creation/ideals/Ideal 71 I /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal/EliminationIdeal 72 I /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal/EliminationIdeal 73 I /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal/EliminationIdeal 74 I /magma/ring-field-algebra/ideal-groebner/elimination/relation/\ RelationIdeal 75 I /magma/ring-field-algebra/ideal-groebner/elimination/\ univariate-elimination-ideal-generator/\ UnivariateEliminationIdealGenerator 76 I /magma/ring-field-algebra/ideal-groebner/elimination/\ univariate-elimination-ideal-generator/\ UnivariateEliminationIdealGenerators 77 I /magma/ring-field-algebra/ideal-groebner/groebner/related/\ EasyIdeal 78 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 79 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 80 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 81 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 82 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/LeadingMonomialIdeal 83 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ operation-element/JacobianIdeal 84 I /magma/ring-field-algebra/invariant-ring/algebra-relations/\ PrimaryIdeal 85 I /magma/ring-field-algebra/invariant-ring/algebra-relations/\ RelationIdeal 86 I /magma/ring-field-algebra/lie_alg/sub-construct/ideal 87 I /magma/ring-field-algebra/matrix/subring-ideal-quotient/ideal 88 I /magma/ring-field-algebra/quadratic/special-ideals/Ideal 89 I /magma/ring-field-algebra/univariate-polynomial/ideal-quotient/\ creation/ideal 90 I /magma/semigroup/finitely-presented/subsemigroup-ideal-quotient/\ subsemigroup-ideal/ideal To view an entry, type ? followed by the number next to it Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: a, b, c, d, e Polynomial ring of rank 1 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e >> L:=FieldOfFractions(quo); ^ Runtime error in quo< ... >: Base ring must be a field or Euclidean ring >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:08:45 2003 Input: ?ideal ?2 A:=PolynomialRing(Rationals(),5);A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:08:42 on modular [Seed = 2221634104] ------------------------------------- 90 matches: 1 O /language/expression/constructor 2 S /magma/ring-field-algebra/alg_grp/subring-ideal-quotient 3 S /magma/ring-field-algebra/alg_quat/ideal-theory 4 S /magma/ring-field-algebra/algebraic-field/ideal 5 S /magma/ring-field-algebra/algebraic-field/ideal-class-group 6 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic 7 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean 8 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-creation 9 S /magma/ring-field-algebra/algebraic-field/ideal/ideal-other 10 S /magma/ring-field-algebra/detail/ideal-quotient 11 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 12 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-completion 13 S /magma/ring-field-algebra/function-field/ideals/ideal-ops-further 14 S /magma/ring-field-algebra/ideal-groebner 15 S /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal 16 S /magma/ring-field-algebra/ideal-groebner/elimination/\ univariate-elimination-ideal-generator 17 S /magma/ring-field-algebra/ideal-groebner/ideal-operation 18 S /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal 19 S /magma/ring-field-algebra/integer/residue-class-rings/ideal 20 S /magma/ring-field-algebra/matrix/subalgebra-ideal 21 S /magma/ring-field-algebra/matrix/subring-ideal-quotient 22 S /magma/ring-field-algebra/univariate-polynomial/ideal-quotient 23 S /magma/ring-field-algebra/univariate-polynomial/ideal-quotient/\ other-ideal 24 S /magma/semigroup/finitely-presented/subsemigroup-ideal-quotient 25 S /magma/semigroup/finitely-presented/subsemigroup-ideal-quotient/\ subsemigroup-ideal 26 I /magma/geometry/algebraic-curve/curves/curves-attributes/\ DefiningIdeal 27 I /magma/geometry/algebraic-curve/curves/curves-attributes/\ JacobianIdeal 28 I /magma/geometry/conic/crvgen0-sec:main/crvgen0-subsec:access/\ DefiningIdeal 29 I /magma/geometry/schemes/schemes-basic/equations/DefiningIdeal 30 I /magma/geometry/schemes/schemes-basic/equations/JacobianIdeal 31 I /magma/module-lattice/quadratic/form-operations/related/Ideal 32 I /magma/ring-field-algebra/affine-algebra/operations/DivisorIdeal 33 I /magma/ring-field-algebra/affine-algebra/operations/PreimageIdeal 34 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/grp-alg-ops/\ AugmentationIdeal 35 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/IsIdeal 36 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsLeftIdeal 37 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsLeftIdeal 38 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsRightIdeal 39 I /magma/ring-field-algebra/alg_grp/grp-alg-ops/subalgebra/\ IsRightIdeal 40 I /magma/ring-field-algebra/alg_grp/subring-ideal-quotient/ideal 41 I /magma/ring-field-algebra/alg_quat/ideal-theory/classes/\ LeftIdealClasses 42 I /magma/ring-field-algebra/alg_quat/ideal-theory/classes/\ RightIdealClasses 43 I /magma/ring-field-algebra/alg_quat/ideal-theory/classes/\ TwoSidedIdealClasses 44 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ CommutatorIdeal 45 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ ideal 46 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ LeftIdeal 47 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 48 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ RightIdeal 49 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ ColonIdeal 50 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-arithmetic/\ ColonIdeal 51 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-creation/\ ideal 52 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 53 I /magma/ring-field-algebra/algebraic-field/operation/Boolean/\ IsPrincipalIdealRing 54 I /magma/ring-field-algebra/algebraically-closed-field/property/\ Ideal 55 I /magma/ring-field-algebra/detail/generic/predicate/IsPID 56 I /magma/ring-field-algebra/detail/generic/predicate/IsPIR 57 I /magma/ring-field-algebra/detail/ideal-quotient/creation/ideal 58 I /magma/ring-field-algebra/detail/ideal-quotient/creation/\ PowerIdeal 59 I /magma/ring-field-algebra/finitely-presented/subalgebra/ideal 60 I /magma/ring-field-algebra/function-field/global/PrincipalIdealMap 61 I /magma/ring-field-algebra/function-field/ideals/arithmetic/\ ColonIdeal 62 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ Ideal 63 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ ideal 64 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ ideal 65 I /magma/ring-field-algebra/function-field/ideals/ideals-creation/\ ideal 66 I /magma/ring-field-algebra/function-field/Places/\ operation-element/element-ops-other/Ideal 67 I /magma/ring-field-algebra/grp_alg/ops/alg-ops/CommutatorIdeal 68 I /magma/ring-field-algebra/grp_alg/subs-quos/subs/ideal 69 I /magma/ring-field-algebra/ideal-groebner/creation/ideals/ideal 70 I /magma/ring-field-algebra/ideal-groebner/creation/ideals/Ideal 71 I /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal/EliminationIdeal 72 I /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal/EliminationIdeal 73 I /magma/ring-field-algebra/ideal-groebner/elimination/\ elimination-ideal/EliminationIdeal 74 I /magma/ring-field-algebra/ideal-groebner/elimination/relation/\ RelationIdeal 75 I /magma/ring-field-algebra/ideal-groebner/elimination/\ univariate-elimination-ideal-generator/\ UnivariateEliminationIdealGenerator 76 I /magma/ring-field-algebra/ideal-groebner/elimination/\ univariate-elimination-ideal-generator/\ UnivariateEliminationIdealGenerators 77 I /magma/ring-field-algebra/ideal-groebner/groebner/related/\ EasyIdeal 78 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 79 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 80 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 81 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/ColonIdeal 82 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ creation-ideal/LeadingMonomialIdeal 83 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ operation-element/JacobianIdeal 84 I /magma/ring-field-algebra/invariant-ring/algebra-relations/\ PrimaryIdeal 85 I /magma/ring-field-algebra/invariant-ring/algebra-relations/\ RelationIdeal 86 I /magma/ring-field-algebra/lie_alg/sub-construct/ideal 87 I /magma/ring-field-algebra/matrix/subring-ideal-quotient/ideal 88 I /magma/ring-field-algebra/quadratic/special-ideals/Ideal 89 I /magma/ring-field-algebra/univariate-polynomial/ideal-quotient/\ creation/ideal 90 I /magma/semigroup/finitely-presented/subsemigroup-ideal-quotient/\ subsemigroup-ideal/ideal To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/alg_grp/subring-ideal-quotient KIND: Section =============================================================================== Construction of Subalgebras, Ideals and Quotient Algebras. Let A = R[G] be a group algebra defined in Magma, where R is a unital ring with a matrix echelon algorithm and G is a group. If A was constructed to use the vector representation for its elements, then subalgebras and left, right and two-sided ideals of A can be constructed. If R is a field, then quotient algebras of A are also possible. A subalgebra or ideal of a group algebra A is not in general a group algebra; hence, a different type is needed for these objects. Two possibilities are provided in Magma. The first is to construct the subalgebra or ideal to have type AlgGrpSub: a subalgebra (which may be an ideal) of a group algebra. Its elements are elements of the group algebra and it remains closely connected to its defining group algebra. By default, ideals of group algebras will be of this type. The alternative is to create the subalgebra or ideal as an associative algebra given by structure constants (type AlgAss). The required structure constants are easily computable from the group algebra. This is the default Magma uses when creating subalgebras of a group algebra. Regardless of the type given to a subalgebra or ideal, the inclusion map back into the group alg ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:16:59 2003 Input: A:=PolynomialRing(Rationals(),5);A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:16:56 on modular [Seed = 3159574578] ------------------------------------- Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: a, b, c, d, e Polynomial ring of rank 1 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e >> I:=ideal;I; ^ User error: Identifier 'R' has not been declared or assigned >> I:=ideal;I; ^ User error: Identifier 'I' has not been declared or assigned >> L:=FieldOfFractions(quo); ^ Runtime error in quo< ... >: Base ring must be a field or Euclidean ring >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:17:41 2003 Input: A:=PolynomialRing(Rationals(),5);A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:17:38 on modular [Seed = 2756399216] ------------------------------------- Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: a, b, c, d, e Polynomial ring of rank 1 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e >> I:=ideal;I; ^ Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring >> I:=ideal;I; ^ User error: Identifier 'I' has not been declared or assigned >> L:=FieldOfFractions(quo); ^ Runtime error in quo< ... >: Base ring must be a field or Euclidean ring >> C:=PolynomialRing(L,4); ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'z0' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta;; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:19:37 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:19:34 on modular [Seed = 2823248776] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ Runtime error in '*': Bad argument types Argument types given: RngMPolElt, RngMPolResElt >> z^2*eta;; ^ User error: Identifier 'eta' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:21:24 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=FieldOfFractions(quo); C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:21:20 on modular [Seed = 3677628525] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ Runtime error in '*': Bad argument types Argument types given: RngMPolElt, RngMPolResElt >> z^2*eta;; ^ User error: Identifier 'eta' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:22:17 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=FieldOfFractions(quo);L; C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:22:14 on modular [Seed = 3274452995] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ Runtime error in '*': Bad argument types Argument types given: RngMPolElt, RngMPolResElt >> z^2*eta;; ^ User error: Identifier 'eta' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:23:23 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; C:=PolynomialRing(L,4); D:=PolynomialRing(A,4); z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:23:20 on modular [Seed = 3358014150] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ Runtime error in '*': Bad argument types Argument types given: RngMPolElt, RngMPolResElt >> z^2*eta;; ^ User error: Identifier 'eta' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:24:42 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; C:=PolynomialRing(L,4);C; D:=PolynomialRing(C,4);D; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:24:39 on modular [Seed = 4245819276] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3 Polynomial ring of rank 4 over Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: eta0, eta1, eta2, eta3 (z0^2 + 2*theta*z0*z1 + 2*theta^2*z0*z2 + 2*theta^3*z0*z3 + theta^2*z1^2 + 2*theta^3*z1*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z2^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z2*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z3^2)*eta0 + (theta*z0^2 + 2*theta^2*z0*z1 + 2*theta^3*z0*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z3 + theta^3*z1^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z2^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z2*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z3^2)*eta1 + (theta^2*z0^2 + 2*theta^3*z0*z1 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z1^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z2^2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z2*z3 + ((2*a^3*b*e + 2*a^3*c*d - 3*a^2*b^2*d - 3*a^2*b*c^2 + 4*a*b^3*c - b^5)/a^5*theta^3 + (2*a^3*c*e + a^3*d^2 - a^2*b^2*e - 4*a^2*b*c*d - a^2*c^3 + a*b^3*d + 3*a*b^2*c^2 - b^4*c)/a^5*theta^2 + (2*a^3*d*e - 2*a^2*b*c*e - 2*a^2*b*d^2 - a^2*c^2*d + a*b^3*e + 3*a*b^2*c*d - b^4*d)/a^5*theta + (a^3*e^2 - 2*a^2*b*d*e - a^2*c^2*e + 3*a*b^2*c*e - b^4*e)/a^5)*z3^2)*eta2 + (theta^3*z0^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z1 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z0*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z1^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z1*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z2^2 + ((4*a^3*b*e + 4*a^3*c*d - 6*a^2*b^2*d - 6*a^2*b*c^2 + 8*a*b^3*c - 2*b^5)/a^5*theta^3 + (4*a^3*c*e + 2*a^3*d^2 - 2*a^2*b^2*e - 8*a^2*b*c*d - 2*a^2*c^3 + 2*a*b^3*d + 6*a*b^2*c^2 - 2*b^4*c)/a^5*theta^2 + (4*a^3*d*e - 4*a^2*b*c*e - 4*a^2*b*d^2 - 2*a^2*c^2*d + 2*a*b^3*e + 6*a*b^2*c*d - 2*b^4*d)/a^5*theta + (2*a^3*e^2 - 4*a^2*b*d*e - 2*a^2*c^2*e + 6*a*b^2*c*e - 2*b^4*e)/a^5)*z2*z3 + ((2*a^4*c*e + a^4*d^2 - 3*a^3*b^2*e - 6*a^3*b*c*d - a^3*c^3 + 4*a^2*b^3*d + 6*a^2*b^2*c^2 - 5*a*b^4*c + b^6)/a^6*theta^3 + (2*a^4*d*e - 4*a^3*b*c*e - 2*a^3*b*d^2 - 3*a^3*c^2*d + a^2*b^3*e + 6*a^2*b^2*c*d + 3*a^2*b*c^3 - a*b^4*d - 4*a*b^3*c^2 + b^5*c)/a^6*theta^2 + (a^4*e^2 - 4*a^3*b*d*e - a^3*c^2*e - 2*a^3*c*d^2 + 3*a^2*b^2*c*e + 3*a^2*b^2*d^2 + 3*a^2*b*c^2*d - a*b^4*e - 4*a*b^3*c*d + b^5*d)/a^6*theta + (-2*a^3*b*e^2 - 2*a^3*c*d*e + 3*a^2*b^2*d*e + 3*a^2*b*c^2*e - 4*a*b^3*c*e + b^5*e)/a^6)*z3^2)*eta3 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:31:40 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; C:=PolynomialRing(L,4);C; D:=PolynomialRing(C,4);D; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; PolynomialCoefficient(z^2*eta, 0); Output: Magma V2.10-6 Fri Dec 5 2003 13:31:36 on modular [Seed = 352052233] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3 Polynomial ring of rank 4 over Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: eta0, eta1, eta2, eta3 (z0^2 + 2*theta*z0*z1 + 2*theta^2*z0*z2 + 2*theta^3*z0*z3 + theta^2*z1^2 + 2*theta^3*z1*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z2^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z2*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z3^2)*eta0 + (theta*z0^2 + 2*theta^2*z0*z1 + 2*theta^3*z0*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z3 + theta^3*z1^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z2^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z2*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z3^2)*eta1 + (theta^2*z0^2 + 2*theta^3*z0*z1 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z1^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z2^2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z2*z3 + ((2*a^3*b*e + 2*a^3*c*d - 3*a^2*b^2*d - 3*a^2*b*c^2 + 4*a*b^3*c - b^5)/a^5*theta^3 + (2*a^3*c*e + a^3*d^2 - a^2*b^2*e - 4*a^2*b*c*d - a^2*c^3 + a*b^3*d + 3*a*b^2*c^2 - b^4*c)/a^5*theta^2 + (2*a^3*d*e - 2*a^2*b*c*e - 2*a^2*b*d^2 - a^2*c^2*d + a*b^3*e + 3*a*b^2*c*d - b^4*d)/a^5*theta + (a^3*e^2 - 2*a^2*b*d*e - a^2*c^2*e + 3*a*b^2*c*e - b^4*e)/a^5)*z3^2)*eta2 + (theta^3*z0^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z1 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z0*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z1^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z1*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z2^2 + ((4*a^3*b*e + 4*a^3*c*d - 6*a^2*b^2*d - 6*a^2*b*c^2 + 8*a*b^3*c - 2*b^5)/a^5*theta^3 + (4*a^3*c*e + 2*a^3*d^2 - 2*a^2*b^2*e - 8*a^2*b*c*d - 2*a^2*c^3 + 2*a*b^3*d + 6*a*b^2*c^2 - 2*b^4*c)/a^5*theta^2 + (4*a^3*d*e - 4*a^2*b*c*e - 4*a^2*b*d^2 - 2*a^2*c^2*d + 2*a*b^3*e + 6*a*b^2*c*d - 2*b^4*d)/a^5*theta + (2*a^3*e^2 - 4*a^2*b*d*e - 2*a^2*c^2*e + 6*a*b^2*c*e - 2*b^4*e)/a^5)*z2*z3 + ((2*a^4*c*e + a^4*d^2 - 3*a^3*b^2*e - 6*a^3*b*c*d - a^3*c^3 + 4*a^2*b^3*d + 6*a^2*b^2*c^2 - 5*a*b^4*c + b^6)/a^6*theta^3 + (2*a^4*d*e - 4*a^3*b*c*e - 2*a^3*b*d^2 - 3*a^3*c^2*d + a^2*b^3*e + 6*a^2*b^2*c*d + 3*a^2*b*c^3 - a*b^4*d - 4*a*b^3*c^2 + b^5*c)/a^6*theta^2 + (a^4*e^2 - 4*a^3*b*d*e - a^3*c^2*e - 2*a^3*c*d^2 + 3*a^2*b^2*c*e + 3*a^2*b^2*d^2 + 3*a^2*b*c^2*d - a*b^4*e - 4*a*b^3*c*d + b^5*d)/a^6*theta + (-2*a^3*b*e^2 - 2*a^3*c*d*e + 3*a^2*b^2*d*e + 3*a^2*b*c^2*e - 4*a*b^3*c*e + b^5*e)/a^6)*z3^2)*eta3 >> PolynomialCoefficient(z^2*eta, 0);; ^ Runtime error in 'PolynomialCoefficient': Bad argument types Argument types given: RngMPolElt, RngIntElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:32:54 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; C:=PolynomialRing(L,4);C; D:=PolynomialRing(C,4);D; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; Q:=z^2*eta; PolynomialCoefficient(Q, theta); Output: Magma V2.10-6 Fri Dec 5 2003 13:32:51 on modular [Seed = 535883609] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3 Polynomial ring of rank 4 over Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: eta0, eta1, eta2, eta3 >> PolynomialCoefficient(Q, theta);; ^ Runtime error in 'PolynomialCoefficient': Bad argument types Argument types given: RngMPolElt, RngMPolResElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:33:45 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; C:=PolynomialRing(L,4);C; D:=PolynomialRing(C,4);D; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:33:42 on modular [Seed = 132708244] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3 Polynomial ring of rank 4 over Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: eta0, eta1, eta2, eta3 (z0^2 + 2*theta*z0*z1 + 2*theta^2*z0*z2 + 2*theta^3*z0*z3 + theta^2*z1^2 + 2*theta^3*z1*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z2^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z2*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z3^2)*eta0 + (theta*z0^2 + 2*theta^2*z0*z1 + 2*theta^3*z0*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z3 + theta^3*z1^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z2^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z2*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z3^2)*eta1 + (theta^2*z0^2 + 2*theta^3*z0*z1 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z1^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z2^2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z2*z3 + ((2*a^3*b*e + 2*a^3*c*d - 3*a^2*b^2*d - 3*a^2*b*c^2 + 4*a*b^3*c - b^5)/a^5*theta^3 + (2*a^3*c*e + a^3*d^2 - a^2*b^2*e - 4*a^2*b*c*d - a^2*c^3 + a*b^3*d + 3*a*b^2*c^2 - b^4*c)/a^5*theta^2 + (2*a^3*d*e - 2*a^2*b*c*e - 2*a^2*b*d^2 - a^2*c^2*d + a*b^3*e + 3*a*b^2*c*d - b^4*d)/a^5*theta + (a^3*e^2 - 2*a^2*b*d*e - a^2*c^2*e + 3*a*b^2*c*e - b^4*e)/a^5)*z3^2)*eta2 + (theta^3*z0^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z1 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z0*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z1^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z1*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z2^2 + ((4*a^3*b*e + 4*a^3*c*d - 6*a^2*b^2*d - 6*a^2*b*c^2 + 8*a*b^3*c - 2*b^5)/a^5*theta^3 + (4*a^3*c*e + 2*a^3*d^2 - 2*a^2*b^2*e - 8*a^2*b*c*d - 2*a^2*c^3 + 2*a*b^3*d + 6*a*b^2*c^2 - 2*b^4*c)/a^5*theta^2 + (4*a^3*d*e - 4*a^2*b*c*e - 4*a^2*b*d^2 - 2*a^2*c^2*d + 2*a*b^3*e + 6*a*b^2*c*d - 2*b^4*d)/a^5*theta + (2*a^3*e^2 - 4*a^2*b*d*e - 2*a^2*c^2*e + 6*a*b^2*c*e - 2*b^4*e)/a^5)*z2*z3 + ((2*a^4*c*e + a^4*d^2 - 3*a^3*b^2*e - 6*a^3*b*c*d - a^3*c^3 + 4*a^2*b^3*d + 6*a^2*b^2*c^2 - 5*a*b^4*c + b^6)/a^6*theta^3 + (2*a^4*d*e - 4*a^3*b*c*e - 2*a^3*b*d^2 - 3*a^3*c^2*d + a^2*b^3*e + 6*a^2*b^2*c*d + 3*a^2*b*c^3 - a*b^4*d - 4*a*b^3*c^2 + b^5*c)/a^6*theta^2 + (a^4*e^2 - 4*a^3*b*d*e - a^3*c^2*e - 2*a^3*c*d^2 + 3*a^2*b^2*c*e + 3*a^2*b^2*d^2 + 3*a^2*b*c^2*d - a*b^4*e - 4*a*b^3*c*d + b^5*d)/a^6*theta + (-2*a^3*b*e^2 - 2*a^3*c*d*e + 3*a^2*b^2*d*e + 3*a^2*b*c^2*e - 4*a*b^3*c*e + b^5*e)/a^6)*z3^2)*eta3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:34:18 2003 Input: A:=FieldOfFractions(PolynomialRing(Rationals(),5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; C:=PolynomialRing(L,4);C; D:=PolynomialRing(C,4);D; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:34:14 on modular [Seed = 717609625] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3 Polynomial ring of rank 4 over Polynomial ring of rank 4 over Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: eta0, eta1, eta2, eta3 (z0^2 + 2*theta*z0*z1 + 2*theta^2*z0*z2 + 2*theta^3*z0*z3 + theta^2*z1^2 + 2*theta^3*z1*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z2^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z2*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z3^2)*eta0 + (theta*z0^2 + 2*theta^2*z0*z1 + 2*theta^3*z0*z2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z3 + theta^3*z1^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z1*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z2^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z2*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z3^2)*eta1 + (theta^2*z0^2 + 2*theta^3*z0*z1 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z3 + (-b/a*theta^3 - c/a*theta^2 - d/a*theta - e/a)*z1^2 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z1*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z3 + ((-a^2*d + 2*a*b*c - b^3)/a^3*theta^3 + (-a^2*e + a*b*d + a*c^2 - b^2*c)/a^3*theta^2 + (a*b*e + a*c*d - b^2*d)/a^3*theta + (a*c*e - b^2*e)/a^3)*z2^2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z2*z3 + ((2*a^3*b*e + 2*a^3*c*d - 3*a^2*b^2*d - 3*a^2*b*c^2 + 4*a*b^3*c - b^5)/a^5*theta^3 + (2*a^3*c*e + a^3*d^2 - a^2*b^2*e - 4*a^2*b*c*d - a^2*c^3 + a*b^3*d + 3*a*b^2*c^2 - b^4*c)/a^5*theta^2 + (2*a^3*d*e - 2*a^2*b*c*e - 2*a^2*b*d^2 - a^2*c^2*d + a*b^3*e + 3*a*b^2*c*d - b^4*d)/a^5*theta + (a^3*e^2 - 2*a^2*b*d*e - a^2*c^2*e + 3*a*b^2*c*e - b^4*e)/a^5)*z3^2)*eta2 + (theta^3*z0^2 + (-2*b/a*theta^3 - 2*c/a*theta^2 - 2*d/a*theta - 2*e/a)*z0*z1 + ((-2*a*c + 2*b^2)/a^2*theta^3 + (-2*a*d + 2*b*c)/a^2*theta^2 + (-2*a*e + 2*b*d)/a^2*theta + 2*b*e/a^2)*z0*z2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z0*z3 + ((-a*c + b^2)/a^2*theta^3 + (-a*d + b*c)/a^2*theta^2 + (-a*e + b*d)/a^2*theta + b*e/a^2)*z1^2 + ((-2*a^2*d + 4*a*b*c - 2*b^3)/a^3*theta^3 + (-2*a^2*e + 2*a*b*d + 2*a*c^2 - 2*b^2*c)/a^3*theta^2 + (2*a*b*e + 2*a*c*d - 2*b^2*d)/a^3*theta + (2*a*c*e - 2*b^2*e)/a^3)*z1*z2 + ((-2*a^3*e + 4*a^2*b*d + 2*a^2*c^2 - 6*a*b^2*c + 2*b^4)/a^4*theta^3 + (2*a^2*b*e + 4*a^2*c*d - 2*a*b^2*d - 4*a*b*c^2 + 2*b^3*c)/a^4*theta^2 + (2*a^2*c*e + 2*a^2*d^2 - 2*a*b^2*e - 4*a*b*c*d + 2*b^3*d)/a^4*theta + (2*a^2*d*e - 4*a*b*c*e + 2*b^3*e)/a^4)*z1*z3 + ((-a^3*e + 2*a^2*b*d + a^2*c^2 - 3*a*b^2*c + b^4)/a^4*theta^3 + (a^2*b*e + 2*a^2*c*d - a*b^2*d - 2*a*b*c^2 + b^3*c)/a^4*theta^2 + (a^2*c*e + a^2*d^2 - a*b^2*e - 2*a*b*c*d + b^3*d)/a^4*theta + (a^2*d*e - 2*a*b*c*e + b^3*e)/a^4)*z2^2 + ((4*a^3*b*e + 4*a^3*c*d - 6*a^2*b^2*d - 6*a^2*b*c^2 + 8*a*b^3*c - 2*b^5)/a^5*theta^3 + (4*a^3*c*e + 2*a^3*d^2 - 2*a^2*b^2*e - 8*a^2*b*c*d - 2*a^2*c^3 + 2*a*b^3*d + 6*a*b^2*c^2 - 2*b^4*c)/a^5*theta^2 + (4*a^3*d*e - 4*a^2*b*c*e - 4*a^2*b*d^2 - 2*a^2*c^2*d + 2*a*b^3*e + 6*a*b^2*c*d - 2*b^4*d)/a^5*theta + (2*a^3*e^2 - 4*a^2*b*d*e - 2*a^2*c^2*e + 6*a*b^2*c*e - 2*b^4*e)/a^5)*z2*z3 + ((2*a^4*c*e + a^4*d^2 - 3*a^3*b^2*e - 6*a^3*b*c*d - a^3*c^3 + 4*a^2*b^3*d + 6*a^2*b^2*c^2 - 5*a*b^4*c + b^6)/a^6*theta^3 + (2*a^4*d*e - 4*a^3*b*c*e - 2*a^3*b*d^2 - 3*a^3*c^2*d + a^2*b^3*e + 6*a^2*b^2*c*d + 3*a^2*b*c^3 - a*b^4*d - 4*a*b^3*c^2 + b^5*c)/a^6*theta^2 + (a^4*e^2 - 4*a^3*b*d*e - a^3*c^2*e - 2*a^3*c*d^2 + 3*a^2*b^2*c*e + 3*a^2*b^2*d^2 + 3*a^2*b*c^2*d - a*b^4*e - 4*a*b^3*c*d + b^5*d)/a^6*theta + (-2*a^3*b*e^2 - 2*a^3*c*d*e + 3*a^2*b^2*d*e + 3*a^2*b*c^2*e - 4*a*b^3*c*e + b^5*e)/a^6)*z3^2)*eta3 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:40:26 2003 Input: R:=PolynomialRing(Rationals(),8);R; A:=FieldOfFractions(PolynomialRing(R,5));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:40:22 on modular [Seed = 1285792335] ------------------------------------- Polynomial ring of rank 8 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3, eta0, eta1, eta2, eta3 Multivariate Rational function field of rank 5 over Polynomial ring of rank 8 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Polynomial ring of rank 8 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 5 over Polynomial ring of rank 8 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 5 over Polynomial ring of rank 8 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] ((z0^2*eta3 + 2*z0*z1*eta2 + 2*z0*z2*eta1 + 2*z0*z3*eta0 + z1^2*eta1 + 2*z1*z2*eta0)*a^6 + (-2*z0*z1*eta3 - 2*z0*z2*eta2 - 2*z0*z3*eta1 - z1^2*eta2 - 2*z1*z2*eta1 - 2*z1*z3*eta0 - z2^2*eta0)*a^5*b + (-2*z0*z2*eta3 - 2*z0*z3*eta2 - z1^2*eta3 - 2*z1*z2*eta2 - 2*z1*z3*eta1 - z2^2*eta1 - 2*z2*z3*eta0)*a^5*c + (-2*z0*z3*eta3 - 2*z1*z2*eta3 - 2*z1*z3*eta2 - z2^2*eta2 - 2*z2*z3*eta1 - z3^2*eta0)*a^5*d + (-2*z1*z3*eta3 - z2^2*eta3 - 2*z2*z3*eta2 - z3^2*eta1)*a^5*e + (2*z0*z2*eta3 + 2*z0*z3*eta2 + z1^2*eta3 + 2*z1*z2*eta2 + 2*z1*z3*eta1 + z2^2*eta1 + 2*z2*z3*eta0)*a^4*b^2 + (4*z0*z3*eta3 + 4*z1*z2*eta3 + 4*z1*z3*eta2 + 2*z2^2*eta2 + 4*z2*z3*eta1 + 2*z3^2*eta0)*a^4*b*c + (4*z1*z3*eta3 + 2*z2^2*eta3 + 4*z2*z3*eta2 + 2*z3^2*eta1)*a^4*b*d + (4*z2*z3*eta3 + 2*z3^2*eta2)*a^4*b*e + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^4*c^2 + (4*z2*z3*eta3 + 2*z3^2*eta2)*a^4*c*d + 2*z3^2*eta3*a^4*c*e + z3^2*eta3*a^4*d^2 + (-2*z0*z3*eta3 - 2*z1*z2*eta3 - 2*z1*z3*eta2 - z2^2*eta2 - 2*z2*z3*eta1 - z3^2*eta0)*a^3*b^3 + (-6*z1*z3*eta3 - 3*z2^2*eta3 - 6*z2*z3*eta2 - 3*z3^2*eta1)*a^3*b^2*c + (-6*z2*z3*eta3 - 3*z3^2*eta2)*a^3*b^2*d - 3*z3^2*eta3*a^3*b^2*e + (-6*z2*z3*eta3 - 3*z3^2*eta2)*a^3*b*c^2 - 6*z3^2*eta3*a^3*b*c*d - z3^2*eta3*a^3*c^3 + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^2*b^4 + (8*z2*z3*eta3 + 4*z3^2*eta2)*a^2*b^3*c + 4*z3^2*eta3*a^2*b^3*d + 6*z3^2*eta3*a^2*b^2*c^2 + (-2*z2*z3*eta3 - z3^2*eta2)*a*b^5 - 5*z3^2*eta3*a*b^4*c + z3^2*eta3*b^6)/a^6*theta^3 + ((z0^2*eta2 + 2*z0*z1*eta1 + 2*z0*z2*eta0 + z1^2*eta0)*a^6 + (-2*z0*z1*eta3 - 2*z0*z2*eta2 - 2*z0*z3*eta1 - z1^2*eta2 - 2*z1*z2*eta1 - 2*z1*z3*eta0 - z2^2*eta0)*a^5*c + (-2*z0*z2*eta3 - 2*z0*z3*eta2 - z1^2*eta3 - 2*z1*z2*eta2 - 2*z1*z3*eta1 - z2^2*eta1 - 2*z2*z3*eta0)*a^5*d + (-2*z0*z3*eta3 - 2*z1*z2*eta3 - 2*z1*z3*eta2 - z2^2*eta2 - 2*z2*z3*eta1 - z3^2*eta0)*a^5*e + (2*z0*z2*eta3 + 2*z0*z3*eta2 + z1^2*eta3 + 2*z1*z2*eta2 + 2*z1*z3*eta1 + z2^2*eta1 + 2*z2*z3*eta0)*a^4*b*c + (2*z0*z3*eta3 + 2*z1*z2*eta3 + 2*z1*z3*eta2 + z2^2*eta2 + 2*z2*z3*eta1 + z3^2*eta0)*a^4*b*d + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^4*b*e + (2*z0*z3*eta3 + 2*z1*z2*eta3 + 2*z1*z3*eta2 + z2^2*eta2 + 2*z2*z3*eta1 + z3^2*eta0)*a^4*c^2 + (4*z1*z3*eta3 + 2*z2^2*eta3 + 4*z2*z3*eta2 + 2*z3^2*eta1)*a^4*c*d + (4*z2*z3*eta3 + 2*z3^2*eta2)*a^4*c*e + (2*z2*z3*eta3 + z3^2*eta2)*a^4*d^2 + 2*z3^2*eta3*a^4*d*e + (-2*z0*z3*eta3 - 2*z1*z2*eta3 - 2*z1*z3*eta2 - z2^2*eta2 - 2*z2*z3*eta1 - z3^2*eta0)*a^3*b^2*c + (-2*z1*z3*eta3 - z2^2*eta3 - 2*z2*z3*eta2 - z3^2*eta1)*a^3*b^2*d + (-2*z2*z3*eta3 - z3^2*eta2)*a^3*b^2*e + (-4*z1*z3*eta3 - 2*z2^2*eta3 - 4*z2*z3*eta2 - 2*z3^2*eta1)*a^3*b*c^2 + (-8*z2*z3*eta3 - 4*z3^2*eta2)*a^3*b*c*d - 4*z3^2*eta3*a^3*b*c*e - 2*z3^2*eta3*a^3*b*d^2 + (-2*z2*z3*eta3 - z3^2*eta2)*a^3*c^3 - 3*z3^2*eta3*a^3*c^2*d + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^2*b^3*c + (2*z2*z3*eta3 + z3^2*eta2)*a^2*b^3*d + z3^2*eta3*a^2*b^3*e + (6*z2*z3*eta3 + 3*z3^2*eta2)*a^2*b^2*c^2 + 6*z3^2*eta3*a^2*b^2*c*d + 3*z3^2*eta3*a^2*b*c^3 + (-2*z2*z3*eta3 - z3^2*eta2)*a*b^4*c - z3^2*eta3*a*b^4*d - 4*z3^2*eta3*a*b^3*c^2 + z3^2*eta3*b^5*c)/a^6*theta^2 + ((z0^2*eta1 + 2*z0*z1*eta0)*a^6 + (-2*z0*z1*eta3 - 2*z0*z2*eta2 - 2*z0*z3*eta1 - z1^2*eta2 - 2*z1*z2*eta1 - 2*z1*z3*eta0 - z2^2*eta0)*a^5*d + (-2*z0*z2*eta3 - 2*z0*z3*eta2 - z1^2*eta3 - 2*z1*z2*eta2 - 2*z1*z3*eta1 - z2^2*eta1 - 2*z2*z3*eta0)*a^5*e + (2*z0*z2*eta3 + 2*z0*z3*eta2 + z1^2*eta3 + 2*z1*z2*eta2 + 2*z1*z3*eta1 + z2^2*eta1 + 2*z2*z3*eta0)*a^4*b*d + (2*z0*z3*eta3 + 2*z1*z2*eta3 + 2*z1*z3*eta2 + z2^2*eta2 + 2*z2*z3*eta1 + z3^2*eta0)*a^4*b*e + (2*z0*z3*eta3 + 2*z1*z2*eta3 + 2*z1*z3*eta2 + z2^2*eta2 + 2*z2*z3*eta1 + z3^2*eta0)*a^4*c*d + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^4*c*e + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^4*d^2 + (4*z2*z3*eta3 + 2*z3^2*eta2)*a^4*d*e + z3^2*eta3*a^4*e^2 + (-2*z0*z3*eta3 - 2*z1*z2*eta3 - 2*z1*z3*eta2 - z2^2*eta2 - 2*z2*z3*eta1 - z3^2*eta0)*a^3*b^2*d + (-2*z1*z3*eta3 - z2^2*eta3 - 2*z2*z3*eta2 - z3^2*eta1)*a^3*b^2*e + (-4*z1*z3*eta3 - 2*z2^2*eta3 - 4*z2*z3*eta2 - 2*z3^2*eta1)*a^3*b*c*d + (-4*z2*z3*eta3 - 2*z3^2*eta2)*a^3*b*c*e + (-4*z2*z3*eta3 - 2*z3^2*eta2)*a^3*b*d^2 - 4*z3^2*eta3*a^3*b*d*e + (-2*z2*z3*eta3 - z3^2*eta2)*a^3*c^2*d - z3^2*eta3*a^3*c^2*e - 2*z3^2*eta3*a^3*c*d^2 + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^2*b^3*d + (2*z2*z3*eta3 + z3^2*eta2)*a^2*b^3*e + (6*z2*z3*eta3 + 3*z3^2*eta2)*a^2*b^2*c*d + 3*z3^2*eta3*a^2*b^2*c*e + 3*z3^2*eta3*a^2*b^2*d^2 + 3*z3^2*eta3*a^2*b*c^2*d + (-2*z2*z3*eta3 - z3^2*eta2)*a*b^4*d - z3^2*eta3*a*b^4*e - 4*z3^2*eta3*a*b^3*c*d + z3^2*eta3*b^5*d)/a^6*theta + (z0^2*eta0*a^6 + (-2*z0*z1*eta3 - 2*z0*z2*eta2 - 2*z0*z3*eta1 - z1^2*eta2 - 2*z1*z2*eta1 - 2*z1*z3*eta0 - z2^2*eta0)*a^5*e + (2*z0*z2*eta3 + 2*z0*z3*eta2 + z1^2*eta3 + 2*z1*z2*eta2 + 2*z1*z3*eta1 + z2^2*eta1 + 2*z2*z3*eta0)*a^4*b*e + (2*z0*z3*eta3 + 2*z1*z2*eta3 + 2*z1*z3*eta2 + z2^2*eta2 + 2*z2*z3*eta1 + z3^2*eta0)*a^4*c*e + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^4*d*e + (2*z2*z3*eta3 + z3^2*eta2)*a^4*e^2 + (-2*z0*z3*eta3 - 2*z1*z2*eta3 - 2*z1*z3*eta2 - z2^2*eta2 - 2*z2*z3*eta1 - z3^2*eta0)*a^3*b^2*e + (-4*z1*z3*eta3 - 2*z2^2*eta3 - 4*z2*z3*eta2 - 2*z3^2*eta1)*a^3*b*c*e + (-4*z2*z3*eta3 - 2*z3^2*eta2)*a^3*b*d*e - 2*z3^2*eta3*a^3*b*e^2 + (-2*z2*z3*eta3 - z3^2*eta2)*a^3*c^2*e - 2*z3^2*eta3*a^3*c*d*e + (2*z1*z3*eta3 + z2^2*eta3 + 2*z2*z3*eta2 + z3^2*eta1)*a^2*b^3*e + (6*z2*z3*eta3 + 3*z3^2*eta2)*a^2*b^2*c*e + 3*z3^2*eta3*a^2*b^2*d*e + 3*z3^2*eta3*a^2*b*c^2*e + (-2*z2*z3*eta3 - z3^2*eta2)*a*b^4*e - 4*z3^2*eta3*a*b^3*c*e + z3^2*eta3*b^5*e)/a^6 Total time: 3.640 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:50:41 2003 Input: R:=FieldOfFractions(PolynomialRing(Rationals(),5));R; A:=PolynomialRing(R,8);A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:50:38 on modular [Seed = 2856666817] ------------------------------------- Multivariate Rational function field of rank 5 over Rational Field Variables: a, b, c, d, e Polynomial ring of rank 8 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3, eta0, eta1, eta2, eta3 Polynomial ring of rank 1 over Polynomial ring of rank 8 over Multivariate Rational function field of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e >> I:=ideal;I; ^ Runtime error in ideal< ... >: Base ring must be a field or Euclidean ring >> I:=ideal;I; ^ User error: Identifier 'I' has not been declared or assigned >> L:=B/I;L; ^ User error: Identifier 'I' has not been declared or assigned >> L:=B/I;L; ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:51:42 2003 Input: R:=PolynomialRing(Rationals(),5);R; A:=PolynomialRing(R,8);A; B:=FieldOfFractions(PolynomialRing(A,1));B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:51:39 on modular [Seed = 3644208503] ------------------------------------- Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: a, b, c, d, e Polynomial ring of rank 8 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: z0, z1, z2, z3, eta0, eta1, eta2, eta3 Multivariate Rational function field of rank 1 over Polynomial ring of rank 8 over Polynomial ring of rank 5 over Rational Field Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e >> I:=ideal;I; ^ Runtime error: No constructor provided for this type of object >> I:=ideal;I; ^ User error: Identifier 'I' has not been declared or assigned >> L:=B/I;L; ^ User error: Identifier 'I' has not been declared or assigned >> L:=B/I;L; ^ User error: Identifier 'L' has not been declared or assigned >> z:=z0+z1*theta+z2*theta^2+z3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; ^ User error: Identifier 'theta' has not been declared or assigned >> z^2*eta; ^ User error: Identifier 'z' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p3E9E7418.dip.t-dialin.net. (62.158.116.24) Time: Fri Dec 5 13:52:49 2003 Input: R:=PolynomialRing(Rationals(),5);R; A:=FieldOfFractions(PolynomialRing(R,8));A; B:=PolynomialRing(A,1);B; f:=a*x^4+b*x^3+c*x^2+d*x+e;f; I:=ideal;I; L:=B/I;L; z:=z0+z1*theta+z2*theta^2+z3*theta^3; eta:=eta0+eta1*theta+eta2*theta^2+eta3*theta^3; z^2*eta; Output: Magma V2.10-6 Fri Dec 5 2003 13:52:46 on modular [Seed = 3241028906] ------------------------------------- Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: a, b, c, d, e Multivariate Rational function field of rank 8 over Polynomial ring of rank 5 over Rational Field Variables: z0, z1, z2, z3, eta0, eta1, eta2, eta3 Polynomial ring of rank 1 over Multivariate Rational function field of rank 8 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: x a*x^4 + b*x^3 + c*x^2 + d*x + e Ideal of Polynomial ring of rank 1 over Multivariate Rational function field of rank 8 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: x Basis: [ a*x^4 + b*x^3 + c*x^2 + d*x + e ] Affine Algebra of rank 1 over Multivariate Rational function field of rank 8 over Polynomial ring of rank 5 over Rational Field Lexicographical Order Variables: theta Quotient relations: [ theta^4 + b/a*theta^3 + c/a*theta^2 + d/a*theta + e/a ] (a^6*z0^2*eta3 + 2*a^6*z0*z1*eta2 - 2*a^5*b*z0*z1*eta3 + 2*a^6*z0*z2*eta1 - 2*a^5*b*z0*z2*eta2 + (-2*a^5*c + 2*a^4*b^2)*z0*z2*eta3 + 2*a^6*z0*z3*eta0 - 2*a^5*b*z0*z3*eta1 + (-2*a^5*c + 2*a^4*b^2)*z0*z3*eta2 + (-2*a^5*d + 4*a^4*b*c - 2*a^3*b^3)*z0*z3*eta3 + a^6*z1^2*eta1 - a^5*b*z1^2*eta2 + (-a^5*c + a^4*b^2)*z1^2*eta3 + 2*a^6*z1*z2*eta0 - 2*a^5*b*z1*z2*eta1 + (-2*a^5*c + 2*a^4*b^2)*z1*z2*eta2 + (-2*a^5*d + 4*a^4*b*c - 2*a^3*b^3)*z1*z2*eta3 - 2*a^5*b*z1*z3*eta0 + (-2*a^5*c + 2*a^4*b^2)*z1*z3*eta1 + (-2*a^5*d + 4*a^4*b*c - 2*a^3*b^3)*z1*z3*eta2 + (-2*a^5*e + 4*a^4*b*d + 2*a^4*c^2 - 6*a^3*b^2*c + 2*a^2*b^4)*z1*z3*eta3 - a^5*b*z2^2*eta0 + (-a^5*c + a^4*b^2)*z2^2*eta1 + (-a^5*d + 2*a^4*b*c - a^3*b^3)*z2^2*eta2 + (-a^5*e + 2*a^4*b*d + a^4*c^2 - 3*a^3*b^2*c + a^2*b^4)*z2^2*eta3 + (-2*a^5*c + 2*a^4*b^2)*z2*z3*eta0 + (-2*a^5*d + 4*a^4*b*c - 2*a^3*b^3)*z2*z3*eta1 + (-2*a^5*e + 4*a^4*b*d + 2*a^4*c^2 - 6*a^3*b^2*c + 2*a^2*b^4)*z2*z3*eta2 + (4*a^4*b*e + 4*a^4*c*d - 6*a^3*b^2*d - 6*a^3*b*c^2 + 8*a^2*b^3*c - 2*a*b^5)*z2*z3*eta3 + (-a^5*d + 2*a^4*b*c - a^3*b^3)*z3^2*eta0 + (-a^5*e + 2*a^4*b*d + a^4*c^2 - 3*a^3*b^2*c + a^2*b^4)*z3^2*eta1 + (2*a^4*b*e + 2*a^4*c*d - 3*a^3*b^2*d - 3*a^3*b*c^2 + 4*a^2*b^3*c - a*b^5)*z3^2*eta2 + (2*a^4*c*e + a^4*d^2 - 3*a^3*b^2*e - 6*a^3*b*c*d - a^3*c^3 + 4*a^2*b^3*d + 6*a^2*b^2*c^2 - 5*a*b^4*c + b^6)*z3^2*eta3)/a^6*theta^3 + (a^6*z0^2*eta2 + 2*a^6*z0*z1*eta1 - 2*a^5*c*z0*z1*eta3 + 2*a^6*z0*z2*eta0 - 2*a^5*c*z0*z2*eta2 + (-2*a^5*d + 2*a^4*b*c)*z0*z2*eta3 - 2*a^5*c*z0*z3*eta1 + (-2*a^5*d + 2*a^4*b*c)*z0*z3*eta2 + (-2*a^5*e + 2*a^4*b*d + 2*a^4*c^2 - 2*a^3*b^2*c)*z0*z3*eta3 + a^6*z1^2*eta0 - a^5*c*z1^2*eta2 + (-a^5*d + a^4*b*c)*z1^2*eta3 - 2*a^5*c*z1*z2*eta1 + (-2*a^5*d + 2*a^4*b*c)*z1*z2*eta2 + (-2*a^5*e + 2*a^4*b*d + 2*a^4*c^2 - 2*a^3*b^2*c)*z1*z2*eta3 - 2*a^5*c*z1*z3*eta0 + (-2*a^5*d + 2*a^4*b*c)*z1*z3*eta1 + (-2*a^5*e + 2*a^4*b*d + 2*a^4*c^2 - 2*a^3*b^2*c)*z1*z3*eta2 + (2*a^4*b*e + 4*a^4*c*d - 2*a^3*b^2*d - 4*a^3*b*c^2 + 2*a^2*b^3*c)*z1*z3*eta3 - a^5*c*z2^2*eta0 + (-a^5*d + a^4*b*c)*z2^2*eta1 + (-a^5*e + a^4*b*d + a^4*c^2 - a^3*b^2*c)*z2^2*eta2 + (a^4*b*e + 2*a^4*c*d - a^3*b^2*d - 2*a^3*b*c^2 + a^2*b^3*c)*z2^2*eta3 + (-2*a^5*d + 2*a^4*b*c)*z2*z3*eta0 + (-2*a^5*e + 2*a^4*b*d + 2*a^4*c^2 - 2*a^3*b^2*c)*z2*z3*eta1 + (2*a^4*b*e + 4*a^4*c*d - 2*a^3*b^2*d - 4*a^3*b*c^2 + 2*a^2*b^3*c)*z2*z3*eta2 + (4*a^4*c*e + 2*a^4*d^2 - 2*a^3*b^2*e - 8*a^3*b*c*d - 2*a^3*c^3 + 2*a^2*b^3*d + 6*a^2*b^2*c^2 - 2*a*b^4*c)*z2*z3*eta3 + (-a^5*e + a^4*b*d + a^4*c^2 - a^3*b^2*c)*z3^2*eta0 + (a^4*b*e + 2*a^4*c*d - a^3*b^2*d - 2*a^3*b*c^2 + a^2*b^3*c)*z3^2*eta1 + (2*a^4*c*e + a^4*d^2 - a^3*b^2*e - 4*a^3*b*c*d - a^3*c^3 + a^2*b^3*d + 3*a^2*b^2*c^2 - a*b^4*c)*z3^2*eta2 + (2*a^4*d*e - 4*a^3*b*c*e - 2*a^3*b*d^2 - 3*a^3*c^2*d + a^2*b^3*e + 6*a^2*b^2*c*d + 3*a^2*b*c^3 - a*b^4*d - 4*a*b^3*c^2 + b^5*c)*z3^2*eta3)/a^6*theta^2 + (a^6*z0^2*eta1 + 2*a^6*z0*z1*eta0 - 2*a^5*d*z0*z1*eta3 - 2*a^5*d*z0*z2*eta2 + (-2*a^5*e + 2*a^4*b*d)*z0*z2*eta3 - 2*a^5*d*z0*z3*eta1 + (-2*a^5*e + 2*a^4*b*d)*z0*z3*eta2 + (2*a^4*b*e + 2*a^4*c*d - 2*a^3*b^2*d)*z0*z3*eta3 - a^5*d*z1^2*eta2 + (-a^5*e + a^4*b*d)*z1^2*eta3 - 2*a^5*d*z1*z2*eta1 + (-2*a^5*e + 2*a^4*b*d)*z1*z2*eta2 + (2*a^4*b*e + 2*a^4*c*d - 2*a^3*b^2*d)*z1*z2*eta3 - 2*a^5*d*z1*z3*eta0 + (-2*a^5*e + 2*a^4*b*d)*z1*z3*eta1 + (2*a^4*b*e + 2*a^4*c*d - 2*a^3*b^2*d)*z1*z3*eta2 + (2*a^4*c*e + 2*a^4*d^2 - 2*a^3*b^2*e - 4*a^3*b*c*d + 2*a^2*b^3*d)*z1*z3*eta3 - a^5*d*z2^2*eta0 + (-a^5*e + a^4*b*d)*z2^2*eta1 + (a^4*b*e + a^4*c*d - a^3*b^2*d)*z2^2*eta2 + (a^4*c*e + a^4*d^2 - a^3*b^2*e - 2*a^3*b*c*d + a^2*b^3*d)*z2^2*eta3 + (-2*a^5*e + 2*a^4*b*d)*z2*z3*eta0 + (2*a^4*b*e + 2*a^4*c*d - 2*a^3*b^2*d)*z2*z3*eta1 + (2*a^4*c*e + 2*a^4*d^2 - 2*a^3*b^2*e - 4*a^3*b*c*d + 2*a^2*b^3*d)*z2*z3*eta2 + (4*a^4*d*e - 4*a^3*b*c*e - 4*a^3*b*d^2 - 2*a^3*c^2*d + 2*a^2*b^3*e + 6*a^2*b^2*c*d - 2*a*b^4*d)*z2*z3*eta3 + (a^4*b*e + a^4*c*d - a^3*b^2*d)*z3^2*eta0 + (a^4*c*e + a^4*d^2 - a^3*b^2*e - 2*a^3*b*c*d + a^2*b^3*d)*z3^2*eta1 + (2*a^4*d*e - 2*a^3*b*c*e - 2*a^3*b*d^2 - a^3*c^2*d + a^2*b^3*e + 3*a^2*b^2*c*d - a*b^4*d)*z3^2*eta2 + (a^4*e^2 - 4*a^3*b*d*e - a^3*c^2*e - 2*a^3*c*d^2 + 3*a^2*b^2*c*e + 3*a^2*b^2*d^2 + 3*a^2*b*c^2*d - a*b^4*e - 4*a*b^3*c*d + b^5*d)*z3^2*eta3)/a^6*theta + (a^6*z0^2*eta0 - 2*a^5*e*z0*z1*eta3 - 2*a^5*e*z0*z2*eta2 + 2*a^4*b*e*z0*z2*eta3 - 2*a^5*e*z0*z3*eta1 + 2*a^4*b*e*z0*z3*eta2 + (2*a^4*c*e - 2*a^3*b^2*e)*z0*z3*eta3 - a^5*e*z1^2*eta2 + a^4*b*e*z1^2*eta3 - 2*a^5*e*z1*z2*eta1 + 2*a^4*b*e*z1*z2*eta2 + (2*a^4*c*e - 2*a^3*b^2*e)*z1*z2*eta3 - 2*a^5*e*z1*z3*eta0 + 2*a^4*b*e*z1*z3*eta1 + (2*a^4*c*e - 2*a^3*b^2*e)*z1*z3*eta2 + (2*a^4*d*e - 4*a^3*b*c*e + 2*a^2*b^3*e)*z1*z3*eta3 - a^5*e*z2^2*eta0 + a^4*b*e*z2^2*eta1 + (a^4*c*e - a^3*b^2*e)*z2^2*eta2 + (a^4*d*e - 2*a^3*b*c*e + a^2*b^3*e)*z2^2*eta3 + 2*a^4*b*e*z2*z3*eta0 + (2*a^4*c*e - 2*a^3*b^2*e)*z2*z3*eta1 + (2*a^4*d*e - 4*a^3*b*c*e + 2*a^2*b^3*e)*z2*z3*eta2 + (2*a^4*e^2 - 4*a^3*b*d*e - 2*a^3*c^2*e + 6*a^2*b^2*c*e - 2*a*b^4*e)*z2*z3*eta3 + (a^4*c*e - a^3*b^2*e)*z3^2*eta0 + (a^4*d*e - 2*a^3*b*c*e + a^2*b^3*e)*z3^2*eta1 + (a^4*e^2 - 2*a^3*b*d*e - a^3*c^2*e + 3*a^2*b^2*c*e - a*b^4*e)*z3^2*eta2 + (-2*a^3*b*e^2 - 2*a^3*c*d*e + 3*a^2*b^2*d*e + 3*a^2*b*c^2*e - 4*a*b^3*c*e + b^5*e)*z3^2*eta3)/a^6 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (130.127.186.116) Time: Fri Dec 5 14:40:13 2003 Input: ? Dihedral Output: Magma V2.10-6 Fri Dec 5 2003 14:40:10 on modular [Seed = 2255054472] ------------------------------------- 7 matches: 1 I /magma/group/finitely-presented/fp-group-construction/standard/\ DihedralGroup 2 I /magma/group/group-overview/extension-standard-group/standard/\ DihedralGroup 3 I /magma/group/group-overview/extension-standard-group/standard/\ DihedralGroup 4 I /magma/group/permutation/building-groups/standard/DihedralGroup 5 I /magma/group/permutation/building-groups/standard/DihedralGroup 6 I /magma/group/polycyclic/subgroup-quotient-homomorphism-extension/\ standard-group/DihedralGroup 7 I /magma/group/soluble/definition/construction-functions/\ DihedralGroup To view an entry, type ? followed by the number next to it Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (130.127.186.116) Time: Fri Dec 5 14:40:30 2003 Input: ? Dihedral 7 Output: Magma V2.10-6 Fri Dec 5 2003 14:40:27 on modular [Seed = 2388750001] ------------------------------------- 7 matches: 1 I /magma/group/finitely-presented/fp-group-construction/standard/\ DihedralGroup 2 I /magma/group/group-overview/extension-standard-group/standard/\ DihedralGroup 3 I /magma/group/group-overview/extension-standard-group/standard/\ DihedralGroup 4 I /magma/group/permutation/building-groups/standard/DihedralGroup 5 I /magma/group/permutation/building-groups/standard/DihedralGroup 6 I /magma/group/polycyclic/subgroup-quotient-homomorphism-extension/\ standard-group/DihedralGroup 7 I /magma/group/soluble/definition/construction-functions/\ DihedralGroup To view an entry, type ? followed by the number next to it 7 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (130.127.186.116) Time: Fri Dec 5 14:44:26 2003 Input: ? Dihedral G:=DihedralGroup(8); DerivedSeries(G); Output: Magma V2.10-6 Fri Dec 5 2003 14:44:23 on modular [Seed = 2806544548] ------------------------------------- 7 matches: 1 I /magma/group/finitely-presented/fp-group-construction/standard/\ DihedralGroup 2 I /magma/group/group-overview/extension-standard-group/standard/\ DihedralGroup 3 I /magma/group/group-overview/extension-standard-group/standard/\ DihedralGroup 4 I /magma/group/permutation/building-groups/standard/DihedralGroup 5 I /magma/group/permutation/building-groups/standard/DihedralGroup 6 I /magma/group/polycyclic/subgroup-quotient-homomorphism-extension/\ standard-group/DihedralGroup 7 I /magma/group/soluble/definition/construction-functions/\ DihedralGroup To view an entry, type ? followed by the number next to it [ Permutation group G acting on a set of cardinality 8 Order = 16 = 2^4 (1, 2, 3, 4, 5, 6, 7, 8) (1, 8)(2, 7)(3, 6)(4, 5), Permutation group acting on a set of cardinality 8 Order = 4 = 2^2 (1, 7, 5, 3)(2, 8, 6, 4), Permutation group acting on a set of cardinality 8 Order = 1 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (130.127.186.116) Time: Fri Dec 5 14:45:13 2003 Input: G:=DihedralGroup(4);; DerivedSeries(G); Output: Magma V2.10-6 Fri Dec 5 2003 14:45:10 on modular [Seed = 3577350791] ------------------------------------- [ Permutation group G acting on a set of cardinality 4 Order = 8 = 2^3 (1, 2, 3, 4) (1, 4)(2, 3), Permutation group acting on a set of cardinality 4 Order = 2 (1, 3)(2, 4), Permutation group acting on a set of cardinality 4 Order = 1 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 5 16:22:15 2003 Input: R := PolynomialRing(RationalField()); CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; Output: Magma V2.10-6 Fri Dec 5 2003 16:22:11 on modular [Seed = 3159585965] ------------------------------------- 11,1,2,x + 2,3,x + 1,5,x - 1,7,x + 2,11,x - 1,13,x - 4[] Total time: 3.149 seconds, Total memory usage: 2.59MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 19:18:40 2003 Input: >L:=LatticeWithGram(8,[8,1,4,3,1,4,1,0,0,2,-12,0,-4,0,20,0,8,0,0,4,24,-4,0,-4,0,8,4,12,0,0,0,4,4,0,0,12]); >L; >M:=MatrixRing(IntegerRing(),8); >H:=elt; >G:=AutomorphismGroup(L,[H]); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 19:18:36 on modular [Seed = 953558891] ------------------------------------- >> L:=LatticeWithGram(8,[8,1,4,3,1,4,1,0,0,2,-12,0,-4,0,20,0,8,0,0,4,24,-4,0, ^ Runtime error in 'LatticeWithGram': Inner product matrix argument is not symmetric and positive definite >> L; ^ User error: Identifier 'L' has not been declared or assigned >> G:=AutomorphismGroup(L,[H]); ^ User error: Identifier 'L' has not been declared or assigned >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Fri Dec 5 19:20:31 2003 Input: >L:=LatticeWithGram(8,[8,1,4,3,1,4,1,0,0,2,-12,0,-4,0,20,0,8,0,0,4,24,-4,0,->4,0,8,4,12,0,0,0,4,4,0,0,12]); >L; >M:=MatrixRing(IntegerRing(),8); >H:=elt1,0,2,1,3,0,0,0,0,1,1,0,0,3,5,1,2,1,-7,1,-2,1,1,6,1,0,1,14,1,0,2,1,3,0,-2,1,->1,0,1,0,0,3,1,0,0,7]>; >G:=AutomorphismGroup(L,[H]); >#G; Output: Magma V2.10-6 Fri Dec 5 2003 19:20:28 on modular [Seed = 1218860939] ------------------------------------- >> 0,0,8,0,0,4,24,-4,0,->4,0,8,4,12,0,0,0,4,4,0,0,12]); ^ User error: bad syntax >> L; ^ User error: Identifier 'L' has not been declared or assigned >> H:=elt1,0,2,1,3,0,0,0,0,1,1,0 ^ User error: bad syntax >> G:=AutomorphismGroup(L,[H]); ^ User error: Identifier 'L' has not been declared or assigned >> #G;; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 04:41:35 2003 Input: SimplexAlphaCodeZ4(2::4) Output: Magma V2.10-6 Sat Dec 6 2003 04:41:31 on modular [Seed = 2238389960] ------------------------------------- >> SimplexAlphaCodeZ4(2::4) ^ User error: bad syntax Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 04:42:32 2003 Input: SimplexAlphaCodez4(2::4) Output: Magma V2.10-6 Sat Dec 6 2003 04:42:29 on modular [Seed = 2372081166] ------------------------------------- >> SimplexAlphaCodez4(2::4); ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 04:43:21 2003 Input: C:=SimplexAlphaCodez4(2::4); Output: Magma V2.10-6 Sat Dec 6 2003 04:43:18 on modular [Seed = 2507869733] ------------------------------------- >> C:=SimplexAlphaCodez4(2::4);; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 04:44:30 2003 Input: C:=SimplexAlphaCodez4(2::Z4); Output: Magma V2.10-6 Sat Dec 6 2003 04:44:27 on modular [Seed = 2591293799] ------------------------------------- >> C:=SimplexAlphaCodez4(2::Z4);; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 04:54:46 2003 Input: SimplexAlphaCodeZ4(2); Output: Magma V2.10-6 Sat Dec 6 2003 04:54:43 on modular [Seed = 2992384727] ------------------------------------- (16, 16, 8) Linear Code over IntegerRing(4) Generator matrix: [0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3] [0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 04:55:29 2003 Input: SimplexBetaCodeZ4(2); Output: Magma V2.10-6 Sat Dec 6 2003 04:55:26 on modular [Seed = 3341377359] ------------------------------------- (6, 16, 4) Linear Code over IntegerRing(4) Generator matrix: [1 0 3 2 3 1] [0 1 2 3 1 1] Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 04:56:16 2003 Input: SimplexBetaCodeZ4(3); Output: Magma V2.10-6 Sat Dec 6 2003 04:56:13 on modular [Seed = 3475068788] ------------------------------------- (28, 64, 16) Linear Code over IntegerRing(4) Generator matrix: [1 0 3 2 0 3 2 1 3 2 1 0 2 1 0 3 3 2 1 0 3 1 1 0 3 2 1 3] [0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 1 1 0 1 2 3 1 1] [0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 0 2 1 1 1 1 0 2] Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 05:04:48 2003 Input: C:=SimplexBetaCodeZ4(3); Output: Magma V2.10-6 Sat Dec 6 2003 05:04:45 on modular [Seed = 3892739667] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 05:05:45 2003 Input: C:=SimplexBetaCodeZ4(3); DualWeightDistribution(C); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 05:05:22 on modular [Seed = 4245908249] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14843 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ip68-99-198-223.ph.ph.cox.net. (68.99.198.223) Time: Sat Dec 6 05:07:17 2003 Input: C:=SimplexBetaCodeZ4(2); DualWeightDistribution(C); Output: Magma V2.10-6 Sat Dec 6 2003 05:07:14 on modular [Seed = 32478294] ------------------------------------- [ <0, 1>, <2, 3>, <3, 44>, <4, 59>, <5, 100>, <6, 49> ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host p3E9C2E56.dip.t-dialin.net. (62.156.46.86) Time: Sat Dec 6 05:29:37 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; MordellWeilRankBounds(E); C := HyperellipticCurve(E); J := Jacobian(C); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Dec 6 2003 05:29:33 on modular [Seed = 1218894016] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 0 2 m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 4*$.1 4*$.1*$.3 + 8*$.2 + 4*$.3^2 $.3 and inverse 1/4*$.1 -1/8*$.1*$.3 + 1/8*$.2 - 1/2*$.3^2 $.3 2 3 <[ 2*$.1^2 - 17488*$.1 - 306092513, 26405/162*$.1^2 - 76961773/54*$.1 - 2020593203587/81, -$.1^2 + 8744*$.1 + 153046258 ], [], []> { Number Field with defining polynomial $.1^2 - 410 over the Rational Field } Total time: 4.109 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host p3E9C2E56.dip.t-dialin.net. (62.156.46.86) Time: Sat Dec 6 05:35:34 2003 Input: E:=EllipticCurve([1,1,1,-14346720,-20921901465]);E; MordellWeilRankBounds(E); C := HyperellipticCurve(E); J := Jacobian(C); TwoSelmerGroupData(J : Bound := 300); TwoSelmerGroupData; Output: Magma V2.10-6 Sat Dec 6 2003 05:35:29 on modular [Seed = 2090005384] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 14346720*x - 20921901465 over Rational Field 0 2 m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 4*$.1 4*$.1*$.3 + 8*$.2 + 4*$.3^2 $.3 and inverse 1/4*$.1 -1/8*$.1*$.3 + 1/8*$.2 - 1/2*$.3^2 $.3 2 3 <[ 2*$.1^2 - 17488*$.1 - 306092513, 163/162*$.1^2 - 475091/54*$.1 - 12473274239/81, -$.1^2 + 8744*$.1 + 153046258 ], [], []> { Number Field with defining polynomial $.1^2 - 410 over the Rational Field } Intrinsic 'TwoSelmerGroupData' Signatures: ( J) -> RngIntElt, RngIntElt, Tup, List [ BoundType, Bound, UseUnits, Points, Fields ] Compute the 2-Selmer group of J (a Jacobian of a hyperelliptic curve defined over the rationals). The first value is the upper bound for the Mordell-Weil rank deduced from the computation, the second value is the dimension of the Selmer group. The third value gives a presentation of the (fake) Selmer group (but is only defined when UseUnits is true). It is a triple , where seq1 is a sequence of elements in L = Q[x]/(f(x)) representing a basis of some subgroup S1 of L^*/(L^*)^2, seq2 and seq3 are sequences of integers representing bases of subgroups S2 and S3 of Q^*/(Q^*)^2, respectively, and the (fake) Selmer group S fits into the exact sequence 0 --> S3 --> S2 --> S1 --> S --> 0. This data is in terms of the possibly modified model of the curve that the algorithm actually uses. As a fourth value, a set of the number fields used in the function is returned. Total time: 4.179 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:31:25 2003 Input: K := NumberField(x^2 + 1); Output: Magma V2.10-6 Sat Dec 6 2003 14:31:22 on modular [Seed = 2154664202] ------------------------------------- >> K := NumberField(x^2 + 1);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:31:44 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 + 1); Output: Magma V2.10-6 Sat Dec 6 2003 14:31:41 on modular [Seed = 2305071124] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:32:01 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 + 1); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:31:58 on modular [Seed = 2440855615] ------------------------------------- 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:32:13 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 1); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:32:10 on modular [Seed = 2574551075] ------------------------------------- >> K := NumberField(x^2 - 1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> MinkowskiBound(K); ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:32:25 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 1); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:32:22 on modular [Seed = 2706157671] ------------------------------------- >> K := NumberField(x^2 - 1); ^ Runtime error in 'NumberField': Argument 1 is not irreducible >> MinkowskiBound(K); ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:32:33 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 + 1); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:32:30 on modular [Seed = 2839853159] ------------------------------------- 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:32:46 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^5 + 239); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:32:43 on modular [Seed = 2975637610] ------------------------------------- 198779 Total time: 3.059 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:33:49 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^5 - 239); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:33:46 on modular [Seed = 3109333411] ------------------------------------- 198779 Total time: 3.069 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:33:56 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 239); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:33:53 on modular [Seed = 3240940000] ------------------------------------- 15 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:34:05 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 2); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:34:02 on modular [Seed = 3374635491] ------------------------------------- 1 Total time: 3.000 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:34:13 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:34:10 on modular [Seed = 3510419939] ------------------------------------- 2 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:34:34 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:34:30 on modular [Seed = 3644115359] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Total time: 3.159 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:39:05 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 + 163); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:39:02 on modular [Seed = 3943097533] ------------------------------------- 8 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 + 163 over its ground order Total time: 3.109 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:39:21 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 + 165); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:39:17 on modular [Seed = 4078894230] ------------------------------------- 16 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 to Set of ideals of Maximal Equation Order with defining polynomial x^2 + 165 over its ground order Total time: 3.199 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 14:41:00 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 14:40:57 on modular [Seed = 2073457869] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Total time: 3.219 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 15:08:01 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 15:07:58 on modular [Seed = 853490259] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Total time: 3.249 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 15:10:57 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 37); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 15:10:53 on modular [Seed = 335420321] ------------------------------------- 3 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 37 over its ground order Total time: 3.159 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 15:11:12 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 93); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 15:11:08 on modular [Seed = 199623592] ------------------------------------- 4 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 93 over its ground order Total time: 3.279 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host pool-141-158-32-245.phil.east.verizon.net. (141.158.32.245) Time: Sat Dec 6 15:11:26 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^3 - 2); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sat Dec 6 2003 15:11:23 on modular [Seed = 65932183] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 3.229 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:33:36 2003 Input: N:=33; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=ComponentGroupOrder(A[i],3); end for; print [N,i,3,cg,11,1]; Output: Magma V2.10-6 Sat Dec 6 2003 18:33:31 on modular [Seed = 2940401561] ------------------------------------- >> print [N,i,3,cg,11,1];; ^ User error: Identifier 'i' has not been declared or assigned Total time: 4.339 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:34:02 2003 Input: N:=33; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=ComponentGroupOrder(A[i],3); print [N,i,3,cg,11,1]; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:33:58 on modular [Seed = 2806710204] ------------------------------------- [ 33, 1, 3, 3, 11, 1 ] Total time: 4.199 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:39:42 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[[]]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cg[j]:=ComponentGroupOrder(A[i],3); Include(~cg,[n[j][1],cg[j]); end for; print cg; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:39:39 on modular [Seed = 2491007826] ------------------------------------- >> Include(~cg,[n[j][1],cg[j]); end for; ^ User error: bad syntax [ [] ] >> print cg; end for;; ^ User error: bad syntax Total time: 3.319 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:40:40 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[[]]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cg[j]:=ComponentGroupOrder(A[i],3); Include(~cg,[n[j][1],cg[j]]); end for; print cg; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:40:36 on modular [Seed = 2221527821] ------------------------------------- >> cg[j]:=ComponentGroupOrder(A[i],3); ^ Runtime error in :=: Sequence mutation failed Total time: 4.209 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:41:50 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[[]]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],3); Include(~cg,[n[j][1],cgo[j]]); end for; print cg; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:41:47 on modular [Seed = 2106600250] ------------------------------------- >> cgo[j]:=ComponentGroupOrder(A[i],3); ^ User error: Identifier 'cgo' has not been declared or assigned Total time: 3.319 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:42:10 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[[]]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],3); Include(~cg,[n[j][1],cgo[j]]); end for; print cg; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:42:05 on modular [Seed = 1972904772] ------------------------------------- [ [], [ 33, 1 ], [ 3, 3 ], [ 11, 3 ] ] Total time: 4.169 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:43:10 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],3); Include(~cg,[n[j][1],cgo[j]]); end for; print cg; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:43:05 on modular [Seed = 1854093467] ------------------------------------- [ [ 33, 1 ], [ 3, 3 ], [ 11, 3 ] ] Total time: 4.259 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:44:34 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],3); Include(~cg,[n[j][1],cgo[j]]); end for; printf "%o",cg; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:44:29 on modular [Seed = 1720398023] ------------------------------------- [ [ 33, 1 ], [ 3, 3 ], [ 11, 3 ] ] Total time: 4.219 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:46:24 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],3); Include(~cg,[n[j][1],cgo[j]]); end for; printf "%o",cg; end for; ComponentGroupOrder(A[1],11); Output: Magma V2.10-6 Sat Dec 6 2003 18:46:18 on modular [Seed = 1319312248] ------------------------------------- [ [ 33, 1 ], [ 3, 3 ], [ 11, 3 ] ]1 Total time: 6.039 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:47:18 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; printf "%o",cg; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:47:12 on modular [Seed = 953511365] ------------------------------------- [ [ 33, 1 ], [ 3, 3 ], [ 11, 1 ] ] Total time: 5.859 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:49:09 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:49:03 on modular [Seed = 819815843] ------------------------------------- [ 33, 1 ][ 3, 3 ][ 11, 1 ][] Total time: 5.809 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:49:57 2003 Input: for N in [11.33] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:49:54 on modular [Seed = 700743031] ------------------------------------- >> n:=Factorization(N); ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldPrElt Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:50:24 2003 Input: for N in [11..33] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:50:15 on modular [Seed = 435440978] ------------------------------------- [ 11, 1 ][ 11, 5 ][] [ 14, 1 ][ 2, 3 ][ 7, 3 ][] [ 15, 1 ][ 3, 1 ][ 5, 1 ][] [ 17, 1 ][] [ 19, 1 ][ 19, 3 ][] Do not know how to compute component group at 2 Total time: 9.209 seconds, Total memory usage: 4.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:51:49 2003 Input: for N in [11..19] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:51:40 on modular [Seed = 301745633] ------------------------------------- [ 11, 1 ][ 11, 5 ][] [ 14, 1 ][ 2, 3 ][ 7, 3 ][] [ 15, 1 ][ 3, 1 ][ 5, 1 ][] [ 17, 1 ][] [ 19, 1 ][ 19, 3 ][] Total time: 8.899 seconds, Total memory usage: 4.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:53:42 2003 Input: for N in [20..25] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:53:39 on modular [Seed = 4162169735] ------------------------------------- Do not know how to compute component group at 2 Total time: 3.279 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:54:05 2003 Input: for N in [21..25] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:54:00 on modular [Seed = 4028474260] ------------------------------------- [ 21, 1 ][ 3, 1 ][ 7, 1 ][] [ 23, 1 ][ 23, 11 ][] Do not know how to compute component group at 2 Total time: 5.369 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:55:21 2003 Input: for N in [26..27] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); cg:=[]; cgo:=[]; for i in [1..#A] do Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:55:08 on modular [Seed = 3825842116] ------------------------------------- [ 26, 1 ][ 2, 3 ][ 13, 3 ][] [ 26, 1 ][ 2, 3 ][ 13, 3 ][ 26, 2 ][ 2, 7 ][ 13, 1 ][] Do not know how to compute component group at 3 Total time: 13.289 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:57:31 2003 Input: for N in [26..27] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:57:19 on modular [Seed = 3661072761] ------------------------------------- [ 26, 1 ][ 2, 3 ][ 13, 3 ][] [ 26, 2 ][ 2, 7 ][ 13, 1 ][] Do not know how to compute component group at 3 Total time: 11.649 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 18:58:54 2003 Input: for N in [29..31] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:58:35 on modular [Seed = 3527377029] ------------------------------------- [ 29, 1 ][ 29, 7 ][] [ 30, 1 ][ 2, 1 ][ 3, 3 ][ 5, 1 ][] [ 31, 1 ][ 31, 5 ][] Total time: 18.739 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:00:16 2003 Input: for N in [33..36] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 18:59:59 on modular [Seed = 3408304584] ------------------------------------- [ 33, 1 ][ 3, 3 ][ 11, 1 ][] [ 34, 1 ][ 2, 3 ][ 17, 1 ][] [ 35, 1 ][ 5, 3 ][ 7, 3 ][] [ 35, 2 ][ 5, 1 ][ 7, 1 ][] Do not know how to compute component group at 2 Total time: 17.180 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:02:18 2003 Input: for N in [37..40] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:02:03 on modular [Seed = 2789995553] ------------------------------------- [ 37, 1 ][] [ 37, 2 ][ 37, 3 ][] [ 38, 1 ][ 2, 9 ][ 19, 3 ][] [ 38, 2 ][ 2, 5 ][ 19, 1 ][] [ 39, 1 ][ 3, 1 ][ 13, 1 ][] [ 39, 2 ][ 3, 7 ][ 13, 1 ][] Do not know how to compute component group at 2 Total time: 14.250 seconds, Total memory usage: 3.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:05:30 2003 Input: for N in [41..44] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:05:10 on modular [Seed = 2608253521] ------------------------------------- [ 41, 1 ][ 41, 5 ][] [ 42, 1 ][ 2, 1 ][ 3, 1 ][ 7, 1 ][] [ 43, 1 ][] [ 43, 2 ][ 43, 7 ][] Do not know how to compute component group at 2 Total time: 19.899 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:06:34 2003 Input: for N in [46..48] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:06:27 on modular [Seed = 2371935730] ------------------------------------- [ 46, 1 ][ 2, 5 ][ 23, 1 ][] [ 47, 1 ][ 47, 23 ][] Do not know how to compute component group at 2 Total time: 6.829 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:08:14 2003 Input: for N in [51..52] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:08:05 on modular [Seed = 2238240156] ------------------------------------- [ 51, 1 ][ 3, 3 ][ 17, 1 ][] [ 51, 2 ][ 3, 1 ][ 17, 1 ][] Do not know how to compute component group at 2 Total time: 8.769 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:09:07 2003 Input: for N in [53..54] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:09:01 on modular [Seed = 2056727196] ------------------------------------- [ 53, 1 ][] [ 53, 2 ][ 53, 13 ][] Do not know how to compute component group at 3 Total time: 6.179 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:10:24 2003 Input: for N in [55..56] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:10:16 on modular [Seed = 1770273274] ------------------------------------- [ 55, 1 ][ 5, 1 ][ 11, 1 ][] [ 55, 2 ][ 5, 7 ][ 11, 1 ][] Do not know how to compute component group at 2 Total time: 7.799 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:11:57 2003 Input: for N in [57..60] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:11:43 on modular [Seed = 1636576805] ------------------------------------- [ 57, 1 ][ 3, 1 ][ 19, 1 ][] [ 57, 2 ][ 3, 1 ][ 19, 1 ][] [ 57, 3 ][ 3, 5 ][ 19, 1 ][] [ 58, 1 ][ 2, 1 ][ 29, 1 ][] [ 58, 2 ][ 2, 5 ][ 29, 1 ][] [ 59, 1 ][ 59, 29 ][] Total time: 13.389 seconds, Total memory usage: 3.97MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:13:34 2003 Input: for N in [60..60] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:13:30 on modular [Seed = 1488263049] ------------------------------------- Total time: 3.949 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:14:02 2003 Input: for N in [61..63] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:13:47 on modular [Seed = 1421417364] ------------------------------------- [ 61, 1 ][] [ 61, 2 ][ 61, 5 ][] [ 62, 1 ][ 2, 1 ][ 31, 1 ][] [ 62, 2 ][ 2, 33 ][ 31, 3 ][] Do not know how to compute component group at 3 Total time: 13.300 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:16:00 2003 Input: for N in [65..68] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:15:37 on modular [Seed = 1202325781] ------------------------------------- [ 65, 1 ][ 5, 1 ][ 13, 1 ][] [ 65, 2 ][ 5, 3 ][ 13, 3 ][] [ 65, 3 ][ 5, 7 ][ 13, 1 ][] Errors: /home/mfd/gomagma: line 2: 17468 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:17:37 2003 Input: for N in [66..66] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:17:14 on modular [Seed = 1054044367] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17477 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:19:58 2003 Input: for N in [67..68] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:19:54 on modular [Seed = 734422650] ------------------------------------- [ 67, 1 ][] [ 67, 2 ][ 67, 1 ][] [ 67, 3 ][ 67, 11 ][] Do not know how to compute component group at 2 Total time: 3.749 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:21:23 2003 Input: for N in [69..72] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:21:01 on modular [Seed = 452417292] ------------------------------------- [ 69, 1 ][ 3, 1 ][ 23, 1 ][] [ 69, 2 ][ 3, 11 ][ 23, 1 ][] [ 70, 1 ][ 2, 1 ][ 5, 1 ][ 7, 1 ][] [ 71, 1 ][ 71, 5 ][] [ 71, 2 ][ 71, 7 ][] Do not know how to compute component group at 2 Total time: 21.449 seconds, Total memory usage: 4.11MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:22:44 2003 Input: for N in [73..75] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:22:26 on modular [Seed = 318726059] ------------------------------------- [ 73, 1 ][] [ 73, 2 ][ 73, 1 ][] [ 73, 3 ][] [ 74, 1 ][ 2, 9 ][ 37, 3 ][] [ 74, 2 ][ 2, 95 ][ 37, 1 ][] Do not know how to compute component group at 5 Total time: 18.049 seconds, Total memory usage: 3.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:24:19 2003 Input: for N in [77..80] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:23:56 on modular [Seed = 165954926] ------------------------------------- [ 77, 1 ][ 7, 1 ][ 11, 1 ][] [ 77, 2 ][ 7, 3 ][ 11, 1 ][] [ 77, 3 ][ 7, 3 ][ 11, 3 ][] [ 77, 4 ][ 7, 1 ][ 11, 1 ][] Errors: /home/mfd/gomagma: line 2: 17522 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:25:36 2003 Input: for N in [78..78] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:25:12 on modular [Seed = 99109142] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17534 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:26:18 2003 Input: for N in [79..80] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:26:14 on modular [Seed = 4078878510] ------------------------------------- [ 79, 1 ][] [ 79, 2 ][ 79, 13 ][] Do not know how to compute component group at 2 Total time: 3.859 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:28:32 2003 Input: for N in [78..78] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:28:08 on modular [Seed = 3943080072] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17552 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:29:32 2003 Input: for N in [78..78] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:29:17 on modular [Seed = 3809388741] ------------------------------------- [ 78, 1 ][ 3, 5 ][] Total time: 14.380 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:31:22 2003 Input: for N in [79..80] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:31:18 on modular [Seed = 3527383422] ------------------------------------- [ 79, 1 ][] [ 79, 2 ][ 79, 13 ][] Do not know how to compute component group at 2 Total time: 3.949 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sat Dec 6 19:31:39 2003 Input: ZI := MaximalOrder(QuadraticField(2)); Output: Magma V2.10-6 Sat Dec 6 2003 19:31:36 on modular [Seed = 3391586649] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sat Dec 6 19:31:51 2003 Input: ZI := MaximalOrder(QuadraticField(2)); (1 + w)^2; Output: Magma V2.10-6 Sat Dec 6 2003 19:31:48 on modular [Seed = 3257895245] ------------------------------------- 2*w + 3 Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sat Dec 6 19:32:14 2003 Input: ZI := MaximalOrder(QuadraticField(33)); Norm(w); Output: Magma V2.10-6 Sat Dec 6 2003 19:32:10 on modular [Seed = 3126325451] ------------------------------------- -8 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:32:47 2003 Input: for N in [82..84] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:32:36 on modular [Seed = 2992634093] ------------------------------------- [ 82, 1 ][ 2, 1 ][ 41, 1 ][] [ 82, 2 ][ 2, 7 ][ 41, 1 ][] [ 83, 1 ][] [ 83, 2 ][ 83, 41 ][] Do not know how to compute component group at 2 Total time: 10.989 seconds, Total memory usage: 3.91MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:34:29 2003 Input: for N in [85..88] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:34:06 on modular [Seed = 2839864236] ------------------------------------- [ 85, 1 ][ 5, 1 ][ 17, 1 ][] [ 85, 2 ][ 5, 1 ][ 17, 1 ][] [ 85, 3 ][ 5, 3 ][ 17, 1 ][] [ 86, 1 ][ 2, 21 ][ 43, 3 ][] [ 86, 2 ][ 2, 55 ][ 43, 1 ][] Errors: /home/mfd/gomagma: line 2: 17618 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:35:52 2003 Input: for N in [87..88] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:35:40 on modular [Seed = 2756308483] ------------------------------------- [ 87, 1 ][ 3, 5 ][ 29, 1 ][] [ 87, 2 ][ 3, 23 ][ 29, 1 ][] Do not know how to compute component group at 2 Total time: 11.710 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:36:38 2003 Input: for N in [89..90] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:36:24 on modular [Seed = 2624706031] ------------------------------------- [ 89, 1 ][] [ 89, 2 ][ 89, 1 ][] [ 89, 3 ][ 89, 11 ][] Do not know how to compute component group at 3 Total time: 13.809 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sat Dec 6 19:36:38 2003 Input: ZI := MaximalOrder(QuadraticField(33)); Norm(w + 2); Output: Magma V2.10-6 Sat Dec 6 2003 19:36:35 on modular [Seed = 2440878329] ------------------------------------- -2 Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:37:42 2003 Input: for N in [91..92] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:37:31 on modular [Seed = 2205076147] ------------------------------------- [ 91, 1 ][ 7, 1 ][ 13, 1 ][] [ 91, 2 ][ 7, 1 ][ 13, 1 ][] [ 91, 3 ][ 7, 7 ][ 13, 1 ][] [ 91, 4 ][ 7, 1 ][ 13, 1 ][] Do not know how to compute component group at 2 Total time: 11.259 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:38:47 2003 Input: for N in [93..96] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:38:24 on modular [Seed = 2056729472] ------------------------------------- [ 93, 1 ][ 3, 1 ][ 31, 1 ][] [ 93, 2 ][ 3, 1 ][ 31, 1 ][] [ 94, 1 ][ 2, 1 ][ 47, 1 ][] [ 94, 2 ][ 2, 47 ][ 47, 1 ][] Errors: /home/mfd/gomagma: line 2: 17664 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sat Dec 6 19:39:09 2003 Input: ZI := MaximalOrder(QuadraticField(33)); Norm(w + 1); Output: Magma V2.10-6 Sat Dec 6 2003 19:39:06 on modular [Seed = 1923038114] ------------------------------------- -6 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:40:09 2003 Input: for N in [95..96] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:39:51 on modular [Seed = 1787241415] ------------------------------------- [ 95, 1 ][ 5, 5 ][ 19, 1 ][] [ 95, 2 ][ 5, 27 ][ 19, 3 ][] Do not know how to compute component group at 2 Total time: 17.719 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:41:05 2003 Input: for N in [97..98] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:40:54 on modular [Seed = 1538659127] ------------------------------------- [ 97, 1 ][] [ 97, 2 ][ 97, 1 ][] Do not know how to compute component group at 7 Total time: 11.380 seconds, Total memory usage: 3.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:42:14 2003 Input: for N in [101..104] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:41:51 on modular [Seed = 1404967782] ------------------------------------- [ 101, 1 ][] [ 101, 2 ][ 101, 25 ][] Errors: /home/mfd/gomagma: line 2: 17705 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:44:16 2003 Input: for N in [103..104] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:44:12 on modular [Seed = 1218773230] ------------------------------------- [ 103, 1 ][] [ 103, 2 ][ 103, 17 ][] Do not know how to compute component group at 2 Total time: 4.029 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:45:16 2003 Input: for N in [105..105] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:44:53 on modular [Seed = 1085081407] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17722 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:46:21 2003 Input: for N in [106..108] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:46:09 on modular [Seed = 1037072918] ------------------------------------- [ 106, 1 ][ 2, 1 ][ 53, 1 ][] [ 106, 2 ][ 2, 5 ][ 53, 1 ][] [ 106, 3 ][ 2, 3 ][ 53, 1 ][] [ 106, 4 ][ 2, 3 ][ 53, 1 ][] [ 107, 1 ][] [ 107, 2 ][ 107, 53 ][] Do not know how to compute component group at 2 Total time: 12.269 seconds, Total memory usage: 4.01MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:48:05 2003 Input: for N in [109..112] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:47:41 on modular [Seed = 717712893] ------------------------------------- [ 109, 1 ][] [ 109, 2 ][ 109, 1 ][] [ 109, 3 ][ 109, 9 ][] [ 110, 1 ][ 2, 7 ][ 5, 1 ][ 11, 3 ][] [ 110, 2 ][ 2, 3 ][ 5, 1 ][ 11, 1 ][] [ 110, 3 ][ 2, 5 ][ 5, 5 ][ 11, 1 ][] Errors: /home/mfd/gomagma: line 2: 17744 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:49:15 2003 Input: for N in [110..112] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:48:52 on modular [Seed = 584017324] ------------------------------------- [ 110, 1 ][ 2, 7 ][ 5, 1 ][ 11, 3 ][] [ 110, 2 ][ 2, 3 ][ 5, 1 ][ 11, 1 ][] Errors: /home/mfd/gomagma: line 2: 17752 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:49:54 2003 Input: for N in [110..110] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:49:31 on modular [Seed = 452418683] ------------------------------------- [ 110, 1 ][ 2, 7 ][ 5, 1 ][ 11, 3 ][] [ 110, 2 ][ 2, 3 ][ 5, 1 ][ 11, 1 ][] [ 110, 3 ][ 2, 5 ][ 5, 5 ][ 11, 1 ][] [ 110, 4 ][ 2, 1 ][ 5, 3 ][ 11, 1 ][] Total time: 22.520 seconds, Total memory usage: 3.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:50:41 2003 Input: for N in [111..112] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:50:26 on modular [Seed = 182930466] ------------------------------------- [ 111, 1 ][ 3, 5 ][ 37, 1 ][] [ 111, 2 ][ 3, 133 ][ 37, 1 ][] Do not know how to compute component group at 2 Total time: 15.289 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:51:29 2003 Input: for N in [113..113] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:51:26 on modular [Seed = 65947127] ------------------------------------- [ 113, 1 ][] [ 113, 2 ][ 113, 1 ][] [ 113, 3 ][ 113, 1 ][] [ 113, 4 ][ 113, 7 ][] Total time: 3.399 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:52:37 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:52:14 on modular [Seed = 4212571455] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17793 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:53:10 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:52:54 on modular [Seed = 4078876015] ------------------------------------- [ 114, 1 ][ 2, 1 ][] [ 114, 2 ][ 2, 5 ][] [ 114, 3 ][ 2, 3 ][] Total time: 15.429 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:54:10 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:53:46 on modular [Seed = 3943083659] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17809 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:55:30 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:55:07 on modular [Seed = 3825836533] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17822 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:56:07 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:55:44 on modular [Seed = 3710949431] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17831 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:56:45 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:56:30 on modular [Seed = 3577253905] ------------------------------------- [ 114, 1 ][ 2, 1 ][] [ 114, 2 ][ 2, 5 ][] [ 114, 3 ][ 2, 3 ][] Total time: 15.189 seconds, Total memory usage: 4.18MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:57:27 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 19:57:10 on modular [Seed = 3441461329] ------------------------------------- [ 114, 1 ][ 3, 5 ][] [ 114, 2 ][ 3, 3 ][] [ 114, 3 ][ 3, 3 ][] Total time: 16.109 seconds, Total memory usage: 4.16MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 19:59:33 2003 Input: for N in [114..114] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 19:59:09 on modular [Seed = 3126328990] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17856 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:01:29 2003 Input: for N in [78..78] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:01:12 on modular [Seed = 2574572859] ------------------------------------- [ 78, 1 ][ 13, 1 ][] Total time: 16.549 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:02:47 2003 Input: for N in [78..78] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:02:33 on modular [Seed = 2440876738] ------------------------------------- [ 78, 1 ][ 2, 1 ][] Total time: 14.429 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:04:08 2003 Input: for N in [115..116] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:03:54 on modular [Seed = 2305084041] ------------------------------------- [ 115, 1 ][ 5, 5 ][ 23, 1 ][] [ 115, 2 ][ 5, 1 ][ 23, 1 ][] [ 115, 3 ][ 5, 1 ][ 23, 1 ][] Do not know how to compute component group at 2 Total time: 13.629 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:05:20 2003 Input: for N in [118..120] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:04:57 on modular [Seed = 2255209797] ------------------------------------- [ 118, 1 ][ 2, 1 ][ 59, 1 ][] [ 118, 2 ][ 2, 19 ][ 59, 1 ][] [ 118, 3 ][ 2, 5 ][ 59, 1 ][] [ 118, 4 ][ 2, 1 ][ 59, 1 ][] Errors: /home/mfd/gomagma: line 2: 17916 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:06:44 2003 Input: for N in [119..120] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:06:22 on modular [Seed = 1889350151] ------------------------------------- [ 119, 1 ][ 7, 9 ][ 17, 3 ][] [ 119, 2 ][ 7, 3 ][ 17, 1 ][] Do not know how to compute component group at 2 Total time: 21.779 seconds, Total memory usage: 3.70MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:07:56 2003 Input: for N in [122..124] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:07:33 on modular [Seed = 1753557572] ------------------------------------- [ 122, 1 ][ 2, 1 ][ 61, 1 ][] [ 122, 2 ][ 2, 39 ][ 61, 3 ][] [ 122, 3 ][ 2, 31 ][ 61, 1 ][] Errors: /home/mfd/gomagma: line 2: 17937 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:08:57 2003 Input: for N in [123..124] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:08:40 on modular [Seed = 1670259075] ------------------------------------- [ 123, 1 ][ 3, 1 ][ 41, 1 ][] [ 123, 2 ][ 3, 5 ][ 41, 1 ][] [ 123, 3 ][ 3, 7 ][ 41, 1 ][] [ 123, 4 ][ 3, 23 ][ 41, 1 ][] Do not know how to compute component group at 2 Total time: 16.030 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:09:53 2003 Input: for N in [127..128] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:09:49 on modular [Seed = 1538660863] ------------------------------------- [ 127, 1 ][] [ 127, 2 ][ 127, 21 ][] Do not know how to compute component group at 2 Total time: 3.889 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:10:59 2003 Input: for N in [129..129] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:10:44 on modular [Seed = 1269172774] ------------------------------------- [ 129, 1 ][ 3, 1 ][ 43, 1 ][] [ 129, 2 ][ 3, 3 ][ 43, 1 ][] [ 129, 3 ][ 3, 7 ][ 43, 1 ][] [ 129, 4 ][ 3, 11 ][ 43, 1 ][] Total time: 15.279 seconds, Total memory usage: 3.81MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:11:53 2003 Input: for N in [130..130] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:11:30 on modular [Seed = 1118765945] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17979 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:12:32 2003 Input: for N in [130..130] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:12:09 on modular [Seed = 987200298] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17987 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:13:06 2003 Input: for N in [129..129] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:12:50 on modular [Seed = 853504985] ------------------------------------- [ 129, 1 ][ 3, 1 ][ 43, 1 ][] [ 129, 2 ][ 3, 3 ][ 43, 1 ][] [ 129, 3 ][ 3, 7 ][ 43, 1 ][] [ 129, 4 ][ 3, 11 ][ 43, 1 ][] Total time: 15.019 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:14:46 2003 Input: for N in [130..130] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:14:28 on modular [Seed = 717712295] ------------------------------------- [ 130, 1 ][ 2, 1 ][ 5, 3 ][] [ 130, 2 ][ 2, 1 ][ 5, 5 ][] [ 130, 3 ][ 2, 1 ][ 5, 1 ][] Total time: 17.340 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:16:10 2003 Input: for N in [131..131] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:16:06 on modular [Seed = 418732087] ------------------------------------- [ 131, 1 ][] [ 131, 2 ][ 131, 65 ][] Total time: 3.369 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:17:19 2003 Input: for N in [133..135] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:16:56 on modular [Seed = 285036769] ------------------------------------- [ 133, 1 ][ 7, 1 ][ 19, 1 ][] [ 133, 2 ][ 7, 5 ][ 19, 1 ][] [ 133, 3 ][ 7, 3 ][ 19, 1 ][] [ 133, 4 ][ 7, 7 ][ 19, 1 ][] Errors: /home/mfd/gomagma: line 2: 18025 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:18:54 2003 Input: for N in [132..132] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:18:31 on modular [Seed = 232803731] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18036 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:19:41 2003 Input: for N in [132..132] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:19:19 on modular [Seed = 99138155] ------------------------------------- [ 132, 1 ][ 3, 5 ][] [ 132, 2 ][ 3, 1 ][] Total time: 21.689 seconds, Total memory usage: 4.60MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:22:24 2003 Input: for N in [99..99] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:22:15 on modular [Seed = 4095298378] ------------------------------------- [ 99, 1 ][ 11, 1 ][] [ 99, 2 ][ 11, 1 ][] [ 99, 3 ][ 11, 1 ][] [ 99, 4 ][ 11, 1 ][] Total time: 7.989 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:24:47 2003 Input: for N in [75..75] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:24:41 on modular [Seed = 4009906639] ------------------------------------- [ 75, 1 ][ 3, 1 ][] [ 75, 2 ][ 3, 1 ][] [ 75, 3 ][ 3, 5 ][] Total time: 6.129 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:27:41 2003 Input: for N in [134..134] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:27:20 on modular [Seed = 3661063259] ------------------------------------- [ 134, 1 ][ 2, 75 ][ 67, 3 ][] [ 134, 2 ][ 2, 323 ][ 67, 1 ][] Total time: 20.849 seconds, Total memory usage: 4.02MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:29:02 2003 Input: for N in [137..137] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:28:58 on modular [Seed = 3577243894] ------------------------------------- [ 137, 1 ][] [ 137, 2 ][ 137, 17 ][] Total time: 3.339 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:30:29 2003 Input: for N in [138..138] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:30:06 on modular [Seed = 3257892645] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18107 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:31:21 2003 Input: for N in [138..138] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:31:07 on modular [Seed = 3176136735] ------------------------------------- [ 138, 1 ][ 2, 1 ][] [ 138, 2 ][ 2, 1 ][] [ 138, 3 ][ 2, 1 ][] [ 138, 4 ][ 2, 11 ][] Total time: 13.869 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:34:34 2003 Input: for N in [138..138] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:34:15 on modular [Seed = 3025733722] ------------------------------------- [ 138, 1 ][ 3, 1 ][] [ 138, 2 ][ 3, 3 ][] [ 138, 3 ][ 3, 1 ][] [ 138, 4 ][ 3, 11 ][] Total time: 19.600 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:36:18 2003 Input: for N in [138..138] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:35:55 on modular [Seed = 2723094048] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18139 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:37:04 2003 Input: for N in [138..138] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..4] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:36:41 on modular [Seed = 2591498698] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18147 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:38:42 2003 Input: for N in [139..139] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:38:38 on modular [Seed = 2507681394] ------------------------------------- [ 139, 1 ][] [ 139, 2 ][ 139, 1 ][] [ 139, 3 ][ 139, 23 ][] Total time: 3.389 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:39:45 2003 Input: for N in [140..140] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:39:22 on modular [Seed = 2371892798] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18164 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:40:31 2003 Input: for N in [140..140] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:40:17 on modular [Seed = 2089928197] ------------------------------------- [ 140, 1 ][ 5, 1 ][] [ 140, 2 ][ 5, 3 ][] Total time: 14.079 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:41:10 2003 Input: for N in [140..140] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:40:53 on modular [Seed = 1956236841] ------------------------------------- [ 140, 1 ][ 7, 5 ][] [ 140, 2 ][ 7, 1 ][] Total time: 16.729 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:43:04 2003 Input: for N in [141..142] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:42:41 on modular [Seed = 1837160324] ------------------------------------- [ 141, 1 ][ 3, 1 ][ 47, 1 ][] [ 141, 2 ][ 3, 3 ][ 47, 1 ][] [ 141, 3 ][ 3, 1 ][ 47, 1 ][] [ 141, 4 ][ 3, 1 ][ 47, 1 ][] [ 141, 5 ][ 3, 7 ][ 47, 1 ][] [ 141, 6 ][ 3, 43 ][ 47, 1 ][] Errors: /home/mfd/gomagma: line 2: 18197 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:44:31 2003 Input: for N in [142..142] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:44:16 on modular [Seed = 1703469037] ------------------------------------- [ 142, 1 ][ 2, 1 ][ 71, 1 ][] [ 142, 2 ][ 2, 3 ][ 71, 1 ][] [ 142, 3 ][ 2, 27 ][ 71, 1 ][] [ 142, 4 ][ 2, 3 ][ 71, 1 ][] [ 142, 5 ][ 2, 9 ][ 71, 1 ][] Total time: 15.210 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:45:41 2003 Input: for N in [143..144] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:45:18 on modular [Seed = 1405020677] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18219 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:46:31 2003 Input: for N in [143..144] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:46:11 on modular [Seed = 1269232208] ------------------------------------- [ 143, 1 ][ 11, 1 ][] [ 143, 2 ][ 11, 7 ][] [ 143, 3 ][ 11, 3 ][] Do not know how to compute component group at 2 Total time: 19.100 seconds, Total memory usage: 3.97MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:47:19 2003 Input: for N in [143..143] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:47:10 on modular [Seed = 1135540901] ------------------------------------- [ 143, 1 ][ 13, 1 ][] [ 143, 2 ][ 13, 9 ][] [ 143, 3 ][ 13, 3 ][] Total time: 8.960 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:49:06 2003 Input: for N in [145..145] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:48:51 on modular [Seed = 1020363847] ------------------------------------- [ 145, 1 ][ 5, 1 ][ 29, 1 ][] [ 145, 2 ][ 5, 7 ][ 29, 1 ][] [ 145, 3 ][ 5, 25 ][ 29, 1 ][] [ 145, 4 ][ 5, 5 ][ 29, 1 ][] Total time: 15.019 seconds, Total memory usage: 3.72MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:50:26 2003 Input: for N in [146..146] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:50:03 on modular [Seed = 734434072] ------------------------------------- [ 146, 1 ][ 2, 27 ][ 73, 3 ][] [ 146, 2 ][ 2, 703 ][ 73, 1 ][] Total time: 22.799 seconds, Total memory usage: 4.06MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:51:26 2003 Input: for N in [147..14] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:51:23 on modular [Seed = 617192647] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:51:43 2003 Input: for N in [147..147] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:51:34 on modular [Seed = 485598402] ------------------------------------- [ 147, 1 ][ 3, 1 ][] [ 147, 2 ][ 3, 1 ][] [ 147, 3 ][ 3, 1 ][] [ 147, 4 ][ 3, 1 ][] [ 147, 5 ][ 3, 7 ][] Total time: 9.119 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:53:09 2003 Input: for N in [149..149] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:53:05 on modular [Seed = 368616044] ------------------------------------- [ 149, 1 ][] [ 149, 2 ][ 149, 37 ][] Total time: 3.329 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:54:33 2003 Input: for N in [150..150] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:54:10 on modular [Seed = 232831543] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18293 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:56:08 2003 Input: for N in [151..151] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:56:04 on modular [Seed = 4212542519] ------------------------------------- >> cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); ^ Runtime error in '[]': Sequence element 2 not defined Total time: 3.479 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:56:26 2003 Input: for N in [151..151] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:56:22 on modular [Seed = 4078847053] ------------------------------------- [ 151, 1 ][] [ 151, 2 ][ 151, 1 ][] [ 151, 3 ][ 151, 25 ][] Total time: 3.549 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:57:23 2003 Input: for N in [152..152] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:57:09 on modular [Seed = 3943062630] ------------------------------------- [ 152, 1 ][ 19, 1 ][] [ 152, 2 ][ 19, 1 ][] [ 152, 3 ][ 19, 1 ][] Total time: 13.689 seconds, Total memory usage: 4.15MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 20:58:33 2003 Input: for N in [153..153] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 20:58:21 on modular [Seed = 3825816225] ------------------------------------- [ 153, 1 ][ 17, 1 ][] [ 153, 2 ][ 17, 1 ][] [ 153, 3 ][ 17, 1 ][] [ 153, 4 ][ 17, 1 ][] [ 153, 5 ][ 17, 1 ][] Total time: 12.479 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:00:21 2003 Input: for N in [155..155] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 20:59:57 on modular [Seed = 3694225977] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18340 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:01:01 2003 Input: for N in [155..155] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 21:00:45 on modular [Seed = 3424746105] ------------------------------------- [ 155, 1 ][ 5, 1 ][] [ 155, 2 ][ 5, 1 ][] [ 155, 3 ][ 5, 5 ][] [ 155, 4 ][ 5, 147 ][] [ 155, 5 ][ 5, 1 ][] Total time: 15.719 seconds, Total memory usage: 3.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:01:59 2003 Input: for N in [155..155] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 21:01:47 on modular [Seed = 3076129476] ------------------------------------- [ 155, 1 ][ 31, 1 ][] [ 155, 2 ][ 31, 1 ][] [ 155, 3 ][ 31, 1 ][] [ 155, 4 ][ 31, 3 ][] [ 155, 5 ][ 31, 1 ][] Total time: 11.939 seconds, Total memory usage: 3.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:04:18 2003 Input: for N in [156..156] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 21:03:55 on modular [Seed = 2940344924] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18391 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:04:52 2003 Input: for N in [156..156] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 21:04:31 on modular [Seed = 2806649456] ------------------------------------- [ 156, 1 ][ 3, 1 ][] [ 156, 2 ][ 3, 3 ][] Total time: 21.270 seconds, Total memory usage: 5.04MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:05:41 2003 Input: for N in [156..156] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 21:05:18 on modular [Seed = 2507677747] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18413 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:06:57 2003 Input: for N in [157..157] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 21:06:54 on modular [Seed = 2371893707] ------------------------------------- [ 157, 1 ][] [ 157, 2 ][ 157, 13 ][] Total time: 3.349 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:07:47 2003 Input: for N in [158..158] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 21:07:24 on modular [Seed = 2238198177] ------------------------------------- [ 158, 1 ][ 2, 1 ][ 79, 1 ][] [ 158, 2 ][ 2, 3 ][ 79, 3 ][] Errors: /home/mfd/gomagma: line 2: 18429 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:08:59 2003 Input: for N in [158..158] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 21:08:36 on modular [Seed = 1923073697] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18437 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:09:40 2003 Input: for N in [158..158] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 21:09:17 on modular [Seed = 2023083202] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18447 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:10:47 2003 Input: for N in [158..158] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 21:10:24 on modular [Seed = 1753602831] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18463 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:11:40 2003 Input: for N in [158..158] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..4] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 21:11:17 on modular [Seed = 1354621794] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18471 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:12:18 2003 Input: for N in [158..158] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 21:12:05 on modular [Seed = 1488317274] ------------------------------------- [ 158, 3 ][ 2, 5 ][] [ 158, 4 ][ 2, 1 ][] [ 158, 5 ][ 2, 1 ][] [ 158, 6 ][ 2, 53 ][] Total time: 13.089 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 6 21:14:08 2003 Input: for N in [159..159] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 21:13:49 on modular [Seed = 1336081637] ------------------------------------- [ 159, 1 ][ 3, 63 ][ 53, 1 ][] [ 159, 2 ][ 3, 107 ][ 53, 1 ][] Total time: 19.090 seconds, Total memory usage: 4.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:27:52 2003 Input: for N in [159..159] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:27:33 on modular [Seed = 2574530763] ------------------------------------- [ 159, 1 ][ 3, 63 ][ 53, 1 ][] [ 159, 2 ][ 3, 107 ][ 53, 1 ][] Total time: 19.180 seconds, Total memory usage: 4.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:49:37 2003 Input: for N in [160..160] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:49:25 on modular [Seed = 1235539322] ------------------------------------- [ 160, 1 ][ 5, 1 ][] [ 160, 2 ][ 5, 1 ][] [ 160, 3 ][ 5, 1 ][] Total time: 12.079 seconds, Total memory usage: 4.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:51:02 2003 Input: for N in [161..161] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 22:50:39 on modular [Seed = 970237376] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18767 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:51:27 2003 Input: for N in [161..161] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:51:18 on modular [Seed = 567066081] ------------------------------------- [ 161, 1 ][ 7, 1 ][] [ 161, 2 ][ 7, 1 ][] [ 161, 3 ][ 7, 19 ][] [ 161, 4 ][ 7, 3 ][] Total time: 9.009 seconds, Total memory usage: 3.83MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:53:16 2003 Input: for N in [162..162] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:53:03 on modular [Seed = 385584511] ------------------------------------- [ 162, 1 ][ 2, 1 ][] [ 162, 2 ][ 2, 1 ][] [ 162, 3 ][ 2, 3 ][] [ 162, 4 ][ 2, 3 ][] Total time: 12.639 seconds, Total memory usage: 4.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:54:12 2003 Input: for N in [163..163] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:54:08 on modular [Seed = 519275784] ------------------------------------- [ 163, 1 ][] [ 163, 2 ][ 163, 1 ][] [ 163, 3 ][ 163, 27 ][] Total time: 3.359 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:55:06 2003 Input: for N in [164..164] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:55:02 on modular [Seed = 49256930] ------------------------------------- Do not know how to compute component group at 2 Total time: 4.109 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:56:41 2003 Input: for N in [165..165] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 22:56:18 on modular [Seed = 149263260] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18814 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:57:24 2003 Input: for N in [165..165] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:57:02 on modular [Seed = 4028459656] ------------------------------------- [ 165, 1 ][ 3, 1 ][ 5, 1 ][] [ 165, 2 ][ 3, 3 ][ 5, 1 ][] [ 165, 3 ][ 3, 5 ][ 5, 5 ][] Total time: 21.840 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:58:19 2003 Input: for N in [165..165] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:58:00 on modular [Seed = 4162151110] ------------------------------------- [ 165, 1 ][ 11, 1 ][] [ 165, 2 ][ 11, 1 ][] [ 165, 3 ][ 11, 1 ][] Total time: 19.030 seconds, Total memory usage: 4.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 22:59:57 2003 Input: for N in [166..166] do n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; end for; Output: Magma V2.10-6 Sat Dec 6 2003 22:59:38 on modular [Seed = 3775691581] ------------------------------------- [ 166, 1 ][ 2, 1 ][ 83, 1 ][] [ 166, 2 ][ 2, 131 ][ 83, 1 ][] [ 166, 3 ][ 2, 7 ][ 83, 1 ][] Total time: 18.229 seconds, Total memory usage: 4.28MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:01:03 2003 Input: N:=167; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:00:59 on modular [Seed = 3510389596] ------------------------------------- [ 167, 1 ][] [ 167, 2 ][ 167, 83 ][] Total time: 3.579 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:02:06 2003 Input: N:=168; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:01:43 on modular [Seed = 3076140774] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18881 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:02:59 2003 Input: N:=168; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:02:36 on modular [Seed = 3159434646] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18890 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:03:49 2003 Input: N:=168; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:03:26 on modular [Seed = 2756263260] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18898 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:04:44 2003 Input: N:=168; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:04:21 on modular [Seed = 2889954591] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18906 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:05:41 2003 Input: N:=168; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:05:18 on modular [Seed = 2658338582] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18920 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:06:44 2003 Input: N:=169; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:06:40 on modular [Seed = 2255167136] ------------------------------------- Do not know how to compute component group at 13 Total time: 3.489 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:07:49 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:07:26 on modular [Seed = 2388858502] ------------------------------------- [ 170, 1 ][ 2, 1 ][ 5, 1 ][] [ 170, 2 ][ 2, 1 ][ 5, 1 ][] [ 170, 3 ][ 2, 3 ][ 5, 3 ][] [ 170, 4 ][ 2, 1 ][ 5, 1 ][] [ 170, 5 ][ 2, 21 ][ 5, 3 ][] [ 170, 6 ][ 2, 1 ][ 5, 1 ][] Total time: 22.840 seconds, Total memory usage: 4.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:08:50 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:08:27 on modular [Seed = 1972956603] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18944 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:10:14 2003 Input: N:=171; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:09:59 on modular [Seed = 2089937694] ------------------------------------- [ 171, 1 ][ 19, 1 ][] [ 171, 2 ][ 19, 1 ][] [ 171, 3 ][ 19, 1 ][] [ 171, 4 ][ 19, 1 ][] [ 171, 5 ][ 19, 3 ][] Total time: 13.799 seconds, Total memory usage: 4.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:11:44 2003 Input: N:=172; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:11:28 on modular [Seed = 1820457833] ------------------------------------- [ 172, 1 ][ 43, 1 ][] [ 172, 2 ][ 43, 1 ][] Total time: 15.729 seconds, Total memory usage: 4.28MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:12:51 2003 Input: N:=173; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:12:47 on modular [Seed = 1471856797] ------------------------------------- [ 173, 1 ][] [ 173, 2 ][ 173, 43 ][] Total time: 3.489 seconds, Total memory usage: 3.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:14:19 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:13:56 on modular [Seed = 1605552430] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 18986 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:14:49 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:14:32 on modular [Seed = 1202376986] ------------------------------------- [ 174, 1 ][ 2, 13 ][] [ 174, 2 ][ 2, 1 ][] [ 174, 3 ][ 2, 11 ][] [ 174, 4 ][ 2, 1 ][] [ 174, 5 ][ 2, 7 ][] Total time: 16.750 seconds, Total memory usage: 5.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:15:44 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:15:21 on modular [Seed = 1252514918] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19007 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:16:41 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:16:18 on modular [Seed = 1037085658] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19016 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:19:39 2003 Input: N:=177; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:19:30 on modular [Seed = 650883841] ------------------------------------- [ 177, 1 ][ 3, 1 ][] [ 177, 2 ][ 3, 5 ][] [ 177, 3 ][ 3, 31 ][] [ 177, 4 ][ 3, 229 ][] Total time: 8.689 seconds, Total memory usage: 4.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:21:36 2003 Input: N:=178; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:21:28 on modular [Seed = 385581995] ------------------------------------- [ 178, 1 ][ 2, 7 ][] [ 178, 2 ][ 2, 3 ][] [ 178, 3 ][ 2, 1 ][] [ 178, 4 ][ 2, 5 ][] Total time: 7.789 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:22:39 2003 Input: N:=179; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:22:36 on modular [Seed = 435457376] ------------------------------------- [ 179, 1 ][] [ 179, 2 ][ 179, 1 ][] [ 179, 3 ][ 179, 89 ][] Total time: 3.449 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:24:05 2003 Input: N:=180; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:23:42 on modular [Seed = 32281914] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19060 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:25:31 2003 Input: N:=181; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:25:27 on modular [Seed = 4095303734] ------------------------------------- [ 181, 1 ][] [ 181, 2 ][ 181, 15 ][] Total time: 3.449 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:26:40 2003 Input: N:=182; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:26:16 on modular [Seed = 4279397218] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19082 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:27:16 2003 Input: N:=182; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:26:53 on modular [Seed = 3876222111] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19090 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:28:01 2003 Input: N:=182; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:27:38 on modular [Seed = 4009917600] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19098 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:28:35 2003 Input: N:=182; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:28:12 on modular [Seed = 3610920190] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19106 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:29:48 2003 Input: N:=183; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:29:36 on modular [Seed = 3727904026] ------------------------------------- [ 183, 1 ][ 3, 1 ][] [ 183, 2 ][ 3, 19 ][] [ 183, 3 ][ 3, 93 ][] Total time: 11.000 seconds, Total memory usage: 4.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:31:31 2003 Input: N:=185; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:31:13 on modular [Seed = 3458423978] ------------------------------------- [ 185, 1 ][ 5, 1 ][] [ 185, 2 ][ 5, 1 ][] [ 185, 3 ][ 5, 1 ][] [ 185, 4 ][ 5, 9 ][] [ 185, 5 ][ 5, 19 ][] Total time: 17.539 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:32:53 2003 Input: N:=186; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:32:30 on modular [Seed = 2975605658] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19140 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:33:25 2003 Input: N:=186; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:33:02 on modular [Seed = 3109301170] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19148 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:34:13 2003 Input: N:=187; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:34:00 on modular [Seed = 2706125676] ------------------------------------- [ 187, 1 ][ 11, 3 ][] [ 187, 2 ][ 11, 3 ][] [ 187, 3 ][ 11, 1 ][] [ 187, 4 ][ 11, 3 ][] [ 187, 5 ][ 11, 1 ][] [ 187, 6 ][ 11, 1 ][] Total time: 12.869 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:35:23 2003 Input: N:=187; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:35:11 on modular [Seed = 2507671327] ------------------------------------- [ 187, 1 ][ 17, 1 ][] [ 187, 2 ][ 17, 1 ][] [ 187, 3 ][ 17, 1 ][] [ 187, 4 ][ 17, 1 ][] [ 187, 5 ][ 17, 1 ][] [ 187, 6 ][ 17, 1 ][] Total time: 12.239 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:37:40 2003 Input: N:=190; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:37:28 on modular [Seed = 2675052131] ------------------------------------- [ 190, 1 ][ 2, 1 ][] [ 190, 2 ][ 2, 11 ][] [ 190, 3 ][ 2, 3 ][] [ 190, 4 ][ 2, 13 ][] Total time: 11.319 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:38:31 2003 Input: N:=190; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:38:08 on modular [Seed = 2271876674] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19186 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:38:57 2003 Input: N:=190; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:38:40 on modular [Seed = 2405572138] ------------------------------------- [ 190, 1 ][ 5, 1 ][] [ 190, 2 ][ 5, 1 ][] [ 190, 3 ][ 5, 3 ][] [ 190, 4 ][ 5, 1 ][] Total time: 17.280 seconds, Total memory usage: 5.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:40:33 2003 Input: N:=191; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:40:29 on modular [Seed = 2140335926] ------------------------------------- [ 191, 1 ][] [ 191, 2 ][ 191, 95 ][] Total time: 3.459 seconds, Total memory usage: 3.70MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:42:12 2003 Input: N:=193; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:42:09 on modular [Seed = 1737160626] ------------------------------------- [ 193, 1 ][] [ 193, 2 ][ 193, 1 ][] [ 193, 3 ][ 193, 1 ][] Total time: 3.519 seconds, Total memory usage: 3.70MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:43:01 2003 Input: N:=194; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:42:45 on modular [Seed = 1870856158] ------------------------------------- [ 194, 1 ][ 2, 1 ][] [ 194, 2 ][ 2, 201 ][] [ 194, 3 ][ 2, 3479 ][] Total time: 16.149 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:44:16 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:44:00 on modular [Seed = 1354620724] ------------------------------------- [ 195, 1 ][ 3, 7 ][] [ 195, 2 ][ 3, 3 ][] [ 195, 3 ][ 3, 1 ][] [ 195, 4 ][ 3, 1 ][] [ 195, 5 ][ 3, 11 ][] Total time: 16.059 seconds, Total memory usage: 5.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:45:08 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:44:45 on modular [Seed = 1488312081] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19244 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:46:33 2003 Input: N:=197; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:46:30 on modular [Seed = 1319354780] ------------------------------------- [ 197, 1 ][] [ 197, 2 ][ 197, 1 ][] [ 197, 3 ][ 197, 49 ][] Total time: 3.529 seconds, Total memory usage: 3.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:47:31 2003 Input: N:=198; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:47:10 on modular [Seed = 920369548] ------------------------------------- [ 198, 1 ][ 2, 1 ][] [ 198, 2 ][ 2, 5 ][] [ 198, 3 ][ 2, 1 ][] [ 198, 4 ][ 2, 3 ][] [ 198, 5 ][ 2, 1 ][] Total time: 21.119 seconds, Total memory usage: 6.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:48:33 2003 Input: N:=198; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:48:10 on modular [Seed = 1054060608] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19274 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:49:41 2003 Input: N:=199; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:49:37 on modular [Seed = 667593010] ------------------------------------- [ 199, 1 ][] [ 199, 2 ][ 199, 1 ][] [ 199, 3 ][ 199, 33 ][] Total time: 3.439 seconds, Total memory usage: 3.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:51:04 2003 Input: N:=201; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:50:53 on modular [Seed = 402299342] ------------------------------------- [ 201, 1 ][ 3, 5 ][] [ 201, 2 ][ 3, 1 ][] [ 201, 3 ][ 3, 3 ][] [ 201, 4 ][ 3, 19 ][] [ 201, 5 ][ 3, 493 ][] Total time: 11.260 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:52:26 2003 Input: N:=202; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:52:18 on modular [Seed = 535990889] ------------------------------------- [ 202, 1 ][ 2, 17 ][] [ 202, 2 ][ 2, 3 ][] [ 202, 3 ][ 2, 51 ][] Total time: 8.039 seconds, Total memory usage: 4.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:53:39 2003 Input: N:=203; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:53:27 on modular [Seed = 149259579] ------------------------------------- [ 203, 1 ][ 7, 1 ][] [ 203, 2 ][ 7, 5 ][] [ 203, 3 ][ 7, 1 ][] [ 203, 4 ][ 7, 1 ][] [ 203, 5 ][ 7, 7 ][] [ 203, 6 ][ 7, 1 ][] [ 203, 7 ][ 7, 3 ][] Total time: 12.539 seconds, Total memory usage: 4.15MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:55:12 2003 Input: N:=204; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 6 2003 23:54:49 on modular [Seed = 4028464413] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19332 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:56:08 2003 Input: N:=205; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:55:57 on modular [Seed = 3859508047] ------------------------------------- [ 205, 1 ][ 5, 1 ][] [ 205, 2 ][ 5, 1 ][] [ 205, 3 ][ 5, 1 ][] [ 205, 4 ][ 5, 1 ][] [ 205, 5 ][ 5, 13 ][] [ 205, 6 ][ 5, 31 ][] [ 205, 7 ][ 5, 7 ][] Total time: 11.199 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:57:36 2003 Input: N:=206; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:57:21 on modular [Seed = 3909379500] ------------------------------------- [ 206, 1 ][ 2, 1 ][] [ 206, 2 ][ 2, 67 ][] [ 206, 3 ][ 2, 51 ][] [ 206, 4 ][ 2, 247 ][] Total time: 15.479 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 6 23:59:35 2003 Input: N:=209; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 6 2003 23:59:13 on modular [Seed = 3727905291] ------------------------------------- [ 209, 1 ][ 11, 3 ][] [ 209, 2 ][ 11, 1 ][] [ 209, 3 ][ 11, 5 ][] [ 209, 4 ][ 11, 45 ][] Total time: 20.920 seconds, Total memory usage: 4.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:01:03 2003 Input: N:=211; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 7 2003 00:01:00 on modular [Seed = 3458418102] ------------------------------------- [ 211, 1 ][ 211, 5 ][] [ 211, 2 ][ 211, 1 ][] [ 211, 3 ][ 211, 1 ][] [ 211, 4 ][ 211, 7 ][] Total time: 3.659 seconds, Total memory usage: 3.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:02:11 2003 Input: N:=213; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 7 2003 00:02:00 on modular [Seed = 2689411996] ------------------------------------- [ 213, 1 ][ 3, 1 ][] [ 213, 2 ][ 3, 1 ][] [ 213, 3 ][ 3, 3 ][] [ 213, 4 ][ 3, 45 ][] [ 213, 5 ][ 3, 1159 ][] Total time: 10.750 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:03:26 2003 Input: N:=214; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 7 2003 00:03:17 on modular [Seed = 2839814728] ------------------------------------- [ 214, 1 ][ 2, 5 ][] [ 214, 2 ][ 2, 1 ][] [ 214, 3 ][ 2, 3 ][] [ 214, 4 ][ 2, 7 ][] [ 214, 5 ][ 2, 109 ][] [ 214, 6 ][ 2, 33 ][] Total time: 8.389 seconds, Total memory usage: 4.83MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:04:48 2003 Input: N:=215; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 7 2003 00:04:28 on modular [Seed = 2440829497] ------------------------------------- [ 215, 1 ][ 5, 1 ][] [ 215, 2 ][ 5, 11 ][] [ 215, 3 ][ 5, 5 ][] [ 215, 4 ][ 5, 93 ][] Total time: 19.889 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:06:20 2003 Input: N:=217; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 7 2003 00:06:07 on modular [Seed = 2271874508] ------------------------------------- [ 217, 1 ][ 7, 1 ][] [ 217, 2 ][ 7, 19 ][] [ 217, 3 ][ 7, 1 ][] [ 217, 4 ][ 7, 31 ][] Total time: 12.669 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:07:46 2003 Input: N:=218; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 7 2003 00:07:29 on modular [Seed = 2405565802] ------------------------------------- [ 218, 1 ][ 2, 3 ][] [ 218, 2 ][ 2, 7 ][] [ 218, 3 ][ 2, 11 ][] [ 218, 4 ][ 2, 205 ][] [ 218, 5 ][ 2, 9 ][] Total time: 16.389 seconds, Total memory usage: 4.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:08:59 2003 Input: N:=219; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 7 2003 00:08:45 on modular [Seed = 1889401566] ------------------------------------- [ 219, 1 ][ 3, 5 ][] [ 219, 2 ][ 3, 1 ][] [ 219, 3 ][ 3, 3 ][] [ 219, 4 ][ 3, 17 ][] [ 219, 5 ][ 3, 1073 ][] Total time: 13.019 seconds, Total memory usage: 4.58MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 00:10:33 2003 Input: N:=220; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Dec 7 2003 00:10:10 on modular [Seed = 1619912993] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 19475 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:05:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(29,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(87,2,+1))))); CongruenceGroupAnemic(B[2],A[1],200); Output: Magma V2.10-6 Sun Dec 7 2003 02:05:16 on modular [Seed = 2106626851] ------------------------------------- Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Total time: 4.419 seconds, Total memory usage: 4.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:07:59 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(37,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(111,2,+1))))); CongruenceGroupAnemic(B[2],A[1],200); CongruenceGroupAnemic(B[2],A[2],200); Output: Magma V2.10-6 Sun Dec 7 2003 02:07:55 on modular [Seed = 1803978194] ------------------------------------- Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 Total time: 4.589 seconds, Total memory usage: 4.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:12:31 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(73,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(146,2,+1))))); for i in [11..#A] do CongruenceGroupAnemic(B[2],A[i],200); end for; Output: Magma V2.10-6 Sun Dec 7 2003 02:12:27 on modular [Seed = 1488303601] ------------------------------------- Total time: 4.189 seconds, Total memory usage: 3.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:13:03 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(73,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(146,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[2],A[i],200); end for; Output: Magma V2.10-6 Sun Dec 7 2003 02:12:58 on modular [Seed = 1085124040] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 Total time: 5.250 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:15:24 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(97,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(194,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[3],A[i],200); end for; Output: Magma V2.10-6 Sun Dec 7 2003 02:15:18 on modular [Seed = 1302372793] ------------------------------------- Abelian Group isomorphic to Z/71 Defined on 1 generator Relations: 71*$.1 = 0 Abelian Group of order 1 Total time: 5.729 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:17:14 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(71,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(213,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[i],200); end for; Output: Magma V2.10-6 Sun Dec 7 2003 02:17:08 on modular [Seed = 1003935677] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/61 Defined on 1 generator Relations: 61*$.1 = 0 Total time: 5.799 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:18:34 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(73,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(219,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[i],200); end for; Output: Magma V2.10-6 Sun Dec 7 2003 02:18:28 on modular [Seed = 567069207] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 Total time: 5.899 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:21:03 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(59,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(177,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[4],A[i],200); end for; Output: Magma V2.10-6 Sun Dec 7 2003 02:20:58 on modular [Seed = 385613246] ------------------------------------- Abelian Group isomorphic to Z/229 Defined on 1 generator Relations: 229*$.1 = 0 Total time: 5.369 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 7 02:22:24 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(155,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[4],A[i],200); end for; Output: Magma V2.10-6 Sun Dec 7 2003 02:22:19 on modular [Seed = 519304263] ------------------------------------- Abelian Group isomorphic to Z/7 + Z/7 Defined on 2 generators Relations: 7*$.1 = 0 7*$.2 = 0 Total time: 4.819 seconds, Total memory usage: 4.24MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sun Dec 7 17:11:06 2003 Input: p:=8157210416556447648087047867900686079357; A:=4591574486179589844468233571495477262868; x:=1748061421014509071233610748622789213027; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sun Dec 7 2003 17:10:55 on modular [Seed = 3544140178] ------------------------------------- [ <2, 5>, <3, 1>, <367, 1>, <6067, 1>, <27773, 1>, <31063, 1>, <65951, 1>, <113209, 1>, <788153, 1>, <7517117, 1> ] Time: 7.290 Total time: 10.269 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sun Dec 7 17:28:13 2003 Input: p:=13561688366760553057065247502881760958056321; A:=5649459778510801098156848827054419732837995; x:=2974230130986230945985316769960896102275067; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sun Dec 7 2003 17:28:01 on modular [Seed = 166043477] ------------------------------------- [ <2, 2>, <3, 1>, <7, 2>, <17, 1>, <863, 1>, <5237, 1>, <6229, 1>, <9679, 1>, <93941, 1>, <94057, 1>, <841307, 1>, <669799037, 1> ] Time: 8.750 Total time: 11.769 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sun Dec 7 17:33:56 2003 Input: p:=13561688366760553057065247502881760958056321; A:=5649459778510801098156848827054419732837995; x:=2974230130986230945985316769960896102275067; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time Order(E); Output: Magma V2.10-6 Sun Dec 7 2003 17:33:44 on modular [Seed = 469208830] ------------------------------------- 13561688366760553057065025186088706674964228 Time: 8.630 Total time: 11.709 seconds, Total memory usage: 3.94MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sun Dec 7 17:54:28 2003 Input: p:=13561688366760553057065247502881760958056321 A:=5649459778510801098156848827054419732837995; x:=2974230130986230945985316769960896102275067; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sun Dec 7 2003 17:54:25 on modular [Seed = 1939858431] ------------------------------------- >> A:=5649459778510801098156848827054419732837995; ^ User error: bad syntax >> K := GF(p); ^ User error: Identifier 'p' has not been declared or assigned >> A := K!A; ^ User error: Identifier 'K' has not been declared or assigned >> x := K!x; ^ User error: Identifier 'K' has not been declared or assigned >> b := x^3 + A*x^2 + x; ^ User error: Identifier 'A' has not been declared or assigned >> E := EllipticCurve([0,b*A,0,b^2,0]); ^ User error: Identifier 'b' has not been declared or assigned >> time FactoredOrder(E);; ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sun Dec 7 17:55:49 2003 Input: p:=13561688366760553057065247502881760958056321; A:=5649459778510801098156848827054419732837995; x:=2974230130986230945985316769960896102275067; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sun Dec 7 2003 17:55:37 on modular [Seed = 1101910405] ------------------------------------- [ <2, 2>, <3, 1>, <7, 2>, <17, 1>, <863, 1>, <5237, 1>, <6229, 1>, <9679, 1>, <93941, 1>, <94057, 1>, <841307, 1>, <669799037, 1> ] Time: 8.750 Total time: 11.789 seconds, Total memory usage: 3.70MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:26:55 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); ClassGroup(K); Units(K); Output: Magma V2.10-6 Sun Dec 7 2003 20:26:52 on modular [Seed = 66056053] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order >> Units(K);; ^ Runtime error in 'Units': Bad argument types Argument types given: FldNum Total time: 3.169 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:27:05 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); ClassGroup(K); UnitGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 20:27:01 on modular [Seed = 469235540] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Total time: 3.219 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:27:29 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); ClassGroup(K); UnitGroup(K); PrincipalUnits(K); Output: Magma V2.10-6 Sun Dec 7 2003 20:27:25 on modular [Seed = 335544132] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order >> PrincipalUnits(K);; ^ User error: Identifier 'PrincipalUnits' has not been declared or assigned Total time: 3.259 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:38:13 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); MinkowskiBound(K); ClassGroup(K); UnitGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 20:38:10 on modular [Seed = 1269277283] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 to Maximal Order of Equation Order with defining polynomial x^2 - 33 over its ground order Total time: 3.219 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:55:07 2003 Input: P := PolynomialRing(Rationals()); K := NumberField(x^2 - 33); Norm(x); Output: Magma V2.10-6 Sun Dec 7 2003 20:55:04 on modular [Seed = 3109379947] ------------------------------------- >> Norm(x);; ^ Runtime error in 'Norm': Bad argument types Argument types given: RngUPolElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:58:49 2003 Input: K := NumberField(x^2 - 33); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 20:58:46 on modular [Seed = 3025686856] ------------------------------------- >> K := NumberField(x^2 - 33); ^ User error: Identifier 'x' has not been declared or assigned >> Norm(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:59:34 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 33); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 20:59:31 on modular [Seed = 2371971492] ------------------------------------- -33 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 20:59:55 2003 Input: R := PolynomialRing(Integers()); ZI := MaximalOrder(NumberField(x^2 - 33)); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 20:59:52 on modular [Seed = 2238276023] ------------------------------------- >> ZI := MaximalOrder(NumberField(x^2 - 33)); ^ Runtime error in 'Name': Bad argument types >> Norm(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:01:11 2003 Input: R := PolynomialRing(Integers()); O := MaximalOrder(NumberField(x^2 - 33)); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 21:01:08 on modular [Seed = 4245756339] ------------------------------------- >> Norm(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:01:20 2003 Input: R := PolynomialRing(Integers()); O := MaximalOrder(NumberField(x^2 - 33)); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 21:01:17 on modular [Seed = 4112060850] ------------------------------------- >> O := MaximalOrder(NumberField(x^2 - 33)); ^ Runtime error in 'Name': Bad argument types >> Norm(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:03:42 2003 Input: R := PolynomialRing(Integers()); O := MaximalOrder(QuadraticField(-33)); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 21:03:39 on modular [Seed = 3727833615] ------------------------------------- 33 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:03:48 2003 Input: O := MaximalOrder(QuadraticField(-33)); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 21:03:45 on modular [Seed = 3594139133] ------------------------------------- 33 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:03:53 2003 Input: O := MaximalOrder(QuadraticField(33)); Norm(w); Output: Magma V2.10-6 Sun Dec 7 2003 21:03:50 on modular [Seed = 767675906] ------------------------------------- -8 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:04:09 2003 Input: O := MaximalOrder(QuadraticField(33)); Norm(w + 2); Output: Magma V2.10-6 Sun Dec 7 2003 21:04:06 on modular [Seed = 633980442] ------------------------------------- -2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:04:18 2003 Input: O := MaximalOrder(QuadraticField(33)); Norm(3 - w); Output: Magma V2.10-6 Sun Dec 7 2003 21:04:15 on modular [Seed = 1037164043] ------------------------------------- -2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:04:44 2003 Input: O := MaximalOrder(QuadraticField(33)); Norm(3 - w); (3 - w)*(2*w - 7); Output: Magma V2.10-6 Sun Dec 7 2003 21:04:41 on modular [Seed = 903468581] ------------------------------------- -2 11*w - 37 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:05:04 2003 Input: O := MaximalOrder(QuadraticField(33)); Norm(3 - w); (3 - w)*(2*w - 7); (w + 1) / (3 - w); Output: Magma V2.10-6 Sun Dec 7 2003 21:05:01 on modular [Seed = 32367205] ------------------------------------- -2 11*w - 37 -5/1*O.1 - 2/1*O.2 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:08:14 2003 Input: O := MaximalOrder(QuadraticField(33)); Norm(3 - w); (3 - w)*(-2*w - 5); Output: Magma V2.10-6 Sun Dec 7 2003 21:08:11 on modular [Seed = 402388277] ------------------------------------- -2 w + 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:15:46 2003 Input: O := MaximalOrder(QuadraticField(37)); Norm(3 - w); (3 - w)*(-2*w - 5); Output: Magma V2.10-6 Sun Dec 7 2003 21:15:43 on modular [Seed = 2106694811] ------------------------------------- -3 w + 3 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:15:54 2003 Input: O := MaximalOrder(QuadraticField(37)); Norm(3 + w); (3 - w)*(-2*w - 5); Output: Magma V2.10-6 Sun Dec 7 2003 21:15:51 on modular [Seed = 2006685321] ------------------------------------- 3 w + 3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:19:38 2003 Input: O := MaximalOrder(QuadraticField(37)); Norm(3 + w); (4 - w)*(3 + w); Output: Magma V2.10-6 Sun Dec 7 2003 21:19:35 on modular [Seed = 1085055198] ------------------------------------- 3 3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:21:38 2003 Input: O := MaximalOrder(QuadraticField(37)); Norm(3 + w); (4 - w)*(3 + w); (w + 3)*(w - 3); Output: Magma V2.10-6 Sun Dec 7 2003 21:21:35 on modular [Seed = 1354534742] ------------------------------------- 3 3 w Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:29:29 2003 Input: O := MaximalOrder(QuadraticField(37)); Norm(3 + w); (4 - w)*(3 + w); (w + 3)*(w - 3); (2*w + 5) * (4 - w); Output: Magma V2.10-6 Sun Dec 7 2003 21:29:26 on modular [Seed = 2706209934] ------------------------------------- 3 3 w w + 2 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:40:52 2003 Input: O := MaximalOrder(QuadraticField(37)); P := PolynomialRing(Rationals()); K := NumberField(x^3 - 2); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 21:40:49 on modular [Seed = 2221432604] ------------------------------------- 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 3.159 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 21:44:54 2003 Input: O := MaximalOrder(QuadraticField(37)); P := PolynomialRing(Rationals()); K := NumberField(x^3 - 2); Discriminant(K); MinkowskiBound(K); ClassGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 21:44:51 on modular [Seed = 2490912286] ------------------------------------- -108 2 Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 3.179 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sun Dec 7 21:54:17 2003 Input: p:=13561688366760553057065247502881760958056321; A:=5649459778510801098156848827054419732837995; x:=2974230130986230945985316769960896102275067; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time E; Output: Magma V2.10-6 Sun Dec 7 2003 21:54:14 on modular [Seed = 4228916227] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 12423706988491213661887873526657825680032\ 99*x^2 + 5781136271182301143530175013646684310503551*x over GF(13561688366760553057065247502881760958056321) Time: 0.000 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:04:41 2003 Input: O := MaximalOrder(CubicField(33)); Norm(3 - w); (3 - w)*(-2*w - 5); Output: Magma V2.10-6 Sun Dec 7 2003 22:04:38 on modular [Seed = 767686723] ------------------------------------- >> O := MaximalOrder(CubicField(33)); ^ User error: Identifier 'CubicField' has not been declared or assigned >> Norm(3 - w); ^ User error: Identifier 'w' has not been declared or assigned >> (3 - w)*(-2*w - 5);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:04:54 2003 Input: O := MaximalOrder(NumberField(33)); Norm(3 - w); (3 - w)*(-2*w - 5); Output: Magma V2.10-6 Sun Dec 7 2003 22:04:51 on modular [Seed = 633991262] ------------------------------------- >> O := MaximalOrder(NumberField(33)); ^ Runtime error in 'NumberField': Bad argument types Argument types given: RngIntElt >> Norm(3 - w); ^ User error: Identifier 'w' has not been declared or assigned >> (3 - w)*(-2*w - 5);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:05:27 2003 Input: w := 2^(1/3); Norm(3 - w); (3 - w)*(-2*w - 5); Output: Magma V2.10-6 Sun Dec 7 2003 22:05:24 on modular [Seed = 836625517] ------------------------------------- 1.740078950105126835232789 -13.085118945958474215263798 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:08:14 2003 Input: K := NumberField(x^3 - 2); Output: Magma V2.10-6 Sun Dec 7 2003 22:08:11 on modular [Seed = 199745336] ------------------------------------- >> K := NumberField(x^3 - 2);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:08:29 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Output: Magma V2.10-6 Sun Dec 7 2003 22:08:26 on modular [Seed = 66049793] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:08:38 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Norm(a); Output: Magma V2.10-6 Sun Dec 7 2003 22:08:35 on modular [Seed = 469225216] ------------------------------------- 2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:08:48 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Norm(a + 2); Output: Magma V2.10-6 Sun Dec 7 2003 22:08:44 on modular [Seed = 335529734] ------------------------------------- 10 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:13:42 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 2); ClassGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 22:13:39 on modular [Seed = 1703523886] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 - 2 over its ground order Total time: 3.129 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:13:52 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 3); ClassGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 22:13:49 on modular [Seed = 2106699320] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 3.149 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:13:58 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 10); ClassGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 22:13:55 on modular [Seed = 1973003822] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to Set of ideals of Maximal Equation Order with defining polynomial x^2 - 10 over its ground order Total time: 3.189 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:14:26 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 2); ClassGroup(K); Regulator(K); log(1 + sqrt(2)); Output: Magma V2.10-6 Sun Dec 7 2003 22:14:23 on modular [Seed = 1302437610] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 - 2 over its ground order 0.8813735870195430252326093249797923090281603282616568999999 >> log(1 + sqrt(2));; ^ User error: Identifier 'sqrt' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:14:41 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 2); ClassGroup(K); Regulator(K); log(1 + a); Output: Magma V2.10-6 Sun Dec 7 2003 22:14:38 on modular [Seed = 1168742131] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 - 2 over its ground order 0.8813735870195430252326093249797923090281603282616568999999 >> log(1 + a);; ^ User error: Identifier 'log' has not been declared or assigned Total time: 3.229 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:14:50 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 2); ClassGroup(K); Regulator(K); ln(1 + a); Output: Magma V2.10-6 Sun Dec 7 2003 22:14:47 on modular [Seed = 1571917522] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 - 2 over its ground order 0.8813735870195430252326093249797923090281603282616568999999 >> ln(1 + a);; ^ User error: Identifier 'ln' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:15:25 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 + 2); ClassGroup(K); Regulator(K); ln(1 + a); Output: Magma V2.10-6 Sun Dec 7 2003 22:15:22 on modular [Seed = 2839902795] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 + 2 over its ground order 1 >> ln(1 + a);; ^ User error: Identifier 'ln' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:15:40 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 + 2); ClassGroup(K); Regulator(K); Output: Magma V2.10-6 Sun Dec 7 2003 22:15:37 on modular [Seed = 2706207312] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 + 2 over its ground order 1 Total time: 3.109 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:20:50 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 + 2); ClassGroup(K); Regulator(K); FundamentalUnits(K); Output: Magma V2.10-6 Sun Dec 7 2003 22:20:46 on modular [Seed = 2371968171] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 + 2 over its ground order 1 >> FundamentalUnits(K); ^ Runtime error in 'FundamentalUnits': Bad argument types Argument types given: FldNum Total time: 3.179 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:20:58 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 + 2); ClassGroup(K); Regulator(K); UnitGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 22:20:55 on modular [Seed = 2255116217] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 + 2 over its ground order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to Maximal Equation Order with defining polynomial x^2 + 2 over its ground order Total time: 3.089 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Sun Dec 7 22:21:14 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 - 2); ClassGroup(K); Regulator(K); UnitGroup(K); Output: Magma V2.10-6 Sun Dec 7 2003 22:21:10 on modular [Seed = 2658291600] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Equation Order with defining polynomial x^2 - 2 over its ground order 0.8813735870195430252326093249797923090281603282616568999999 Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 to Maximal Equation Order with defining polynomial x^2 - 2 over its ground order Total time: 3.229 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:23:54 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:23:44 on modular [Seed = 3925996236] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 6427*y + 122197, x*y + 2*x + 6433*y + 122261, 15*x + 30*y^2 + 6420*y + 122145, y^3 + 24*y^2 + 6431*y + 122169, 45*y^2 + 765585, 6435*y + 122265, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 2, y + 2 ] Total time: 3.029 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:27:58 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:27:55 on modular [Seed = 4246136096] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 6427*y + 122197, x*y + 2*x + 6433*y + 122261, 15*x + 30*y^2 + 6420*y + 122145, y^3 + 24*y^2 + 6431*y + 122169, 45*y^2 + 765585, 6435*y + 122265, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 2, y + 2 ] Total time: 3.019 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:30:40 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:30:37 on modular [Seed = 3425164151] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 6427, x*y + 2*x + 6433*y + 6431, 45*x + 6390*y, y^3 + 24*y^2 + 6431*y + 6339, 45*y^2 + 6255, 6435 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ 1 ] Total time: 2.919 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:33:45 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:33:42 on modular [Seed = 3527001250] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 19297, x*y + 317*x + 6118*y + 19301, 495*x + 5940*y + 19305, y^3 + 24*y^2 + 6431*y + 19209, 45*y^2 + 31995, 6435*y + 19305, 32175 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 2.999 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:34:19 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(32175); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:34:16 on modular [Seed = 3660696708] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 19297, x*y + 317*x + 6118*y + 19301, 495*x + 5940*y + 19305, y^3 + 24*y^2 + 6431*y + 19209, 45*y^2 + 31995, 6435*y + 19305, 32175 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 3.029 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:43:59 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(32175); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:43:56 on modular [Seed = 836380072] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 487*y + 26662, x*y + 2*x + 493*y + 26726, 15*x + 30*y^2 + 480*y + 26610, y^3 + 24*y^2 + 491*y + 26634, 45*y^2 + 44865, 495*y + 26730, 45045 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.939 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:44:31 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(495); Factorization(45045); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:44:28 on modular [Seed = 953363649] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 487*y + 26662, x*y + 2*x + 493*y + 26726, 15*x + 30*y^2 + 480*y + 26610, y^3 + 24*y^2 + 491*y + 26634, 45*y^2 + 44865, 495*y + 26730, 45045 ] [ <3, 2>, <5, 1>, <11, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.939 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:47:20 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(495); Factorization(45045); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:47:17 on modular [Seed = 266607791] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 487*y + 26662, x*y + 2*x + 493*y + 26726, 15*x + 30*y^2 + 480*y + 26610, y^3 + 24*y^2 + 491*y + 26634, 45*y^2 + 44865, 495*y + 26730, 45045 ] [ <3, 2>, <5, 1>, <11, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.939 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:49:04 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(495); Factorization(45045); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:49:01 on modular [Seed = 385680862] ------------------------------------- [ x^2 + 23*x + y^2 + 472*y + 982, x*y + 2*x + 493*y + 986, 45*x + 450*y + 990, y^3 + 24*y^2 + 491*y + 894, 45*y^2 + 31995, 495*y + 990, 32175 ] [ <3, 2>, <5, 1>, <11, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.969 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:49:35 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(32175); Factorization(45); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:49:31 on modular [Seed = 519375920] ------------------------------------- [ x^2 + 23*x + y^2 + 472*y + 982, x*y + 2*x + 493*y + 986, 45*x + 450*y + 990, y^3 + 24*y^2 + 491*y + 894, 45*y^2 + 31995, 495*y + 990, 32175 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.989 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:50:14 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(32175); Factorization(495); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:50:11 on modular [Seed = 1870953849] ------------------------------------- [ x^2 + 23*x + y^2 + 472*y + 982, x*y + 2*x + 493*y + 986, 45*x + 450*y + 990, y^3 + 24*y^2 + 491*y + 894, 45*y^2 + 31995, 495*y + 990, 32175 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <11, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.989 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:52:14 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +1632*x^5 - 1200*x^4 + 1680*x^3 + 3000*x^2 - 162*x - 225; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(32175); Factorization(495); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:52:11 on modular [Seed = 1905943551] ------------------------------------- [ x^2 + 23*x + y^2 + 2452*y + 2467, x*y + 2*x + 2473*y + 2471, 45*x + 2430*y, y^3 + 24*y^2 + 2471*y + 2379, 45*y^2 + 2295, 2475 ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <11, 1> ] [ x + 10*y, y^2 + 7 ] [ 1 ] Total time: 3.089 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:52:37 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +1632*x^5 - 1200*x^4 + 1680*x^3 + 3000*x^2 - 162*x - 225; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(2475); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:52:34 on modular [Seed = 2039638942] ------------------------------------- [ x^2 + 23*x + y^2 + 2452*y + 2467, x*y + 2*x + 2473*y + 2471, 45*x + 2430*y, y^3 + 24*y^2 + 2471*y + 2379, 45*y^2 + 2295, 2475 ] [ <3, 2>, <5, 2>, <11, 1> ] [ x + 10*y, y^2 + 7 ] [ 1 ] Total time: 2.929 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:52:53 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +1632*x^5 - 1200*x^4 + 1680*x^3 + 3000*x^2 - 162*x - 225; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(2475); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:52:50 on modular [Seed = 1101681590] ------------------------------------- [ x^2 + 23*x + y^2 + 2452*y + 2467, x*y + 2*x + 2473*y + 2471, 45*x + 2430*y, y^3 + 24*y^2 + 2471*y + 2379, 45*y^2 + 2295, 2475 ] [ <3, 2>, <5, 2>, <11, 1> ] [ x + 10*y, y^2 + 7 ] Total time: 2.929 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:54:11 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +1632*x^5 - 1200*x^4 + 1680*x^3 + 3000*x^2 - 162*x - 225; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(2475); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:54:08 on modular [Seed = 1235376204] ------------------------------------- [ x^2 + 23*x + y^2 + 2452*y + 2467, x*y + 2*x + 2473*y + 2471, 45*x + 2430*y, y^3 + 24*y^2 + 2471*y + 2379, 45*y^2 + 2295, 2475 ] [ <3, 2>, <5, 2>, <11, 1> ] [ x + 10*y, y^2 + 7 ] Total time: 2.919 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:56:29 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 ; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(2475); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:56:26 on modular [Seed = 1605652176] ------------------------------------- [ x^2 + 23*x + y^2 + 472*y + 982, x*y + 2*x + 493*y + 986, 45*x + 450*y + 990, y^3 + 24*y^2 + 491*y + 894, 45*y^2 + 31995, 495*y + 990, 32175 ] [ <3, 2>, <5, 2>, <11, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.929 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 02:57:31 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 ; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(495); Factorization(32175); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 02:57:28 on modular [Seed = 2806822506] ------------------------------------- [ x^2 + 23*x + y^2 + 472*y + 982, x*y + 2*x + 493*y + 986, 45*x + 450*y + 990, y^3 + 24*y^2 + 491*y + 894, 45*y^2 + 31995, 495*y + 990, 32175 ] [ <3, 2>, <5, 1>, <11, 1> ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.959 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:00:06 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225) +2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 ; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(495); Factorization(45045); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:00:03 on modular [Seed = 3076302609] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 487*y + 26662, x*y + 2*x + 493*y + 26726, 15*x + 30*y^2 + 480*y + 26610, y^3 + 24*y^2 + 491*y + 26634, 45*y^2 + 44865, 495*y + 26730, 45045 ] [ <3, 2>, <5, 1>, <11, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 2.949 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:01:12 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64 -(1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(495); Factorization(45045); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:01:09 on modular [Seed = 2321652330] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 487*y + 26662, x*y + 2*x + 493*y + 26726, 15*x + 30*y^2 + 480*y + 26610, y^3 + 24*y^2 + 491*y + 26634, 45*y^2 + 44865, 495*y + 26730, 45045 ] [ <3, 2>, <5, 1>, <11, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 2, y + 2 ] Total time: 3.009 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:02:28 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(495); Factorization(45045); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:02:25 on modular [Seed = 2457443750] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 19297, x*y + 317*x + 6118*y + 19301, 495*x + 5940*y + 19305, y^3 + 24*y^2 + 6431*y + 19209, 45*y^2 + 31995, 6435*y + 19305, 32175 ] [ <3, 2>, <5, 1>, <11, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 2.999 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:03:00 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(32175); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:02:57 on modular [Seed = 2591135118] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 19297, x*y + 317*x + 6118*y + 19301, 495*x + 5940*y + 19305, y^3 + 24*y^2 + 6431*y + 19209, 45*y^2 + 31995, 6435*y + 19305, 32175 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 3.039 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:07:58 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(32175); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:07:54 on modular [Seed = 3942704532] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 6427, x*y + 2*x + 6433*y + 6431, 45*x + 6390*y, y^3 + 24*y^2 + 6431*y + 6339, 45*y^2 + 6255, 6435 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 2>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 2.949 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:08:20 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) + 73*(x-y)-81905; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:08:17 on modular [Seed = 4078501287] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 6427, x*y + 2*x + 6433*y + 6431, 45*x + 6390*y, y^3 + 24*y^2 + 6431*y + 6339, 45*y^2 + 6255, 6435 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 3.009 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:09:54 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:09:51 on modular [Seed = 4212192529] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 6427*y + 122197, x*y + 2*x + 6433*y + 122261, 15*x + 30*y^2 + 6420*y + 122145, y^3 + 24*y^2 + 6431*y + 122169, 45*y^2 + 765585, 6435*y + 122265, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 3.009 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:10:22 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:10:19 on modular [Seed = 3357787654] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 6427*y + 122197, x*y + 2*x + 6433*y + 122261, 15*x + 30*y^2 + 6420*y + 122145, y^3 + 24*y^2 + 6431*y + 122169, 45*y^2 + 765585, 6435*y + 122265, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 3.029 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:10:53 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:10:50 on modular [Seed = 3744781040] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 6427*y + 122197, x*y + 2*x + 6433*y + 122261, 15*x + 30*y^2 + 6420*y + 122145, y^3 + 24*y^2 + 6431*y + 122169, 45*y^2 + 765585, 6435*y + 122265, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 2, y + 2 ] Total time: 3.029 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:13:25 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)-2592*y^5+2160*y^4+720*y^3- 600*y^2-18*y-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:13:22 on modular [Seed = 650980256] ------------------------------------- [ x^2 + 8*x + 16*y^2 + 6427*y + 122197, x*y + 2*x + 6433*y + 122261, 15*x + 30*y^2 + 6420*y + 122145, y^3 + 24*y^2 + 6431*y + 122169, 45*y^2 + 765585, 6435*y + 122265, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 2, y + 2 ] Total time: 2.949 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:15:24 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3- 600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:15:20 on modular [Seed = 734013206] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 643496, 495*x + 5940*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 2.939 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:17:11 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:17:08 on modular [Seed = 1020735644] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 2.999 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:19:17 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:19:14 on modular [Seed = 132910113] ------------------------------------- [ x^2 + 8*x + y^2 + 203693482*y + 203693482, x*y + 2*x + 15*y^2 + 203693488*y + 203693426, 15*x + 203693475*y, 2*y^3 + 18*y^2 + 203693482*y + 203693418, 30*y^2 + 203693370, 203693490 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] Total time: 2.949 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:19:48 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(203693490); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:19:45 on modular [Seed = 266601482] ------------------------------------- [ x^2 + 8*x + y^2 + 203693482*y + 203693482, x*y + 2*x + 15*y^2 + 203693488*y + 203693426, 15*x + 203693475*y, 2*y^3 + 18*y^2 + 203693482*y + 203693418, 30*y^2 + 203693370, 203693490 ] [ <2, 1>, <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] Total time: 3.009 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:20:12 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575 -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(203693490); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:20:09 on modular [Seed = 519378179] ------------------------------------- [ x^2 + 8*x + y^2 + 203693482*y + 203693482, x*y + 2*x + 15*y^2 + 203693488*y + 203693426, 15*x + 203693475*y, 2*y^3 + 18*y^2 + 203693482*y + 203693418, 30*y^2 + 203693370, 203693490 ] [ <2, 1>, <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] Total time: 2.999 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:21:52 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(203693490); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:21:49 on modular [Seed = 1619749849] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 363738371, 15*x + 14549520*y + 363738375, y^3 + 9*y^2 + 14549531*y + 363738339, 15*y^2 + 3011753685, 14549535*y + 363738375, 3011753745 ] [ <2, 1>, <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] Total time: 2.999 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:22:37 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:22:34 on modular [Seed = 1753441158] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 363738371, 15*x + 14549520*y + 363738375, y^3 + 9*y^2 + 14549531*y + 363738339, 15*y^2 + 3011753685, 14549535*y + 363738375, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] Total time: 3.039 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:22:59 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -(2097152*y^7 - 1835008*y^6 - 1146880*y^5 + 1003520*y^4 + 132608*y^3 - 116032*y^2 - 1800*y + 1575); I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:22:56 on modular [Seed = 1889237940] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 363738371, 15*x + 14549520*y + 363738375, y^3 + 9*y^2 + 14549531*y + 363738339, 15*y^2 + 3011753685, 14549535*y + 363738375, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 2, y + 2 ] Total time: 3.019 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:24:21 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:24:18 on modular [Seed = 2039640943] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ 1 ] [ 1 ] Total time: 2.919 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:25:00 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Output: Magma V2.10-6 Mon Dec 8 2003 03:24:57 on modular [Seed = 1101679420] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] Total time: 3.019 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:26:27 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:26:24 on modular [Seed = 1455250626] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 2.949 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:28:28 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:28:25 on modular [Seed = 1504858196] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 2.929 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:29:08 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:29:05 on modular [Seed = 2706024660] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 2.929 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:30:26 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:30:23 on modular [Seed = 2958801163] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] Total time: 3.019 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:31:17 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:31:14 on modular [Seed = 3109204047] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] Total time: 2.979 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:31:39 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:31:36 on modular [Seed = 2187955022] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 2.929 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Mon Dec 8 03:32:32 2003 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Mon Dec 8 2003 03:32:28 on modular [Seed = 2321646258] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 2.979 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 8 10:53:30 2003 Input: p:=9550932766611135096816626304308249655491758024828481; A:=7815321472539189627938862782913297744781636192838638; x:=1185887644953320037767425682166312846655566052325616; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time Order(E); Output: Magma V2.10-6 Mon Dec 8 2003 10:53:08 on modular [Seed = 3942664850] ------------------------------------- 9550932766611135096816626287718325777257305201861752 Time: 18.660 Total time: 21.689 seconds, Total memory usage: 3.71MB ************** MAGMA ***************** Host roam240-67.fas.harvard.edu. (140.247.240.67) Time: Mon Dec 8 14:44:46 2003 Input: Factor(389); Output: Magma V2.10-6 Mon Dec 8 2003 14:44:43 on modular [Seed = 3324849527] ------------------------------------- >> Factor(389);; ^ Runtime error in 'Factor': Bad argument types Argument types given: RngIntElt Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam240-67.fas.harvard.edu. (140.247.240.67) Time: Mon Dec 8 14:44:58 2003 Input: Factorization(389); Output: Magma V2.10-6 Mon Dec 8 2003 14:44:55 on modular [Seed = 4262794579] ------------------------------------- [ <389, 1> ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:02:15 2003 Input: N:=220; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:01:52 on modular [Seed = 2940572248] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10424 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:03:08 2003 Input: N:=220; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:02:45 on modular [Seed = 3611159509] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10432 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:05:26 2003 Input: N:=221; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Mon Dec 8 2003 18:05:12 on modular [Seed = 3677480804] ------------------------------------- [ 221, 1 ][ 13, 1 ][] [ 221, 2 ][ 13, 3 ][] [ 221, 3 ][ 13, 1 ][] [ 221, 4 ][ 13, 1 ][] [ 221, 5 ][ 13, 1 ][] [ 221, 6 ][ 13, 1 ][] [ 221, 7 ][ 13, 9 ][] Total time: 13.949 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:06:37 2003 Input: N:=221; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Mon Dec 8 2003 18:06:14 on modular [Seed = 3458527807] ------------------------------------- [ 221, 1 ][ 17, 1 ][] [ 221, 2 ][ 17, 1 ][] [ 221, 3 ][ 17, 1 ][] [ 221, 4 ][ 17, 1 ][] [ 221, 5 ][ 17, 7 ][] [ 221, 6 ][ 17, 1 ][] [ 221, 7 ][ 17, 3 ][] Total time: 22.829 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:09:32 2003 Input: N:=222; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:09:09 on modular [Seed = 4129082740] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10465 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:10:12 2003 Input: N:=222; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:09:49 on modular [Seed = 4262774100] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10473 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:11:02 2003 Input: N:=222; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:10:39 on modular [Seed = 4010136599] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10488 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:11:54 2003 Input: N:=222; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:11:31 on modular [Seed = 402468130] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10497 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:12:29 2003 Input: N:=222; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:12:06 on modular [Seed = 536159567] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10505 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 8 18:13:06 2003 Input: N:=222; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; Include(~cg,[N,i]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 8 2003 18:12:43 on modular [Seed = 132988282] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10513 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:41:33 2003 Input: >L:=LatticeWithGram(2,[5,3,7]); >L; >GenusRepresentatives(L); >SpinorRepresentatives(L); Output: Magma V2.10-6 Mon Dec 8 2003 21:41:29 on modular [Seed = 2304999620] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [5 3] [3 7] [ Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [5 2] [2 6], Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [ 2 0] [ 0 13] ] [ Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [5 2] [2 6], Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [ 2 0] [ 0 13] ] Total time: 3.109 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:43:23 2003 Input: >L:=LatticeWithGram(2,[1,0,30]); >L; >GenusRepresentatives(L); >SpinorRepresentatives(L); Output: Magma V2.10-6 Mon Dec 8 2003 21:43:20 on modular [Seed = 2992159598] ------------------------------------- Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [ 1 0] [ 0 30] [ Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [ 1 0] [ 0 30] ] [ Standard Lattice of rank 2 and degree 2 Inner Product Matrix: [ 1 0] [ 0 30] ] Total time: 3.049 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:44:21 2003 Input: >L:=LatticeWithGram(4,[1,0,1,0,0,1,0,0,0,2]); >L; >GenusRepresentatives(L); >SpinorRepresentatives(L); Output: Magma V2.10-6 Mon Dec 8 2003 21:44:18 on modular [Seed = 3125850796] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 2] [ Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 2] ] [ Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 2] ] Total time: 3.049 seconds, Total memory usage: 2.26MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:44:39 2003 Input: >L:=LatticeWithGram(4,[1,0,1,0,0,2,0,0,0,2]); >L; >GenusRepresentatives(L); >SpinorRepresentatives(L); Output: Magma V2.10-6 Mon Dec 8 2003 21:44:36 on modular [Seed = 2722671266] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [1 0 0 0] [0 1 0 0] [0 0 2 0] [0 0 0 2] [ Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [1 0 0 0] [0 1 0 0] [0 0 2 0] [0 0 0 2] ] [ Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [1 0 0 0] [0 1 0 0] [0 0 2 0] [0 0 0 2] ] Total time: 3.059 seconds, Total memory usage: 2.26MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:45:07 2003 Input: >L:=LatticeWithGram(4,[2,1,2,0,0,2,0,0,0,2]); >L; >GenusRepresentatives(L); >SpinorRepresentatives(L); Output: Magma V2.10-6 Mon Dec 8 2003 21:45:04 on modular [Seed = 3594313458] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [2 1 0 0] [1 2 0 0] [0 0 2 0] [0 0 0 2] [ Standard Lattice of rank 4 and degree 4 Minimum: 2 Kissing number: 10 Inner Product Matrix: [2 1 0 0] [1 2 0 0] [0 0 2 0] [0 0 0 2] ] [ Standard Lattice of rank 4 and degree 4 Minimum: 2 Kissing number: 10 Inner Product Matrix: [2 0 1 0] [0 2 0 0] [1 0 2 0] [0 0 0 2] ] Total time: 3.139 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:45:35 2003 Input: >L:=LatticeWithGram(4,[2,1,2,0,0,2,0,0,0,6]); >L; >GenusRepresentatives(L); >SpinorRepresentatives(L); Output: Magma V2.10-6 Mon Dec 8 2003 21:45:32 on modular [Seed = 3728004742] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [2 1 0 0] [1 2 0 0] [0 0 2 0] [0 0 0 6] [ Standard Lattice of rank 4 and degree 4 Minimum: 2 Kissing number: 8 Inner Product Matrix: [2 1 0 0] [1 2 0 0] [0 0 2 0] [0 0 0 6] ] [ Standard Lattice of rank 4 and degree 4 Minimum: 2 Kissing number: 8 Inner Product Matrix: [2 0 1 0] [0 2 0 0] [1 0 2 0] [0 0 0 6] ] Total time: 3.079 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:46:06 2003 Input: >L:=LatticeWithGram(4,[3,1,7,0,0,2,0,0,0,6]); >L; >GenusRepresentatives(L); >SpinorRepresentatives(L); Output: Magma V2.10-6 Mon Dec 8 2003 21:46:03 on modular [Seed = 3324825273] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [3 1 0 0] [1 7 0 0] [0 0 2 0] [0 0 0 6] [ Standard Lattice of rank 4 and degree 4 Minimum: 2 Kissing number: 2 Inner Product Matrix: [2 0 0 0] [0 3 0 1] [0 0 6 0] [0 1 0 7], Standard Lattice of rank 4 and degree 4 Minimum: 1 Inner Product Matrix: [ 1 0 0 0] [ 0 4 0 0] [ 0 0 6 0] [ 0 0 0 10], Standard Lattice of rank 4 and degree 4 Minimum: 1 Inner Product Matrix: [ 1 0 0 0] [ 0 2 0 0] [ 0 0 2 0] [ 0 0 0 60], Standard Lattice of rank 4 and degree 4 Minimum: 4 Inner Product Matrix: [ 4 0 0 2] [ 0 4 2 -2] [ 0 2 5 -2] [ 2 -2 -2 6], Standard Lattice of rank 4 and degree 4 Minimum: 2 Inner Product Matrix: [ 2 0 0 0] [ 0 2 0 0] [ 0 0 4 0] [ 0 0 0 15] ] [ Standard Lattice of rank 4 and degree 4 Minimum: 2 Kissing number: 2 Inner Product Matrix: [2 0 0 0] [0 3 0 1] [0 0 6 0] [0 1 0 7], Standard Lattice of rank 4 and degree 4 Minimum: 1 Inner Product Matrix: [ 1 0 0 0] [ 0 4 0 0] [ 0 0 6 0] [ 0 0 0 10], Standard Lattice of rank 4 and degree 4 Minimum: 1 Inner Product Matrix: [ 1 0 0 0] [ 0 2 0 0] [ 0 0 2 0] [ 0 0 0 60], Standard Lattice of rank 4 and degree 4 Minimum: 4 Inner Product Matrix: [ 4 0 0 2] [ 0 4 2 -2] [ 0 2 5 -2] [ 2 -2 -2 6], Standard Lattice of rank 4 and degree 4 Minimum: 2 Inner Product Matrix: [ 2 0 0 0] [ 0 2 0 0] [ 0 0 4 0] [ 0 0 0 15] ] Total time: 3.669 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:47:07 2003 Input: >L:=LatticeWithGram(4,[3,1,7,0,0,2,0,0,0,6]); >L; >M:=GenusRepresentatives(L); >#M; >N:=SpinorRepresentatives(L); >#N; Output: Magma V2.10-6 Mon Dec 8 2003 21:47:03 on modular [Seed = 3374563706] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [3 1 0 0] [1 7 0 0] [0 0 2 0] [0 0 0 6] 5 5 Total time: 3.669 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:47:47 2003 Input: >L:=LatticeWithGram(4,[3,1,7,0,0,2,0,0,0,6]); >L; >M:=GenusRepresentatives(L); >#M; >M; >N:=SpinorRepresentatives(L); >#N; Output: Magma V2.10-6 Mon Dec 8 2003 21:47:43 on modular [Seed = 4045142314] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [3 1 0 0] [1 7 0 0] [0 0 2 0] [0 0 0 6] 5 [ Standard Lattice of rank 4 and degree 4 Minimum: 2 Kissing number: 2 Inner Product Matrix: [2 0 0 0] [0 3 0 1] [0 0 6 0] [0 1 0 7], Standard Lattice of rank 4 and degree 4 Minimum: 1 Inner Product Matrix: [ 1 0 0 0] [ 0 4 0 0] [ 0 0 6 0] [ 0 0 0 10], Standard Lattice of rank 4 and degree 4 Minimum: 1 Inner Product Matrix: [ 1 0 0 0] [ 0 2 0 0] [ 0 0 2 0] [ 0 0 0 60], Standard Lattice of rank 4 and degree 4 Minimum: 4 Inner Product Matrix: [ 4 0 0 2] [ 0 4 2 -2] [ 0 2 5 -2] [ 2 -2 -2 6], Standard Lattice of rank 4 and degree 4 Minimum: 2 Inner Product Matrix: [ 2 0 0 0] [ 0 2 0 0] [ 0 0 4 0] [ 0 0 0 15] ] 5 Total time: 3.709 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.196.32.3) Time: Mon Dec 8 21:48:48 2003 Input: >L:=LatticeWithGram(4,[3,1,7,0,0,2,0,0,0,6]); >L; >M:=GenusRepresentatives(L); >#M; > >N:=SpinorRepresentatives(L); >#N; Output: Magma V2.10-6 Mon Dec 8 2003 21:48:44 on modular [Seed = 4178837217] ------------------------------------- Standard Lattice of rank 4 and degree 4 Inner Product Matrix: [3 1 0 0] [1 7 0 0] [0 0 2 0] [0 0 0 6] 5 >> > ^ User error: bad syntax 5 Total time: 3.659 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 05:53:42 2003 Input: N:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 05:53:39 on modular [Seed = 3308213112] ------------------------------------- >> cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); ^ Runtime error in '[]': Sequence element 2 not defined Total time: 3.189 seconds, Total memory usage: 2.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 05:54:00 2003 Input: N:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 05:53:57 on modular [Seed = 3711388438] ------------------------------------- [ 11, 1, 1 ][ 11, 5, 5 ][] Total time: 3.149 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 05:57:55 2003 Input: N:=14; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 05:57:49 on modular [Seed = 3993271117] ------------------------------------- [ 14, 1, 1 ][ 2, 3, 1 ][ 7, 3, 3 ][] Total time: 6.249 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 05:59:07 2003 Input: N:=15; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 05:59:01 on modular [Seed = 3859575581] ------------------------------------- [ 15, 1, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][] Total time: 5.289 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 05:59:35 2003 Input: N:=17; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 05:59:31 on modular [Seed = 4262750947] ------------------------------------- [ 17, 1, 1 ][] Total time: 3.169 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:00:16 2003 Input: N:=19; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:00:04 on modular [Seed = 249862711] ------------------------------------- [ 19, 1, 1 ][ 19, 3, 3 ][] Total time: 3.539 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:01:07 2003 Input: N:=21; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:01:01 on modular [Seed = 536185727] ------------------------------------- [ 21, 1, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] Total time: 4.949 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:01:38 2003 Input: N:=23; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],cgo[j],tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:01:34 on modular [Seed = 734117800] ------------------------------------- [ 23, 1, 1 ][ 23, 11, 11 ][] Total time: 3.449 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:03:26 2003 Input: N:=23; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:03:22 on modular [Seed = 1152307379] ------------------------------------- [ 23, 1, 1 ][ 23, 11, 1 ][] Total time: 3.619 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:04:16 2003 Input: N:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:04:12 on modular [Seed = 1488112505] ------------------------------------- [ 11, 1, 1 ][ 11, 5, 1 ][] Total time: 3.639 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:04:45 2003 Input: N:=14; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:04:37 on modular [Seed = 1354416920] ------------------------------------- [ 14, 1, 1 ][ 2, 1, 3 ][ 7, 3, 1 ][] Total time: 6.989 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:05:48 2003 Input: N:=15; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:05:43 on modular [Seed = 1636561643] ------------------------------------- [ 15, 1, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][] Total time: 5.109 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:06:13 2003 Input: N:=17; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:06:10 on modular [Seed = 2039737046] ------------------------------------- [ 17, 1, 1 ][] Total time: 3.169 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:06:43 2003 Input: N:=19; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:06:40 on modular [Seed = 1889199037] ------------------------------------- [ 19, 1, 1 ][ 19, 3, 1 ][] Total time: 3.229 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:07:27 2003 Input: N:=21; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:07:22 on modular [Seed = 2288130927] ------------------------------------- [ 21, 1, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] Total time: 4.959 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:07:51 2003 Input: N:=23; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:07:47 on modular [Seed = 2154435214] ------------------------------------- [ 23, 1, 1 ][ 23, 11, 1 ][] Total time: 3.159 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:08:50 2003 Input: N:=26; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:08:37 on modular [Seed = 2557610659] ------------------------------------- [ 26, 1, 1 ][ 2, 1, 3 ][ 13, 3, 1 ][] [ 26, 2, 1 ][ 2, 7, 1 ][ 13, 1, 1 ][] Total time: 12.019 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:10:27 2003 Input: N:=29; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:10:24 on modular [Seed = 2839755524] ------------------------------------- [ 29, 1, 1 ][ 29, 7, 1 ][] Total time: 3.179 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.2.237.28) Time: Tue Dec 9 06:10:37 2003 Input: factor(123) Output: Magma V2.10-6 Tue Dec 9 2003 06:10:34 on modular [Seed = 2706060038] ------------------------------------- [ <3, 1>, <41, 1> ] 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.2.237.28) Time: Tue Dec 9 06:11:13 2003 Input: factor(65706677346410716693277290133297748787629461731187083886926467723500222615379581578876215678872009742417817845623) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 06:10:50 on modular [Seed = 3109235470] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 12980 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:11:15 2003 Input: N:=30; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:10:56 on modular [Seed = 3125815415] ------------------------------------- [ 30, 1, 1 ][ 2, 1, 1 ][ 3, 3, 1 ][ 5, 1, 1 ][] Total time: 18.469 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:11:48 2003 Input: N:=31; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:11:44 on modular [Seed = 3308214072] ------------------------------------- [ 31, 1, 1 ][ 31, 5, 1 ][] Total time: 3.179 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:12:25 2003 Input: N:=33; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:12:18 on modular [Seed = 3627174343] ------------------------------------- [ 33, 1, 1 ][ 3, 1, 3 ][ 11, 1, 1 ][] Total time: 6.049 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:13:00 2003 Input: N:=34; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:12:54 on modular [Seed = 4028260811] ------------------------------------- [ 34, 1, 1 ][ 2, 3, 1 ][ 17, 1, 1 ][] Total time: 5.529 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:13:42 2003 Input: N:=35; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:13:29 on modular [Seed = 32215124] ------------------------------------- [ 35, 1, 1 ][ 5, 1, 3 ][ 7, 3, 1 ][] [ 35, 2, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] Total time: 11.250 seconds, Total memory usage: 3.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:14:47 2003 Input: N:=37; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:14:42 on modular [Seed = 435390647] ------------------------------------- [ 37, 1, 1 ][] [ 37, 2, 1 ][ 37, 3, 1 ][] Total time: 3.289 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:15:33 2003 Input: N:=38; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:15:21 on modular [Seed = 768064744] ------------------------------------- [ 38, 1, 1 ][ 2, 1, 9 ][ 19, 3, 1 ][] [ 38, 2, 1 ][ 2, 5, 1 ][ 19, 1, 1 ][] Total time: 11.099 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:16:13 2003 Input: N:=39; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:16:05 on modular [Seed = 634369244] ------------------------------------- [ 39, 1, 1 ][ 3, 1, 1 ][ 13, 1, 1 ][] [ 39, 2, 1 ][ 3, 7, 1 ][ 13, 1, 1 ][] Total time: 7.090 seconds, Total memory usage: 3.54MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:16:58 2003 Input: N:=41; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:16:54 on modular [Seed = 1054125588] ------------------------------------- [ 41, 1, 1 ][ 41, 5, 1 ][] Total time: 3.179 seconds, Total memory usage: 2.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:17:40 2003 Input: N:=42; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:17:20 on modular [Seed = 920430202] ------------------------------------- [ 42, 1, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] Total time: 19.760 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:18:11 2003 Input: N:=43; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:18:08 on modular [Seed = 1319427634] ------------------------------------- [ 43, 1, 1 ][] [ 43, 2, 1 ][ 43, 7, 1 ][] Total time: 3.319 seconds, Total memory usage: 2.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:19:24 2003 Input: N:=46; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:19:17 on modular [Seed = 1084936441] ------------------------------------- [ 46, 1, 1 ][ 2, 1, 5 ][ 23, 1, 1 ][] Total time: 6.259 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:19:56 2003 Input: N:=47; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:19:53 on modular [Seed = 1488111757] ------------------------------------- [ 47, 1, 1 ][ 47, 23, 1 ][] Total time: 3.199 seconds, Total memory usage: 2.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:25:25 2003 Input: N:=51; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:25:17 on modular [Seed = 1687087733] ------------------------------------- [ 51, 1, 1 ][ 3, 3, 1 ][ 17, 1, 1 ][] [ 51, 2, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] Total time: 8.670 seconds, Total memory usage: 3.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:26:23 2003 Input: N:=53; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:26:19 on modular [Seed = 2090267179] ------------------------------------- [ 53, 1, 1 ][] [ 53, 2, 1 ][ 53, 13, 1 ][] Total time: 3.279 seconds, Total memory usage: 2.95MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:27:16 2003 Input: N:=55; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:27:08 on modular [Seed = 1973418997] ------------------------------------- [ 55, 1, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] [ 55, 2, 1 ][ 5, 1, 7 ][ 11, 1, 1 ][] Total time: 7.309 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:28:20 2003 Input: N:=57; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:28:12 on modular [Seed = 2372338509] ------------------------------------- [ 57, 1, 1 ][ 3, 1, 1 ][ 19, 1, 1 ][] [ 57, 2, 1 ][ 3, 1, 1 ][ 19, 1, 1 ][] [ 57, 3, 1 ][ 3, 5, 1 ][ 19, 1, 1 ][] Total time: 8.009 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:29:00 2003 Input: N:=58; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:28:52 on modular [Seed = 2238647165] ------------------------------------- [ 58, 1, 1 ][ 2, 1, 1 ][ 29, 1, 1 ][] [ 58, 2, 1 ][ 2, 5, 1 ][ 29, 1, 1 ][] Total time: 7.500 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:29:29 2003 Input: N:=59; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:29:25 on modular [Seed = 2641825924] ------------------------------------- [ 59, 1, 1 ][ 59, 29, 1 ][] Total time: 3.269 seconds, Total memory usage: 2.95MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:29:58 2003 Input: N:=61; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:29:55 on modular [Seed = 2508134570] ------------------------------------- [ 61, 1, 1 ][] [ 61, 2, 1 ][ 61, 5, 1 ][] Total time: 3.269 seconds, Total memory usage: 2.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:30:46 2003 Input: N:=62; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:30:33 on modular [Seed = 2756585969] ------------------------------------- [ 62, 1, 1 ][ 2, 1, 1 ][ 31, 1, 1 ][] [ 62, 2, 1 ][ 2, 1, 33 ][ 31, 3, 1 ][] Total time: 13.000 seconds, Total memory usage: 3.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:31:47 2003 Input: N:=63; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:31:44 on modular [Seed = 3176607761] ------------------------------------- Do not know how to compute component group at 3 Total time: 3.429 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:32:43 2003 Input: N:=65; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:32:30 on modular [Seed = 3042916471] ------------------------------------- [ 65, 1, 1 ][ 5, 1, 1 ][ 13, 1, 1 ][] [ 65, 2, 1 ][ 5, 1, 3 ][ 13, 3, 1 ][] [ 65, 3, 1 ][ 5, 7, 1 ][ 13, 1, 1 ][] Total time: 13.139 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:33:42 2003 Input: N:=67; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:33:39 on modular [Seed = 3441902034] ------------------------------------- [ 67, 1, 1 ][] [ 67, 2, 1 ][ 67, 1, 1 ][] [ 67, 3, 1 ][ 67, 11, 1 ][] Total time: 3.299 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:34:32 2003 Input: N:=69; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:34:23 on modular [Seed = 3308210678] ------------------------------------- [ 69, 1, 1 ][ 3, 1, 1 ][ 23, 1, 1 ][] [ 69, 2, 1 ][ 3, 1, 11 ][ 23, 1, 1 ][] Total time: 9.029 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:35:24 2003 Input: N:=70; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:35:08 on modular [Seed = 3644020153] ------------------------------------- [ 70, 1, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] Total time: 15.739 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:35:49 2003 Input: N:=71; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:35:46 on modular [Seed = 3510328655] ------------------------------------- [ 71, 1, 1 ][ 71, 5, 1 ][] [ 71, 2, 1 ][ 71, 7, 1 ][] Total time: 3.279 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:36:30 2003 Input: N:=73; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:36:26 on modular [Seed = 3925894748] ------------------------------------- [ 73, 1, 1 ][] [ 73, 2, 1 ][ 73, 1, 1 ][] [ 73, 3, 1 ][] Total time: 3.329 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:37:05 2003 Input: N:=74; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:36:50 on modular [Seed = 3792203324] ------------------------------------- [ 74, 1, 1 ][ 2, 1, 9 ][ 37, 3, 1 ][] [ 74, 2, 1 ][ 2, 95, 1 ][ 37, 1, 1 ][] Total time: 14.979 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:38:07 2003 Input: N:=75; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:38:01 on modular [Seed = 4195381743] ------------------------------------- [ 75, 1, 1 ][ 3, 1, 1 ][] [ 75, 2, 1 ][ 3, 1, 1 ][] [ 75, 3, 1 ][ 3, 5, 1 ][] Total time: 6.159 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:39:16 2003 Input: N:=77; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:39:10 on modular [Seed = 4061690272] ------------------------------------- [ 77, 1, 1 ][ 7, 1, 1 ][] [ 77, 2, 1 ][ 7, 1, 3 ][] [ 77, 3, 1 ][ 7, 3, 1 ][] [ 77, 4, 1 ][ 7, 1, 1 ][] Total time: 5.849 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:40:00 2003 Input: N:=77; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:39:44 on modular [Seed = 233277062] ------------------------------------- [ 77, 1, 1 ][ 7, 1, 1 ][ 11, 1, 1 ][] [ 77, 2, 1 ][ 7, 1, 3 ][ 11, 1, 1 ][] [ 77, 3, 1 ][ 7, 3, 1 ][ 11, 1, 3 ][] [ 77, 4, 1 ][ 7, 1, 1 ][ 11, 1, 1 ][] Total time: 15.159 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:41:15 2003 Input: N:=78; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 06:40:52 on modular [Seed = 519345617] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13333 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:42:08 2003 Input: N:=78; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 06:41:45 on modular [Seed = 369073895] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13342 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:42:38 2003 Input: N:=78; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:42:23 on modular [Seed = 768059193] ------------------------------------- [ 78, 1, 1 ][ 2, 1, 1 ][] Total time: 14.579 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:43:06 2003 Input: N:=78; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:42:51 on modular [Seed = 634367765] ------------------------------------- [ 78, 1, 1 ][ 3, 1, 5 ][] Total time: 14.679 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:44:32 2003 Input: N:=79; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:44:29 on modular [Seed = 1037547435] ------------------------------------- [ 79, 1, 1 ][] [ 79, 2, 1 ][ 79, 13, 1 ][] Total time: 3.349 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:45:51 2003 Input: N:=82; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:45:41 on modular [Seed = 1235469223] ------------------------------------- [ 82, 1, 1 ][ 2, 1, 1 ][ 41, 1, 1 ][] [ 82, 2, 1 ][ 2, 7, 1 ][ 41, 1, 1 ][] Total time: 9.609 seconds, Total memory usage: 3.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:46:17 2003 Input: N:=83; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:46:14 on modular [Seed = 1101776972] ------------------------------------- [ 83, 1, 1 ][] [ 83, 2, 1 ][ 83, 41, 1 ][] Total time: 3.329 seconds, Total memory usage: 2.98MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:47:06 2003 Input: N:=85; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:46:56 on modular [Seed = 1488114019] ------------------------------------- [ 85, 1, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] [ 85, 2, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] [ 85, 3, 1 ][ 5, 3, 1 ][ 17, 1, 1 ][] Total time: 9.409 seconds, Total memory usage: 3.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:47:46 2003 Input: N:=86; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:47:30 on modular [Seed = 1354422537] ------------------------------------- [ 86, 1, 1 ][ 2, 1, 21 ][ 43, 3, 1 ][] [ 86, 2, 1 ][ 2, 55, 1 ][ 43, 1, 1 ][] Total time: 15.769 seconds, Total memory usage: 3.58MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:48:38 2003 Input: N:=87; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:48:26 on modular [Seed = 1753407977] ------------------------------------- [ 87, 1, 1 ][ 3, 5, 1 ][ 29, 1, 1 ][] [ 87, 2, 1 ][ 3, 1, 23 ][ 29, 1, 1 ][] Total time: 11.099 seconds, Total memory usage: 3.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:49:47 2003 Input: N:=89; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:49:43 on modular [Seed = 1619716540] ------------------------------------- [ 89, 1, 1 ][] [ 89, 2, 1 ][ 89, 1, 1 ][] [ 89, 3, 1 ][ 89, 11, 1 ][] Total time: 3.409 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:50:43 2003 Input: N:=91; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:50:33 on modular [Seed = 1906047347] ------------------------------------- [ 91, 1, 1 ][ 7, 1, 1 ][ 13, 1, 1 ][] [ 91, 2, 1 ][ 7, 1, 1 ][ 13, 1, 1 ][] [ 91, 3, 1 ][ 7, 7, 1 ][ 13, 1, 1 ][] [ 91, 4, 1 ][ 7, 1, 1 ][ 13, 1, 1 ][] Total time: 10.519 seconds, Total memory usage: 3.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:51:48 2003 Input: N:=93; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:51:37 on modular [Seed = 2288124106] ------------------------------------- [ 93, 1, 1 ][ 3, 1, 1 ][ 31, 1, 1 ][] [ 93, 2, 1 ][ 3, 1, 1 ][ 31, 1, 1 ][] Total time: 10.429 seconds, Total memory usage: 3.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:52:32 2003 Input: N:=94; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:52:21 on modular [Seed = 2154432766] ------------------------------------- [ 94, 1, 1 ][ 2, 1, 1 ][ 47, 1, 1 ][] [ 94, 2, 1 ][ 2, 1, 47 ][ 47, 1, 1 ][] Total time: 10.269 seconds, Total memory usage: 3.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:53:45 2003 Input: N:=95; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:53:28 on modular [Seed = 2557612075] ------------------------------------- [ 95, 1, 1 ][ 5, 5, 1 ][ 19, 1, 1 ][] [ 95, 2, 1 ][ 5, 1, 27 ][ 19, 3, 1 ][] Total time: 16.859 seconds, Total memory usage: 3.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:54:28 2003 Input: N:=97; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:54:25 on modular [Seed = 2541559661] ------------------------------------- [ 97, 1, 1 ][] [ 97, 2, 1 ][ 97, 1, 1 ][] Total time: 3.349 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:55:23 2003 Input: N:=99; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:55:15 on modular [Seed = 2739479691] ------------------------------------- [ 99, 1, 1 ][ 11, 1, 1 ][] [ 99, 2, 1 ][ 11, 1, 1 ][] [ 99, 3, 1 ][ 11, 1, 1 ][] [ 99, 4, 1 ][ 11, 1, 1 ][] Total time: 8.399 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:57:02 2003 Input: N:=101; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:56:59 on modular [Seed = 3125820730] ------------------------------------- [ 101, 1, 1 ][] [ 101, 2, 1 ][ 101, 25, 1 ][] Total time: 3.379 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:57:52 2003 Input: N:=103; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:57:48 on modular [Seed = 2992125189] ------------------------------------- [ 103, 1, 1 ][] [ 103, 2, 1 ][ 103, 17, 1 ][] Total time: 3.239 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:58:59 2003 Input: N:=106; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:58:47 on modular [Seed = 3391114550] ------------------------------------- [ 106, 1, 1 ][ 2, 1, 1 ][ 53, 1, 1 ][] [ 106, 2, 1 ][ 2, 1, 5 ][ 53, 1, 1 ][] [ 106, 3, 1 ][ 2, 3, 1 ][ 53, 1, 1 ][] [ 106, 4, 1 ][ 2, 3, 1 ][ 53, 1, 1 ][] Total time: 11.429 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 06:59:39 2003 Input: N:=107; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 06:59:35 on modular [Seed = 3240839149] ------------------------------------- [ 107, 1, 1 ][] [ 107, 2, 1 ][ 107, 53, 1 ][] Total time: 3.329 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:04:11 2003 Input: N:=109; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:04:08 on modular [Seed = 4279597772] ------------------------------------- [ 109, 1, 1 ][] [ 109, 2, 1 ][ 109, 1, 1 ][] [ 109, 3, 1 ][ 109, 9, 1 ][] Total time: 3.349 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:04:59 2003 Input: N:=110; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:04:36 on modular [Seed = 4145902248] ------------------------------------- [ 110, 1, 1 ][ 2, 1, 7 ][ 5, 1, 1 ][ 11, 3, 1 ][] [ 110, 2, 1 ][ 2, 3, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] [ 110, 3, 1 ][ 2, 5, 1 ][ 5, 5, 1 ][ 11, 1, 1 ][] [ 110, 4, 1 ][ 2, 1, 1 ][ 5, 3, 1 ][ 11, 1, 1 ][] Total time: 22.670 seconds, Total memory usage: 3.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:05:49 2003 Input: N:=111; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:05:35 on modular [Seed = 301700244] ------------------------------------- [ 111, 1, 1 ][ 3, 1, 5 ][ 37, 1, 1 ][] [ 111, 2, 1 ][ 3, 133, 1 ][ 37, 1, 1 ][] Total time: 14.019 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:06:36 2003 Input: N:=113; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:06:32 on modular [Seed = 784641005] ------------------------------------- [ 113, 1, 1 ][] [ 113, 2, 1 ][ 113, 1, 1 ][] [ 113, 3, 1 ][ 113, 1, 1 ][] [ 113, 4, 1 ][ 113, 7, 1 ][] Total time: 3.419 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:07:37 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 07:07:14 on modular [Seed = 650945502] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13612 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:08:45 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 07:08:22 on modular [Seed = 1054128642] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13620 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:09:27 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:09:11 on modular [Seed = 920433243] ------------------------------------- [ 114, 1, 1 ][ 2, 1, 1 ][] Total time: 15.889 seconds, Total memory usage: 4.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:09:50 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:09:35 on modular [Seed = 1319422523] ------------------------------------- [ 114, 1, 1 ][ 2, 1, 1 ][] [ 114, 2, 1 ][ 2, 5, 1 ][] [ 114, 3, 1 ][ 2, 3, 1 ][] Total time: 15.209 seconds, Total memory usage: 4.03MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:10:32 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:10:15 on modular [Seed = 1504959988] ------------------------------------- [ 114, 1, 1 ][ 3, 1, 5 ][] [ 114, 2, 1 ][ 3, 1, 3 ][] [ 114, 3, 1 ][ 3, 3, 1 ][] Total time: 15.739 seconds, Total memory usage: 4.01MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:13:29 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 07:13:06 on modular [Seed = 1455215886] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13660 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:14:00 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 07:13:37 on modular [Seed = 1854205205] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13668 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:14:24 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:14:08 on modular [Seed = 1720509948] ------------------------------------- [ 114, 2, 1 ][ 2, 5, 1 ][] Total time: 15.419 seconds, Total memory usage: 4.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:19:48 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(57,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(114,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:19:43 on modular [Seed = 2423919173] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Total time: 5.759 seconds, Total memory usage: 4.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:20:50 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(57,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(114,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:20:44 on modular [Seed = 2739479221] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Total time: 5.809 seconds, Total memory usage: 4.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:28:51 2003 Input: N:=115; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:28:38 on modular [Seed = 1037548994] ------------------------------------- [ 115, 1, 1 ][ 5, 1, 5 ][ 23, 1, 1 ][] [ 115, 2, 1 ][ 5, 1, 1 ][ 23, 1, 1 ][] [ 115, 3, 1 ][ 5, 1, 1 ][ 23, 1, 1 ][] Total time: 12.669 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:29:49 2003 Input: N:=118; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:29:36 on modular [Seed = 887016205] ------------------------------------- [ 118, 1, 1 ][ 2, 1, 1 ][ 59, 1, 1 ][] [ 118, 2, 1 ][ 2, 1, 19 ][ 59, 1, 1 ][] [ 118, 3, 1 ][ 2, 5, 1 ][ 59, 1, 1 ][] [ 118, 4, 1 ][ 2, 1, 1 ][ 59, 1, 1 ][] Total time: 12.929 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:31:04 2003 Input: N:=119; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:30:43 on modular [Seed = 1169144383] ------------------------------------- [ 119, 1, 1 ][ 7, 9, 1 ][ 17, 1, 3 ][] [ 119, 2, 1 ][ 7, 1, 3 ][ 17, 1, 1 ][] Total time: 20.279 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:32:25 2003 Input: N:=119; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:32:05 on modular [Seed = 1555473296] ------------------------------------- [ 119, 1, 1 ][ 7, 9, 1 ][ 17, 1, 3 ][] [ 119, 2, 1 ][ 7, 1, 3 ][ 17, 1, 1 ][] Total time: 20.159 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:33:46 2003 Input: N:=122; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:33:26 on modular [Seed = 1472047433] ------------------------------------- [ 122, 1, 1 ][ 2, 1, 1 ][ 61, 1, 1 ][] [ 122, 2, 1 ][ 2, 1, 39 ][ 61, 3, 1 ][] [ 122, 3, 1 ][ 2, 31, 1 ][ 61, 1, 1 ][] Total time: 19.619 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:34:37 2003 Input: N:=123; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:34:21 on modular [Seed = 1871024427] ------------------------------------- [ 123, 1, 1 ][ 3, 1, 1 ][ 41, 1, 1 ][] [ 123, 2, 1 ][ 3, 5, 1 ][ 41, 1, 1 ][] [ 123, 3, 1 ][ 3, 7, 1 ][ 41, 1, 1 ][] [ 123, 4, 1 ][ 3, 1, 23 ][ 41, 1, 1 ][] Total time: 15.339 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:35:50 2003 Input: N:=127; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:35:46 on modular [Seed = 1973390302] ------------------------------------- [ 127, 1, 1 ][] [ 127, 2, 1 ][ 127, 21, 1 ][] Total time: 3.439 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:36:44 2003 Input: N:=127; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:36:41 on modular [Seed = 2355524188] ------------------------------------- [ 127, 1, 1 ][] [ 127, 2, 1 ][ 127, 21, 1 ][] Total time: 3.359 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:37:46 2003 Input: N:=129; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:37:31 on modular [Seed = 2255256452] ------------------------------------- [ 129, 1, 1 ][ 3, 1, 1 ][ 43, 1, 1 ][] [ 129, 2, 1 ][ 3, 3, 1 ][ 43, 1, 1 ][] [ 129, 3, 1 ][ 3, 1, 7 ][ 43, 1, 1 ][] [ 129, 4, 1 ][ 3, 11, 1 ][ 43, 1, 1 ][] Total time: 14.869 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:42:38 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(129,2,+1))))); for i in [1..#A] do CongruemceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:42:34 on modular [Seed = 3475321852] ------------------------------------- >> for i in [1..#A] do CongruemceGroupAnemic(A[i],B[2],200); end for; ^ User error: Identifier 'CongruemceGroupAnemic' has not been declared or assigned Total time: 4.309 seconds, Total memory usage: 3.15MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:42:40 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(129,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:42:35 on modular [Seed = 3223993586] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Total time: 5.179 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:44:44 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(129,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:44:39 on modular [Seed = 3744801633] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 4.599 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:45:41 2003 Input: N:=130; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:45:23 on modular [Seed = 3925874176] ------------------------------------- [ 130, 1, 1 ][ 2, 1, 1 ][ 5, 3, 1 ][] [ 130, 2, 1 ][ 2, 1, 1 ][ 5, 1, 5 ][] [ 130, 3, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][] Total time: 17.449 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:47:03 2003 Input: N:=130; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:46:49 on modular [Seed = 3842973397] ------------------------------------- [ 130, 1, 1 ][ 5, 3, 1 ][] [ 130, 2, 1 ][ 5, 1, 5 ][] [ 130, 3, 1 ][ 5, 1, 1 ][] Total time: 13.210 seconds, Total memory usage: 4.13MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:48:00 2003 Input: N:=130; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:47:47 on modular [Seed = 4246144647] ------------------------------------- [ 130, 1, 1 ][ 5, 3, 1 ][] [ 130, 2, 1 ][ 5, 1, 5 ][] [ 130, 3, 1 ][ 5, 1, 1 ][] Total time: 13.210 seconds, Total memory usage: 4.13MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:49:15 2003 Input: N:=131; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:49:12 on modular [Seed = 4095610677] ------------------------------------- [ 131, 1, 1 ][] [ 131, 2, 1 ][ 131, 65, 1 ][] Total time: 3.349 seconds, Total memory usage: 3.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:50:17 2003 Input: N:=132; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:49:56 on modular [Seed = 233305841] ------------------------------------- [ 132, 1, 1 ][ 3, 1, 5 ][] [ 132, 2, 1 ][ 3, 1, 1 ][] Total time: 21.430 seconds, Total memory usage: 4.48MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:51:32 2003 Input: N:=133; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:51:18 on modular [Seed = 301722462] ------------------------------------- [ 133, 1, 1 ][ 7, 1, 1 ][ 19, 1, 1 ][] [ 133, 2, 1 ][ 7, 5, 1 ][ 19, 1, 1 ][] [ 133, 3, 1 ][ 7, 3, 1 ][ 19, 1, 1 ][] [ 133, 4, 1 ][ 7, 1, 7 ][ 19, 1, 1 ][] Total time: 13.729 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:52:41 2003 Input: N:=134; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:52:20 on modular [Seed = 717279398] ------------------------------------- [ 134, 1, 1 ][ 2, 1, 75 ][ 67, 3, 1 ][] [ 134, 2, 1 ][ 2, 323, 1 ][ 67, 1, 1 ][] Total time: 20.879 seconds, Total memory usage: 3.86MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:53:11 2003 Input: N:=134; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:52:49 on modular [Seed = 583587979] ------------------------------------- [ 134, 1, 1 ][ 2, 1, 75 ][ 67, 3, 1 ][] [ 134, 2, 1 ][ 2, 323, 1 ][ 67, 1, 1 ][] Total time: 20.989 seconds, Total memory usage: 3.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:54:52 2003 Input: N:=137; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:54:49 on modular [Seed = 1003602474] ------------------------------------- [ 137, 1, 1 ][] [ 137, 2, 1 ][ 137, 17, 1 ][] Total time: 3.429 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:56:00 2003 Input: N:=138; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 07:55:37 on modular [Seed = 937283190] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14143 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:56:34 2003 Input: N:=138; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:56:14 on modular [Seed = 1336260137] ------------------------------------- [ 138, 1, 1 ][ 3, 1, 1 ][] [ 138, 2, 1 ][ 3, 3, 1 ][] [ 138, 3, 1 ][ 3, 1, 1 ][] [ 138, 4, 1 ][ 3, 11, 1 ][] Total time: 19.869 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:57:50 2003 Input: N:=139; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:57:46 on modular [Seed = 1504944283] ------------------------------------- [ 139, 1, 1 ][] [ 139, 2, 1 ][ 139, 1, 1 ][] [ 139, 3, 1 ][ 139, 23, 1 ][] Total time: 3.449 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:58:46 2003 Input: N:=140; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 07:58:23 on modular [Seed = 1371252918] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14169 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:59:19 2003 Input: N:=140; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:59:05 on modular [Seed = 1770230136] ------------------------------------- [ 140, 1, 1 ][ 5, 1, 1 ][] [ 140, 2, 1 ][ 5, 3, 1 ][] Total time: 13.939 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 07:59:47 2003 Input: N:=140; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 07:59:31 on modular [Seed = 1636538714] ------------------------------------- [ 140, 1, 1 ][ 7, 1, 5 ][] [ 140, 2, 1 ][ 7, 1, 1 ][] Total time: 16.739 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:02:47 2003 Input: N:=141; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:02:31 on modular [Seed = 2255257193] ------------------------------------- [ 141, 1, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 2, 1 ][ 3, 1, 3 ][ 47, 1, 1 ][] [ 141, 3, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 4, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 5, 1 ][ 3, 7, 1 ][ 47, 1, 1 ][] [ 141, 6, 1 ][ 3, 1, 43 ][ 47, 1, 1 ][] Total time: 16.379 seconds, Total memory usage: 3.81MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:03:55 2003 Input: N:=141; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:03:39 on modular [Seed = 2675271868] ------------------------------------- [ 141, 1, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 2, 1 ][ 3, 1, 3 ][ 47, 1, 1 ][] [ 141, 3, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 4, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 5, 1 ][ 3, 7, 1 ][ 47, 1, 1 ][] [ 141, 6, 1 ][ 3, 1, 43 ][ 47, 1, 1 ][] Total time: 16.209 seconds, Total memory usage: 3.71MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:08:23 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(47,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(141,2,+1))))); CongruenceGroupAnemic(B[5],A[1],200); Output: Magma V2.10-6 Tue Dec 9 2003 08:08:18 on modular [Seed = 2907134951] ------------------------------------- Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 4.889 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:09:38 2003 Input: N:=142; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:09:22 on modular [Seed = 2790019116] ------------------------------------- [ 142, 1, 1 ][ 2, 1, 1 ][ 71, 1, 1 ][] [ 142, 2, 1 ][ 2, 1, 3 ][ 71, 1, 1 ][] [ 142, 3, 1 ][ 2, 1, 27 ][ 71, 1, 1 ][] [ 142, 4, 1 ][ 2, 3, 1 ][ 71, 1, 1 ][] [ 142, 5, 1 ][ 2, 9, 1 ][ 71, 1, 1 ][] Total time: 15.669 seconds, Total memory usage: 3.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:15:15 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(71,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(142,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[1],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:15:09 on modular [Seed = 3493471493] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 5.189 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:17:57 2003 Input: N:=143; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 08:17:34 on modular [Seed = 3925876364] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14306 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:18:43 2003 Input: N:=143; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A-1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 08:18:20 on modular [Seed = 3792180854] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14314 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:19:24 2003 Input: N:=143; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 08:19:00 on modular [Seed = 4246145329] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14325 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:20:04 2003 Input: N:=143; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:19:46 on modular [Seed = 4112449807] ------------------------------------- [ 143, 1, 1 ][ 11, 1, 1 ][] [ 143, 2, 1 ][ 11, 7, 1 ][] [ 143, 3, 1 ][ 11, 1, 3 ][] Total time: 18.479 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:21:03 2003 Input: N:=143; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:20:54 on modular [Seed = 199358522] ------------------------------------- [ 143, 1, 1 ][ 13, 1, 1 ][] [ 143, 2, 1 ][ 13, 1, 9 ][] [ 143, 3, 1 ][ 13, 3, 1 ][] Total time: 8.939 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:23:16 2003 Input: N:=145; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:23:00 on modular [Seed = 301720226] ------------------------------------- [ 145, 1, 1 ][ 5, 1, 1 ][ 29, 1, 1 ][] [ 145, 2, 1 ][ 5, 7, 1 ][ 29, 1, 1 ][] [ 145, 3, 1 ][ 5, 1, 25 ][ 29, 1, 1 ][] [ 145, 4, 1 ][ 5, 5, 1 ][ 29, 1, 1 ][] Total time: 15.349 seconds, Total memory usage: 3.78MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:23:39 2003 Input: N:=145; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:23:23 on modular [Seed = 418573268] ------------------------------------- [ 145, 1, 1 ][ 5, 1, 1 ][ 29, 1, 1 ][] [ 145, 2, 1 ][ 5, 7, 1 ][ 29, 1, 1 ][] [ 145, 3, 1 ][ 5, 1, 25 ][ 29, 1, 1 ][] [ 145, 4, 1 ][ 5, 5, 1 ][ 29, 1, 1 ][] Total time: 15.189 seconds, Total memory usage: 3.78MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:24:47 2003 Input: N:=146; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:24:24 on modular [Seed = 784653345] ------------------------------------- [ 146, 1, 1 ][ 2, 1, 27 ][ 73, 3, 1 ][] [ 146, 2, 1 ][ 2, 703, 1 ][ 73, 1, 1 ][] Total time: 22.770 seconds, Total memory usage: 4.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:26:02 2003 Input: N:=147; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:25:52 on modular [Seed = 836485974] ------------------------------------- [ 147, 1, 1 ][ 3, 1, 1 ][] [ 147, 2, 1 ][ 3, 1, 1 ][] [ 147, 3, 1 ][ 3, 1, 1 ][] [ 147, 4, 1 ][ 3, 1, 1 ][] [ 147, 5, 1 ][ 3, 7, 1 ][] Total time: 9.010 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:27:38 2003 Input: N:=149; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:27:34 on modular [Seed = 953338617] ------------------------------------- [ 149, 1, 1 ][] [ 149, 2, 1 ][ 149, 37, 1 ][] Total time: 3.479 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:28:41 2003 Input: N:=151; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:28:37 on modular [Seed = 1472046677] ------------------------------------- [ 151, 1, 1 ][] [ 151, 2, 1 ][ 151, 1, 1 ][] [ 151, 3, 1 ][ 151, 25, 1 ][] Total time: 3.479 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:29:37 2003 Input: N:=152; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:29:23 on modular [Seed = 1605742187] ------------------------------------- [ 152, 1, 1 ][ 19, 1, 1 ][] [ 152, 2, 1 ][ 19, 1, 1 ][] [ 152, 3, 1 ][ 19, 1, 1 ][] Total time: 13.769 seconds, Total memory usage: 4.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:30:31 2003 Input: N:=153; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:30:18 on modular [Seed = 1619693837] ------------------------------------- [ 153, 1, 1 ][ 17, 1, 1 ][] [ 153, 2, 1 ][ 17, 1, 1 ][] [ 153, 3, 1 ][ 17, 1, 1 ][] [ 153, 4, 1 ][ 17, 1, 1 ][] [ 153, 5, 1 ][ 17, 1, 1 ][] Total time: 12.279 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:32:08 2003 Input: N:=155; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 08:31:45 on modular [Seed = 1989969840] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14449 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:32:56 2003 Input: N:=155; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:32:40 on modular [Seed = 2123665281] ------------------------------------- [ 155, 1, 1 ][ 5, 1, 1 ][] [ 155, 2, 1 ][ 5, 1, 1 ][] [ 155, 3, 1 ][ 5, 5, 1 ][] [ 155, 4, 1 ][ 5, 1, 147 ][] [ 155, 5, 1 ][ 5, 1, 1 ][] Total time: 15.659 seconds, Total memory usage: 3.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:34:02 2003 Input: N:=155; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A-2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 08:33:39 on modular [Seed = 2255255218] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14465 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:34:47 2003 Input: N:=155; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:34:43 on modular [Seed = 2372369913] ------------------------------------- [ 155, 1, 1 ][] [ 155, 2, 1 ][] [ 155, 3, 1 ][] [ 155, 4, 1 ][] [ 155, 5, 1 ][] Total time: 3.819 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:35:33 2003 Input: N:=155; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:35:21 on modular [Seed = 2440782095] ------------------------------------- [ 155, 1, 1 ][ 31, 1, 1 ][] [ 155, 2, 1 ][ 31, 1, 1 ][] [ 155, 3, 1 ][ 31, 1, 1 ][] [ 155, 4, 1 ][ 31, 3, 1 ][] [ 155, 5, 1 ][ 31, 1, 1 ][] Total time: 11.939 seconds, Total memory usage: 3.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:38:26 2003 Input: N:=156; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:38:05 on modular [Seed = 2806859933] ------------------------------------- [ 156, 1, 1 ][ 3, 1, 1 ][] [ 156, 2, 1 ][ 3, 3, 1 ][] Total time: 21.049 seconds, Total memory usage: 4.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:39:37 2003 Input: N:=157; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:39:31 on modular [Seed = 2940551227] ------------------------------------- [ 157, 1, 1 ][] [ 157, 2, 1 ][ 157, 13, 1 ][] Total time: 3.519 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:40:58 2003 Input: N:=158; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:40:44 on modular [Seed = 3210039396] ------------------------------------- [ 158, 1, 1 ][ 2, 1, 1 ][] [ 158, 2, 1 ][ 2, 1, 3 ][] [ 158, 3, 1 ][ 2, 5, 1 ][] [ 158, 4, 1 ][ 2, 1, 1 ][] [ 158, 5, 1 ][ 2, 1, 1 ][] [ 158, 6, 1 ][ 2, 1, 53 ][] Total time: 13.059 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:42:12 2003 Input: N:=158; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:41:57 on modular [Seed = 3324782820] ------------------------------------- [ 158, 1, 1 ][ 79, 1, 1 ][] [ 158, 2, 1 ][ 79, 3, 1 ][] [ 158, 3, 1 ][ 79, 1, 1 ][] [ 158, 4, 1 ][ 79, 1, 1 ][] [ 158, 5, 1 ][ 79, 1, 1 ][] [ 158, 6, 1 ][ 79, 1, 1 ][] Total time: 14.939 seconds, Total memory usage: 4.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:44:20 2003 Input: N:=159; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:44:00 on modular [Seed = 3441894250] ------------------------------------- [ 159, 1, 1 ][ 3, 63, 1 ][ 53, 1, 1 ][] [ 159, 2, 1 ][ 3, 1, 107 ][ 53, 1, 1 ][] Total time: 20.010 seconds, Total memory usage: 4.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:45:37 2003 Input: N:=160; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:45:25 on modular [Seed = 3510320931] ------------------------------------- [ 160, 1, 1 ][ 5, 1, 1 ][] [ 160, 2, 1 ][ 5, 1, 1 ][] [ 160, 3, 1 ][ 5, 1, 1 ][] Total time: 12.250 seconds, Total memory usage: 4.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:46:41 2003 Input: N:=161; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:46:32 on modular [Seed = 3627169255] ------------------------------------- [ 161, 1, 1 ][ 7, 1, 1 ][] [ 161, 2, 1 ][ 7, 1, 1 ][] [ 161, 3, 1 ][ 7, 1, 19 ][] [ 161, 4, 1 ][ 7, 3, 1 ][] Total time: 9.019 seconds, Total memory usage: 3.73MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:48:04 2003 Input: N:=162; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:47:51 on modular [Seed = 4010082927] ------------------------------------- [ 162, 1, 1 ][ 2, 1, 1 ][] [ 162, 2, 1 ][ 2, 1, 1 ][] [ 162, 3, 1 ][ 2, 3, 1 ][] [ 162, 4, 1 ][ 2, 3, 1 ][] Total time: 12.609 seconds, Total memory usage: 4.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:49:25 2003 Input: N:=163; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:49:21 on modular [Seed = 4145879569] ------------------------------------- [ 163, 1, 1 ][] [ 163, 2, 1 ][ 163, 1, 1 ][] [ 163, 3, 1 ][ 163, 27, 1 ][] Total time: 3.429 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:50:47 2003 Input: N:=165; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 08:50:24 on modular [Seed = 116189728] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14592 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:51:31 2003 Input: N:=165; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:51:08 on modular [Seed = 249881156] ------------------------------------- [ 165, 1, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][] [ 165, 2, 1 ][ 3, 3, 1 ][ 5, 1, 1 ][] [ 165, 3, 1 ][ 3, 5, 1 ][ 5, 5, 1 ][] Total time: 22.559 seconds, Total memory usage: 4.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:52:48 2003 Input: N:=166; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:52:29 on modular [Seed = 402520972] ------------------------------------- [ 166, 1, 1 ][ 2, 1, 1 ][ 83, 1, 1 ][] [ 166, 2, 1 ][ 2, 1, 131 ][ 83, 1, 1 ][] [ 166, 3, 1 ][ 2, 7, 1 ][ 83, 1, 1 ][] Total time: 18.569 seconds, Total memory usage: 4.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:54:32 2003 Input: N:=167; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:54:29 on modular [Seed = 485947151] ------------------------------------- [ 167, 1, 1 ][] [ 167, 2, 1 ][ 167, 83, 1 ][] Total time: 3.419 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:55:55 2003 Input: N:=172; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:55:51 on modular [Seed = 550161217] ------------------------------------- Do not know how to compute component group at 2 Total time: 4.319 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:56:28 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 08:56:05 on modular [Seed = 683852635] ------------------------------------- [ 170, 1, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][] [ 170, 2, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][] Errors: /home/mfd/gomagma: line 2: 14638 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 08:57:04 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 08:56:53 on modular [Seed = 1054135709] ------------------------------------- [ 170, 1, 1 ][ 2, 1, 1 ][] [ 170, 2, 1 ][ 2, 1, 1 ][] [ 170, 3, 1 ][ 2, 1, 3 ][] [ 170, 4, 1 ][ 2, 1, 1 ][] [ 170, 5, 1 ][ 2, 21, 1 ][] [ 170, 6, 1 ][ 2, 1, 1 ][] Total time: 11.250 seconds, Total memory usage: 4.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:02:05 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[1],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:01:59 on modular [Seed = 2006818214] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Total time: 5.959 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:05:29 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[1],300); end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:05:23 on modular [Seed = 2675275322] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Total time: 6.609 seconds, Total memory usage: 5.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:06:25 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[1],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:06:19 on modular [Seed = 2756595065] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Total time: 6.009 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:07:02 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[4],A[1],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:06:56 on modular [Seed = 2907129259] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 6.099 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:07:49 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[1],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:07:43 on modular [Seed = 3042925980] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Total time: 6.039 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:09:51 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[1],200); end for; for i in [1..#A] do Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],2)),3))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],2)),-3))); end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:09:45 on modular [Seed = 3125826069] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 [ <2, 1> ] [ <2, 2> ] [ <2, 1>, <7, 1> ] [ <2, 1> ] [ <2, 1>, <3, 1> ] [ <2, 1>, <3, 1> ] Total time: 5.979 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:12:28 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(B[5],A[1],200); end for; for i in [1..#A] do Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],2)),3))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],2)),-3))); end for; CongruenceGroupAnemic(B[5],A[3],200); Output: Magma V2.10-6 Tue Dec 9 2003 09:12:21 on modular [Seed = 3407948936] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 [ <2, 1> ] [ <2, 2> ] [ <2, 1>, <7, 1> ] [ <2, 1> ] [ <2, 1>, <3, 1> ] [ <2, 1>, <3, 1> ] Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 6.119 seconds, Total memory usage: 4.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:16:28 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#B] do CongruenceGroupAnemic(B[i],A[3],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:16:21 on modular [Seed = 3694541551] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 6.759 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:22:11 2003 Input: N:=171; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:21:57 on modular [Seed = 3909291113] ------------------------------------- [ 171, 1, 1 ][ 19, 1, 1 ][] [ 171, 2, 1 ][ 19, 1, 1 ][] [ 171, 3, 1 ][ 19, 1, 1 ][] [ 171, 4, 1 ][ 19, 1, 1 ][] [ 171, 5, 1 ][ 19, 3, 1 ][] Total time: 13.599 seconds, Total memory usage: 4.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:23:25 2003 Input: N:=172; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:23:09 on modular [Seed = 4045083706] ------------------------------------- [ 172, 1, 1 ][ 43, 1, 1 ][] [ 172, 2, 1 ][ 43, 1, 1 ][] Total time: 16.090 seconds, Total memory usage: 4.28MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:24:14 2003 Input: N:=173; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:24:10 on modular [Seed = 4178779637] ------------------------------------- [ 173, 1, 1 ][] [ 173, 2, 1 ][ 173, 43, 1 ][] Total time: 3.579 seconds, Total memory usage: 3.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:25:25 2003 Input: N:=173; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:25:21 on modular [Seed = 165932381] ------------------------------------- [ 173, 1, 1 ][] [ 173, 2, 1 ][ 173, 43, 1 ][] Total time: 3.569 seconds, Total memory usage: 3.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:26:15 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:25:58 on modular [Seed = 301725026] ------------------------------------- [ 174, 1, 1 ][ 2, 1, 13 ][] [ 174, 2, 1 ][ 2, 1, 1 ][] [ 174, 3, 1 ][ 2, 1, 11 ][] [ 174, 4, 1 ][ 2, 1, 1 ][] [ 174, 5, 1 ][ 2, 7, 1 ][] Total time: 16.859 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:26:38 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:26:21 on modular [Seed = 435420561] ------------------------------------- [ 174, 1, 1 ][ 2, 1, 13 ][] [ 174, 2, 1 ][ 2, 1, 1 ][] [ 174, 3, 1 ][ 2, 1, 11 ][] [ 174, 4, 1 ][ 2, 1, 1 ][] [ 174, 5, 1 ][ 2, 7, 1 ][] Total time: 16.709 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:28:50 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 09:28:27 on modular [Seed = 600424493] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14886 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:30:18 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 09:29:55 on modular [Seed = 734120013] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14894 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:31:14 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 09:30:51 on modular [Seed = 1003608229] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14910 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:32:08 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..4] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 09:31:45 on modular [Seed = 1118347670] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 14919 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:34:02 2003 Input: N:=177; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:33:53 on modular [Seed = 1438627585] ------------------------------------- [ 177, 1, 1 ][ 3, 1, 1 ][] [ 177, 2, 1 ][ 3, 5, 1 ][] [ 177, 3, 1 ][ 3, 31, 1 ][] [ 177, 4, 1 ][ 3, 1, 229 ][] Total time: 8.989 seconds, Total memory usage: 4.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:35:25 2003 Input: N:=177; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:35:16 on modular [Seed = 1504951288] ------------------------------------- [ 177, 1, 1 ][ 3, 1, 1 ][] [ 177, 2, 1 ][ 3, 5, 1 ][] [ 177, 3, 1 ][ 3, 31, 1 ][] [ 177, 4, 1 ][ 3, 1, 229 ][] Total time: 9.039 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:36:56 2003 Input: N:=178; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:36:48 on modular [Seed = 1669956198] ------------------------------------- [ 178, 1, 1 ][ 2, 1, 7 ][] [ 178, 2, 1 ][ 2, 3, 1 ][] [ 178, 3, 1 ][ 2, 1, 1 ][] [ 178, 4, 1 ][ 2, 5, 1 ][] Total time: 7.949 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:37:56 2003 Input: N:=179; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:37:52 on modular [Seed = 1803651630] ------------------------------------- [ 179, 1, 1 ][] [ 179, 2, 1 ][ 179, 1, 1 ][] [ 179, 3, 1 ][ 179, 89, 1 ][] Total time: 3.579 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:38:43 2003 Input: N:=181; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:38:39 on modular [Seed = 1939444249] ------------------------------------- [ 181, 1, 1 ][] [ 181, 2, 1 ][ 181, 15, 1 ][] Total time: 3.509 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:39:40 2003 Input: N:=183; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:39:29 on modular [Seed = 2073139935] ------------------------------------- [ 183, 1, 1 ][ 3, 1, 1 ][] [ 183, 2, 1 ][ 3, 1, 19 ][] [ 183, 3, 1 ][ 3, 93, 1 ][] Total time: 11.170 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:41:01 2003 Input: N:=185; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:40:43 on modular [Seed = 2338417253] ------------------------------------- [ 185, 1, 1 ][ 5, 1, 1 ][] [ 185, 2, 1 ][ 5, 1, 1 ][] [ 185, 3, 1 ][ 5, 1, 1 ][] [ 185, 4, 1 ][ 5, 1, 9 ][] [ 185, 5, 1 ][ 5, 19, 1 ][] Total time: 17.680 seconds, Total memory usage: 4.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:42:23 2003 Input: N:=185; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:42:09 on modular [Seed = 2457367254] ------------------------------------- [ 185, 1, 1 ][ 37, 1, 1 ][] [ 185, 2, 1 ][ 37, 1, 1 ][] [ 185, 3, 1 ][ 37, 1, 1 ][] [ 185, 4, 1 ][ 37, 3, 1 ][] [ 185, 5, 1 ][ 37, 1, 1 ][] Total time: 13.929 seconds, Total memory usage: 4.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:43:22 2003 Input: N:=185; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:43:08 on modular [Seed = 2773435868] ------------------------------------- [ 185, 1, 1 ][ 37, 1, 1 ][] [ 185, 2, 1 ][ 37, 1, 1 ][] [ 185, 3, 1 ][ 37, 1, 1 ][] [ 185, 4, 1 ][ 37, 3, 1 ][] [ 185, 5, 1 ][ 37, 1, 1 ][] Total time: 13.819 seconds, Total memory usage: 4.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:46:59 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:46:42 on modular [Seed = 2873193724] ------------------------------------- [ 170, 3, 1 ][ 5, 3, 1 ][] Total time: 16.579 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:51:44 2003 Input: N:=187; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:51:22 on modular [Seed = 3341621672] ------------------------------------- [ 187, 1, 1 ][ 11, 1, 3 ][ 17, 1, 1 ][] [ 187, 2, 1 ][ 11, 3, 1 ][ 17, 1, 1 ][] [ 187, 3, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] [ 187, 4, 1 ][ 11, 3, 1 ][ 17, 1, 1 ][] [ 187, 5, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] [ 187, 6, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] Total time: 21.539 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:53:17 2003 Input: N:=190; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 09:52:54 on modular [Seed = 3374520074] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15052 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 9 09:53:43 2003 Input: N:=190; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 09:53:31 on modular [Seed = 3510308664] ------------------------------------- [ 190, 1, 1 ][ 2, 1, 1 ][] [ 190, 2, 1 ][ 2, 11, 1 ][] [ 190, 3, 1 ][ 2, 3, 1 ][] [ 190, 4, 1 ][ 2, 1, 13 ][] Total time: 11.389 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:11:41 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],10); end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:11:36 on modular [Seed = 165924901] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 5.279 seconds, Total memory usage: 3.33MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:13:29 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],10); end for; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],2)),3))); Output: Magma V2.10-6 Tue Dec 9 2003 10:13:24 on modular [Seed = 519358350] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 [ <2, 1>, <7, 1> ] Total time: 5.299 seconds, Total memory usage: 3.32MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:14:27 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],100); end for; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],2)),3))); Output: Magma V2.10-6 Tue Dec 9 2003 10:14:21 on modular [Seed = 650969071] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 [ <2, 1>, <7, 1> ] Total time: 5.659 seconds, Total memory usage: 3.53MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:14:41 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(170,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],2)),3))); Output: Magma V2.10-6 Tue Dec 9 2003 10:14:35 on modular [Seed = 784660465] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 [ <2, 1>, <7, 1> ] Total time: 6.249 seconds, Total memory usage: 4.48MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:18:18 2003 Input: N:=191; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:18:14 on modular [Seed = 953344138] ------------------------------------- [ 191, 1, 1 ][] [ 191, 2, 1 ][] Total time: 3.199 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:18:43 2003 Input: N:=191; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:18:40 on modular [Seed = 1118345878] ------------------------------------- [ 191, 1, 1 ][] [ 191, 2, 1 ][ 191, 95, 1 ][] Total time: 3.559 seconds, Total memory usage: 3.70MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:19:28 2003 Input: N:=193; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:19:24 on modular [Seed = 1252037298] ------------------------------------- [ 193, 1, 1 ][] [ 193, 2, 1 ][ 193, 1, 1 ][] [ 193, 3, 1 ][ 193, 1, 1 ][] Total time: 3.479 seconds, Total memory usage: 3.71MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:20:25 2003 Input: N:=194; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:20:09 on modular [Seed = 1521519991] ------------------------------------- [ 194, 1, 1 ][ 2, 1, 1 ][] [ 194, 2, 1 ][ 2, 1, 201 ][] [ 194, 3, 1 ][ 2, 3479, 1 ][] Total time: 15.809 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:21:14 2003 Input: N:=194; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:20:55 on modular [Seed = 1653126449] ------------------------------------- [ 194, 1, 1 ][ 97, 1, 1 ][] [ 194, 2, 1 ][ 97, 3, 1 ][] [ 194, 3, 1 ][ 97, 1, 1 ][] Total time: 18.590 seconds, Total memory usage: 4.52MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:25:54 2003 Input: N:=161; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:25:35 on modular [Seed = 1889183259] ------------------------------------- [ 161, 1, 1 ][ 23, 1, 1 ][] [ 161, 2, 1 ][ 23, 1, 1 ][] [ 161, 3, 1 ][ 23, 1, 1 ][] [ 161, 4, 1 ][ 23, 1, 3 ][] Total time: 18.819 seconds, Total memory usage: 3.86MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:30:56 2003 Input: N:=163; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:30:53 on modular [Seed = 2187876139] ------------------------------------- [ 163, 1, 1 ][] [ 163, 2, 1 ][ 163, 1, 1 ][] [ 163, 3, 1 ][ 163, 27, 1 ][] Total time: 3.429 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:31:29 2003 Input: N:=183; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:31:13 on modular [Seed = 2321571663] ------------------------------------- [ 183, 1, 1 ][ 61, 1, 1 ][] [ 183, 2, 1 ][ 61, 1, 1 ][] [ 183, 3, 1 ][ 61, 1, 1 ][] Total time: 15.609 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:33:36 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 10:33:13 on modular [Seed = 2557627557] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15260 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:35:34 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:35:17 on modular [Seed = 2907142428] ------------------------------------- [ 195, 1, 1 ][ 3, 1, 7 ][] [ 195, 2, 1 ][ 3, 3, 1 ][] [ 195, 3, 1 ][ 3, 1, 1 ][] [ 195, 4, 1 ][ 3, 1, 1 ][] [ 195, 5, 1 ][ 3, 1, 11 ][] Total time: 15.889 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:36:24 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 10:36:00 on modular [Seed = 3042926928] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15281 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:37:19 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:36:56 on modular [Seed = 3193204130] ------------------------------------- [ 195, 2, 1 ][ 5, 1, 7 ][] Total time: 22.619 seconds, Total memory usage: 5.06MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:39:27 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 10:39:04 on modular [Seed = 3324777818] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15298 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:40:26 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 10:40:02 on modular [Seed = 3577677315] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15313 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:43:48 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(65,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(195,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:43:41 on modular [Seed = 3727953015] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Total time: 6.269 seconds, Total memory usage: 4.47MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:44:58 2003 Input: N:=197; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:44:55 on modular [Seed = 3876402452] ------------------------------------- [ 197, 1, 1 ][] [ 197, 2, 1 ][ 197, 1, 1 ][] [ 197, 3, 1 ][ 197, 49, 1 ][] Total time: 3.509 seconds, Total memory usage: 3.82MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:45:51 2003 Input: N:=198; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:45:30 on modular [Seed = 3942726389] ------------------------------------- [ 198, 1, 1 ][ 2, 1, 1 ][] [ 198, 2, 1 ][ 2, 1, 5 ][] [ 198, 3, 1 ][ 2, 1, 1 ][] [ 198, 4, 1 ][ 2, 3, 1 ][] [ 198, 5, 1 ][ 2, 1, 1 ][] Total time: 20.969 seconds, Total memory usage: 6.02MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:47:07 2003 Input: N:=198; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 10:46:44 on modular [Seed = 4229311900] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15352 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:47:51 2003 Input: N:=198; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 10:47:28 on modular [Seed = 65655440] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15360 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:48:28 2003 Input: N:=198; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 10:48:05 on modular [Seed = 182508476] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15369 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:51:44 2003 Input: N:=199; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:51:40 on modular [Seed = 435407254] ------------------------------------- [ 199, 1, 1 ][] [ 199, 2, 1 ][ 199, 1, 1 ][] [ 199, 3, 1 ][ 199, 33, 1 ][] Total time: 3.569 seconds, Total memory usage: 3.76MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:53:05 2003 Input: N:=201; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:52:54 on modular [Seed = 567013876] ------------------------------------- [ 201, 1, 1 ][ 3, 1, 5 ][] [ 201, 2, 1 ][ 3, 1, 1 ][] [ 201, 3, 1 ][ 3, 3, 1 ][] [ 201, 4, 1 ][ 3, 1, 19 ][] [ 201, 5, 1 ][ 3, 493, 1 ][] Total time: 11.170 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:54:12 2003 Input: N:=201; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:53:55 on modular [Seed = 683861816] ------------------------------------- [ 201, 1, 1 ][ 67, 1, 1 ][] [ 201, 2, 1 ][ 67, 1, 1 ][] [ 201, 3, 1 ][ 67, 1, 1 ][] [ 201, 4, 1 ][ 67, 1, 1 ][] [ 201, 5, 1 ][ 67, 1, 1 ][] Total time: 17.489 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:55:58 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(201,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],10); end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:55:53 on modular [Seed = 887028670] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Total time: 4.479 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:58:06 2003 Input: N:=202; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:57:58 on modular [Seed = 1118342215] ------------------------------------- [ 202, 1, 1 ][ 2, 1, 17 ][] [ 202, 2, 1 ][ 2, 1, 3 ][] [ 202, 3, 1 ][ 2, 51, 1 ][] Total time: 8.209 seconds, Total memory usage: 4.64MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:58:59 2003 Input: N:=202; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:58:38 on modular [Seed = 1252033639] ------------------------------------- [ 202, 1, 1 ][ 101, 1, 1 ][] [ 202, 2, 1 ][ 101, 1, 1 ][] [ 202, 3, 1 ][ 101, 1, 1 ][] Total time: 19.069 seconds, Total memory usage: 4.66MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 10:59:48 2003 Input: N:=202; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 10:59:29 on modular [Seed = 1387830320] ------------------------------------- [ 202, 1, 1 ][ 101, 1, 1 ][] [ 202, 2, 1 ][ 101, 1, 1 ][] [ 202, 3, 1 ][ 101, 1, 1 ][] Total time: 18.969 seconds, Total memory usage: 4.66MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:01:06 2003 Input: N:=203; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:00:53 on modular [Seed = 1653124308] ------------------------------------- [ 203, 1, 1 ][ 7, 1, 1 ][] [ 203, 2, 1 ][ 7, 5, 1 ][] [ 203, 3, 1 ][ 7, 1, 1 ][] [ 203, 4, 1 ][ 7, 1, 1 ][] [ 203, 5, 1 ][ 7, 1, 7 ][] [ 203, 6, 1 ][ 7, 1, 1 ][] [ 203, 7, 1 ][ 7, 3, 1 ][] Total time: 12.500 seconds, Total memory usage: 4.15MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:02:25 2003 Input: N:=203; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:02:02 on modular [Seed = 2140516742] ------------------------------------- [ 203, 1, 1 ][ 29, 1, 1 ][] [ 203, 2, 1 ][ 29, 1, 1 ][] [ 203, 3, 1 ][ 29, 1, 1 ][] [ 203, 4, 1 ][ 29, 1, 1 ][] [ 203, 5, 1 ][ 29, 1, 1 ][] [ 203, 6, 1 ][ 29, 1, 1 ][] [ 203, 7, 1 ][ 29, 1, 3 ][] Total time: 22.629 seconds, Total memory usage: 4.16MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:17:22 2003 Input: N:=205; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:17:11 on modular [Seed = 2641843993] ------------------------------------- [ 205, 1, 1 ][ 5, 1, 1 ][] [ 205, 2, 1 ][ 5, 1, 1 ][] [ 205, 3, 1 ][ 5, 1, 1 ][] [ 205, 4, 1 ][ 5, 1, 1 ][] [ 205, 5, 1 ][ 5, 13, 1 ][] [ 205, 6, 1 ][ 5, 1, 31 ][] [ 205, 7, 1 ][ 5, 7, 1 ][] Total time: 11.279 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:18:55 2003 Input: N:=206; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:18:38 on modular [Seed = 2856345719] ------------------------------------- [ 206, 1, 1 ][ 2, 1, 1 ][] [ 206, 2, 1 ][ 2, 1, 67 ][] [ 206, 3, 1 ][ 2, 1, 51 ][] [ 206, 4, 1 ][ 2, 247, 1 ][] Total time: 15.519 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:20:03 2003 Input: N:=206; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:19:42 on modular [Seed = 2992143279] ------------------------------------- [ 206, 1, 1 ][ 103, 1, 1 ][] [ 206, 2, 1 ][ 103, 1, 1 ][] [ 206, 3, 1 ][ 103, 3, 1 ][] [ 206, 4, 1 ][ 103, 1, 1 ][] Total time: 20.340 seconds, Total memory usage: 4.78MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:21:34 2003 Input: N:=205; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:21:18 on modular [Seed = 3257404351] ------------------------------------- [ 205, 1, 1 ][ 41, 1, 1 ][] [ 205, 2, 1 ][ 41, 1, 1 ][] [ 205, 3, 1 ][ 41, 1, 1 ][] [ 205, 4, 1 ][ 41, 1, 1 ][] [ 205, 5, 1 ][ 41, 1, 1 ][] [ 205, 6, 1 ][ 41, 1, 1 ][] [ 205, 7, 1 ][ 41, 1, 1 ][] Total time: 15.659 seconds, Total memory usage: 4.28MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:24:53 2003 Input: N:=209; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:24:32 on modular [Seed = 3357671563] ------------------------------------- [ 209, 1, 1 ][ 11, 3, 1 ][] [ 209, 2, 1 ][ 11, 1, 1 ][] [ 209, 3, 1 ][ 11, 5, 1 ][] [ 209, 4, 1 ][ 11, 1, 45 ][] Total time: 20.969 seconds, Total memory usage: 4.18MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:25:27 2003 Input: N:=209; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:25:13 on modular [Seed = 3560840382] ------------------------------------- [ 209, 1, 1 ][ 19, 1, 1 ][] [ 209, 2, 1 ][ 19, 1, 1 ][] [ 209, 3, 1 ][ 19, 1, 5 ][] [ 209, 4, 1 ][ 19, 3, 1 ][] Total time: 13.300 seconds, Total memory usage: 4.16MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:27:29 2003 Input: N:=211; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:27:25 on modular [Seed = 3792185868] ------------------------------------- [ 211, 1, 1 ][ 211, 5, 1 ][] [ 211, 2, 1 ][ 211, 1, 1 ][] [ 211, 3, 1 ][ 211, 1, 1 ][] [ 211, 4, 1 ][ 211, 7, 1 ][] Total time: 3.599 seconds, Total memory usage: 3.90MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:28:45 2003 Input: N:=213; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:28:35 on modular [Seed = 3909299929] ------------------------------------- [ 213, 1, 1 ][ 3, 1, 1 ][] [ 213, 2, 1 ][ 3, 1, 1 ][] [ 213, 3, 1 ][ 3, 3, 1 ][] [ 213, 4, 1 ][ 3, 45, 1 ][] [ 213, 5, 1 ][ 3, 1, 1159 ][] Total time: 10.239 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:30:15 2003 Input: N:=214; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:30:07 on modular [Seed = 4195368310] ------------------------------------- [ 214, 1, 1 ][ 2, 1, 5 ][] [ 214, 2, 1 ][ 2, 1, 1 ][] [ 214, 3, 1 ][ 2, 3, 1 ][] [ 214, 4, 1 ][ 2, 7, 1 ][] [ 214, 5, 1 ][ 2, 1, 109 ][] [ 214, 6, 1 ][ 2, 33, 1 ][] Total time: 8.279 seconds, Total memory usage: 4.83MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:33:44 2003 Input: N:=213; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:33:23 on modular [Seed = 1185710103] ------------------------------------- [ 213, 1, 1 ][ 71, 1, 1 ][] [ 213, 2, 1 ][ 71, 1, 1 ][] [ 213, 3, 1 ][ 71, 1, 1 ][] [ 213, 4, 1 ][ 71, 1, 1 ][] [ 213, 5, 1 ][ 71, 1, 1 ][] Total time: 20.469 seconds, Total memory usage: 4.55MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:36:43 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(107,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(214,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:36:37 on modular [Seed = 2423936391] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 5.919 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:38:33 2003 Input: N:=215; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:38:13 on modular [Seed = 2958718407] ------------------------------------- [ 215, 1, 1 ][ 5, 1, 1 ][] [ 215, 2, 1 ][ 5, 11, 1 ][] [ 215, 3, 1 ][ 5, 5, 1 ][] [ 215, 4, 1 ][ 5, 1, 93 ][] Total time: 20.319 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:39:35 2003 Input: N:=215; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:39:17 on modular [Seed = 3092413711] ------------------------------------- [ 215, 1, 1 ][ 43, 1, 1 ][] [ 215, 2, 1 ][ 43, 1, 1 ][] [ 215, 3, 1 ][ 43, 1, 1 ][] [ 215, 4, 1 ][ 43, 3, 1 ][] Total time: 17.709 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:42:01 2003 Input: N:=214; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:41:39 on modular [Seed = 3374517640] ------------------------------------- [ 214, 1, 1 ][ 107, 1, 1 ][] [ 214, 2, 1 ][ 107, 1, 1 ][] [ 214, 3, 1 ][ 107, 1, 1 ][] [ 214, 4, 1 ][ 107, 1, 1 ][] [ 214, 5, 1 ][ 107, 1, 1 ][] [ 214, 6, 1 ][ 107, 1, 1 ][] Total time: 21.389 seconds, Total memory usage: 4.94MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:44:09 2003 Input: N:=217; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:43:57 on modular [Seed = 3660586517] ------------------------------------- [ 217, 1, 1 ][ 7, 1, 1 ][] [ 217, 2, 1 ][ 7, 19, 1 ][] [ 217, 3, 1 ][ 7, 1, 1 ][] [ 217, 4, 1 ][ 7, 1, 31 ][] Total time: 12.479 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:44:46 2003 Input: N:=217; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:44:31 on modular [Seed = 3792184847] ------------------------------------- [ 217, 1, 1 ][ 31, 1, 1 ][] [ 217, 2, 1 ][ 31, 1, 1 ][] [ 217, 3, 1 ][ 31, 1, 1 ][] [ 217, 4, 1 ][ 31, 1, 1 ][] Total time: 14.769 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:46:06 2003 Input: N:=218; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:45:50 on modular [Seed = 4010093779] ------------------------------------- [ 218, 1, 1 ][ 2, 3, 1 ][] [ 218, 2, 1 ][ 2, 1, 7 ][] [ 218, 3, 1 ][ 2, 11, 1 ][] [ 218, 4, 1 ][ 2, 205, 1 ][] [ 218, 5, 1 ][ 2, 1, 9 ][] Total time: 16.020 seconds, Total memory usage: 4.88MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:46:53 2003 Input: N:=218; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:46:32 on modular [Seed = 4145886365] ------------------------------------- [ 218, 1, 1 ][ 109, 1, 1 ][] [ 218, 2, 1 ][ 109, 1, 1 ][] [ 218, 3, 1 ][ 109, 1, 1 ][] [ 218, 4, 1 ][ 109, 1, 1 ][] [ 218, 5, 1 ][ 109, 3, 1 ][] Total time: 20.649 seconds, Total memory usage: 4.94MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:48:30 2003 Input: N:=219; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:48:16 on modular [Seed = 4229316398] ------------------------------------- [ 219, 1, 1 ][ 3, 1, 5 ][] [ 219, 2, 1 ][ 3, 1, 1 ][] [ 219, 3, 1 ][ 3, 3, 1 ][] [ 219, 4, 1 ][ 3, 1, 17 ][] [ 219, 5, 1 ][ 3, 1073, 1 ][] Total time: 13.079 seconds, Total memory usage: 4.58MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:49:18 2003 Input: N:=219; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:48:59 on modular [Seed = 116180476] ------------------------------------- [ 219, 1, 1 ][ 73, 1, 1 ][] [ 219, 2, 1 ][ 73, 1, 1 ][] [ 219, 3, 1 ][ 73, 1, 1 ][] [ 219, 4, 1 ][ 73, 1, 1 ][] [ 219, 5, 1 ][ 73, 1, 1 ][] Total time: 19.280 seconds, Total memory usage: 4.59MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:51:21 2003 Input: N:=78; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:51:05 on modular [Seed = 435411809] ------------------------------------- [ 78, 1, 1 ][ 13, 1, 1 ][] Total time: 16.479 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:52:12 2003 Input: N:=78; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:51:58 on modular [Seed = 634382218] ------------------------------------- [ 78, 1, 1 ][ 2, 1, 1 ][] Total time: 13.839 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:54:10 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 11:53:47 on modular [Seed = 768076855] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15916 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:55:59 2003 Input: N:=130; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:55:43 on modular [Seed = 953350582] ------------------------------------- [ 130, 1, 1 ][ 13, 1, 1 ][] [ 130, 2, 1 ][ 13, 1, 1 ][] [ 130, 3, 1 ][ 13, 1, 1 ][] Total time: 16.319 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:56:22 2003 Input: N:=130; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 11:56:13 on modular [Seed = 1084916204] ------------------------------------- [ 130, 1, 1 ][ 2, 1, 1 ][] [ 130, 2, 1 ][ 2, 1, 1 ][] [ 130, 3, 1 ][ 2, 1, 1 ][] Total time: 8.800 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:58:14 2003 Input: N:=132; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 11:57:51 on modular [Seed = 1252035140] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15947 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:58:45 2003 Input: N:=132; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 11:58:22 on modular [Seed = 1387827837] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15955 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 11:59:51 2003 Input: N:=132; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 11:59:28 on modular [Seed = 1521523243] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15963 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:01:13 2003 Input: N:=156; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:00:50 on modular [Seed = 1820765359] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 15981 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:02:50 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:02:34 on modular [Seed = 2304816802] ------------------------------------- [ 170, 1, 1 ][ 5, 1, 1 ][] Total time: 16.500 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:03:45 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:03:28 on modular [Seed = 2440605424] ------------------------------------- [ 170, 2, 1 ][ 5, 1, 1 ][] Total time: 16.510 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:04:41 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..4] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:04:24 on modular [Seed = 2557585153] ------------------------------------- [ 170, 4, 1 ][ 5, 1, 1 ][] Total time: 16.659 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:05:09 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [5..5] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:04:52 on modular [Seed = 2689179413] ------------------------------------- [ 170, 5, 1 ][ 5, 1, 3 ][] Total time: 16.699 seconds, Total memory usage: 4.85MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:06:19 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [6..6] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:06:02 on modular [Seed = 2890240855] ------------------------------------- [ 170, 6, 1 ][ 5, 1, 1 ][] Total time: 16.659 seconds, Total memory usage: 4.85MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:07:03 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:06:52 on modular [Seed = 3059714203] ------------------------------------- [ 170, 1, 1 ][ 2, 1, 1 ][] Total time: 11.239 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:07:39 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:07:16 on modular [Seed = 3193405691] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16063 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:08:55 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:08:31 on modular [Seed = 3325032520] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16071 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:09:26 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:09:03 on modular [Seed = 3458723936] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16079 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:10:32 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:10:14 on modular [Seed = 3728203817] ------------------------------------- [ 174, 1, 1 ][ 2, 1, 13 ][] [ 174, 2, 1 ][ 2, 1, 1 ][] Total time: 17.250 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:11:16 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..2] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:10:53 on modular [Seed = 3859799034] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16103 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:11:50 2003 Input: N:=174; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:11:27 on modular [Seed = 3993490384] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16111 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:12:47 2003 Input: N:=178; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:12:30 on modular [Seed = 4178625670] ------------------------------------- [ 178, 1, 1 ][ 89, 1, 1 ][] [ 178, 2, 1 ][ 89, 1, 1 ][] [ 178, 3, 1 ][ 89, 1, 1 ][] [ 178, 4, 1 ][ 89, 1, 1 ][] Total time: 17.409 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:14:08 2003 Input: N:=177; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:13:51 on modular [Seed = 31997134] ------------------------------------- [ 177, 1, 1 ][ 59, 1, 1 ][] [ 177, 2, 1 ][ 59, 1, 1 ][] [ 177, 3, 1 ][ 59, 1, 1 ][] [ 177, 4, 1 ][ 59, 1, 1 ][] Total time: 16.709 seconds, Total memory usage: 4.13MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:15:54 2003 Input: N:=183; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:15:38 on modular [Seed = 233058615] ------------------------------------- [ 183, 1, 1 ][ 61, 1, 1 ][] [ 183, 2, 1 ][ 61, 1, 1 ][] [ 183, 3, 1 ][ 61, 1, 1 ][] Total time: 16.420 seconds, Total memory usage: 4.11MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:17:33 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:17:10 on modular [Seed = 402533249] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16151 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:18:30 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:18:07 on modular [Seed = 536224720] ------------------------------------- [ 195, 3, 1 ][ 5, 1, 1 ][] Total time: 22.799 seconds, Total memory usage: 5.06MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:19:02 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 9 2003 12:18:39 on modular [Seed = 700454342] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16169 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 12:21:31 2003 Input: N:=201; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 9 2003 12:21:14 on modular [Seed = 953222066] ------------------------------------- [ 201, 1, 1 ][ 67, 1, 1 ][] [ 201, 2, 1 ][ 67, 1, 1 ][] [ 201, 3, 1 ][ 67, 1, 1 ][] [ 201, 4, 1 ][ 67, 1, 1 ][] [ 201, 5, 1 ][ 67, 1, 1 ][] Total time: 17.590 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:38:07 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(62,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Tue Dec 9 2003 13:38:02 on modular [Seed = 4195603312] ------------------------------------- Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Total time: 4.219 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:39:07 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(23,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(69,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Tue Dec 9 2003 13:39:02 on modular [Seed = 2039500992] ------------------------------------- Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Total time: 4.329 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:41:50 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(86,2,+1))))); CongruenceGroupAnemic(A[1],B[1],200); Output: Magma V2.10-6 Tue Dec 9 2003 13:41:45 on modular [Seed = 1720667760] ------------------------------------- Abelian Group of order 1 Total time: 4.520 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:42:43 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(86,2,+1))))); CongruenceGroupAnemic(A[2],B[1],200); Output: Magma V2.10-6 Tue Dec 9 2003 13:42:38 on modular [Seed = 1572107708] ------------------------------------- Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 4.529 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:43:42 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(29,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(87,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Tue Dec 9 2003 13:43:38 on modular [Seed = 1421704433] ------------------------------------- Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Total time: 4.389 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:45:05 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(52,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(106,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[1],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:45:00 on modular [Seed = 1218539291] ------------------------------------- Abelian Group of order 1 Total time: 4.959 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:45:55 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(53,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(106,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[1],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:45:51 on modular [Seed = 1084843872] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Total time: 4.719 seconds, Total memory usage: 4.25MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:47:04 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(53,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(106,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:46:59 on modular [Seed = 920588778] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 4.859 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:49:31 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(61,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(122,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:49:24 on modular [Seed = 3425036935] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Total time: 6.029 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:50:07 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(41,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(123,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:50:02 on modular [Seed = 3176438680] ------------------------------------- Abelian Group isomorphic to Z/46 Defined on 1 generator Relations: 46*$.1 = 0 Total time: 4.810 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:51:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(19,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(133,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:51:34 on modular [Seed = 3026031229] ------------------------------------- Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 4.539 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:52:26 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(134,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[1],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:52:21 on modular [Seed = 2839580467] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 5.209 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:53:41 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(47,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(141,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[6],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:53:34 on modular [Seed = 2705884400] ------------------------------------- Abelian Group isomorphic to Z/43 Defined on 1 generator Relations: 43*$.1 = 0 Total time: 5.689 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:55:18 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(155,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:55:12 on modular [Seed = 2507976826] ------------------------------------- Abelian Group isomorphic to Z/7 + Z/7 Defined on 2 generators Relations: 7*$.1 = 0 7*$.2 = 0 Total time: 5.849 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:56:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(79,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(158,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[6],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:56:15 on modular [Seed = 2338500155] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/53 Defined on 1 generator Relations: 53*$.1 = 0 Total time: 5.769 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:57:00 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(53,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(159,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:56:54 on modular [Seed = 2188093195] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/107 Defined on 1 generator Relations: 107*$.1 = 0 Total time: 5.639 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:58:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(83,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(166,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:57:53 on modular [Seed = 2073190196] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/131 Defined on 1 generator Relations: 131*$.1 = 0 Total time: 5.770 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:59:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(59,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(177,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:58:55 on modular [Seed = 1889096801] ------------------------------------- Abelian Group isomorphic to Z/229 Defined on 1 generator Relations: 229*$.1 = 0 Total time: 5.269 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 13:59:41 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(61,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(183,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 13:59:36 on modular [Seed = 1770016143] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Total time: 5.529 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:00:33 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(97,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(194,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 14:00:27 on modular [Seed = 1488026861] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/67 Defined on 1 generator Relations: 67*$.1 = 0 Total time: 6.289 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:01:56 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(201,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 14:01:49 on modular [Seed = 1020600159] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Total time: 6.629 seconds, Total memory usage: 4.42MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:02:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(101,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(202,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[1],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 14:02:32 on modular [Seed = 903616003] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Total time: 6.579 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:03:19 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(41,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(205,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[6],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 14:03:13 on modular [Seed = 767823394] ------------------------------------- Abelian Group isomorphic to Z/62 Defined on 1 generator Relations: 62*$.1 = 0 Total time: 6.069 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:04:08 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(103,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(206,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 14:04:00 on modular [Seed = 634128123] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/67 Defined on 1 generator Relations: 67*$.1 = 0 Total time: 6.959 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:05:02 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(71,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(213,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; Output: Magma V2.10-6 Tue Dec 9 2003 14:04:54 on modular [Seed = 452147634] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/61 Defined on 1 generator Relations: 61*$.1 = 0 Total time: 7.009 seconds, Total memory usage: 4.42MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:06:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(71,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(213,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; 19*61; Output: Magma V2.10-6 Tue Dec 9 2003 14:06:06 on modular [Seed = 250031214] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/61 Defined on 1 generator Relations: 61*$.1 = 0 1159 Total time: 6.879 seconds, Total memory usage: 4.42MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:07:26 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(107,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(214,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; 19*61; Output: Magma V2.10-6 Tue Dec 9 2003 14:07:18 on modular [Seed = 82650652] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/109 Defined on 1 generator Relations: 109*$.1 = 0 1159 Total time: 7.159 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Tue Dec 9 14:08:18 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(215,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; 19*61; Output: Magma V2.10-6 Tue Dec 9 2003 14:08:12 on modular [Seed = 4229291550] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 1159 Total time: 6.199 seconds, Total memory usage: 4.43MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 14:54:07 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Norm(a + a + 1); Output: Magma V2.10-6 Tue Dec 9 2003 14:54:03 on modular [Seed = 1636333127] ------------------------------------- 17 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 14:54:18 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Norm(a^2 + a + 1); Output: Magma V2.10-6 Tue Dec 9 2003 14:54:15 on modular [Seed = 1504726595] ------------------------------------- 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 15:37:03 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 + 2); Norm(a^2 + a + 1); Regulator(K); Output: Magma V2.10-6 Tue Dec 9 2003 15:37:00 on modular [Seed = 2624950669] ------------------------------------- 3 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 15:37:28 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 + 3); Norm(a^2 + a + 1); Regulator(K); Output: Magma V2.10-6 Tue Dec 9 2003 15:37:25 on modular [Seed = 2491259244] ------------------------------------- 7 1 Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 15:37:35 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^2 + 93); Norm(a^2 + a + 1); Regulator(K); Output: Magma V2.10-6 Tue Dec 9 2003 15:37:32 on modular [Seed = 2355462525] ------------------------------------- 8557 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 15:43:21 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Norm(a^2 + a + 1); Regulator(K); (r*a^2 + s*a + t)^2; Output: Magma V2.10-6 Tue Dec 9 2003 15:43:15 on modular [Seed = 2022798567] ------------------------------------- 1 1.34737734832938410091818789144565304628306227332299999999977 >> (r*a^2 + s*a + t)^2;; ^ User error: Identifier 'r' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 24-193-146-215.nyc.rr.com. (24.193.146.215) Time: Tue Dec 9 16:32:05 2003 Input: 5476456546546456546*657567567657567 Output: Magma V2.10-6 Tue Dec 9 2003 16:32:02 on modular [Seed = 2756551818] ------------------------------------- 3601140210694912785367357373583582 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 16:43:46 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Norm(a^2 + a + 1); Regulator(K); Output: Magma V2.10-6 Tue Dec 9 2003 16:43:43 on modular [Seed = 2204827376] ------------------------------------- 1 1.34737734832938410091818789144565304628306227332299999999977 Total time: 3.109 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 4n33.math.upenn.edu. (130.91.49.169) Time: Tue Dec 9 16:44:55 2003 Input: R := PolynomialRing(Integers()); K := NumberField(x^3 - 2); Norm(a^2 + a + 1); Regulator(K); Discriminant(K); Output: Magma V2.10-6 Tue Dec 9 2003 16:44:51 on modular [Seed = 1871057479] ------------------------------------- 1 1.34737734832938410091818789144565304628306227332299999999977 -108 Total time: 3.119 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host dsl-200-67-218-93.prod-infinitum.com.mx. (200.67.218.93) Time: Wed Dec 10 00:00:49 2003 Input: Pi Output: Magma V2.10-6 Wed Dec 10 2003 00:00:46 on modular [Seed = 1302649413] ------------------------------------- Intrinsic 'Pi' Signatures: ( R) -> FldReElt ( R) -> FldReElt ( R) -> FldPrElt Create pi to the precision of R as a real number. ( R, p) -> FldPrElt Create pi to the precision p as an element of R. Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Wed Dec 10 17:02:08 2003 Input: p:=5214992488521222360623470091045256749679250526710700189; A:=3759792043339524693131140911259246976098727081053401537; x:=2716279087309208417592093077887621077438621627474359414; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time Order(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 10 2003 17:01:45 on modular [Seed = 3374408043] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21666 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Wed Dec 10 17:10:05 2003 Input: p:=5214992488521222360623470091045256749679250526710700189; A:=3759792043339524693131140911259246976098727081053401537; x:=2716279087309208417592093077887621077438621627474359414; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time Order(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 10 2003 17:09:42 on modular [Seed = 3694426641] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21687 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ppp-225-66-245.friaco.access.uk.tiscali.com. (80.225.66.245) Time: Wed Dec 10 23:55:08 2003 Input: 7+9 Output: Magma V2.10-6 Wed Dec 10 2003 23:55:05 on modular [Seed = 1354274718] ------------------------------------- 16 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 12-211-91-0.client.attbi.com. (12.211.91.0) Time: Thu Dec 11 02:03:31 2003 Input: 2^100 Output: Magma V2.10-6 Thu Dec 11 2003 02:03:28 on modular [Seed = 1454473200] ------------------------------------- 1267650600228229401496703205376 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 12-211-91-0.client.attbi.com. (12.211.91.0) Time: Thu Dec 11 02:03:52 2003 Input: 10 mod 2 Output: Magma V2.10-6 Thu Dec 11 2003 02:03:49 on modular [Seed = 1589213165] ------------------------------------- 0 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 12-211-91-0.client.attbi.com. (12.211.91.0) Time: Thu Dec 11 02:04:08 2003 Input: 10 mod 4 Output: Magma V2.10-6 Thu Dec 11 2003 02:04:05 on modular [Seed = 650186661] ------------------------------------- 2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 12-211-91-0.client.attbi.com. (12.211.91.0) Time: Thu Dec 11 02:05:31 2003 Input: 3805315313^2 mod 13639711499 Output: Magma V2.10-6 Thu Dec 11 2003 02:05:28 on modular [Seed = 718078580] ------------------------------------- 11415450632 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 12-211-91-0.client.attbi.com. (12.211.91.0) Time: Thu Dec 11 02:08:44 2003 Input: 3172612029^2 mod 13639711499 Output: Magma V2.10-6 Thu Dec 11 2003 02:08:41 on modular [Seed = 869538732] ------------------------------------- 2836452919 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 12-211-91-0.client.attbi.com. (12.211.91.0) Time: Thu Dec 11 02:09:33 2003 Input: 4650507231^2 mod 13639711499 Output: Magma V2.10-6 Thu Dec 11 2003 02:09:30 on modular [Seed = 1004280951] ------------------------------------- 3172612029 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:17:24 2003 Input: c_4_1_4 := RepetitionCode(GF(2),4); Output: Magma V2.10-6 Thu Dec 11 2003 11:17:19 on modular [Seed = 2722432365] ------------------------------------- Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:18:16 2003 Input: c_4_1_4 := RepetitionCode(GF(2),4); c_6_1_6 := RepetitionCode(GF(2),6); c_4_3_2 := Dual( c_4_1_4 ); c_8_4_4 := PlotkinSum( c_4_3_2 , c_4_1_4 ); c_7_4_3 := PunctureCode( c_8_4_4 , 8 ); c_6_3_3 := ShortenCode( c_7_4_3 , 7 ); c_12_4_6 := PlotkinSum( c_6_3_3 , c_6_1_6 ); c_12_4_6; Output: Magma V2.10-6 Thu Dec 11 2003 11:18:13 on modular [Seed = 1488977859] ------------------------------------- [12, 4, 6] Linear Code over GF(2) Generator matrix: [1 0 0 1 1 0 0 1 1 0 0 1] [0 1 0 1 0 1 0 1 0 1 0 1] [0 0 1 1 1 1 0 0 1 1 1 1] [0 0 0 0 0 0 1 1 1 1 1 1] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:21:27 2003 Input: C := BCHCode(GF(2), 18, 8); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:21:24 on modular [Seed = 2124011684] ------------------------------------- >> C := BCHCode(GF(2), 18, 8); ^ Runtime error in 'BCHCode': Order of argument 1 (2) and argument 2 (18) are not coprime >> C;; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:21:46 2003 Input: C := BCHCode(GF(2), 17, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:21:43 on modular [Seed = 2005979582] ------------------------------------- [17, 1, 17] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:22:01 2003 Input: C := BCHCode(GF(2), 15, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:21:58 on modular [Seed = 1871235479] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:23:01 2003 Input: C := BCHCode(GF(2), 13, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:22:58 on modular [Seed = 1686356696] ------------------------------------- [13, 1, 13] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 1 1 1 1 1 1 1 1 1 1 1 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:23:11 2003 Input: C := BCHCode(GF(2), 15, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:23:08 on modular [Seed = 486259374] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:31:13 2003 Input: C := BCHCode(GF(2), 15, 5); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:31:10 on modular [Seed = 4111618405] ------------------------------------- [15, 7, 5] BCH code (d = 5, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 0 0 1 0 0 0 1 0 1 1] [0 1 0 0 0 0 0 1 1 0 0 1 1 1 0] [0 0 1 0 0 0 0 0 1 1 0 0 1 1 1] [0 0 0 1 0 0 0 1 0 1 1 1 0 0 0] [0 0 0 0 1 0 0 0 1 0 1 1 1 0 0] [0 0 0 0 0 1 0 0 0 1 0 1 1 1 0] [0 0 0 0 0 0 1 0 0 0 1 0 1 1 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:31:29 2003 Input: C := BCHCode(GF(2), 15, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:31:26 on modular [Seed = 3976874349] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:32:30 2003 Input: C := BCHCode(GF(2), 15, 7); C2 := LengthenCode(C); C3 := ExtendCode(C2, 2); Output: Magma V2.10-6 Thu Dec 11 2003 11:32:27 on modular [Seed = 2608609502] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:32:40 2003 Input: C := BCHCode(GF(2), 15, 7); C2 := LengthenCode(C); Output: Magma V2.10-6 Thu Dec 11 2003 11:32:37 on modular [Seed = 2473865448] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:32:47 2003 Input: C := BCHCode(GF(2), 15, 7); C2 := LengthenCode(C); C2; Output: Magma V2.10-6 Thu Dec 11 2003 11:32:44 on modular [Seed = 2339121401] ------------------------------------- [16, 5, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:33:19 2003 Input: C := BCHCode(GF(2), 15, 7); C2 := ExtendCode(C, 3); C2; Output: Magma V2.10-6 Thu Dec 11 2003 11:33:16 on modular [Seed = 2154242962] ------------------------------------- [18, 5, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:33:44 2003 Input: C := BCHCode(GF(2), 23, 7); C2 := ExtendCode(C, 3); C2; Output: Magma V2.10-6 Thu Dec 11 2003 11:33:41 on modular [Seed = 3109952130] ------------------------------------- [26, 1, 24] Linear Code over GF(2) Generator matrix: [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:33:54 2003 Input: C := BCHCode(GF(2), 23, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:33:51 on modular [Seed = 2975208064] ------------------------------------- [23, 1, 23] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:34:06 2003 Input: C := BCHCode(GF(2), 31, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:34:02 on modular [Seed = 1572535930] ------------------------------------- [31, 16, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1] Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:43:40 2003 Input: C := GolayCode(GF(2), false); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:43:37 on modular [Seed = 2040453277] ------------------------------------- [23, 12, 7] Unextended Golay Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:45:10 2003 Input: C := GolayCode(GF(2), false); C1 := PunctureCode(C, 23); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:45:07 on modular [Seed = 1837813027] ------------------------------------- [22, 12, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:46:00 2003 Input: C := GolayCode(GF(2), false); C1 := PunctureCode(C, 23); C2 := PunctureCode(C1, 22); C3 := PunctureCode(C2, 21); C4 := PunctureCode(C3, 20); C5 := PunctureCode(C4, 19); C5; Output: Magma V2.10-6 Thu Dec 11 2003 11:45:56 on modular [Seed = 1686357117] ------------------------------------- [18, 12, 3] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:47:16 2003 Input: C = BCHCode(GF(2), 15, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:47:13 on modular [Seed = 486259920] ------------------------------------- >> C = BCHCode(GF(2), 15, 7); ^ User error: Identifier 'C' has not been declared or assigned >> C;; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:47:41 2003 Input: C := BCHCode(GF(2), 15, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 11:47:38 on modular [Seed = 351515875] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:49:01 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 17, 7, 2); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:48:58 on modular [Seed = 250195625] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [17, 1, 17] BCH code (d = 7, b = 2) over GF(2) Generator matrix: [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] Total time: 2.959 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:51:09 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 17, 7, 15); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:51:06 on modular [Seed = 734835724] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [17, 0, 17] BCH code (d = 7, b = 15) over GF(2) Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:51:30 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 7, 3); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:51:27 on modular [Seed = 3661448456] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [21, 4, 9] BCH code (d = 7, b = 3) over GF(2) Generator matrix: [1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0] [0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1] [0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1] [0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:52:00 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 23, 7, 89); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:51:57 on modular [Seed = 3526708514] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [23, 0, 23] BCH code (d = 7, b = 20) over GF(2) Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:52:10 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 23, 7, 3); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:52:07 on modular [Seed = 3391968544] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [23, 1, 23] BCH code (d = 7, b = 3) over GF(2) Generator matrix: [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:52:20 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 7, 3); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:52:17 on modular [Seed = 3257228638] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [21, 4, 9] BCH code (d = 7, b = 3) over GF(2) Generator matrix: [1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0] [0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1] [0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1] [0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:52:31 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C1; Output: Magma V2.10-6 Thu Dec 11 2003 11:52:28 on modular [Seed = 4196230507] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [21, 6, 7] BCH code (d = 5, b = 3) over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:54:30 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C2 := PunctureCode(C1, 21); C3 := PunctureCode(C2, 20); C4 := PunctureCode(C3, 19); C4; Output: Magma V2.10-6 Thu Dec 11 2003 11:54:26 on modular [Seed = 3858856185] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [18, 6, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:57:24 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C2 := PunctureCode(C1, 21); C3 := PunctureCode(C2, 20); C4 := PunctureCode(C3, 19); C4; v := [0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0]; b, d := Decode(C4, v); b; d; Output: Magma V2.10-6 Thu Dec 11 2003 11:57:21 on modular [Seed = 2540702011] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [18, 6, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1] >> v := [0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0]; ^ User error: bad syntax >> b, d := Decode(C4, v); ^ User error: Identifier 'v' has not been declared or assigned >> b; ^ User error: Identifier 'b' has not been declared or assigned >> d;; ^ User error: Identifier 'd' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:57:49 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C2 := PunctureCode(C1, 21); C3 := PunctureCode(C2, 20); C4 := PunctureCode(C3, 19); C4; v := [0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0]; Output: Magma V2.10-6 Thu Dec 11 2003 11:57:46 on modular [Seed = 2389251033] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [18, 6, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1] >> v := [0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0]; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:58:26 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C2 := PunctureCode(C1, 21); C3 := PunctureCode(C2, 20); C4 := PunctureCode(C3, 19); C4; v := [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; b,d := Decode(C4, v); b; d; Output: Magma V2.10-6 Thu Dec 11 2003 11:58:23 on modular [Seed = 2170952947] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [18, 6, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1] >> b,d := Decode(C4, v); ^ Runtime error in 'Decode': Bad argument types Argument types given: Code, SeqEnum[RngIntElt] >> b; ^ User error: Identifier 'b' has not been declared or assigned >> d; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 11:59:08 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C2 := PunctureCode(C1, 21); C3 := PunctureCode(C2, 20); C4 := PunctureCode(C3, 19); C4; v := [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; v; Output: Magma V2.10-6 Thu Dec 11 2003 11:59:05 on modular [Seed = 3109954749] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [18, 6, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1] [ 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 12:00:01 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C2 := PunctureCode(C1, 21); C3 := PunctureCode(C2, 20); C4 := PunctureCode(C3, 19); C4; v := [0,0,0,1,1,1]; b,d := encode(C4, v); Output: Magma V2.10-6 Thu Dec 11 2003 11:59:58 on modular [Seed = 2975214690] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [18, 6, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1] >> b,d := encode(C4, v);; ^ User error: Identifier 'encode' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 12:00:11 2003 Input: C := BCHCode(GF(2), 15, 7); C; C1 := BCHCode(GF(2), 21, 5, 3); C2 := PunctureCode(C1, 21); C3 := PunctureCode(C2, 20); C4 := PunctureCode(C3, 19); C4; v := [0,0,0,1,1,1]; b,d := Encode(C4, v); Output: Magma V2.10-6 Thu Dec 11 2003 12:00:08 on modular [Seed = 2689023333] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] [18, 6, 6] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0] [0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1] [0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0] [0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0] [0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1] [0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1] >> b,d := Encode(C4, v);; ^ User error: Identifier 'Encode' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 11 12:08:02 2003 Input: C := BCHCode(GF(2), 15, 7); C; Output: Magma V2.10-6 Thu Dec 11 2003 12:07:59 on modular [Seed = 2090592079] ------------------------------------- [15, 5, 7] BCH code (d = 7, b = 1) over GF(2) Generator matrix: [1 0 0 0 0 1 1 1 0 1 1 0 0 1 0] [0 1 0 0 0 0 1 1 1 0 1 1 0 0 1] [0 0 1 0 0 1 1 0 1 0 1 1 1 1 0] [0 0 0 1 0 0 1 1 0 1 0 1 1 1 1] [0 0 0 0 1 1 1 0 1 1 0 0 1 0 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ABesancon-103-1-2-62.w81-48.abo.wanadoo.fr. (81.48.130.62) Time: Thu Dec 11 15:53:19 2003 Input: 424 Output: Magma V2.10-6 Thu Dec 11 2003 15:53:16 on modular [Seed = 1303030568] ------------------------------------- 424 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 211pc.wohnheimb.uni-frankfurt.de. (141.2.119.30) Time: Thu Dec 11 17:57:51 2003 Input: 2+3 Output: Magma V2.10-6 Thu Dec 11 2003 17:57:48 on modular [Seed = 2405975739] ------------------------------------- 5 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-203-33-160-115.NSW.netspace.net.au. (203.33.160.115) Time: Thu Dec 11 22:09:55 2003 Input: 1 Output: Magma V2.10-6 Thu Dec 11 2003 22:09:49 on modular [Seed = 3728265462] ------------------------------------- 1 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host AC8DD6CF.ipt.aol.com. (172.141.214.207) Time: Fri Dec 12 02:49:14 2003 Input: D=q-8(q^2)+28(q^3)-64(q^4)+126(q^5)-224(q^6) Output: Magma V2.10-6 Fri Dec 12 2003 02:49:11 on modular [Seed = 2372649000] ------------------------------------- >> D=q-8(q^2)+28(q^3)-64(q^4)+126(q^5)-224(q^6) ^ User error: Identifier 'q' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host AC8DD6CF.ipt.aol.com. (172.141.214.207) Time: Fri Dec 12 03:09:12 2003 Input: x-8(x^2)=a a^3 Output: Magma V2.10-6 Fri Dec 12 2003 03:09:09 on modular [Seed = 1787568799] ------------------------------------- >> a^3; ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host AC8DD6CF.ipt.aol.com. (172.141.214.207) Time: Fri Dec 12 03:09:32 2003 Input: x-8(x^2)=a; a^3 Output: Magma V2.10-6 Fri Dec 12 2003 03:09:29 on modular [Seed = 318003963] ------------------------------------- >> x-8(x^2)=a; ^ User error: Identifier 'a' has not been declared or assigned >> a^3; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.253.124.19) Time: Fri Dec 12 04:18:19 2003 Input: /* * An implementation of a search for a non-skewed NFS polynomial, based * on Brian Murphy's thesis. * * By Contini - May, 2000. * * Please report bugs, improvements, and suggestions to * contini@maths.usyd.edu.au */ /* * A polynomial for n can be reconstructed from its degree d and its * value of m1 (assuming m2 = 1). This function does that. */ function m1ToPoly( n, m1, d ) rem := n; coeffs := []; for i := d to 0 by -1 do temp := m1^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; m1div2 := m1 div 2; /* adjust the coefficients to be between -m1div2 and m1div2 */ for i := d+1 to 2 by -1 do if coeffs[i] gt m1div2 then coeffs[i] -:= m1; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(), 2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; return F; end function; /* * Compute cont_p (defined in section 3.2.1 of Murphy's thesis) of * homogeneous polynomial F corresponding to univariate polynomial f * for the prime p . The following input values are required: * - disc should be the discriminant of f . * - bound is the size of the sample space to look through in * order to estimate cont_p for the case of p dividing disc . * For example, bound=10000 may be a good choice. */ function ComputeCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; /* * Compute the alpha value corresponding to polynomial F . For * primes p that divide the discriminant, do a random sampling of * bound elements to estimate cont_p (the expected exponent of * prime p on the set of F values). Include an early abort strategy: * if by the time we reach abort_p , the estimated alpha value is > * abort_alpha then stop the computation and return (the estimated) alpha . * If the early abort will not be used, then just set abort_p and * abort_alpha to 0. * Function uses primes up to max_p . */ function ComputeAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := ComputeCont_p( p, disc, bound, F, f ); alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; /* * Compute rho( x ) where rho is the Dickman rho function. * This can be optimized by precomputing the coefficients of * the polynomials and storing those coefficients for future calls. */ function DickmanRho( x ); if x le 1.0 then return 1.0; end if; k := Ceiling( x ); zeta := k - x; c := []; c[1] := 1.0 - Log( 2.0 ); for i in [1..54] do c[i+1] := 1.0 /(i * 2^i); end for; prev_c := []; l := 2; while l lt k do for i in [0..54] do prev_c[i+1] := c[i+1]; end for; for i in [1..54] do sum := 0.0; for j in [0..i-1] do sum := sum + prev_c[j+1]/(i * (l + 1.0)^(i-j) ); end for; c[i+1] := sum; end for; sum := 0.0; for j in [1..54] do sum +:= c[j+1]/( j + 1.0 ); end for; c[1] := sum/l; l +:= 1; end while; rho_k := 0.0; for i in [0..54] do rho_k +:= c[i+1] * zeta^i; end for; return rho_k; end function; /* * Quickly compute an approximation to the Dickman rho function. */ function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; /* * Rate the polynomial pair F1 and F2 , where F1 has degree d * and corresponding alpha value and F2 is linear. B1 and B2 * represent upperbounds for the primes in the algebraic and rational * factor bases, respectively. High ratings tend to mean better * polynomials. * * Actually, we modify his rating method in 2 ways. * First, we divide through by K (the number of intervals) so that * the rating is not proportional to the number of intervals we choose. * Second, we add in a log B1^d to the numerator of u1 (which is * equivalent to adding d to the whole quantity of u1 ) so that the * rho values are more typical of what will happen in practice. A * similar modification is done to the u2 computation. */ function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; /* * Let X be a sequence, where X[i] represents the ranking * of the i'th best polynomial under some ranking scheme. This * function computes the correlation coefficient of the ranking scheme * (i.e. it gives us an idea of how good the ranking scheme is). * * for example, to compute the correlation coefficient of the E-rank * in table 6.4 of Murphy's thesis, you would send in X := * [ 1, 3, 6, 7, 2, 8, 4, 10, 5, 9, 15, 11, 18, 13, 12, 14, 17, 16 ] . * * Remark: there seem to be small differences between Murphy's and my * calculations. */ function CorrelationCoeff( X ) /* compute eXY = expected value of X * Y where Y is identity perumtation */ eXY := &+[X[i]*i: i in [1..#X]]/(#X + 0.0); eX := (#X+1.0)/2.0; eX2 := &+[X[i]*X[i]: i in [1..#X]]/(#X + 0.0); sigma := Sqrt( eX2 - eX*eX ); return (eXY - eX*eX)/sigma^2; end function; /* * Choose a leading coefficient for our polynomial. We want this leading * coefficient to have lots of small prime factors, and to be close to * high_a_d . This procedure uses randomness, so that we should get a * new leading coefficient every time it is called (assuming it is not * called too many times). */ function ChooseLeadingCoeff( high_a_d ); /* Start with some value for the leading coefficient c that has * many small prime factors. However, don't let this start value * get too close to high_a_d , since this can severely limit the * number of unique leading coefficients we can get. */ c := 32 * 27 * 25 * 49 ; c_limit := high_a_d div 300; if 10*c gt c_limit then c := 2 * 3 * 5 * 7; if 10*c gt c_limit then c := 2 * 3; if 10*c gt c_limit then c := 2; end if; end if; end if; if high_a_d lt 1000 then primes := [2, 3, 5, 7, 11]; else primes := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]; end if; num_primes := #primes; min := high_a_d div 2; while c lt min do p := primes[ Random( 1, num_primes ) ]; if c*p le high_a_d then c := c * p; end if; end while; return c; end function; /* * Let n be the number we want to factor. This algorithm works * something like Murphy's procedure 5.1.4 to find a good NFS polynomial. * (though I've modified it to fit my own understanding, so there are * definitely some differences from procedure 5.1.4). Remark: this * function alone randomly chooses one leading coefficient a_d for * the polynomials being searched. The user should try calling this * several times so several leading coefficients are tried. * * Returns a sequence of tuples which contain candidate polynomials and * information about those candidates. More precisely, the tuple has * the following items (in this order): * - the polynomial F ( F is homogeneous). * - a rating for the polynomial F (see 5.7 in Murphy's thesis). * - the alpha value (see section 3.2.3 of Murphy's thesis) of candidate * polynomial F . * - the m1 value corresponding to polynomial F (i.e F(m1, m2) = n ). * - the m2 value corresponding to polynomial F . This function * always has m2=1 . * * Description of input variables: * n the number we want to factor. * * chi only consider polynomials that have all their * leading coefficients <= m1 * chi * * max_k for each choice of the leading coefficient, only * consider polynomials whose m1 lies within this * range: [best_m1-max_k..best_m1+max_k] , where * "best_m1" indicates the m1 which minimizes the * coefficient a_{d-1} of polynomial F (where d * is the degree of F ). This is used to limit the * amount of time spent on a single leading coefficient. * Also the number of m1 considered may be even * smaller than the range indicated above since some of * these m1 may correspond to a different leading * coefficient. * * max_alpha The maximum value of alpha to allow for a polynomial * to be a candidate. Generally you want this to be * a negative number, say -1.0 or smaller. Values less * than -3.0 are considered very good. * * max_cands maximum number of candidate polynomials to allow. * (this is used to limit the amount of time spent * on a single choice for the leading coefficient). * */ function PolySearch1( n, chi, max_k, max_alpha, max_cands ); /* The set of return polynomials */ candidates := []; /* select a degree according to the asymptotic formula */ d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); print "degree ", d; /* Compute B - an upper bound for the factor base primes. This will be used in Murphy's rating scheme for the candidate polynomials */ dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); P := PolynomialRing(Integers(), 2); m2 := 1; /* Need to choose m1 between n^[1/(d+1)] and n^[1/d] . Murphy's procedure 5.1.4 actually requests that m1 is significantly larger than n^[1/(d+1)]. (This is implied by the request that a_d is significantly smaller than its corresponding m1 ). We allow the lowest m1 to be the geometric mean of these two values. The use of the geomretic mean just seems to work well - it can be changed. */ low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); low_a_d := n div high_m1^d; high_a_d := n div low_m1^d; c := ChooseLeadingCoeff( high_a_d ); print "using leading coeff ", c; a_d := c; if a_d lt low_a_d then a_d := ((low_a_d div c) + 1) * c; end if; /* The value of m1 that causes a_{d-1} to be minimized */ best_m1 := Iroot( n div a_d, d ); /* Determine a_{d-1} for this value of best_m1 */ a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * chi ); /* we try values between values [best_m1-k...best_m1+k] */ k := (coeff_bound - a_dminus1) div (a_d * d); if k gt max_k then k := max_k; end if; print "k=",k; for m1 in [best_m1-k..best_m1+k] do rem := n; coeffs := []; for i := d to 0 by -1 do temp := m1^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; m1div2 := m1 div 2; /* adjust the coefficients to be between -m1div2 and m1div2 */ for i := d+1 to 2 by -1 do if coeffs[i] gt m1div2 then coeffs[i] -:= m1; coeffs[i-1] +:= 1; end if; end for; /* check that the coefficients are sufficiently small */ small_coeffs := true; for i in [1..#coeffs] do if Abs( coeffs[i] ) gt coeff_bound then small_coeffs := false; break; end if; end for; if small_coeffs eq false then continue; end if; F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; /* obtain a quick estimate for alpha */ alpha := ComputeAlpha( F, 2500, 11, max_alpha+0.5, 100 ); print m1, alpha; if alpha le max_alpha then /* get a more accurate value for alpha */ alpha := ComputeAlpha( F, 10000, 0, 0, 2000 ); print "recomputed alpha: ", alpha; if alpha gt max_alpha then continue; end if; /* create the linear polynomial */ F2 := X*m2 - Y*m1; rating := RatePolynomials( F, F2, alpha, B, B, d ); Append( ~candidates, ); if #candidates eq max_cands then break; end if; print F; print ""; end if; end for; return candidates; end function; /* * Let n be the number we want to factor. This algorithm calls a * function named PolySearch1() which is similar to Murphy's procedure 5.1.4 * to find a good NFS polynomial. Each call to PolySearch1() uses a * (hopefully) new leading coefficient, that is somewhat randomly chosen. * Up to max_leading_coeffs will be tried. * * Returns a sequence of tuples which contain candidate polynomials and * information about those candidates. More precisely, the tuple has * the following items (in this order): * - the polynomial F ( F is homogeneous). * - a rating for the polynomial F (see 5.7 in Murphy's thesis). * - the alpha value (see section 3.2.3 of Murphy's thesis) of candidate * polynomial F . * - the m1 value corresponding to polynomial F (i.e F(m1, m2) = n ). * - the m2 value corresponding to polynomial F . This function * always has m2=1 . * * Description of input variables: * n the number we want to factor. * * chi only consider polynomials that have all their * leading coefficients <= m1 * chi * * max_k for each choice of the leading coefficient, only * consider polynomials whose m1 lies within this * range: [best_m1-max_k..best_m1+max_k] , where * "best_m1" indicates the m1 which minimizes the * coefficient a_{d-1} of polynomial F (where d * is the degree of F ). This is used to limit the * amount of time spent on a single leading coefficient. * Also the number of m1 considered may be even * smaller than the range indicated above since some of * these m1 may correspond to a different leading * coefficient. * * max_alpha The maximum value of alpha to allow for a polynomial * to be a candidate. Generally you want this to be * a negative number, say -1.0 or smaller. Values less * than -3.0 are considered very good. * * max_cands maximum number of candidate polynomials to allow. * (this is used to limit the amount of time spent * on a single choice for the leading coefficient). * */ function MurphyPolynomial1( n, chi, max_k, max_alpha, max_cands, max_leading_coeffs ); candidates := []; for i in [1..max_leading_coeffs] do new_cands := PolySearch1( n, chi, max_k, max_alpha, max_cands ); for j in [1..#new_cands] do Append( ~candidates, new_cands[j] ); end for; max_cands -:= #new_cands; if max_cands eq 0 then break; end if; end for; return candidates; end function; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host 3(NXDOMAIN) (213.253.124.19) Time: Fri Dec 12 04:18:45 2003 Input: /* * An implementation of a search for a non-skewed NFS polynomial, based * on Brian Murphy's thesis. * * By Contini - May, 2000. * * Please report bugs, improvements, and suggestions to * contini@maths.usyd.edu.au */ /* * A polynomial for n can be reconstructed from its degree d and its * value of m1 (assuming m2 = 1). This function does that. */ function m1ToPoly( n, m1, d ) rem := n; coeffs := []; for i := d to 0 by -1 do temp := m1^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; m1div2 := m1 div 2; /* adjust the coefficients to be between -m1div2 and m1div2 */ for i := d+1 to 2 by -1 do if coeffs[i] gt m1div2 then coeffs[i] -:= m1; coeffs[i-1] +:= 1; end if; end for; P := PolynomialRing(Integers(), 2); F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; return F; end function; /* * Compute cont_p (defined in section 3.2.1 of Murphy's thesis) of * homogeneous polynomial F corresponding to univariate polynomial f * for the prime p . The following input values are required: * - disc should be the discriminant of f . * - bound is the size of the sample space to look through in * order to estimate cont_p for the case of p dividing disc . * For example, bound=10000 may be a good choice. */ function ComputeCont_p( p, disc, bound, F, f ); if disc mod p eq 0 then /* estimate using some small sample space */ cont_p := 0; upper_limit := bound^2; for i in [1..bound] do repeat a := Random( upper_limit ); b := Random( upper_limit ); until Gcd( a, b ) eq 1; value := Evaluate( F, [a, b] ); while value mod p eq 0 do value div:= p; cont_p +:= 1; end while; end for; cont_p := cont_p / (0.0 + bound); else K := GF(p); roots_mod_p := Roots( f, K ); q_p := #roots_mod_p; /* add in the contribution of the projective roots */ d := Degree( f ); if Coefficient(f, d) mod p eq 0 then q_p +:= 1; end if; cont_p := q_p * p / (p * p - 1.0); end if; return cont_p; end function; /* * Compute the alpha value corresponding to polynomial F . For * primes p that divide the discriminant, do a random sampling of * bound elements to estimate cont_p (the expected exponent of * prime p on the set of F values). Include an early abort strategy: * if by the time we reach abort_p , the estimated alpha value is > * abort_alpha then stop the computation and return (the estimated) alpha . * If the early abort will not be used, then just set abort_p and * abort_alpha to 0. * Function uses primes up to max_p . */ function ComputeAlpha( F, bound, abort_p, abort_alpha, max_p ); Q := PolynomialRing(Integers()); f := Q!Evaluate( F, [X, 1] ); disc := Discriminant( f ); a_d := Coefficient(f, Degree(f)); primes := [p : p in [1..max_p] | IsPrime(p)]; alpha := 0.0; for p in primes do cont_p := ComputeCont_p( p, disc, bound, F, f ); alpha +:= (1.0/(p-1) - cont_p)*Log(p); /* early-abort strategy */ if p eq abort_p and alpha gt abort_alpha then break; end if; end for; return alpha; end function; /* * Compute rho( x ) where rho is the Dickman rho function. * This can be optimized by precomputing the coefficients of * the polynomials and storing those coefficients for future calls. */ function DickmanRho( x ); if x le 1.0 then return 1.0; end if; k := Ceiling( x ); zeta := k - x; c := []; c[1] := 1.0 - Log( 2.0 ); for i in [1..54] do c[i+1] := 1.0 /(i * 2^i); end for; prev_c := []; l := 2; while l lt k do for i in [0..54] do prev_c[i+1] := c[i+1]; end for; for i in [1..54] do sum := 0.0; for j in [0..i-1] do sum := sum + prev_c[j+1]/(i * (l + 1.0)^(i-j) ); end for; c[i+1] := sum; end for; sum := 0.0; for j in [1..54] do sum +:= c[j+1]/( j + 1.0 ); end for; c[1] := sum/l; l +:= 1; end while; rho_k := 0.0; for i in [0..54] do rho_k +:= c[i+1] * zeta^i; end for; return rho_k; end function; /* * Quickly compute an approximation to the Dickman rho function. */ function ApproxDickmanRho( u ); if u le 1.0 then return 1.0; end if; return u^-u; end function; /* * Rate the polynomial pair F1 and F2 , where F1 has degree d * and corresponding alpha value and F2 is linear. B1 and B2 * represent upperbounds for the primes in the algebraic and rational * factor bases, respectively. High ratings tend to mean better * polynomials. * * Actually, we modify his rating method in 2 ways. * First, we divide through by K (the number of intervals) so that * the rating is not proportional to the number of intervals we choose. * Second, we add in a log B1^d to the numerator of u1 (which is * equivalent to adding d to the whole quantity of u1 ) so that the * rho values are more typical of what will happen in practice. A * similar modification is done to the u2 computation. */ function RatePolynomials( F1, F2, alpha, B1, B2, d ) pi := Pi(RealField()); K := 1000; rating := 0.0; logB1 := Log( B1 ); logB2 := Log( B2 ); for i in [1..K] do theta := pi/K*(i - 0.5); tmp := Abs( Evaluate( F1, [Cos( theta ), Sin( theta ) ] ) ); u1 := ( Log( tmp ) + alpha ) / logB1 + d; tmp := Abs( Evaluate( F2, [Cos( theta ), Sin( theta ) ] ) ); u2 := Log( tmp ) / logB2 + 1.0; rating +:= ApproxDickmanRho( u1 ) * ApproxDickmanRho( u2 ); end for; return rating/K; end function; /* * Let X be a sequence, where X[i] represents the ranking * of the i'th best polynomial under some ranking scheme. This * function computes the correlation coefficient of the ranking scheme * (i.e. it gives us an idea of how good the ranking scheme is). * * for example, to compute the correlation coefficient of the E-rank * in table 6.4 of Murphy's thesis, you would send in X := * [ 1, 3, 6, 7, 2, 8, 4, 10, 5, 9, 15, 11, 18, 13, 12, 14, 17, 16 ] . * * Remark: there seem to be small differences between Murphy's and my * calculations. */ function CorrelationCoeff( X ) /* compute eXY = expected value of X * Y where Y is identity perumtation */ eXY := &+[X[i]*i: i in [1..#X]]/(#X + 0.0); eX := (#X+1.0)/2.0; eX2 := &+[X[i]*X[i]: i in [1..#X]]/(#X + 0.0); sigma := Sqrt( eX2 - eX*eX ); return (eXY - eX*eX)/sigma^2; end function; /* * Choose a leading coefficient for our polynomial. We want this leading * coefficient to have lots of small prime factors, and to be close to * high_a_d . This procedure uses randomness, so that we should get a * new leading coefficient every time it is called (assuming it is not * called too many times). */ function ChooseLeadingCoeff( high_a_d ); /* Start with some value for the leading coefficient c that has * many small prime factors. However, don't let this start value * get too close to high_a_d , since this can severely limit the * number of unique leading coefficients we can get. */ c := 32 * 27 * 25 * 49 ; c_limit := high_a_d div 300; if 10*c gt c_limit then c := 2 * 3 * 5 * 7; if 10*c gt c_limit then c := 2 * 3; if 10*c gt c_limit then c := 2; end if; end if; end if; if high_a_d lt 1000 then primes := [2, 3, 5, 7, 11]; else primes := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]; end if; num_primes := #primes; min := high_a_d div 2; while c lt min do p := primes[ Random( 1, num_primes ) ]; if c*p le high_a_d then c := c * p; end if; end while; return c; end function; /* * Let n be the number we want to factor. This algorithm works * something like Murphy's procedure 5.1.4 to find a good NFS polynomial. * (though I've modified it to fit my own understanding, so there are * definitely some differences from procedure 5.1.4). Remark: this * function alone randomly chooses one leading coefficient a_d for * the polynomials being searched. The user should try calling this * several times so several leading coefficients are tried. * * Returns a sequence of tuples which contain candidate polynomials and * information about those candidates. More precisely, the tuple has * the following items (in this order): * - the polynomial F ( F is homogeneous). * - a rating for the polynomial F (see 5.7 in Murphy's thesis). * - the alpha value (see section 3.2.3 of Murphy's thesis) of candidate * polynomial F . * - the m1 value corresponding to polynomial F (i.e F(m1, m2) = n ). * - the m2 value corresponding to polynomial F . This function * always has m2=1 . * * Description of input variables: * n the number we want to factor. * * chi only consider polynomials that have all their * leading coefficients <= m1 * chi * * max_k for each choice of the leading coefficient, only * consider polynomials whose m1 lies within this * range: [best_m1-max_k..best_m1+max_k] , where * "best_m1" indicates the m1 which minimizes the * coefficient a_{d-1} of polynomial F (where d * is the degree of F ). This is used to limit the * amount of time spent on a single leading coefficient. * Also the number of m1 considered may be even * smaller than the range indicated above since some of * these m1 may correspond to a different leading * coefficient. * * max_alpha The maximum value of alpha to allow for a polynomial * to be a candidate. Generally you want this to be * a negative number, say -1.0 or smaller. Values less * than -3.0 are considered very good. * * max_cands maximum number of candidate polynomials to allow. * (this is used to limit the amount of time spent * on a single choice for the leading coefficient). * */ function PolySearch1( n, chi, max_k, max_alpha, max_cands ); /* The set of return polynomials */ candidates := []; /* select a degree according to the asymptotic formula */ d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); print "degree ", d; /* Compute B - an upper bound for the factor base primes. This will be used in Murphy's rating scheme for the candidate polynomials */ dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); B := Round( Exp( 0.5*e ) ); P := PolynomialRing(Integers(), 2); m2 := 1; /* Need to choose m1 between n^[1/(d+1)] and n^[1/d] . Murphy's procedure 5.1.4 actually requests that m1 is significantly larger than n^[1/(d+1)]. (This is implied by the request that a_d is significantly smaller than its corresponding m1 ). We allow the lowest m1 to be the geometric mean of these two values. The use of the geomretic mean just seems to work well - it can be changed. */ low_m1 := Iroot( Iroot( n, d+1 ) * Iroot( n, d ) , 2 ); high_m1 := Iroot( n, d ); low_a_d := n div high_m1^d; high_a_d := n div low_m1^d; c := ChooseLeadingCoeff( high_a_d ); print "using leading coeff ", c; a_d := c; if a_d lt low_a_d then a_d := ((low_a_d div c) + 1) * c; end if; /* The value of m1 that causes a_{d-1} to be minimized */ best_m1 := Iroot( n div a_d, d ); /* Determine a_{d-1} for this value of best_m1 */ a_dminus1 := (n - a_d*best_m1^d) div best_m1^(d-1); coeff_bound := Round( best_m1 * chi ); /* we try values between values [best_m1-k...best_m1+k] */ k := (coeff_bound - a_dminus1) div (a_d * d); if k gt max_k then k := max_k; end if; print "k=",k; for m1 in [best_m1-k..best_m1+k] do rem := n; coeffs := []; for i := d to 0 by -1 do temp := m1^i; coeff := rem div temp; Append (~coeffs, coeff); rem -:= coeff*temp; end for; m1div2 := m1 div 2; /* adjust the coefficients to be between -m1div2 and m1div2 */ for i := d+1 to 2 by -1 do if coeffs[i] gt m1div2 then coeffs[i] -:= m1; coeffs[i-1] +:= 1; end if; end for; /* check that the coefficients are sufficiently small */ small_coeffs := true; for i in [1..#coeffs] do if Abs( coeffs[i] ) gt coeff_bound then small_coeffs := false; break; end if; end for; if small_coeffs eq false then continue; end if; F := P!0; for i in [0..d] do F +:= coeffs[i+1]*X^(d-i)*Y^i; end for; /* obtain a quick estimate for alpha */ alpha := ComputeAlpha( F, 2500, 11, max_alpha+0.5, 100 ); print m1, alpha; if alpha le max_alpha then /* get a more accurate value for alpha */ alpha := ComputeAlpha( F, 10000, 0, 0, 2000 ); print "recomputed alpha: ", alpha; if alpha gt max_alpha then continue; end if; /* create the linear polynomial */ F2 := X*m2 - Y*m1; rating := RatePolynomials( F, F2, alpha, B, B, d ); Append( ~candidates, ); if #candidates eq max_cands then break; end if; print F; print ""; end if; end for; return candidates; end function; /* * Let n be the number we want to factor. This algorithm calls a * function named PolySearch1() which is similar to Murphy's procedure 5.1.4 * to find a good NFS polynomial. Each call to PolySearch1() uses a * (hopefully) new leading coefficient, that is somewhat randomly chosen. * Up to max_leading_coeffs will be tried. * * Returns a sequence of tuples which contain candidate polynomials and * information about those candidates. More precisely, the tuple has * the following items (in this order): * - the polynomial F ( F is homogeneous). * - a rating for the polynomial F (see 5.7 in Murphy's thesis). * - the alpha value (see section 3.2.3 of Murphy's thesis) of candidate * polynomial F . * - the m1 value corresponding to polynomial F (i.e F(m1, m2) = n ). * - the m2 value corresponding to polynomial F . This function * always has m2=1 . * * Description of input variables: * n the number we want to factor. * * chi only consider polynomials that have all their * leading coefficients <= m1 * chi * * max_k for each choice of the leading coefficient, only * consider polynomials whose m1 lies within this * range: [best_m1-max_k..best_m1+max_k] , where * "best_m1" indicates the m1 which minimizes the * coefficient a_{d-1} of polynomial F (where d * is the degree of F ). This is used to limit the * amount of time spent on a single leading coefficient. * Also the number of m1 considered may be even * smaller than the range indicated above since some of * these m1 may correspond to a different leading * coefficient. * * max_alpha The maximum value of alpha to allow for a polynomial * to be a candidate. Generally you want this to be * a negative number, say -1.0 or smaller. Values less * than -3.0 are considered very good. * * max_cands maximum number of candidate polynomials to allow. * (this is used to limit the amount of time spent * on a single choice for the leading coefficient). * */ function MurphyPolynomial1( n, chi, max_k, max_alpha, max_cands, max_leading_coeffs ); candidates := []; for i in [1..max_leading_coeffs] do new_cands := PolySearch1( n, chi, max_k, max_alpha, max_cands ); for j in [1..#new_cands] do Append( ~candidates, new_cands[j] ); end for; max_cands -:= #new_cands; if max_cands eq 0 then break; end if; end for; return candidates; end function; Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed. ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Fri Dec 12 05:33:48 2003 Input: p:=6124304827429735546123425103102892562385732953863411; A:=2825727939751163729165098219363301344190165245389208; x:=4187661666989931282717069293695997208234416189531855; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FacotredOrder(E); Output: Magma V2.10-6 Fri Dec 12 2003 05:33:44 on modular [Seed = 1854458029] ------------------------------------- >> time FacotredOrder(E); ^ User error: Identifier 'FacotredOrder' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Fri Dec 12 05:34:21 2003 Input: p:=6124304827429735546123425103102892562385732953863411; A:=2825727939751163729165098219363301344190165245389208; x:=4187661666989931282717069293695997208234416189531855; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 12 2003 05:33:57 on modular [Seed = 1719713976] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29741 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Fri Dec 12 05:36:16 2003 Input: p:=6124304827429735546123425103102892562385732953863411; A:=2825727939751163729165098219363301344190165245389208; x:=4187661666989931282717069293695997208234416189531855; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time Order(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 12 2003 05:35:53 on modular [Seed = 1905775667] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29754 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ABesancon-103-1-3-183.w81-49.abo.wanadoo.fr. (81.49.188.183) Time: Fri Dec 12 10:59:04 2003 Input: 130475260650438030173474313895577390123 Output: Magma V2.10-6 Fri Dec 12 2003 10:59:01 on modular [Seed = 3960092177] ------------------------------------- 130475260650438030173474313895577390123 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host port-213-148-153-163.reverse.qsc.de. (213.148.153.163) Time: Fri Dec 12 13:52:09 2003 Input: 5+5 Output: Magma V2.10-6 Fri Dec 12 2003 13:52:05 on modular [Seed = 1370775601] ------------------------------------- 10 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 15:42:12 2003 Input: p:=[];p[1]:=1;p[2]:=2; for i in [3..30] do p[i]:=1+p[i-1]*p[i-2]; end for; print p; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 12 2003 15:41:48 on modular [Seed = 3176704645] ------------------------------------- [ 1, 2, 3, 7, 22, 155, 3411, 528706, 1803416167, 953476947989903, 1719515742866809222961802, 1639518622529236077952144318816050685207, 2819178082162327154499022366029959843954512194276761760087463015, 4622094965931392147909656344999844030891066376725823165468409735193174734927137\ 785883868307641020119106, 13030508821626608982777703896518162096154431599989318\ 5112999739784706920930259523158106337431234334586721517680816827540091067505800\ 29963148787116972417343852669864591, 602282492279649460890511292953253754367654\ 3423435544340839807873422268767838535306840628552168094209666677334740603638415\ 5498743787893941586043512034954345294948406414779160634934145672079109189999034\ 026783850717431799435695451686835940316743161454145010953219711975647, 7848047328761232318753873367083493547601617987288974595774379134786126869912604\ 7353299121483273362759719787413901752908722227235081822642241939473803530464727\ 2081333476475303191079087012522290541034954095082305129110982572772845266170421\ 8434192723959927109385249559988932859736761670212267694825832605235908665355083\ 7459866970697304684102192153565632194978884937909901799037188874407063039725264\ 2415185335066123796000091667948579615378, 4726741504694960478461317046947040158211057009097671211058126792457809753246059\ 0513063698880394424762218654012453143732715209869140676064079248457158971482445\ 9610385412230964069050030199097788716098710585121611047950365588371470482607414\ 8321658850395445135275781608859107563458092908420815219831418890925186185930353\ 9876337533518647192519099936099233070437822361793541697694181829054926594277714\ 9891298158022952551450239177009326587016478802045578048021734293107207148845792\ 9964055063729701416392867625933831593067746021690689435754231799218362669121987\ 6790544289373319029406989470113100180620316710739414570255242072285166514508734\ 222104797245858666835178786380099186011105117661192423170136171762699567, 3709569103966613243382305798306875510078974959847659598427444073738804987554992\ 9679710020819507136810881972875481815665862303549613985380261502528528425572376\ 0914087220711522683597089445752665059842969474157209046278698112539404017011218\ 2218542890169911818495558123372762387690417025696233157631623224388359428539917\ 2535654385767226925501077308696520923002538779934263073359388999450091992676611\ 7876040207583494954137941300751246509350319317489790981299460941243341415704830\ 2961710382781458659682015802487588745828283829489091531626264133016120201799334\ 1857639164736657497943340707804666207349046298703836197597709879691497212617225\ 4408616997183431066374269856011218084244099813973136758400588456609322306956556\ 5219429880610135992061869227678796922425386095351584859689373384660832686280437\ 3706929020554853985759872940938214402309727449251255821569333318805983719939682\ 6617073889487301343881961668343049416025008008855630319358689096640573378093615\ 3253207733339302904139186508883675232472941807039972855348113982120376845375444\ 9081241930839506647739446782754993350246673383886164986555438234171093350816743\ 732137628888647755088551827141327, 17534174248253085767189154856226914791561973\ 8080652368803252567061988491179187021916914188419996477364737472570223884747993\ 0223426053097145967690996470827639741214178829102256730660285335897590626256859\ 6433306098132065370913926364068298174317072057070781235003980129893727480621534\ 5800705125658253878549487232073836718080830205096040055094948717021041395217447\ 0463819011632566714785185416743409593547567307031813816096014244647143134774638\ 0118842602451564080325224624161040339134905955728639314390005314709175381534698\ 1264030348253139771652074901980920223748526362678648328999615455408593521811721\ 6813273513473546392651162610560614752929261509271797792370039651881077176205403\ 4152919510400823971115215218239088983127795319871687602558395573005403520390174\ 6781412521453911512903115640828662197821206904211523444823268182125780648783018\ 7190876472518066043196967904722664025752653869578373438543969130512997950422945\ 2488430571902284337520530311119329367484414774187581258942151164305549851826190\ 0215129064174915053008148695581943952882023380217606834729140551553723128063786\ 6671722390435953639484251802431568141134691206450071885143876619585571254198759\ 3704918859797101030201897827126567152266017035767369856953213088550565008281736\ 2030108181448983233127361809694745049016557010048728856617255743572825770782640\ 2386570983986128143274932106238981130834435982464597651374385034307423063160042\ 8089137754769032290521104702825776162036286554938767187779900776949143492595587\ 1980604501118602469979429224614471313110473397439319530907166046996319214140162\ 5524913209082340838438984757308960409037732095268649799966475349863205471205445\ 0175862974822358085288487206367276037188482431671909909499278609543207467663620\ 1792215638775984882249154562270075405913406748473867181518090322240744394229076\ 5120065454814517274806285221975200470391760776856665950705410, 6504423105488666372650835881315187696423266507400341694128368306385740176028734\ 4649951608708862287744983909405883203469114775677628621459673973325550187602105\ 8283653209787575020403914209955379159869258099422069242601020463559723853548224\ 2957092348339570269649292228979975058887630636573164512250998861241371069464911\ 5327995704669987743332456699058720961205729607073063733333381619685039027055298\ 6585194867171851995827664220333389458750374967921850340489140866212078219996879\ 7867435082152651504630943328221859383025226524112749223294030376539767218866132\ 6640525429481590433916833159698817710145723546405096411399736327168238813814431\ 9053145701211913342821492930515887319572029060727582780401289562128660590471090\ 0019018936014788220534937771620172349493850921943456060039938646944650561899117\ 3485352889863023569438830512682811777341628259665130511745738547387071061971860\ 3098922621260212360751055164960333815497764244985011370106035104403133146088831\ 5904490161700623116165840171507451414583682978666114148222895082443308261616743\ 2034203506964941831867394159121342378097420654286737286239259869093558734753643\ 0738742411288150523147268208549876799506565047294400137361566705261464386713152\ 6692881347200500674073590737634260201015196244152445368735159623910304010011716\ 4772647098333471932754860493948215403130453277611468847717293327803312298457211\ 0638580798401116502768558703695837413821617404477767825038107093062283615048577\ 4596423798561356289845071417433767608939978484919063085625388684421350757822049\ 3731245648047698320407254647657256903574243853432024349595184592142843343648265\ 4838436483051950351201647481603409831460049768203663211911637190416156480772000\ 3510041985880021835495041791127276072668443236026942356111978991039078174371681\ 2204703474816121073817236139068553717400935922149318125869973065048812022550303\ 5735024057707342652922979036287049364747689748777430638358789123475987383324130\ 7464855387665676123223046765307953327269681759207367969592831989299721547610384\ 5990022077501109700839306449960951299110455227971363738316119140893460758611902\ 5432119267005076978553153016289738314244012368431335062732530972211733788319649\ 0946076317643178212166016570155499375836775146402909352173663604169330663423201\ 9064628982859265124709365093828389307161168903259078900974354845461307608045106\ 6940840844360217543300690562148235433805783662892476067182862673791340497443758\ 7049378143943731669086530290461235451434346126994975781591994195449165085947289\ 3433019209618121458885698973271291148207513382205744570346575538680449476898593\ 3806529479918428771620049570247397194393384650566614998001389203106760473780206\ 7812780636164718124053927561413346009437181643434852300341499350220225707543868\ 7516133309555466595597677878812408764669002966142429641250574391453410555150531\ 4427754780521284856132324067530283608697202130667041093247384973766125540903290\ 0809514120410933204846289452620936476331491090191907020487759666013023119029730\ 2258930747364011800578724937463436725229028023099413479071, 1140496881160017382789733222619183244106887148530857980935687423294586912548704\ 5534802704809250653335068920052959814566242164639708281392582750203256565445822\ 8425280346316676347823190728760975763244333125534151945333980619561573752575107\ 0640119840128846522021982528964925126519748105428481868545182219866577411335696\ 6766513689949177509734792289667294422969298448254522370060833211734915819029794\ 2341351798755505836243614512415639045763036196123294783328604342106540529622575\ 7001631590637092847064045960763912147198865834250824268569085072195295551780717\ 1890715834935304235596859569645453381114633204872831626333864366378117175427803\ 7215687002234806788689606772251731010642773852391973829762425051283885217652299\ 4478029708374863357625420583580160630068061491173466951837550024776626005083329\ 2212285996762109264706355435799676303249550380064737000179809511215764340152851\ 5540943819731661050484034418585722075493330891196616805519685508835956029160660\ 8506454465513262161350408634318187039442618059993590217034027861027750967746677\ 1907471472116059691366229598146661619828030974386316917508127234282351773460446\ 1243073422003087080921985688401348020977414529391682005162784364595638674725268\ 5293609421609642022674179695814657369144966771690307178215742283927294954936254\ 6634309508755857615824655840322947767281464873972649245925838467714234582394433\ 3599364238678554006423170898795115503174130100291713100811610602472964046164394\ 1722601038238904297482185174272459377083920245804682804636228596899024089739799\ 9722692177009685104773615887023470259092935614558617640036839447649724115590418\ 2134128173976821663689513677530836809246671588132570861870592921083158583640853\ 5100765546652733614072844306879784546480714664829214414484285846308089550809845\ 6950973040303341136665178900806366432510460323550 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 2953 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 15:44:41 2003 Input: p:=[];p[1]:=1;p[2]:=2; for j in [3..10] do p[j]:=1+p[j]; for i in [3..j] do p[i]:=p[i-1]*p[i-2]; end for; end for; print p; Output: Magma V2.10-6 Fri Dec 12 2003 15:44:38 on modular [Seed = 2806165541] ------------------------------------- >> for j in [3..10] do p[j]:=1+p[j]; ^ Runtime error in '[]': Sequence element 3 not defined [ 1, 2 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 15:46:01 2003 Input: p:=[];p[1]:=1;p[2]:=2; for j in [3..10] do for i in [3..j] do p[i]:=p[i-1]*p[i-2]; end for; p[j]:=1+p[j]; end for; print p; Output: Magma V2.10-6 Fri Dec 12 2003 15:45:58 on modular [Seed = 2423621282] ------------------------------------- [ 1, 2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869185 ] Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 17:03:32 2003 Input: p:=[];p[1]:=2;p[2]:=1+p[1];q:=p[1]*p[2]; p[3]:=1+q; q:=q*p[3]; for i in [4..10] do p[i]:=1+q; q:=q*p[i]; end for; print p; Output: Magma V2.10-6 Fri Dec 12 2003 17:03:29 on modular [Seed = 1236028747] ------------------------------------- [ 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807, 1655066473245199641984681954444391800175131527063774978418513887665358686395724\ 06808911988131737645185443 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 17:05:20 2003 Input: p:=[];p[1]:=2;p[2]:=1+p[1];q:=p[1]*p[2]; p[3]:=1+q; q:=q*p[3]; for i in [4..10] do p[i]:=1+q; q:=q*p[i]; p[i]:=Factorization(p); end for; print ; Output: Magma V2.10-6 Fri Dec 12 2003 17:05:17 on modular [Seed = 3025252378] ------------------------------------- >> for i in [4..10] do p[i]:=1+q; q:=q*p[i]; p[i]:=Factorization(p); end for; ^ Runtime error in 'Factorization': Bad argument types Argument types given: SeqEnum[RngIntElt] >> print ;; ^ User error: bad syntax Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 17:05:57 2003 Input: p:=[];p[1]:=2;p[2]:=1+p[1];q:=p[1]*p[2]; p[3]:=1+q; q:=q*p[3]; for i in [4..10] do p[i]:=1+q; q:=q*p[i]; p[i]:=Factorization(p[i]); end for; print ; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 12 2003 17:05:34 on modular [Seed = 3159996449] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3215 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 17:06:17 2003 Input: p:=[];p[1]:=2;p[2]:=1+p[1];q:=p[1]*p[2]; p[3]:=1+q; q:=q*p[3]; for i in [4..5] do p[i]:=1+q; q:=q*p[i]; p[i]:=Factorization(p[i]); end for; print ; Output: Magma V2.10-6 Fri Dec 12 2003 17:06:14 on modular [Seed = 2840374604] ------------------------------------- >> print ;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 17:06:28 2003 Input: p:=[];p[1]:=2;p[2]:=1+p[1];q:=p[1]*p[2]; p[3]:=1+q; q:=q*p[3]; for i in [4..5] do p[i]:=1+q; q:=q*p[i]; p[i]:=Factorization(p[i]); end for; print p; Output: Magma V2.10-6 Fri Dec 12 2003 17:06:25 on modular [Seed = 2440336707] ------------------------------------- [ 2, 3, 7, 43, 1807 ] Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 17:06:48 2003 Input: p:=[];p[1]:=2;p[2]:=1+p[1];q:=p[1]*p[2]; p[3]:=1+q; q:=q*p[3]; for i in [4..9] do p[i]:=1+q; q:=q*p[i]; p[i]:=Factorization(p[i]); end for; print p; Output: Magma V2.10-6 Fri Dec 12 2003 17:06:42 on modular [Seed = 2575080792] ------------------------------------- [ 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807 ] Total time: 5.449 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host io.yourlibrary.ca. (208.181.90.67) Time: Fri Dec 12 17:07:34 2003 Input: p:=[];p[1]:=2;p[2]:=1+p[1];q:=p[1]*p[2]; p[3]:=1+q; q:=q*p[3]; for i in [4..10] do p[i]:=1+q; q:=q*p[i]; p[i]:=Factorization(p[i]); end for; print p; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 12 2003 17:07:10 on modular [Seed = 2271380667] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 3252 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ppp-207-167-100-225.sndg-pm4-2.dialup.nethere.net. (207.167.100.225) Time: Fri Dec 12 17:43:50 2003 Input: sqrt(14)/(sqrt(6)+sqrt(7)-1) Output: Magma V2.10-6 Fri Dec 12 2003 17:43:46 on modular [Seed = 3441997404] ------------------------------------- >> sqrt(14)/(sqrt(6)+sqrt(7)-1); ^ User error: Identifier 'sqrt' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-225.sndg-pm4-2.dialup.nethere.net. (207.167.100.225) Time: Fri Dec 12 17:44:28 2003 Input: (14^(1/2))/((6^(1/2))+(7^(1/2))-1) Output: Magma V2.10-6 Fri Dec 12 2003 17:44:25 on modular [Seed = 902844110] ------------------------------------- 0.9136598646026928174214875916 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-225.sndg-pm4-2.dialup.nethere.net. (207.167.100.225) Time: Fri Dec 12 17:44:45 2003 Input: factor((14^(1/2))/((6^(1/2))+(7^(1/2))-1)) Output: Magma V2.10-6 Fri Dec 12 2003 17:44:42 on modular [Seed = 1037584085] ------------------------------------- factor( x: 0.9136598646026928174214875916 ) In file "/home/was/magma/packages/misc/code/misc.m", line 96, column 24: >> return Factorization(x); ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldReElt Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-225.sndg-pm4-2.dialup.nethere.net. (207.167.100.225) Time: Fri Dec 12 17:45:04 2003 Input: simplify((14^(1/2))/((6^(1/2))+(7^(1/2))-1)) Output: Magma V2.10-6 Fri Dec 12 2003 17:45:01 on modular [Seed = 785077745] ------------------------------------- >> simplify((14^(1/2))/((6^(1/2))+(7^(1/2))-1)); ^ User error: Identifier 'simplify' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:03:11 2003 Input: N:=451; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:02:48 on modular [Seed = 1787807805] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4165 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:03:40 2003 Input: N:=449; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 00:03:34 on modular [Seed = 1653063915] ------------------------------------- [ 449, 1, 1 ][] [ 449, 2, 1 ][ 449, 7, 1 ][] Total time: 4.479 seconds, Total memory usage: 5.66MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:07:08 2003 Input: N:=448; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [9..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 00:07:01 on modular [Seed = 1955714350] ------------------------------------- Do not know how to compute component group at 2 Total time: 6.459 seconds, Total memory usage: 3.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:08:22 2003 Input: N:=447; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:07:59 on modular [Seed = 1269754571] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4196 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:09:00 2003 Input: N:=447; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:08:37 on modular [Seed = 1135010489] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4204 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:10:18 2003 Input: N:=447; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:09:55 on modular [Seed = 1522530902] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4213 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:12:02 2003 Input: N:=446; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:11:39 on modular [Seed = 2857306638] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4229 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:13:15 2003 Input: N:=446; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..3] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:12:52 on modular [Seed = 2722562649] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4237 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:13:48 2003 Input: N:=446; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:13:25 on modular [Seed = 3109820771] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4246 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:15:38 2003 Input: N:=445; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:15:15 on modular [Seed = 2355696576] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4259 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:24:14 2003 Input: N:=44; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 00:24:09 on modular [Seed = 2507147459] ------------------------------------- [ 44, 1, 1 ][ 11, 1, 1 ][] Total time: 5.119 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:24:50 2003 Input: N:=444; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:24:27 on modular [Seed = 3960041800] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4291 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:25:56 2003 Input: N:=443; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 00:25:51 on modular [Seed = 4279919119] ------------------------------------- [ 443, 1, 1 ][] [ 443, 2, 1 ][ 443, 1, 1 ][] [ 443, 3, 1 ][ 443, 1, 1 ][] [ 443, 4, 1 ][ 443, 1, 1 ][] [ 443, 5, 1 ][ 443, 221, 1 ][] Total time: 4.469 seconds, Total memory usage: 5.62MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:27:29 2003 Input: N:=442; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:27:06 on modular [Seed = 4145179634] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4312 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:28:03 2003 Input: N:=442; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:27:40 on modular [Seed = 3475657644] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4320 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 00:29:49 2003 Input: N:=437; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 00:29:26 on modular [Seed = 3307231580] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 4330 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 04:45:57 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(144,2,+1))))); E:=EllipticCurve(EllipticCurveDatabase(),4176,19,1); E; Factorization(Numerator(Discriminant(E)); for i in [1..#A] do CongruenceGroupAnemic(A[i],Parent(Newform(E)),200); end for; Output: Magma V2.10-6 Sat Dec 13 2003 04:45:51 on modular [Seed = 1302900136] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 345*x - 5157 over Rational Field >> Factorization(Numerator(Discriminant(E)); ^ User error: bad syntax Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 5.199 seconds, Total memory usage: 4.73MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 04:46:16 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(144,2,+1))))); E:=EllipticCurve(EllipticCurveDatabase(),4176,19,1); E; Factorization(Numerator(Discriminant(E))); for i in [1..#A] do CongruenceGroupAnemic(A[i],Parent(Newform(E)),200); end for; Output: Magma V2.10-6 Sat Dec 13 2003 04:46:11 on modular [Seed = 1168156044] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 345*x - 5157 over Rational Field [ <2, 4>, <3, 3>, <29, 5> ] Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 5.119 seconds, Total memory usage: 4.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 04:47:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(144,2,+1))))); E:=EllipticCurve(EllipticCurveDatabase(),4176,19,1); E; Factorization(Numerator(Discriminant(E))); for i in [1..#A] do CongruenceGroupAnemic(A[i],Parent(Newform(E)),200); EllipticCurve(A[i]); end for; Output: Magma V2.10-6 Sat Dec 13 2003 04:47:08 on modular [Seed = 1572373099] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 345*x - 5157 over Rational Field [ <2, 4>, <3, 3>, <29, 5> ] Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 + 6*x + 7 over Rational Field Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Elliptic Curve defined by y^2 = x^3 - 1 over Rational Field Total time: 5.259 seconds, Total memory usage: 5.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 04:48:19 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(144,2,+1))))); E:=EllipticCurve(EllipticCurveDatabase(),4176,14,1); E; Factorization(Numerator(Discriminant(E))); for i in [1..#A] do CongruenceGroupAnemic(A[i],Parent(Newform(E)),200); EllipticCurve(A[i]); end for; Output: Magma V2.10-6 Sat Dec 13 2003 04:48:13 on modular [Seed = 1437633058] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 3105*x + 139239 over Rational Field [ <2, 4>, <3, 9>, <29, 5> ] Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 + 6*x + 7 over Rational Field Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Elliptic Curve defined by y^2 = x^3 - 1 over Rational Field Total time: 5.289 seconds, Total memory usage: 5.39MB ************** MAGMA ***************** Host APoitiers-106-1-30-114.w81-249.abo.wanadoo.fr. (81.249.161.114) Time: Sat Dec 13 08:19:47 2003 Input: 2+3 Output: Magma V2.10-6 Sat Dec 13 2003 08:19:43 on modular [Seed = 2675683672] ------------------------------------- 5 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host APoitiers-106-1-30-114.w81-249.abo.wanadoo.fr. (81.249.161.114) Time: Sat Dec 13 08:20:13 2003 Input: solve x=3*x+2 Output: Magma V2.10-6 Sat Dec 13 2003 08:20:10 on modular [Seed = 4010525389] ------------------------------------- >> solve x=3*x+2 ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host CPE-24-164-246-39.new.rr.com. (24.164.246.39) Time: Sat Dec 13 08:28:11 2003 Input: (e^(1.92*log((2^512)^(1/3))*log(log((2^512)^(2/3)))))+0/(365*24*60*60*10^6) Output: Magma V2.10-6 Sat Dec 13 2003 08:28:08 on modular [Seed = 3324176902] ------------------------------------- >> (e^(1.92*log((2^512)^(1/3))*log(log((2^512)^(2/3)))))+0/(365*24*60*60*10^6) ^ User error: Identifier 'e' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host CPE-24-164-246-39.new.rr.com. (24.164.246.39) Time: Sat Dec 13 08:28:28 2003 Input: (exp(1.92*log((2^512)^(1/3))*log(log((2^512)^(2/3)))))+0/(365*24*60*60*10^6) Output: Magma V2.10-6 Sat Dec 13 2003 08:28:25 on modular [Seed = 3728405007] ------------------------------------- >> (exp(1.92*log((2^512)^(1/3))*log(log((2^512)^(2/3)))))+0/(365*24*60*60*10^6 ^ User error: Identifier 'log' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host CPE-24-164-246-39.new.rr.com. (24.164.246.39) Time: Sat Dec 13 08:43:03 2003 Input: 1*1.9 Output: Magma V2.10-6 Sat Dec 13 2003 08:43:00 on modular [Seed = 1020793983] ------------------------------------- 1.89999999999999999999999999999 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host CPE-24-164-246-39.new.rr.com. (24.164.246.39) Time: Sat Dec 13 08:43:39 2003 Input: e Output: Magma V2.10-6 Sat Dec 13 2003 08:43:36 on modular [Seed = 351288507] ------------------------------------- >> e ^ User error: Identifier 'e' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 11:59:07 2003 Input: N:=219; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 11:58:44 on modular [Seed = 1854542863] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6731 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 11:59:29 2003 Input: N:=219; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 11:59:16 on modular [Seed = 1989282871] ------------------------------------- [ 219, 1, 1 ][ 3, 1, 5 ][] [ 219, 2, 1 ][ 3, 1, 1 ][] [ 219, 3, 1 ][ 3, 3, 1 ][] [ 219, 4, 1 ][ 3, 1, 17 ][] [ 219, 5, 1 ][ 3, 1073, 1 ][] Total time: 13.469 seconds, Total memory usage: 4.65MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:00:03 2003 Input: N:=221; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 11:59:49 on modular [Seed = 2124023006] ------------------------------------- [ 221, 1, 1 ][ 13, 1, 1 ][] [ 221, 2, 1 ][ 13, 1, 3 ][] [ 221, 3, 1 ][ 13, 1, 1 ][] [ 221, 4, 1 ][ 13, 1, 1 ][] [ 221, 5, 1 ][ 13, 1, 1 ][] [ 221, 6, 1 ][ 13, 1, 1 ][] [ 221, 7, 1 ][ 13, 9, 1 ][] Total time: 13.989 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:00:33 2003 Input: N:=226; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:00:24 on modular [Seed = 1219244741] ------------------------------------- [ 226, 1, 1 ][ 2, 3, 1 ][] [ 226, 2, 1 ][ 2, 1, 7 ][] [ 226, 3, 1 ][ 2, 1, 3 ][] [ 226, 4, 1 ][ 2, 779, 1 ][] Total time: 9.299 seconds, Total memory usage: 5.06MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:01:17 2003 Input: N:=235; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:01:05 on modular [Seed = 2722551894] ------------------------------------- [ 235, 1, 1 ][ 5, 1, 9 ][] [ 235, 2, 1 ][ 5, 1, 3 ][] [ 235, 3, 1 ][ 5, 3, 1 ][] [ 235, 4, 1 ][ 5, 1, 1 ][] [ 235, 5, 1 ][ 5, 1, 1 ][] Total time: 12.579 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:03:23 2003 Input: N:=238; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:03:11 on modular [Seed = 2857292736] ------------------------------------- [ 238, 1, 1 ][ 2, 1, 1 ][] [ 238, 2, 1 ][ 2, 1, 5 ][] [ 238, 3, 1 ][ 2, 1, 1 ][] [ 238, 4, 1 ][ 2, 7, 1 ][] [ 238, 5, 1 ][ 2, 1, 1 ][] [ 238, 6, 1 ][ 2, 1, 61 ][] Total time: 12.189 seconds, Total memory usage: 6.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:04:39 2003 Input: N:=246; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 12:04:16 on modular [Seed = 2992032519] ------------------------------------- [ 246, 1, 1 ][ 2, 1, 3 ][] [ 246, 2, 1 ][ 2, 1, 11 ][] [ 246, 3, 1 ][ 2, 1, 7 ][] [ 246, 4, 1 ][ 2, 1, 1 ][] Errors: /home/mfd/gomagma: line 2: 6807 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:05:44 2003 Input: N:=246; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [5..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:05:22 on modular [Seed = 2170943606] ------------------------------------- [ 246, 5, 1 ][ 2, 3, 1 ][] [ 246, 6, 1 ][ 2, 25, 1 ][] [ 246, 7, 1 ][ 2, 1, 1 ][] Total time: 22.149 seconds, Total memory usage: 7.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:06:51 2003 Input: N:=249; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:06:39 on modular [Seed = 2305683891] ------------------------------------- [ 249, 1, 1 ][ 3, 1, 1 ][] [ 249, 2, 1 ][ 3, 1, 3 ][] [ 249, 3, 1 ][ 3, 31, 1 ][] [ 249, 4, 1 ][ 3, 35, 1 ][] [ 249, 5, 1 ][ 3, 1, 2711 ][] Total time: 11.509 seconds, Total memory usage: 4.97MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:07:42 2003 Input: N:=258; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 12:07:19 on modular [Seed = 2440423923] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6836 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:08:26 2003 Input: N:=262; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:08:16 on modular [Seed = 2575163708] ------------------------------------- [ 262, 1, 1 ][ 2, 1, 1 ][] [ 262, 2, 1 ][ 2, 11, 1 ][] [ 262, 3, 1 ][ 2, 1, 3 ][] [ 262, 4, 1 ][ 2, 1, 313 ][] [ 262, 5, 1 ][ 2, 33, 1 ][] [ 262, 6, 1 ][ 2, 1, 1 ][] Total time: 9.709 seconds, Total memory usage: 5.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:09:59 2003 Input: N:=267; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:09:44 on modular [Seed = 3775240476] ------------------------------------- [ 267, 1, 1 ][ 3, 1, 17 ][] [ 267, 2, 1 ][ 3, 3, 1 ][] [ 267, 3, 1 ][ 3, 1, 3 ][] [ 267, 4, 1 ][ 3, 25, 1 ][] [ 267, 5, 1 ][ 3, 113, 1 ][] [ 267, 6, 1 ][ 3, 1, 39 ][] Total time: 14.149 seconds, Total memory usage: 5.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:10:44 2003 Input: N:=270; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 12:10:21 on modular [Seed = 4044720425] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 6868 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:11:23 2003 Input: N:=273; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:11:01 on modular [Seed = 4179463929] ------------------------------------- [ 273, 1, 1 ][ 3, 1, 1 ][] [ 273, 2, 1 ][ 3, 1, 1 ][] [ 273, 3, 1 ][ 3, 1, 7 ][] [ 273, 4, 1 ][ 3, 1, 1 ][] [ 273, 5, 1 ][ 3, 9, 1 ][] Total time: 22.150 seconds, Total memory usage: 5.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:11:50 2003 Input: N:=274; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:11:38 on modular [Seed = 3240474286] ------------------------------------- [ 274, 1, 1 ][ 2, 1, 1 ][] [ 274, 2, 1 ][ 2, 1, 11 ][] [ 274, 3, 1 ][ 2, 7, 1 ][] [ 274, 4, 1 ][ 2, 1, 109 ][] [ 274, 5, 1 ][ 2, 3427, 1 ][] Total time: 11.260 seconds, Total memory usage: 5.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:12:59 2003 Input: N:=285; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:12:38 on modular [Seed = 3358375787] ------------------------------------- [ 285, 1, 1 ][ 3, 1, 1 ][] [ 285, 2, 1 ][ 3, 1, 1 ][] [ 285, 3, 1 ][ 3, 5, 1 ][] [ 285, 4, 1 ][ 3, 1, 47 ][] [ 285, 5, 1 ][ 3, 1, 19 ][] [ 285, 6, 1 ][ 3, 1, 1 ][] [ 285, 7, 1 ][ 3, 3, 1 ][] Total time: 21.520 seconds, Total memory usage: 6.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:22:20 2003 Input: N:=262; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; if Dimension(A[i]) eq 1 then print LocalInformation(EllipticCurve(A[i]),n[j][1]); end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:22:15 on modular [Seed = 667112132] ------------------------------------- >> then print LocalInformation(EllipticCurve(A[i]),n[j][1]); end if; ^ User error: Identifier 'j' has not been declared or assigned Total time: 5.149 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:24:31 2003 Input: N:=262; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); if Dimension(A[i]) eq 1 then print LocalInformation(EllipticCurve(A[i]),n[j][1]); end if; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:24:21 on modular [Seed = 684481609] ------------------------------------- <2, 1, 1, 1, I1> [ 262, 1, 1 ][ 2, 1, 1 ][] <2, 11, 1, 11, I11> [ 262, 2, 1 ][ 2, 11, 1 ][] [ 262, 3, 1 ][ 2, 1, 3 ][] [ 262, 4, 1 ][ 2, 1, 313 ][] [ 262, 5, 1 ][ 2, 33, 1 ][] [ 262, 6, 1 ][ 2, 1, 1 ][] Total time: 9.829 seconds, Total memory usage: 5.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 12:25:52 2003 Input: N:=274; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); if Dimension(A[i]) eq 1 then print LocalInformation(EllipticCurve(A[i]),n[j][1]); end if; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 12:25:41 on modular [Seed = 1037650316] ------------------------------------- <2, 2, 1, 2, I2> [ 274, 1, 1 ][ 2, 1, 1 ][] <2, 11, 1, 1, I11> [ 274, 2, 1 ][ 2, 1, 11 ][] <2, 7, 1, 7, I7> [ 274, 3, 1 ][ 2, 7, 1 ][] [ 274, 4, 1 ][ 2, 1, 109 ][] [ 274, 5, 1 ][ 2, 3427, 1 ][] Total time: 10.859 seconds, Total memory usage: 5.56MB ************** MAGMA ***************** Host AMarseille-108-1-29-56.w81-250.abo.wanadoo.fr. (81.250.140.56) Time: Sat Dec 13 12:35:49 2003 Input: 123^12 Output: Magma V2.10-6 Sat Dec 13 2003 12:35:45 on modular [Seed = 318136519] ------------------------------------- 11991163848716906297072721 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 16:55:32 2003 Input: : N:=274; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; RealTamagawaNumber(A[i]); end for; Output: Magma V2.10-6 Sat Dec 13 2003 16:55:29 on modular [Seed = 1404561056] ------------------------------------- >> : N:=274; ^ User error: bad syntax >> n:=Factorization(N); ^ User error: Identifier 'N' has not been declared or assigned >> uspidalSubspace(ModularSymbols(N,2,+1))))); ^ User error: Identifier 'N' has not been declared or assigned >> for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; ^ User error: Identifier 'A' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 16:55:55 2003 Input: N:=274; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; RealTamagawaNumber(A[i]); end for; Output: Magma V2.10-6 Sat Dec 13 2003 16:55:44 on modular [Seed = 1539305113] ------------------------------------- [ 274, 1, 1 ][ 2, 1, 1 ][] >> RealTamagawaNumber(A[i]); ^ Runtime error in 'RealTamagawaNumber': Argument 1 must have sign 0. Total time: 10.929 seconds, Total memory usage: 5.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:18:52 2003 Input: N:=274; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); if Dimension(A[i]) eq 1 then print TorsionSubgroup(EllipticCurve(A[i])); end if; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:18:41 on modular [Seed = 3290459047] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 [ 274, 1, 1 ][ 2, 1, 1 ][] Abelian Group of order 1 [ 274, 2, 1 ][ 2, 1, 11 ][] Abelian Group of order 1 [ 274, 3, 1 ][ 2, 7, 1 ][] [ 274, 4, 1 ][ 2, 1, 109 ][] [ 274, 5, 1 ][ 2, 3427, 1 ][] Total time: 11.149 seconds, Total memory usage: 5.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:26:29 2003 Input: N:=274; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); if Dimension(A[i]) eq 1 then print Order(TorsionSubgroup(EllipticCurve(A[i]))); end if; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:26:17 on modular [Seed = 3711529206] ------------------------------------- 2 [ 274, 1, 1 ][ 2, 1, 1 ][] 1 [ 274, 2, 1 ][ 2, 1, 11 ][] 1 [ 274, 3, 1 ][ 2, 7, 1 ][] [ 274, 4, 1 ][ 2, 1, 109 ][] [ 274, 5, 1 ][ 2, 3427, 1 ][] Total time: 11.340 seconds, Total memory usage: 5.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:26:49 2003 Input: N:=274; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); if Dimension(A[i]) eq 1 then print Order(TorsionSubgroup(EllipticCurve(A[i]))); end if; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:26:38 on modular [Seed = 650283801] ------------------------------------- 2 [ 274, 1, 1 ][ 2, 1, 1 ][] 1 [ 274, 2, 1 ][ 2, 1, 11 ][] 1 [ 274, 3, 1 ][ 2, 7, 1 ][] [ 274, 4, 1 ][ 2, 1, 109 ][] [ 274, 5, 1 ][ 2, 3427, 1 ][] Total time: 11.269 seconds, Total memory usage: 5.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:27:20 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); if Dimension(A[i]) eq 1 then print Order(TorsionSubgroup(EllipticCurve(A[i]))); end if; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:27:05 on modular [Seed = 785023798] ------------------------------------- 2 [ 114, 1, 1 ][ 2, 1, 1 ][] 4 [ 114, 2, 1 ][ 2, 5, 1 ][] 6 [ 114, 3, 1 ][ 2, 3, 1 ][] Total time: 15.479 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Sat Dec 13 17:28:40 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); if Dimension(A[i]) eq 1 then print Order(TorsionSubgroup(EllipticCurve(A[i]))); end if; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:28:23 on modular [Seed = 919772063] ------------------------------------- 2 [ 114, 1, 1 ][ 2, 1, 1 ][] 4 [ 114, 2, 1 ][ 2, 5, 1 ][] 6 [ 114, 3, 1 ][ 2, 3, 1 ][] Total time: 16.279 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:41:04 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); if Dimension(A[i]) eq 1 tam[j]:= LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:41:00 on modular [Seed = 368164680] ------------------------------------- >> tam[j]:= LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); ^ User error: bad syntax >> Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); ^ User error: Identifier 'j' has not been declared or assigned >> end for; ^ User error: bad syntax >> for k in [1..#cg] do printf "%o",cg[k]; end for; print []; ^ User error: Identifier 'cg' has not been declared or assigned [] >> end for; ^ User error: bad syntax Total time: 4.479 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:43:12 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); if Dimension(A[i]) eq 1 tam[j]:= LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) );end if; Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:43:07 on modular [Seed = 502904775] ------------------------------------- >> tam[j]:= LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) );end if; ^ User error: bad syntax >> Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); ^ User error: Identifier 'j' has not been declared or assigned >> end for; ^ User error: bad syntax >> for k in [1..#cg] do printf "%o",cg[k]; end for; print []; ^ User error: Identifier 'cg' has not been declared or assigned [] >> end for; ^ User error: bad syntax Total time: 4.529 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:45:33 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); if Dimension(A[i]) eq 1 then tam[j]:= LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) );end if; Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:45:17 on modular [Seed = 1770897462] ------------------------------------- >> Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); ^ Runtime error in 'Include': Cannot lift element into sequence Total time: 15.619 seconds, Total memory usage: 4.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:47:26 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); if Dimension(A[i]) eq 1 then tam[j]:= LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); tam[j]:=Numerator(tam[j]); end if; Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:47:11 on modular [Seed = 1888803262] ------------------------------------- >> tam[j]:=Numerator(tam[j]); end if; ^ Runtime error in 'Numerator': Bad argument types Argument types given: RngIntElt Total time: 15.649 seconds, Total memory usage: 4.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:48:01 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); if Dimension(A[i]) eq 1 then tam[j]:= LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); tam[j]:=Numerator(tam[j]); end if; Include(~cg,[n[j][1],tam[j],cgo[j]/tam[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:47:45 on modular [Seed = 2023542856] ------------------------------------- >> tam[j]:=Numerator(tam[j]); end if; ^ Runtime error in 'Numerator': Bad argument types Argument types given: RngIntElt Total time: 15.709 seconds, Total memory usage: 4.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:50:34 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then mde[j]:= cgo[j]/LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:50:18 on modular [Seed = 1269818304] ------------------------------------- >> Include(~cg,[n[j][1],tam[j],mde[j]]); ^ Runtime error in 'Include': Cannot lift element into sequence Total time: 15.340 seconds, Total memory usage: 4.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:51:35 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then mde[j]:= Numerator(cgo[j]/LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) )); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 17:51:12 on modular [Seed = 1387723411] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 7795 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:52:22 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then mde[j]:= Numerator(cgo[j]/LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) )); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:52:06 on modular [Seed = 1522466157] ------------------------------------- [ 114, 1, 1 ][ 2, 1, 1 ][] [ 114, 2, 1 ][ 2, 5, 1 ][] [ 114, 3, 1 ][ 2, 3, 1 ][] Total time: 15.359 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:55:02 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=LCM(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:54:45 on modular [Seed = 2722497846] ------------------------------------- 2 [ 114, 1, 1 ][ 2, 1, 1 ][] 20 [ 114, 2, 1 ][ 2, 5, 1 ][] 6 [ 114, 3, 1 ][ 2, 3, 1 ][] Total time: 16.090 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:58:29 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=HCF(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:58:25 on modular [Seed = 2305634105] ------------------------------------- >> cm:=HCF(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); print cm; ^ User error: Identifier 'HCF' has not been declared or assigned Total time: 4.359 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 17:59:31 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=HCF(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 17:59:26 on modular [Seed = 2440378238] ------------------------------------- >> cm:=HCF(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); print cm; ^ User error: Identifier 'HCF' has not been declared or assigned Total time: 4.469 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:03:18 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:03:02 on modular [Seed = 4078392948] ------------------------------------- 1 [ 114, 1, 1 ][ 2, 1, 1 ][] 1 [ 114, 2, 1 ][ 2, 5, 5 ][] 3 [ 114, 3, 1 ][ 2, 3, 1 ][] Total time: 15.589 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:03:50 2003 Input: N:=114; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:03:33 on modular [Seed = 4213136927] ------------------------------------- [ 114, 1, 1 ][ 2, 1, 1 ][] [ 114, 2, 1 ][ 2, 5, 5 ][] [ 114, 3, 1 ][ 2, 3, 1 ][] Total time: 15.839 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:05:47 2003 Input: N:=129; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:05:32 on modular [Seed = 3324142299] ------------------------------------- [ 129, 1, 1 ][ 3, 1, 1 ][ 43, 1, 1 ][] [ 129, 2, 1 ][ 3, 3, 3 ][ 43, 1, 1 ][] [ 129, 3, 1 ][ 3, 1, 7 ][ 43, 1, 1 ][] [ 129, 4, 1 ][ 3, 11, 1 ][ 43, 1, 1 ][] Total time: 14.760 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:07:09 2003 Input: N:=134; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:06:56 on modular [Seed = 3458886271] ------------------------------------- [ 134, 1, 1 ][ 2, 1, 75 ][] [ 134, 2, 1 ][ 2, 323, 1 ][] Total time: 12.519 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:07:57 2003 Input: N:=141; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:07:40 on modular [Seed = 3593630283] ------------------------------------- [ 141, 1, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 2, 1 ][ 3, 1, 3 ][ 47, 1, 1 ][] [ 141, 3, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 4, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 141, 5, 1 ][ 3, 7, 7 ][ 47, 1, 1 ][] [ 141, 6, 1 ][ 3, 1, 43 ][ 47, 1, 1 ][] Total time: 16.809 seconds, Total memory usage: 4.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:09:36 2003 Input: N:=142; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:09:20 on modular [Seed = 3728375263] ------------------------------------- [ 142, 1, 1 ][ 2, 1, 1 ][ 71, 1, 1 ][] [ 142, 2, 1 ][ 2, 1, 3 ][ 71, 1, 1 ][] [ 142, 3, 1 ][ 2, 1, 27 ][ 71, 1, 1 ][] [ 142, 4, 1 ][ 2, 3, 1 ][ 71, 1, 1 ][] [ 142, 5, 1 ][ 2, 9, 9 ][ 71, 1, 1 ][] Total time: 15.840 seconds, Total memory usage: 4.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:11:14 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 18:10:51 on modular [Seed = 801868916] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 7951 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:11:44 2003 Input: N:=170; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:11:32 on modular [Seed = 936613043] ------------------------------------- [ 170, 1, 1 ][ 2, 1, 1 ][] [ 170, 2, 1 ][ 2, 1, 1 ][] [ 170, 3, 1 ][ 2, 1, 3 ][] [ 170, 4, 1 ][ 2, 1, 1 ][] [ 170, 5, 1 ][ 2, 21, 7 ][] [ 170, 6, 1 ][ 2, 1, 1 ][] Total time: 11.659 seconds, Total memory usage: 4.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:14:43 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A-1] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:14:27 on modular [Seed = 65511792] ------------------------------------- [ 195, 1, 1 ][ 3, 1, 7 ][] [ 195, 2, 1 ][ 3, 3, 3 ][] [ 195, 3, 1 ][ 3, 1, 1 ][] [ 195, 4, 1 ][ 3, 1, 1 ][] Total time: 16.059 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:15:47 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A-1] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:15:31 on modular [Seed = 284471971] ------------------------------------- [ 195, 1, 1 ][ 3, 1, 7 ][] [ 195, 2, 1 ][ 3, 3, 3 ][] [ 195, 3, 1 ][ 3, 1, 1 ][] [ 195, 4, 1 ][ 3, 1, 1 ][] Total time: 15.929 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:17:11 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 18:16:48 on modular [Seed = 419216088] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 7992 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:18:23 2003 Input: N:=195; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 13 2003 18:18:00 on modular [Seed = 1619313000] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 8000 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:19:10 2003 Input: N:=201; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:18:58 on modular [Seed = 1754057002] ------------------------------------- [ 201, 1, 1 ][ 3, 1, 5 ][] [ 201, 2, 1 ][ 3, 1, 1 ][] [ 201, 3, 1 ][ 3, 3, 3 ][] [ 201, 4, 1 ][ 3, 1, 19 ][] [ 201, 5, 1 ][ 3, 493, 1 ][] Total time: 11.319 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 18:21:17 2003 Input: N:=214; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sat Dec 13 2003 18:21:08 on modular [Seed = 2023545276] ------------------------------------- [ 214, 1, 1 ][ 2, 1, 5 ][] [ 214, 2, 1 ][ 2, 1, 1 ][] [ 214, 3, 1 ][ 2, 3, 1 ][] [ 214, 4, 1 ][ 2, 7, 7 ][] [ 214, 5, 1 ][ 2, 1, 109 ][] [ 214, 6, 1 ][ 2, 33, 1 ][] Total time: 8.389 seconds, Total memory usage: 4.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:10:28 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; Factorization(Numerator(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); Factorization(Numerator(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do CongruenceGroupAnemic(A[i],B[k],200); end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:10:23 on modular [Seed = 31819361] ------------------------------------- 1 >> ckeOperator(A[i],p)),+(p+1)))); ^ User error: bad syntax >> ckeOperator(A[i],p)),-(p+1)))); ^ User error: bad syntax Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 5.319 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:11:49 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; Factorization(Numerator(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1))); Factorization(Numerator(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do CongruenceGroupAnemic(A[i],B[k],200); end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:11:44 on modular [Seed = 953991159] ------------------------------------- 1 >> Factorization(Numerator(CharacteristicPolynomial(DualHeckeOperator(A[i],p)) ^ Runtime error in 'Numerator': Bad argument types Argument types given: RngUPolElt, RngIntElt >> Factorization(Numerator(CharacteristicPolynomial(DualHeckeOperator(A[i],p)) ^ Runtime error in 'Numerator': Bad argument types Argument types given: RngUPolElt, RngIntElt Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 5.309 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:12:33 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do CongruenceGroupAnemic(A[i],B[k],200); end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:12:27 on modular [Seed = 819247060] ------------------------------------- 1 [ <2, 2>, <5, 1> ] [ <2, 2>, <5, 1> ] Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 5.269 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:13:50 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; CongruenceGroupAnemic(A[i],B[k],200); end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:13:45 on modular [Seed = 684502654] ------------------------------------- 1 [ <2, 2>, <5, 1> ] [ <2, 2>, <5, 1> ] 209 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 5.449 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:24:03 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 or Numerator(g/2) ge 3 then print [ p, k, g ]; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:23:59 on modular [Seed = 1201914871] ------------------------------------- 1 [ <2, 2>, <5, 1> ] [ <2, 2>, <5, 1> ] 209 >> if g ge 2 or Numerator(g/2) ge 3 then print [ p, k, g ]; end for; ^ User error: bad syntax Total time: 3.799 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:24:26 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 or Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:24:21 on modular [Seed = 2074083233] ------------------------------------- 1 [ <2, 2>, <5, 1> ] [ <2, 2>, <5, 1> ] 209 1 [ 19, 1, 2 ] 2 [ 19, 2, 2 ] 3 [ 19, 3, 10 ] 4 [ 19, 4, 2 ] Total time: 5.169 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:25:05 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:24:59 on modular [Seed = 1837754777] ------------------------------------- 1 [ <2, 2>, <5, 1> ] [ <2, 2>, <5, 1> ] 209 1 2 3 [ 19, 3, 10 ] 4 Total time: 5.239 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:26:55 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); print[ p, f1, f2 ]; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:26:49 on modular [Seed = 1619321638] ------------------------------------- 1 >> nomial(DualHeckeOperator(A[i],p)),-(p+1)))); print[ p, f1, f2 ]; ^ Runtime error in [ ... ]: Could not find a valid universe 209 1 2 3 [ 19, 3, 10 ] 4 Total time: 5.179 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:27:09 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); print [ p, f1, f2 ]; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:27:04 on modular [Seed = 2540901600] ------------------------------------- 1 >> nomial(DualHeckeOperator(A[i],p)),-(p+1)))); print [ p, f1, f2 ]; ^ Runtime error in [ ... ]: Could not find a valid universe 209 1 2 3 [ 19, 3, 10 ] 4 Total time: 5.149 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:27:30 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); print ([ p, f1, f2 ]); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:27:25 on modular [Seed = 2406157549] ------------------------------------- 1 >> nomial(DualHeckeOperator(A[i],p)),-(p+1)))); print ([ p, f1, f2 ]); ^ Runtime error in [ ... ]: Could not find a valid universe 209 1 2 3 [ 19, 3, 10 ] 4 Total time: 5.229 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:28:18 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); print ([ p, f1, f2 ]); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:28:13 on modular [Seed = 2271413301] ------------------------------------- 1 >> nomial(DualHeckeOperator(A[i],p)),-(p+1)))); print ([ p, f1, f2 ]); ^ Runtime error in [ ... ]: Could not find a valid universe 209 1 2 3 [ 19, 3, 10 ] 4 Total time: 5.249 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:30:07 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); print ([ [< p,1>], f1, f2 ]); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); print (N*p); for k in [1..#B] do print k; g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:30:01 on modular [Seed = 3093052094] ------------------------------------- 1 [ [ <19, 1> ], [ <2, 2>, <5, 1> ], [ <2, 2>, <5, 1> ] ] 209 1 2 3 [ 19, 3, 10 ] 4 Total time: 5.379 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:31:26 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); print ([ [< p,1>], f1, f2 ]); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:31:20 on modular [Seed = 2940939736] ------------------------------------- 1 [ [ <19, 1> ], [ <2, 2>, <5, 1> ], [ <2, 2>, <5, 1> ] ] [ 19, 3, 10 ] Total time: 5.119 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:36:43 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; rp:=[]; Include(~rp,[]); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:36:38 on modular [Seed = 2722505499] ------------------------------------- 1 >> nomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~ ^ Runtime error in 'Include': Cannot lift element into sequence >> nomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~ ^ Runtime error in 'Include': Cannot lift element into sequence [ <19, 1> ][ 19, 3, 10 ] Total time: 5.169 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:37:36 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:37:31 on modular [Seed = 3661519646] ------------------------------------- 1 <19, 1><2, 2><5, 1>[ 19, 3, 10 ] Total time: 5.159 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:38:45 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:38:40 on modular [Seed = 3425193203] ------------------------------------- 1 <19, 1><2, 2><5, 1>[ 209, 3, 10 ] Total time: 5.139 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:40:08 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:40:03 on modular [Seed = 4246306193] ------------------------------------- 1 <11, 19><2, 2><5, 1>[ 209, 3, 10 ] Total time: 5.229 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:40:59 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=19; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:40:54 on modular [Seed = 4094719053] ------------------------------------- 1 <1, 19><2, 2><5, 1>[ 209, 3, 10 ] Total time: 5.179 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:42:02 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=17; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:41:56 on modular [Seed = 3959974935] ------------------------------------- 1 <1, 17><2, 2><5, 1><2, 4> Total time: 5.589 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:43:34 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=13; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:43:29 on modular [Seed = 3825212346] ------------------------------------- 1 <1, 13><2, 1><5, 1><3, 2>[ 143, 2, 9 ] Total time: 4.839 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:44:49 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:44:44 on modular [Seed = 436070027] ------------------------------------- 1 <1, 7><2, 1><5, 1><3, 1>[ 77, 2, 3 ] Total time: 4.719 seconds, Total memory usage: 4.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:50:35 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:50:31 on modular [Seed = 15007481] ------------------------------------- 1 <1, 5><5, 1><7, 1>[ 55, 2, 7 ] Total time: 4.139 seconds, Total memory usage: 4.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:51:20 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:51:16 on modular [Seed = 953992498] ------------------------------------- 1 <1, 3><5, 1><3, 1>[ 33, 1, 3 ] Total time: 3.999 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:52:20 2003 Input: N:=14; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=13; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:52:14 on modular [Seed = 819252576] ------------------------------------- 1 <1, 13><2, 1><3, 2><5, 1>[ 182, 2, 5 ] [ 182, 5, 3 ] Total time: 6.000 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:57:56 2003 Input: N:=14; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=11; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:57:50 on modular [Seed = 633461157] ------------------------------------- 1 <1, 11><2, 2><3, 1> Total time: 5.989 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 20:59:10 2003 Input: N:=14; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 20:59:06 on modular [Seed = 1437706657] ------------------------------------- 1 <1, 5><2, 1><3, 1> Total time: 4.520 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:00:24 2003 Input: N:=14; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:00:19 on modular [Seed = 1820890945] ------------------------------------- 1 <1, 3><2, 1><3, 1> Total time: 4.389 seconds, Total memory usage: 4.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:03:08 2003 Input: N:=15; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=13; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:03:01 on modular [Seed = 2474076248] ------------------------------------- 1 <1, 13><2, 4><2, 2><3, 1>[ 195, 1, 3 ] [ 195, 3, 8 ] Total time: 6.069 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:05:43 2003 Input: N:=15; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=11; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:05:37 on modular [Seed = 2220916459] ------------------------------------- 1 <1, 11><2, 4><2, 3> Total time: 6.099 seconds, Total memory usage: 4.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:06:41 2003 Input: N:=15; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:06:36 on modular [Seed = 3159901710] ------------------------------------- 1 <1, 7><2, 3> Total time: 5.009 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:07:47 2003 Input: N:=17; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=11; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:07:42 on modular [Seed = 3025161796] ------------------------------------- 1 <1, 11><2, 2><3, 1>[ 187, 1, 3 ] [ 187, 4, 3 ] Total time: 5.709 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:10:44 2003 Input: N:=17; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:10:39 on modular [Seed = 2755681573] ------------------------------------- 1 <1, 7><2, 2><3, 1>[ 119, 2, 12 ] Total time: 4.749 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:12:28 2003 Input: N:=17; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:12:23 on modular [Seed = 3694666949] ------------------------------------- 1 <1, 5><2, 3><2, 2> Total time: 4.909 seconds, Total memory usage: 4.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 13 21:13:32 2003 Input: N:=17; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sat Dec 13 2003 21:13:27 on modular [Seed = 3559926925] ------------------------------------- 1 <1, 3><2, 2> Total time: 4.169 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sat Dec 13 21:43:57 2003 Input: p:=553114664478262993662992814601370587114291; A:=40966084797429702693950460217354379157348; x:=533053314677380263196867073349308049555813; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sat Dec 13 2003 21:43:46 on modular [Seed = 3808891551] ------------------------------------- [ <2, 6>, <3, 2>, <5, 1>, <13, 1>, <257, 1>, <401, 1>, <1877, 1>, <5449, 1>, <98801, 1>, <331249, 1>, <1179259, 1>, <363158021, 1> ] Time: 7.670 Total time: 10.759 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sat Dec 13 21:49:36 2003 Input: p:=339253988826893206353360433625657116128281; A:=260361346374401909631724509038029771271344; x:=66742510291512323582483844228134433498285; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sat Dec 13 2003 21:49:29 on modular [Seed = 401860531] ------------------------------------- [ <2, 5>, <3, 1>, <7, 1>, <11, 2>, <37, 1>, <199, 1>, <769, 1>, <2087, 1>, <10223, 1>, <11279, 1>, <51797, 1>, <64717, 1>, <913471051, 1> ] Time: 4.720 Total time: 7.699 seconds, Total memory usage: 3.17MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sat Dec 13 21:50:31 2003 Input: p:=339253988826893206353360433625657116128281; A:=260361346374401909631724509038029771271344; x:=66742510291512323582483844228134433498285; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sat Dec 13 2003 21:50:23 on modular [Seed = 115537652] ------------------------------------- [ <2, 5>, <3, 1>, <7, 1>, <11, 2>, <37, 1>, <199, 1>, <769, 1>, <2087, 1>, <10223, 1>, <11279, 1>, <51797, 1>, <64717, 1>, <913471051, 1> ] Time: 4.920 Total time: 8.019 seconds, Total memory usage: 3.53MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Sat Dec 13 21:54:01 2003 Input: p:=30504342109530022290339930441561275249401; A:=9342892432085679490956563169985504595437; x:=19773273366217957565463217887580880542915; K := GF(p); A := K!A; x := K!x; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); time FactoredOrder(E); Output: Magma V2.10-6 Sat Dec 13 2003 21:53:50 on modular [Seed = 1539290360] ------------------------------------- [ <2, 2>, <3, 4>, <13, 1>, <37, 1>, <113, 1>, <1123, 1>, <9431, 1>, <247913, 1>, <497773, 1>, <508129, 1>, <2608260793, 1> ] Time: 7.710 Total time: 10.779 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:38:10 2003 Input: N:=19; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:11; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:38:07 on modular [Seed = 2154055843] ------------------------------------- 1 >> uspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:11; rp:=[]; Inclu ^ User error: bad syntax >> nomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~ ^ User error: Identifier 'p' has not been declared or assigned >> nomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~ ^ User error: Identifier 'f1' has not been declared or assigned >> nomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~ ^ User error: Identifier 'p' has not been declared or assigned >> nomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~ ^ User error: Identifier 'f2' has not been declared or assigned >> for j in [1..#rp] do printf "%o",rp[j]; end for; ^ User error: Identifier 'rp' has not been declared or assigned >> uspidalSubspace(ModularSymbols(N*p,2,+1))))); ^ User error: Identifier 'p' has not been declared or assigned >> for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 2.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:38:26 2003 Input: N:=19; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=11; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:38:21 on modular [Seed = 3093065961] ------------------------------------- 1 <1, 11><3, 2><3, 1><5, 1>[ 209, 1, 3 ] [ 209, 4, 15 ] Total time: 5.099 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:49:08 2003 Input: N:=19; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:49:03 on modular [Seed = 3644661514] ------------------------------------- 1 <1, 7><3, 2><7, 1>[ 133, 3, 3 ] [ 133, 4, 7 ] Total time: 5.149 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:50:43 2003 Input: N:=19; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:50:38 on modular [Seed = 3408858873] ------------------------------------- 1 <1, 5><3, 1><3, 2>[ 95, 2, 9 ] Total time: 4.409 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:51:49 2003 Input: N:=19; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:51:44 on modular [Seed = 3274114735] ------------------------------------- 1 <1, 3><2, 1><3, 1> Total time: 4.519 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:52:44 2003 Input: N:=19; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:52:39 on modular [Seed = 4044698698] ------------------------------------- 1 <1, 3><2, 1><3, 1> Total time: 4.459 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:52:57 2003 Input: N:=19; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:52:52 on modular [Seed = 3909954625] ------------------------------------- 1 <1, 2><3, 1>[ 38, 1, 3 ] Total time: 4.029 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:54:14 2003 Input: N:=17; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:54:10 on modular [Seed = 3775211007] ------------------------------------- 1 <1, 2><2, 2><2, 1> Total time: 4.059 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:54:48 2003 Input: N:=15; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:54:44 on modular [Seed = 519756321] ------------------------------------- 1 <1, 2><2, 2><2, 1> Total time: 4.339 seconds, Total memory usage: 4.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:55:34 2003 Input: N:=11; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:55:30 on modular [Seed = 183422531] ------------------------------------- 1 <1, 2><5, 1> Total time: 3.279 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 00:58:28 2003 Input: N:=20; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 00:58:22 on modular [Seed = 31835620] ------------------------------------- 1 <1, 7><2, 1><3, 1><5, 1>[ 140, 1, 5 ] [ 140, 2, 3 ] Total time: 5.739 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:00:47 2003 Input: N:=20; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:00:43 on modular [Seed = 819262368] ------------------------------------- 1 <1, 3><2, 1><3, 1> Total time: 4.069 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:04:27 2003 Input: N:=21; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:04:22 on modular [Seed = 1589287971] ------------------------------------- 1 <1, 7><3, 2><7, 1>[ 147, 3, 3 ] Total time: 5.439 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:06:18 2003 Input: N:=21; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:06:13 on modular [Seed = 1236110215] ------------------------------------- 1 <1, 5><2, 3><2, 2> Total time: 4.899 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:07:50 2003 Input: N:=21; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:07:45 on modular [Seed = 1101365355] ------------------------------------- 1 <1, 2><2, 2><2, 1>[ 42, 1, 8 ] Total time: 4.389 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:11:45 2003 Input: N:=23; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:11:39 on modular [Seed = 1905635697] ------------------------------------- 1 <1, 7><2, 2><11, 1><19, 1>[ 161, 3, 19 ] Total time: 5.489 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:13:02 2003 Input: N:=23; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:12:57 on modular [Seed = 1770891547] ------------------------------------- 1 <1, 5><2, 2><11, 1><5, 1>[ 115, 1, 5 ] Total time: 4.799 seconds, Total memory usage: 4.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:13:45 2003 Input: N:=23; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:13:39 on modular [Seed = 1636147689] ------------------------------------- 1 <1, 3><11, 1>[ 69, 2, 11 ] Total time: 4.339 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:15:54 2003 Input: N:=23; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:15:50 on modular [Seed = 2625610641] ------------------------------------- 1 <1, 2><11, 1><5, 1>[ 46, 1, 5 ] Total time: 4.069 seconds, Total memory usage: 4.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:17:10 2003 Input: N:=24; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:17:04 on modular [Seed = 2490870767] ------------------------------------- 1 <1, 7><2, 3> Total time: 6.439 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:18:01 2003 Input: N:=24; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:17:55 on modular [Seed = 2356130564] ------------------------------------- 1 <1, 5><2, 3><2, 2>[ 120, 2, 8 ] Total time: 5.699 seconds, Total memory usage: 4.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:19:31 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:19:24 on modular [Seed = 2221390707] ------------------------------------- 2 <1, 7><3, 2><7, 1>[ 182, 1, 7 ] [ 182, 5, 3 ] Total time: 6.019 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:22:06 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:22:00 on modular [Seed = 3025635879] ------------------------------------- 2 <1, 5><3, 2><3, 1>[ 130, 1, 3 ] Total time: 5.609 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:23:57 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:23:52 on modular [Seed = 2890895951] ------------------------------------- 2 <1, 3><3, 1><5, 1>[ 78, 1, 5 ] Total time: 4.759 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:28:27 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:28:21 on modular [Seed = 4179281383] ------------------------------------- 2 <2, 7><7, 1><3, 2>[ 182, 3, 3 ] [ 182, 4, 3 ] Total time: 6.209 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:29:37 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:29:31 on modular [Seed = 4044541345] ------------------------------------- 2 <2, 5><7, 1><5, 1>[ 130, 2, 5 ] Total time: 5.689 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:30:22 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:30:18 on modular [Seed = 3791773315] ------------------------------------- 2 <2, 3><7, 1> Total time: 4.659 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:31:03 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:30:58 on modular [Seed = 419112096] ------------------------------------- 2 <2, 3><7, 1> Total time: 4.849 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:31:20 2003 Input: N:=26; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:31:15 on modular [Seed = 284372153] ------------------------------------- 2 <2, 3><7, 1> Total time: 4.799 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:33:33 2003 Input: N:=27; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:33:27 on modular [Seed = 149631781] ------------------------------------- 1 <1, 7><3, 2><7, 1>[ 189, 2, 3 ] [ 189, 4, 3 ] [ 189, 5, 3 ] [ 189, 6, 7 ] Total time: 6.039 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:37:06 2003 Input: N:=27; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:37:00 on modular [Seed = 98975506] ------------------------------------- 1 <1, 5><2, 1><3, 1>[ 135, 3, 3 ] [ 135, 4, 3 ] Total time: 5.269 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:39:10 2003 Input: N:=27; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:39:05 on modular [Seed = 1037961134] ------------------------------------- 1 <1, 2><3, 1>[ 54, 1, 3 ] [ 54, 2, 3 ] Total time: 4.279 seconds, Total memory usage: 4.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:41:07 2003 Input: N:=29; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:41:01 on modular [Seed = 768481226] ------------------------------------- 1 <1, 7><2, 3><7, 1>[ 203, 5, 7 ] Total time: 5.809 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:43:33 2003 Input: N:=29; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:43:28 on modular [Seed = 633740463] ------------------------------------- 1 <1, 5><7, 2><5, 2>[ 145, 2, 7 ] [ 145, 3, 25 ] Total time: 5.439 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:47:27 2003 Input: N:=29; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:47:23 on modular [Seed = 1454730807] ------------------------------------- 1 <1, 3><7, 1><23, 1>[ 87, 2, 23 ] Total time: 4.489 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:48:24 2003 Input: N:=29; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:48:19 on modular [Seed = 1319991015] ------------------------------------- 1 <1, 2><2, 1><7, 1> Total time: 4.549 seconds, Total memory usage: 4.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:49:52 2003 Input: N:=30; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:49:43 on modular [Seed = 1185247579] ------------------------------------- 1 <1, 7><2, 2><3, 1>[ 210, 2, 12 ] [ 210, 4, 12 ] Total time: 9.479 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:52:57 2003 Input: N:=31; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=7; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:52:51 on modular [Seed = 1619220409] ------------------------------------- 1 <1, 7><5, 1><19, 1><31, 1>[ 217, 2, 19 ] [ 217, 4, 31 ] Total time: 5.479 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:55:14 2003 Input: N:=31; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:55:08 on modular [Seed = 2625612490] ------------------------------------- 1 <1, 5><5, 2><7, 2>[ 155, 3, 5 ] [ 155, 4, 49 ] Total time: 5.549 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:57:14 2003 Input: N:=31; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:57:09 on modular [Seed = 2507580234] ------------------------------------- 1 <1, 3><2, 2><5, 1> Total time: 4.739 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:57:44 2003 Input: N:=31; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:57:39 on modular [Seed = 2372844404] ------------------------------------- 1 <1, 2><5, 1><11, 1>[ 62, 2, 11 ] Total time: 4.399 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 01:58:48 2003 Input: N:=32; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 01:58:43 on modular [Seed = 3126431619] ------------------------------------- 1 <1, 5><2, 3><2, 2>[ 160, 3, 8 ] Total time: 5.629 seconds, Total memory usage: 4.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:00:50 2003 Input: N:=32; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:00:45 on modular [Seed = 2856951597] ------------------------------------- 1 <1, 3><2, 2> Total time: 4.749 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:01:41 2003 Input: N:=33; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:01:35 on modular [Seed = 3493061893] ------------------------------------- 1 <1, 5><2, 3><2, 2> Total time: 6.049 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:02:34 2003 Input: N:=33; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:02:29 on modular [Seed = 3358325975] ------------------------------------- 1 <1, 2><2, 1><2, 2> Total time: 4.919 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:05:52 2003 Input: N:=34; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:05:46 on modular [Seed = 4246653229] ------------------------------------- 1 <1, 5><2, 1><3, 1>[ 170, 1, 6 ] [ 170, 3, 3 ] [ 170, 5, 3 ] Total time: 6.439 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:08:40 2003 Input: N:=34; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:08:34 on modular [Seed = 4111910557] ------------------------------------- 1 <1, 3><2, 1><3, 1>[ 102, 2, 6 ] Total time: 5.559 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:11:05 2003 Input: N:=35; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:11:00 on modular [Seed = 250428435] ------------------------------------- 2 <1, 3><3, 1><5, 1>[ 105, 2, 5 ] Total time: 4.859 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:13:21 2003 Input: N:=35; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:13:16 on modular [Seed = 115684499] ------------------------------------- 2 <1, 2><3, 1> Total time: 4.679 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:14:04 2003 Input: N:=35; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:13:59 on modular [Seed = 1054674064] ------------------------------------- 2 <2, 3><2, 4> Total time: 4.869 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:15:07 2003 Input: N:=35; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:15:02 on modular [Seed = 717822149] ------------------------------------- 2 <2, 2><2, 3><2, 1> Total time: 4.649 seconds, Total memory usage: 4.27MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:15:57 2003 Input: N:=36; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:15:50 on modular [Seed = 633738266] ------------------------------------- 1 <1, 5><2, 1><3, 1>[ 180, 1, 6 ] Total time: 6.369 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:21:44 2003 Input: N:=37; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:21:39 on modular [Seed = 1134588889] ------------------------------------- 2 <1, 5><2, 3><2, 2>[ 185, 5, 8 ] Total time: 5.689 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:25:18 2003 Input: N:=37; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:25:14 on modular [Seed = 2140950588] ------------------------------------- 2 <1, 3><7, 1>[ 111, 2, 7 ] Total time: 4.599 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:25:26 2003 Input: N:=37; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:25:21 on modular [Seed = 2006210575] ------------------------------------- 2 <1, 3><7, 1>[ 111, 2, 7 ] Total time: 4.609 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:26:34 2003 Input: N:=37; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:26:30 on modular [Seed = 1854751185] ------------------------------------- 2 <1, 2><5, 1>[ 74, 2, 5 ] Total time: 4.489 seconds, Total memory usage: 4.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:30:20 2003 Input: N:=37; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=5; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:30:14 on modular [Seed = 2675749120] ------------------------------------- 2 <2, 5><2, 1><3, 1>[ 185, 4, 6 ] Total time: 5.869 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:32:01 2003 Input: N:=37; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=3; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:31:57 on modular [Seed = 2524297314] ------------------------------------- 2 <2, 3><3, 1><5, 1>[ 111, 1, 5 ] Total time: 4.589 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 02:34:56 2003 Input: N:=37; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=2; p:=2; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Sun Dec 14 2003 02:34:51 on modular [Seed = 2389549836] ------------------------------------- 2 <2, 2><3, 1>[ 74, 1, 3 ] Total time: 4.479 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:16:44 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(37,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(74,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Sun Dec 14 2003 11:16:37 on modular [Seed = 1619252186] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 4.599 seconds, Total memory usage: 4.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:17:32 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(37,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(111,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Sun Dec 14 2003 11:17:28 on modular [Seed = 469281119] ------------------------------------- Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 4.529 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:18:08 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(29,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(145,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Sun Dec 14 2003 11:18:03 on modular [Seed = 334537076] ------------------------------------- Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 4.559 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:18:53 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(17,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(187,2,+1))))); CongruenceGroupAnemic(A[1],B[4],200); Output: Magma V2.10-6 Sun Dec 14 2003 11:18:48 on modular [Seed = 199801151] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 4.789 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:19:36 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Sun Dec 14 2003 11:19:31 on modular [Seed = 65057228] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Total time: 4.839 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:19:46 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Sun Dec 14 2003 11:19:41 on modular [Seed = 1004046842] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Total time: 4.799 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:24:42 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); R:=PolynomialRing(GF(19)); Factorization(!CharacteristicPolynomial(DualHeckeOperator(B[2],2))); Output: Magma V2.10-6 Sun Dec 14 2003 11:24:39 on modular [Seed = 734567088] ------------------------------------- >> Factorization(!CharacteristicPolynomial(DualHeckeOperator(B[2],2))); ^ User error: bad syntax Total time: 3.839 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:24:59 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); R:=PolynomialRing(GF(19)); Factorization(CharacteristicPolynomial(DualHeckeOperator(B[2],2))); Output: Magma V2.10-6 Sun Dec 14 2003 11:24:55 on modular [Seed = 599823016] ------------------------------------- [ <$.1^3 + 3*$.1^2 - 3, 1> ] Total time: 3.899 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:25:28 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); R:=PolynomialRing(GF(19)); Factorization!(CharacteristicPolynomial(DualHeckeOperator(B[2],2))); Output: Magma V2.10-6 Sun Dec 14 2003 11:25:24 on modular [Seed = 3610535551] ------------------------------------- >> Factorization!(CharacteristicPolynomial(DualHeckeOperator(B[2],2))); ^ Runtime error in '!': Illegal coercion Total time: 3.909 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:27:14 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); R:=PolynomialRing(GF(19)); Factorization(R!CharacteristicPolynomial(DualHeckeOperator(B[2],2))); Output: Magma V2.10-6 Sun Dec 14 2003 11:27:10 on modular [Seed = 3358292170] ------------------------------------- [ , , ] Total time: 3.959 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:29:51 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); R:=PolynomialRing(GF(19)); Factorization(R!CharacteristicPolynomial(DualHeckeOperator(B[2],2))); A:SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); CharacteristicPolynomial(DualHeckeOperator(A[1],2)); Output: Magma V2.10-6 Sun Dec 14 2003 11:29:47 on modular [Seed = 3223548007] ------------------------------------- [ , , ] >> A:SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(Modul ^ User error: bad syntax >> CharacteristicPolynomial(DualHeckeOperator(A[1],2));; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.829 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:30:07 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); R:=PolynomialRing(GF(19)); Factorization(R!CharacteristicPolynomial(DualHeckeOperator(B[2],2))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); CharacteristicPolynomial(DualHeckeOperator(A[1],2)); Output: Magma V2.10-6 Sun Dec 14 2003 11:30:03 on modular [Seed = 4145305760] ------------------------------------- [ , , ] $.1^2 - $.1 - 1 Total time: 3.899 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:31:02 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); R:=PolynomialRing(GF(19)); Factorization(R!CharacteristicPolynomial(DualHeckeOperator(B[2],2))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); Factorization(R!CharacteristicPolynomial(DualHeckeOperator(A[1],2))); Output: Magma V2.10-6 Sun Dec 14 2003 11:30:58 on modular [Seed = 3893053430] ------------------------------------- [ , , ] [ , ] Total time: 3.939 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:38:47 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],2)),3))); Output: Magma V2.10-6 Sun Dec 14 2003 11:38:43 on modular [Seed = 2642292946] ------------------------------------- [ <3, 1>, <17, 1> ] Total time: 3.969 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:39:30 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],2)),-3))); Output: Magma V2.10-6 Sun Dec 14 2003 11:39:26 on modular [Seed = 2507553015] ------------------------------------- [ <3, 1> ] Total time: 3.899 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:39:56 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(47,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],2)),3))); Output: Magma V2.10-6 Sun Dec 14 2003 11:39:53 on modular [Seed = 2372804744] ------------------------------------- >> al(DualHeckeOperator(B[2],2)),3))); ^ Runtime error in '[]': Sequence element 2 not defined Total time: 3.029 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:40:09 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(47,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[1],2)),3))); Output: Magma V2.10-6 Sun Dec 14 2003 11:40:06 on modular [Seed = 3160347014] ------------------------------------- [ <23, 1> ] Total time: 3.099 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:41:03 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],2)),3))); Output: Magma V2.10-6 Sun Dec 14 2003 11:41:00 on modular [Seed = 3042318453] ------------------------------------- [ <3, 1>, <17, 1> ] Total time: 3.849 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:41:33 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(215,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],2)),3))); Output: Magma V2.10-6 Sun Dec 14 2003 11:41:29 on modular [Seed = 2907570248] ------------------------------------- [ <3, 1>, <11, 1> ] Total time: 3.889 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:42:23 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(218,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[4],2)),3))); Output: Magma V2.10-6 Sun Dec 14 2003 11:42:18 on modular [Seed = 2772830227] ------------------------------------- [ <2, 2> ] Total time: 4.779 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:42:51 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(218,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[4],3)),4))); Output: Magma V2.10-6 Sun Dec 14 2003 11:42:46 on modular [Seed = 1522136583] ------------------------------------- [ <5, 1> ] Total time: 4.669 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:43:25 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(218,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[4],5)),6))); Output: Magma V2.10-6 Sun Dec 14 2003 11:43:21 on modular [Seed = 1387396640] ------------------------------------- [ <2, 2>, <5, 1> ] Total time: 4.709 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:45:07 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(218,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(109,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Sun Dec 14 2003 11:45:01 on modular [Seed = 1320018584] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Abelian Group of order 1 Total time: 5.889 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:48:24 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(274,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[4],3)),4))); Output: Magma V2.10-6 Sun Dec 14 2003 11:48:18 on modular [Seed = 1168567884] ------------------------------------- [ <2, 2>, <5, 1> ] Total time: 5.209 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:48:32 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(274,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[4],3)),4))); Output: Magma V2.10-6 Sun Dec 14 2003 11:48:26 on modular [Seed = 2107561596] ------------------------------------- [ <2, 2>, <5, 1> ] Total time: 5.169 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:48:45 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(74,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[4],3)),4))); Output: Magma V2.10-6 Sun Dec 14 2003 11:48:42 on modular [Seed = 1972821572] ------------------------------------- >> al(DualHeckeOperator(B[4],3)),4))); ^ Runtime error in '[]': Sequence element 4 not defined Total time: 3.559 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:49:04 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(74,2,+1))))); Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],3)),4))); Output: Magma V2.10-6 Sun Dec 14 2003 11:49:01 on modular [Seed = 1838073419] ------------------------------------- [ <19, 1> ] Total time: 3.599 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:57:18 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(74,2,+1))))); s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],3)),4))); fs:=1; for j in [1..#s] fs:=fs*s[j][1]; end for; tam:=TamagawaNumber(B[2],2); cm:=GCD(tam,fs); Output: Magma V2.10-6 Sun Dec 14 2003 11:57:07 on modular [Seed = 368491565] ------------------------------------- >> omial(DualHeckeOperator(B[2],3)),4))); fs:=1; for j in [1..#s] fs:=fs*s[j][ ^ User error: bad syntax Total time: 10.609 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:57:39 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(74,2,+1))))); s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],3)),4))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; tam:=TamagawaNumber(B[2],2); cm:=GCD(tam,fs); Output: Magma V2.10-6 Sun Dec 14 2003 11:57:28 on modular [Seed = 233743406] ------------------------------------- Total time: 10.599 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 11:58:41 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(74,2,+1))))); s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],3)),4))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; tam:=TamagawaNumber(B[2],2); print tam; cm:=GCD(tam,fs); print cm; Output: Magma V2.10-6 Sun Dec 14 2003 11:58:30 on modular [Seed = 99003624] ------------------------------------- 19 95 19 Total time: 11.379 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:07:44 2003 Input: N:=74; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then q:=3; s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(B[2],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; tam:=TamagawaNumber(B[2],2); print tam; cm:=GCD(tam,fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:07:40 on modular [Seed = 3695147867] ------------------------------------- >> omial(DualHeckeOperator(B[2],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs* ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.709 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:08:09 2003 Input: N:=74; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then q:=3; s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; tam:=TamagawaNumber(B[2],2); print tam; cm:=GCD(tam,fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:08:06 on modular [Seed = 3560403833] ------------------------------------- >> tam:=TamagawaNumber(B[2],2); print tam; ^ User error: Identifier 'B' has not been declared or assigned Total time: 3.579 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:09:08 2003 Input: N:=74; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then q:=3; s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; tam:=TamagawaNumber(A[i],2); print tam; cm:=GCD(tam,fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:08:56 on modular [Seed = 3425659583] ------------------------------------- 3 1 1 >> Include(~cg,[n[j][1],tam[j],mde[j]]); ^ Runtime error in '[]': Bad argument types Total time: 11.459 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:09:55 2003 Input: N:=74; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then q:=3; s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; tam:=TamagawaNumber(A[i],2); print tam; cm:=GCD(tam,fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:09:43 on modular [Seed = 3290915527] ------------------------------------- 3 1 1 >> Include(~cg,[n[j][1],tam[j],mde[j]]); ^ Runtime error in '[]': Bad argument types Total time: 11.059 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:12:39 2003 Input: N:=74; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then q:=3; s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; cm:=GCD(tam[j],fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:12:23 on modular [Seed = 4095169112] ------------------------------------- 3 1 3 3 [ 74, 1, 1 ][ 2, 1, 9 ][ 37, 3, 1 ][] 19 19 19 1 [ 74, 2, 1 ][ 2, 95, 5 ][ 37, 1, 1 ][] Total time: 15.109 seconds, Total memory usage: 3.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:14:47 2003 Input: N:=111; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; cm:=GCD(tam[j],fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:14:33 on modular [Seed = 3960424910] ------------------------------------- 2 1 2 1 [ 111, 1, 1 ][ 3, 1, 5 ][ 37, 1, 1 ][] 38 19 38 1 [ 111, 2, 1 ][ 3, 133, 7 ][ 37, 1, 1 ][] Total time: 14.259 seconds, Total memory usage: 3.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:16:36 2003 Input: N:=134; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; cm:=GCD(tam[j],fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:16:15 on modular [Seed = 2675718683] ------------------------------------- 3 1 3 3 [ 134, 1, 1 ][ 2, 1, 75 ][ 67, 3, 1 ][] 17 17 17 1 [ 134, 2, 1 ][ 2, 323, 19 ][ 67, 1, 1 ][] Total time: 21.100 seconds, Total memory usage: 3.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:18:40 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(134,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); Output: Magma V2.10-6 Sun Dec 14 2003 12:18:35 on modular [Seed = 2338860987] ------------------------------------- Abelian Group of order 1 Total time: 5.000 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:20:47 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(134,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); CongruenceGroupAnemic(A[1],B[2],200); TamagawaNumber(B[2],2); Output: Magma V2.10-6 Sun Dec 14 2003 12:20:33 on modular [Seed = 2221350974] ------------------------------------- Abelian Group of order 1 323 Total time: 13.349 seconds, Total memory usage: 5.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:21:37 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(134,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Sun Dec 14 2003 12:21:24 on modular [Seed = 3008368892] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 323 Total time: 13.049 seconds, Total memory usage: 5.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:23:47 2003 Input: N:=86; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; cm:=GCD(tam[j],fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:23:32 on modular [Seed = 2823490407] ------------------------------------- 15 1 15 3 [ 86, 1, 1 ][ 2, 1, 21 ][ 43, 3, 1 ][] 11 11 11 1 [ 86, 2, 1 ][ 2, 55, 5 ][ 43, 1, 1 ][] Total time: 15.099 seconds, Total memory usage: 3.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:25:05 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(86,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Sun Dec 14 2003 12:24:53 on modular [Seed = 2688746270] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 55 Total time: 11.809 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:27:15 2003 Input: N:=111; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; cm:=GCD(tam[j],fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:27:01 on modular [Seed = 1387393133] ------------------------------------- 2 1 2 1 [ 111, 1, 1 ][ 3, 1, 5 ][ 37, 1, 1 ][] 38 19 38 1 [ 111, 2, 1 ][ 3, 133, 7 ][ 37, 1, 1 ][] Total time: 14.179 seconds, Total memory usage: 3.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:28:42 2003 Input: N:=122; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; print fs; cm:=GCD(tam[j],fs); print cm; mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:28:22 on modular [Seed = 1252649126] ------------------------------------- [ 122, 1, 1 ][ 2, 1, 1 ][ 61, 1, 1 ][] 3 1 3 3 [ 122, 2, 1 ][ 2, 1, 39 ][ 61, 3, 1 ][] 62 31 62 1 [ 122, 3, 1 ][ 2, 31, 1 ][ 61, 1, 1 ][] Total time: 19.629 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:30:56 2003 Input: N:=134; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:30:34 on modular [Seed = 1168565285] ------------------------------------- [ 134, 1, 1 ][ 2, 1, 75 ][ 67, 3, 1 ][] [ 134, 2, 1 ][ 2, 323, 19 ][ 67, 1, 1 ][] Total time: 20.680 seconds, Total memory usage: 3.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:31:26 2003 Input: N:=134; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:31:04 on modular [Seed = 1922159472] ------------------------------------- [ 134, 1, 1 ][ 2, 1, 75 ][ 67, 3, 1 ][] [ 134, 2, 1 ][ 2, 323, 19 ][ 67, 1, 1 ][] Total time: 20.959 seconds, Total memory usage: 3.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:32:47 2003 Input: N:=145; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:32:32 on modular [Seed = 1787415424] ------------------------------------- [ 145, 1, 1 ][ 5, 1, 1 ][ 29, 1, 1 ][] [ 145, 2, 1 ][ 5, 7, 1 ][ 29, 1, 1 ][] [ 145, 3, 1 ][ 5, 1, 25 ][ 29, 1, 1 ][] [ 145, 4, 1 ][ 5, 5, 1 ][ 29, 1, 1 ][] Total time: 15.359 seconds, Total memory usage: 4.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:35:20 2003 Input: N:=146; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:34:57 on modular [Seed = 1652671097] ------------------------------------- [ 146, 1, 1 ][ 2, 1, 27 ][ 73, 3, 1 ][] [ 146, 2, 1 ][ 2, 703, 19 ][ 73, 1, 1 ][] Total time: 22.149 seconds, Total memory usage: 3.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:36:23 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(146,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(73,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Sun Dec 14 2003 12:36:08 on modular [Seed = 536657869] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 703 Total time: 15.019 seconds, Total memory usage: 5.15MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:37:52 2003 Input: N:=159; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:37:32 on modular [Seed = 401913745] ------------------------------------- [ 159, 1, 1 ][ 3, 63, 21 ][ 53, 1, 1 ][] [ 159, 2, 1 ][ 3, 1, 107 ][ 53, 1, 1 ][] Total time: 20.000 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:38:51 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(159,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(53,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[1],200); end for; TamagawaNumber(B[1],3); Output: Magma V2.10-6 Sun Dec 14 2003 12:38:42 on modular [Seed = 267161719] ------------------------------------- Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 63 Total time: 9.550 seconds, Total memory usage: 5.27MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:43:46 2003 Input: N:=183; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:43:24 on modular [Seed = 1071423833] ------------------------------------- [ 183, 1, 1 ][ 3, 1, 1 ][ 61, 1, 1 ][] [ 183, 2, 1 ][ 3, 1, 19 ][ 61, 1, 1 ][] [ 183, 3, 1 ][ 3, 93, 3 ][ 61, 1, 1 ][] Total time: 22.489 seconds, Total memory usage: 4.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:44:51 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(183,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(61,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for; TamagawaNumber(B[3],3); Output: Magma V2.10-6 Sun Dec 14 2003 12:44:39 on modular [Seed = 936684010] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 93 Total time: 12.139 seconds, Total memory usage: 5.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:46:49 2003 Input: N:=187; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:46:28 on modular [Seed = 549699214] ------------------------------------- [ 187, 1, 1 ][ 11, 1, 3 ][ 17, 1, 1 ][] [ 187, 2, 1 ][ 11, 3, 1 ][ 17, 1, 1 ][] [ 187, 3, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] [ 187, 4, 1 ][ 11, 3, 3 ][ 17, 1, 1 ][] [ 187, 5, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] [ 187, 6, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] Total time: 21.000 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:47:13 2003 Input: N:=187; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:46:52 on modular [Seed = 3627763086] ------------------------------------- [ 187, 1, 1 ][ 11, 1, 3 ][ 17, 1, 1 ][] [ 187, 2, 1 ][ 11, 3, 1 ][ 17, 1, 1 ][] [ 187, 3, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] [ 187, 4, 1 ][ 11, 3, 3 ][ 17, 1, 1 ][] [ 187, 5, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] [ 187, 6, 1 ][ 11, 1, 1 ][ 17, 1, 1 ][] Total time: 20.879 seconds, Total memory usage: 4.86MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:48:34 2003 Input: N:=190; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:48:23 on modular [Seed = 3493023213] ------------------------------------- [ 190, 1, 1 ][ 2, 1, 1 ][] [ 190, 2, 1 ][ 2, 11, 11 ][] [ 190, 3, 1 ][ 2, 3, 1 ][] [ 190, 4, 1 ][ 2, 1, 13 ][] Total time: 11.309 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:49:33 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(190,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Sun Dec 14 2003 12:49:20 on modular [Seed = 3358283058] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 11 Total time: 12.750 seconds, Total memory usage: 6.48MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:50:51 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(190,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(95,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Sun Dec 14 2003 12:50:38 on modular [Seed = 4179256397] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 11 Total time: 12.719 seconds, Total memory usage: 6.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:53:21 2003 Input: N:=195; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Dec 14 2003 12:52:58 on modular [Seed = 4128598742] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 26028 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:54:46 2003 Input: N:=194; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Dec 14 2003 12:54:23 on modular [Seed = 3993858683] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 26036 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:55:19 2003 Input: N:=194; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:55:15 on modular [Seed = 2591621571] ------------------------------------- >> cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); ^ Runtime error in '[]': Sequence element 3 not defined Total time: 4.479 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:56:22 2003 Input: N:=194; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 12:56:06 on modular [Seed = 2473593087] ------------------------------------- [ 194, 3, 1 ][ 2, 3479, 497 ][] Total time: 15.869 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:57:08 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(194,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(97,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for; TamagawaNumber(B[3],2); Output: Magma V2.10-6 Sun Dec 14 2003 12:56:50 on modular [Seed = 2338853043] ------------------------------------- Abelian Group isomorphic to Z/71 Defined on 1 generator Relations: 71*$.1 = 0 Abelian Group of order 1 3479 Total time: 17.319 seconds, Total memory usage: 5.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 12:58:46 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(194,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(97,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for; TamagawaNumber(B[3],2); 3479/(7*71); Output: Magma V2.10-6 Sun Dec 14 2003 12:58:29 on modular [Seed = 2204112924] ------------------------------------- Abelian Group isomorphic to Z/71 Defined on 1 generator Relations: 71*$.1 = 0 Abelian Group of order 1 3479 7 Total time: 16.930 seconds, Total memory usage: 5.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:00:50 2003 Input: N:=197; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:00:47 on modular [Seed = 3008375206] ------------------------------------- [ 197, 1, 1 ][] [ 197, 2, 1 ][ 197, 1, 1 ][] [ 197, 3, 1 ][ 197, 49, 7 ][] Total time: 3.599 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:02:19 2003 Input: N:=201; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Dec 14 2003 13:01:56 on modular [Seed = 1572784016] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 26116 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:03:04 2003 Input: N:=201; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [5..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Dec 14 2003 13:02:41 on modular [Seed = 1438044109] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 26124 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:04:19 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(201,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; TamagawaNumber(B[5],3); Factorization(493); Output: Magma V2.10-6 Sun Dec 14 2003 13:04:06 on modular [Seed = 1303303170] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 493 [ <17, 1>, <29, 1> ] Total time: 12.579 seconds, Total memory usage: 5.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:05:35 2003 Input: N:=201; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [5..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:05:22 on modular [Seed = 2056905537] ------------------------------------- [ 201, 5, 1 ][ 3, 493, 29 ][] Total time: 11.399 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:06:30 2003 Input: N:=202; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:06:22 on modular [Seed = 1972825266] ------------------------------------- [ 202, 3, 1 ][ 2, 51, 1 ][] Total time: 8.099 seconds, Total memory usage: 4.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:07:38 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(202,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(101,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for; TamagawaNumber(B[3],2); Output: Magma V2.10-6 Sun Dec 14 2003 13:07:28 on modular [Seed = 1838085332] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 51 Total time: 9.689 seconds, Total memory usage: 5.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:09:29 2003 Input: N:=202; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:09:21 on modular [Seed = 1703345517] ------------------------------------- [ 202, 3, 1 ][ 2, 51, 3 ][] Total time: 8.079 seconds, Total memory usage: 4.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:11:35 2003 Input: N:=206; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:11:20 on modular [Seed = 368479620] ------------------------------------- [ 206, 4, 1 ][ 2, 247, 19 ][] Total time: 15.050 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:12:27 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(206,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(103,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; TamagawaNumber(B[4],2); Output: Magma V2.10-6 Sun Dec 14 2003 13:12:10 on modular [Seed = 233739694] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 247 Total time: 16.489 seconds, Total memory usage: 5.97MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:14:05 2003 Input: N:=213; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..4] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:13:54 on modular [Seed = 82285375] ------------------------------------- [ 213, 4, 1 ][ 3, 45, 45 ][] Total time: 10.199 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:15:05 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(213,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(71,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; TamagawaNumber(B[4],3); Output: Magma V2.10-6 Sun Dec 14 2003 13:14:54 on modular [Seed = 1054714361] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 Defined on 2 generators Relations: 3*$.1 = 0 3*$.2 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 45 Total time: 11.399 seconds, Total memory usage: 5.73MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:16:27 2003 Input: N:=214; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [6..6] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:16:19 on modular [Seed = 768522887] ------------------------------------- [ 214, 6, 1 ][ 2, 33, 11 ][] Total time: 8.059 seconds, Total memory usage: 4.86MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:17:20 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(214,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(107,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[6],200); end for; TamagawaNumber(B[6],2); Output: Magma V2.10-6 Sun Dec 14 2003 13:17:11 on modular [Seed = 633779035] ------------------------------------- Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 33 Total time: 9.259 seconds, Total memory usage: 6.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:18:26 2003 Input: N:=215; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:18:05 on modular [Seed = 3711847385] ------------------------------------- [ 215, 2, 1 ][ 5, 11, 1 ][] Total time: 20.219 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:19:08 2003 Input: N:=217; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:18:55 on modular [Seed = 3577103107] ------------------------------------- [ 217, 2, 1 ][ 7, 19, 19 ][] Total time: 12.369 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:20:09 2003 Input: N:=218; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..4] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:19:52 on modular [Seed = 3442367324] ------------------------------------- [ 218, 4, 1 ][ 2, 205, 41 ][] Total time: 16.579 seconds, Total memory usage: 4.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:21:00 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(218,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(109,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; TamagawaNumber(B[4],2); Output: Magma V2.10-6 Sun Dec 14 2003 13:20:43 on modular [Seed = 4195970136] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Abelian Group of order 1 205 Total time: 17.420 seconds, Total memory usage: 6.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:21:55 2003 Input: N:=219; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [5..5] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Dec 14 2003 13:21:42 on modular [Seed = 4111884442] ------------------------------------- [ 219, 5, 1 ][ 3, 1073, 29 ][] Total time: 13.069 seconds, Total memory usage: 4.58MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Dec 14 13:22:50 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(219,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(73,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; TamagawaNumber(B[5],3); Output: Magma V2.10-6 Sun Dec 14 2003 13:22:36 on modular [Seed = 3977148632] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 1073 Total time: 14.389 seconds, Total memory usage: 5.83MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:07:28 2003 Input: roots(7*n^3-12*m*n^2+6*m^2*n-2*m^3) Output: Magma V2.10-6 Mon Dec 15 2003 00:07:25 on modular [Seed = 4111960874] ------------------------------------- >> roots(7*n^3-12*m*n^2+6*m^2*n-2*m^3); ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:08:22 2003 Input: roots(7*x^3-12*y*x^2+6*y^2*x-2*y^3) Output: Magma V2.10-6 Mon Dec 15 2003 00:08:19 on modular [Seed = 4246700908] ------------------------------------- >> roots(7*x^3-12*y*x^2+6*y^2*x-2*y^3); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:19:17 2003 Input: f:=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); roots(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:19:14 on modular [Seed = 3193750974] ------------------------------------- >> f:=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); roots(f); ^ User error: Identifier 'x' has not been declared or assigned >> f:=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); roots(f); ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:21:03 2003 Input: Z:=IntegerRing();S:=PolynomialRing(Z,2);x:=S.1;y:=S.2;f:=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); roots(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:21:00 on modular [Seed = 1522016695] ------------------------------------- >> :=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); roots(f); ^ User error: Identifier 'roots' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:21:15 2003 Input: Z:=IntegerRing();S:=PolynomialRing(Z,2);x:=S.1;y:=S.2;f:=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); root(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:21:12 on modular [Seed = 1168588508] ------------------------------------- >> :=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); root(f); ^ User error: Identifier 'root' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:22:12 2003 Input: Z:=IntegerRing();S:=PolynomialRing(Z,2);f:=(7*x^3-12*y*x^2+6*y^2*x-2*y^3); root(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:22:09 on modular [Seed = 1303328541] ------------------------------------- >> Z:=IntegerRing();S:=PolynomialRing(Z,2);f:=(7*x^3-12*y*x^2+6*y^2*x-2*y ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:23:08 2003 Input: Z=IntegerRing(); S := PolynomialRing(Z,2); f := (7*x^3-12*y*x^2+6*y^2*x-2*y^3); root(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:23:05 on modular [Seed = 1972834077] ------------------------------------- >> Z=IntegerRing(); S := PolynomialRing(Z,2); f := (7*x^3-12*y*x^2+6*y^2 ^ User error: Identifier 'Z' has not been declared or assigned >> Z=IntegerRing(); S := PolynomialRing(Z,2); f := (7*x^3-12*y*x^2+6*y^2 ^ User error: Identifier 'Z' has not been declared or assigned >> Z=IntegerRing(); S := PolynomialRing(Z,2); f := (7*x^3-12*y*x^2+6*y^2 ^ User error: Identifier 'x' has not been declared or assigned >> 7*x^3-12*y*x^2+6*y^2*x-2*y^3); root(f); ^ User error: Identifier 'f' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:23:41 2003 Input: Z:=IntegerRing(); S := PolynomialRing(Z,2); f := (7*x^3-12*y*x^2+6*y^2*x-2*y^3); root(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:23:38 on modular [Seed = 2107574134] ------------------------------------- >> (7*x^3-12*y*x^2+6*y^2*x-2*y^3); root(f); ^ User error: Identifier 'root' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:23:52 2003 Input: Z:=IntegerRing(); S := PolynomialRing(Z,2); f := (7*x^3-12*y*x^2+6*y^2*x-2*y^3); roots(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:23:49 on modular [Seed = 1703354193] ------------------------------------- >> (7*x^3-12*y*x^2+6*y^2*x-2*y^3); roots(f); ^ User error: Identifier 'roots' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-207-167-100-141.sndg-pm4-2.dialup.nethere.net. (207.167.100.141) Time: Mon Dec 15 00:25:41 2003 Input: Z:=IntegerRing(); S := PolynomialRing(Z,2); f := (7*x^3-12*y*x^2+6*y^2*x-2*y^3); Factorization(f) Output: Magma V2.10-6 Mon Dec 15 2003 00:25:38 on modular [Seed = 301165458] ------------------------------------- [ <7*x^3 - 12*x^2*y + 6*x*y^2 - 2*y^3, 1> ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cs6710219-166.houston.rr.com. (67.10.219.166) Time: Mon Dec 15 02:25:12 2003 Input: 2+2 Output: Magma V2.10-6 Mon Dec 15 2003 02:25:09 on modular [Seed = 953837245] ------------------------------------- 4 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (220.73.165.141) Time: Mon Dec 15 04:43:57 2003 Input: er32r32r32 Output: Magma V2.10-6 Mon Dec 15 2003 04:43:53 on modular [Seed = 536715787] ------------------------------------- >> er32r32r32; ^ User error: Identifier 'er32r32r32' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (220.73.165.141) Time: Mon Dec 15 04:44:06 2003 Input: er32r32r32 Output: Magma V2.10-6 Mon Dec 15 2003 04:44:03 on modular [Seed = 802001409] ------------------------------------- >> er32r32r32; ^ User error: Identifier 'er32r32r32' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Mon Dec 15 11:07:40 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(94,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(47,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Mon Dec 15 2003 11:07:31 on modular [Seed = 334622749] ------------------------------------- Abelian Group isomorphic to Z/47 Defined on 1 generator Relations: 47*$.1 = 0 1 Total time: 6.220 seconds, Total memory usage: 4.84MB ************** MAGMA ***************** Host cd4402709.cable.wanadoo.nl. (212.64.39.9) Time: Mon Dec 15 16:57:00 2003 Input: 2^66 Output: Magma V2.10-6 Mon Dec 15 2003 16:56:57 on modular [Seed = 2659159982] ------------------------------------- 73786976294838206464 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host bluebottle.newcastle.edu.au. (134.148.20.33) Time: Mon Dec 15 20:27:48 2003 Input: Factorial(20); Output: Magma V2.10-6 Mon Dec 15 2003 20:27:45 on modular [Seed = 785338084] ------------------------------------- 2432902008176640000 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.155.167.219) Time: Tue Dec 16 07:07:52 2003 Input: plot sin(x) Output: Magma V2.10-6 Tue Dec 16 2003 07:07:49 on modular [Seed = 1635822496] ------------------------------------- >> plot sin(x) ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:19:50 2003 Input: N:=242; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 16 2003 18:19:39 on modular [Seed = 2254842562] ------------------------------------- [ 242, 1, 1 ][ 2, 1, 1 ][] [ 242, 2, 1 ][ 2, 1, 1 ][] [ 242, 3, 1 ][ 2, 1, 3 ][] [ 242, 4, 1 ][ 2, 1, 5 ][] [ 242, 5, 1 ][ 2, 33, 3 ][] [ 242, 6, 1 ][ 2, 5, 1 ][] Total time: 10.019 seconds, Total memory usage: 5.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:23:57 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(242,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(121,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; TamagawaNumber(B[4],2); Output: Magma V2.10-6 Tue Dec 16 2003 18:23:45 on modular [Seed = 2524331480] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 1 Total time: 11.399 seconds, Total memory usage: 6.86MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:26:33 2003 Input: N:=242; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 16 2003 18:26:22 on modular [Seed = 2856976763] ------------------------------------- [ 242, 1, 1 ][ 2, 1, 1 ][] [ 242, 2, 1 ][ 2, 1, 1 ][] [ 242, 3, 1 ][ 2, 1, 3 ][] [ 242, 4, 1 ][ 2, 1, 5 ][] [ 242, 5, 1 ][ 2, 33, 3 ][] [ 242, 6, 1 ][ 2, 5, 1 ][] Total time: 9.789 seconds, Total memory usage: 5.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:27:17 2003 Input: N:=363; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 16 2003 18:26:57 on modular [Seed = 2705394223] ------------------------------------- [ 363, 1, 1 ][ 3, 1, 3 ][] [ 363, 2, 1 ][ 3, 1, 3 ][] [ 363, 3, 1 ][ 3, 1, 3 ][] [ 363, 4, 1 ][ 3, 1, 3 ][] [ 363, 5, 1 ][ 3, 1, 1 ][] [ 363, 6, 1 ][ 3, 1, 1 ][] [ 363, 7, 1 ][ 3, 5, 5 ][] [ 363, 8, 1 ][ 3, 5, 1 ][] [ 363, 9, 1 ][ 3, 5, 5 ][] [ 363, 10, 1 ][ 3, 11, 1 ][] Total time: 19.329 seconds, Total memory usage: 7.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:28:23 2003 Input: N:=560; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Tue Dec 16 2003 18:28:11 on modular [Seed = 3092779772] ------------------------------------- Do not know how to compute component group at 2 Total time: 11.679 seconds, Total memory usage: 5.25MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:29:17 2003 Input: N:=605; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 16 2003 18:28:54 on modular [Seed = 2958039753] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 28927 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:30:20 2003 Input: N:=605; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 16 2003 18:29:57 on modular [Seed = 1235870578] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 28935 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:31:04 2003 Input: N:=605; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 16 2003 18:30:41 on modular [Seed = 1488515767] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 28950 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:34:20 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(121,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(605,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Tue Dec 16 2003 18:34:09 on modular [Seed = 1370617966] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Total time: 10.239 seconds, Total memory usage: 4.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:37:11 2003 Input: N:=605; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [12..12] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 16 2003 18:36:48 on modular [Seed = 1703267643] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 28971 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Tue Dec 16 18:38:48 2003 Input: N:=605; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); TamagawaNumber(A[12],5); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 16 2003 18:38:25 on modular [Seed = 2056966725] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 28980 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ppp-66-63-130-214.sndg-c5300-4.dialup.nethere.net. (66.63.130.214) Time: Wed Dec 17 00:23:31 2003 Input: E:=EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);Generators(E) Output: Magma V2.10-6 Wed Dec 17 2003 00:23:28 on modular [Seed = 2204325023] ------------------------------------- Warning: rank computed (0) is only a lower bound (It may still be correct, though) [ (2455071434840 : 3305698655129313830 : 1) ] Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-66-63-130-214.sndg-c5300-4.dialup.nethere.net. (66.63.130.214) Time: Wed Dec 17 00:25:16 2003 Input: E:=EllipticCurve([0,586851077698033,0,-32886111111117259190017080384,0]);Generators(E) Output: Magma V2.10-6 Wed Dec 17 2003 00:25:10 on modular [Seed = 2541174893] ------------------------------------- Warning: rank computed (0) is only a lower bound (It may still be correct, though) [ (0 : 0 : 1), (-137004588403704 : 3598511142291037875000 : 1) ] Total time: 5.799 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-66-63-130-214.sndg-c5300-4.dialup.nethere.net. (66.63.130.214) Time: Wed Dec 17 00:29:11 2003 Input: E:=EllipticCurve([0,17923043717329441,0,-32530745659578681552271561958400,0]);Generators(E) Output: Magma V2.10-6 Wed Dec 17 2003 00:28:57 on modular [Seed = 2823323261] ------------------------------------- Warning: rank computed (0) is only a lower bound (It may still be correct, though) [ (0 : 0 : 1), (7601609963011680 : -1107990364308371272602720 : 1) ] Total time: 13.000 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ppp-66-63-130-214.sndg-c5300-4.dialup.nethere.net. (66.63.130.214) Time: Wed Dec 17 00:29:46 2003 Input: E:=EllipticCurve([0,33236258933233,0,-3041245986244291199359212139584,0]);Generators(E) Output: Magma V2.10-6 Wed Dec 17 2003 00:29:40 on modular [Seed = 2688579112] ------------------------------------- Warning: rank computed (0) is only a lower bound (It may still be correct, though) [ (-1760614158266929 : 0 : 1), (4181981817148296 : 246984605084870071830600 : 1) ] Total time: 5.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-66-63-130-214.sndg-c5300-4.dialup.nethere.net. (66.63.130.214) Time: Wed Dec 17 00:37:47 2003 Input: E:=EllipticCurve([0,-440293294084,0,-2337288146288640000,0]);Generators(E) Output: Magma V2.10-6 Wed Dec 17 2003 00:37:44 on modular [Seed = 1252695721] ------------------------------------- Warning: rank computed (0) is only a lower bound (It may still be correct, though) [ (0 : 0 : 1), (880599859200 : 584325558971596800 : 1) ] Total time: 3.490 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 08:48:03 2003 Input: dfsad Output: Magma V2.10-6 Wed Dec 17 2003 08:47:59 on modular [Seed = 2304174144] ------------------------------------- >> dfsad; ^ User error: Identifier 'dfsad' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 08:49:30 2003 Input: jInvariant(L) Output: Magma V2.10-6 Wed Dec 17 2003 08:49:27 on modular [Seed = 2437869616] ------------------------------------- >> jInvariant(L); ^ User error: Identifier 'L' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 08:49:46 2003 Input: L:=[1,i]; jInvariant(L) Output: Magma V2.10-6 Wed Dec 17 2003 08:49:43 on modular [Seed = 2571565096] ------------------------------------- >> L:=[1,i]; ^ User error: Identifier 'i' has not been declared or assigned >> jInvariant(L); ^ User error: Identifier 'L' has not been declared or assigned Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 08:49:48 2003 Input: L:=[1,i]; jInvariant(L); Output: Magma V2.10-6 Wed Dec 17 2003 08:49:45 on modular [Seed = 2759574811] ------------------------------------- >> L:=[1,i]; ^ User error: Identifier 'i' has not been declared or assigned >> jInvariant(L);; ^ User error: Identifier 'L' has not been declared or assigned Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 08:50:02 2003 Input: L:=[1,w]; jInvariant(L); Output: Magma V2.10-6 Wed Dec 17 2003 08:49:58 on modular [Seed = 2843134441] ------------------------------------- >> L:=[1,w]; ^ User error: Identifier 'w' has not been declared or assigned >> jInvariant(L);; ^ User error: Identifier 'L' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 08:53:40 2003 Input: ListCategories(); Output: Magma V2.10-6 Wed Dec 17 2003 08:53:37 on modular [Seed = 1151018208] ------------------------------------- GrpFrml PowGrpAlgSub Aff GrpFrmlElt PowIdl Alg GrpGPC PowIsoSch AlgAss GrpGPCElt PowMap AlgAssElt GrpLie PowMapAut AlgBas GrpLieElt PowMapSch AlgBasElt GrpMat PowModTupRng AlgChtr GrpMatBSGS PowSeqEnum AlgChtrElt GrpMatElt PowSetEnum AlgClff GrpMatProj PowSetFormal AlgClffElt GrpMatProjElt PowSetIndx AlgElt GrpPC PowSetMulti AlgExt GrpPCElt PowStr AlgExtElt GrpPCRepnProc PowerGroup AlgFP GrpPCpQuotientProc Prj AlgFPElt GrpPSL2 PrjProd AlgFPG GrpPSL2Elt PrjScrl AlgFPGElt GrpPerm Process AlgFPNew GrpPermBSGS Program AlgFPNewElt GrpPermBasim Pt AlgFPRes GrpPermCox PtEll AlgFPResElt GrpPermDcosElt PtHyp AlgGen GrpPermElt QuadBin AlgGenElt GrpPermLcosElt QuadBinElt AlgGrp GrpPermRcosElt Rec AlgGrpElt GrpPermTransProc RecField AlgGrpSub GrpRWS RecFrmt AlgLie GrpRWSElt Ref AlgLieElt GrpRandProc Rel AlgMat GrpSLP RelElt AlgMatElt GrpSLPElt Rng AlgQuat Grph RngCyc AlgQuatElt GrphDir RngCycElt AlgQuatOrd GrphEdge RngElt AlgQuatOrdElt GrphEdgeSet RngFrm AlgSym GrphNet RngFrmElt AlgSymElt GrphRes RngFunG Any GrphResVert RngFunGElt ArrAssoc GrphSpl RngFunOrd Aut GrphSplVert RngFunOrdElt AutCrvEll GrphUnd RngFunOrdG Bool GrphVert RngFunOrdGElt BoolElt GrphVertSet RngFunOrdIdl CNCMPol Hackobj RngGal CNCMPolElt HatHat RngGalElt CNCMPolG HomCrvEll RngHck CNCMPolGElt HomGrp RngHckElt CNCMPolRes HomGrpProc RngInt CNCMPolResElt Inc RngIntElt Cat IncBlk RngIntEltFact Clstr IncBlkSet RngIntRes Code IncGeom RngIntResElt Cop IncLsp RngInvar CopElt IncNsp RngInvarON CosetGeom IncPt RngInvarOld Crv IncPtSet RngLoc CrvCon Infty RngLocElt CrvEll Intrinsic RngLocEltNew CrvEllOld IsoCrvEll RngLocNew CrvEllPtOld JacHyp RngMPol CrvHyp JacHypPt RngMPolElt CrvHypOld LP RngMPolLoc CrvHypPtOld Lat RngMPolRes CrvMod LatElt RngMPolResElt CrvRat LatEnumProc RngMPolSub Crypt LatKant RngOrd CryptKey LinearSys RngOrdElt CryptTxt List RngOrdFracIdl Cyc MPI RngOrdIdl DB MPol RngOrdRes DBUser MPolElt RngOrdResElt DiffFun Map RngPad DiffFunElt MapAutSch RngPadElt DivCrv MapChn RngPadRes DivCrvElt MapCrvEll RngPadResElt DivFun MapCrvEll RngPadResExt DivFunElt MapIsoCrvEll RngPadResExtElt DivNum MapIsoSch RngPowLaz DivNumElt MapSch RngPowLazElt Dsgn Mod RngQuad Empty ModAlg RngQuadElt ExtRe ModAlgElt RngQuadFracIdl ExtReElt ModBrdt RngQuadIdl Fbr ModBrdtElt RngRelK File ModCoho RngRelKElt Fld ModComplex RngSLPol FldAC ModCpx RngSLPolElt FldACElt ModDed RngSer FldAb ModDedElt RngSerElt FldAbFun ModED RngSerLaur FldAlg ModEDElt RngSerLaurElt FldAlgElt ModElt RngSerPow FldCom ModExt RngSerPowElt FldComElt ModExtElt RngSerPuis FldCyc ModFld RngSerPuisElt FldCycElt ModFldElt RngUPol FldElt ModFrm RngUPolElt FldFin ModFrmElt RngUPolRes FldFinElt ModGrp RngUPolResElt FldFun ModGrpElt RngVal FldFunElt ModMPol RngValElt FldFunG ModMPolElt RngWitt FldFunGElt ModMatFld RngWittElt FldFunRat ModMatFldElt RootDtm FldFunRatElt ModMatGrp RootSys FldFunRatEltOld ModMatGrpElt SQProc FldFunRatMElt ModMatRng Sch FldFunRatUElt ModMatRngElt SchGrpEll FldLoc ModRng SeqEnum FldLocElt ModRngElt Set FldLocEltNew ModSS SetCart FldLocNew ModSSElt SetCsp FldNum ModSym SetCspElt FldNumElt ModSymElt SetEnum FldOrd ModTheta SetFormal FldOrdElt ModThetaElt SetGIndx FldPad ModTupFld SetIndx FldPadElt ModTupFldElt SetMulti FldPr ModTupRng SetPt FldPrElt ModTupRngElt SetPtEll FldQuad MonDivLst SetPtHyp FldQuadElt MonFP Setq FldRat MonFPElt SgpFP FldRatElt MonOrd SgpFPElt FldRe MonOrdElt Socket FldReElt MonPlc SolRepProc FldResLst MonPlcElt SpcFld FldResLstElt MonRWS SpcFldElt GSet MonRWSElt SpcHyp GSetEnum MonStg SpcHypArc Grp MonStgElt SpcHypElt GrpAb MonTbl SpcHypPgon GrpAbElt Mtrx SpcRng GrpAbGen MtrxS SpcRngElt GrpAbGenElt MtrxSpcElt SrfKum GrpAtc MtrxSprs SrfKumPt GrpAtcElt MtrxSprsStr Str GrpAuto MultiRet SubFldLat GrpAutoElt NFSProc SubFldLatElt GrpBrd NwtnPgon SubGrpLat GrpBrdClassProc NwtnPgonFace SubGrpLatElt GrpBrdElt PackageRef SubModLat GrpCayg PicCrv SubModLatElt GrpCaygElt PicCrvElt SymAlgQuat GrpDrch Plane SymCrvEll GrpDrchElt PlaneAff SymFry GrpElt PlaneLn SymGen GrpFP PlaneLnSet SymGenLoc GrpFPCos PlaneProj SymKod GrpFPCosElt PlanePt Tbl GrpFPCosetEnumProc PlanePtSet Thue GrpFPCox PlcCrv Tup GrpFPCoxElt PlcCrvElt Unassign GrpFPDcos PlcEnum UndefRef GrpFPDcosElt PlcFun UserProgram GrpFPElt PlcFunElt UserProgramShell GrpFPExtProc PlcNum VSrfK3 GrpFPHomsProc PlcNumElt VSrfK3Seq GrpFPLixProc PowAut VarargNum GrpFPTietzeProc PowAutSch GrpFPTietzeProcOld PowGSetEnum Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:00:09 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomailRing(X); f:=Y^4+y+x^5; F:=FunctionField(f); F; Output: Magma V2.10-6 Wed Dec 17 2003 09:00:06 on modular [Seed = 1384975473] ------------------------------------- >> Y:=PolynomailRing(X); ^ User error: Identifier 'PolynomailRing' has not been declared or assigned >> f:=Y^4+y+x^5; ^ User error: Identifier 'Y' has not been declared or assigned >> F:=FunctionField(f); ^ User error: Identifier 'f' has not been declared or assigned >> F;; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:00:36 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomailRing(X); f:=Y^4+y+x^5; F:=FunctionField(f); F; Signature(f); Output: Magma V2.10-6 Wed Dec 17 2003 09:00:33 on modular [Seed = 1518666910] ------------------------------------- >> Y:=PolynomailRing(X); ^ User error: Identifier 'PolynomailRing' has not been declared or assigned >> f:=Y^4+y+x^5; ^ User error: Identifier 'Y' has not been declared or assigned >> F:=FunctionField(f); ^ User error: Identifier 'f' has not been declared or assigned >> F; ^ User error: Identifier 'F' has not been declared or assigned >> Signature(f);; ^ User error: Identifier 'f' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:01:03 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomialRing(X); f:=Y^4+y+x^5; F:=FunctionField(f); F; Signature(f); Output: Magma V2.10-6 Wed Dec 17 2003 09:01:00 on modular [Seed = 1656569019] ------------------------------------- >> f:=Y^4+y+x^5; ^ Runtime error in '^': Bad argument types Argument types given: RngUPol, RngIntElt >> F:=FunctionField(f); ^ User error: Identifier 'f' has not been declared or assigned >> F; ^ User error: Identifier 'F' has not been declared or assigned >> Signature(f);; ^ User error: Identifier 'f' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:01:11 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomialRing(X); f:=Y^4+y+x^5; F:=FunctionField(f); F; Output: Magma V2.10-6 Wed Dec 17 2003 09:01:08 on modular [Seed = 81484517] ------------------------------------- >> f:=Y^4+y+x^5; ^ Runtime error in '^': Bad argument types Argument types given: RngUPol, RngIntElt >> F:=FunctionField(f); ^ User error: Identifier 'f' has not been declared or assigned >> F; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:01:31 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomialRing(X); f:=y^4+y+x^5; F:=FunctionField(f); F; Output: Magma V2.10-6 Wed Dec 17 2003 09:01:27 on modular [Seed = 215175934] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:01:50 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomialRing(X); f:=y^4+y+x^5; F:=FunctionField(f); F; Signature(F); Output: Magma V2.10-6 Wed Dec 17 2003 09:01:47 on modular [Seed = 348867226] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 >> Signature(F);; ^ Runtime error in 'Signature': Bad argument types Argument types given: FldFun Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:02:29 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomialRing(X); f:=y^4+y+x^5; F:=FunctionField(f); F; Genus(F); Output: Magma V2.10-6 Wed Dec 17 2003 09:02:26 on modular [Seed = 482558635] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:02:48 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomialRing(X); f:=y^4+y+x^5; F:=FunctionField(f); F; Genus(F); Signature(F); Output: Magma V2.10-6 Wed Dec 17 2003 09:02:45 on modular [Seed = 787575662] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 >> Signature(F);; ^ Runtime error in 'Signature': Bad argument types Argument types given: FldFun Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fw.math.ku.dk. (130.225.103.21) Time: Wed Dec 17 09:03:36 2003 Input: 2+2 Output: Magma V2.10-6 Wed Dec 17 2003 09:03:33 on modular [Seed = 3557525924] ------------------------------------- 4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:03:39 2003 Input: K:=GF(2,4); X:=FunctionField(K); Y:=PolynomialRing(X); f:=y^4+y+x^5; F:=FunctionField(f); F; Genus(F); DimensionOfExactConstantField(F); Output: Magma V2.10-6 Wed Dec 17 2003 09:03:36 on modular [Seed = 3507391660] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 1 Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host fw.math.ku.dk. (130.225.103.21) Time: Wed Dec 17 09:03:53 2003 Input: print 2+2; Output: Magma V2.10-6 Wed Dec 17 2003 09:03:50 on modular [Seed = 3778985186] ------------------------------------- 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fw.math.ku.dk. (130.225.103.21) Time: Wed Dec 17 09:05:36 2003 Input: 2+2 Output: Magma V2.10-6 Wed Dec 17 2003 09:05:33 on modular [Seed = 4046367769] ------------------------------------- 4 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fw.math.ku.dk. (130.225.103.21) Time: Wed Dec 17 09:06:43 2003 Input: print 2+3; Output: Magma V2.10-6 Wed Dec 17 2003 09:06:40 on modular [Seed = 2471284262] ------------------------------------- 5 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fw.math.ku.dk. (130.225.103.21) Time: Wed Dec 17 09:10:41 2003 Input: print 2+6; Output: Magma V2.10-6 Wed Dec 17 2003 09:10:38 on modular [Seed = 1689991422] ------------------------------------- 8 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fw.math.ku.dk. (130.225.103.21) Time: Wed Dec 17 09:10:56 2003 Input: print 2^6; Output: Magma V2.10-6 Wed Dec 17 2003 09:10:53 on modular [Seed = 1823682757] ------------------------------------- 64 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fw.math.ku.dk. (130.225.103.21) Time: Wed Dec 17 09:11:16 2003 Input: for i:=1 to 5 do print i; end for; Output: Magma V2.10-6 Wed Dec 17 2003 09:11:13 on modular [Seed = 1957375793] ------------------------------------- 1 2 3 4 5 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:12:22 2003 Input: s:=sqrt(-14); jInvariant(s); Output: Magma V2.10-6 Wed Dec 17 2003 09:12:19 on modular [Seed = 399002640] ------------------------------------- >> s:=sqrt(-14); ^ User error: Identifier 'sqrt' has not been declared or assigned >> jInvariant(s);; ^ User error: Identifier 's' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:16:19 2003 Input: s:=i; jInvariant(s); Output: Magma V2.10-6 Wed Dec 17 2003 09:16:16 on modular [Seed = 3862543506] ------------------------------------- >> s:=i; ^ User error: Identifier 'i' has not been declared or assigned >> jInvariant(s);; ^ User error: Identifier 's' has not been declared or assigned Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:16:32 2003 Input: s:=13; jInvariant(s); Output: Magma V2.10-6 Wed Dec 17 2003 09:16:30 on modular [Seed = 3912676243] ------------------------------------- >> jInvariant(s);; ^ Runtime error in 'jInvariant': Imaginary part of argument should be positive Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:16:50 2003 Input: s:=i*2; jInvariant(s); Output: Magma V2.10-6 Wed Dec 17 2003 09:16:47 on modular [Seed = 4230194935] ------------------------------------- >> s:=i*2; ^ User error: Identifier 'i' has not been declared or assigned >> jInvariant(s);; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:18:30 2003 Input: C := ComplexField(); R := PowerSeriesRing(C); jInvariant(x); Output: Magma V2.10-6 Wed Dec 17 2003 09:18:27 on modular [Seed = 2487996003] ------------------------------------- $.1^-1 + 744 + 196884*$.1 + 21493760*$.1^2 + 864299970*$.1^3 + 20245856256*$.1^4 + 333202640600*$.1^5 + 4252023300096*$.1^6 + 44656994071935*$.1^7 + 401490886656000*$.1^8 + 3176440229784420*$.1^9 + 22567393309593600*$.1^10 + 146211911499519294*$.1^11 + 874313719685775360*$.1^12 + 4872010111798142520*$.1^13 + 25497827389410525184*$.1^14 + 126142916465781843075*$.1^15 + 593121772421445058560*$.1^16 + 2662842413150775245160*$.1^17 + 11459912788444786513920*$.1^18 + O($.1^19) Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:25:33 2003 Input: C := ComplexField(); x:=i jInvariant(x); Output: Magma V2.10-6 Wed Dec 17 2003 09:25:30 on modular [Seed = 3177375139] ------------------------------------- >> jInvariant(x);; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:26:34 2003 Input: C := ComplexField(); 1/4*i Output: Magma V2.10-6 Wed Dec 17 2003 09:26:31 on modular [Seed = 1117592214] ------------------------------------- 1/4*i Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:26:49 2003 Input: C := ComplexField(); Pi(C)+1/4*i Output: Magma V2.10-6 Wed Dec 17 2003 09:26:46 on modular [Seed = 1251283631] ------------------------------------- 3.141592653589793238462643383254 + 1/4*i Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:26:55 2003 Input: C := ComplexField(); Pi(C)+1/4*i; Output: Magma V2.10-6 Wed Dec 17 2003 09:26:52 on modular [Seed = 1384975037] ------------------------------------- 3.141592653589793238462643383254 + 1/4*i Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:27:16 2003 Input: C := ComplexField(); Pi(C)+1/4*i; jInvariant(i); Output: Magma V2.10-6 Wed Dec 17 2003 09:27:13 on modular [Seed = 1518666456] ------------------------------------- 3.141592653589793238462643383254 + 1/4*i 1727.99999999999999999999999997415 + 0.E-26*i Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:27:25 2003 Input: C := ComplexField(); jInvariant(i); Output: Magma V2.10-6 Wed Dec 17 2003 09:27:22 on modular [Seed = 1656568555] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:27:33 2003 Input: C := ComplexField(); jInvariant(2*i); Output: Magma V2.10-6 Wed Dec 17 2003 09:27:30 on modular [Seed = 1790259963] ------------------------------------- 287495.99999999999999999999996691277 + 0.E-23*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:27:54 2003 Input: C := ComplexField(); x:=sqrt(-14); jInvariant(2*i); Output: Magma V2.10-6 Wed Dec 17 2003 09:27:51 on modular [Seed = 1907239381] ------------------------------------- >> x:=sqrt(-14); ^ User error: Identifier 'sqrt' has not been declared or assigned 287495.99999999999999999999996691277 + 0.E-23*i Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:28:48 2003 Input: C := ComplexField(); x:=Sqrt(-14); jInvariant(2*i); Output: Magma V2.10-6 Wed Dec 17 2003 09:28:45 on modular [Seed = 2040933927] ------------------------------------- 287495.99999999999999999999996691277 + 0.E-23*i Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 09:29:00 2003 Input: C := ComplexField(); x:=Sqrt(-14); jInvariant(x); Output: Magma V2.10-6 Wed Dec 17 2003 09:28:57 on modular [Seed = 31348331] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host w06p41.rz.tu-harburg.de. (134.28.148.136) Time: Wed Dec 17 10:06:45 2003 Input: 2+77 Output: Magma V2.10-6 Wed Dec 17 2003 10:06:42 on modular [Seed = 3524107411] ------------------------------------- 79 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 10:38:04 2003 Input: C := ComplexField(); x:=Sqrt(-14); y:=jInvariant(x); f:=MinimalPolynomial(y); M:=NumberField(f); M; Output: Magma V2.10-6 Wed Dec 17 2003 10:38:01 on modular [Seed = 1656563065] ------------------------------------- >> f:=MinimalPolynomial(y); ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldPrElt >> M:=NumberField(f); ^ User error: Identifier 'f' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 10:39:52 2003 Input: C := ComplexField(); x:=Sqrt(-14); y:=jInvariant(x); f:=MinimalPolynomial(y,Q); M:=NumberField(f); M; Output: Magma V2.10-6 Wed Dec 17 2003 10:39:49 on modular [Seed = 1790258669] ------------------------------------- >> f:=MinimalPolynomial(y,Q); ^ User error: Identifier 'Q' has not been declared or assigned >> M:=NumberField(f); ^ User error: Identifier 'f' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 10:43:40 2003 Input: C := ComplexField(); x:=Sqrt(-14); y:=jInvariant(x); f:=MinimalPolynomial(y); M:=NumberField(f); M; Output: Magma V2.10-6 Wed Dec 17 2003 10:43:37 on modular [Seed = 2057649297] ------------------------------------- >> f:=MinimalPolynomial(y); ^ Runtime error in 'MinimalPolynomial': Bad argument types Argument types given: FldPrElt >> M:=NumberField(f); ^ User error: Identifier 'f' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 10:52:15 2003 Input: C := ComplexField(); x:=Sqrt(-14); y:=jInvariant(x); Output: Magma V2.10-6 Wed Dec 17 2003 10:52:09 on modular [Seed = 215173351] ------------------------------------- Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 10:52:24 2003 Input: C := ComplexField(); x:=Sqrt(-14); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 10:52:21 on modular [Seed = 348868835] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 10:53:47 2003 Input: C := ComplexField(); x:=Sqrt(-3); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 10:53:43 on modular [Seed = 499277399] ------------------------------------- 53999.99999999999999999999998593792 + 0.E-24*i Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 10:54:41 2003 Input: C := ComplexField(); x:=Sqrt(-2); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 10:54:38 on modular [Seed = 637167193] ------------------------------------- 7999.99999999999999999999999844903 + 0.E-24*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:03:26 2003 Input: C := ComplexField(); x:=Sqrt(-3); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 11:03:23 on modular [Seed = 4146640638] ------------------------------------- 53999.99999999999999999999998593792 + 0.E-24*i Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:07:02 2003 Input: C := ComplexField(); x:=Sqrt(-14); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 11:06:59 on modular [Seed = 2776294852] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:09:17 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 11:09:14 on modular [Seed = 2993549914] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:42:31 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; f:=x^2+41*y^2; Lattice(f); Output: Magma V2.10-6 Wed Dec 17 2003 11:42:28 on modular [Seed = 1723457107] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i >> Lattice(f);; ^ Runtime error in 'Lattice': Bad argument types Argument types given: FldPrElt Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:44:27 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Q:=QuadraticForms(-41); print Q; Lattice(Q); Output: Magma V2.10-6 Wed Dec 17 2003 11:44:24 on modular [Seed = 1907280344] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i >> Q:=QuadraticForms(-41); ^ Runtime error in 'QuadraticForms': Argument is not a discriminant >> print Q; ^ User error: Identifier 'Q' has not been declared or assigned >> Lattice(Q);; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:45:43 2003 Input: Q:=QuadraticForms(-41); print Q; Lattice(Q); Output: Magma V2.10-6 Wed Dec 17 2003 11:45:40 on modular [Seed = 2107820552] ------------------------------------- >> Q:=QuadraticForms(-41); ^ Runtime error in 'QuadraticForms': Argument is not a discriminant >> print Q; ^ User error: Identifier 'Q' has not been declared or assigned >> Lattice(Q);; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:46:11 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Q:=QuadraticForms(-41); print Q; Lattice(Q); Output: Magma V2.10-6 Wed Dec 17 2003 11:46:08 on modular [Seed = 98218516] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i >> Q:=QuadraticForms(-41); ^ Runtime error in 'QuadraticForms': Argument is not a discriminant >> print Q; ^ User error: Identifier 'Q' has not been declared or assigned >> Lattice(Q);; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:46:29 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Q := QuadraticForms(-163); print Q; Lattice(Q); Output: Magma V2.10-6 Wed Dec 17 2003 11:46:26 on modular [Seed = 231914030] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i Binary quadratic forms of discriminant -163 >> Lattice(Q);; ^ Runtime error in 'Lattice': Bad argument types Argument types given: QuadBin Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:47:03 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Q := QuadraticForms(-163); Q; Lattice(Q); Output: Magma V2.10-6 Wed Dec 17 2003 11:47:00 on modular [Seed = 365601488] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i Binary quadratic forms of discriminant -163 >> Lattice(Q);; ^ Runtime error in 'Lattice': Bad argument types Argument types given: QuadBin Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:47:45 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Q:=x^2+41y^2; Lattice(Q); Output: Magma V2.10-6 Wed Dec 17 2003 11:47:41 on modular [Seed = 499297009] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i >> Q:=x^2+41y^2; ^ User error: bad syntax >> Lattice(Q);; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:47:54 2003 Input: C := ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Q:=x^2+41*y^2; Lattice(Q); Output: Magma V2.10-6 Wed Dec 17 2003 11:47:51 on modular [Seed = 620467154] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i >> Lattice(Q);; ^ Runtime error in 'Lattice': Bad argument types Argument types given: FldPrElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:55:52 2003 Input: C := ComplexField(); x:=Sqrt(-41); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 11:55:49 on modular [Seed = 988123118] ------------------------------------- 296853791705949233.0026726245123 + 0.E-11*i Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 11:58:34 2003 Input: C := ComplexField(); x:=(-1+Sqrt(-41))/2; y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 11:58:31 on modular [Seed = 3306844595] ------------------------------------- -544842161.52997224185465281772583999442 + 7.6768996883 E-20*i Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:03:03 2003 Input: C := ComplexField(); x:=(-2+Sqrt(-41))/5; y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 12:02:58 on modular [Seed = 3912653546] ------------------------------------- -1832.51158041991500380297426369446 + 1800.393479955524039524631994370127*i Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:04:58 2003 Input: C := ComplexField(); x:=(-1+Sqrt(-41))/3; jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 12:04:54 on modular [Seed = 4046340614] ------------------------------------- -332798.410724264846430804772332667966 + 577711.89065421558056949116172860218*i >> y; ^ User error: Identifier 'y' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:05:11 2003 Input: C := ComplexField(); x:=(-1+Sqrt(-41))/3; y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 12:05:08 on modular [Seed = 4246883960] ------------------------------------- -332798.410724264846430804772332667966 + 577711.89065421558056949116172860218*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:05:54 2003 Input: C := ComplexField(); x:=(-1+Sqrt(-41))/6; y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 12:05:51 on modular [Seed = 2237281835] ------------------------------------- 1255.1859544932706970374260047613073849457889 + 470.70321831716687046600824748585*i Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:11:54 2003 Input: C := ComplexField(); x:=(1+Sqrt(-7))/2; y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 12:11:51 on modular [Seed = 2504664195] ------------------------------------- -3374.99999999999999999999999896602 + 2.04472746606 E-25*i Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:15:02 2003 Input: C := ComplexField(); x:=Sqrt(-2); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 12:14:58 on modular [Seed = 2621648079] ------------------------------------- 7999.99999999999999999999999844903 + 0.E-24*i Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:25:35 2003 Input: C := ComplexField(); x1:=Sqrt(-41); y1:=jInvariant(x1); y1; Output: Magma V2.10-6 Wed Dec 17 2003 12:25:32 on modular [Seed = 1284760192] ------------------------------------- 296853791705949233.0026726245123 + 0.E-11*i Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 12:27:37 2003 Input: C := ComplexField(); x1:=Sqrt(-41); y1:=jInvariant(x1); x2:=(-1+Sqrt(-41))/2; y2:=jInvariant(x2); x3:=(-2+Sqrt(-41))/5; y3:=jInvariant(x3); x4:=(-1+Sqrt(-41))/3; y4:=jInvariant(x4); x5:=(-1+Sqrt(-41))/6; y5:=jInvariant(x5); y:=y1+y2+y3+y4+y5; y; Output: Magma V2.10-6 Wed Dec 17 2003 12:27:34 on modular [Seed = 1418459410] ------------------------------------- 296853791160773695.73635019117500633001 + 579982.98735248827147942800771904156*i Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 13:02:56 2003 Input: C := ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=Sqrt(-14)/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); y:=y1+y2+y3+y4; y; Output: Magma V2.10-6 Wed Dec 17 2003 13:02:53 on modular [Seed = 704023588] ------------------------------------- 16220384511.99999999999999998742 - 2.06795153114 E-25*i Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 13:07:56 2003 Input: C := ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=Sqrt(-14)/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); z1:=y1+y2+y3+y4; z1; z2:=y1*y2+y2*y3+y3*y4+y4*y1; z2; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z3; z4:=y1*y2*y3*y4; z4; Output: Magma V2.10-6 Wed Dec 17 2003 13:07:53 on modular [Seed = 921276943] ------------------------------------- 16220384511.99999999999999998742 - 2.06795153114 E-25*i 2068766124818431.99999999999752731127 - 34512574080753.73432571016033243438*i -2257767342088912895.99999999540159478783 - 0.0000000003492459654*i 10064086044321563803647.9999818801 + 0.000002503395080*i Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 13:09:33 2003 Input: C := ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=Sqrt(-14)/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); y1; y2; y3; y4; z1:=y1+y2+y3+y4; z1; z2:=y1*y2+y2*y3+y3*y4+y4*y1; z2; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z3; z4:=y1*y2*y3*y4; z4; Output: Magma V2.10-6 Wed Dec 17 2003 13:09:30 on modular [Seed = 1054972580] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199628774 + 2127.76194138925212063251332929418*i -562.189330472902256983178199150560 - 2127.76194138925212063251332950098*i 16220384511.99999999999999998742 - 2.06795153114 E-25*i 2068766124818431.99999999999752731127 - 34512574080753.73432571016033243438*i -2257767342088912895.99999999540159478783 - 0.0000000003492459654*i 10064086044321563803647.9999818801 + 0.000002503395080*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 13:11:50 2003 Input: C := ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=Sqrt(-14)/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); y1:=16220257532; y2:=128104; y3:=-562 + 2127*i; y4:=-562 - 2127*i; z1:=y1+y2+y3+y4; z1; z2:=y1*y2+y2*y3+y3*y4+y4*y1; z2; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z3; z4:=y1*y2*y3*y4; z4; Output: Magma V2.10-6 Wed Dec 17 2003 13:11:47 on modular [Seed = 3440537326] ------------------------------------- 16220384512 2068764018991869 - 34500215293356*i -2257030746340536844 10056882472299433778144 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 13:15:44 2003 Input: C := ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=Sqrt(-14)/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); y1:=16220257532; y2:=128104; y3:=-562 + 2127*i; y4:=-562 - 2127*i; z1:=y1+y2+y3+y4; z1; z2:=y1*y2+y2*y3+y3*y4+y4*y1+y1*y3+y2*y4; z2; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z3; z4:=y1*y2*y3*y4; z4; Output: Magma V2.10-6 Wed Dec 17 2003 13:15:40 on modular [Seed = 3657791702] ------------------------------------- 16220384512 2059648162264437 -2257030746340536844 10056882472299433778144 Total time: 3.020 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 13:19:14 2003 Input: C := ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=Sqrt(-14)/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); z1:=y1+y2+y3+y4; z1; z2:=y1*y2+y2*y3+y3*y4+y4*y1+y1*y3+y2*y4; z2; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z3; z4:=y1*y2*y3*y4; z4; Output: Magma V2.10-6 Wed Dec 17 2003 13:19:10 on modular [Seed = 3812377277] ------------------------------------- 16220384511.99999999999999998742 - 2.06795153114 E-25*i 2059647197077503.99999999999755573298 - 3.6877442831 E-15*i -2257767342088912895.99999999540159478783 - 0.0000000003492459654*i 10064086044321563803647.9999818801 + 0.000002503395080*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h0006258f9aae.ne.client2.attbi.com. (24.61.40.225) Time: Wed Dec 17 21:26:41 2003 Input: 1+1 Output: Magma V2.10-6 Wed Dec 17 2003 21:26:38 on modular [Seed = 2571613949] ------------------------------------- 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Wed Dec 17 22:55:39 2003 Input: C:= ComplexField(); x:=(1+Sqrt(-7))/2; y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 22:55:36 on modular [Seed = 1552041565] ------------------------------------- -3374.99999999999999999999999896602 + 2.04472746606 E-25*i Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:06:17 2003 Input: C(i) := complexField x := squareroot(-4) y := jInvariant(x) y; Output: Magma V2.10-6 Wed Dec 17 2003 23:06:14 on modular [Seed = 3077156664] ------------------------------------- >> x := squareroot(-4) ^ User error: bad syntax >> y;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:06:21 2003 Input: C(i) := complexField x := squareroot(-4) y := jInvariant(x) y; Output: Magma V2.10-6 Wed Dec 17 2003 23:06:18 on modular [Seed = 2943465260] ------------------------------------- >> x := squareroot(-4) ^ User error: bad syntax >> y;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:06:40 2003 Input: C(i) := complexField x := sqrt(-4) y := jInvariant(x) y; Output: Magma V2.10-6 Wed Dec 17 2003 23:06:37 on modular [Seed = 2809773907] ------------------------------------- >> x := sqrt(-4) ^ User error: bad syntax >> y;; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:10:42 2003 Input: C(i) := complexField x := SquareRoot(-4) y := jInvariant(x) y; Output: Magma V2.10-6 Wed Dec 17 2003 23:10:39 on modular [Seed = 2337643533] ------------------------------------- >> x := SquareRoot(-4) ^ User error: bad syntax >> y;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:13:32 2003 Input: C := ComplexField(); x1:=Sqrt(-4); y1:=jInvariant(x1); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:13:29 on modular [Seed = 2187105490] ------------------------------------- >> y; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:13:55 2003 Input: C := ComplexField(); x:=Sqrt(-4); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:13:52 on modular [Seed = 4196723779] ------------------------------------- 287495.99999999999999999999996691277 + 0.E-23*i Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:14:57 2003 Input: C := ComplexField(); x:=Sqrt(-8); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:14:54 on modular [Seed = 4063028341] ------------------------------------- 52249767.137718184836513595778571957765 + 0.E-21*i Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:15:23 2003 Input: C := ComplexField(); x:=Sqrt(-12); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:15:20 on modular [Seed = 3996186639] ------------------------------------- 2835807690.42228352772984605116 + 0.E-19*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:15:37 2003 Input: C := ComplexField(); x:=Sqrt(-16); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:15:34 on modular [Seed = 3862491193] ------------------------------------- 82226316329.59499766938284028711 + 0.E-18*i Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:15:49 2003 Input: C := ComplexField(); x:=Sqrt(-20); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:15:46 on modular [Seed = 3507472154] ------------------------------------- 1597177180157.23860127436090611263 + 0.E-16*i Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:15:58 2003 Input: C := ComplexField(); x:=Sqrt(-28); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:15:55 on modular [Seed = 3373784843] ------------------------------------- 274917323965134.40721796589110326181 + 0.E-14*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:16:09 2003 Input: C := ComplexField(); x:=Sqrt(-56); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:16:06 on modular [Seed = 3240088830] ------------------------------------- 263096730270589981984.5308338515 + 0.000000000*i Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:16:22 2003 Input: C := ComplexField(); x:=Sqrt(-108); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:16:19 on modular [Seed = 954608915] ------------------------------------- 22804995243537595825770536075.5000000000 + 0.000000000*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:16:33 2003 Input: C := ComplexField(); x:=Sqrt(-256); y:=jInvariant(x); y; Output: Magma V2.10-6 Wed Dec 17 2003 23:16:30 on modular [Seed = 820913430] ------------------------------------- 4.57133788608809215663019487750 E43 + 0.*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:30:33 2003 Input: C := ComplexField(); n := 14; h := -4n; a1 := 1; b1 := Sqrt(h)/2; a2 := 2; b2 := Sqrt(h)/2; a3 := 3; b3 := (2 + Sqrt(h))/2; a4 := 3; b4 := (-2 + Sqrt(h))/2; y1 := jInvariant(a1, b1); y2 := jInvariant(a2, b2); y3 := jInvariant(a3, b3); y4 := jInvariant(a4, b4); y1; y2; y3; y4; Output: Magma V2.10-6 Wed Dec 17 2003 23:30:30 on modular [Seed = 298779471] ------------------------------------- >> n := 14; h := -4n; ^ User error: bad syntax >> a1 := 1; b1 := Sqrt(h)/2; ^ User error: Identifier 'h' has not been declared or assigned >> a2 := 2; b2 := Sqrt(h)/2; ^ User error: Identifier 'h' has not been declared or assigned >> a3 := 3; b3 := (2 + Sqrt(h))/2; ^ User error: Identifier 'h' has not been declared or assigned >> a4 := 3; b4 := (-2 + Sqrt(h))/2; ^ User error: Identifier 'h' has not been declared or assigned >> y1 := jInvariant(a1, b1); y2 := jInvariant(a2, b2); ^ User error: Identifier 'b1' has not been declared or assigned >> y1 := jInvariant(a1, b1); y2 := jInvariant(a2, b2); ^ User error: Identifier 'b2' has not been declared or assigned >> y3 := jInvariant(a3, b3); y4 := jInvariant(a4, b4); ^ User error: Identifier 'b3' has not been declared or assigned >> y3 := jInvariant(a3, b3); y4 := jInvariant(a4, b4); ^ User error: Identifier 'b4' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y1' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y2' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y3' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y4' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:30:48 2003 Input: C := ComplexField(); n := 14; h := -4*n; a1 := 1; b1 := Sqrt(h)/2; a2 := 2; b2 := Sqrt(h)/2; a3 := 3; b3 := (2 + Sqrt(h))/2; a4 := 3; b4 := (-2 + Sqrt(h))/2; y1 := jInvariant(a1, b1); y2 := jInvariant(a2, b2); y3 := jInvariant(a3, b3); y4 := jInvariant(a4, b4); y1; y2; y3; y4; Output: Magma V2.10-6 Wed Dec 17 2003 23:30:45 on modular [Seed = 165092164] ------------------------------------- >> y1 := jInvariant(a1, b1); y2 := jInvariant(a2, b2); ^ Runtime error in 'jInvariant': Bad argument types Argument types given: FldPrElt, FldPrElt >> y1 := jInvariant(a1, b1); y2 := jInvariant(a2, b2); ^ Runtime error in 'jInvariant': Bad argument types Argument types given: FldPrElt, FldPrElt >> y3 := jInvariant(a3, b3); y4 := jInvariant(a4, b4); ^ Runtime error in 'jInvariant': Bad argument types Argument types given: FldPrElt, FldPrElt >> y3 := jInvariant(a3, b3); y4 := jInvariant(a4, b4); ^ Runtime error in 'jInvariant': Bad argument types Argument types given: FldPrElt, FldPrElt >> y1; y2; y3; y4; ^ User error: Identifier 'y1' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y2' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y3' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y4' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:32:08 2003 Input: C := ComplexField(); n := 14; h := -4*n; a1 := 1; b1 := Sqrt(h)/2; a2 := 2; b2 := Sqrt(h)/2; a3 := 3; b3 := (2 + Sqrt(h))/2; a4 := 3; b4 := (-2 + Sqrt(h))/2; y1 := jInvariant(b1); y2 := jInvariant(b2); y3 := jInvariant(b3); y4 := jInvariant(b4); y1; y2; y3; y4; Output: Magma V2.10-6 Wed Dec 17 2003 23:32:05 on modular [Seed = 31396860] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 16220257532.059502697452916043438 + 0.E-18*i 16220257532.059502697452916043655 + 4.6390307862 E-18*i 16220257532.059502697452916043655 - 4.6390307862 E-18*i Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:33:46 2003 Input: C := ComplexField(); n := 14; h := -4*n; x1 := Sqrt(h)/2; y1 := jInvariant(x1); y1; Output: Magma V2.10-6 Wed Dec 17 2003 23:33:43 on modular [Seed = 2107862114] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:45:54 2003 Input: C := ComplexField(); n := 5; h := -4*n; a1 := 1; b1 := 0; c1 := 5; a2 := 2; b2 := 2; c2 := 3; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; y1 := jInvariant(x1); y2 := jInvariant(x2); y1; y2; Output: Magma V2.10-6 Wed Dec 17 2003 23:45:51 on modular [Seed = 1502041758] ------------------------------------- 1264538.90947514050932022704701375289 + 0.E-22*i 2060.94946856904690322538567313625 + 0.E-25*i Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:48:25 2003 Input: C := ComplexField(); n := 14; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 2; b2 := 0; c2 := 7; a1 := 3; b1 := 2; c1 := 5; a2 := 3; b2 := -2; c2 := 5; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Wed Dec 17 2003 23:48:22 on modular [Seed = 1384930556] ------------------------------------- >> x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; ^ User error: Identifier 'b3' has not been declared or assigned >> x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; ^ User error: Identifier 'b4' has not been declared or assigned >> y3 := jInvariant(x3); y4 := jInvariant(x4); ^ User error: Identifier 'x3' has not been declared or assigned >> y3 := jInvariant(x3); y4 := jInvariant(x4); ^ User error: Identifier 'x4' has not been declared or assigned -562.189330472902256983178199279807 - 2127.76194138925212063251332950098*i -562.189330472902256983178199732171 + 2127.76194138925212063251332924248*i >> y1; y2; y3; y4; ^ User error: Identifier 'y3' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y4' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:48:53 2003 Input: C := ComplexField(); n := 14; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 2; b2 := 0; c2 := 7; a3 := 3; b3 := 2; c3 := 5; a4 := 3; b4 := -2; c4 := 5; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Wed Dec 17 2003 23:48:50 on modular [Seed = 1251230912] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199279807 - 2127.76194138925212063251332950098*i -562.189330472902256983178199732171 + 2127.76194138925212063251332924248*i Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:49:58 2003 Input: C := ComplexField(); n := 64; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 4; b2 := 4; c2 := 17; a3 := 5; b3 := 2; c3 := 13; a4 := 5; b4 := -2; c4 := 13; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Wed Dec 17 2003 23:49:55 on modular [Seed = 1117539465] ------------------------------------- 6761166974781862431471.3793350458 + 0.000000000*i 287495.99999999999999999999997353022 + 2.7708666650 E-23*i -18054.368005675433796168716165862020 + 13647.89611310521125513126224918105*i -18054.368005675433796168716160071755 - 13647.89611310521125513126225641888*i Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:51:49 2003 Input: C := ComplexField(); n := 27; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 4; b3 := 2; c3 := 7; a3 := 4; b4 := -2; c4 := 7; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y1; y2; y3; Output: Magma V2.10-6 Wed Dec 17 2003 23:51:46 on modular [Seed = 3010313961] ------------------------------------- >> x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; ^ User error: Identifier 'b2' has not been declared or assigned >> y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); ^ User error: Identifier 'x2' has not been declared or assigned 151013228704515.49785340860307769617 + 0.E-14*i >> y1; y2; y3; ^ User error: Identifier 'y2' has not been declared or assigned -2815.96517931614089412006271725230 - 1.5123605439 E-25*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:52:22 2003 Input: C := ComplexField(); n := 27; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 4; b2 := 2; c2 := 7; a3 := 4; b4 := -2; c4 := 7; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y1; y2; y3; Output: Magma V2.10-6 Wed Dec 17 2003 23:52:19 on modular [Seed = 2876614160] ------------------------------------- >> x3 := (-b3 + Sqrt(h)/2)/a3; ^ User error: Identifier 'b3' has not been declared or assigned >> y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); ^ User error: Identifier 'x3' has not been declared or assigned 151013228704515.49785340860307769617 + 0.E-14*i -2815.96517931614089412006271725230 - 1.5123605439 E-25*i >> y1; y2; y3; ^ User error: Identifier 'y3' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc205.postech.ac.kr. (141.223.33.30) Time: Wed Dec 17 23:52:36 2003 Input: C := ComplexField(); n := 27; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 4; b2 := 2; c2 := 7; a3 := 4; b3 := -2; c3 := 7; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y1; y2; y3; Output: Magma V2.10-6 Wed Dec 17 2003 23:52:33 on modular [Seed = 2742922762] ------------------------------------- 151013228704515.49785340860307769617 + 0.E-14*i -2815.96517931614089412006271725230 - 1.5123605439 E-25*i -2815.96517931614089412006271725230 + 1.5126129793 E-25*i Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:07:22 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:07:25 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:07:28 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:07:45 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: Magma V2.10-6 Thu Dec 18 2003 00:07:41 on modular [Seed = 298784827] ------------------------------------- [ Modular symbols space for Gamma_0(389) of weight 2 and dimension 2 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 4 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 6 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 12 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 40 over Rational Field ] Total time: 4.269 seconds, Total memory usage: 3.50MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:08:37 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:09:47 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:09:54 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:10:47 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:11:16 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: An error occured in the MAGMA system call. ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Dec 18 00:12:04 2003 Input: NewformDecomposition(CuspidalSubspace(ModularSymbols(389))); Output: Magma V2.10-6 Thu Dec 18 2003 00:12:00 on modular [Seed = 2237369746] ------------------------------------- [ Modular symbols space for Gamma_0(389) of weight 2 and dimension 2 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 4 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 6 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 12 over Rational Field, Modular symbols space for Gamma_0(389) of weight 2 and dimension 40 over Rational Field ] Total time: 4.269 seconds, Total memory usage: 3.50MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 00:36:00 2003 Input: c := ComplexField(); n := 64; h := -4*n: a1 := 1; b1 := 0; c1 := n; a2 := 4; b2 := 4; c2 := 17; a3 := 1; b3 := 2; c3 := 13; a4 := 5; b4 := -2; c4 := 13; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Thu Dec 18 2003 00:35:57 on modular [Seed = 3691175766] ------------------------------------- >> n := 64; h := -4*n: ^ User error: bad syntax >> x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; ^ User error: Identifier 'h' has not been declared or assigned >> x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; ^ User error: Identifier 'h' has not been declared or assigned >> x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; ^ User error: Identifier 'h' has not been declared or assigned >> x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; ^ User error: Identifier 'h' has not been declared or assigned >> y1 := jInvariant(x1); y2 := jInvariant(x2); ^ User error: Identifier 'x1' has not been declared or assigned >> y1 := jInvariant(x1); y2 := jInvariant(x2); ^ User error: Identifier 'x2' has not been declared or assigned >> y3 := jInvariant(x3); y4 := jInvariant(x4); ^ User error: Identifier 'x3' has not been declared or assigned >> y3 := jInvariant(x3); y4 := jInvariant(x4); ^ User error: Identifier 'x4' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y1' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y2' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y3' has not been declared or assigned >> y1; y2; y3; y4; ^ User error: Identifier 'y4' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 00:36:25 2003 Input: c := ComplexField(); n := 64; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 4; b2 := 4; c2 := 17; a3 := 1; b3 := 2; c3 := 13; a4 := 5; b4 := -2; c4 := 13; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Thu Dec 18 2003 00:36:22 on modular [Seed = 3273506850] ------------------------------------- 6761166974781862431471.3793350458 + 0.000000000*i 287495.99999999999999999999997353022 + 2.7708666650 E-23*i 6761166974781862431471.3793351650 + 0.0000013439921627*i -18054.368005675433796168716160071755 - 13647.89611310521125513126225641888*i Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 00:37:09 2003 Input: c := ComplexField(); n := 64; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 4; b2 := 4; c2 := 17; a3 := 5; b3 := 2; c3 := 13; a4 := 5; b4 := -2; c4 := 13; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Thu Dec 18 2003 00:37:06 on modular [Seed = 3390359807] ------------------------------------- 6761166974781862431471.3793350458 + 0.000000000*i 287495.99999999999999999999997353022 + 2.7708666650 E-23*i -18054.368005675433796168716165862020 + 13647.89611310521125513126224918105*i -18054.368005675433796168716160071755 - 13647.89611310521125513126225641888*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 00:38:42 2003 Input: c := ComplexField(); n := 14; h := -4*n; a1 := 1; b1 := 0; c1 := n; a2 := 2; b2 := 0; c2 := 7; a3 := 3; b3 := 2; c3 := 5; a4 := 3; b4 := -2; c4 := 5; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Thu Dec 18 2003 00:38:39 on modular [Seed = 1054882903] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199279807 - 2127.76194138925212063251332950098*i -562.189330472902256983178199732171 + 2127.76194138925212063251332924248*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 00:42:18 2003 Input: C := ComplexField(); n := 7; h := -4*n; x := Sqrt(h); y := jInvarinat(x); y; Output: Magma V2.10-6 Thu Dec 18 2003 00:42:15 on modular [Seed = 787492655] ------------------------------------- >> y := jInvarinat(x); ^ User error: Identifier 'jInvarinat' has not been declared or assigned >> y; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 00:42:37 2003 Input: C := ComplexField(); n := 7; h := -4*n; x := Sqrt(h); y := jInvariant(x); y; Output: Magma V2.10-6 Thu Dec 18 2003 00:42:34 on modular [Seed = 399054443] ------------------------------------- 274917323965134.40721796589110326181 + 0.E-14*i Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc102.postech.ac.kr. (141.223.33.21) Time: Thu Dec 18 01:18:01 2003 Input: C := ComplexField(); n := 14; h := -4 * n; a1 := 1; b1 := 0; a2 := 2; b2 := 0; a3 := 3; b3 := 2; a4 := 3; b4 := -2; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; Output: Magma V2.10-6 Thu Dec 18 2003 01:17:58 on modular [Seed = 3093741848] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199279807 - 2127.76194138925212063251332950098*i -562.189330472902256983178199732171 + 2127.76194138925212063251332924248*i Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc102.postech.ac.kr. (141.223.33.21) Time: Thu Dec 18 01:24:46 2003 Input: C := ComplexField(); n := 14; h := -4 * n; a1 := 1; b1 := 0; a2 := 2; b2 := 0; a3 := 3; b3 := 2; a4 := 3; b4 := -2; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; q1 := w-1; q2 := w-2; q3 := q1 * q2; q3; Output: Magma V2.10-6 Thu Dec 18 2003 01:24:43 on modular [Seed = 2504778376] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199279807 - 2127.76194138925212063251332950098*i -562.189330472902256983178199732171 + 2127.76194138925212063251332924248*i >> q1 := w-1; ^ User error: Identifier 'w' has not been declared or assigned >> q2 := w-2; ^ User error: Identifier 'w' has not been declared or assigned >> q3 := q1 * q2; ^ User error: Identifier 'q1' has not been declared or assigned >> q3;; ^ User error: Identifier 'q3' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc102.postech.ac.kr. (141.223.33.21) Time: Thu Dec 18 01:32:27 2003 Input: C := ComplexField(); n := 14; h := -4 * n; a1 := 1; b1 := 0; a2 := 2; b2 := 0; a3 := 3; b3 := 2; a4 := 3; b4 := -2; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; c1 := -(y1+y2+y1+y4); c2 := y1*y2+y1*y3+y1*y4+y2*y3+y2*y4+y3*y4; c3 := -(y1*y2*y3+y1*y2*y4+y2*y3*y4); c4 := y1*y2*y3*y4; c1; c2; c3; c4; Output: Magma V2.10-6 Thu Dec 18 2003 01:32:24 on modular [Seed = 2387671104] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199279807 - 2127.76194138925212063251332950098*i -562.189330472902256983178199732171 + 2127.76194138925212063251332924248*i -32440642606.24883317035517301405 - 2127.76194138925212063251332924248*i 2059647197077503.99999999999755573298 - 4.4409315902 E-15*i 2336328987086138266.55145567213185131549 + 0.0000000005820764563*i 10064086044321563803647.9999818801 + 0.0000023841857910*i Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc102.postech.ac.kr. (141.223.33.21) Time: Thu Dec 18 01:39:48 2003 Input: C := ComplexField(); n := 14; h := -4 * n; a1 := 1; b1 := 0; a2 := 2; b2 := 0; a3 := 3; b3 := 2; a4 := 3; b4 := -2; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; c1 := -(y1+y2+y3+y4); c2 := y1*y2+y1*y3+y1*y4+y2*y3+y2*y4+y3*y4; c3 := -(y1*y2*y3+y1*y2*y4+y2*y3*y4); c4 := y1*y2*y3*y4; c1; c2; c3; c4; Output: Magma V2.10-6 Thu Dec 18 2003 01:39:45 on modular [Seed = 3356933199] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199279807 - 2127.76194138925212063251332950098*i -562.189330472902256983178199732171 + 2127.76194138925212063251332924248*i -16220384511.99999999999999998742 + 2.5849394137 E-25*i 2059647197077503.99999999999755573298 - 4.4409315902 E-15*i 2336328987086138266.55145567213185131549 + 0.0000000005820764563*i 10064086044321563803647.9999818801 + 0.0000023841857910*i Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc102.postech.ac.kr. (141.223.33.21) Time: Thu Dec 18 01:45:16 2003 Input: C := ComplexField(); n := 64; h := -4 * n; a1 := 1; b1 := 0; a2 := 4; b2 := 4; a3 := 5; b3 := 2; a4 := 5; b4 := -2; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; x4 := (-b4 + Sqrt(h)/2)/a4; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y4 := jInvariant(x4); y1; y2; y3; y4; c1 := -(y1+y2+y3+y4); c2 := y1*y2+y1*y3+y1*y4+y2*y3+y2*y4+y3*y4; c3 := -(y1*y2*y3+y1*y2*y4+y2*y3*y4); c4 := y1*y2*y3*y4; c1; c2; c3; c4; Output: Magma V2.10-6 Thu Dec 18 2003 01:45:13 on modular [Seed = 570381037] ------------------------------------- 6761166974781862431471.3793350458 + 0.000000000*i 287495.99999999999999999999997353022 + 2.7708666650 E-23*i -18054.368005675433796168716165862020 + 13647.89611310521125513126224918105*i -18054.368005675433796168716160071755 - 13647.89611310521125513126225641888*i -6761166974781862682858.6433236598 + 0.E-15*i 1699671267160824272502652089.4062500000 + 0.109374999999999997174*i 7.0188466559781651882271486317198 E31 + 20480.0*i 9.95667818212005556660530597588 E35 + 486539264.*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc102.postech.ac.kr. (141.223.33.21) Time: Thu Dec 18 01:50:13 2003 Input: C := ComplexField(); n := 27; h := -4 * n; a1 := 1; b1 := 0; a2 := 4; b2 := 2; a3 := 4; b3 := -2; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; x3 := (-b3 + Sqrt(h)/2)/a3; y1 := jInvariant(x1); y2 := jInvariant(x2); y3 := jInvariant(x3); y1; y2; y3; c1 := -(y1+y2+y3); c2 := y1*y2+y1*y3+y2*y3; c3 := -y1*y2*y3; c1; c2; c3; Output: Magma V2.10-6 Thu Dec 18 2003 01:50:10 on modular [Seed = 499346442] ------------------------------------- 151013228704515.49785340860307769617 + 0.E-14*i -2815.96517931614089412006271725230 - 1.5123605439 E-25*i -2815.96517931614089412006271725230 + 1.5126129793 E-25*i -151013228698883.56749477632128986215 + 0.E-14*i -850495987288111098.44418085973302368074 + 0.E-20*i -1197483542686876850953.12991496920 + 0.000000000*i Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc102.postech.ac.kr. (141.223.33.21) Time: Thu Dec 18 01:54:22 2003 Input: C := ComplexField(); n := 5; h := -4 * n; a1 := 1; b1 := 0; a2 := 2; b2 := 2; x1 := (-b1 + Sqrt(h)/2)/a1; x2 := (-b2 + Sqrt(h)/2)/a2; y1 := jInvariant(x1); y2 := jInvariant(x2); y1; y2; c1 := -(y1+y2); c2 := y1*y2; c1; c2; Output: Magma V2.10-6 Thu Dec 18 2003 01:54:19 on modular [Seed = 114849320] ------------------------------------- 1264538.90947514050932022704701375289 + 0.E-22*i 2060.94946856904690322538567313625 + 0.E-25*i -1266599.85894370955622345243267654938 + 0.E-22*i 2606150793.46767294235360598977 + 0.E-19*i Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 02:12:28 2003 Input: C := ComplexField(); x1:=Sqrt(-14);y1:=jInvariant(x1); x2:=Sqrt(-14)/2;y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3;y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3;y4:=jInvariant(x4); z1:=y1+y2+y3+y4; z2:=y1*y2+y2*y3+y3*y4+y4*y1; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z4:=y1*y2*y3*y4; z1;z2;z3;z4; Output: Magma V2.10-6 Thu Dec 18 2003 02:12:25 on modular [Seed = 1568878897] ------------------------------------- 16220384511.99999999999999998742 - 2.06795153114 E-25*i 2068766124818431.99999999999752731127 - 34512574080753.73432571016033243438*i -2257767342088912895.99999999540159478783 - 0.0000000003492459654*i 10064086044321563803647.9999818801 + 0.000002503395080*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 02:46:15 2003 Input: C := ComplexField(); x1:=Sqrt(-27);y1:=jInvariant(x1); x2:=(-1+Sqrt(-27))/4;y2:=jInvariant(x2); x3:=(1+Sqrt(-27))/4 ;y3:=jInvariant(x3); x1;x2;x3; z1:=y1+y2+y3; z2:=y1*y2+y2*y3+y3*y1; z3:=y1*y2*y3; z1;z2;z3; Output: Magma V2.10-6 Thu Dec 18 2003 02:46:12 on modular [Seed = 2538206182] ------------------------------------- 5.196152422706631880582339024499*i -1/4 + 1.299038105676657970145584756124*i 1/4 + 1.299038105676657970145584756124*i 151013228705999.99999999999985789145 + 0.E-15*i 224179462187999999.99999999987267074175 - 1.4551915228 E-11*i 1879994705687999999999.9999976456 + 0.000000000*i Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 03:04:36 2003 Input: C := ComplexField(); x1:=Sqrt(-6);y1:=jInvariant(x1); x2:=Sqrt(-6)/2;y2:=jInvariant(x2); x1;x2; z1:=y1+y2; z2:=y1*y2; z1;z2; Output: Magma V2.10-6 Thu Dec 18 2003 03:04:33 on modular [Seed = 3762192452] ------------------------------------- 2.449489742783178098197284074703*i 1.224744871391589049098642037351*i 4834943.99999999999999999999841181322 + 0.E-22*i 14670139391.99999999999999999327 + 0.E-18*i Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 03:32:20 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-11+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; z1;z2;z3;z4; Output: Magma V2.10-6 Thu Dec 18 2003 03:32:17 on modular [Seed = 1071736346] ------------------------------------- 82028232174463.99999999999994138022 - 75249.430095134301278622811298557730*i 739545196161544956707.17874726653 - 6172577724418746741.4615325210*i -31245812532058645009460794.030273437500 - 55779874792590898372787848.7646484375*i -7.252350722556221726317448639666 E29 + 1.172052934927196222134150425749 E30*i -1.57816569686227799935875750109 E31 + 2.0500513353818016690498038256965 E31*i -3.438877675902838151843235228937 E34 + 5.56725832351767635969767979807 E34*i 82028232174463.99999999999994138022 - 75249.430095134301278622811298557730*i 739545196161544956707.17874726653 - 6172577724418746741.4615325210*i -31245812532058645009460794.030273437500 - 55779874792590898372787848.7646484375*i -7.252350722556221726317448639666 E29 + 1.172052934927196222134150425749 E30*i Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 03:32:43 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-11+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 03:32:40 on modular [Seed = 553548092] ------------------------------------- 82028232174463.99999999999994138022 - 75249.430095134301278622811298557730*i 739545196161544956707.17874726653 - 6172577724418746741.4615325210*i -31245812532058645009460794.030273437500 - 55779874792590898372787848.7646484375*i -7.252350722556221726317448639666 E29 + 1.172052934927196222134150425749 E30*i -1.57816569686227799935875750109 E31 + 2.0500513353818016690498038256965 E31*i -3.438877675902838151843235228937 E34 + 5.56725832351767635969767979807 E34*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 03:33:33 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-11+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 03:33:29 on modular [Seed = 720663367] ------------------------------------- 82028232174463.99999999999994138022 - 75249.430095134301278622811298557730*i 739545196161544956707.17874726653 - 6172577724418746741.4615325210*i -31245812532058645009460794.030273437500 - 55779874792590898372787848.7646484375*i -7.252350722556221726317448639666 E29 + 1.172052934927196222134150425749 E30*i -1.57816569686227799935875750109 E31 + 2.0500513353818016690498038256965 E31*i -3.438877675902838151843235228937 E34 + 5.56725832351767635969767979807 E34*i Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 03:35:14 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-11+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); x1;x2;x3;x4;x5;x6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; Output: Magma V2.10-6 Thu Dec 18 2003 03:35:11 on modular [Seed = 532760212] ------------------------------------- 5.099019513592784830028224108993*i 2.54950975679639241501411205449*i 1/3 + 1.69967317119759494334274136964*i -11/3 + 1.69967317119759494334274136964*i 2/5 + 1.0198039027185569660056448217836*i -2/5 + 1.0198039027185569660056448217836*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 03:36:19 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-11+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); x1;x2;x3;x4;x5;x6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1; Output: Magma V2.10-6 Thu Dec 18 2003 03:36:16 on modular [Seed = 14571572] ------------------------------------- 5.099019513592784830028224108993*i 2.54950975679639241501411205449*i 1/3 + 1.69967317119759494334274136964*i -11/3 + 1.69967317119759494334274136964*i 2/5 + 1.0198039027185569660056448217836*i -2/5 + 1.0198039027185569660056448217836*i 82028232174463.99999999999994138022 - 75249.430095134301278622811298557730*i Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host com2pc6.postech.ac.kr. (141.223.34.207) Time: Thu Dec 18 04:47:20 2003 Input: j( Output: Magma V2.10-6 Thu Dec 18 2003 04:47:17 on modular [Seed = 2320810526] ------------------------------------- >> j(; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host com2pc6.postech.ac.kr. (141.223.34.207) Time: Thu Dec 18 04:47:39 2003 Input: j(-2) Output: Magma V2.10-6 Thu Dec 18 2003 04:47:36 on modular [Seed = 4113284476] ------------------------------------- >> j(-2); ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host com2pc6.postech.ac.kr. (141.223.34.207) Time: Thu Dec 18 04:48:55 2003 Input: j(-15) Output: Magma V2.10-6 Thu Dec 18 2003 04:48:52 on modular [Seed = 3762202581] ------------------------------------- >> j(-15) ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:10:01 2003 Input: N:=196; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:09:54 on modular [Seed = 1401808766] ------------------------------------- >> cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); ^ Runtime error in '[]': Sequence element 3 not defined Total time: 4.849 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:11:12 2003 Input: N:=198; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:10:16 on modular [Seed = 2759463059] ------------------------------------- [ 198, 1, 1 ][ 11, 3, 1 ][] [ 198, 2, 1 ][ 11, 1, 1 ][] [ 198, 3, 1 ][ 11, 1, 1 ][] [ 198, 4, 1 ][ 11, 1, 1 ][] [ 198, 5, 1 ][ 11, 1, 1 ][] Total time: 55.189 seconds, Total memory usage: 6.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:16:44 2003 Input: N:=166; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:16:25 on modular [Seed = 2454462772] ------------------------------------- [ 166, 1, 1 ][ 2, 1, 1 ][ 83, 1, 1 ][] [ 166, 2, 1 ][ 2, 1, 131 ][ 83, 1, 1 ][] [ 166, 3, 1 ][ 2, 7, 1 ][ 83, 1, 1 ][] Total time: 18.319 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:17:37 2003 Input: N:=66; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:17:10 on modular [Seed = 3929299315] ------------------------------------- [ 66, 1, 1 ][ 2, 1, 1 ][ 3, 3, 1 ][ 11, 1, 1 ][] [ 66, 2, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 11, 1, 1 ][] [ 66, 3, 1 ][ 2, 5, 1 ][ 3, 5, 1 ][ 11, 1, 1 ][] Total time: 26.359 seconds, Total memory usage: 4.66MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:22:50 2003 Input: N:=198; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:22:44 on modular [Seed = 4196682705] ------------------------------------- Do not know how to compute component group at 3 Total time: 5.479 seconds, Total memory usage: 3.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:27:45 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(198,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(99,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Thu Dec 18 2003 06:27:22 on modular [Seed = 3440606712] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 1 Total time: 22.549 seconds, Total memory usage: 7.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:28:42 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(198,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(66,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],2); Output: Magma V2.10-6 Thu Dec 18 2003 06:28:19 on modular [Seed = 3290068152] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 1 Total time: 22.809 seconds, Total memory usage: 7.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:30:56 2003 Input: N:=102; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:30:38 on modular [Seed = 3574293796] ------------------------------------- [ 102, 1, 1 ][ 3, 1, 1 ][] [ 102, 2, 1 ][ 3, 3, 1 ][] [ 102, 3, 1 ][ 3, 1, 1 ][] Total time: 17.799 seconds, Total memory usage: 4.75MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:31:42 2003 Input: N:=102; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:30:56 on modular [Seed = 3524026893] ------------------------------------- [ 102, 1, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 102, 2, 1 ][ 2, 1, 3 ][ 3, 3, 1 ][ 17, 1, 1 ][] [ 102, 3, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] Total time: 45.680 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:33:37 2003 Input: N:=105; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:33:12 on modular [Seed = 620399474] ------------------------------------- [ 105, 1, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 105, 2, 1 ][ 3, 1, 5 ][ 5, 1, 1 ][ 7, 1, 1 ][] Total time: 24.770 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 06:35:04 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-11+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1; Output: Magma V2.10-6 Thu Dec 18 2003 06:35:01 on modular [Seed = 971478770] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230611934182 - 37624.71504756715063931140564845168*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 82028232174463.99999999999994138022 - 75249.430095134301278622811298557730*i Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 06:35:45 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1; Output: Magma V2.10-6 Thu Dec 18 2003 06:35:42 on modular [Seed = 248553518] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230625169072 + 37624.71504756715063931140564100705*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 82028232174463.99999999999994138022 - 9.09898673743 E-24*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 06:36:08 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6 Output: Magma V2.10-6 Thu Dec 18 2003 06:36:05 on modular [Seed = 131705100] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230625169072 + 37624.71504756715063931140564100705*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 82028232174463.99999999999994138022 - 9.09898673743 E-24*i 739545196164376195071.9999992102 - 0.00000000081445258793252282917*i -31013571054009020830449663.9614257812 - 0.0077438650132588137287*i 1.378339984770204496120635386764 E30 + 591.37886428850060838158*i 2.57350396422293342005647105004 E31 + 11907.5000000000*i 6.54371797303335452423236759422 E34 + 32505856.*i Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:36:27 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(105,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(35,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; TamagawaNumber(B[2],3); Output: Magma V2.10-6 Thu Dec 18 2003 06:36:17 on modular [Seed = 482521603] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 1 Total time: 9.759 seconds, Total memory usage: 5.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:38:14 2003 Input: N:=114; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:37:21 on modular [Seed = 332250444] ------------------------------------- [ 114, 1, 1 ][ 2, 1, 1 ][ 3, 1, 5 ][ 19, 1, 1 ][] [ 114, 2, 1 ][ 2, 5, 5 ][ 3, 1, 3 ][ 19, 1, 1 ][] [ 114, 3, 1 ][ 2, 3, 1 ][ 3, 3, 1 ][ 19, 1, 1 ][] Total time: 52.099 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:41:06 2003 Input: N:=132; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:40:14 on modular [Seed = 1318118270] ------------------------------------- [ 132, 1, 1 ][ 3, 1, 5 ][ 11, 1, 1 ][] [ 132, 2, 1 ][ 3, 1, 1 ][ 11, 1, 1 ][] Total time: 50.899 seconds, Total memory usage: 4.87MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:44:01 2003 Input: N:=150; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:43:08 on modular [Seed = 1167845543] ------------------------------------- [ 150, 1, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 150, 2, 1 ][ 2, 1, 1 ][ 3, 1, 3 ][] [ 150, 3, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] Total time: 51.310 seconds, Total memory usage: 5.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:50:11 2003 Input: N:=168; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:49:08 on modular [Seed = 3026853806] ------------------------------------- [ 168, 1, 1 ][ 3, 1, 3 ][ 7, 1, 1 ][] [ 168, 2, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] Total time: 61.720 seconds, Total memory usage: 5.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:52:48 2003 Input: N:=170; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:52:05 on modular [Seed = 2571579986] ------------------------------------- [ 170, 1, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 17, 3, 1 ][] [ 170, 2, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] [ 170, 3, 1 ][ 2, 1, 3 ][ 5, 3, 1 ][ 17, 1, 1 ][] [ 170, 4, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] [ 170, 5, 1 ][ 2, 21, 7 ][ 5, 1, 3 ][ 17, 1, 1 ][] [ 170, 6, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] Total time: 42.569 seconds, Total memory usage: 4.97MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:56:59 2003 Input: N:=174; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:55:41 on modular [Seed = 3929292921] ------------------------------------- [ 174, 1, 1 ][ 2, 1, 13 ][ 3, 1, 1 ][ 29, 1, 1 ][] [ 174, 2, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 29, 1, 1 ][] [ 174, 3, 1 ][ 2, 1, 11 ][ 3, 21, 7 ][ 29, 1, 1 ][] [ 174, 4, 1 ][ 2, 1, 1 ][ 3, 1, 3 ][ 29, 1, 1 ][] [ 174, 5, 1 ][ 2, 7, 1 ][ 3, 7, 1 ][ 29, 1, 1 ][] Total time: 77.809 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 06:59:49 2003 Input: N:=180; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 06:58:54 on modular [Seed = 4129841062] ------------------------------------- [ 180, 1, 1 ][ 5, 1, 1 ][] Total time: 54.689 seconds, Total memory usage: 6.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:01:56 2003 Input: N:=182; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:00:53 on modular [Seed = 3323490077] ------------------------------------- [ 182, 1, 1 ][ 2, 1, 11 ][ 7, 1, 7 ][ 13, 1, 1 ][] [ 182, 2, 1 ][ 2, 1, 7 ][ 7, 1, 1 ][ 13, 1, 5 ][] [ 182, 3, 1 ][ 2, 5, 5 ][ 7, 1, 3 ][ 13, 1, 1 ][] [ 182, 4, 1 ][ 2, 1, 1 ][ 7, 1, 3 ][ 13, 1, 1 ][] [ 182, 5, 1 ][ 2, 9, 3 ][ 7, 1, 1 ][ 13, 1, 1 ][] Total time: 62.809 seconds, Total memory usage: 5.03MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 07:05:16 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 07:05:12 on modular [Seed = 670666738] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230625169072 + 37624.71504756715063931140564100705*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 82028232174463.99999999999994138022 - 9.09898673743 E-24*i 739545196164376195071.9999992102 - 0.00000000081445258793252282917*i -31013571054009020830449663.9614257812 - 0.0077438650132588137287*i 1.378339984770204496120635386764 E30 + 591.37886428850060838158*i 2.57350396422293342005647105004 E31 + 11907.5000000000*i 6.54371797303335452423236759422 E34 + 32505856.*i Total time: 3.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:05:37 2003 Input: N:=186; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:04:06 on modular [Seed = 787515061] ------------------------------------- [ 186, 1, 1 ][ 2, 1, 1 ][ 3, 1, 11 ][ 31, 1, 1 ][] [ 186, 2, 1 ][ 2, 1, 7 ][ 3, 1, 1 ][ 31, 1, 1 ][] [ 186, 3, 1 ][ 2, 5, 1 ][ 3, 5, 1 ][ 31, 1, 1 ][] [ 186, 4, 1 ][ 2, 19, 19 ][ 3, 1, 1 ][ 31, 1, 1 ][] Total time: 90.710 seconds, Total memory usage: 5.45MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 07:08:10 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 07:08:07 on modular [Seed = 904630975] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230625169072 + 37624.71504756715063931140564100705*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 82028232174463.99999999999994138022 - 9.09898673743 E-24*i 739545196164376195071.9999992102 - 0.00000000081445258793252282917*i -31013571054009020830449663.9614257812 - 0.0077438650132588137287*i 1.378339984770204496120635386764 E30 + 591.37886428850060838158*i 2.57350396422293342005647105004 E31 + 11907.5000000000*i 88073233566650.99617146620534313683 + 3.9079850465 E-14*i Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:08:44 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(186,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(93,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; TamagawaNumber(B[4],2); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Dec 18 2003 07:08:21 on modular [Seed = 215133076] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Errors: /home/mfd/gomagma: line 2: 4641 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:10:53 2003 Input: N:=195; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:10:00 on modular [Seed = 131703090] ------------------------------------- [ 195, 1, 1 ][ 3, 1, 7 ][ 5, 1, 1 ][ 13, 1, 3 ][] [ 195, 2, 1 ][ 3, 3, 3 ][ 5, 1, 7 ][ 13, 1, 1 ][] [ 195, 3, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 13, 1, 1 ][] [ 195, 4, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 13, 1, 1 ][] [ 195, 5, 1 ][ 3, 1, 11 ][ 5, 1, 1 ][ 13, 1, 1 ][] Total time: 52.310 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 07:11:27 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 07:11:24 on modular [Seed = 281982545] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230625169072 + 37624.71504756715063931140564100705*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 82028232174463.99999999999994138022 - 9.09898673743 E-24*i 739545196164376195071.9999992102 - 0.00000000081445258793252282917*i -31013571054009020830449663.9614257812 - 0.0077438650132588137287*i 1.378339984770204496120635386764 E30 + 591.37886428850060838158*i 2.57350396422293342005647105004 E31 + 11907.5000000000*i 6.54371797303335452423236759422 E34 + 32505856.*i Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:13:16 2003 Input: B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(195,2,+1))))); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(65,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; TamagawaNumber(B[5],2); Output: Magma V2.10-6 Thu Dec 18 2003 07:13:09 on modular [Seed = 1284696756] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/22 Defined on 1 generator Relations: 22*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 1 Total time: 6.349 seconds, Total memory usage: 4.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:14:14 2003 Input: N:=197; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:14:10 on modular [Seed = 1384970093] ------------------------------------- [ 197, 1, 1 ][] [ 197, 2, 1 ][ 197, 1, 1 ][] [ 197, 3, 1 ][ 197, 49, 7 ][] Total time: 3.599 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:17:19 2003 Input: N:=204; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:15:53 on modular [Seed = 499365960] ------------------------------------- [ 204, 1, 1 ][ 3, 1, 11 ][ 17, 1, 1 ][] [ 204, 2, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] Total time: 84.909 seconds, Total memory usage: 6.06MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 07:17:20 2003 Input: C := ComplexField(); x1:=Sqrt(-5);y1:=jInvariant(x1); x2:=(-1+Sqrt(-5))/2;y2:=jInvariant(x2); x1;x2; z1=y1+y2; z2=y1*y2; z1;z2; Output: Magma V2.10-6 Thu Dec 18 2003 07:17:17 on modular [Seed = 1351546289] ------------------------------------- 2.236067977499789696409173668722*i -1/2 + 1.118033988749894848204586834361*i >> z1=y1+y2; ^ User error: Identifier 'z1' has not been declared or assigned >> z2=y1*y2; ^ User error: Identifier 'z2' has not been declared or assigned >> z1;z2;; ^ User error: Identifier 'z1' has not been declared or assigned >> z1;z2;; ^ User error: Identifier 'z2' has not been declared or assigned Total time: 3.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 07:17:37 2003 Input: C := ComplexField(); x1:=Sqrt(-5);y1:=jInvariant(x1); x2:=(-1+Sqrt(-5))/2;y2:=jInvariant(x2); x1;x2; z1:=y1+y2; z2:=y1*y2; z1;z2; Output: Magma V2.10-6 Thu Dec 18 2003 07:17:34 on modular [Seed = 2220499318] ------------------------------------- 2.236067977499789696409173668722*i -1/2 + 1.118033988749894848204586834361*i 1263999.99999999999999999999962942308 + 0.E-22*i -681471999.99999999999999999962052923963 + 4.06575814634 E-20*i Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 07:17:47 2003 Input: C := ComplexField(); x1:=Sqrt(-5);y1:=jInvariant(x1); x2:=(-1+Sqrt(-5))/2;y2:=jInvariant(x2); y1:y2 z1:=y1+y2; z2:=y1*y2; z1;z2; Output: Magma V2.10-6 Thu Dec 18 2003 07:17:43 on modular [Seed = 3962718503] ------------------------------------- >> z1:=y1+y2; ^ User error: bad syntax >> z1;z2;; ^ User error: Identifier 'z1' has not been declared or assigned -681471999.99999999999999999962052923963 + 4.06575814634 E-20*i Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 07:17:55 2003 Input: C := ComplexField(); x1:=Sqrt(-5);y1:=jInvariant(x1); x2:=(-1+Sqrt(-5))/2;y2:=jInvariant(x2); y1;y2; z1:=y1+y2; z2:=y1*y2; z1;z2; Output: Magma V2.10-6 Thu Dec 18 2003 07:17:52 on modular [Seed = 4096413992] ------------------------------------- 1264538.90947514050932022704701375289 + 0.E-22*i -538.90947514050932022704741057987 + 4.2509666066 E-26*i 1263999.99999999999999999999962942308 + 0.E-22*i -681471999.99999999999999999962052923963 + 4.06575814634 E-20*i Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:20:13 2003 Input: N:=138; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:19:15 on modular [Seed = 3507451326] ------------------------------------- [ 138, 1, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 23, 1, 1 ][] [ 138, 2, 1 ][ 2, 1, 1 ][ 3, 3, 1 ][ 23, 1, 1 ][] [ 138, 3, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 23, 1, 1 ][] [ 138, 4, 1 ][ 2, 11, 1 ][ 3, 11, 1 ][ 23, 1, 1 ][] Total time: 57.589 seconds, Total memory usage: 4.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:23:20 2003 Input: N:=165; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:22:44 on modular [Seed = 1234692726] ------------------------------------- [ 165, 1, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] [ 165, 2, 1 ][ 3, 3, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] [ 165, 3, 1 ][ 3, 5, 1 ][ 5, 5, 1 ][ 11, 1, 1 ][] Total time: 36.279 seconds, Total memory usage: 4.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 07:25:50 2003 Input: N:=190; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 07:25:05 on modular [Seed = 1151002574] ------------------------------------- [ 190, 1, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 19, 1, 1 ][] [ 190, 2, 1 ][ 2, 11, 11 ][ 5, 1, 1 ][ 19, 1, 1 ][] [ 190, 3, 1 ][ 2, 3, 1 ][ 5, 3, 1 ][ 19, 1, 1 ][] [ 190, 4, 1 ][ 2, 1, 13 ][ 5, 1, 1 ][ 19, 1, 1 ][] Total time: 45.050 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 08:14:15 2003 Input: C := ComplexField(); x1:=Sqrt(-21);y1:=jInvariant(x1); x2:=(-1+Sqrt(-21))/2 ;y2:=jInvariant(x2); x3:=Sqrt(-21)/3 ;y3:=jInvariant(x3); x4:=(-2+Sqrt(-21))/5 ;y4:=jInvariant(x4); z1:=y1+y2+y3+y4; z2:=y1*y2+y2*y3+y3*y4+y4*y1; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z4:=y1*y2*y3*y4; z1;z2;z3;z4; Output: Magma V2.10-6 Thu Dec 18 2003 08:14:12 on modular [Seed = 3590865369] ------------------------------------- 3196800946943.99999999999999794608 + 0.E-16*i -5713193480168521727.99999999487772583961 - 1.16539667639 E-10*i -88821246589810089394175.9998893737 - 0.0000017007114342*i -5133201653210986057826303.9901123046 + 0.003295898437*i Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 08:14:36 2003 Input: C := ComplexField(); x1:=Sqrt(-21);y1:=jInvariant(x1); x2:=(-1+Sqrt(-21))/2 ;y2:=jInvariant(x2); x3:=Sqrt(-21)/3 ;y3:=jInvariant(x3); x4:=(-2+Sqrt(-21))/5 ;y4:=jInvariant(x4); y1;y2;y3;y4; z1:=y1+y2+y3+y4; z2:=y1*y2+y2*y3+y3*y4+y4*y1; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z4:=y1*y2*y3*y4; z1;z2;z3;z4; Output: Magma V2.10-6 Thu Dec 18 2003 08:14:33 on modular [Seed = 754105151] ------------------------------------- 3196802718613.91329280328999662419 + 0.E-16*i -1787216.60124765701986744310137767552 - 7.6962287370 E-23*i 15488.68089312424459226714340319500 + 0.E-24*i 58.00706172948527653405559355019932205157744 - 3.8774091210 E-26*i 3196800946943.99999999999999794608 + 0.E-16*i -5713193480168521727.99999999487772583961 - 1.16539667639 E-10*i -88821246589810089394175.9998893737 - 0.0000017007114342*i -5133201653210986057826303.9901123046 + 0.003295898437*i Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 08:34:12 2003 Input: C := ComplexField(); x1:=Sqrt(-38);y1:=jInvariant(x1); x2:=Sqrt(-38)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-38))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-38))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-38))/6;y5:=jInvariant(x5); x6:=(-2+Sqrt(-38))/6;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 08:34:09 on modular [Seed = 1723397533] ------------------------------------- 66246265662298399.44546048835036344826 + 0.E-12*i 257384243.204380667330012153123794870976 + 0.E-20*i -201569.250294795745398294909268501625 - 350415.98576912791428450263093642611*i -201569.250294795745398294909347910964 + 350415.98576912791428450263089010399*i 247.925374217874988651278079307195681694103 - 328.73069290953675179300385450169*i 247.925374217874988651278079161792839643766 + 328.73069290953675179300385446291*i 66246265919279999.99999999993906385498 + 0.E-16*i 17024071380555203519999999.9770507812 - 0.0000023874454288790713404*i -6.85454429479948368895999998962 E30 - 638.374509334563732055115026220448*i 2.78305862478709361426528700173 E36 + 603948286.75000214017927646636*i 1.380504171426125758791679997180 E39 + 1.8861027327 E11*i 4.72390748138731280269311998734 E41 + 2.11106232460 E14*i Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host koch.mat.uniroma3.it. (193.204.165.149) Time: Thu Dec 18 08:56:06 2003 Input: gcd(24,36) Output: Magma V2.10-6 Thu Dec 18 2003 08:56:03 on modular [Seed = 2354184789] ------------------------------------- >> gcd(24,36); ^ User error: Identifier 'gcd' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 08:56:59 2003 Input: c:=GolayCode(2, true); c; Output: Magma V2.10-6 Thu Dec 18 2003 08:56:56 on modular [Seed = 2454462352] ------------------------------------- >> c:=GolayCode(2, true); ^ Runtime error in 'GolayCode': Bad argument types Argument types given: RngIntElt, BoolElt >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 08:57:28 2003 Input: c:=GolayCode(2); c; Output: Magma V2.10-6 Thu Dec 18 2003 08:57:25 on modular [Seed = 3962724739] ------------------------------------- >> c:=GolayCode(2); ^ Runtime error in 'GolayCode': Bad argument types Argument types given: RngIntElt >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 08:57:46 2003 Input: C := GolayCode(2); c; Output: Magma V2.10-6 Thu Dec 18 2003 08:57:43 on modular [Seed = 3845875864] ------------------------------------- >> C := GolayCode(2); ^ Runtime error in 'GolayCode': Bad argument types Argument types given: RngIntElt >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 08:58:08 2003 Input: C := GolayCode(GF(2)); c; Output: Magma V2.10-6 Thu Dec 18 2003 08:58:04 on modular [Seed = 4063002549] ------------------------------------- >> C := GolayCode(GF(2)); ^ Runtime error in 'GolayCode': Bad argument types Argument types given: FldFin >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 08:58:19 2003 Input: C := GolayCode(GF(2), true); c; Output: Magma V2.10-6 Thu Dec 18 2003 08:58:16 on modular [Seed = 3407169177] ------------------------------------- >> c;; ^ User error: Identifier 'c' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 08:58:27 2003 Input: C := GolayCode(GF(2), true); C; Output: Magma V2.10-6 Thu Dec 18 2003 08:58:24 on modular [Seed = 3223211370] ------------------------------------- [24, 12, 8] Extended Golay Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 08:59:54 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); D; Output: Magma V2.10-6 Thu Dec 18 2003 08:59:51 on modular [Seed = 3724563235] ------------------------------------- [23, 11, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1] [0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1] [0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:00:57 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; Output: Magma V2.10-6 Thu Dec 18 2003 09:00:54 on modular [Seed = 804365072] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc203.postech.ac.kr. (141.223.33.28) Time: Thu Dec 18 09:04:04 2003 Input: C:=ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Output: Magma V2.10-6 Thu Dec 18 2003 09:04:01 on modular [Seed = 265389047] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 09:04:37 2003 Input: C=ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Output: Magma V2.10-6 Thu Dec 18 2003 09:04:34 on modular [Seed = 114854621] ------------------------------------- >> C=ComplexField(); ^ User error: bad syntax 1727.99999999999999999999999997415 + 0.E-26*i Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 09:04:50 2003 Input: C:=ComplexField(); x:=Sqrt(-1); y:=jInvariant(x); y; Output: Magma V2.10-6 Thu Dec 18 2003 09:04:47 on modular [Seed = 298819015] ------------------------------------- 1727.99999999999999999999999997415 + 0.E-26*i Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:17:40 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; F := GolayCode(GF(2), true); F; Output: Magma V2.10-6 Thu Dec 18 2003 09:17:37 on modular [Seed = 2074473299] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] [24, 12, 8] Extended Golay Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:18:43 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; Output: Magma V2.10-6 Thu Dec 18 2003 09:18:40 on modular [Seed = 1974205724] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:19:25 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; b, d := Decode(E, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 09:19:21 on modular [Seed = 1284686863] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 2.999 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:20:08 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[5] := 1 - w[5]; w[20] := 1 - w[20]; b, d := Decode(E, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 09:20:05 on modular [Seed = 1552078048] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> w[20] := 1 - w[20]; ^ Runtime error in '[]': Argument 2 (20) should be in the range [1 .. 18] true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.079 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:20:25 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 09:20:22 on modular [Seed = 1468653528] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 2.999 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:22:46 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); b; d; P := ParityCheckMatrix(E); P; Output: Magma V2.10-6 Thu Dec 18 2003 09:22:43 on modular [Seed = 2926586292] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1] Total time: 3.019 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:34:58 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); b; d; P := ParityCheckMatrix(E); P; Output: Magma V2.10-6 Thu Dec 18 2003 09:34:55 on modular [Seed = 3077125009] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1] Total time: 3.029 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:35:59 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); b; d; a := E ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; v P := ParityCheckMatrix(E); P; Output: Magma V2.10-6 Thu Dec 18 2003 09:35:56 on modular [Seed = 2187069159] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) >> P := ParityCheckMatrix(E); ^ User error: bad syntax >> P; ^ User error: Identifier 'P' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:36:16 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); b; d; a := E ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; P := ParityCheckMatrix(E); P; Output: Magma V2.10-6 Thu Dec 18 2003 09:36:13 on modular [Seed = 2638420457] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1] Total time: 3.059 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:36:56 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); b; d; a := E ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; b := a; b[0] := 1; b; Output: Magma V2.10-6 Thu Dec 18 2003 09:36:53 on modular [Seed = 2487881784] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) >> b[0] := 1; ^ Runtime error in :=: Vector index is not in the range [1 .. 18] (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) Total time: 3.009 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:37:15 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); b; d; a := E ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; b := a; b[1] := 1; b; Output: Magma V2.10-6 Thu Dec 18 2003 09:37:12 on modular [Seed = 4012993374] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) true (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) (1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) Total time: 3.079 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:38:10 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; v := E ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; v; w[5] := 1 - w[5]; w[14] := 1 - w[14]; b, d := Decode(E, w); a := E ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; b := a; b[1] := 1; c, d := Decode(E, b); c; d; Output: Magma V2.10-6 Thu Dec 18 2003 09:38:06 on modular [Seed = 3862454784] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) true (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) Total time: 3.009 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:39:00 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; P := ParityCheckMatrix(E); P; Output: Magma V2.10-6 Thu Dec 18 2003 09:38:57 on modular [Seed = 4029576152] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:39:29 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); E; P := ParityCheckMatrix(E); Output: Magma V2.10-6 Thu Dec 18 2003 09:39:26 on modular [Seed = 3407169788] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 09:39:48 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); E := ShortenCode(D, 23); F := ShortenCode(E, 22); G := ShortenCode(F, 21); D := ShortenCode(G, 20); E := ShortenCode(D, 19); P := ParityCheckMatrix(E); P; Output: Magma V2.10-6 Thu Dec 18 2003 09:39:45 on modular [Seed = 3256631770] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 09:52:00 2003 Input: C:=ComplexField(); x:=Sqrt(-2); y:=jInvariant(x); y; Output: Magma V2.10-6 Thu Dec 18 2003 09:51:57 on modular [Seed = 165120300] ------------------------------------- 7999.99999999999999999999999844903 + 0.E-24*i Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 09:54:31 2003 Input: N:=234; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 09:54:05 on modular [Seed = 81429665] ------------------------------------- Do not know how to compute component group at 3 Total time: 25.689 seconds, Total memory usage: 7.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 09:56:09 2003 Input: N:=234; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 09:55:00 on modular [Seed = 281972988] ------------------------------------- [ 234, 1, 1 ][ 13, 1, 1 ][] [ 234, 2, 1 ][ 13, 1, 1 ][] [ 234, 3, 1 ][ 13, 1, 1 ][] [ 234, 4, 1 ][ 13, 1, 1 ][] [ 234, 5, 1 ][ 13, 1, 1 ][] Total time: 68.529 seconds, Total memory usage: 7.20MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 09:57:36 2003 Input: C:=ComplexField(); x1:=Sqrt(-5); y1:=jInvariant(x1); x2:(-1+Sqrt(-6))/2; y2:=jInvariant(x2); y1;y2; Output: Magma V2.10-6 Thu Dec 18 2003 09:57:33 on modular [Seed = 1807062046] ------------------------------------- >> x2:(-1+Sqrt(-6))/2; ^ User error: bad syntax >> y2:=jInvariant(x2); ^ User error: Identifier 'x2' has not been declared or assigned 1264538.90947514050932022704701375289 + 0.E-22*i >> y1;y2; ^ User error: Identifier 'y2' has not been declared or assigned Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 09:57:39 2003 Input: N:=234; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 09:57:13 on modular [Seed = 1756796681] ------------------------------------- [ 234, 1, 1 ][ 2, 1, 1 ][] [ 234, 2, 1 ][ 2, 1, 7 ][] [ 234, 3, 1 ][ 2, 1, 1 ][] [ 234, 4, 1 ][ 2, 1, 1 ][] [ 234, 5, 1 ][ 2, 1, 1 ][] Total time: 26.039 seconds, Total memory usage: 7.11MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 09:58:47 2003 Input: C:=ComplexField(); x1:=Sqrt(-5); y1:=jInvariant(x1); x2:{-1+Sqrt(-6)}/2; y2:=jInvariant(x2); y1;y2; Output: Magma V2.10-6 Thu Dec 18 2003 09:58:44 on modular [Seed = 2057602550] ------------------------------------- >> x2:{-1+Sqrt(-6)}/2; ^ User error: bad syntax >> y2:=jInvariant(x2); ^ User error: Identifier 'x2' has not been declared or assigned 1264538.90947514050932022704701375289 + 0.E-22*i >> y1;y2; ^ User error: Identifier 'y2' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 09:59:37 2003 Input: C:=ComplexField(); x1:=Sqrt(-5); y1:=jInvariant(x1); x2:=(-1+Sqrt(-6))/2; y2:=jInvariant(x2); y1;y2; Output: Magma V2.10-6 Thu Dec 18 2003 09:59:34 on modular [Seed = 1940753549] ------------------------------------- 1264538.90947514050932022704701375289 + 0.E-22*i -1539.196950172495621064226645709032 + 8.7962539605 E-26*i Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 10:03:11 2003 Input: C:=ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=(Sqrt(-14))/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y2:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y2:=jInvariant(x4); y1;y2;y3;y4; Output: Magma V2.10-6 Thu Dec 18 2003 10:03:07 on modular [Seed = 1451796693] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i -562.189330472902256983178199150560 - 2127.76194138925212063251332950098*i >> y1;y2;y3;y4; ^ User error: Identifier 'y3' has not been declared or assigned >> y1;y2;y3;y4; ^ User error: Identifier 'y4' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 10:03:27 2003 Input: C:=ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=(Sqrt(-14))/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); y1;y2;y3;y4; Output: Magma V2.10-6 Thu Dec 18 2003 10:03:23 on modular [Seed = 2943439164] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199628774 + 2127.76194138925212063251332929418*i -562.189330472902256983178199150560 - 2127.76194138925212063251332950098*i Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Thu Dec 18 10:03:29 2003 Input: C:=ComplexField(); x1:=Sqrt(-14); y1:=jInvariant(x1); x2:=(Sqrt(-14))/2; y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3; y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3; y4:=jInvariant(x4); y1;y2;y3;y4; Output: Magma V2.10-6 Thu Dec 18 2003 10:03:25 on modular [Seed = 2726059063] ------------------------------------- 16220257532.059502697452916043438 + 0.E-18*i 128104.319158248351597910108112778871 + 0.E-23*i -562.189330472902256983178199628774 + 2127.76194138925212063251332929418*i -562.189330472902256983178199150560 - 2127.76194138925212063251332950098*i Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 10:04:23 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(117,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(234,2,+1))))); for i in [1..#A] doCongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 10:04:16 on modular [Seed = 2993441898] ------------------------------------- >> for i in [1..#A] doCongruenceGroupAnemic(A[i],B[2],200); end for; ^ User error: bad syntax Total time: 6.799 seconds, Total memory usage: 3.71MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 10:04:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(117,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(234,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 10:04:32 on modular [Seed = 2320791458] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 7.799 seconds, Total memory usage: 4.62MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 10:11:15 2003 Input: N:=306; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 10:09:38 on modular [Seed = 2270788509] ------------------------------------- [ 306, 1, 1 ][ 17, 1, 1 ][] [ 306, 2, 1 ][ 17, 1, 1 ][] [ 306, 3, 1 ][ 17, 1, 1 ][] [ 306, 4, 1 ][ 17, 1, 1 ][] [ 306, 5, 1 ][ 17, 3, 1 ][] [ 306, 6, 1 ][ 17, 1, 1 ][] Total time: 95.909 seconds, Total memory usage: 9.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 10:14:15 2003 Input: N:=342; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 10:12:23 on modular [Seed = 2521328233] ------------------------------------- [ 342, 1, 1 ][ 19, 1, 1 ][] [ 342, 2, 1 ][ 19, 1, 1 ][] [ 342, 3, 1 ][ 19, 1, 1 ][] [ 342, 4, 1 ][ 19, 1, 1 ][] [ 342, 5, 1 ][ 19, 1, 1 ][] [ 342, 6, 1 ][ 19, 1, 1 ][] [ 342, 7, 1 ][ 19, 1, 1 ][] Total time: 111.209 seconds, Total memory usage: 11.00MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 10:16:23 2003 Input: N:=342; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 10:14:30 on modular [Seed = 4012971153] ------------------------------------- [ 342, 1, 1 ][ 19, 1, 1 ][] [ 342, 2, 1 ][ 19, 1, 1 ][] [ 342, 3, 1 ][ 19, 1, 1 ][] [ 342, 4, 1 ][ 19, 1, 1 ][] [ 342, 5, 1 ][ 19, 1, 1 ][] [ 342, 6, 1 ][ 19, 1, 1 ][] [ 342, 7, 1 ][ 19, 1, 1 ][] Total time: 112.009 seconds, Total memory usage: 11.00MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 10:18:41 2003 Input: C := GolayCode(GF(2), true); C; Output: Magma V2.10-6 Thu Dec 18 2003 10:18:37 on modular [Seed = 3674546622] ------------------------------------- [24, 12, 8] Extended Golay Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1] Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 10:19:33 2003 Input: N:=414; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 10:17:10 on modular [Seed = 3323477272] ------------------------------------- [ 414, 1, 1 ][ 23, 1, 1 ][] [ 414, 2, 1 ][ 23, 1, 1 ][] [ 414, 3, 1 ][ 23, 1, 1 ][] [ 414, 4, 1 ][ 23, 1, 1 ][] [ 414, 5, 1 ][ 23, 3, 1 ][] [ 414, 6, 1 ][ 23, 1, 1 ][] [ 414, 7, 1 ][ 23, 1, 1 ][] Total time: 142.429 seconds, Total memory usage: 14.31MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 10:24:02 2003 Input: C := GolayCode(GF(2), true); C; P := ParityCheckMatrix(C); P; Output: Magma V2.10-6 Thu Dec 18 2003 10:23:59 on modular [Seed = 787535750] ------------------------------------- [24, 12, 8] Extended Golay Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1] [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 10:26:56 2003 Input: C := GolayCode(GF(2), false); C; P := ParityCheckMatrix(C); P; Output: Magma V2.10-6 Thu Dec 18 2003 10:26:53 on modular [Seed = 837798187] ------------------------------------- [23, 12, 7] Unextended Golay Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1] [0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1] [0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 10:34:26 2003 Input: N:=522; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 10:31:20 on modular [Seed = 14612335] ------------------------------------- Current total memory usage: 4.6MB, failed memory request: 16384.0MB System error: Out of memory. All virtual memory has been exhausted so Magma cannot perform this statement. Total time: 185.560 seconds, Total memory usage: 4.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 11:00:30 2003 Input: N:=522; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 10:58:28 on modular [Seed = 1923908593] ------------------------------------- Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 1923908593 Time to this point: 121.76 Segmentation fault Total time: 121.779 seconds, Total memory usage: 4.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 11:04:41 2003 Input: N:=90; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 11:04:14 on modular [Seed = 1568910724] ------------------------------------- [ 90, 1, 1 ][ 5, 3, 1 ][] [ 90, 2, 1 ][ 5, 1, 1 ][] [ 90, 3, 1 ][ 5, 1, 1 ][] Total time: 27.039 seconds, Total memory usage: 4.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 11:05:54 2003 Input: N:=126; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 11:05:24 on modular [Seed = 2709475010] ------------------------------------- [ 126, 1, 1 ][ 7, 1, 1 ][] [ 126, 2, 1 ][ 7, 1, 1 ][] Total time: 29.729 seconds, Total memory usage: 4.83MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:12:57 2003 Input: C := GolayCode(GF(2), false); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; Output: Magma V2.10-6 Thu Dec 18 2003 11:12:54 on modular [Seed = 2976865424] ------------------------------------- >> D := ShortenCode(C, 24); ^ Runtime error in 'ShortenCode': Value for component index (24) should be in the range [1..23] >> C := ShortenCode(D, 23); ^ User error: Identifier 'D' has not been declared or assigned [19, 8, 7] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0] [0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0] [0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 1] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1] [0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0] [0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:13:24 2003 Input: C := GolayCode(GF(2), false); D := ShortenCode(C, 24); D; Output: Magma V2.10-6 Thu Dec 18 2003 11:13:21 on modular [Seed = 3093714366] ------------------------------------- >> D := ShortenCode(C, 24); ^ Runtime error in 'ShortenCode': Value for component index (24) should be in the range [1..23] >> D; ^ User error: Identifier 'D' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:13:34 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); D; Output: Magma V2.10-6 Thu Dec 18 2003 11:13:31 on modular [Seed = 2387633026] ------------------------------------- [23, 11, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1] [0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1] [0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:14:06 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; Output: Magma V2.10-6 Thu Dec 18 2003 11:14:03 on modular [Seed = 2504751353] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:15:35 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 0; w[2] := 0; w[3] := 0; b, d := Decode(C, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 11:15:32 on modular [Seed = 2554754331] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) Total time: 3.099 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:15:52 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 0; w[2] := 0; w[3] := 0; w[4] := 0; b, d := Decode(C, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 11:15:49 on modular [Seed = 4012966525] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) Total time: 3.009 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:16:06 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 1; w[2] := 0; w[3] := 0; w[4] := 0; b, d := Decode(C, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 11:16:03 on modular [Seed = 4129823506] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) Total time: 3.009 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:16:33 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 1; w[2] := 0; w[3] := 0; w[4] := 0; w[5] := 0; w[6] := 0; b, d := Decode(C, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 11:16:29 on modular [Seed = 4246933511] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0) Total time: 3.039 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:17:02 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 1; w[2] := 0; w[3] := 0; w[4] := 0; w[5] := 0; b, d := Decode(C, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 11:16:58 on modular [Seed = 3290048793] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0) Total time: 3.109 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:23:05 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 1; w[2] := 0; w[3] := 0; w[7] := 0; w[5] := 0; b, d := Decode(C, w); b; d; Output: Magma V2.10-6 Thu Dec 18 2003 11:23:02 on modular [Seed = 3524016531] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) Total time: 3.069 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:28:59 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 1; w[2] := 0; w[3] := 0; w[7] := 0; w[5] := 0; b, d := Decode(C, w); b; d; IsSelfDual(C); Output: Magma V2.10-6 Thu Dec 18 2003 11:28:55 on modular [Seed = 570411968] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) false Total time: 3.109 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 11:29:30 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 1; w[2] := 0; w[3] := 0; w[7] := 0; w[5] := 0; b, d := Decode(C, w); b; d; IsSelfDual(C); IsPerfect(C); Output: Magma V2.10-6 Thu Dec 18 2003 11:29:27 on modular [Seed = 921230583] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] true (0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0) false false Total time: 3.059 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:49:07 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]; w := v; w[1] := 1; w[2] := 0; w[3] := 0; w[7] := 0; w[5] := 0; Output: Magma V2.10-6 Thu Dec 18 2003 14:49:04 on modular [Seed = 4063218023] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:50:00 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := [0, 0, 1, 0, 0, 0]; E := v * C; E; Output: Magma V2.10-6 Thu Dec 18 2003 14:49:55 on modular [Seed = 3239901703] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> E := v * C; ^ Runtime error in '*': Bad argument types Argument types given: SeqEnum[RngIntElt], Code >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:51:25 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := [0, 0, 1, 0, 0, 0]; E := v * C; E; Output: Magma V2.10-6 Thu Dec 18 2003 14:51:22 on modular [Seed = 3540969932] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> E := v * C; ^ Runtime error in '*': Bad argument types Argument types given: SeqEnum[RngIntElt], Code >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:51:40 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := [0, 0, 1, 0, 0, 0]; E := C * C; E; Output: Magma V2.10-6 Thu Dec 18 2003 14:51:36 on modular [Seed = 3657949367] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> E := C * C; ^ Runtime error in '*': Bad argument types Argument types given: Code, Code >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:51:53 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := [0, 0, 1, 0, 0, 0]; E := CC; E; Output: Magma V2.10-6 Thu Dec 18 2003 14:51:49 on modular [Seed = 753997405] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> E := CC; ^ User error: Identifier 'CC' has not been declared or assigned >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:52:51 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; ee := 1 + 1; v := [0, 0, 1, 0, 0, 0]; E := CC; E; Output: Magma V2.10-6 Thu Dec 18 2003 14:52:48 on modular [Seed = 904400769] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> E := CC; ^ User error: Identifier 'CC' has not been declared or assigned >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:53:02 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; ee := 1 * 1; v := [0, 0, 1, 0, 0, 0]; E := CC; E; Output: Magma V2.10-6 Thu Dec 18 2003 14:52:59 on modular [Seed = 1055065217] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> E := CC; ^ User error: Identifier 'CC' has not been declared or assigned >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 14:53:22 2003 Input: K := FiniteField(2); C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; ee := 1 * 1; v := [0, 0, 1, 0, 0, 0]; E := v * C; E; Output: Magma V2.10-6 Thu Dec 18 2003 14:53:19 on modular [Seed = 131743116] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> E := v * C; ^ Runtime error in '*': Bad argument types Argument types given: SeqEnum[RngIntElt], Code >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 15:47:58 2003 Input: C:= GolayCode(GF(2), true); C; Output: Magma V2.10-6 Thu Dec 18 2003 15:47:55 on modular [Seed = 2876671732] ------------------------------------- [24, 12, 8] Extended Golay Code over GF(2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0] [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Thu Dec 18 15:51:12 2003 Input: C:= GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; Output: Magma V2.10-6 Thu Dec 18 2003 15:51:09 on modular [Seed = 2254154399] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ts23-a184.Moscow.dial.rol.ru. (212.46.254.184) Time: Thu Dec 18 19:01:06 2003 Input: 3462346256745357586784674865678456783568358656 Output: Magma V2.10-6 Thu Dec 18 2003 19:01:03 on modular [Seed = 2107669984] ------------------------------------- 3462346256745357586784674865678456783568358656 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:32:10 2003 Input: N:=220; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:31:24 on modular [Seed = 2254176120] ------------------------------------- [ 220, 1, 1 ][ 5, 3, 1 ][ 11, 1, 1 ][] [ 220, 2, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] Total time: 46.159 seconds, Total memory usage: 6.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:34:07 2003 Input: N:=220; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:33:20 on modular [Seed = 2387867388] ------------------------------------- [ 220, 1, 1 ][ 5, 3, 1 ][ 11, 1, 1 ][] [ 220, 2, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] Total time: 46.559 seconds, Total memory usage: 6.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:36:38 2003 Input: N:=221; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:36:06 on modular [Seed = 2638275913] ------------------------------------- [ 221, 1, 1 ][ 13, 1, 1 ][ 17, 1, 1 ][] [ 221, 2, 1 ][ 13, 1, 3 ][ 17, 1, 1 ][] [ 221, 3, 1 ][ 13, 1, 1 ][ 17, 1, 1 ][] [ 221, 4, 1 ][ 13, 1, 1 ][ 17, 1, 1 ][] [ 221, 5, 1 ][ 13, 1, 1 ][ 17, 7, 1 ][] [ 221, 6, 1 ][ 13, 1, 1 ][ 17, 1, 1 ][] [ 221, 7, 1 ][ 13, 9, 3 ][ 17, 1, 3 ][] Total time: 32.489 seconds, Total memory usage: 4.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:39:44 2003 Input: N:=222; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:37:55 on modular [Seed = 3845690020] ------------------------------------- [ 222, 1, 1 ][ 2, 1, 1 ][ 3, 1, 3 ][ 37, 1, 1 ][] [ 222, 2, 1 ][ 2, 1, 23 ][ 3, 1, 9 ][ 37, 1, 1 ][] [ 222, 3, 1 ][ 2, 1, 13 ][ 3, 1, 1 ][ 37, 1, 1 ][] [ 222, 4, 1 ][ 2, 1, 1 ][ 3, 1, 11 ][ 37, 1, 1 ][] [ 222, 5, 1 ][ 2, 3, 1 ][ 3, 3, 1 ][ 37, 1, 1 ][] Total time: 108.699 seconds, Total memory usage: 6.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:42:30 2003 Input: N:=223; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:42:26 on modular [Seed = 3591086215] ------------------------------------- [ 223, 1, 1 ][] [ 223, 2, 1 ][ 223, 1, 1 ][] [ 223, 3, 1 ][ 223, 37, 1 ][] Total time: 3.529 seconds, Total memory usage: 4.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:43:54 2003 Input: N:=224; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:43:35 on modular [Seed = 670716337] ------------------------------------- [ 224, 1, 1 ][ 7, 1, 1 ][] [ 224, 2, 1 ][ 7, 1, 1 ][] [ 224, 3, 1 ][ 7, 1, 1 ][] [ 224, 4, 1 ][ 7, 1, 1 ][] Total time: 19.489 seconds, Total memory usage: 5.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:45:35 2003 Input: N:=226; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:45:07 on modular [Seed = 98070583] ------------------------------------- [ 226, 1, 1 ][ 2, 3, 3 ][ 113, 1, 1 ][] [ 226, 2, 1 ][ 2, 1, 7 ][ 113, 1, 1 ][] [ 226, 3, 1 ][ 2, 1, 3 ][ 113, 1, 1 ][] [ 226, 4, 1 ][ 2, 779, 41 ][ 113, 1, 1 ][] Total time: 27.170 seconds, Total memory usage: 5.06MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:50:11 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(113,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(226,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for;print 3; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for;print 4; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:50:04 on modular [Seed = 2692601021] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Abelian Group of order 1 Total time: 7.399 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:52:51 2003 Input: N:=227; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:52:47 on modular [Seed = 2876694357] ------------------------------------- [ 227, 1, 1 ][] [ 227, 2, 1 ][ 227, 1, 1 ][] [ 227, 3, 1 ][ 227, 1, 1 ][] [ 227, 4, 1 ][ 227, 1, 1 ][] [ 227, 5, 1 ][ 227, 113, 1 ][] Total time: 3.709 seconds, Total memory usage: 4.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:57:22 2003 Input: N:=228; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:55:41 on modular [Seed = 3060516122] ------------------------------------- [ 228, 1, 1 ][ 3, 1, 3 ][ 19, 1, 1 ][] [ 228, 2, 1 ][ 3, 1, 1 ][ 19, 1, 1 ][] [ 228, 3, 1 ][ 3, 3, 1 ][ 19, 1, 1 ][] Total time: 100.229 seconds, Total memory usage: 6.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 19:58:25 2003 Input: N:=229; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:58:21 on modular [Seed = 3194211506] ------------------------------------- [ 229, 1, 1 ][] [ 229, 2, 1 ][ 229, 1, 1 ][] [ 229, 3, 1 ][ 229, 19, 1 ][] Total time: 3.649 seconds, Total memory usage: 4.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:00:26 2003 Input: N:=230; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 19:59:26 on modular [Seed = 2304048070] ------------------------------------- [ 230, 1, 1 ][ 2, 1, 5 ][ 5, 1, 5 ][ 23, 3, 1 ][] [ 230, 2, 1 ][ 2, 1, 43 ][ 5, 3, 1 ][ 23, 1, 1 ][] [ 230, 3, 1 ][ 2, 11, 1 ][ 5, 11, 1 ][ 23, 1, 1 ][] [ 230, 4, 1 ][ 2, 57, 19 ][ 5, 1, 1 ][ 23, 1, 1 ][] Total time: 58.790 seconds, Total memory usage: 6.03MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:02:34 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(115,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(230,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for;print 3; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for;print 4; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:02:27 on modular [Seed = 3895826922] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/43 Defined on 1 generator Relations: 43*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 7.559 seconds, Total memory usage: 4.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:03:46 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(23,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(230,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 20:03:40 on modular [Seed = 4263743411] ------------------------------------- Abelian Group of order 1 Total time: 5.969 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:03:58 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(23,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(230,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[1],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 20:03:52 on modular [Seed = 3373578384] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 6.069 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:05:31 2003 Input: N:=231; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:04:30 on modular [Seed = 3507265646] ------------------------------------- [ 231, 1, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][ 11, 1, 1 ][] [ 231, 2, 1 ][ 3, 1, 25 ][ 7, 1, 1 ][ 11, 1, 1 ][] [ 231, 3, 1 ][ 3, 5, 1 ][ 7, 5, 1 ][ 11, 1, 1 ][] [ 231, 4, 1 ][ 3, 1, 3 ][ 7, 1, 3 ][ 11, 1, 1 ][] [ 231, 5, 1 ][ 3, 7, 7 ][ 7, 1, 1 ][ 11, 1, 1 ][] Total time: 60.209 seconds, Total memory usage: 5.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:07:11 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(11,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(231,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 20:07:05 on modular [Seed = 3707809221] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 5.519 seconds, Total memory usage: 4.58MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:08:25 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(77,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(235,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for;print 3; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for;print 5; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:08:18 on modular [Seed = 620319878] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 6.639 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:08:44 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(77,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(231,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for;print 3; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for;print 5; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:08:37 on modular [Seed = 754015385] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 7.019 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:10:06 2003 Input: N:=232; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:09:43 on modular [Seed = 904414658] ------------------------------------- [ 232, 1, 1 ][ 29, 1, 1 ][] [ 232, 2, 1 ][ 29, 1, 1 ][] [ 232, 3, 1 ][ 29, 1, 1 ][] [ 232, 4, 1 ][ 29, 1, 1 ][] Total time: 23.110 seconds, Total memory usage: 5.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:11:35 2003 Input: N:=233; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:11:31 on modular [Seed = 81357671] ------------------------------------- [ 233, 1, 1 ][] [ 233, 2, 1 ][ 233, 1, 1 ][] [ 233, 3, 1 ][ 233, 29, 1 ][] Total time: 3.709 seconds, Total memory usage: 4.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:14:24 2003 Input: N:=235; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:13:55 on modular [Seed = 332299488] ------------------------------------- [ 235, 1, 1 ][ 5, 1, 9 ][ 47, 1, 1 ][] [ 235, 2, 1 ][ 5, 1, 3 ][ 47, 1, 1 ][] [ 235, 3, 1 ][ 5, 3, 3 ][ 47, 1, 1 ][] [ 235, 4, 1 ][ 5, 1, 1 ][ 47, 1, 1 ][] [ 235, 5, 1 ][ 5, 1, 1 ][ 47, 1, 1 ][] Total time: 28.909 seconds, Total memory usage: 4.95MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:15:35 2003 Input: N:=236; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:15:29 on modular [Seed = 1907105632] ------------------------------------- Do not know how to compute component group at 2 Total time: 4.779 seconds, Total memory usage: 3.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:16:10 2003 Input: N:=236; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:15:46 on modular [Seed = 2040796955] ------------------------------------- [ 236, 1, 1 ][ 59, 1, 1 ][] [ 236, 2, 1 ][ 59, 1, 1 ][] [ 236, 3, 1 ][ 59, 1, 1 ][] Total time: 23.559 seconds, Total memory usage: 5.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:17:26 2003 Input: N:=237; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:16:57 on modular [Seed = 1100754920] ------------------------------------- [ 237, 1, 1 ][ 3, 1, 31 ][ 79, 1, 1 ][] [ 237, 2, 1 ][ 3, 1, 3 ][ 79, 1, 1 ][] [ 237, 3, 1 ][ 3, 25, 5 ][ 79, 1, 1 ][] Total time: 28.899 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:18:46 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(79,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(237,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[1],200); end for;print 2; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[2],200); end for;print 3; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:18:39 on modular [Seed = 1535522196] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 3 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 Total time: 6.459 seconds, Total memory usage: 4.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:28:11 2003 Input: N:=238; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:27:10 on modular [Seed = 3862661672] ------------------------------------- [ 238, 1, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 238, 2, 1 ][ 2, 1, 5 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 238, 3, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 238, 4, 1 ][ 2, 7, 7 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 238, 5, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 238, 6, 1 ][ 2, 1, 61 ][ 7, 1, 1 ][ 17, 1, 1 ][] Total time: 60.389 seconds, Total memory usage: 6.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:31:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(119,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(238,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[6],200); Output: Magma V2.10-6 Thu Dec 18 2003 20:31:33 on modular [Seed = 4130053411] ------------------------------------- User error: syntax error at end of input Total time: 5.659 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:32:00 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(119,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(238,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[6],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 20:31:53 on modular [Seed = 4263744727] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/122 Defined on 1 generator Relations: 122*$.1 = 0 Total time: 7.039 seconds, Total memory usage: 4.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:32:30 2003 Input: N:=239; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:32:27 on modular [Seed = 3323702477] ------------------------------------- [ 239, 1, 1 ][] [ 239, 2, 1 ][ 239, 119, 1 ][] Total time: 3.619 seconds, Total memory usage: 4.13MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:35:24 2003 Input: N:=240; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:33:24 on modular [Seed = 3457393802] ------------------------------------- [ 240, 1, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][] [ 240, 2, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][] [ 240, 3, 1 ][ 3, 1, 3 ][ 5, 1, 1 ][] [ 240, 4, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][] Total time: 119.660 seconds, Total memory usage: 8.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:36:55 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(80,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(240,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 20:36:46 on modular [Seed = 3674649301] ------------------------------------- Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 8.539 seconds, Total memory usage: 4.75MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:38:52 2003 Input: N:=241; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:38:48 on modular [Seed = 482440619] ------------------------------------- [ 241, 1, 1 ][] [ 241, 2, 1 ][ 241, 5, 1 ][] Total time: 3.649 seconds, Total memory usage: 4.14MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:39:43 2003 Input: N:=242; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:39:33 on modular [Seed = 332298969] ------------------------------------- [ 242, 1, 1 ][ 2, 1, 1 ][] [ 242, 2, 1 ][ 2, 1, 1 ][] [ 242, 3, 1 ][ 2, 1, 3 ][] [ 242, 4, 1 ][ 2, 1, 5 ][] [ 242, 5, 1 ][ 2, 33, 3 ][] [ 242, 6, 1 ][ 2, 5, 1 ][] Total time: 9.839 seconds, Total memory usage: 5.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:40:03 2003 Input: N:=242; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:39:53 on modular [Seed = 198599421] ------------------------------------- [ 242, 1, 1 ][ 2, 1, 1 ][] [ 242, 2, 1 ][ 2, 1, 1 ][] [ 242, 3, 1 ][ 2, 1, 3 ][] [ 242, 4, 1 ][ 2, 1, 5 ][] [ 242, 5, 1 ][ 2, 33, 3 ][] [ 242, 6, 1 ][ 2, 5, 1 ][] Total time: 9.869 seconds, Total memory usage: 5.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:42:25 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(121,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(242,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for;print 4; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for;print 5; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for;print 6; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[6],200); end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:42:18 on modular [Seed = 1021400153] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Total time: 7.229 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:44:59 2003 Input: N:=244; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:44:35 on modular [Seed = 871257135] ------------------------------------- [ 244, 1, 1 ][ 61, 1, 1 ][] [ 244, 2, 1 ][ 61, 1, 1 ][] Total time: 24.379 seconds, Total memory usage: 5.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:46:07 2003 Input: N:=245; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:45:43 on modular [Seed = 670711935] ------------------------------------- [ 245, 1, 1 ][ 5, 1, 3 ][] [ 245, 2, 1 ][ 5, 1, 1 ][] [ 245, 3, 1 ][ 5, 3, 3 ][] [ 245, 4, 1 ][ 5, 1, 1 ][] [ 245, 5, 1 ][ 5, 1, 1 ][] [ 245, 6, 1 ][ 5, 1, 1 ][] [ 245, 7, 1 ][ 5, 7, 1 ][] [ 245, 8, 1 ][ 5, 1, 1 ][] Total time: 23.770 seconds, Total memory usage: 5.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:50:57 2003 Input: N:=246; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:48:44 on modular [Seed = 1251421609] ------------------------------------- [ 246, 1, 1 ][ 2, 1, 3 ][ 3, 1, 1 ][ 41, 1, 1 ][] [ 246, 2, 1 ][ 2, 1, 11 ][ 3, 1, 1 ][ 41, 1, 1 ][] [ 246, 3, 1 ][ 2, 1, 7 ][ 3, 3, 3 ][ 41, 1, 1 ][] [ 246, 4, 1 ][ 2, 1, 1 ][ 3, 3, 1 ][ 41, 1, 1 ][] [ 246, 5, 1 ][ 2, 3, 3 ][ 3, 1, 7 ][ 41, 1, 1 ][] [ 246, 6, 1 ][ 2, 25, 5 ][ 3, 5, 1 ][ 41, 1, 1 ][] [ 246, 7, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 41, 1, 1 ][] Total time: 131.270 seconds, Total memory usage: 7.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:53:49 2003 Input: N:=247; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:53:20 on modular [Seed = 2024086903] ------------------------------------- [ 247, 1, 1 ][ 13, 5, 1 ][ 19, 1, 1 ][] [ 247, 2, 1 ][ 13, 3, 1 ][ 19, 1, 1 ][] [ 247, 3, 1 ][ 13, 1, 1 ][ 19, 1, 1 ][] [ 247, 4, 1 ][ 13, 1, 5 ][ 19, 7, 1 ][] [ 247, 5, 1 ][ 13, 1, 1 ][ 19, 1, 1 ][] Total time: 29.149 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:55:40 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(19,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(247,2,+1))))); for i in [1..#B] do CongruenceGroupAnemic(A[1],B[i],200); end for; Output: Magma V2.10-6 Thu Dec 18 2003 20:55:34 on modular [Seed = 2220482829] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 5.429 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:56:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(19,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(247,2,+1))))); for i in [1..#B] do CongruenceGroupAnemic(A[1],B[i],200); print i;end for; Output: Magma V2.10-6 Thu Dec 18 2003 20:56:15 on modular [Seed = 3160529180] ------------------------------------- Abelian Group of order 1 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Total time: 5.449 seconds, Total memory usage: 4.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:58:17 2003 Input: N:=248; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:57:52 on modular [Seed = 3026833547] ------------------------------------- [ 248, 1, 1 ][ 31, 1, 1 ][] [ 248, 2, 1 ][ 31, 1, 1 ][] [ 248, 3, 1 ][ 31, 1, 1 ][] [ 248, 4, 1 ][ 31, 1, 1 ][] [ 248, 5, 1 ][ 31, 1, 1 ][] Total time: 24.840 seconds, Total memory usage: 5.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 20:59:25 2003 Input: N:=249; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 20:58:53 on modular [Seed = 2876690409] ------------------------------------- [ 249, 1, 1 ][ 3, 1, 1 ][ 83, 1, 1 ][] [ 249, 2, 1 ][ 3, 1, 3 ][ 83, 1, 1 ][] [ 249, 3, 1 ][ 3, 31, 31 ][ 83, 1, 1 ][] [ 249, 4, 1 ][ 3, 35, 5 ][ 83, 1, 1 ][] [ 249, 5, 1 ][ 3, 1, 2711 ][ 83, 1, 1 ][] Total time: 31.739 seconds, Total memory usage: 5.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 21:00:54 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(83,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(249,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for;print 4; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for;print 5; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); //erdos Output: Magma V2.10-6 Thu Dec 18 2003 21:00:48 on modular [Seed = 3624254487] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 4 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 5 User error: syntax error at end of input Total time: 6.279 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 21:01:36 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(83,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(249,2,+1))))); for i in [1..#A] do CongruenceGroupAnemic(A[i],B[3],200); end for;print 4; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[4],200); end for;print 5; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[5],200); end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 21:01:29 on modular [Seed = 4263746075] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 4 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2711 Defined on 1 generator Relations: 2711*$.1 = 0 Total time: 6.569 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:09:52 2003 Input: N:=250; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:09:41 on modular [Seed = 2859990593] ------------------------------------- [ 250, 1, 1 ][ 2, 1, 1 ][] [ 250, 2, 1 ][ 2, 1, 11 ][] [ 250, 3, 1 ][ 2, 55, 11 ][] [ 250, 4, 1 ][ 2, 5, 1 ][] Total time: 11.099 seconds, Total memory usage: 6.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:14:49 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(125,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(250,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 22:14:42 on modular [Seed = 3657926886] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/10 Defined on 2 generators Relations: 2*$.1 = 0 10*$.2 = 0 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/10 Defined on 2 generators Relations: 2*$.1 = 0 10*$.2 = 0 Total time: 7.189 seconds, Total memory usage: 4.65MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:16:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(125,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(250,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 22:16:03 on modular [Seed = 3457391779] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/10 Defined on 2 generators Relations: 2*$.1 = 0 10*$.2 = 0 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/10 Defined on 2 generators Relations: 2*$.1 = 0 10*$.2 = 0 Total time: 7.329 seconds, Total memory usage: 4.65MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:18:19 2003 Input: N:=251; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:18:16 on modular [Seed = 3323696160] ------------------------------------- [ 251, 1, 1 ][] [ 251, 2, 1 ][ 251, 125, 25 ][] Total time: 3.689 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:22:58 2003 Input: N:=252; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:21:52 on modular [Seed = 4130055993] ------------------------------------- [ 252, 1, 1 ][ 7, 1, 1 ][] [ 252, 2, 1 ][ 7, 1, 1 ][] Total time: 64.860 seconds, Total memory usage: 8.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:24:19 2003 Input: N:=253; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:23:50 on modular [Seed = 3996368566] ------------------------------------- [ 253, 1, 1 ][ 11, 1, 19 ][ 23, 1, 1 ][] [ 253, 2, 1 ][ 11, 5, 1 ][ 23, 5, 1 ][] [ 253, 3, 1 ][ 11, 1, 1 ][ 23, 1, 1 ][] [ 253, 4, 1 ][ 11, 1, 1 ][ 23, 1, 23 ][] Total time: 28.699 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:25:44 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(23,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(253,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 22:25:38 on modular [Seed = 3812537167] ------------------------------------- 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 4 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 5.649 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:28:07 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(11,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(253,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 22:28:02 on modular [Seed = 415586119] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Total time: 5.729 seconds, Total memory usage: 4.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:31:38 2003 Input: N:=253; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:31:09 on modular [Seed = 148195304] ------------------------------------- [ 253, 1, 1 ][ 11, 1, 19 ][ 23, 1, 1 ][] [ 253, 2, 1 ][ 11, 5, 1 ][ 23, 5, 1 ][] [ 253, 3, 1 ][ 11, 1, 1 ][ 23, 1, 1 ][] [ 253, 4, 1 ][ 11, 1, 1 ][ 23, 1, 23 ][] Total time: 28.569 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:36:18 2003 Input: N:=23; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=11; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ p, k, g ]; end if; end for; Output: Magma V2.10-6 Thu Dec 18 2003 22:36:13 on modular [Seed = 1071804943] ------------------------------------- 1 <11, 1><2, 2><5, 1><19, 1>[ 11, 1, 19 ] [ 11, 2, 5 ] Total time: 5.759 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:41:49 2003 Input: N:=23; A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); #A; i:=1; p:=11; rp:=[]; Include(~rp,); f1:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),+(p+1)))); for j in [1..#f1] do Include(~rp,f1[j]); end for; f2:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],p)),-(p+1)))); for j in [1..#f2] do Include(~rp,f2[j]); end for; for j in [1..#rp] do printf "%o",rp[j]; end for; B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N*p,2,+1))))); for k in [1..#B] do g:=Order(CongruenceGroupAnemic(A[i],B[k],200)); if g ge 2 and Numerator(g/2) ge 3 then print [ N*p, k, g ]; end if; end for; Output: Magma V2.10-6 Thu Dec 18 2003 22:41:43 on modular [Seed = 804414277] ------------------------------------- 1 <1, 11><2, 2><5, 1><11, 1><19, 1>[ 253, 1, 19 ] [ 253, 2, 5 ] Total time: 5.739 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:44:22 2003 Input: N:=253; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:43:53 on modular [Seed = 654011074] ------------------------------------- [ 253, 1, 1 ][ 11, 1, 19 ][ 23, 1, 1 ][] [ 253, 2, 1 ][ 11, 5, 1 ][ 23, 5, 1 ][] [ 253, 3, 1 ][ 11, 1, 1 ][ 23, 1, 1 ][] [ 253, 4, 1 ][ 11, 1, 1 ][ 23, 1, 23 ][] Total time: 28.639 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:45:29 2003 Input: N:=253; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:44:59 on modular [Seed = 1585649016] ------------------------------------- [ 253, 1, 1 ][ 11, 1, 19 ][ 23, 1, 1 ][] [ 253, 2, 1 ][ 11, 5, 1 ][ 23, 5, 1 ][] [ 253, 3, 1 ][ 11, 1, 1 ][ 23, 1, 1 ][] [ 253, 4, 1 ][ 11, 1, 1 ][ 23, 1, 23 ][] Total time: 29.039 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:51:54 2003 Input: N:=254; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:51:16 on modular [Seed = 1150881517] ------------------------------------- [ 254, 1, 1 ][ 2, 1, 3 ][ 127, 1, 1 ][] [ 254, 2, 1 ][ 2, 3, 3 ][ 127, 1, 1 ][] [ 254, 3, 1 ][ 2, 1, 1 ][ 127, 1, 1 ][] [ 254, 4, 1 ][ 2, 9, 3 ][ 127, 1, 1 ][] [ 254, 5, 1 ][ 2, 17, 17 ][ 127, 1, 1 ][] [ 254, 6, 1 ][ 2, 1, 3447 ][ 127, 3, 1 ][] Total time: 38.190 seconds, Total memory usage: 5.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:55:58 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(127,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(254,2,+1))))); for j in [5..6] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 22:55:51 on modular [Seed = 2074489505] ------------------------------------- 5 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/1149 Defined on 1 generator Relations: 1149*$.1 = 0 Total time: 6.789 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 22:59:49 2003 Input: N:=255; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 22:58:43 on modular [Seed = 1940798237] ------------------------------------- [ 255, 1, 1 ][ 3, 1, 3 ][ 5, 1, 13 ][ 17, 1, 1 ][] [ 255, 2, 1 ][ 3, 1, 11 ][ 5, 1, 1 ][ 17, 1, 5 ][] [ 255, 3, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] [ 255, 4, 1 ][ 3, 51, 17 ][ 5, 1, 9 ][ 17, 1, 1 ][] Total time: 65.729 seconds, Total memory usage: 6.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:01:27 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(85,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(255,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 23:01:20 on modular [Seed = 2370882176] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/34 Defined on 1 generator Relations: 34*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 7.729 seconds, Total memory usage: 4.71MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:03:40 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(51,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(255,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 23:03:33 on modular [Seed = 2237186573] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 4 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 7.009 seconds, Total memory usage: 4.55MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:05:04 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(15,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(255,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 23:04:57 on modular [Seed = 3160537928] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 6.569 seconds, Total memory usage: 4.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:06:07 2003 Input: N:=257; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 23:06:02 on modular [Seed = 2959996551] ------------------------------------- [ 257, 1, 1 ][] [ 257, 2, 1 ][ 257, 1, 1 ][] Total time: 3.559 seconds, Total memory usage: 3.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:09:57 2003 Input: N:=258; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 23:07:38 on modular [Seed = 2859985981] ------------------------------------- [ 258, 1, 1 ][ 2, 1, 3 ][ 3, 1, 1 ][ 43, 1, 1 ][] [ 258, 2, 1 ][ 2, 1, 7 ][ 3, 1, 7 ][ 43, 1, 1 ][] [ 258, 3, 1 ][ 2, 1, 1 ][ 3, 5, 5 ][ 43, 1, 1 ][] [ 258, 4, 1 ][ 2, 3, 3 ][ 3, 1, 1 ][ 43, 1, 1 ][] [ 258, 5, 1 ][ 2, 1, 1 ][ 3, 1, 19 ][ 43, 1, 1 ][] [ 258, 6, 1 ][ 2, 7, 1 ][ 3, 7, 1 ][ 43, 1, 1 ][] [ 258, 7, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 43, 1, 1 ][] Total time: 137.679 seconds, Total memory usage: 7.15MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:13:34 2003 Input: N:=259; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 23:13:02 on modular [Seed = 3657932553] ------------------------------------- [ 259, 1, 1 ][ 7, 3, 3 ][ 37, 1, 1 ][] [ 259, 2, 1 ][ 7, 1, 7 ][ 37, 1, 1 ][] [ 259, 3, 1 ][ 7, 1, 1 ][ 37, 1, 1 ][] [ 259, 4, 1 ][ 7, 1, 7 ][ 37, 1, 1 ][] [ 259, 5, 1 ][ 7, 3, 1 ][ 37, 1, 1 ][] [ 259, 6, 1 ][ 7, 1, 1 ][ 37, 1, 1 ][] [ 259, 7, 1 ][ 7, 57, 3 ][ 37, 1, 1 ][] Total time: 30.190 seconds, Total memory usage: 4.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:14:35 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(37,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(259,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Thu Dec 18 2003 23:14:28 on modular [Seed = 3440413172] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Total time: 6.279 seconds, Total memory usage: 4.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:17:42 2003 Input: N:=260; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 23:16:40 on modular [Seed = 3239871860] ------------------------------------- [ 260, 1, 1 ][ 5, 1, 1 ][ 13, 1, 1 ][] [ 260, 2, 1 ][ 5, 3, 1 ][ 13, 1, 1 ][] Total time: 62.000 seconds, Total memory usage: 6.78MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Dec 18 23:18:58 2003 Input: N:=260; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Thu Dec 18 2003 23:17:57 on modular [Seed = 4179934481] ------------------------------------- [ 260, 1, 1 ][ 5, 1, 1 ][ 13, 1, 1 ][] [ 260, 2, 1 ][ 5, 3, 1 ][ 13, 1, 1 ][] Total time: 61.629 seconds, Total memory usage: 6.78MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 23:45:08 2003 Input: C := ComplexField(); x1:=Sqrt(-38);y1:=jInvariant(x1); x2:=Sqrt(-38)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-38))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-38))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-38))/6;y5:=jInvariant(x5); x6:=(-2+Sqrt(-38))/6;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6+y3*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 23:45:04 on modular [Seed = 198620743] ------------------------------------- 66246265662298399.44546048835036344826 + 0.E-12*i 257384243.204380667330012153123794870976 + 0.E-20*i -201569.250294795745398294909268501625 - 350415.98576912791428450263093642611*i -201569.250294795745398294909347910964 + 350415.98576912791428450263089010399*i 247.925374217874988651278079307195681694103 - 328.73069290953675179300385450169*i 247.925374217874988651278079161792839643766 + 328.73069290953675179300385446291*i 66246265919279999.99999999993906385498 + 0.E-16*i 17024071380555203519999999.9770507812 - 0.0000023874454288790713404*i -6.85454429479948368895999998962 E30 - 638.374509334563732055115026220448*i 2.78305862478709361429299199342 E36 + 603948286.75000214017927646636*i 1.380504171426125758791679997180 E39 + 1.8861027327 E11*i 4.72390748138731280269311998734 E41 + 2.11106232460 E14*i Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Thu Dec 18 23:58:01 2003 Input: C := ComplexField(); x1:=Sqrt(-38);y1:=jInvariant(x1); x2:=Sqrt(-38)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-38))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-38))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-38))/6;y5:=jInvariant(x5); x6:=(-2+Sqrt(-38))/6;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6+y3*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Thu Dec 18 2003 23:57:58 on modular [Seed = 603887977] ------------------------------------- 66246265662298399.44546048835036344826 + 0.E-12*i 257384243.204380667330012153123794870976 + 0.E-20*i -201569.250294795745398294909268501625 - 350415.98576912791428450263093642611*i -201569.250294795745398294909347910964 + 350415.98576912791428450263089010399*i 247.925374217874988651278079307195681694103 - 328.73069290953675179300385450169*i 247.925374217874988651278079161792839643766 + 328.73069290953675179300385446291*i 66246265919279999.99999999993906385498 + 0.E-16*i 17024071380555203519999999.9770507812 - 0.0000023874454288790713404*i -6.85454429479948368895999998962 E30 - 638.374509334563732055115026220448*i 2.78305862478709361429299199342 E36 + 603948286.75000214017927646636*i 1.380504171426125758791679997180 E39 + 1.8861027327 E11*i 4.72390748138731280269311998734 E41 + 2.11106232460 E14*i Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:00:48 2003 Input: N:=261; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:00:23 on modular [Seed = 1284634295] ------------------------------------- [ 261, 1, 1 ][ 29, 1, 1 ][] [ 261, 2, 1 ][ 29, 1, 1 ][] [ 261, 3, 1 ][ 29, 1, 1 ][] [ 261, 4, 1 ][ 29, 1, 1 ][] [ 261, 5, 1 ][ 29, 1, 1 ][] Total time: 24.629 seconds, Total memory usage: 5.06MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:02:01 2003 Input: N:=262; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:01:28 on modular [Seed = 1990971202] ------------------------------------- [ 262, 1, 1 ][ 2, 1, 1 ][ 131, 1, 1 ][] [ 262, 2, 1 ][ 2, 11, 11 ][ 131, 1, 1 ][] [ 262, 3, 1 ][ 2, 1, 3 ][ 131, 1, 1 ][] [ 262, 4, 1 ][ 2, 1, 313 ][ 131, 1, 1 ][] [ 262, 5, 1 ][ 2, 33, 3 ][ 131, 1, 1 ][] [ 262, 6, 1 ][ 2, 1, 1 ][ 131, 1, 1 ][] Total time: 33.130 seconds, Total memory usage: 5.35MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 00:04:53 2003 Input: C := ComplexField(); x1:=Sqrt(-38);y1:=jInvariant(x1); x2:=Sqrt(-38)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-38))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-38))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-38))/6;y5:=jInvariant(x5); x6:=(-2+Sqrt(-38))/6;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1*y2; z2:=y1+y2; z3:=y3*y4; z4:=y3+y4; z5:=y5*y6; z6:=y5+y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Fri Dec 19 2003 00:04:50 on modular [Seed = 1623054734] ------------------------------------- 66246265662298399.44546048835036344826 + 0.E-12*i 257384243.204380667330012153123794870976 + 0.E-20*i -201569.250294795745398294909268501625 - 350415.98576912791428450263093642611*i -201569.250294795745398294909347910964 + 350415.98576912791428450263089010399*i 247.925374217874988651278079307195681694103 - 328.73069290953675179300385450169*i 247.925374217874988651278079161792839643766 + 328.73069290953675179300385446291*i 17050744952607023165563283.9797363281 + 0.000000000*i 66246265919682642.64984115567949629621 + 0.E-12*i 163421525746.95567163471191162241 + 3.8163916468 E-17*i -403138.50058959149079658981861641258 - 4.6322114299 E-23*i 169530.85964185750860064715596965670 + 3.8050308171 E-23*i 495.850748435749977302556158468988521337869 - 3.8774091210 E-26*i Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:05:50 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(131,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(262,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:05:42 on modular [Seed = 2454661800] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/313 Defined on 1 generator Relations: 313*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 7.909 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:08:22 2003 Input: N:=263; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:08:18 on modular [Seed = 3591073288] ------------------------------------- [ 263, 1, 1 ][] [ 263, 2, 1 ][ 263, 131, 1 ][] Total time: 3.679 seconds, Total memory usage: 3.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:12:18 2003 Input: N:=264; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:10:18 on modular [Seed = 4029499350] ------------------------------------- [ 264, 1, 1 ][ 3, 1, 1 ][ 11, 1, 1 ][] [ 264, 2, 1 ][ 3, 1, 1 ][ 11, 1, 1 ][] [ 264, 3, 1 ][ 3, 7, 7 ][ 11, 1, 1 ][] [ 264, 4, 1 ][ 3, 1, 1 ][ 11, 1, 1 ][] Total time: 118.669 seconds, Total memory usage: 8.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:14:11 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(88,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(264,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:14:02 on modular [Seed = 499165980] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.069 seconds, Total memory usage: 4.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:15:28 2003 Input: N:=265; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:14:54 on modular [Seed = 365470528] ------------------------------------- [ 265, 1, 1 ][ 5, 1, 3 ][ 53, 1, 1 ][] [ 265, 2, 1 ][ 5, 1, 1 ][ 53, 1, 1 ][] [ 265, 3, 1 ][ 5, 1, 1 ][ 53, 1, 1 ][] [ 265, 4, 1 ][ 5, 1, 1 ][ 53, 1, 1 ][] [ 265, 5, 1 ][ 5, 1, 31 ][ 53, 1, 1 ][] [ 265, 6, 1 ][ 5, 27, 9 ][ 53, 1, 1 ][] [ 265, 7, 1 ][ 5, 5, 5 ][ 53, 1, 1 ][] [ 265, 8, 1 ][ 5, 1, 1 ][ 53, 1, 1 ][] Total time: 31.850 seconds, Total memory usage: 4.65MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 00:15:30 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1+y2+y3+y4+y5+y6; z2:=y1*y2+y1*y3+y1*y4+y1*y5+y1*y6+y2*y3+y2*y4+y2*y5+y2*y6+y3*y4+y3*y5+y3*y6+y4*y5+y4*y6+y5*y6; z3:=y1*y2*y3+y1*y2*y4+y1*y2*y5+y1*y2*y6+y1*y3*y4+y1*y3*y5+y1*y3*y6+y1*y4*y5+y1*y4*y6+y1*y5*y6+y2*y3*y4+y2*y3*y5+y2*y3*y6+y2*y4*y5+y2*y4*y6+y2*y5*y6+y3*y4*y5+y3*y4*y6+y3*y5*y6+y4*y5*y6; z4:=y1*y2*y3*y4+y1*y2*y3*y5+y1*y2*y3*y6+y1*y2*y4*y5+y1*y2*y4*y6+y1*y2*y5*y6+y1*y3*y4*y5+y1*y3*y4*y6+y1*y3*y5*y6+y1*y4*y5*y6+y2*y3*y4*y5+y2*y3*y4*y6+y2*y3*y5*y6+y2*y4*y5*y6+y3*y4*y5*y6; z5:=y1*y2*y3*y4*y5+y1*y2*y3*y4*y6+y1*y2*y3*y5*y6+y1*y2*y4*y5*y6+y1*y3*y4*y5*y6+y2*y3*y4*y5*y6; z6:=y1*y2*y3*y4*y5*y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Fri Dec 19 2003 00:15:26 on modular [Seed = 248756347] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230625169072 + 37624.71504756715063931140564100705*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 82028232174463.99999999999994138022 - 9.09898673743 E-24*i 739545196164376195071.9999992102 - 0.00000000081445258793252282917*i -31013571054009020830449663.9614257812 - 0.0077438650132588137287*i 1.378339984770204584193868953398 E30 + 591.37886428850064746143*i 2.57350396422293342005647105004 E31 + 11907.5000000000*i 6.54371797303335452423236759422 E34 + 32505856.*i Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:17:16 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(53,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(265,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:17:09 on modular [Seed = 954568438] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 4 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 6 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 7.359 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 00:17:40 2003 Input: C := ComplexField(); x1:=Sqrt(-26);y1:=jInvariant(x1); x2:=Sqrt(-26)/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-26))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-26))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-26))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-26))/5;y6:=jInvariant(x6); y1;y2;y3;y4;y5;y6; z1:=y1*y2; z2:=y1+y2; z3:=y3*y4; z4:=y3+y4; z5:=y5*y6; z6:=y5+y6; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Fri Dec 19 2003 00:17:36 on modular [Seed = 820872923] ------------------------------------- 82028223158723.22122617568541613763 + 0.E-15*i 9057687.389011105444236082734383197923 + 0.E-21*i -20983.170648695065239252230610279821 - 37624.71504756715063931140565010604*i -20983.170648695065239252230625169072 + 37624.71504756715063931140564100705*i 9.86553005450038475019579161077 - 217.61929147801460303398176038521*i 9.86553005450038475019579159785 + 217.61929147801460303398176038521*i 742986002447756026099.8627735525 + 0.000000000*i 82028232216410.61023728112965081038 + 0.E-15*i 1855912632.88288405955288080885403484421 + 7.4538899343 E-19*i -41966.341297390130478504461235448893 - 9.09898673743 E-24*i 47455.484706649329592800570031104970 + 2.4815418375 E-24*i 19.73106010900076950039158320863 + 0.E-26*i Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:20:09 2003 Input: N:=266; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:18:37 on modular [Seed = 804428313] ------------------------------------- [ 266, 1, 1 ][ 2, 1, 13 ][ 7, 1, 7 ][ 19, 1, 1 ][] [ 266, 2, 1 ][ 2, 1, 11 ][ 7, 1, 1 ][ 19, 1, 11 ][] [ 266, 3, 1 ][ 2, 81, 27 ][ 7, 3, 1 ][ 19, 1, 1 ][] [ 266, 4, 1 ][ 2, 19, 19 ][ 7, 1, 11 ][ 19, 1, 1 ][] Total time: 91.119 seconds, Total memory usage: 6.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:22:16 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(133,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(266,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:22:07 on modular [Seed = 1602415428] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 4 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Total time: 8.569 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:23:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(266,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:23:03 on modular [Seed = 1468719995] ------------------------------------- 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Total time: 7.279 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:24:36 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(14,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(266,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:24:29 on modular [Seed = 1318320856] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 6.869 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:25:37 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(14,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(266,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:25:30 on modular [Seed = 2057817771] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 6.839 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 00:29:39 2003 Input: C := ComplexField(); x1:=Sqrt(-41);y1:=jInvariant(x1); x2:=(-1+Sqrt(-41))/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-41))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-41))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-41))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-41))/5;y6:=jInvariant(x6); x7:=(1+Sqrt(-41))/6;y7:=jInvariant(x7); x8:=(-1+Sqrt(-41))/6;y8:=jInvariant(x8); y1;y2;y3;y4;y5;y6;y7;y8; z1:=y1*y2; z2:=y1+y2; z3:=y3*y4; z4:=y3+y4; z5:=y5*y6; z6:=y5+y6; z7:=y7+y8; z8:=y7*y8; z1;z2;z3;z4;z5;z6; Output: Magma V2.10-6 Fri Dec 19 2003 00:29:36 on modular [Seed = 1907147434] ------------------------------------- 296853791705949233.0026726245123 + 0.E-11*i -544842161.52997224185465281772583999442 + 7.6768996883 E-20*i -332798.410724264846430804772206936513 - 577711.89065421558056949116179477663*i -332798.410724264846430804772332667966 + 577711.89065421558056949116172860218*i -1832.51158041991500380297426289313 - 1800.393479955524039524631995378254*i -1832.51158041991500380297426369446 + 1800.393479955524039524631994370127*i 1255.1859544932706970374260048743984843182732 - 470.70321831716687046600824748585*i 1255.1859544932706970374260047613073849457889 + 470.70321831716687046600824748585*i -161738461531437526158924729.09375000000 + 0.019531250000*i 296853791161107071.47270038266287883743 + 0.E-11*i 444505810783.86481861118563089357 + 9.020562075078 E-17*i -665596.82144852969286160954453298703 - 6.6174448989 E-23*i 6599515.375039456555834514959203368554 + 3.2590916128 E-21*i -3665.0231608398300076059485265617561 - 1.008126371074 E-24*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 00:29:51 2003 Input: C := ComplexField(); x1:=Sqrt(-41);y1:=jInvariant(x1); x2:=(-1+Sqrt(-41))/2;y2:=jInvariant(x2); x3:=(1+Sqrt(-41))/3;y3:=jInvariant(x3); x4:=(-1+Sqrt(-41))/3;y4:=jInvariant(x4); x5:=(2+Sqrt(-41))/5;y5:=jInvariant(x5); x6:=(-2+Sqrt(-41))/5;y6:=jInvariant(x6); x7:=(1+Sqrt(-41))/6;y7:=jInvariant(x7); x8:=(-1+Sqrt(-41))/6;y8:=jInvariant(x8); y1;y2;y3;y4;y5;y6;y7;y8; z1:=y1*y2; z2:=y1+y2; z3:=y3*y4; z4:=y3+y4; z5:=y5*y6; z6:=y5+y6; z7:=y7+y8; z8:=y7*y8; z1;z2;z3;z4;z5;z6;z7;z8 Output: Magma V2.10-6 Fri Dec 19 2003 00:29:48 on modular [Seed = 1873992888] ------------------------------------- 296853791705949233.0026726245123 + 0.E-11*i -544842161.52997224185465281772583999442 + 7.6768996883 E-20*i -332798.410724264846430804772206936513 - 577711.89065421558056949116179477663*i -332798.410724264846430804772332667966 + 577711.89065421558056949116172860218*i -1832.51158041991500380297426289313 - 1800.393479955524039524631995378254*i -1832.51158041991500380297426369446 + 1800.393479955524039524631994370127*i 1255.1859544932706970374260048743984843182732 - 470.70321831716687046600824748585*i 1255.1859544932706970374260047613073849457889 + 470.70321831716687046600824748585*i -161738461531437526158924729.09375000000 + 0.019531250000*i 296853791161107071.47270038266287883743 + 0.E-11*i 444505810783.86481861118563089357 + 9.020562075078 E-17*i -665596.82144852969286160954453298703 - 6.6174448989 E-23*i 6599515.375039456555834514959203368554 + 3.2590916128 E-21*i -3665.0231608398300076059485265617561 - 1.008126371074 E-24*i 2510.371908986541394074852009635705869264062 + 0.E-26*i 1797053.300091321474368922354812659585080081431 + 5.32253990820517885757 E-23*i Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:30:31 2003 Input: N:=267; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:29:54 on modular [Seed = 1740297390] ------------------------------------- [ 267, 1, 1 ][ 3, 1, 17 ][ 89, 1, 1 ][] [ 267, 2, 1 ][ 3, 3, 1 ][ 89, 1, 1 ][] [ 267, 3, 1 ][ 3, 1, 3 ][ 89, 1, 1 ][] [ 267, 4, 1 ][ 3, 25, 5 ][ 89, 1, 1 ][] [ 267, 5, 1 ][ 3, 113, 113 ][ 89, 1, 1 ][] [ 267, 6, 1 ][ 3, 1, 39 ][ 89, 1, 1 ][] Total time: 37.190 seconds, Total memory usage: 5.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:31:31 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(89,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(267,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 00:31:23 on modular [Seed = 2420974240] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/113 Defined on 1 generator Relations: 113*$.1 = 0 6 Abelian Group of order 1 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Total time: 8.149 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:33:46 2003 Input: N:=268; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:33:18 on modular [Seed = 2370846472] ------------------------------------- [ 268, 1, 1 ][ 67, 1, 1 ][] [ 268, 2, 1 ][ 67, 1, 1 ][] [ 268, 3, 1 ][ 67, 1, 1 ][] Total time: 27.569 seconds, Total memory usage: 5.62MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:35:31 2003 Input: N:=269; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:35:27 on modular [Seed = 3093629372] ------------------------------------- [ 269, 1, 1 ][] [ 269, 2, 1 ][ 269, 1, 1 ][] [ 269, 3, 1 ][ 269, 67, 1 ][] Total time: 3.699 seconds, Total memory usage: 3.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:37:28 2003 Input: N:=270; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:36:50 on modular [Seed = 2959933912] ------------------------------------- [ 270, 1, 1 ][ 2, 1, 5 ][] [ 270, 2, 1 ][ 2, 1, 1 ][] [ 270, 3, 1 ][ 2, 15, 5 ][] [ 270, 4, 1 ][ 2, 1, 1 ][] Total time: 37.079 seconds, Total memory usage: 9.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:56:27 2003 Input: N:=270; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:55:49 on modular [Seed = 3557390634] ------------------------------------- [ 270, 1, 1 ][ 2, 1, 5 ][] [ 270, 2, 1 ][ 2, 1, 1 ][] [ 270, 3, 1 ][ 2, 15, 5 ][] [ 270, 4, 1 ][ 2, 1, 1 ][] Total time: 37.720 seconds, Total memory usage: 9.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 00:58:31 2003 Input: N:=270; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 00:57:12 on modular [Seed = 3423690991] ------------------------------------- [ 270, 1, 1 ][ 5, 3, 1 ][] [ 270, 2, 1 ][ 5, 1, 1 ][] [ 270, 3, 1 ][ 5, 1, 1 ][] [ 270, 4, 1 ][ 5, 1, 1 ][] Total time: 78.270 seconds, Total memory usage: 9.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:00:31 2003 Input: N:=271; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:00:28 on modular [Seed = 4079902484] ------------------------------------- [ 271, 1, 1 ][] [ 271, 2, 1 ][ 271, 45, 3 ][] Total time: 3.669 seconds, Total memory usage: 3.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:02:36 2003 Input: N:=272; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:02:08 on modular [Seed = 415609698] ------------------------------------- [ 272, 1, 1 ][ 17, 1, 1 ][] [ 272, 2, 1 ][ 17, 1, 1 ][] [ 272, 3, 1 ][ 17, 1, 1 ][] [ 272, 4, 1 ][ 17, 1, 1 ][] [ 272, 5, 1 ][ 17, 1, 1 ][] [ 272, 6, 1 ][ 17, 1, 1 ][] Total time: 27.770 seconds, Total memory usage: 5.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:04:32 2003 Input: N:=273; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:03:14 on modular [Seed = 281918377] ------------------------------------- [ 273, 1, 1 ][ 3, 1, 1 ][ 7, 3, 3 ][ 13, 1, 1 ][] [ 273, 2, 1 ][ 3, 1, 1 ][ 7, 1, 7 ][ 13, 1, 3 ][] [ 273, 3, 1 ][ 3, 1, 7 ][ 7, 1, 1 ][ 13, 1, 1 ][] [ 273, 4, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][ 13, 1, 1 ][] [ 273, 5, 1 ][ 3, 9, 3 ][ 7, 1, 1 ][ 13, 1, 1 ][] Total time: 76.539 seconds, Total memory usage: 5.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:05:34 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(91,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(273,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:05:25 on modular [Seed = 231778097] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Total time: 8.019 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:06:41 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(39,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(273,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:06:34 on modular [Seed = 98086773] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Total time: 7.109 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:07:24 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(21,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(273,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:07:16 on modular [Seed = 837589951] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 6.639 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:08:35 2003 Input: N:=274; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:07:59 on modular [Seed = 703890316] ------------------------------------- [ 274, 1, 1 ][ 2, 1, 1 ][ 137, 1, 1 ][] [ 274, 2, 1 ][ 2, 1, 11 ][ 137, 1, 1 ][] [ 274, 3, 1 ][ 2, 7, 7 ][ 137, 1, 1 ][] [ 274, 4, 1 ][ 2, 1, 109 ][ 137, 1, 1 ][] [ 274, 5, 1 ][ 2, 3427, 149 ][ 137, 1, 1 ][] Total time: 35.849 seconds, Total memory usage: 5.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:09:35 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(137,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(274,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:09:27 on modular [Seed = 654020395] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/109 Defined on 1 generator Relations: 109*$.1 = 0 5 Abelian Group isomorphic to Z/149 Defined on 1 generator Relations: 149*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 7.979 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:10:45 2003 Input: N:=275; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:10:23 on modular [Seed = 1368193028] ------------------------------------- [ 275, 1, 1 ][ 11, 1, 1 ][] [ 275, 2, 1 ][ 11, 1, 1 ][] [ 275, 3, 1 ][ 11, 1, 1 ][] [ 275, 4, 1 ][ 11, 5, 1 ][] [ 275, 5, 1 ][ 11, 1, 1 ][] [ 275, 6, 1 ][ 11, 1, 1 ][] [ 275, 7, 1 ][ 11, 1, 1 ][] [ 275, 8, 1 ][ 11, 1, 1 ][] Total time: 22.199 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:15:40 2003 Input: N:=276; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:13:39 on modular [Seed = 1234493760] ------------------------------------- [ 276, 1, 1 ][ 3, 1, 5 ][ 23, 1, 1 ][] [ 276, 2, 1 ][ 3, 7, 1 ][ 23, 1, 1 ][] Total time: 119.270 seconds, Total memory usage: 7.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:21:43 2003 Input: N:=276; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:19:43 on modular [Seed = 2141378586] ------------------------------------- [ 276, 1, 1 ][ 3, 1, 5 ][ 23, 1, 1 ][] [ 276, 2, 1 ][ 3, 7, 1 ][ 23, 1, 1 ][] Total time: 119.539 seconds, Total memory usage: 7.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:22:41 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(92,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(276,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:22:33 on modular [Seed = 1857275997] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 8.159 seconds, Total memory usage: 4.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:26:48 2003 Input: N:=276; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:24:50 on modular [Seed = 1740292559] ------------------------------------- [ 276, 1, 1 ][ 3, 1, 5 ][ 23, 1, 1 ][] [ 276, 2, 1 ][ 3, 7, 7 ][ 23, 1, 1 ][] Total time: 116.709 seconds, Total memory usage: 7.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:29:03 2003 Input: N:=253; q:=13; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:28:47 on modular [Seed = 2471376406] ------------------------------------- [ 253, 1, 1 ][ 11, 1, 19 ][] [ 253, 2, 1 ][ 11, 5, 1 ][] [ 253, 3, 1 ][ 11, 1, 1 ][] [ 253, 4, 1 ][ 11, 1, 1 ][] Total time: 15.659 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:29:57 2003 Input: N:=277; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:29:54 on modular [Seed = 2287283568] ------------------------------------- [ 277, 1, 1 ][] [ 277, 2, 1 ][ 277, 1, 1 ][] [ 277, 3, 1 ][ 277, 1, 1 ][] [ 277, 4, 1 ][ 277, 23, 1 ][] Total time: 3.749 seconds, Total memory usage: 3.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:31:17 2003 Input: N:=278; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:30:35 on modular [Seed = 3144032170] ------------------------------------- [ 278, 1, 1 ][ 2, 1, 3 ][ 139, 3, 1 ][] [ 278, 2, 1 ][ 2, 1, 1 ][ 139, 1, 1 ][] [ 278, 3, 1 ][ 2, 1, 7 ][ 139, 1, 1 ][] [ 278, 4, 1 ][ 2, 1, 271 ][ 139, 1, 1 ][] [ 278, 5, 1 ][ 2, 1435, 41 ][ 139, 1, 1 ][] Total time: 41.620 seconds, Total memory usage: 5.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:33:16 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(139,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(278,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:33:08 on modular [Seed = 3010336525] ------------------------------------- 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 2 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/271 Defined on 1 generator Relations: 271*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 8.289 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:42:32 2003 Input: N:=280; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:41:25 on modular [Seed = 2759394859] ------------------------------------- [ 280, 1, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 280, 2, 1 ][ 5, 5, 5 ][ 7, 3, 3 ][] [ 280, 3, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 280, 4, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] Total time: 67.209 seconds, Total memory usage: 8.06MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:43:19 2003 Input: N:=281; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:43:16 on modular [Seed = 3691085250] ------------------------------------- [ 281, 1, 1 ][] [ 281, 2, 1 ][ 281, 35, 1 ][] Total time: 3.679 seconds, Total memory usage: 3.98MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:46:12 2003 Input: N:=282; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:43:50 on modular [Seed = 3557389800] ------------------------------------- [ 282, 1, 1 ][ 2, 3, 3 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 282, 2, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 282, 3, 1 ][ 2, 1, 3 ][ 3, 1, 1 ][ 47, 1, 1 ][] [ 282, 4, 1 ][ 2, 1, 5 ][ 3, 3, 1 ][ 47, 1, 1 ][] [ 282, 5, 1 ][ 2, 115, 5 ][ 3, 23, 1 ][ 47, 1, 1 ][] Total time: 141.229 seconds, Total memory usage: 7.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:47:57 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(141,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(282,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:47:47 on modular [Seed = 3239862728] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 10.209 seconds, Total memory usage: 4.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:49:19 2003 Input: N:=283; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:49:15 on modular [Seed = 4263730831] ------------------------------------- [ 283, 1, 1 ][] [ 283, 2, 1 ][ 283, 47, 1 ][] Total time: 3.689 seconds, Total memory usage: 4.01MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:51:32 2003 Input: N:=285; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:50:11 on modular [Seed = 4013051734] ------------------------------------- [ 285, 1, 1 ][ 3, 1, 1 ][ 5, 1, 3 ][ 19, 1, 1 ][] [ 285, 2, 1 ][ 3, 1, 1 ][ 5, 3, 3 ][ 19, 1, 1 ][] [ 285, 3, 1 ][ 3, 5, 5 ][ 5, 1, 1 ][ 19, 1, 1 ][] [ 285, 4, 1 ][ 3, 1, 47 ][ 5, 1, 1 ][ 19, 1, 1 ][] [ 285, 5, 1 ][ 3, 1, 19 ][ 5, 3, 3 ][ 19, 1, 3 ][] [ 285, 6, 1 ][ 3, 1, 1 ][ 5, 1, 7 ][ 19, 1, 1 ][] [ 285, 7, 1 ][ 3, 3, 1 ][ 5, 3, 1 ][ 19, 1, 1 ][] Total time: 80.419 seconds, Total memory usage: 6.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:52:34 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(95,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(285,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:52:25 on modular [Seed = 3879368916] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/94 Defined on 1 generator Relations: 94*$.1 = 0 5 Abelian Group isomorphic to Z/38 Defined on 1 generator Relations: 38*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 8.630 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:55:04 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(57,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(285,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:54:55 on modular [Seed = 532840633] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Total time: 8.369 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:55:57 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(15,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(285,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:55:50 on modular [Seed = 198612196] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 7.489 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:58:30 2003 Input: N:=286; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 01:57:12 on modular [Seed = 64920914] ------------------------------------- [ 286, 1, 1 ][ 2, 1, 3 ][ 11, 1, 1 ][ 13, 1, 1 ][] [ 286, 2, 1 ][ 2, 1, 5 ][ 11, 1, 1 ][ 13, 3, 1 ][] [ 286, 3, 1 ][ 2, 3, 3 ][ 11, 1, 5 ][ 13, 1, 1 ][] [ 286, 4, 1 ][ 2, 13, 13 ][ 11, 1, 1 ][ 13, 1, 1 ][] [ 286, 5, 1 ][ 2, 5, 1 ][ 11, 1, 1 ][ 13, 5, 1 ][] [ 286, 6, 1 ][ 2, 1, 1 ][ 11, 1, 1 ][ 13, 1, 1 ][] [ 286, 7, 1 ][ 2, 1, 139 ][ 11, 1, 1 ][ 13, 1, 1 ][] Total time: 78.039 seconds, Total memory usage: 6.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 01:59:36 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(143,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(286,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 01:59:27 on modular [Seed = 988259564] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/15 Defined on 1 generator Relations: 15*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/139 Defined on 1 generator Relations: 139*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 9.229 seconds, Total memory usage: 4.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:01:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(26,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(286,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:01:31 on modular [Seed = 1568718863] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 7.849 seconds, Total memory usage: 4.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:03:49 2003 Input: N:=287; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:03:04 on modular [Seed = 1435027684] ------------------------------------- [ 287, 1, 1 ][ 7, 1, 1 ][ 41, 1, 1 ][] [ 287, 2, 1 ][ 7, 19, 19 ][ 41, 1, 1 ][] [ 287, 3, 1 ][ 7, 1, 13 ][ 41, 1, 1 ][] [ 287, 4, 1 ][ 7, 1, 1 ][ 41, 1, 1 ][] [ 287, 5, 1 ][ 7, 21, 1 ][ 41, 1, 3 ][] [ 287, 6, 1 ][ 7, 1, 37 ][ 41, 1, 1 ][] Total time: 44.750 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:04:38 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(41,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(287,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:04:32 on modular [Seed = 1284624469] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 3 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 4 Abelian Group of order 1 5 Abelian Group of order 1 6 Abelian Group isomorphic to Z/74 Defined on 1 generator Relations: 74*$.1 = 0 Total time: 6.339 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:07:31 2003 Input: N:=290; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:06:08 on modular [Seed = 2024137729] ------------------------------------- [ 290, 1, 1 ][ 2, 1, 1 ][ 5, 1, 3 ][ 29, 1, 1 ][] [ 290, 2, 1 ][ 2, 1, 23 ][ 5, 1, 1 ][ 29, 3, 1 ][] [ 290, 3, 1 ][ 2, 1, 13 ][ 5, 27, 9 ][ 29, 1, 1 ][] [ 290, 4, 1 ][ 2, 3, 1 ][ 5, 1, 7 ][ 29, 1, 1 ][] [ 290, 5, 1 ][ 2, 49, 7 ][ 5, 7, 1 ][ 29, 1, 1 ][] Total time: 82.329 seconds, Total memory usage: 7.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:09:30 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(145,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(290,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:09:21 on modular [Seed = 1940842571] ------------------------------------- 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 4 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.639 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:13:24 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(58,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(290,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:13:16 on modular [Seed = 1623063157] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Total time: 8.299 seconds, Total memory usage: 4.48MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:15:56 2003 Input: N:=291; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:15:15 on modular [Seed = 2671904005] ------------------------------------- [ 291, 1, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 2, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 3, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 4, 1 ][ 3, 1, 23 ][ 97, 1, 1 ][] [ 291, 5, 1 ][ 3, 1, 13 ][ 97, 1, 1 ][] [ 291, 6, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 7, 1 ][ 3, 11, 1 ][ 97, 1, 1 ][] [ 291, 8, 1 ][ 3, 6811, 973 ][ 97, 1, 1 ][] Total time: 41.139 seconds, Total memory usage: 5.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:17:06 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(97,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(291,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:16:58 on modular [Seed = 2538212709] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 5 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 8 Abelian Group isomorphic to Z/139 Defined on 1 generator Relations: 139*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 7.919 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:18:49 2003 Input: N:=291; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:18:08 on modular [Seed = 2404521638] ------------------------------------- [ 291, 1, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 2, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 3, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 4, 1 ][ 3, 1, 23 ][ 97, 1, 1 ][] [ 291, 5, 1 ][ 3, 1, 13 ][ 97, 1, 1 ][] [ 291, 6, 1 ][ 3, 1, 1 ][ 97, 1, 1 ][] [ 291, 7, 1 ][ 3, 11, 11 ][ 97, 1, 1 ][] [ 291, 8, 1 ][ 3, 6811, 973 ][ 97, 1, 1 ][] Total time: 40.720 seconds, Total memory usage: 5.38MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 02:19:32 2003 Input: C:=ComplexField(); x1:=Sqrt(-27); x2:=(1+Sqrt(-27))/4; x3:=(-1+Sqrt(-27))/4; y1:=jInvariant(x1); y2:=jInvariant(x2); y3:=jInvariant(x3); y1;y2;y3; z1:=y1+y2+y3; z2:=y1*y2+y1*y3+y2*y3; z3:=y1*y2*y3; z1;z2;z3; Output: Magma V2.10-6 Fri Dec 19 2003 02:19:29 on modular [Seed = 2254118686] ------------------------------------- 151013228704515.49785340860307769617 + 0.E-14*i 742.251073295698393080526292457965334763331 - 3449.386723302192889385635416192632*i 742.251073295698393080526292458773128330277 + 3449.386723302192889385635416140933*i 151013228705999.99999999999985789145 + 0.E-15*i 224179462187999999.99999999987267074175 - 1.4551915228 E-11*i 1879994705687999999999.9999976754 + 0.00000002980232238*i Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:22:00 2003 Input: N:=293; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:21:56 on modular [Seed = 3060477627] ------------------------------------- [ 293, 1, 1 ][] [ 293, 2, 1 ][ 293, 73, 1 ][] Total time: 3.799 seconds, Total memory usage: 4.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:24:03 2003 Input: N:=294; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:22:38 on modular [Seed = 2926786185] ------------------------------------- [ 294, 1, 1 ][ 2, 1, 5 ][ 3, 1, 3 ][] [ 294, 2, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 294, 3, 1 ][ 2, 1, 5 ][ 3, 3, 1 ][] [ 294, 4, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 294, 5, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 294, 6, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 294, 7, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] Total time: 85.130 seconds, Total memory usage: 9.75MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:27:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(98,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(294,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:26:51 on modular [Seed = 3707783935] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 6 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.219 seconds, Total memory usage: 4.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:31:49 2003 Input: N:=295; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:31:10 on modular [Seed = 3440401386] ------------------------------------- [ 295, 1, 1 ][ 5, 1, 1 ][ 59, 1, 1 ][] [ 295, 2, 1 ][ 5, 107, 107 ][ 59, 1, 1 ][] [ 295, 3, 1 ][ 5, 5, 1 ][ 59, 1, 1 ][] [ 295, 4, 1 ][ 5, 1, 6629 ][ 59, 1, 1 ][] Total time: 38.389 seconds, Total memory usage: 4.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:33:17 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(59,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(295,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:33:10 on modular [Seed = 3306705770] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/107 Defined on 1 generator Relations: 107*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/6629 Defined on 1 generator Relations: 6629*$.1 = 0 Total time: 6.729 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:34:26 2003 Input: N:=297; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n-1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:34:21 on modular [Seed = 4230048280] ------------------------------------- Do not know how to compute component group at 3 Total time: 4.750 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:35:08 2003 Input: N:=297; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:34:41 on modular [Seed = 4096352764] ------------------------------------- [ 297, 1, 1 ][ 11, 1, 1 ][] [ 297, 2, 1 ][ 11, 1, 1 ][] [ 297, 3, 1 ][ 11, 1, 1 ][] [ 297, 4, 1 ][ 11, 1, 1 ][] [ 297, 5, 1 ][ 11, 1, 1 ][] [ 297, 6, 1 ][ 11, 1, 1 ][] [ 297, 7, 1 ][ 11, 3, 1 ][] [ 297, 8, 1 ][ 11, 1, 3 ][] Total time: 26.590 seconds, Total memory usage: 5.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:36:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(27,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(297,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:36:06 on modular [Seed = 3762124190] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 8 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 6.889 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host nat-147-226-228-26.bsu.edu. (147.226.228.26) Time: Fri Dec 19 02:36:34 2003 Input: 225 Output: Magma V2.10-6 Fri Dec 19 2003 02:36:31 on modular [Seed = 432311422] ------------------------------------- 225 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:38:08 2003 Input: N:=298; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:37:29 on modular [Seed = 315590579] ------------------------------------- [ 298, 1, 1 ][ 2, 1, 1 ][ 149, 1, 1 ][] [ 298, 2, 1 ][ 2, 9, 9 ][ 149, 1, 1 ][] [ 298, 3, 1 ][ 2, 1, 69 ][ 149, 1, 1 ][] [ 298, 4, 1 ][ 2, 1, 13 ][ 149, 1, 1 ][] [ 298, 5, 1 ][ 2, 725, 145 ][ 149, 1, 1 ][] Total time: 38.709 seconds, Total memory usage: 6.04MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:38:58 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(149,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(298,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:38:50 on modular [Seed = 181902872] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/69 Defined on 1 generator Relations: 69*$.1 = 0 4 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 5 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 Total time: 8.339 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:41:40 2003 Input: N:=299; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:40:51 on modular [Seed = 988262049] ------------------------------------- [ 299, 1, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 2, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 3, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 4, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 5, 1 ][ 13, 11, 1 ][ 23, 1, 1 ][] [ 299, 6, 1 ][ 13, 3, 1 ][ 23, 1, 3 ][] [ 299, 7, 1 ][ 13, 1, 289 ][ 23, 7, 1 ][] Total time: 48.669 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:42:33 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(23,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(299,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:42:27 on modular [Seed = 854566601] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group of order 1 5 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 6 Abelian Group of order 1 7 Abelian Group isomorphic to Z/17 + Z/17 Defined on 2 generators Relations: 17*$.1 = 0 17*$.2 = 0 Total time: 6.309 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:44:32 2003 Input: N:=299; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:43:43 on modular [Seed = 720877853] ------------------------------------- [ 299, 1, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 2, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 3, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 4, 1 ][ 13, 1, 1 ][ 23, 1, 1 ][] [ 299, 5, 1 ][ 13, 11, 11 ][ 23, 1, 1 ][] [ 299, 6, 1 ][ 13, 3, 1 ][ 23, 1, 3 ][] [ 299, 7, 1 ][ 13, 1, 289 ][ 23, 7, 1 ][] Total time: 49.000 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:47:04 2003 Input: N:=300; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:45:53 on modular [Seed = 670741646] ------------------------------------- [ 300, 1, 1 ][ 3, 1, 3 ][] [ 300, 2, 1 ][ 3, 1, 1 ][] [ 300, 3, 1 ][ 3, 3, 1 ][] [ 300, 4, 1 ][ 3, 1, 1 ][] Total time: 70.809 seconds, Total memory usage: 10.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:48:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(100,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(300,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:47:59 on modular [Seed = 1602407784] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.169 seconds, Total memory usage: 4.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:49:52 2003 Input: N:=301; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:49:15 on modular [Seed = 1217780267] ------------------------------------- [ 301, 1, 1 ][ 7, 7, 1 ][ 43, 1, 1 ][] [ 301, 2, 1 ][ 7, 1, 1 ][ 43, 1, 1 ][] [ 301, 3, 1 ][ 7, 1, 17 ][ 43, 1, 1 ][] [ 301, 4, 1 ][ 7, 11, 1 ][ 43, 1, 1 ][] Total time: 37.010 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:50:40 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(43,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(301,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:50:33 on modular [Seed = 2040851368] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 2 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 4 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 6.569 seconds, Total memory usage: 4.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:52:49 2003 Input: N:=302; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:52:03 on modular [Seed = 1907155018] ------------------------------------- [ 302, 1, 1 ][ 2, 1, 3 ][ 151, 1, 1 ][] [ 302, 2, 1 ][ 2, 15, 3 ][ 151, 1, 1 ][] [ 302, 3, 1 ][ 2, 5, 5 ][ 151, 1, 1 ][] [ 302, 4, 1 ][ 2, 1, 7 ][ 151, 1, 1 ][] [ 302, 5, 1 ][ 2, 1, 3879 ][ 151, 3, 1 ][] [ 302, 6, 1 ][ 2, 779, 41 ][ 151, 1, 1 ][] Total time: 46.540 seconds, Total memory usage: 6.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:54:05 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(151,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(302,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:53:56 on modular [Seed = 1790442470] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 4 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/431 Defined on 1 generator Relations: 431*$.1 = 0 6 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Total time: 8.710 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:57:09 2003 Input: N:=303; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 02:56:24 on modular [Seed = 1723594326] ------------------------------------- [ 303, 1, 1 ][ 3, 7, 7 ][ 101, 1, 1 ][] [ 303, 2, 1 ][ 3, 1, 1 ][ 101, 1, 1 ][] [ 303, 3, 1 ][ 3, 1, 1 ][ 101, 1, 1 ][] [ 303, 4, 1 ][ 3, 51, 1 ][ 101, 1, 1 ][] [ 303, 5, 1 ][ 3, 1, 1103 ][ 101, 1, 1 ][] Total time: 44.139 seconds, Total memory usage: 5.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 02:57:54 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(101,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(303,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 02:57:47 on modular [Seed = 2655194877] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/17648 Defined on 1 generator Relations: 17648*$.1 = 0 Total time: 7.689 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:01:24 2003 Input: N:=303; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 03:00:40 on modular [Seed = 2387804606] ------------------------------------- [ 303, 1, 1 ][ 3, 7, 7 ][ 101, 1, 1 ][] [ 303, 2, 1 ][ 3, 1, 1 ][ 101, 1, 1 ][] [ 303, 3, 1 ][ 3, 1, 1 ][ 101, 1, 1 ][] [ 303, 4, 1 ][ 3, 51, 3 ][ 101, 1, 1 ][] [ 303, 5, 1 ][ 3, 1, 1103 ][ 101, 1, 1 ][] Total time: 43.810 seconds, Total memory usage: 5.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:03:34 2003 Input: N:=305; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 03:02:49 on modular [Seed = 2826250009] ------------------------------------- [ 305, 1, 1 ][ 5, 1, 3 ][ 61, 1, 1 ][] [ 305, 2, 1 ][ 5, 37, 37 ][ 61, 1, 1 ][] [ 305, 3, 1 ][ 5, 1, 417 ][ 61, 3, 1 ][] [ 305, 4, 1 ][ 5, 279, 9 ][ 61, 1, 1 ][] Total time: 44.519 seconds, Total memory usage: 5.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:04:22 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(61,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(305,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 03:04:15 on modular [Seed = 2709270086] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/37 Defined on 1 generator Relations: 37*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/139 Defined on 1 generator Relations: 139*$.1 = 0 4 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 Total time: 6.979 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:06:16 2003 Input: N:=306; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 03:05:43 on modular [Seed = 3707786130] ------------------------------------- [ 306, 1, 1 ][ 2, 1, 1 ][] [ 306, 2, 1 ][ 2, 1, 3 ][] [ 306, 3, 1 ][ 2, 3, 3 ][] [ 306, 4, 1 ][ 2, 1, 1 ][] [ 306, 5, 1 ][ 2, 1, 5 ][] [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 33.110 seconds, Total memory usage: 9.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:07:07 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(153,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(306,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 03:06:56 on modular [Seed = 3457368182] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.509 seconds, Total memory usage: 4.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:09:58 2003 Input: N:=306; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 03:09:25 on modular [Seed = 3340389098] ------------------------------------- [ 306, 1, 1 ][ 2, 1, 1 ][] [ 306, 2, 1 ][ 2, 1, 3 ][] [ 306, 3, 1 ][ 2, 3, 3 ][] [ 306, 4, 1 ][ 2, 1, 1 ][] [ 306, 5, 1 ][ 2, 1, 5 ][] [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 32.540 seconds, Total memory usage: 9.21MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 03:12:07 2003 Input: C:=ComlexField(); x1:=Sqrt(-17); y1:=jInvariant(x1); y1; Output: Magma V2.10-6 Fri Dec 19 2003 03:12:03 on modular [Seed = 3912524834] ------------------------------------- >> C:=ComlexField(); ^ User error: Identifier 'ComlexField' has not been declared or assigned 178211465582.57236317285989136288 + 0.E-17*i Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathpc402.postech.ac.kr. (141.223.33.57) Time: Fri Dec 19 03:12:19 2003 Input: C:=ComplexField(); x1:=Sqrt(-17); y1:=jInvariant(x1); y1; Output: Magma V2.10-6 Fri Dec 19 2003 03:12:16 on modular [Seed = 3795808026] ------------------------------------- 178211465582.57236317285989136288 + 0.E-17*i Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:12:22 2003 Input: N:=306; q:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 03:11:49 on modular [Seed = 4130044715] ------------------------------------- [ 306, 1, 1 ][ 2, 1, 1 ][] [ 306, 2, 1 ][ 2, 1, 3 ][] [ 306, 3, 1 ][ 2, 3, 3 ][] [ 306, 4, 1 ][ 2, 1, 1 ][] [ 306, 5, 1 ][ 2, 1, 5 ][] [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 32.449 seconds, Total memory usage: 9.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:13:29 2003 Input: N:=306; q:=13; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 03:12:57 on modular [Seed = 532845313] ------------------------------------- [ 306, 1, 1 ][ 2, 1, 1 ][] [ 306, 2, 1 ][ 2, 1, 3 ][] [ 306, 3, 1 ][ 2, 3, 3 ][] [ 306, 4, 1 ][ 2, 1, 1 ][] [ 306, 5, 1 ][ 2, 1, 5 ][] [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 31.949 seconds, Total memory usage: 9.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 03:16:28 2003 Input: N:=307; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 03:16:24 on modular [Seed = 48205517] ------------------------------------- [ 307, 1, 1 ][] [ 307, 2, 1 ][ 307, 1, 1 ][] [ 307, 3, 1 ][ 307, 1, 1 ][] [ 307, 4, 1 ][ 307, 1, 1 ][] [ 307, 5, 1 ][ 307, 3, 1 ][] [ 307, 6, 1 ][ 307, 17, 1 ][] [ 307, 7, 1 ][ 307, 1, 1 ][] Total time: 4.109 seconds, Total memory usage: 4.45MB ************** MAGMA ***************** Host mathpc204.postech.ac.kr. (141.223.33.29) Time: Fri Dec 19 03:24:30 2003 Input: C := ComplexField(); x1:=Sqrt(-14);y1:=jInvariant(x1); x2:=Sqrt(-14)/2;y2:=jInvariant(x2); x3:=(-1+Sqrt(-14))/3;y3:=jInvariant(x3); x4:=(1+Sqrt(-14))/3;y4:=jInvariant(x4); z1:=y1+y2+y3+y4; z2:=y1*y2+y2*y3+y3*y4+y4*y1; z3:=y1*y2*y3+y2*y3*y4+y3*y4*y1+y4*y1*y2; z4:=y1*y2*y3*y4; z1;z2;z3;z4; Output: Magma V2.10-6 Fri Dec 19 2003 03:24:27 on modular [Seed = 1055110290] ------------------------------------- 16220384511.99999999999999998742 - 2.06795153114 E-25*i 2068766124818431.99999999999752731127 - 34512574080753.73432571016033243438*i -2257767342088912895.99999999540159478783 - 0.0000000003492459654*i 10064086044321563803647.9999818801 + 0.000002503395080*i Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (129.175.117.80) Time: Fri Dec 19 07:54:24 2003 Input: 2+2 Output: Magma V2.10-6 Fri Dec 19 2003 07:54:20 on modular [Seed = 1318290849] ------------------------------------- 4 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (129.175.117.80) Time: Fri Dec 19 07:54:38 2003 Input: 2+3 Output: Magma V2.10-6 Fri Dec 19 2003 07:54:35 on modular [Seed = 1973993325] ------------------------------------- 5 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 10:56:46 2003 Input: : N:=308; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 10:56:43 on modular [Seed = 382351011] ------------------------------------- >> : N:=308; q:=3; ^ User error: bad syntax >> n:=Factorization(N); ^ User error: Identifier 'N' has not been declared or assigned >> uspidalSubspace(ModularSymbols(N,2,+1))))); ^ User error: Identifier 'N' has not been declared or assigned >> for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; ^ User error: Identifier 'A' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 10:58:25 2003 Input: N:=308; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 10:57:05 on modular [Seed = 787615473] ------------------------------------- [ 308, 1, 1 ][ 7, 1, 1 ][ 11, 1, 1 ][] [ 308, 2, 1 ][ 7, 1, 5 ][ 11, 1, 1 ][] [ 308, 3, 1 ][ 7, 1, 1 ][ 11, 3, 1 ][] Total time: 79.430 seconds, Total memory usage: 7.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:00:55 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(44,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(308,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:00:47 on modular [Seed = 1055007135] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 7.509 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:02:26 2003 Input: N:=309; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:01:44 on modular [Seed = 1150835618] ------------------------------------- [ 309, 1, 1 ][ 3, 5, 5 ][ 103, 1, 1 ][] [ 309, 2, 1 ][ 3, 1, 89 ][ 103, 1, 1 ][] [ 309, 3, 1 ][ 3, 1, 9 ][ 103, 1, 1 ][] [ 309, 4, 1 ][ 3, 325, 25 ][ 103, 1, 1 ][] Total time: 41.489 seconds, Total memory usage: 5.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:03:17 2003 Input: N:=309; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:02:35 on modular [Seed = 1551909449] ------------------------------------- [ 309, 1, 1 ][ 3, 5, 5 ][ 103, 1, 1 ][] [ 309, 2, 1 ][ 3, 1, 89 ][ 103, 1, 1 ][] [ 309, 3, 1 ][ 3, 1, 9 ][ 103, 1, 1 ][] [ 309, 4, 1 ][ 3, 325, 25 ][ 103, 1, 1 ][] Total time: 41.950 seconds, Total memory usage: 5.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:04:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(103,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(309,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:03:53 on modular [Seed = 1435061042] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/89 Defined on 1 generator Relations: 89*$.1 = 0 3 Abelian Group isomorphic to Z/3 + Z/3 Defined on 2 generators Relations: 3*$.1 = 0 3*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 4 Abelian Group isomorphic to Z/5 + Z/5 Defined on 2 generators Relations: 5*$.1 = 0 5*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 Total time: 7.389 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:06:47 2003 Input: N:=310; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:05:15 on modular [Seed = 1723496659] ------------------------------------- [ 310, 1, 1 ][ 2, 3, 3 ][ 5, 1, 1 ][ 31, 1, 1 ][] [ 310, 2, 1 ][ 2, 3, 1 ][ 5, 1, 1 ][ 31, 1, 1 ][] [ 310, 3, 1 ][ 2, 1, 3 ][ 5, 1, 1 ][ 31, 1, 1 ][] [ 310, 4, 1 ][ 2, 1, 23 ][ 5, 1, 1 ][ 31, 1, 1 ][] [ 310, 5, 1 ][ 2, 25, 5 ][ 5, 5, 1 ][ 31, 1, 1 ][] Total time: 90.799 seconds, Total memory usage: 7.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:07:38 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(105,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(310,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:07:29 on modular [Seed = 2124571441] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.169 seconds, Total memory usage: 4.62MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:08:40 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(155,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(310,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:08:30 on modular [Seed = 3407337147] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/12 Defined on 1 generator Relations: 12*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/46 Defined on 1 generator Relations: 46*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.699 seconds, Total memory usage: 4.66MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:11:00 2003 Input: N:=311; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:10:56 on modular [Seed = 3674720197] ------------------------------------- [ 311, 1, 1 ][] [ 311, 2, 1 ][ 311, 155, 1 ][] Total time: 3.879 seconds, Total memory usage: 4.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:13:57 2003 Input: N:=312; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:11:34 on modular [Seed = 3929470674] ------------------------------------- [ 312, 1, 1 ][ 3, 1, 1 ][ 13, 1, 1 ][] [ 312, 2, 1 ][ 3, 1, 1 ][ 13, 1, 1 ][] [ 312, 3, 1 ][ 3, 1, 1 ][ 13, 1, 1 ][] [ 312, 4, 1 ][ 3, 1, 5 ][ 13, 1, 3 ][] [ 312, 5, 1 ][ 3, 3, 3 ][ 13, 1, 1 ][] [ 312, 6, 1 ][ 3, 1, 1 ][ 13, 1, 1 ][] Total time: 139.680 seconds, Total memory usage: 9.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:18:00 2003 Input: N:=313; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:17:56 on modular [Seed = 4163167042] ------------------------------------- [ 313, 1, 1 ][] [ 313, 2, 1 ][ 313, 1, 1 ][] [ 313, 3, 1 ][ 313, 13, 1 ][] Total time: 3.959 seconds, Total memory usage: 4.20MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:19:11 2003 Input: C := GolayCode(GF(2), true); D := Shorten(C, 24); Output: Magma V2.10-6 Fri Dec 19 2003 11:19:07 on modular [Seed = 265491705] ------------------------------------- >> D := Shorten(C, 24); ^ User error: Identifier 'Shorten' has not been declared or assigned Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:19:28 2003 Input: N:=314; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:18:35 on modular [Seed = 4029475621] ------------------------------------- [ 314, 1, 1 ][ 2, 1, 5 ][ 157, 1, 1 ][] [ 314, 2, 1 ][ 2, 1, 6441 ][ 157, 3, 1 ][] [ 314, 3, 1 ][ 2, 56011, 709 ][ 157, 1, 1 ][] Total time: 51.409 seconds, Total memory usage: 6.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:20:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(157,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(314,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:20:05 on modular [Seed = 449183777] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/2147 Defined on 1 generator Relations: 2147*$.1 = 0 3 Abelian Group isomorphic to Z/709 Defined on 1 generator Relations: 709*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 7.759 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:20:37 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); v := C ! [0,0,0,1,0,1,,1,1,0,0,1,0,0,1,1,0,1,1]; b, d := Decode(C, v); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:20:34 on modular [Seed = 315492429] ------------------------------------- >> v := C ! [0,0,0,1,0,1,,1,1,0,0,1,0,0,1,1,0,1,1]; ^ User error: bad syntax >> b, d := Decode(C, v); ^ User error: Identifier 'v' has not been declared or assigned >> d; ^ User error: Identifier 'd' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:20:52 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); v := C ! [0,0,0,1,0,1,1,1,0,0,1,0,0,1,1,0,1,1]; b, d := Decode(C, v); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:20:49 on modular [Seed = 637091657] ------------------------------------- >> v := C ! [0,0,0,1,0,1,1,1,0,0,1,0,0,1,1,0,1,1]; ^ Runtime error in '!': Result is not in the given structure >> b, d := Decode(C, v); ^ User error: Identifier 'v' has not been declared or assigned >> d; ^ User error: Identifier 'd' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:21:25 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; Output: Magma V2.10-6 Fri Dec 19 2003 11:21:21 on modular [Seed = 1021322928] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:22:42 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; Output: Magma V2.10-6 Fri Dec 19 2003 11:22:39 on modular [Seed = 820783858] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:23:10 2003 Input: N:=315; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:21:58 on modular [Seed = 938159516] ------------------------------------- [ 315, 1, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 2, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 3, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 4, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 5, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 6, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] Total time: 71.040 seconds, Total memory usage: 7.96MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:23:21 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := [0,0,0,1,0,1,1,1,0,0,1,0,0,1,1,0,1,1]; b ,d := Decode(C, w); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:23:18 on modular [Seed = 1184521405] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] >> b ,d := Decode(C, w); ^ Runtime error in 'Decode': Bad argument types Argument types given: Code, SeqEnum[RngIntElt] >> d; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:23:56 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; b ,d := Decode(C, v); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:23:52 on modular [Seed = 1518748495] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.269 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:24:33 2003 Input: N:=315; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:23:21 on modular [Seed = 1501905837] ------------------------------------- [ 315, 1, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 2, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 3, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 4, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 5, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] [ 315, 6, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][] Total time: 71.270 seconds, Total memory usage: 7.96MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:24:45 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[5] := 1 - w[5]; w[15] := 1 - w[15]; w[16] := 1 - w[16]; b ,d := Decode(C, w); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:24:42 on modular [Seed = 1807184428] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.069 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:25:05 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[5] := 1 - w[5]; w[15] := 1 - w[15]; w[16] := 1 - w[16]; w[17] := 1 - w[17]; b ,d := Decode(C, w); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:25:02 on modular [Seed = 2124572461] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0) Total time: 3.049 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:25:25 2003 Input: C := GolayCode(GF(2), true); D := ShortenCode(C, 24); C := ShortenCode(D, 23); D := ShortenCode(C, 22); C := ShortenCode(D, 21); D := ShortenCode(C, 20); C := ShortenCode(D, 19); C; v := C ! [0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[5] := 1 - w[5]; w[15] := 1 - w[15]; w[16] := 1 - w[16]; b ,d := Decode(C, w); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:25:22 on modular [Seed = 1907189774] ------------------------------------- [18, 6, 8] Linear Code over GF(2) Generator matrix: [1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1] [0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0] [0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0] [0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1] (0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.029 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:26:11 2003 Input: N:=317; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:26:07 on modular [Seed = 2287243546] ------------------------------------- [ 317, 1, 1 ][] [ 317, 2, 1 ][ 317, 79, 1 ][] Total time: 3.849 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:26:17 2003 Input: C := GolayCode(GF(2), true); v := C ! [0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[5] := 1 - w[5]; w[15] := 1 - w[15]; w[16] := 1 - w[16]; b ,d := Decode(C, w); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:26:14 on modular [Seed = 2153552171] ------------------------------------- (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.099 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:27:21 2003 Input: C := GolayCode(GF(2), true); v := C ! [0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[11] := 1 - w[11]; w[21] := 1 - w[21]; w[22] := 1 - w[22]; b ,d := Decode(C, w); d; Output: Magma V2.10-6 Fri Dec 19 2003 11:27:18 on modular [Seed = 2487782783] ------------------------------------- (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.359 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:27:32 2003 Input: C := GolayCode(GF(2), true); v := C ! [0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[11] := 1 - w[11]; w[21] := 1 - w[21]; w[22] := 1 - w[22]; b ,d := Decode(C, w); d; v; Output: Magma V2.10-6 Fri Dec 19 2003 11:27:28 on modular [Seed = 2943596114] ------------------------------------- (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.239 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:27:49 2003 Input: C := GolayCode(GF(2), true); v := C ! [0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[11] := 1 - w[11]; w[21] := 1 - w[21]; w[22] := 1 - w[22]; w[23] := 1 - w[23]; b ,d := Decode(C, w); d; v; Output: Magma V2.10-6 Fri Dec 19 2003 11:27:46 on modular [Seed = 2793062057] ------------------------------------- (1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0) (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.329 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:28:20 2003 Input: C := GolayCode(GF(2), true); v := C ! [0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[11] := 1 - w[11]; w[12] := 1 - w[12]; w[21] := 1 - w[21]; w[22] := 1 - w[22]; b ,d := Decode(C, w); d; v; Output: Magma V2.10-6 Fri Dec 19 2003 11:28:17 on modular [Seed = 3110445461] ------------------------------------- (1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0) (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.259 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host 3(NXDOMAIN) (216.95.198.132) Time: Fri Dec 19 11:28:38 2003 Input: C := GolayCode(GF(2), true); v := C ! [0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0]; w := v; w[11] := 1 - w[11]; w[12] := 1 - w[12]; w[21] := 1 - w[21]; b ,d := Decode(C, w); d; v; Output: Magma V2.10-6 Fri Dec 19 2003 11:28:34 on modular [Seed = 2959911055] ------------------------------------- (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) (0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0) Total time: 3.329 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:29:36 2003 Input: N:=318; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:26:42 on modular [Seed = 2605154900] ------------------------------------- [ 318, 1, 1 ][ 2, 1, 1 ][ 3, 1, 3 ][ 53, 1, 1 ][] [ 318, 2, 1 ][ 2, 1, 17 ][ 3, 1, 3 ][ 53, 1, 1 ][] [ 318, 3, 1 ][ 2, 1, 3 ][ 3, 3, 1 ][ 53, 1, 1 ][] [ 318, 4, 1 ][ 2, 1, 1 ][ 3, 1, 5 ][ 53, 1, 1 ][] [ 318, 5, 1 ][ 2, 11, 11 ][ 3, 1, 1 ][ 53, 1, 1 ][] [ 318, 6, 1 ][ 2, 1, 43 ][ 3, 5, 1 ][ 53, 1, 1 ][] [ 318, 7, 1 ][ 2, 13, 1 ][ 3, 13, 1 ][ 53, 1, 1 ][] Total time: 171.490 seconds, Total memory usage: 9.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:30:26 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(159,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(318,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:30:14 on modular [Seed = 3724723781] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 6 Abelian Group isomorphic to Z/43 Defined on 1 generator Relations: 43*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 Total time: 10.729 seconds, Total memory usage: 4.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:31:25 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(106,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(318,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:31:14 on modular [Seed = 3591032329] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.710 seconds, Total memory usage: 4.65MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:42:10 2003 Input: N:=318; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 19 2003 11:33:46 on modular [Seed = 3996318089] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 13027 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:42:16 2003 Input: N:=318; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:39:20 on modular [Seed = 3778934612] ------------------------------------- [ 318, 1, 1 ][ 2, 1, 1 ][ 3, 1, 3 ][ 53, 1, 1 ][] [ 318, 2, 1 ][ 2, 1, 17 ][ 3, 1, 3 ][ 53, 1, 1 ][] [ 318, 3, 1 ][ 2, 1, 3 ][ 3, 3, 1 ][ 53, 1, 1 ][] [ 318, 4, 1 ][ 2, 1, 1 ][ 3, 1, 5 ][ 53, 1, 1 ][] [ 318, 5, 1 ][ 2, 11, 11 ][ 3, 1, 1 ][ 53, 1, 1 ][] [ 318, 6, 1 ][ 2, 1, 43 ][ 3, 5, 5 ][ 53, 1, 1 ][] [ 318, 7, 1 ][ 2, 13, 1 ][ 3, 13, 1 ][ 53, 1, 1 ][] Total time: 170.419 seconds, Total memory usage: 9.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:44:28 2003 Input: N:=319; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:43:48 on modular [Seed = 214964676] ------------------------------------- [ 319, 1, 1 ][ 11, 1, 1 ][ 29, 1, 1 ][] [ 319, 2, 1 ][ 11, 17, 1 ][ 29, 3, 3 ][] [ 319, 3, 1 ][ 11, 1, 1 ][ 29, 1, 1 ][] [ 319, 4, 1 ][ 11, 5, 1 ][ 29, 1, 15 ][] [ 319, 5, 1 ][ 11, 1, 167 ][ 29, 1, 1 ][] Total time: 40.029 seconds, Total memory usage: 4.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:45:21 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(29,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(319,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:45:15 on modular [Seed = 31266070] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group of order 1 5 Abelian Group isomorphic to Z/167 Defined on 1 generator Relations: 167*$.1 = 0 Total time: 6.169 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:46:36 2003 Input: N:=319; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:45:56 on modular [Seed = 432344401] ------------------------------------- [ 319, 1, 1 ][ 11, 1, 1 ][ 29, 1, 1 ][] [ 319, 2, 1 ][ 11, 17, 17 ][ 29, 3, 3 ][] [ 319, 3, 1 ][ 11, 1, 1 ][ 29, 1, 1 ][] [ 319, 4, 1 ][ 11, 5, 1 ][ 29, 1, 15 ][] [ 319, 5, 1 ][ 11, 1, 167 ][ 29, 1, 1 ][] Total time: 40.579 seconds, Total memory usage: 4.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:47:47 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(11,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(319,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:47:40 on modular [Seed = 298649008] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/15 Defined on 1 generator Relations: 15*$.1 = 0 5 Abelian Group of order 1 Total time: 6.109 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:49:01 2003 Input: N:=320; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:48:31 on modular [Seed = 703937989] ------------------------------------- [ 320, 1, 1 ][ 5, 1, 1 ][] [ 320, 2, 1 ][ 5, 1, 1 ][] [ 320, 3, 1 ][ 5, 1, 1 ][] [ 320, 4, 1 ][ 5, 1, 1 ][] [ 320, 5, 1 ][ 5, 1, 1 ][] [ 320, 6, 1 ][ 5, 1, 1 ][] [ 320, 7, 1 ][ 5, 1, 1 ][] Total time: 28.829 seconds, Total memory usage: 7.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:50:41 2003 Input: N:=321; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:49:53 on modular [Seed = 603926558] ------------------------------------- [ 321, 1, 1 ][ 3, 1, 5 ][ 107, 1, 1 ][] [ 321, 2, 1 ][ 3, 41, 41 ][ 107, 1, 1 ][] [ 321, 3, 1 ][ 3, 261, 87 ][ 107, 1, 1 ][] [ 321, 4, 1 ][ 3, 1, 14051 ][ 107, 1, 1 ][] Total time: 47.149 seconds, Total memory usage: 5.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:51:19 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(107,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(321,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:51:11 on modular [Seed = 1284529983] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 3 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/14051 Defined on 1 generator Relations: 14051*$.1 = 0 Total time: 8.019 seconds, Total memory usage: 4.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:54:50 2003 Input: N:=322; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 11:53:17 on modular [Seed = 1201362102] ------------------------------------- [ 322, 1, 1 ][ 2, 1, 7 ][ 7, 1, 1 ][ 23, 1, 1 ][] [ 322, 2, 1 ][ 2, 1, 1 ][ 7, 3, 3 ][ 23, 1, 1 ][] [ 322, 3, 1 ][ 2, 5, 5 ][ 7, 1, 1 ][ 23, 1, 1 ][] [ 322, 4, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][ 23, 1, 1 ][] [ 322, 5, 1 ][ 2, 1, 5 ][ 7, 1, 1 ][ 23, 1, 1 ][] [ 322, 6, 1 ][ 2, 11, 1 ][ 7, 11, 1 ][ 23, 1, 1 ][] [ 322, 7, 1 ][ 2, 11, 11 ][ 7, 1, 1 ][ 23, 1, 1 ][] Total time: 92.919 seconds, Total memory usage: 7.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 11:59:37 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(161,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(322,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 11:59:26 on modular [Seed = 1435059255] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 7 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 10.609 seconds, Total memory usage: 4.86MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:00:53 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(46,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(322,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:00:45 on modular [Seed = 1723496407] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 8.589 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:02:28 2003 Input: N:=323; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:01:37 on modular [Seed = 2287245685] ------------------------------------- [ 323, 1, 1 ][ 17, 1, 5 ][ 19, 1, 1 ][] [ 323, 2, 1 ][ 17, 1, 1 ][ 19, 1, 1 ][] [ 323, 3, 1 ][ 17, 7, 7 ][ 19, 3, 3 ][] [ 323, 4, 1 ][ 17, 1, 1 ][ 19, 1, 1 ][] [ 323, 5, 1 ][ 17, 1, 9 ][ 19, 9, 3 ][] [ 323, 6, 1 ][ 17, 5, 1 ][ 19, 1, 1 ][] Total time: 50.229 seconds, Total memory usage: 5.03MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:03:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(19,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(323,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:03:07 on modular [Seed = 2153550023] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 4 Abelian Group of order 1 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group of order 1 Total time: 6.019 seconds, Total memory usage: 4.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:04:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(17,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(323,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:04:04 on modular [Seed = 2554628112] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Total time: 6.039 seconds, Total memory usage: 4.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:08:37 2003 Input: N:=326; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:07:45 on modular [Seed = 2926748099] ------------------------------------- [ 326, 1, 1 ][ 2, 1, 9 ][ 163, 1, 1 ][] [ 326, 2, 1 ][ 2, 1, 9 ][ 163, 3, 1 ][] [ 326, 3, 1 ][ 2, 5, 5 ][ 163, 1, 1 ][] [ 326, 4, 1 ][ 2, 1, 611 ][ 163, 1, 1 ][] [ 326, 5, 1 ][ 2, 67527, 1647 ][ 163, 1, 1 ][] Total time: 51.860 seconds, Total memory usage: 6.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:09:17 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(163,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(326,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:09:08 on modular [Seed = 2809899039] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/611 Defined on 1 generator Relations: 611*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/549 Defined on 1 generator Relations: 549*$.1 = 0 Abelian Group of order 1 Total time: 8.939 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:11:11 2003 Input: N:=327; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:10:24 on modular [Seed = 3060447418] ------------------------------------- [ 327, 1, 1 ][ 3, 1, 1 ][ 109, 1, 1 ][] [ 327, 2, 1 ][ 3, 1, 13 ][ 109, 1, 1 ][] [ 327, 3, 1 ][ 3, 1, 107 ][ 109, 1, 1 ][] [ 327, 4, 1 ][ 3, 7645, 139 ][ 109, 1, 1 ][] Total time: 46.989 seconds, Total memory usage: 5.86MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:11:56 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(109,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(327,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:11:48 on modular [Seed = 3457335446] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/214 Defined on 1 generator Relations: 214*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/139 Defined on 1 generator Relations: 139*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 7.879 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 12:17:51 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(109,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(327,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:17:43 on modular [Seed = 3691041127] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/214 Defined on 1 generator Relations: 214*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/139 Defined on 1 generator Relations: 139*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 7.849 seconds, Total memory usage: 4.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:20:01 2003 Input: N:=329; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:19:08 on modular [Seed = 3574192597] ------------------------------------- [ 329, 1, 1 ][ 7, 1, 9 ][ 47, 1, 1 ][] [ 329, 2, 1 ][ 7, 1, 1 ][ 47, 1, 1 ][] [ 329, 3, 1 ][ 7, 1, 1 ][ 47, 1, 1 ][] [ 329, 4, 1 ][ 7, 1, 19 ][ 47, 1, 1 ][] [ 329, 5, 1 ][ 7, 83, 83 ][ 47, 1, 1 ][] [ 329, 6, 1 ][ 7, 1, 31 ][ 47, 1, 1 ][] [ 329, 7, 1 ][ 7, 3, 1 ][ 47, 1, 3 ][] Total time: 52.689 seconds, Total memory usage: 5.24MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 12:20:47 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(47,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(329,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:20:40 on modular [Seed = 3828934784] ------------------------------------- 1 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 5 Abelian Group isomorphic to Z/83 Defined on 1 generator Relations: 83*$.1 = 0 6 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 7 Abelian Group of order 1 Total time: 6.899 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:29:32 2003 Input: N:=330; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:22:13 on modular [Seed = 4230017077] ------------------------------------- Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 4230017077 Time to this point: 435.32 Segmentation fault Errors: Magma: Fatal Error: Magma: Irrecoverable error; exiting ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:50:21 2003 Input: N:=330; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:46:49 on modular [Seed = 482351774] ------------------------------------- Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Wed Apr 23 11:13:24 EST 2003 Initial seed: 482351774 Time to this point: 210.3 Segmentation fault Errors: Magma: Fatal Error: Magma: Irrecoverable error; exiting ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:51:19 2003 Input: N:=331; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:51:15 on modular [Seed = 570238137] ------------------------------------- [ 331, 1, 1 ][] [ 331, 2, 1 ][ 331, 1, 1 ][] [ 331, 3, 1 ][ 331, 1, 1 ][] [ 331, 4, 1 ][ 331, 55, 1 ][] Total time: 3.949 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:53:40 2003 Input: N:=330; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:51:52 on modular [Seed = 971324554] ------------------------------------- Current total memory usage: 4.1MB, failed memory request: 16384.0MB System error: Out of memory. All virtual memory has been exhausted so Magma cannot perform this statement. Total time: 107.900 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:56:23 2003 Input: N:=334; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:55:37 on modular [Seed = 1217678554] ------------------------------------- [ 334, 1, 1 ][ 2, 1, 1 ][ 167, 1, 1 ][] [ 334, 2, 1 ][ 2, 1, 5 ][ 167, 1, 1 ][] [ 334, 3, 1 ][ 2, 1, 63 ][ 167, 1, 1 ][] [ 334, 4, 1 ][ 2, 99, 99 ][ 167, 1, 1 ][] [ 334, 5, 1 ][ 2, 1, 791 ][ 167, 1, 1 ][] [ 334, 6, 1 ][ 2, 77, 11 ][ 167, 1, 1 ][] Total time: 45.610 seconds, Total memory usage: 6.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:57:27 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(167,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(334,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:57:17 on modular [Seed = 1083983030] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/3 + Z/21 Defined on 2 generators Relations: 3*$.1 = 0 21*$.2 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/3 + Z/33 Defined on 2 generators Relations: 3*$.1 = 0 33*$.2 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/791 Defined on 1 generator Relations: 791*$.1 = 0 6 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Total time: 9.429 seconds, Total memory usage: 4.62MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 12:59:18 2003 Input: N:=335; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 12:58:22 on modular [Seed = 1485069164] ------------------------------------- [ 335, 1, 1 ][ 5, 1, 1 ][ 67, 1, 1 ][] [ 335, 2, 1 ][ 5, 1, 9 ][ 67, 1, 1 ][] [ 335, 3, 1 ][ 5, 1, 1 ][ 67, 1, 1 ][] [ 335, 4, 1 ][ 5, 1, 177 ][ 67, 3, 1 ][] [ 335, 5, 1 ][ 5, 1377, 81 ][ 67, 1, 1 ][] Total time: 54.729 seconds, Total memory usage: 5.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:00:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(67,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(335,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 12:59:52 on modular [Seed = 1468748996] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 + Z/3 Defined on 2 generators Relations: 3*$.1 = 0 3*$.2 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/59 Defined on 1 generator Relations: 59*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/9 + Z/9 Defined on 2 generators Relations: 9*$.1 = 0 9*$.2 = 0 Abelian Group of order 1 Total time: 8.189 seconds, Total memory usage: 4.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:03:56 2003 Input: N:=336; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:01:23 on modular [Seed = 1974040205] ------------------------------------- [ 336, 1, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] [ 336, 2, 1 ][ 3, 3, 3 ][ 7, 1, 1 ][] [ 336, 3, 1 ][ 3, 1, 3 ][ 7, 1, 1 ][] [ 336, 4, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] [ 336, 5, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] [ 336, 6, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][] Total time: 152.529 seconds, Total memory usage: 11.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:05:18 2003 Input: N:=337; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:05:14 on modular [Seed = 2153546321] ------------------------------------- [ 337, 1, 1 ][] [ 337, 2, 1 ][ 337, 7, 1 ][] Total time: 4.099 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:06:12 2003 Input: N:=338; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:05:49 on modular [Seed = 2554632814] ------------------------------------- [ 338, 1, 1 ][ 2, 1, 1 ][] [ 338, 2, 1 ][ 2, 1, 7 ][] [ 338, 3, 1 ][ 2, 1, 3 ][] [ 338, 4, 1 ][ 2, 1, 1 ][] [ 338, 5, 1 ][ 2, 1, 1 ][] [ 338, 6, 1 ][ 2, 3, 3 ][] [ 338, 7, 1 ][ 2, 1, 41 ][] [ 338, 8, 1 ][ 2, 533, 41 ][] Total time: 21.699 seconds, Total memory usage: 7.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:07:22 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(169,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(338,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:07:13 on modular [Seed = 2538313421] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 8 Abelian Group of order 1 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Abelian Group of order 1 Total time: 8.509 seconds, Total memory usage: 4.55MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:09:54 2003 Input: N:=339; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:09:01 on modular [Seed = 2943594009] ------------------------------------- [ 339, 1, 1 ][ 3, 1, 9 ][ 113, 1, 1 ][] [ 339, 2, 1 ][ 3, 9, 9 ][ 113, 1, 1 ][] [ 339, 3, 1 ][ 3, 3, 3 ][ 113, 1, 1 ][] [ 339, 4, 1 ][ 3, 1, 7 ][ 113, 1, 1 ][] [ 339, 5, 1 ][ 3, 1, 1 ][ 113, 1, 1 ][] [ 339, 6, 1 ][ 3, 13, 13 ][ 113, 1, 1 ][] [ 339, 7, 1 ][ 3, 1, 121 ][ 113, 1, 1 ][] [ 339, 8, 1 ][ 3, 247, 13 ][ 113, 1, 1 ][] Total time: 53.269 seconds, Total memory usage: 6.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:10:44 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(113,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(339,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:10:34 on modular [Seed = 3210985390] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group of order 1 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/22 Defined on 1 generator Relations: 22*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group of order 1 Total time: 9.559 seconds, Total memory usage: 4.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:20:17 2003 Input: N:=340; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:18:45 on modular [Seed = 3390485700] ------------------------------------- [ 340, 1, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] [ 340, 2, 1 ][ 5, 1, 1 ][ 17, 1, 1 ][] Total time: 91.529 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:22:15 2003 Input: N:=341; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:21:21 on modular [Seed = 3741557109] ------------------------------------- [ 341, 1, 1 ][ 11, 1, 1 ][ 31, 1, 1 ][] [ 341, 2, 1 ][ 11, 1, 1 ][ 31, 1, 1 ][] [ 341, 3, 1 ][ 11, 1, 147 ][ 31, 3, 1 ][] [ 341, 4, 1 ][ 11, 1, 1 ][ 31, 1, 39 ][] Total time: 53.750 seconds, Total memory usage: 5.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:23:07 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(341,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:23:01 on modular [Seed = 3591023576] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 3 Abelian Group isomorphic to Z/7 + Z/7 Defined on 2 generators Relations: 7*$.1 = 0 7*$.2 = 0 4 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 6.209 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:27:12 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(11,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(341,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:27:06 on modular [Seed = 3762068753] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/39 Defined on 1 generator Relations: 39*$.1 = 0 Total time: 6.129 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:29:49 2003 Input: N:=342; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:29:13 on modular [Seed = 4229988494] ------------------------------------- [ 342, 1, 1 ][ 2, 1, 1 ][] [ 342, 2, 1 ][ 2, 1, 5 ][] [ 342, 3, 1 ][ 2, 1, 5 ][] [ 342, 4, 1 ][ 2, 1, 3 ][] [ 342, 5, 1 ][ 2, 1, 1 ][] [ 342, 6, 1 ][ 2, 3, 3 ][] [ 342, 7, 1 ][ 2, 1, 1 ][] Total time: 35.950 seconds, Total memory usage: 10.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:31:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(171,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(342,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:30:50 on modular [Seed = 332361667] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 11.109 seconds, Total memory usage: 4.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:34:40 2003 Input: N:=345; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 13:32:58 on modular [Seed = 737628283] ------------------------------------- [ 345, 1, 1 ][ 3, 1, 1 ][ 5, 1, 5 ][ 23, 1, 1 ][] [ 345, 2, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 23, 1, 3 ][] [ 345, 3, 1 ][ 3, 5, 5 ][ 5, 1, 3 ][ 23, 1, 1 ][] [ 345, 4, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 23, 1, 1 ][] [ 345, 5, 1 ][ 3, 1, 1 ][ 5, 1, 1 ][ 23, 1, 1 ][] [ 345, 6, 1 ][ 3, 1, 1 ][ 5, 3, 3 ][ 23, 1, 1 ][] [ 345, 7, 1 ][ 3, 1, 9 ][ 5, 1, 1 ][ 23, 1, 1 ][] [ 345, 8, 1 ][ 3, 1, 1 ][ 5, 11, 11 ][ 23, 3, 3 ][] [ 345, 9, 1 ][ 3, 15, 5 ][ 5, 1, 1 ][ 23, 1, 1 ][] [ 345, 10, 1 ][ 3, 11, 1 ][ 5, 11, 1 ][ 23, 1, 1 ][] Total time: 101.350 seconds, Total memory usage: 7.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:36:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(115,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(345,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:36:10 on modular [Seed = 620256820] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 + Z/3 Defined on 2 generators Relations: 3*$.1 = 0 3*$.2 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 10 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 10.309 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:37:25 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(69,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(345,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:37:15 on modular [Seed = 1021331053] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 9 Abelian Group of order 1 Abelian Group of order 1 10 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 8.929 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 13:38:22 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(15,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(345,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 13:38:13 on modular [Seed = 887639723] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 5 Abelian Group of order 1 6 Abelian Group of order 1 7 Abelian Group of order 1 8 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 9 Abelian Group of order 1 10 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 8.439 seconds, Total memory usage: 4.65MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:04:06 2003 Input: N:=346; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:03:19 on modular [Seed = 1974010120] ------------------------------------- [ 346, 1, 1 ][ 2, 1, 1 ][ 173, 1, 1 ][] [ 346, 2, 1 ][ 2, 7, 7 ][ 173, 1, 1 ][] [ 346, 3, 1 ][ 2, 1, 469 ][ 173, 1, 1 ][] [ 346, 4, 1 ][ 2, 1, 31 ][ 173, 1, 1 ][] [ 346, 5, 1 ][ 2, 2291, 79 ][ 173, 1, 1 ][] Total time: 47.409 seconds, Total memory usage: 7.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:05:03 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(173,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(346,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:04:57 on modular [Seed = 2204104528] ------------------------------------- >> uspidalSubspace(ModularSymbols(173,+1))))); ^ Runtime error in 'ModularSymbols': Argument 2 (1) should be >= 2 >> for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; ^ User error: Identifier 'A' has not been declared or assigned Total time: 5.939 seconds, Total memory usage: 3.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:05:21 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(173,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(346,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:05:12 on modular [Seed = 2672028541] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/469 Defined on 1 generator Relations: 469*$.1 = 0 4 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 5 Abelian Group isomorphic to Z/79 Defined on 1 generator Relations: 79*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 Total time: 8.859 seconds, Total memory usage: 4.67MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:06:08 2003 Input: N:=347 q:=2 n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:06:05 on modular [Seed = 2538333312] ------------------------------------- >> N:=347 q:=2 ^ User error: bad syntax >> n:=Factorization(N); ^ User error: Identifier 'N' has not been declared or assigned >> uspidalSubspace(ModularSymbols(N,2,+1))))); ^ User error: Identifier 'N' has not been declared or assigned >> for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; ^ User error: Identifier 'A' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:06:23 2003 Input: N:=347; q:=2 n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:06:19 on modular [Seed = 2943605902] ------------------------------------- >> n:=Factorization(N); ^ User error: bad syntax >> for j in [1..#n] do ^ User error: Identifier 'n' has not been declared or assigned Total time: 3.559 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:07:32 2003 Input: N:=347; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:07:28 on modular [Seed = 2809910493] ------------------------------------- [ 347, 1, 1 ][] [ 347, 2, 1 ][ 347, 1, 1 ][] [ 347, 3, 1 ][ 347, 1, 1 ][] [ 347, 4, 1 ][ 347, 173, 1 ][] Total time: 4.029 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:11:29 2003 Input: N:=348; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:08:45 on modular [Seed = 3210988552] ------------------------------------- [ 348, 1, 1 ][ 3, 1, 15 ][ 29, 1, 1 ][] [ 348, 2, 1 ][ 3, 1, 1 ][ 29, 1, 1 ][] [ 348, 3, 1 ][ 3, 7, 7 ][ 29, 1, 1 ][] [ 348, 4, 1 ][ 3, 1, 1 ][ 29, 1, 1 ][] Total time: 162.470 seconds, Total memory usage: 10.76MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:13:34 2003 Input: N:=348; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:10:49 on modular [Seed = 3373644794] ------------------------------------- [ 348, 1, 1 ][ 3, 1, 15 ][ 29, 1, 1 ][] [ 348, 2, 1 ][ 3, 1, 1 ][ 29, 1, 1 ][] [ 348, 3, 1 ][ 3, 7, 7 ][ 29, 1, 1 ][] [ 348, 4, 1 ][ 3, 1, 1 ][ 29, 1, 1 ][] Total time: 162.909 seconds, Total memory usage: 10.76MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:14:44 2003 Input: N:=349; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:14:40 on modular [Seed = 3641026803] ------------------------------------- [ 349, 1, 1 ][] [ 349, 2, 1 ][ 349, 29, 1 ][] Total time: 3.999 seconds, Total memory usage: 4.57MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:17:24 2003 Input: N:=350; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:17:01 on modular [Seed = 3574178930] ------------------------------------- [ 350, 1, 1 ][ 2, 1, 3 ][] [ 350, 2, 1 ][ 2, 1, 1 ][] [ 350, 3, 1 ][ 2, 1, 11 ][] [ 350, 4, 1 ][ 2, 1, 1 ][] [ 350, 5, 1 ][ 2, 11, 11 ][] [ 350, 6, 1 ][ 2, 3, 1 ][] [ 350, 7, 1 ][ 2, 1, 5 ][] [ 350, 8, 1 ][ 2, 5, 1 ][] Total time: 21.430 seconds, Total memory usage: 10.68MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 14:21:24 2003 Input: N:=351; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:20:51 on modular [Seed = 4163143777] ------------------------------------- [ 351, 1, 1 ][ 13, 1, 1 ][] [ 351, 2, 1 ][ 13, 3, 1 ][] [ 351, 3, 1 ][ 13, 1, 1 ][] [ 351, 4, 1 ][ 13, 1, 1 ][] [ 351, 5, 1 ][ 13, 3, 1 ][] [ 351, 6, 1 ][ 13, 1, 19 ][] Total time: 33.149 seconds, Total memory usage: 6.87MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:22:32 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(175,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(350,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:22:20 on modular [Seed = 4029448214] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Total time: 12.209 seconds, Total memory usage: 4.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:26:53 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(27,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(351,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:26:46 on modular [Seed = 248668657] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Total time: 7.079 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:29:23 2003 Input: N:=352; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:28:44 on modular [Seed = 114976867] ------------------------------------- [ 352, 1, 1 ][ 11, 1, 1 ][] [ 352, 2, 1 ][ 11, 1, 1 ][] [ 352, 3, 1 ][ 11, 1, 1 ][] [ 352, 4, 1 ][ 11, 1, 3 ][] [ 352, 5, 1 ][ 11, 1, 1 ][] [ 352, 6, 1 ][ 11, 3, 3 ][] [ 352, 7, 1 ][ 11, 1, 1 ][] [ 352, 8, 1 ][ 11, 1, 1 ][] Total time: 37.849 seconds, Total memory usage: 7.97MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:30:16 2003 Input: N:=353; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:30:12 on modular [Seed = 382367963] ------------------------------------- [ 353, 1, 1 ][] [ 353, 2, 1 ][ 353, 1, 1 ][] [ 353, 3, 1 ][ 353, 1, 1 ][] [ 353, 4, 1 ][ 353, 11, 1 ][] Total time: 4.159 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:34:14 2003 Input: N:=354; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:30:56 on modular [Seed = 787628247] ------------------------------------- [ 354, 1, 1 ][ 2, 1, 5 ][ 3, 1, 3 ][ 59, 1, 1 ][] [ 354, 2, 1 ][ 2, 1, 1 ][ 3, 1, 3 ][ 59, 1, 1 ][] [ 354, 3, 1 ][ 2, 1, 1 ][ 3, 3, 1 ][ 59, 1, 1 ][] [ 354, 4, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 59, 1, 1 ][] [ 354, 5, 1 ][ 2, 11, 11 ][ 3, 1, 9 ][ 59, 1, 1 ][] [ 354, 6, 1 ][ 2, 7, 7 ][ 3, 1, 1 ][ 59, 1, 1 ][] [ 354, 7, 1 ][ 2, 1, 11 ][ 3, 5, 5 ][ 59, 1, 1 ][] [ 354, 8, 1 ][ 2, 551, 19 ][ 3, 29, 1 ][ 59, 1, 1 ][] Total time: 197.050 seconds, Total memory usage: 10.63MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:35:37 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(177,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(354,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:35:24 on modular [Seed = 1038176456] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 12.159 seconds, Total memory usage: 5.00MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:36:32 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(118,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(354,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:36:21 on modular [Seed = 904485129] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 11.179 seconds, Total memory usage: 4.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:38:24 2003 Input: N:=355; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:37:35 on modular [Seed = 1301356859] ------------------------------------- [ 355, 1, 1 ][ 5, 3, 1 ][ 71, 1, 1 ][] [ 355, 2, 1 ][ 5, 1, 1 ][ 71, 1, 1 ][] [ 355, 3, 1 ][ 5, 427, 61 ][ 71, 1, 1 ][] [ 355, 4, 1 ][ 5, 1, 1 ][ 71, 1, 1 ][] [ 355, 5, 1 ][ 5, 1, 36977 ][ 71, 1, 1 ][] Total time: 48.480 seconds, Total memory usage: 5.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:41:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(71,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(355,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:40:53 on modular [Seed = 1368209949] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/61 Defined on 1 generator Relations: 61*$.1 = 0 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group isomorphic to Z/103 Defined on 1 generator Relations: 103*$.1 = 0 Abelian Group isomorphic to Z/359 Defined on 1 generator Relations: 359*$.1 = 0 Total time: 7.819 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:45:12 2003 Input: N:=357; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:43:20 on modular [Seed = 1773470392] ------------------------------------- [ 357, 1, 1 ][ 3, 1, 17 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 357, 2, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 357, 3, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][ 17, 1, 3 ][] [ 357, 4, 1 ][ 3, 7, 7 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 357, 5, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 357, 6, 1 ][ 3, 47, 47 ][ 7, 1, 1 ][ 17, 3, 3 ][] [ 357, 7, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][ 17, 1, 1 ][] [ 357, 8, 1 ][ 3, 1, 223 ][ 7, 1, 1 ][ 17, 1, 1 ][] Total time: 111.360 seconds, Total memory usage: 7.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:46:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(119,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(357,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:46:29 on modular [Seed = 2024018660] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/47 Defined on 1 generator Relations: 47*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 8 Abelian Group isomorphic to Z/223 Defined on 1 generator Relations: 223*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 9.460 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:47:28 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(51,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(357,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:47:19 on modular [Seed = 1890327230] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Total time: 8.729 seconds, Total memory usage: 4.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:48:09 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(21,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(357,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:48:01 on modular [Seed = 2287264368] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group of order 1 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 4 Abelian Group of order 1 5 Abelian Group of order 1 6 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 7 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 8 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 8.179 seconds, Total memory usage: 4.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:49:44 2003 Input: N:=358; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:48:53 on modular [Seed = 2153572780] ------------------------------------- [ 358, 1, 1 ][ 2, 1, 17 ][ 179, 1, 1 ][] [ 358, 2, 1 ][ 2, 3, 1 ][ 179, 1, 1 ][] [ 358, 3, 1 ][ 2, 1, 85 ][ 179, 1, 1 ][] [ 358, 4, 1 ][ 2, 29, 29 ][ 179, 1, 1 ][] [ 358, 5, 1 ][ 2, 5, 1 ][ 179, 1, 1 ][] [ 358, 6, 1 ][ 2, 79, 79 ][ 179, 1, 1 ][] [ 358, 7, 1 ][ 2, 1, 13 ][ 179, 1, 1 ][] Total time: 50.970 seconds, Total memory usage: 7.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:50:29 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(179,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(358,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:50:19 on modular [Seed = 2454649824] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/79 Defined on 1 generator Relations: 79*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 10.119 seconds, Total memory usage: 4.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:51:24 2003 Input: N:=359; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:51:20 on modular [Seed = 2859909915] ------------------------------------- [ 359, 1, 1 ][] [ 359, 2, 1 ][ 359, 1, 1 ][] [ 359, 3, 1 ][ 359, 1, 1 ][] [ 359, 4, 1 ][ 359, 179, 1 ][] Total time: 4.129 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:54:13 2003 Input: N:=362; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:53:13 on modular [Seed = 2726218370] ------------------------------------- [ 362, 1, 1 ][ 2, 1, 1 ][ 181, 1, 1 ][] [ 362, 2, 1 ][ 2, 7, 7 ][ 181, 1, 1 ][] [ 362, 3, 1 ][ 2, 1, 29 ][ 181, 1, 1 ][] [ 362, 4, 1 ][ 2, 161, 23 ][ 181, 1, 1 ][] [ 362, 5, 1 ][ 2, 1, 7173 ][ 181, 3, 1 ][] [ 362, 6, 1 ][ 2, 221, 17 ][ 181, 1, 1 ][] Total time: 59.779 seconds, Total memory usage: 7.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:55:02 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(181,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(362,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:54:53 on modular [Seed = 3177305401] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 3 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 4 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2391 Defined on 1 generator Relations: 2391*$.1 = 0 6 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 9.209 seconds, Total memory usage: 4.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:57:05 2003 Input: N:=363; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:56:46 on modular [Seed = 3373637950] ------------------------------------- [ 363, 1, 1 ][ 3, 1, 3 ][] [ 363, 2, 1 ][ 3, 1, 3 ][] [ 363, 3, 1 ][ 3, 1, 3 ][] [ 363, 4, 1 ][ 3, 1, 3 ][] [ 363, 5, 1 ][ 3, 1, 1 ][] [ 363, 6, 1 ][ 3, 1, 1 ][] [ 363, 7, 1 ][ 3, 5, 5 ][] [ 363, 8, 1 ][ 3, 5, 1 ][] [ 363, 9, 1 ][ 3, 5, 5 ][] [ 363, 10, 1 ][ 3, 11, 1 ][] Total time: 18.899 seconds, Total memory usage: 7.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 14:58:17 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(121,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(363,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 14:58:07 on modular [Seed = 3239945863] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 9 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 10 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Total time: 9.579 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:01:03 2003 Input: N:=364; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 14:59:22 on modular [Seed = 3624189771] ------------------------------------- [ 364, 1, 1 ][ 7, 1, 1 ][ 13, 1, 1 ][] [ 364, 2, 1 ][ 7, 5, 5 ][ 13, 1, 1 ][] [ 364, 3, 1 ][ 7, 1, 3 ][ 13, 1, 1 ][] [ 364, 4, 1 ][ 7, 1, 1 ][ 13, 1, 1 ][] Total time: 100.289 seconds, Total memory usage: 9.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:15:00 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(52,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(364,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:14:51 on modular [Seed = 2709373586] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 4 Abelian Group of order 1 Total time: 9.049 seconds, Total memory usage: 4.63MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:16:37 2003 Input: N:=365; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:15:38 on modular [Seed = 3177307871] ------------------------------------- [ 365, 1, 1 ][ 5, 11, 11 ][ 73, 1, 1 ][] [ 365, 2, 1 ][ 5, 13, 13 ][ 73, 1, 1 ][] [ 365, 3, 1 ][ 5, 1, 19 ][ 73, 1, 1 ][] [ 365, 4, 1 ][ 5, 185, 5 ][ 73, 1, 1 ][] [ 365, 5, 1 ][ 5, 1, 81 ][ 73, 3, 1 ][] Total time: 59.000 seconds, Total memory usage: 5.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:17:17 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(73,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(365,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:17:08 on modular [Seed = 3407325191] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/27 Defined on 1 generator Relations: 27*$.1 = 0 Total time: 8.219 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:21:44 2003 Input: N:=366; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:18:03 on modular [Seed = 3273629744] ------------------------------------- [ 366, 1, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 61, 1, 1 ][] [ 366, 2, 1 ][ 2, 1, 19 ][ 3, 3, 3 ][ 61, 1, 1 ][] [ 366, 3, 1 ][ 2, 1, 1 ][ 3, 3, 1 ][ 61, 1, 1 ][] [ 366, 4, 1 ][ 2, 7, 7 ][ 3, 1, 13 ][ 61, 1, 1 ][] [ 366, 5, 1 ][ 2, 5, 5 ][ 3, 1, 1 ][ 61, 1, 1 ][] [ 366, 6, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 61, 1, 1 ][] [ 366, 7, 1 ][ 2, 5, 1 ][ 3, 5, 1 ][ 61, 1, 1 ][] [ 366, 8, 1 ][ 2, 1, 13 ][ 3, 1, 17 ][ 61, 1, 1 ][] Total time: 219.099 seconds, Total memory usage: 11.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:22:46 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(183,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(366,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:22:34 on modular [Seed = 31285260] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 11.500 seconds, Total memory usage: 4.93MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:23:47 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(122,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(366,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:23:36 on modular [Seed = 670778984] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.949 seconds, Total memory usage: 4.78MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:25:14 2003 Input: N:=367; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:25:10 on modular [Seed = 1284517357] ------------------------------------- [ 367, 1, 1 ][] [ 367, 2, 1 ][ 367, 61, 1 ][] Total time: 4.129 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:28:24 2003 Input: N:=370; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:26:24 on modular [Seed = 1418212771] ------------------------------------- [ 370, 1, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 37, 1, 1 ][] [ 370, 2, 1 ][ 2, 1, 3 ][ 5, 1, 3 ][ 37, 3, 1 ][] [ 370, 3, 1 ][ 2, 1, 11 ][ 5, 1, 1 ][ 37, 1, 1 ][] [ 370, 4, 1 ][ 2, 3, 1 ][ 5, 3, 1 ][ 37, 1, 1 ][] [ 370, 5, 1 ][ 2, 1, 3 ][ 5, 13, 13 ][ 37, 1, 1 ][] [ 370, 6, 1 ][ 2, 3, 3 ][ 5, 1, 1 ][ 37, 1, 1 ][] [ 370, 7, 1 ][ 2, 5, 5 ][ 5, 1, 31 ][ 37, 1, 1 ][] Total time: 119.659 seconds, Total memory usage: 9.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:29:38 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(185,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(370,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:29:27 on modular [Seed = 1535589371] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 6 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 11.689 seconds, Total memory usage: 4.88MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:31:38 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(74,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(370,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:31:28 on modular [Seed = 1823486795] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 5 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 Total time: 9.689 seconds, Total memory usage: 4.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:34:13 2003 Input: N:=371; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:33:09 on modular [Seed = 1957178358] ------------------------------------- [ 371, 1, 1 ][ 7, 1, 1 ][ 53, 1, 1 ][] [ 371, 2, 1 ][ 7, 3, 3 ][ 53, 1, 1 ][] [ 371, 3, 1 ][ 7, 5, 5 ][ 53, 1, 1 ][] [ 371, 4, 1 ][ 7, 1, 1 ][ 53, 1, 1 ][] [ 371, 5, 1 ][ 7, 1, 191 ][ 53, 1, 1 ][] [ 371, 6, 1 ][ 7, 27, 9 ][ 53, 1, 3 ][] Total time: 63.659 seconds, Total memory usage: 5.86MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:35:31 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(53,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(371,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:35:23 on modular [Seed = 2270943627] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/191 Defined on 1 generator Relations: 191*$.1 = 0 6 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 7.339 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:40:09 2003 Input: N:=372; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:36:59 on modular [Seed = 2404635107] ------------------------------------- [ 372, 1, 1 ][ 3, 1, 1 ][ 31, 1, 1 ][] [ 372, 2, 1 ][ 3, 1, 1 ][ 31, 1, 1 ][] [ 372, 3, 1 ][ 3, 1, 1 ][ 31, 1, 1 ][] [ 372, 4, 1 ][ 3, 9, 3 ][ 31, 1, 1 ][] [ 372, 5, 1 ][ 3, 1, 1 ][ 31, 1, 1 ][] Total time: 188.459 seconds, Total memory usage: 11.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:41:14 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(124,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(372,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 15:41:03 on modular [Seed = 2672018119] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 11.279 seconds, Total memory usage: 4.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:42:28 2003 Input: N:=373; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:42:24 on modular [Seed = 2809920016] ------------------------------------- [ 373, 1, 1 ][] [ 373, 2, 1 ][ 373, 1, 1 ][] [ 373, 3, 1 ][ 373, 31, 1 ][] Total time: 4.119 seconds, Total memory usage: 4.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 15:44:58 2003 Input: N:=374; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 15:42:59 on modular [Seed = 2943611515] ------------------------------------- [ 374, 1, 1 ][ 2, 1, 5 ][ 11, 1, 1 ][ 17, 1, 1 ][] [ 374, 2, 1 ][ 2, 1, 125 ][ 11, 1, 1 ][ 17, 3, 1 ][] [ 374, 3, 1 ][ 2, 111, 37 ][ 11, 1, 9 ][ 17, 1, 1 ][] [ 374, 4, 1 ][ 2, 1, 75 ][ 11, 3, 1 ][ 17, 1, 1 ][] [ 374, 5, 1 ][ 2, 65, 13 ][ 11, 1, 1 ][ 17, 5, 1 ][] Total time: 118.600 seconds, Total memory usage: 9.11MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:33:52 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(187,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(374,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 16:33:41 on modular [Seed = 954493323] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/25 Defined on 1 generator Relations: 25*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/37 Defined on 1 generator Relations: 37*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/5 + Z/5 Defined on 2 generators Relations: 5*$.1 = 0 5*$.2 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Total time: 11.079 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:36:15 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(34,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(374,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 16:36:06 on modular [Seed = 1301355789] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 4 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 8.090 seconds, Total memory usage: 4.66MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:38:15 2003 Input: N:=375; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 16:37:52 on modular [Seed = 1435043299] ------------------------------------- [ 375, 1, 1 ][ 3, 1, 1 ][] [ 375, 2, 1 ][ 3, 1, 31 ][] [ 375, 3, 1 ][ 3, 5, 1 ][] [ 375, 4, 1 ][ 3, 31, 31 ][] [ 375, 5, 1 ][ 3, 1, 29 ][] [ 375, 6, 1 ][ 3, 145, 29 ][] Total time: 23.139 seconds, Total memory usage: 8.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:38:57 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(125,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(375,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 16:38:47 on modular [Seed = 1568738748] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 5 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 6 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 9.300 seconds, Total memory usage: 4.59MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:41:50 2003 Input: N:=377; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 16:40:48 on modular [Seed = 1840325131] ------------------------------------- [ 377, 1, 1 ][ 13, 1, 1 ][ 29, 1, 1 ][] [ 377, 2, 1 ][ 13, 1, 1 ][ 29, 1, 1 ][] [ 377, 3, 1 ][ 13, 1, 1 ][ 29, 1, 1 ][] [ 377, 4, 1 ][ 13, 31, 31 ][ 29, 1, 1 ][] [ 377, 5, 1 ][ 13, 1, 161 ][ 29, 7, 1 ][] [ 377, 6, 1 ][ 13, 15, 1 ][ 29, 1, 3 ][] Total time: 61.690 seconds, Total memory usage: 5.71MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:42:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(29,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(377,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 16:42:32 on modular [Seed = 1974024891] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 5 Abelian Group isomorphic to Z/161 Defined on 1 generator Relations: 161*$.1 = 0 6 Abelian Group of order 1 Total time: 6.719 seconds, Total memory usage: 4.35MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:46:39 2003 Input: N:=378; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for z in [1..2] do for j in [1..(2*z-1)] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 16:45:55 on modular [Seed = 2237254416] ------------------------------------- Do not know how to compute component group at 3 Total time: 43.389 seconds, Total memory usage: 13.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:50:01 2003 Input: N:=378; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for z in [1..2] do j:=(2*z-1); cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 16:47:32 on modular [Seed = 2370945919] ------------------------------------- [ 378, 1, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][] [ 378, 2, 1 ][ 2, 1, 3 ][ 7, 3, 1 ][] [ 378, 3, 1 ][ 2, 1, 5 ][ 7, 1, 7 ][] [ 378, 4, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][] [ 378, 5, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][] [ 378, 6, 1 ][ 2, 5, 5 ][ 7, 1, 7 ][] [ 378, 7, 1 ][ 2, 9, 3 ][ 7, 1, 1 ][] [ 378, 8, 1 ][ 2, 3, 1 ][ 7, 3, 1 ][] Total time: 146.639 seconds, Total memory usage: 13.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:51:05 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(189,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(378,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 16:50:51 on modular [Seed = 2776229912] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 8 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 13.349 seconds, Total memory usage: 5.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:53:53 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(54,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(378,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 16:53:42 on modular [Seed = 2909921741] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 7 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 8 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 11.000 seconds, Total memory usage: 4.90MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:55:55 2003 Input: N:=379; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 16:55:51 on modular [Seed = 3194155615] ------------------------------------- [ 379, 1, 1 ][] [ 379, 2, 1 ][ 379, 63, 3 ][] Total time: 4.139 seconds, Total memory usage: 4.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 16:58:32 2003 Input: N:=380; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 16:56:46 on modular [Seed = 3323629022] ------------------------------------- [ 380, 1, 1 ][ 5, 1, 5 ][ 19, 1, 1 ][] [ 380, 2, 1 ][ 5, 1, 1 ][ 19, 1, 1 ][] [ 380, 3, 1 ][ 5, 7, 7 ][ 19, 1, 1 ][] [ 380, 4, 1 ][ 5, 3, 1 ][ 19, 1, 1 ][] Total time: 104.770 seconds, Total memory usage: 10.79MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:01:08 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(76,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(380,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:00:59 on modular [Seed = 3591019723] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 4 Abelian Group of order 1 Total time: 9.569 seconds, Total memory usage: 4.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:02:40 2003 Input: N:=381; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:01:42 on modular [Seed = 3946291627] ------------------------------------- [ 381, 1, 1 ][ 3, 1, 1 ][ 127, 1, 1 ][] [ 381, 2, 1 ][ 3, 5, 5 ][ 127, 1, 1 ][] [ 381, 3, 1 ][ 3, 1, 19 ][ 127, 1, 1 ][] [ 381, 4, 1 ][ 3, 1, 647 ][ 127, 1, 1 ][] [ 381, 5, 1 ][ 3, 109, 109 ][ 127, 1, 1 ][] Total time: 57.680 seconds, Total memory usage: 6.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:03:22 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(127,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(381,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:03:13 on modular [Seed = 4079991124] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/647 Defined on 1 generator Relations: 647*$.1 = 0 5 Abelian Group isomorphic to Z/109 Defined on 1 generator Relations: 109*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 Total time: 8.519 seconds, Total memory usage: 4.38MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:05:06 2003 Input: N:=382; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:04:09 on modular [Seed = 4213682468] ------------------------------------- [ 382, 1, 1 ][ 2, 1, 5 ][ 191, 1, 1 ][] [ 382, 2, 1 ][ 2, 967, 967 ][ 191, 1, 1 ][] [ 382, 3, 1 ][ 2, 11, 11 ][ 191, 1, 1 ][] [ 382, 4, 1 ][ 2, 1, 69047 ][ 191, 1, 1 ][] Total time: 56.349 seconds, Total memory usage: 7.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:05:53 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(191,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(382,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:05:44 on modular [Seed = 265504306] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/967 Defined on 1 generator Relations: 967*$.1 = 0 3 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/69047 Defined on 1 generator Relations: 69047*$.1 = 0 Total time: 9.259 seconds, Total memory usage: 4.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:06:58 2003 Input: N:=383; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:06:54 on modular [Seed = 399203948] ------------------------------------- [ 383, 1, 1 ][] [ 383, 2, 1 ][ 383, 1, 1 ][] [ 383, 3, 1 ][ 383, 191, 1 ][] Total time: 4.119 seconds, Total memory usage: 4.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:08:52 2003 Input: N:=384; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:08:03 on modular [Seed = 532895449] ------------------------------------- [ 384, 1, 1 ][ 3, 1, 1 ][] [ 384, 2, 1 ][ 3, 1, 1 ][] [ 384, 3, 1 ][ 3, 1, 1 ][] [ 384, 4, 1 ][ 3, 3, 3 ][] [ 384, 5, 1 ][ 3, 1, 1 ][] [ 384, 6, 1 ][ 3, 1, 3 ][] [ 384, 7, 1 ][ 3, 1, 3 ][] [ 384, 8, 1 ][ 3, 3, 3 ][] Total time: 48.040 seconds, Total memory usage: 11.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:09:49 2003 Input: N:=384; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:09:01 on modular [Seed = 670789343] ------------------------------------- [ 384, 1, 1 ][ 3, 1, 1 ][] [ 384, 2, 1 ][ 3, 1, 1 ][] [ 384, 3, 1 ][ 3, 1, 1 ][] [ 384, 4, 1 ][ 3, 3, 3 ][] [ 384, 5, 1 ][ 3, 1, 1 ][] [ 384, 6, 1 ][ 3, 1, 3 ][] [ 384, 7, 1 ][ 3, 1, 3 ][] [ 384, 8, 1 ][ 3, 3, 3 ][] Total time: 47.650 seconds, Total memory usage: 11.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:13:00 2003 Input: N:=385; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:11:08 on modular [Seed = 938180430] ------------------------------------- [ 385, 1, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][ 11, 1, 1 ][] [ 385, 2, 1 ][ 5, 1, 1 ][ 7, 1, 1 ][ 11, 1, 1 ][] [ 385, 3, 1 ][ 5, 1, 1 ][ 7, 1, 9 ][ 11, 1, 1 ][] [ 385, 4, 1 ][ 5, 1, 1 ][ 7, 3, 1 ][ 11, 1, 1 ][] [ 385, 5, 1 ][ 5, 1, 5 ][ 7, 1, 1 ][ 11, 1, 1 ][] [ 385, 6, 1 ][ 5, 1, 1 ][ 7, 25, 25 ][ 11, 5, 5 ][] [ 385, 7, 1 ][ 5, 5, 1 ][ 7, 5, 1 ][ 11, 1, 1 ][] [ 385, 8, 1 ][ 5, 7, 7 ][ 7, 1, 1 ][ 11, 1, 19 ][] Total time: 110.379 seconds, Total memory usage: 7.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:15:53 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(77,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(385,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:15:43 on modular [Seed = 988183984] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 5 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 6 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 8 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 Total time: 9.880 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:17:04 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(55,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(385,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:16:55 on modular [Seed = 1117652368] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 + Z/6 Defined on 2 generators Relations: 3*$.1 = 0 6*$.2 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 + Z/10 Defined on 2 generators Relations: 5*$.1 = 0 10*$.2 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 8.759 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:18:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(35,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(385,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:17:52 on modular [Seed = 1251347551] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group of order 1 Abelian Group isomorphic to Z/38 Defined on 1 generator Relations: 38*$.1 = 0 Total time: 8.689 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:20:01 2003 Input: N:=386; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:18:53 on modular [Seed = 1385042970] ------------------------------------- [ 386, 1, 1 ][ 2, 1, 29 ][ 193, 1, 1 ][] [ 386, 2, 1 ][ 2, 31, 31 ][ 193, 1, 1 ][] [ 386, 3, 1 ][ 2, 1, 4065 ][ 193, 3, 1 ][] [ 386, 4, 1 ][ 2, 422047, 4351 ][ 193, 1, 1 ][] Total time: 67.299 seconds, Total memory usage: 7.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:23:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(193,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(386,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:23:10 on modular [Seed = 1656629033] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/1355 Defined on 1 generator Relations: 1355*$.1 = 0 4 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/229 Defined on 1 generator Relations: 229*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.049 seconds, Total memory usage: 4.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:25:24 2003 Input: N:=389; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:25:20 on modular [Seed = 1907176612] ------------------------------------- [ 389, 1, 1 ][] [ 389, 2, 1 ][ 389, 1, 1 ][] [ 389, 3, 1 ][ 389, 1, 1 ][] [ 389, 4, 1 ][ 389, 1, 1 ][] [ 389, 5, 1 ][ 389, 97, 1 ][] Total time: 4.299 seconds, Total memory usage: 5.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:27:23 2003 Input: N:=391; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:26:28 on modular [Seed = 2040872296] ------------------------------------- [ 391, 1, 1 ][ 17, 1, 1 ][ 23, 1, 1 ][] [ 391, 2, 1 ][ 17, 1, 1 ][ 23, 1, 1 ][] [ 391, 3, 1 ][ 17, 5, 1 ][ 23, 5, 1 ][] [ 391, 4, 1 ][ 17, 1, 109 ][ 23, 3, 1 ][] [ 391, 5, 1 ][ 17, 1, 1 ][ 23, 1, 7 ][] Total time: 54.029 seconds, Total memory usage: 5.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:28:06 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(23,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(391,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:27:59 on modular [Seed = 2170406379] ------------------------------------- 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 2 Abelian Group of order 1 3 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group isomorphic to Z/109 Defined on 1 generator Relations: 109*$.1 = 0 5 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 7.319 seconds, Total memory usage: 4.46MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:30:12 2003 Input: N:=393; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:29:11 on modular [Seed = 2304101691] ------------------------------------- [ 393, 1, 1 ][ 3, 1, 23 ][ 131, 1, 1 ][] [ 393, 2, 1 ][ 3, 1, 3 ][ 131, 1, 1 ][] [ 393, 3, 1 ][ 3, 1931, 1931 ][ 131, 1, 1 ][] [ 393, 4, 1 ][ 3, 1, 7613 ][ 131, 1, 1 ][] [ 393, 5, 1 ][ 3, 55, 5 ][ 131, 1, 1 ][] Total time: 61.029 seconds, Total memory usage: 7.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:30:57 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(131,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(393,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:30:48 on modular [Seed = 2571491972] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/1931 Defined on 1 generator Relations: 1931*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/7613 Defined on 1 generator Relations: 7613*$.1 = 0 5 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Total time: 8.819 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:32:42 2003 Input: N:=394; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:31:43 on modular [Seed = 2709381867] ------------------------------------- [ 394, 1, 1 ][ 2, 25, 25 ][ 197, 1, 1 ][] [ 394, 2, 1 ][ 2, 55, 5 ][ 197, 1, 1 ][] [ 394, 3, 1 ][ 2, 15, 1 ][ 197, 1, 1 ][] [ 394, 4, 1 ][ 2, 31, 31 ][ 197, 1, 1 ][] [ 394, 5, 1 ][ 2, 1, 109 ][ 197, 1, 1 ][] [ 394, 6, 1 ][ 2, 1, 1087 ][ 197, 1, 1 ][] Total time: 58.069 seconds, Total memory usage: 8.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:33:39 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(197,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(394,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:33:29 on modular [Seed = 2843077141] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/25 Defined on 1 generator Relations: 25*$.1 = 0 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 3 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/109 Defined on 1 generator Relations: 109*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/1087 Defined on 1 generator Relations: 1087*$.1 = 0 Total time: 10.119 seconds, Total memory usage: 4.68MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 17:37:00 2003 Input: N:=394; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:36:01 on modular [Seed = 3160473320] ------------------------------------- [ 394, 1, 1 ][ 2, 25, 25 ][ 197, 1, 1 ][] [ 394, 2, 1 ][ 2, 55, 5 ][ 197, 1, 1 ][] [ 394, 3, 1 ][ 2, 15, 5 ][ 197, 1, 1 ][] [ 394, 4, 1 ][ 2, 31, 31 ][ 197, 1, 1 ][] [ 394, 5, 1 ][ 2, 1, 109 ][ 197, 1, 1 ][] [ 394, 6, 1 ][ 2, 1, 1087 ][ 197, 1, 1 ][] Total time: 58.270 seconds, Total memory usage: 8.20MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 17:39:09 2003 Input: N:=395; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:38:00 on modular [Seed = 3289941513] ------------------------------------- [ 395, 1, 1 ][ 5, 1, 1 ][ 79, 1, 1 ][] [ 395, 2, 1 ][ 5, 3, 3 ][ 79, 1, 1 ][] [ 395, 3, 1 ][ 5, 5, 1 ][ 79, 1, 1 ][] [ 395, 4, 1 ][ 5, 1, 3 ][ 79, 1, 1 ][] [ 395, 5, 1 ][ 5, 3, 3 ][ 79, 1, 1 ][] [ 395, 6, 1 ][ 5, 97, 97 ][ 79, 1, 1 ][] [ 395, 7, 1 ][ 5, 1, 1 ][ 79, 1, 1 ][] [ 395, 8, 1 ][ 5, 1, 52197 ][ 79, 3, 1 ][] Total time: 68.199 seconds, Total memory usage: 6.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:40:05 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(79,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(395,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:39:55 on modular [Seed = 3474165489] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/97 Defined on 1 generator Relations: 97*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group of order 1 Abelian Group isomorphic to Z/17399 Defined on 1 generator Relations: 17399*$.1 = 0 Total time: 8.969 seconds, Total memory usage: 4.44MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 17:43:54 2003 Input: N:=396; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:41:44 on modular [Seed = 3691027825] ------------------------------------- [ 396, 1, 1 ][ 11, 1, 1 ][] [ 396, 2, 1 ][ 11, 1, 1 ][] [ 396, 3, 1 ][ 11, 1, 1 ][] Total time: 129.380 seconds, Total memory usage: 14.38MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 17:47:01 2003 Input: N:=397; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:46:57 on modular [Seed = 3812598535] ------------------------------------- [ 397, 1, 1 ][] [ 397, 2, 1 ][ 397, 1, 1 ][] [ 397, 3, 1 ][ 397, 11, 1 ][] [ 397, 4, 1 ][ 397, 3, 1 ][] [ 397, 5, 1 ][ 397, 1, 1 ][] Total time: 4.329 seconds, Total memory usage: 5.08MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 17:52:25 2003 Input: N:=398; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:51:16 on modular [Seed = 248689134] ------------------------------------- [ 398, 1, 1 ][ 2, 1, 5 ][ 199, 1, 1 ][] [ 398, 2, 1 ][ 2, 1, 11 ][ 199, 1, 1 ][] [ 398, 3, 1 ][ 2, 99, 99 ][ 199, 1, 1 ][] [ 398, 4, 1 ][ 2, 1, 120447 ][ 199, 3, 1 ][] [ 398, 5, 1 ][ 2, 3725, 745 ][ 199, 1, 1 ][] Total time: 67.979 seconds, Total memory usage: 8.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:53:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(199,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(398,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:53:00 on modular [Seed = 637115245] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 3 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 + Z/3 Defined on 2 generators Relations: 3*$.1 = 0 3*$.2 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 + Z/3 + Z/4461 Defined on 3 generators Relations: 3*$.1 = 0 3*$.2 = 0 4461*$.3 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/149 Defined on 1 generator Relations: 149*$.1 = 0 Abelian Group of order 1 Total time: 10.319 seconds, Total memory usage: 4.74MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 17:57:58 2003 Input: N:=399; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 17:55:49 on modular [Seed = 1217722041] ------------------------------------- [ 399, 1, 1 ][ 3, 1, 5 ][ 7, 1, 3 ][ 19, 1, 1 ][] [ 399, 2, 1 ][ 3, 1, 3 ][ 7, 1, 1 ][ 19, 1, 1 ][] [ 399, 3, 1 ][ 3, 1, 1 ][ 7, 1, 1 ][ 19, 1, 3 ][] [ 399, 4, 1 ][ 3, 1, 13 ][ 7, 1, 1 ][ 19, 1, 1 ][] [ 399, 5, 1 ][ 3, 29, 29 ][ 7, 1, 11 ][ 19, 1, 1 ][] [ 399, 6, 1 ][ 3, 1, 29 ][ 7, 13, 13 ][ 19, 1, 1 ][] [ 399, 7, 1 ][ 3, 243, 81 ][ 7, 3, 1 ][ 19, 1, 1 ][] Total time: 128.370 seconds, Total memory usage: 9.00MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 17:59:51 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(133,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(399,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 17:59:40 on modular [Seed = 2024064416] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/26 Defined on 1 generator Relations: 26*$.1 = 0 5 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/27 Defined on 1 generator Relations: 27*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.679 seconds, Total memory usage: 4.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:00:57 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(57,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(399,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:00:47 on modular [Seed = 2655134341] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 6 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Total time: 9.399 seconds, Total memory usage: 4.54MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 18:02:14 2003 Input: N:=401; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:02:10 on modular [Seed = 3194094280] ------------------------------------- [ 401, 1, 1 ][] [ 401, 2, 1 ][ 401, 25, 5 ][] Total time: 4.119 seconds, Total memory usage: 5.10MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 18:07:24 2003 Input: N:=402; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:03:22 on modular [Seed = 3323624056] ------------------------------------- [ 402, 1, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 67, 1, 1 ][] [ 402, 2, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][ 67, 1, 1 ][] [ 402, 3, 1 ][ 2, 1, 1 ][ 3, 9, 3 ][ 67, 1, 1 ][] [ 402, 4, 1 ][ 2, 1, 1 ][ 3, 1, 3 ][ 67, 1, 1 ][] [ 402, 5, 1 ][ 2, 1, 23 ][ 3, 1, 37 ][ 67, 1, 1 ][] [ 402, 6, 1 ][ 2, 5, 1 ][ 3, 1, 37 ][ 67, 1, 1 ][] [ 402, 7, 1 ][ 2, 11, 1 ][ 3, 11, 1 ][ 67, 1, 1 ][] Total time: 240.690 seconds, Total memory usage: 12.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:08:32 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(201,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(402,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:08:19 on modular [Seed = 3407310892] ------------------------------------- 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 13.500 seconds, Total memory usage: 5.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:09:37 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(134,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(402,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:09:26 on modular [Seed = 3624166138] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 5 Abelian Group isomorphic to Z/37 Defined on 1 generator Relations: 37*$.1 = 0 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/37 Defined on 1 generator Relations: 37*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 Total time: 11.629 seconds, Total memory usage: 4.99MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:11:20 2003 Input: N:=403; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:10:22 on modular [Seed = 64993630] ------------------------------------- [ 403, 1, 1 ][ 13, 1, 1 ][ 31, 1, 1 ][] [ 403, 2, 1 ][ 13, 11, 11 ][ 31, 1, 1 ][] [ 403, 3, 1 ][ 13, 1, 41 ][ 31, 7, 1 ][] [ 403, 4, 1 ][ 13, 1, 1 ][ 31, 1, 1 ][] [ 403, 5, 1 ][ 13, 1, 1 ][ 31, 1, 1 ][] Total time: 57.419 seconds, Total memory usage: 5.96MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:12:02 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(403,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:11:55 on modular [Seed = 231847861] ------------------------------------- 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 2 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 3 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 4 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 5 Abelian Group of order 1 Total time: 6.669 seconds, Total memory usage: 4.28MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:14:27 2003 Input: N:=405; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:13:51 on modular [Seed = 365538361] ------------------------------------- [ 405, 1, 1 ][ 5, 1, 1 ][] [ 405, 2, 1 ][ 5, 1, 1 ][] [ 405, 3, 1 ][ 5, 1, 1 ][] [ 405, 4, 1 ][ 5, 3, 1 ][] [ 405, 5, 1 ][ 5, 1, 1 ][] [ 405, 6, 1 ][ 5, 1, 1 ][] [ 405, 7, 1 ][ 5, 1, 11 ][] [ 405, 8, 1 ][ 5, 11, 11 ][] [ 405, 9, 1 ][ 5, 3, 1 ][] [ 405, 10, 1 ][ 5, 1, 1 ][] Total time: 34.919 seconds, Total memory usage: 9.18MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:15:29 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(81,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(405,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:15:21 on modular [Seed = 553425322] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 5 Abelian Group of order 1 6 Abelian Group of order 1 7 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 8 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 9 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 10 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 8.509 seconds, Total memory usage: 4.62MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:16:09 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(81,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(405,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:16:01 on modular [Seed = 687116698] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 5 Abelian Group of order 1 6 Abelian Group of order 1 7 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 8 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 9 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 10 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 8.439 seconds, Total memory usage: 4.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:16:30 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(81,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(405,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:16:22 on modular [Seed = 820808181] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 5 Abelian Group of order 1 6 Abelian Group of order 1 7 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 8 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 9 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 10 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Total time: 8.479 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:20:41 2003 Input: N:=406; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:18:25 on modular [Seed = 954499194] ------------------------------------- [ 406, 1, 1 ][ 2, 1, 5 ][ 7, 1, 3 ][ 29, 1, 1 ][] [ 406, 2, 1 ][ 2, 1, 1 ][ 7, 5, 5 ][ 29, 1, 1 ][] [ 406, 3, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][ 29, 3, 1 ][] [ 406, 4, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][ 29, 1, 1 ][] [ 406, 5, 1 ][ 2, 13, 13 ][ 7, 1, 3 ][ 29, 1, 1 ][] [ 406, 6, 1 ][ 2, 1, 25 ][ 7, 1, 1 ][ 29, 1, 1 ][] [ 406, 7, 1 ][ 2, 7, 1 ][ 7, 7, 1 ][ 29, 1, 1 ][] Total time: 135.279 seconds, Total memory usage: 10.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:23:06 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(203,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(406,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:22:54 on modular [Seed = 1217724165] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/16 Defined on 1 generator Relations: 16*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/5 + Z/5 Defined on 2 generators Relations: 5*$.1 = 0 5*$.2 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 7 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Total time: 12.329 seconds, Total memory usage: 4.97MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:24:41 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(58,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(406,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:24:31 on modular [Seed = 1468784891] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.899 seconds, Total memory usage: 4.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:26:50 2003 Input: N:=407; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:25:41 on modular [Seed = 1673516181] ------------------------------------- [ 407, 1, 1 ][ 11, 1, 7 ][ 37, 1, 1 ][] [ 407, 2, 1 ][ 11, 3, 1 ][ 37, 7, 7 ][] [ 407, 3, 1 ][ 11, 1, 45 ][ 37, 3, 1 ][] [ 407, 4, 1 ][ 11, 323, 17 ][ 37, 1, 41 ][] Total time: 68.579 seconds, Total memory usage: 6.16MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:27:42 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(37,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(407,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:27:34 on modular [Seed = 1807211790] ------------------------------------- 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/15 Defined on 1 generator Relations: 15*$.1 = 0 4 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group of order 1 Total time: 7.709 seconds, Total memory usage: 4.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:28:31 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(11,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(407,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 18:28:24 on modular [Seed = 1940899304] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Total time: 6.789 seconds, Total memory usage: 4.29MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:32:55 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:29:23 on modular [Seed = 2057751722] ------------------------------------- [ 408, 1, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 2, 1 ][ 3, 5, 5 ][ 17, 1, 1 ][] [ 408, 3, 1 ][ 3, 1, 3 ][ 17, 1, 5 ][] [ 408, 4, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 5, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 6, 1 ][ 3, 3, 3 ][ 17, 1, 1 ][] Total time: 210.699 seconds, Total memory usage: 14.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 18:47:00 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 18:43:26 on modular [Seed = 2521441419] ------------------------------------- [ 408, 1, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 2, 1 ][ 3, 5, 5 ][ 17, 1, 1 ][] [ 408, 3, 1 ][ 3, 1, 3 ][ 17, 1, 5 ][] [ 408, 4, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 5, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 6, 1 ][ 3, 3, 3 ][ 17, 1, 1 ][] Total time: 212.050 seconds, Total memory usage: 14.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 19:05:58 2003 Input: 1+2; Output: Magma V2.10-6 Fri Dec 19 2003 19:05:55 on modular [Seed = 3524165554] ------------------------------------- 3 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 19:19:05 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 19:15:29 on modular [Seed = 3845738055] ------------------------------------- [ 408, 1, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] Total time: 213.870 seconds, Total memory usage: 14.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 19:22:40 2003 Input: N:=409; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 19:22:35 on modular [Seed = 4196815794] ------------------------------------- [ 409, 1, 1 ][] [ 409, 2, 1 ][ 409, 17, 1 ][] Total time: 4.739 seconds, Total memory usage: 5.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 19:23:18 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 19:19:44 on modular [Seed = 3962586703] ------------------------------------- [ 408, 2, 1 ][ 3, 5, 5 ][ 17, 1, 1 ][] Total time: 212.060 seconds, Total memory usage: 14.10MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 19:25:40 2003 Input: N:=410; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 19:23:18 on modular [Seed = 81309040] ------------------------------------- [ 410, 1, 1 ][ 2, 1, 1 ][ 5, 3, 1 ][ 41, 1, 1 ][] [ 410, 2, 1 ][ 2, 1, 3 ][ 5, 1, 1 ][ 41, 1, 1 ][] [ 410, 3, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 41, 1, 1 ][] [ 410, 4, 1 ][ 2, 3, 3 ][ 5, 1, 1 ][ 41, 1, 1 ][] [ 410, 5, 1 ][ 2, 1, 5 ][ 5, 1, 1 ][ 41, 1, 1 ][] [ 410, 6, 1 ][ 2, 1, 13 ][ 5, 1, 1 ][ 41, 3, 1 ][] [ 410, 7, 1 ][ 2, 1, 1 ][ 5, 1, 1 ][ 41, 1, 1 ][] [ 410, 8, 1 ][ 2, 15, 3 ][ 5, 5, 1 ][ 41, 1, 1 ][] [ 410, 9, 1 ][ 2, 33, 11 ][ 5, 1, 7 ][ 41, 1, 1 ][] Total time: 141.379 seconds, Total memory usage: 11.48MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 19:27:32 2003 Input: N:=411; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 19:26:22 on modular [Seed = 382385722] ------------------------------------- [ 411, 1, 1 ][ 3, 1, 29 ][ 137, 1, 1 ][] [ 411, 2, 1 ][ 3, 31, 31 ][ 137, 1, 1 ][] [ 411, 3, 1 ][ 3, 71, 71 ][ 137, 1, 1 ][] [ 411, 4, 1 ][ 3, 437, 19 ][ 137, 1, 1 ][] [ 411, 5, 1 ][ 3, 1, 7753 ][ 137, 1, 1 ][] Total time: 69.119 seconds, Total memory usage: 7.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 19:47:01 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 19:43:28 on modular [Seed = 820810754] ------------------------------------- [ 408, 1, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 2, 1 ][ 3, 5, 5 ][ 17, 1, 1 ][] [ 408, 3, 1 ][ 3, 1, 3 ][ 17, 1, 5 ][] [ 408, 4, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 5, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 6, 1 ][ 3, 3, 3 ][ 17, 1, 1 ][] Total time: 212.160 seconds, Total memory usage: 14.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:04:11 2003 Input: 1+1; Output: Magma V2.10-6 Fri Dec 19 2003 20:04:08 on modular [Seed = 1790375264] ------------------------------------- 2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:07:45 2003 Input: N:=413; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:06:36 on modular [Seed = 2007754985] ------------------------------------- [ 413, 1, 1 ][ 7, 1, 19 ][ 59, 1, 1 ][] [ 413, 2, 1 ][ 7, 1, 7 ][ 59, 1, 1 ][] [ 413, 3, 1 ][ 7, 1, 1 ][ 59, 1, 1 ][] [ 413, 4, 1 ][ 7, 1, 227 ][ 59, 1, 1 ][] [ 413, 5, 1 ][ 7, 661, 661 ][ 59, 1, 1 ][] [ 413, 6, 1 ][ 7, 15, 1 ][ 59, 1, 3 ][] Total time: 69.299 seconds, Total memory usage: 6.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:14:11 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:10:24 on modular [Seed = 2270894341] ------------------------------------- [ 408, 1, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 2, 1 ][ 3, 5, 5 ][ 17, 1, 1 ][] [ 408, 3, 1 ][ 3, 1, 3 ][ 17, 1, 5 ][] Total time: 218.429 seconds, Total memory usage: 14.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:14:28 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:10:51 on modular [Seed = 2320897043] ------------------------------------- [ 408, 4, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 5, 1 ][ 3, 1, 1 ][ 17, 1, 1 ][] [ 408, 6, 1 ][ 3, 3, 3 ][ 17, 1, 1 ][] Total time: 216.449 seconds, Total memory usage: 14.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:27:51 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:26:40 on modular [Seed = 2843030523] ------------------------------------- [ 408, 1, 1 ][ 3, 1, 1 ][] [ 408, 2, 1 ][ 3, 5, 5 ][] [ 408, 3, 1 ][ 3, 1, 3 ][] Total time: 70.569 seconds, Total memory usage: 14.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:30:17 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:27:45 on modular [Seed = 2893035071] ------------------------------------- [ 408, 1, 1 ][ 17, 1, 1 ][] [ 408, 2, 1 ][ 17, 1, 1 ][] [ 408, 3, 1 ][ 17, 1, 5 ][] Total time: 150.800 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:32:22 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:31:11 on modular [Seed = 3239925916] ------------------------------------- [ 408, 4, 1 ][ 3, 1, 1 ][] [ 408, 5, 1 ][ 3, 1, 1 ][] [ 408, 6, 1 ][ 3, 3, 3 ][] Total time: 70.059 seconds, Total memory usage: 14.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:34:10 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:31:34 on modular [Seed = 3289931184] ------------------------------------- [ 408, 4, 1 ][ 17, 1, 1 ][] [ 408, 5, 1 ][ 17, 1, 1 ][] [ 408, 6, 1 ][ 17, 1, 1 ][] Total time: 153.399 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:34:20 2003 Input: N:=408; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:33:00 on modular [Seed = 3423622402] ------------------------------------- [ 408, 1, 1 ][ 3, 1, 1 ][] [ 408, 2, 1 ][ 3, 5, 5 ][] [ 408, 3, 1 ][ 3, 1, 3 ][] Total time: 75.949 seconds, Total memory usage: 14.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:34:54 2003 Input: N:=411; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:34:30 on modular [Seed = 3724691194] ------------------------------------- [ 411, 1, 1 ][ 3, 1, 29 ][] [ 411, 2, 1 ][ 3, 31, 31 ][] [ 411, 3, 1 ][ 3, 71, 71 ][] [ 411, 4, 1 ][ 3, 437, 19 ][] [ 411, 5, 1 ][ 3, 1, 7753 ][] Total time: 23.059 seconds, Total memory usage: 7.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:37:00 2003 Input: N:=411; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:36:04 on modular [Seed = 3929436780] ------------------------------------- [ 411, 1, 1 ][ 137, 1, 1 ][] [ 411, 2, 1 ][ 137, 1, 1 ][] [ 411, 3, 1 ][ 137, 1, 1 ][] [ 411, 4, 1 ][ 137, 1, 1 ][] [ 411, 5, 1 ][ 137, 1, 1 ][] Total time: 55.189 seconds, Total memory usage: 7.65MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:40:54 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(136,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(408,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 20:40:40 on modular [Seed = 4196822368] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 13.679 seconds, Total memory usage: 5.16MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:42:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(24,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(408,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 20:42:08 on modular [Seed = 31299312] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 12.059 seconds, Total memory usage: 4.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:43:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(205,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(410,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 20:42:56 on modular [Seed = 164994856] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/26 Defined on 1 generator Relations: 26*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 13.750 seconds, Total memory usage: 5.12MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:44:57 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(82,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(410,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 20:44:47 on modular [Seed = 332367261] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 Total time: 10.219 seconds, Total memory usage: 4.75MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:45:43 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(137,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(411,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 20:45:33 on modular [Seed = 532908451] ------------------------------------- 1 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group of order 1 2 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/71 Defined on 1 generator Relations: 71*$.1 = 0 4 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/15506 Defined on 1 generator Relations: 15506*$.1 = 0 Total time: 9.029 seconds, Total memory usage: 4.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:47:24 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(59,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(413,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 20:47:16 on modular [Seed = 670806530] ------------------------------------- 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 2 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/227 Defined on 1 generator Relations: 227*$.1 = 0 5 Abelian Group isomorphic to Z/661 Defined on 1 generator Relations: 661*$.1 = 0 6 Abelian Group of order 1 Total time: 7.529 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:51:06 2003 Input: N:=414; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for z in [1..2] do j:=(2*z-1); cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:48:08 on modular [Seed = 804502134] ------------------------------------- [ 414, 1, 1 ][ 2, 1, 1 ][ 23, 1, 1 ][] [ 414, 2, 1 ][ 2, 5, 5 ][ 23, 1, 1 ][] [ 414, 3, 1 ][ 2, 1, 1 ][ 23, 1, 1 ][] [ 414, 4, 1 ][ 2, 1, 1 ][ 23, 1, 1 ][] [ 414, 5, 1 ][ 2, 1, 7 ][ 23, 3, 1 ][] [ 414, 6, 1 ][ 2, 1, 11 ][ 23, 1, 1 ][] [ 414, 7, 1 ][ 2, 21, 7 ][ 23, 1, 1 ][] Total time: 176.659 seconds, Total memory usage: 13.87MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:54:07 2003 Input: N:=414; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:53:22 on modular [Seed = 1100862930] ------------------------------------- [ 414, 1, 1 ][ 2, 1, 1 ][] [ 414, 2, 1 ][ 2, 5, 5 ][] [ 414, 3, 1 ][ 2, 1, 1 ][] [ 414, 4, 1 ][ 2, 1, 1 ][] [ 414, 5, 1 ][ 2, 1, 7 ][] [ 414, 6, 1 ][ 2, 1, 11 ][] [ 414, 7, 1 ][ 2, 21, 7 ][] Total time: 44.049 seconds, Total memory usage: 13.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:55:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(207,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(414,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 20:54:55 on modular [Seed = 1301404067] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 3 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 6 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Total time: 14.289 seconds, Total memory usage: 5.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 20:57:04 2003 Input: N:=414; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:54:42 on modular [Seed = 1217715371] ------------------------------------- [ 414, 1, 1 ][ 23, 1, 1 ][] [ 414, 2, 1 ][ 23, 1, 1 ][] [ 414, 3, 1 ][ 23, 1, 1 ][] [ 414, 4, 1 ][ 23, 1, 1 ][] [ 414, 5, 1 ][ 23, 3, 1 ][] [ 414, 6, 1 ][ 23, 1, 1 ][] [ 414, 7, 1 ][ 23, 1, 1 ][] Total time: 140.089 seconds, Total memory usage: 14.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:00:51 2003 Input: N:=415; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 20:59:49 on modular [Seed = 1602473291] ------------------------------------- [ 415, 1, 1 ][ 5, 1, 1 ][ 83, 1, 1 ][] [ 415, 2, 1 ][ 5, 11, 1 ][ 83, 1, 1 ][] [ 415, 3, 1 ][ 5, 1, 1069 ][ 83, 1, 1 ][] [ 415, 4, 1 ][ 5, 1, 1 ][ 83, 1, 1 ][] [ 415, 5, 1 ][ 5, 7, 1 ][ 83, 1, 1 ][] Total time: 62.029 seconds, Total memory usage: 6.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:01:37 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(83,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(415,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:01:29 on modular [Seed = 2124606470] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/1069 Defined on 1 generator Relations: 1069*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 Defined on 5 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 2*$.5 = 0 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 Total time: 8.149 seconds, Total memory usage: 4.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:03:24 2003 Input: N:=415; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:02:22 on modular [Seed = 2254050345] ------------------------------------- [ 415, 1, 1 ][ 5, 1, 1 ][ 83, 1, 1 ][] [ 415, 2, 1 ][ 5, 11, 11 ][ 83, 1, 1 ][] [ 415, 3, 1 ][ 5, 1, 1069 ][ 83, 1, 1 ][] [ 415, 4, 1 ][ 5, 1, 1 ][ 83, 1, 1 ][] [ 415, 5, 1 ][ 5, 7, 1 ][ 83, 1, 1 ][] Total time: 61.849 seconds, Total memory usage: 6.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:04:46 2003 Input: N:=415; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:03:46 on modular [Seed = 2387746701] ------------------------------------- [ 415, 1, 1 ][ 5, 1, 1 ][ 83, 1, 1 ][] [ 415, 2, 1 ][ 5, 11, 11 ][ 83, 1, 1 ][] [ 415, 3, 1 ][ 5, 1, 1069 ][ 83, 1, 1 ][] [ 415, 4, 1 ][ 5, 1, 1 ][ 83, 1, 1 ][] [ 415, 5, 1 ][ 5, 7, 1 ][ 83, 1, 1 ][] Total time: 59.709 seconds, Total memory usage: 6.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:07:12 2003 Input: N:=416; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:06:21 on modular [Seed = 2638285825] ------------------------------------- [ 416, 1, 1 ][ 13, 1, 1 ][] [ 416, 2, 1 ][ 13, 1, 1 ][] [ 416, 3, 1 ][ 13, 1, 1 ][] [ 416, 4, 1 ][ 13, 1, 5 ][] [ 416, 5, 1 ][ 13, 1, 1 ][] [ 416, 6, 1 ][ 13, 1, 1 ][] Total time: 50.169 seconds, Total memory usage: 9.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:08:28 2003 Input: N:=416; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:07:38 on modular [Seed = 2776183886] ------------------------------------- [ 416, 1, 1 ][ 13, 1, 1 ][] [ 416, 2, 1 ][ 13, 1, 1 ][] [ 416, 3, 1 ][ 13, 1, 1 ][] [ 416, 4, 1 ][ 13, 1, 5 ][] [ 416, 5, 1 ][ 13, 1, 1 ][] [ 416, 6, 1 ][ 13, 1, 1 ][] Total time: 49.949 seconds, Total memory usage: 9.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:09:23 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(32,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(416,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:09:15 on modular [Seed = 2909879783] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Total time: 7.869 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:11:07 2003 Input: N:=417; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:10:02 on modular [Seed = 3177262534] ------------------------------------- [ 417, 1, 1 ][ 3, 1, 9 ][ 139, 1, 1 ][] [ 417, 2, 1 ][ 3, 19, 19 ][ 139, 1, 1 ][] [ 417, 3, 1 ][ 3, 1, 37 ][ 139, 1, 1 ][] [ 417, 4, 1 ][ 3, 91, 13 ][ 139, 1, 1 ][] [ 417, 5, 1 ][ 3, 1, 29 ][ 139, 1, 1 ][] [ 417, 6, 1 ][ 3, 35, 7 ][ 139, 1, 1 ][] Total time: 65.490 seconds, Total memory usage: 7.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:12:19 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(139,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(417,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:12:09 on modular [Seed = 3624159264] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/37 Defined on 1 generator Relations: 37*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group of order 1 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/29 Defined on 1 generator Relations: 29*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 Total time: 9.519 seconds, Total memory usage: 4.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:15:33 2003 Input: N:=418; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:13:14 on modular [Seed = 3762057179] ------------------------------------- [ 418, 1, 1 ][ 2, 13, 13 ][ 11, 1, 1 ][ 19, 1, 1 ][] [ 418, 2, 1 ][ 2, 1, 1 ][ 11, 1, 1 ][ 19, 1, 1 ][] [ 418, 3, 1 ][ 2, 1, 1 ][ 11, 1, 1 ][ 19, 1, 1 ][] [ 418, 4, 1 ][ 2, 1, 43 ][ 11, 1, 1 ][ 19, 1, 1 ][] [ 418, 5, 1 ][ 2, 1, 3 ][ 11, 3, 1 ][ 19, 1, 1 ][] [ 418, 6, 1 ][ 2, 45, 3 ][ 11, 3, 1 ][ 19, 5, 1 ][] [ 418, 7, 1 ][ 2, 1, 7 ][ 11, 1, 1 ][ 19, 1, 1 ][] [ 418, 8, 1 ][ 2, 7, 7 ][ 11, 1, 7 ][ 19, 1, 1 ][] Total time: 137.970 seconds, Total memory usage: 10.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:17:29 2003 Input: N:=418; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:16:13 on modular [Seed = 4013121539] ------------------------------------- [ 418, 1, 1 ][ 2, 13, 13 ][ 11, 1, 1 ][] [ 418, 2, 1 ][ 2, 1, 1 ][ 11, 1, 1 ][] [ 418, 3, 1 ][ 2, 1, 1 ][ 11, 1, 1 ][] [ 418, 4, 1 ][ 2, 1, 43 ][ 11, 1, 1 ][] [ 418, 5, 1 ][ 2, 1, 3 ][ 11, 3, 1 ][] [ 418, 6, 1 ][ 2, 45, 3 ][ 11, 3, 1 ][] [ 418, 7, 1 ][ 2, 1, 7 ][ 11, 1, 1 ][] [ 418, 8, 1 ][ 2, 7, 7 ][ 11, 1, 7 ][] Total time: 75.649 seconds, Total memory usage: 10.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:18:42 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(209,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(418,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:18:29 on modular [Seed = 4163139212] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/43 Defined on 1 generator Relations: 43*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/6 Defined on 2 generators Relations: 2*$.1 = 0 6*$.2 = 0 6 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/10 Defined on 2 generators Relations: 2*$.1 = 0 10*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/6 Defined on 2 generators Relations: 2*$.1 = 0 6*$.2 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 8 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/4 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 4*$.3 = 0 Total time: 12.889 seconds, Total memory usage: 4.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:19:16 2003 Input: N:=418; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:18:07 on modular [Seed = 4146821545] ------------------------------------- [ 418, 1, 1 ][ 19, 1, 1 ][] [ 418, 2, 1 ][ 19, 1, 1 ][] [ 418, 3, 1 ][ 19, 1, 1 ][] [ 418, 4, 1 ][ 19, 1, 1 ][] [ 418, 5, 1 ][ 19, 1, 1 ][] [ 418, 6, 1 ][ 19, 5, 1 ][] [ 418, 7, 1 ][ 19, 1, 1 ][] [ 418, 8, 1 ][ 19, 1, 1 ][] Total time: 68.149 seconds, Total memory usage: 10.95MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:21:10 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(38,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(418,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:21:00 on modular [Seed = 248677122] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 6 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 9.920 seconds, Total memory usage: 4.66MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:23:09 2003 Input: N:=419; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:23:04 on modular [Seed = 382376862] ------------------------------------- [ 419, 1, 1 ][] [ 419, 2, 1 ][ 419, 209, 1 ][] Total time: 4.289 seconds, Total memory usage: 5.32MB ************** MAGMA ***************** Host www-cache0.usyd.edu.au. (129.78.64.100) Time: Fri Dec 19 21:25:35 2003 Input: p := RandomPrime(168); K := GF(p); K; number := 10; for i := 1 to number do E := EllipticCurve([ Random(K) : i in [1..2] ]); "nCurve number", i; E; "n"; time n := SEA(E); "Order is", Factorization(n); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 19 2003 21:25:12 on modular [Seed = 653961774] ------------------------------------- Finite field of size 25941910753976582413079653967792874873026625782083 nCurve number 1 Elliptic Curve defined by y^2 = x^3 + 60856238427309698798335023450228172942723\ 0940825*x + 3671419312817502469672680129134569870492266929425 over GF(25941910753976582413079653967792874873026625782083) n Time: 15.020 Order is [ <2, 3>, <5, 1>, <17, 1>, <839, 1>, <3280036640047, 1>, <13862845794250274171937939240953, 1> ] nCurve number 2 Elliptic Curve defined by y^2 = x^3 + 19427076137316037574639400769406368639626\ 887580685*x + 5218632639122590660602655467436901119834308620019 over GF(25941910753976582413079653967792874873026625782083) n Errors: /home/mfd/gomagma: line 2: 16166 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:32:00 2003 Input: N:=420; q:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:27:06 on modular [Seed = 787653204] ------------------------------------- [ 420, 1, 1 ][ 3, 1, 7 ][] [ 420, 2, 1 ][ 3, 1, 5 ][] [ 420, 3, 1 ][ 3, 3, 1 ][] [ 420, 4, 1 ][ 3, 1, 1 ][] Total time: 282.610 seconds, Total memory usage: 22.92MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:32:33 2003 Input: N:=420; q:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Dec 19 2003 21:24:10 on modular [Seed = 516068308] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 16158 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:35:08 2003 Input: N:=421; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:35:03 on modular [Seed = 1268236572] ------------------------------------- [ 421, 1, 1 ][] [ 421, 2, 1 ][ 421, 35, 1 ][] Total time: 4.619 seconds, Total memory usage: 5.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:37:05 2003 Input: N:=422; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:35:48 on modular [Seed = 1401936343] ------------------------------------- [ 422, 1, 1 ][ 2, 1, 1 ][ 211, 1, 1 ][] [ 422, 2, 1 ][ 2, 1, 209 ][ 211, 1, 1 ][] [ 422, 3, 1 ][ 2, 1, 49 ][ 211, 1, 1 ][] [ 422, 4, 1 ][ 2, 1, 69 ][ 211, 3, 1 ][] [ 422, 5, 1 ][ 2, 223, 223 ][ 211, 1, 1 ][] [ 422, 6, 1 ][ 2, 2173, 41 ][ 211, 1, 1 ][] Total time: 73.929 seconds, Total memory usage: 8.95MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:38:04 2003 Input: N:=422; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:37:39 on modular [Seed = 1535627688] ------------------------------------- [ 422, 1, 1 ][ 2, 1, 1 ][] [ 422, 2, 1 ][ 2, 1, 209 ][] [ 422, 3, 1 ][ 2, 1, 49 ][] [ 422, 4, 1 ][ 2, 1, 69 ][] [ 422, 5, 1 ][ 2, 223, 223 ][] [ 422, 6, 1 ][ 2, 2173, 41 ][] Total time: 24.209 seconds, Total memory usage: 8.95MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:38:35 2003 Input: N:=420; q:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:32:32 on modular [Seed = 1055045118] ------------------------------------- [ 420, 1, 1 ][ 5, 1, 5 ][] [ 420, 2, 1 ][ 5, 1, 1 ][] [ 420, 3, 1 ][ 5, 1, 1 ][] [ 420, 4, 1 ][ 5, 1, 1 ][] Total time: 361.880 seconds, Total memory usage: 23.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:39:08 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(211,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(422,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:38:55 on modular [Seed = 1807213140] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/223 Defined on 1 generator Relations: 223*$.1 = 0 6 Abelian Group of order 1 Abelian Group isomorphic to Z/32 Defined on 1 generator Relations: 32*$.1 = 0 Abelian Group isomorphic to Z/41 Defined on 1 generator Relations: 41*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 11.969 seconds, Total memory usage: 4.91MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:39:36 2003 Input: N:=422; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:38:41 on modular [Seed = 1756684633] ------------------------------------- [ 422, 1, 1 ][ 211, 1, 1 ][] [ 422, 2, 1 ][ 211, 1, 1 ][] [ 422, 3, 1 ][ 211, 1, 1 ][] [ 422, 4, 1 ][ 211, 3, 1 ][] [ 422, 5, 1 ][ 211, 1, 1 ][] [ 422, 6, 1 ][ 211, 1, 1 ][] Total time: 54.760 seconds, Total memory usage: 9.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:44:51 2003 Input: N:=426; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:43:04 on modular [Seed = 2220362940] ------------------------------------- [ 426, 1, 1 ][ 2, 1, 5 ][ 3, 1, 3 ][] [ 426, 2, 1 ][ 2, 1, 9 ][ 3, 15, 5 ][] [ 426, 3, 1 ][ 2, 5, 1 ][ 3, 5, 1 ][] [ 426, 4, 1 ][ 2, 1, 31 ][ 3, 1, 7 ][] [ 426, 5, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 426, 6, 1 ][ 2, 11, 11 ][ 3, 1, 5 ][] [ 426, 7, 1 ][ 2, 133, 19 ][ 3, 49, 7 ][] Total time: 106.160 seconds, Total memory usage: 13.81MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:46:01 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(213,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(426,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:45:46 on modular [Seed = 2487753806] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 7 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 14.380 seconds, Total memory usage: 5.13MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:47:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(142,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(426,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:47:00 on modular [Seed = 2621447096] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Total time: 13.369 seconds, Total memory usage: 5.00MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:48:08 2003 Input: N:=426; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:45:30 on modular [Seed = 2437749083] ------------------------------------- [ 426, 1, 1 ][ 71, 1, 1 ][] [ 426, 2, 1 ][ 71, 1, 1 ][] [ 426, 3, 1 ][ 71, 1, 1 ][] [ 426, 4, 1 ][ 71, 1, 1 ][] [ 426, 5, 1 ][ 71, 1, 1 ][] [ 426, 6, 1 ][ 71, 1, 1 ][] [ 426, 7, 1 ][ 71, 1, 1 ][] Total time: 156.679 seconds, Total memory usage: 14.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:51:18 2003 Input: N:=427; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:50:14 on modular [Seed = 3010409557] ------------------------------------- [ 427, 1, 1 ][ 7, 1, 3 ][ 61, 1, 1 ][] [ 427, 2, 1 ][ 7, 1, 1 ][ 61, 1, 1 ][] [ 427, 3, 1 ][ 7, 1, 1 ][ 61, 1, 1 ][] [ 427, 4, 1 ][ 7, 1, 3 ][ 61, 1, 1 ][] [ 427, 5, 1 ][ 7, 139, 1 ][ 61, 1, 1 ][] [ 427, 6, 1 ][ 7, 217, 7 ][ 61, 1, 1 ][] [ 427, 7, 1 ][ 7, 1, 313 ][ 61, 1, 1 ][] Total time: 64.189 seconds, Total memory usage: 6.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:52:05 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(61,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(427,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 21:51:57 on modular [Seed = 3144105462] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/139 Defined on 1 generator Relations: 139*$.1 = 0 6 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group isomorphic to Z/313 Defined on 1 generator Relations: 313*$.1 = 0 Total time: 8.319 seconds, Total memory usage: 4.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:53:51 2003 Input: N:=427; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:52:47 on modular [Seed = 3273606588] ------------------------------------- [ 427, 1, 1 ][ 7, 1, 3 ][ 61, 1, 1 ][] [ 427, 2, 1 ][ 7, 1, 1 ][ 61, 1, 1 ][] [ 427, 3, 1 ][ 7, 1, 1 ][ 61, 1, 1 ][] [ 427, 4, 1 ][ 7, 1, 3 ][ 61, 1, 1 ][] [ 427, 5, 1 ][ 7, 139, 139 ][ 61, 1, 1 ][] [ 427, 6, 1 ][ 7, 217, 7 ][ 61, 1, 1 ][] [ 427, 7, 1 ][ 7, 1, 313 ][ 61, 1, 1 ][] Total time: 64.580 seconds, Total memory usage: 6.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:55:46 2003 Input: N:=427; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:55:15 on modular [Seed = 3490469315] ------------------------------------- [ 427, 1, 1 ][ 7, 1, 3 ][] [ 427, 2, 1 ][ 7, 1, 1 ][] [ 427, 3, 1 ][ 7, 1, 1 ][] [ 427, 4, 1 ][ 7, 1, 3 ][] [ 427, 5, 1 ][ 7, 139, 139 ][] [ 427, 6, 1 ][ 7, 217, 7 ][] [ 427, 7, 1 ][ 7, 1, 313 ][] Total time: 30.629 seconds, Total memory usage: 6.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 21:59:20 2003 Input: N:=429; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 21:56:57 on modular [Seed = 3624164769] ------------------------------------- [ 429, 1, 1 ][ 3, 1, 1 ][ 11, 1, 1 ][ 13, 1, 1 ][] [ 429, 2, 1 ][ 3, 1, 1 ][ 11, 1, 1 ][ 13, 1, 1 ][] [ 429, 3, 1 ][ 3, 1, 3 ][ 11, 1, 1 ][ 13, 1, 1 ][] [ 429, 4, 1 ][ 3, 23, 23 ][ 11, 7, 1 ][ 13, 1, 1 ][] [ 429, 5, 1 ][ 3, 1, 129 ][ 11, 1, 1 ][ 13, 1, 3 ][] [ 429, 6, 1 ][ 3, 5, 5 ][ 11, 1, 25 ][ 13, 1, 1 ][] [ 429, 7, 1 ][ 3, 5, 1 ][ 11, 1, 1 ][ 13, 5, 1 ][] [ 429, 8, 1 ][ 3, 1, 379 ][ 11, 1, 1 ][ 13, 1, 1 ][] Total time: 143.290 seconds, Total memory usage: 9.66MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:00:36 2003 Input: N:=429; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:00:06 on modular [Seed = 3895749854] ------------------------------------- [ 429, 1, 1 ][ 3, 1, 1 ][] [ 429, 2, 1 ][ 3, 1, 1 ][] [ 429, 3, 1 ][ 3, 1, 3 ][] [ 429, 4, 1 ][ 3, 23, 23 ][] [ 429, 5, 1 ][ 3, 1, 129 ][] [ 429, 6, 1 ][ 3, 5, 5 ][] [ 429, 7, 1 ][ 3, 5, 1 ][] [ 429, 8, 1 ][ 3, 1, 379 ][] Total time: 29.889 seconds, Total memory usage: 9.66MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:02:26 2003 Input: N:=429; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:01:19 on modular [Seed = 2107767165] ------------------------------------- [ 429, 1, 1 ][ 11, 1, 1 ][] [ 429, 2, 1 ][ 11, 1, 1 ][] [ 429, 3, 1 ][ 11, 1, 1 ][] [ 429, 4, 1 ][ 11, 7, 1 ][] [ 429, 5, 1 ][ 11, 1, 1 ][] [ 429, 6, 1 ][ 11, 1, 25 ][] [ 429, 7, 1 ][ 11, 1, 1 ][] [ 429, 8, 1 ][ 11, 1, 1 ][] Total time: 66.729 seconds, Total memory usage: 9.82MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:04:56 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(143,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(429,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:04:44 on modular [Seed = 1907225154] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/129 Defined on 1 generator Relations: 129*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/758 Defined on 1 generator Relations: 758*$.1 = 0 Total time: 11.889 seconds, Total memory usage: 4.81MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:05:10 2003 Input: N:=429; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:04:09 on modular [Seed = 1974072867] ------------------------------------- [ 429, 1, 1 ][ 13, 1, 1 ][] [ 429, 2, 1 ][ 13, 1, 1 ][] [ 429, 3, 1 ][ 13, 1, 1 ][] [ 429, 4, 1 ][ 13, 1, 1 ][] [ 429, 5, 1 ][ 13, 1, 3 ][] [ 429, 6, 1 ][ 13, 1, 1 ][] [ 429, 7, 1 ][ 13, 5, 1 ][] [ 429, 8, 1 ][ 13, 1, 1 ][] Total time: 60.319 seconds, Total memory usage: 9.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:06:49 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(39,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(429,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:06:39 on modular [Seed = 1622991776] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 + Z/10 Defined on 2 generators Relations: 5*$.1 = 0 10*$.2 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.779 seconds, Total memory usage: 4.60MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:10:25 2003 Input: N:=430; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:09:17 on modular [Seed = 1485101690] ------------------------------------- [ 430, 1, 1 ][ 2, 1, 3 ][ 5, 1, 1 ][] [ 430, 2, 1 ][ 2, 1, 1 ][ 5, 5, 5 ][] [ 430, 3, 1 ][ 2, 9, 3 ][ 5, 1, 1 ][] [ 430, 4, 1 ][ 2, 15, 15 ][ 5, 5, 5 ][] [ 430, 5, 1 ][ 2, 1, 177 ][ 5, 1, 1 ][] [ 430, 6, 1 ][ 2, 3, 3 ][ 5, 1, 19 ][] [ 430, 7, 1 ][ 2, 7, 1 ][ 5, 7, 1 ][] [ 430, 8, 1 ][ 2, 1, 223 ][ 5, 1, 17 ][] Total time: 68.239 seconds, Total memory usage: 12.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:11:47 2003 Input: N:=430; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:10:39 on modular [Seed = 1217710744] ------------------------------------- [ 430, 1, 1 ][ 2, 1, 3 ][ 5, 1, 1 ][] [ 430, 2, 1 ][ 2, 1, 1 ][ 5, 5, 5 ][] [ 430, 3, 1 ][ 2, 9, 3 ][ 5, 1, 1 ][] [ 430, 4, 1 ][ 2, 15, 15 ][ 5, 5, 5 ][] [ 430, 5, 1 ][ 2, 1, 177 ][ 5, 1, 1 ][] [ 430, 6, 1 ][ 2, 3, 3 ][ 5, 1, 19 ][] [ 430, 7, 1 ][ 2, 7, 1 ][ 5, 7, 1 ][] [ 430, 8, 1 ][ 2, 1, 223 ][ 5, 1, 17 ][] Total time: 67.819 seconds, Total memory usage: 12.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:14:33 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(215,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(430,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:14:20 on modular [Seed = 1071890124] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 5 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/59 Defined on 1 generator Relations: 59*$.1 = 0 Abelian Group of order 1 6 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/223 Defined on 1 generator Relations: 223*$.1 = 0 Total time: 12.339 seconds, Total memory usage: 5.19MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:15:56 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(86,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(430,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:15:45 on modular [Seed = 871346861] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 7 Abelian Group of order 1 Abelian Group of order 1 8 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group of order 1 Total time: 10.469 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:16:59 2003 Input: N:=431; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:16:54 on modular [Seed = 737651570] ------------------------------------- [ 431, 1, 1 ][] [ 431, 2, 1 ][ 431, 1, 1 ][] [ 431, 3, 1 ][ 431, 1, 1 ][] [ 431, 4, 1 ][ 431, 1, 1 ][] [ 431, 5, 1 ][ 431, 1, 1 ][] [ 431, 6, 1 ][ 431, 215, 1 ][] Total time: 4.689 seconds, Total memory usage: 5.47MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:17:45 2003 Input: N:=433; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:17:40 on modular [Seed = 603955976] ------------------------------------- [ 433, 1, 1 ][] [ 433, 2, 1 ][ 433, 1, 1 ][] [ 433, 3, 1 ][ 433, 1, 1 ][] [ 433, 4, 1 ][ 433, 9, 3 ][] Total time: 4.549 seconds, Total memory usage: 5.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:21:56 2003 Input: N:=434; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:20:10 on modular [Seed = 281841797] ------------------------------------- [ 434, 1, 1 ][ 2, 1, 3 ][ 7, 1, 1 ][] [ 434, 2, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][] [ 434, 3, 1 ][ 2, 3, 3 ][ 7, 1, 1 ][] [ 434, 4, 1 ][ 2, 5, 5 ][ 7, 1, 1 ][] [ 434, 5, 1 ][ 2, 9, 3 ][ 7, 1, 1 ][] [ 434, 6, 1 ][ 2, 1, 17 ][ 7, 1, 1 ][] [ 434, 7, 1 ][ 2, 17, 17 ][ 7, 1, 1 ][] [ 434, 8, 1 ][ 2, 1, 61 ][ 7, 1, 25 ][] [ 434, 9, 1 ][ 2, 85, 17 ][ 7, 5, 1 ][] Total time: 101.169 seconds, Total memory usage: 11.73MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:22:00 2003 Input: N:=434; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:19:09 on modular [Seed = 466066377] ------------------------------------- [ 434, 1, 1 ][ 2, 1, 3 ][ 7, 1, 1 ][ 31, 1, 1 ][] [ 434, 2, 1 ][ 2, 1, 1 ][ 7, 1, 1 ][ 31, 1, 1 ][] [ 434, 3, 1 ][ 2, 3, 3 ][ 7, 1, 1 ][ 31, 1, 1 ][] [ 434, 4, 1 ][ 2, 5, 5 ][ 7, 1, 1 ][ 31, 1, 1 ][] [ 434, 5, 1 ][ 2, 9, 3 ][ 7, 1, 1 ][ 31, 1, 1 ][] [ 434, 6, 1 ][ 2, 1, 17 ][ 7, 1, 1 ][ 31, 1, 7 ][] [ 434, 7, 1 ][ 2, 17, 17 ][ 7, 1, 1 ][ 31, 1, 1 ][] [ 434, 8, 1 ][ 2, 1, 61 ][ 7, 1, 25 ][ 31, 1, 1 ][] [ 434, 9, 1 ][ 2, 85, 17 ][ 7, 5, 1 ][ 31, 1, 1 ][] Total time: 169.580 seconds, Total memory usage: 11.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:24:13 2003 Input: N:=434; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:23:26 on modular [Seed = 65010898] ------------------------------------- [ 434, 1, 1 ][ 2, 1, 3 ][] [ 434, 2, 1 ][ 2, 1, 1 ][] [ 434, 3, 1 ][ 2, 3, 3 ][] [ 434, 4, 1 ][ 2, 5, 5 ][] [ 434, 5, 1 ][ 2, 9, 3 ][] [ 434, 6, 1 ][ 2, 1, 17 ][] [ 434, 7, 1 ][ 2, 17, 17 ][] [ 434, 8, 1 ][ 2, 1, 61 ][] [ 434, 9, 1 ][ 2, 85, 17 ][] Total time: 47.180 seconds, Total memory usage: 11.73MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:25:20 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(217,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(434,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:25:06 on modular [Seed = 4079947166] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group of order 1 7 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/122 Defined on 1 generator Relations: 122*$.1 = 0 9 Abelian Group of order 1 Abelian Group isomorphic to Z/17 Defined on 1 generator Relations: 17*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 13.250 seconds, Total memory usage: 5.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:25:52 2003 Input: N:=434; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:24:49 on modular [Seed = 4196795527] ------------------------------------- [ 434, 1, 1 ][ 7, 1, 1 ][] [ 434, 2, 1 ][ 7, 1, 1 ][] [ 434, 3, 1 ][ 7, 1, 1 ][] [ 434, 4, 1 ][ 7, 1, 1 ][] [ 434, 5, 1 ][ 7, 1, 1 ][] [ 434, 6, 1 ][ 7, 1, 1 ][] [ 434, 7, 1 ][ 7, 1, 1 ][] [ 434, 8, 1 ][ 7, 1, 25 ][] [ 434, 9, 1 ][ 7, 5, 1 ][] Total time: 62.389 seconds, Total memory usage: 11.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:28:51 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(62,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(434,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:28:40 on modular [Seed = 3862567025] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 7 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 + Z/10 Defined on 2 generators Relations: 5*$.1 = 0 10*$.2 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 10.260 seconds, Total memory usage: 4.72MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:32:36 2003 Input: N:=434; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:31:17 on modular [Seed = 3590990636] ------------------------------------- [ 434, 1, 1 ][ 31, 1, 1 ][] [ 434, 2, 1 ][ 31, 1, 1 ][] [ 434, 3, 1 ][ 31, 1, 1 ][] [ 434, 4, 1 ][ 31, 1, 1 ][] [ 434, 5, 1 ][ 31, 1, 1 ][] [ 434, 6, 1 ][ 31, 1, 7 ][] [ 434, 7, 1 ][ 31, 1, 1 ][] [ 434, 8, 1 ][ 31, 1, 1 ][] [ 434, 9, 1 ][ 31, 1, 1 ][] Total time: 78.299 seconds, Total memory usage: 11.98MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:36:28 2003 Input: N:=434; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:35:10 on modular [Seed = 3373610456] ------------------------------------- [ 434, 1, 1 ][ 31, 1, 1 ][] [ 434, 2, 1 ][ 31, 1, 1 ][] [ 434, 3, 1 ][ 31, 1, 1 ][] [ 434, 4, 1 ][ 31, 1, 1 ][] [ 434, 5, 1 ][ 31, 1, 1 ][] [ 434, 6, 1 ][ 31, 1, 7 ][] [ 434, 7, 1 ][ 31, 1, 1 ][] [ 434, 8, 1 ][ 31, 1, 1 ][] [ 434, 9, 1 ][ 31, 1, 1 ][] Total time: 78.050 seconds, Total memory usage: 12.00MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:38:46 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(14,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(434,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:38:36 on modular [Seed = 3239918210] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.769 seconds, Total memory usage: 4.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:40:38 2003 Input: N:=435; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:40:00 on modular [Seed = 2976729694] ------------------------------------- [ 435, 1, 1 ][ 3, 1, 5 ][] [ 435, 2, 1 ][ 3, 3, 1 ][] [ 435, 3, 1 ][ 3, 1, 1 ][] [ 435, 4, 1 ][ 3, 1, 1 ][] [ 435, 5, 1 ][ 3, 1, 1 ][] [ 435, 6, 1 ][ 3, 19, 19 ][] [ 435, 7, 1 ][ 3, 9, 9 ][] [ 435, 8, 1 ][ 3, 7, 1 ][] [ 435, 9, 1 ][ 3, 1, 19 ][] [ 435, 10, 1 ][ 3, 1, 1 ][] Total time: 38.060 seconds, Total memory usage: 10.68MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:42:12 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(145,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(435,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:41:58 on modular [Seed = 2793037023] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 Abelian Group of order 1 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 + Z/6 Defined on 2 generators Relations: 3*$.1 = 0 6*$.2 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 9 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*$.1 = 0 10 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 13.419 seconds, Total memory usage: 4.87MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:42:35 2003 Input: N:=435; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:41:44 on modular [Seed = 2843038254] ------------------------------------- [ 435, 1, 1 ][ 5, 1, 7 ][] [ 435, 2, 1 ][ 5, 1, 1 ][] [ 435, 3, 1 ][ 5, 1, 1 ][] [ 435, 4, 1 ][ 5, 1, 1 ][] [ 435, 5, 1 ][ 5, 1, 11 ][] [ 435, 6, 1 ][ 5, 1, 1 ][] [ 435, 7, 1 ][ 5, 1, 1 ][] [ 435, 8, 1 ][ 5, 7, 1 ][] [ 435, 9, 1 ][ 5, 1, 1 ][] [ 435, 10, 1 ][ 5, 1, 1 ][] Total time: 50.269 seconds, Total memory usage: 10.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:43:21 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(87,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(435,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:43:10 on modular [Seed = 2571461544] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 5 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 9 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 10 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 Total time: 11.329 seconds, Total memory usage: 4.71MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:46:43 2003 Input: N:=435; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:45:25 on modular [Seed = 2204072233] ------------------------------------- [ 435, 1, 1 ][ 29, 1, 1 ][] [ 435, 2, 1 ][ 29, 1, 1 ][] [ 435, 3, 1 ][ 29, 1, 1 ][] [ 435, 4, 1 ][ 29, 1, 1 ][] [ 435, 5, 1 ][ 29, 1, 1 ][] [ 435, 6, 1 ][ 29, 1, 1 ][] [ 435, 7, 1 ][ 29, 1, 1 ][] [ 435, 8, 1 ][ 29, 1, 1 ][] [ 435, 9, 1 ][ 29, 1, 7 ][] [ 435, 10, 1 ][ 29, 1, 1 ][] Total time: 78.569 seconds, Total memory usage: 10.94MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:48:32 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(15,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(435,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:48:22 on modular [Seed = 2057732994] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group of order 1 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group of order 1 9 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 10 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.989 seconds, Total memory usage: 4.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:50:17 2003 Input: N:=437; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:49:03 on modular [Seed = 1924041635] ------------------------------------- [ 437, 1, 1 ][ 19, 1, 1 ][ 23, 1, 1 ][] [ 437, 2, 1 ][ 19, 1, 1 ][ 23, 1, 1 ][] [ 437, 3, 1 ][ 19, 1, 1 ][ 23, 1, 1 ][] [ 437, 4, 1 ][ 19, 11, 11 ][ 23, 1, 1 ][] [ 437, 5, 1 ][ 19, 1, 1 ][ 23, 1, 1 ][] [ 437, 6, 1 ][ 19, 1, 1 ][ 23, 1, 1 ][] [ 437, 7, 1 ][ 19, 1, 81 ][ 23, 5, 1 ][] [ 437, 8, 1 ][ 19, 3, 1 ][ 23, 1, 9 ][] Total time: 73.569 seconds, Total memory usage: 6.51MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:51:00 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(23,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(437,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:50:52 on modular [Seed = 1622972418] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 5 Abelian Group of order 1 6 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 7 Abelian Group isomorphic to Z/9 + Z/9 Defined on 2 generators Relations: 9*$.1 = 0 9*$.2 = 0 8 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 7.849 seconds, Total memory usage: 4.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:51:49 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(19,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(437,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:51:42 on modular [Seed = 1485086824] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group of order 1 4 Abelian Group of order 1 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/12 Defined on 1 generator Relations: 12*$.1 = 0 Total time: 7.619 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:54:57 2003 Input: N:=438; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:52:58 on modular [Seed = 1351395508] ------------------------------------- [ 438, 1, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 438, 2, 1 ][ 2, 1, 7 ][ 3, 1, 1 ][] [ 438, 3, 1 ][ 2, 1, 3 ][ 3, 3, 1 ][] [ 438, 4, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 438, 5, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 438, 6, 1 ][ 2, 9, 3 ][ 3, 3, 1 ][] [ 438, 7, 1 ][ 2, 1, 1 ][ 3, 1, 1 ][] [ 438, 8, 1 ][ 2, 1, 23 ][ 3, 1, 7 ][] [ 438, 9, 1 ][ 2, 5, 5 ][ 3, 1, 29 ][] Total time: 118.720 seconds, Total memory usage: 14.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:56:04 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(219,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(438,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:55:49 on modular [Seed = 1167700606] ------------------------------------- 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/46 Defined on 1 generator Relations: 46*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 9 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 14.949 seconds, Total memory usage: 5.31MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:57:22 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(146,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(438,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 22:57:09 on modular [Seed = 1038207702] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/2 + Z/14 Defined on 2 generators Relations: 2*$.1 = 0 14*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/58 Defined on 1 generator Relations: 58*$.1 = 0 Total time: 12.879 seconds, Total memory usage: 5.13MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 22:58:30 2003 Input: N:=439; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:58:26 on modular [Seed = 854508974] ------------------------------------- [ 439, 1, 1 ][] [ 439, 2, 1 ][ 439, 1, 1 ][] [ 439, 3, 1 ][ 439, 73, 1 ][] Total time: 4.389 seconds, Total memory usage: 5.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:01:27 2003 Input: N:=440; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 22:59:12 on modular [Seed = 720821316] ------------------------------------- [ 440, 1, 1 ][ 5, 1, 3 ][ 11, 1, 1 ][] [ 440, 2, 1 ][ 5, 3, 3 ][ 11, 1, 1 ][] [ 440, 3, 1 ][ 5, 3, 3 ][ 11, 1, 1 ][] [ 440, 4, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] [ 440, 5, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] [ 440, 6, 1 ][ 5, 1, 13 ][ 11, 1, 1 ][] [ 440, 7, 1 ][ 5, 1, 1 ][ 11, 1, 1 ][] Total time: 134.209 seconds, Total memory usage: 14.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:02:34 2003 Input: N:=440; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:01:30 on modular [Seed = 148176620] ------------------------------------- [ 440, 1, 1 ][ 5, 1, 3 ][] [ 440, 2, 1 ][ 5, 3, 3 ][] [ 440, 3, 1 ][ 5, 3, 3 ][] [ 440, 4, 1 ][ 5, 1, 1 ][] [ 440, 5, 1 ][ 5, 1, 1 ][] [ 440, 6, 1 ][ 5, 1, 13 ][] [ 440, 7, 1 ][ 5, 1, 1 ][] Total time: 63.050 seconds, Total memory usage: 14.30MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:03:31 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(88,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(440,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:03:18 on modular [Seed = 4280486535] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 Abelian Group isomorphic to Z/26 Defined on 1 generator Relations: 26*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Total time: 12.829 seconds, Total memory usage: 5.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:04:39 2003 Input: N:=440; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:03:14 on modular [Seed = 14480764] ------------------------------------- [ 440, 1, 1 ][ 11, 1, 1 ][] [ 440, 2, 1 ][ 11, 1, 1 ][] [ 440, 3, 1 ][ 11, 1, 1 ][] [ 440, 4, 1 ][ 11, 1, 1 ][] [ 440, 5, 1 ][ 11, 1, 1 ][] [ 440, 6, 1 ][ 11, 1, 1 ][] [ 440, 7, 1 ][ 11, 1, 1 ][] Total time: 84.039 seconds, Total memory usage: 14.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:07:53 2003 Input: N:=442; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:06:20 on modular [Seed = 3979417647] ------------------------------------- [ 442, 1, 1 ][ 2, 1, 1 ][ 13, 1, 1 ][] [ 442, 2, 1 ][ 2, 1, 1 ][ 13, 1, 1 ][] [ 442, 3, 1 ][ 2, 1, 1 ][ 13, 1, 1 ][] [ 442, 4, 1 ][ 2, 11, 11 ][ 13, 1, 1 ][] [ 442, 5, 1 ][ 2, 1, 1 ][ 13, 1, 1 ][] [ 442, 6, 1 ][ 2, 1, 11 ][ 13, 1, 1 ][] [ 442, 7, 1 ][ 2, 1, 7 ][ 13, 1, 1 ][] [ 442, 8, 1 ][ 2, 1, 5 ][ 13, 1, 1 ][] [ 442, 9, 1 ][ 2, 1, 1 ][ 13, 1, 1 ][] Total time: 91.819 seconds, Total memory usage: 11.39MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:09:03 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(221,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(442,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:08:48 on modular [Seed = 3762033870] ------------------------------------- 1 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/11 Defined on 1 generator Relations: 11*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/22 Defined on 1 generator Relations: 22*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 8 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/16 Defined on 1 generator Relations: 16*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 14.449 seconds, Total memory usage: 5.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:09:45 2003 Input: N:=442; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:08:30 on modular [Seed = 3845722533] ------------------------------------- [ 442, 1, 1 ][ 17, 1, 1 ][] [ 442, 2, 1 ][ 17, 1, 3 ][] [ 442, 3, 1 ][ 17, 1, 1 ][] [ 442, 4, 1 ][ 17, 1, 5 ][] [ 442, 5, 1 ][ 17, 3, 3 ][] [ 442, 6, 1 ][ 17, 1, 5 ][] [ 442, 7, 1 ][ 17, 7, 7 ][] [ 442, 8, 1 ][ 17, 1, 1 ][] [ 442, 9, 1 ][ 17, 1, 1 ][] Total time: 74.289 seconds, Total memory usage: 11.76MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:10:34 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(34,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(442,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:10:25 on modular [Seed = 3440457986] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 8 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 9 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.569 seconds, Total memory usage: 4.74MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:22:10 2003 Input: N:=442; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:20:56 on modular [Seed = 3060418528] ------------------------------------- [ 442, 1, 1 ][ 17, 1, 1 ][] [ 442, 2, 1 ][ 17, 1, 3 ][] [ 442, 3, 1 ][ 17, 1, 1 ][] Total time: 73.669 seconds, Total memory usage: 11.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:24:26 2003 Input: N:=442; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [4..6] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:23:12 on modular [Seed = 2926731104] ------------------------------------- [ 442, 4, 1 ][ 17, 1, 5 ][] [ 442, 5, 1 ][ 17, 3, 3 ][] [ 442, 6, 1 ][ 17, 1, 5 ][] Total time: 73.440 seconds, Total memory usage: 11.64MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:26:57 2003 Input: N:=442; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [7..9] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [3..3] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:25:44 on modular [Seed = 2743030677] ------------------------------------- [ 442, 7, 1 ][ 17, 7, 7 ][] [ 442, 8, 1 ][ 17, 1, 1 ][] [ 442, 9, 1 ][ 17, 1, 1 ][] Total time: 72.259 seconds, Total memory usage: 11.61MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:28:07 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(26,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(442,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:27:56 on modular [Seed = 2605148969] ------------------------------------- 1 Abelian Group of order 1 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 3 Abelian Group of order 1 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 5 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 6 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 7 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 8 Abelian Group of order 1 Abelian Group of order 1 9 Abelian Group of order 1 Abelian Group of order 1 Total time: 10.079 seconds, Total memory usage: 4.77MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:29:52 2003 Input: N:=443; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:29:47 on modular [Seed = 2420932565] ------------------------------------- [ 443, 1, 1 ][] [ 443, 2, 1 ][ 443, 1, 1 ][] [ 443, 3, 1 ][ 443, 1, 1 ][] [ 443, 4, 1 ][ 443, 1, 1 ][] [ 443, 5, 1 ][ 443, 221, 1 ][] Total time: 4.499 seconds, Total memory usage: 5.63MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:32:00 2003 Input: N:=444; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:30:48 on modular [Seed = 2204068997] ------------------------------------- [ 444, 1, 1 ][ 3, 1, 1 ][] [ 444, 2, 1 ][ 3, 1, 1 ][] [ 444, 3, 1 ][ 3, 1, 3 ][] [ 444, 4, 1 ][ 3, 15, 1 ][] Total time: 71.289 seconds, Total memory usage: 15.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:33:46 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(148,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(444,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:33:34 on modular [Seed = 2024052251] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 11.899 seconds, Total memory usage: 5.12MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:36:22 2003 Input: N:=444; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:35:11 on modular [Seed = 1857192044] ------------------------------------- [ 444, 1, 1 ][ 3, 1, 1 ][] [ 444, 2, 1 ][ 3, 1, 1 ][] [ 444, 3, 1 ][ 3, 1, 3 ][] [ 444, 4, 1 ][ 3, 15, 5 ][] Total time: 70.039 seconds, Total memory usage: 15.22MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:38:36 2003 Input: N:=445; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:37:28 on modular [Seed = 1723501331] ------------------------------------- [ 445, 1, 1 ][ 5, 1, 5 ][ 89, 1, 1 ][] [ 445, 2, 1 ][ 5, 3, 1 ][ 89, 1, 1 ][] [ 445, 3, 1 ][ 5, 1, 1 ][ 89, 1, 1 ][] [ 445, 4, 1 ][ 5, 1, 1 ][ 89, 1, 1 ][] [ 445, 5, 1 ][ 5, 35, 7 ][ 89, 1, 1 ][] [ 445, 6, 1 ][ 5, 521, 521 ][ 89, 1, 1 ][] [ 445, 7, 1 ][ 5, 1, 4121 ][ 89, 1, 1 ][] Total time: 67.550 seconds, Total memory usage: 7.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:39:35 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(89,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(445,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:39:25 on modular [Seed = 1501934681] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 5 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 6 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/521 Defined on 1 generator Relations: 521*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4121 Defined on 1 generator Relations: 4121*$.1 = 0 Total time: 9.819 seconds, Total memory usage: 4.49MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:41:40 2003 Input: N:=446; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:40:18 on modular [Seed = 1318232961] ------------------------------------- [ 446, 1, 1 ][ 2, 1, 3 ][ 223, 1, 1 ][] [ 446, 2, 1 ][ 2, 1, 1 ][ 223, 1, 1 ][] [ 446, 3, 1 ][ 2, 3, 3 ][ 223, 1, 1 ][] [ 446, 4, 1 ][ 2, 7, 7 ][ 223, 1, 1 ][] [ 446, 5, 1 ][ 2, 3087, 441 ][ 223, 1, 1 ][] [ 446, 6, 1 ][ 2, 1, 1078059 ][ 223, 3, 1 ][] Total time: 80.819 seconds, Total memory usage: 9.65MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:42:34 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(223,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(446,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:42:23 on modular [Seed = 1184541204] ------------------------------------- 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 3 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 4 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 5 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 Abelian Group isomorphic to Z/63 Defined on 1 generator Relations: 63*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/359353 Defined on 1 generator Relations: 359353*$.1 = 0 Total time: 11.549 seconds, Total memory usage: 4.77MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:45:26 2003 Input: N:=447; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:44:11 on modular [Seed = 1055052504] ------------------------------------- [ 447, 1, 1 ][ 3, 1, 13 ][ 149, 1, 1 ][] [ 447, 2, 1 ][ 3, 219, 73 ][ 149, 1, 1 ][] [ 447, 3, 1 ][ 3, 3475, 695 ][ 149, 1, 1 ][] [ 447, 4, 1 ][ 3, 1, 408113 ][ 149, 1, 1 ][] Total time: 74.509 seconds, Total memory usage: 8.27MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:46:19 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(149,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(447,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:46:09 on modular [Seed = 770819649] ------------------------------------- 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group isomorphic to Z/219 Defined on 1 generator Relations: 219*$.1 = 0 3 Abelian Group isomorphic to Z/139 Defined on 1 generator Relations: 139*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/408113 Defined on 1 generator Relations: 408113*$.1 = 0 Total time: 9.559 seconds, Total memory usage: 4.68MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:49:51 2003 Input: N:=447; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:48:36 on modular [Seed = 637128444] ------------------------------------- [ 447, 1, 1 ][ 3, 1, 13 ][ 149, 1, 1 ][] [ 447, 2, 1 ][ 3, 219, 219 ][ 149, 1, 1 ][] [ 447, 3, 1 ][ 3, 3475, 695 ][ 149, 1, 1 ][] [ 447, 4, 1 ][ 3, 1, 408113 ][ 149, 1, 1 ][] Total time: 74.699 seconds, Total memory usage: 8.27MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:51:00 2003 Input: N:=447; q:=5; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:50:35 on modular [Seed = 399244657] ------------------------------------- [ 447, 1, 1 ][ 3, 1, 13 ][] [ 447, 2, 1 ][ 3, 219, 219 ][] [ 447, 3, 1 ][ 3, 3475, 695 ][] [ 447, 4, 1 ][ 3, 1, 408113 ][] Total time: 24.139 seconds, Total memory usage: 8.27MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:53:02 2003 Input: N:=448; q:=3; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:52:11 on modular [Seed = 265544969] ------------------------------------- [ 448, 1, 1 ][ 7, 1, 1 ][] [ 448, 2, 1 ][ 7, 1, 1 ][] [ 448, 3, 1 ][ 7, 1, 1 ][] [ 448, 4, 1 ][ 7, 1, 1 ][] [ 448, 5, 1 ][ 7, 1, 1 ][] [ 448, 6, 1 ][ 7, 1, 1 ][] [ 448, 7, 1 ][ 7, 1, 1 ][] [ 448, 8, 1 ][ 7, 1, 1 ][] [ 448, 9, 1 ][ 7, 1, 1 ][] [ 448, 10, 1 ][ 7, 1, 1 ][] Total time: 50.209 seconds, Total memory usage: 11.86MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:54:13 2003 Input: N:=449; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:54:09 on modular [Seed = 4229961328] ------------------------------------- [ 449, 1, 1 ][] [ 449, 2, 1 ][ 449, 7, 1 ][] Total time: 4.369 seconds, Total memory usage: 5.64MB ************** MAGMA ***************** Host h24-87-78-5.vc.shawcable.net. (24.87.78.5) Time: Fri Dec 19 23:56:06 2003 Input: N:=450; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Fri Dec 19 2003 23:54:51 on modular [Seed = 4146798225] ------------------------------------- [ 450, 1, 1 ][ 2, 1, 3 ][] [ 450, 2, 1 ][ 2, 1, 5 ][] [ 450, 3, 1 ][ 2, 1, 1 ][] [ 450, 4, 1 ][ 2, 1, 1 ][] [ 450, 5, 1 ][ 2, 1, 1 ][] [ 450, 6, 1 ][ 2, 1, 1 ][] [ 450, 7, 1 ][ 2, 1, 1 ][] Total time: 75.069 seconds, Total memory usage: 20.13MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Dec 19 23:59:08 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(225,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(450,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Fri Dec 19 2003 23:58:50 on modular [Seed = 3946251164] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 6 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 7 Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group of order 1 Total time: 18.279 seconds, Total memory usage: 6.03MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:08:00 2003 Input: N:=306; q:=7; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [#A..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:07:29 on modular [Seed = 2943568323] ------------------------------------- [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 31.459 seconds, Total memory usage: 9.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:09:02 2003 Input: N:=306; q:=11; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [#A..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:08:29 on modular [Seed = 2809872791] ------------------------------------- [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 32.470 seconds, Total memory usage: 9.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:10:31 2003 Input: N:=306; q:=11; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [#A..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:09:58 on modular [Seed = 2655156293] ------------------------------------- 11 [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 32.569 seconds, Total memory usage: 9.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:11:13 2003 Input: N:=306; q:=13; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [#A..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:10:41 on modular [Seed = 2404608291] ------------------------------------- 13 [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 31.940 seconds, Total memory usage: 9.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:11:54 2003 Input: N:=306; q:=19; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [#A..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:11:22 on modular [Seed = 2270912768] ------------------------------------- 19 [ 306, 6, 1 ][ 2, 15, 1 ][] Total time: 31.859 seconds, Total memory usage: 9.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:12:40 2003 Input: N:=306; q:=23; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [#A..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:12:07 on modular [Seed = 2141428260] ------------------------------------- 23 [ 306, 6, 1 ][ 2, 15, 5 ][] Total time: 32.869 seconds, Total memory usage: 9.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:14:53 2003 Input: N:=253; q:=23; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:14:38 on modular [Seed = 1890358706] ------------------------------------- 23 [ 253, 2, 1 ][ 11, 5, 5 ][] Total time: 15.279 seconds, Total memory usage: 4.56MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:16:41 2003 Input: N:=237; q:=23; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:16:29 on modular [Seed = 1689813045] ------------------------------------- 23 [ 237, 3, 1 ][ 3, 25, 5 ][] Total time: 12.029 seconds, Total memory usage: 4.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:22:39 2003 Input: N:=237; q:=2; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [3..3] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:22:27 on modular [Seed = 1418246075] ------------------------------------- 2 [ 237, 3, 1 ][ 3, 25, 5 ][] Total time: 11.760 seconds, Total memory usage: 4.84MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:23:42 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(79,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(237,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Sat Dec 20 2003 00:23:35 on modular [Seed = 1284550631] ------------------------------------- 1 Abelian Group of order 1 Abelian Group isomorphic to Z/31 Defined on 1 generator Relations: 31*$.1 = 0 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 3 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 2*$.4 = 0 Total time: 6.399 seconds, Total memory usage: 4.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:26:17 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(29,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(145,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Sat Dec 20 2003 00:26:12 on modular [Seed = 1100849993] ------------------------------------- 1 Abelian Group of order 1 2 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 3 Abelian Group isomorphic to Z/5 + Z/5 Defined on 2 generators Relations: 5*$.1 = 0 5*$.2 = 0 4 Abelian Group of order 1 Total time: 5.399 seconds, Total memory usage: 4.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:27:24 2003 Input: N:=145; q:=2; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:27:16 on modular [Seed = 971365361] ------------------------------------- 2 [ 145, 2, 1 ][ 5, 7, 1 ][] Total time: 8.319 seconds, Total memory usage: 3.78MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:27:59 2003 Input: N:=145; q:=3; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [2..2] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:27:50 on modular [Seed = 837669787] ------------------------------------- 3 [ 145, 2, 1 ][ 5, 7, 7 ][] Total time: 8.139 seconds, Total memory usage: 3.69MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:31:56 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(145,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(290,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Sat Dec 20 2003 00:31:46 on modular [Seed = 570278047] ------------------------------------- 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 2 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/23 Defined on 1 generator Relations: 23*$.1 = 0 Abelian Group of order 1 3 Abelian Group of order 1 Abelian Group of order 1 Abelian Group of order 1 Abelian Group isomorphic to Z/13 Defined on 1 generator Relations: 13*$.1 = 0 4 Abelian Group isomorphic to Z/8 Defined on 1 generator Relations: 8*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 5 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/14 Defined on 1 generator Relations: 14*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 9.510 seconds, Total memory usage: 4.58MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:33:44 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(58,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(290,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Sat Dec 20 2003 00:33:35 on modular [Seed = 432404810] ------------------------------------- 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Abelian Group of order 1 2 Abelian Group of order 1 Abelian Group of order 1 3 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Abelian Group of order 1 4 Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 5 Abelian Group of order 1 Abelian Group of order 1 Total time: 8.389 seconds, Total memory usage: 4.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:34:48 2003 Input: N:=290; q:=3; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [5..5] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:34:31 on modular [Seed = 315552265] ------------------------------------- 3 [ 290, 5, 1 ][ 2, 49, 7 ][] Total time: 16.819 seconds, Total memory usage: 7.40MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:36:51 2003 Input: N:=341; q:=2; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..1] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:36:18 on modular [Seed = 115009192] ------------------------------------- 2 [ 341, 1, 1 ][ 11, 1, 1 ][] Total time: 32.399 seconds, Total memory usage: 5.23MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:37:47 2003 Input: N:=341; q:=2; print q; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..1] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [2..2] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j],Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; //erdos Output: Magma V2.10-6 Sat Dec 20 2003 00:37:21 on modular [Seed = 4263649683] ------------------------------------- 2 [ 341, 1, 1 ][ 31, 1, 1 ][] Total time: 26.139 seconds, Total memory usage: 5.22MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:38:21 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(341,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Sat Dec 20 2003 00:38:14 on modular [Seed = 4129958348] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 3 Abelian Group isomorphic to Z/7 + Z/7 Defined on 2 generators Relations: 7*$.1 = 0 7*$.2 = 0 4 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 6.329 seconds, Total memory usage: 4.33MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:41:38 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(11,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(341,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Sat Dec 20 2003 00:41:32 on modular [Seed = 3256753330] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 2 Abelian Group of order 1 3 Abelian Group of order 1 4 Abelian Group isomorphic to Z/39 Defined on 1 generator Relations: 39*$.1 = 0 Total time: 6.129 seconds, Total memory usage: 4.36MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Dec 20 00:42:50 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(11,2,+1))))); B:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(31,2,+1))))); for j in [1..#B] do print j; for i in [1..#A] do CongruenceGroupAnemic(A[i],B[j],200); end for;end for; Output: Magma V2.10-6 Sat Dec 20 2003 00:42:46 on modular [Seed = 3127272592] ------------------------------------- 1 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 3.849 seconds, Total memory usage: 3.95MB ************** MAGMA ***************** Host ad4-m118.net.hinet.hr. (195.29.132.118) Time: Sat Dec 20 02:29:57 2003 Input: x=[[2,5],[3,8]]; qflll(x,1); Output: Magma V2.10-6 Sat Dec 20 2003 02:29:54 on modular [Seed = 3690994133] ------------------------------------- >> x=[[2,5],[3,8]]; ^ User error: Identifier 'x' has not been declared or assigned >> qflll(x,1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.190.141.186) Time: Sat Dec 20 11:19:21 2003 Input: A := AffineSpace(Rationals(),2); C := Curve(A,x^2-y^3); p := Origin(A); IsCusp(C,p); IsDoublePoint(C,p); IsReduced(TangentCone(C,p)); D := Curve(A,x^2 - y^3 - y^2); IsAnalyticallyIrreducible(D,p); IsNode(D,p); Output: Magma V2.10-6 Sat Dec 20 2003 11:19:18 on modular [Seed = 2203634288] ------------------------------------- true true false false true Total time: 3.169 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.190.141.186) Time: Sat Dec 20 11:19:38 2003 Input: A := AffineSpace(Rationals(),2); C := Curve(A,x^2-y^3); p := Origin(A); IsCusp(C,p); IsDoublePoint(C,p); IsReduced(TangentCone(C,p)); D := Curve(A,x^2 - y^3 - y^2); IsAnalyticallyIrreducible(D,p); IsNode(D,p); Output: Magma V2.10-6 Sat Dec 20 2003 11:19:34 on modular [Seed = 2091333022] ------------------------------------- true true false false true Total time: 3.079 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 000-246-640.area1.spcsdns.net. (68.27.191.178) Time: Sat Dec 20 11:31:47 2003 Input: 2+2 Output: Magma V2.10-6 Sat Dec 20 2003 11:31:44 on modular [Seed = 3540555223] ------------------------------------- 4 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:26:56 2003 Input: Log(2,1920834759802137698123074593872904752093847) Output: Magma V2.10-6 Sat Dec 20 2003 18:26:53 on modular [Seed = 3591189274] ------------------------------------- 140.462713401478518347519089487041 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:28:15 2003 Input: F:=GF(2); K:=GF(2^300); K; Output: Magma V2.10-6 Sat Dec 20 2003 18:28:12 on modular [Seed = 3239716284] ------------------------------------- Finite field of size 2^300 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:28:48 2003 Input: F:=GF(2); K:=GF(2^300); K; EllipticCurve(3); Output: Magma V2.10-6 Sat Dec 20 2003 18:28:44 on modular [Seed = 3424069776] ------------------------------------- Finite field of size 2^300 Warning! Deprecated function EllipticCurve(j) called. This function will be removed in a future release; use EllipticCurveFromjInvariant(j) instead. Elliptic Curve defined by y^2 + x*y = x^3 + 12/575*x + 1/1725 over Rational Field Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:29:06 2003 Input: F:=GF(2); K:=GF(2^300); K; EllipticCurve(K,3); Output: Magma V2.10-6 Sat Dec 20 2003 18:29:03 on modular [Seed = 3077329913] ------------------------------------- Finite field of size 2^300 >> EllipticCurve(K,3);; ^ Runtime error in 'EllipticCurve': Bad argument types Argument types given: FldFin, RngIntElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:29:17 2003 Input: F:=GF(2); K:=GF(2^300); K; EllipticCurve(K!3); Output: Magma V2.10-6 Sat Dec 20 2003 18:29:14 on modular [Seed = 3194313349] ------------------------------------- Finite field of size 2^300 Warning! Deprecated function EllipticCurve(j) called. This function will be removed in a future release; use EllipticCurveFromjInvariant(j) instead. Elliptic Curve defined by y^2 + x*y = x^3 + 1 over GF(2^300) Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:29:52 2003 Input: F:=GF(2); K:=GF(2^300); K; E:=EllipticCurve(K!3); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:29:48 on modular [Seed = 2826128565] ------------------------------------- Finite field of size 2^300 Warning! Deprecated function EllipticCurve(j) called. This function will be removed in a future release; use EllipticCurveFromjInvariant(j) instead. 2037035976334486086268445688409378161051468393737835163532945699668533836685346\ 590081763504 Total time: 3.349 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:30:38 2003 Input: F:=GF(2); K:=GF(2^300); K; SetVerbose("SEA",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:30:33 on modular [Seed = 2554559600] ------------------------------------- Finite field of size 2^300 Order to be computed over smaller field Finite field of size 2 Enumerating points over the smaller field. Found 4 points over the subfield of size 2^1 2037035976334486086268445688409378161051468393737835163532945699668533836685346\ 590081763504 Total time: 3.419 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:30:57 2003 Input: F:=GF(2); K:=GF(2^301); K; SetVerbose("SEA",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:30:54 on modular [Seed = 2203608924] ------------------------------------- Finite field of size 2^301 Order to be computed over smaller field Finite field of size 2 Enumerating points over the smaller field. Found 4 points over the subfield of size 2^1 4074071952668972172536891376818756322102936791070867453740233881963177741887073\ 501874850252 Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:31:33 2003 Input: F:=GF(2); K:=GF(2^301); K; SetVerbose("SEA",5); SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:31:30 on modular [Seed = 2320592425] ------------------------------------- Finite field of size 2^301 Order to be computed over smaller field Finite field of size 2 Enumerating points over the smaller field. Found 4 points over the subfield of size 2^1 4074071952668972172536891376818756322102936791070867453740233881963177741887073\ 501874850252 Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:32:28 2003 Input: F:=GF(2); t:=2^301; K:=GF(NextPrime(t)); K; SetVerbose("SEA",5); SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 20 2003 18:32:05 on modular [Seed = 1957662961] ------------------------------------- Finite field of size 4074071952668972172536891376818756322102936787331872501272\ 280898708762599526673412366794779 Computing torsion data for Elliptic Curve defined by y^2 = x^3 + 15323529326324855117067199051723010644837\ 16912655513349119838695996219729916173793252887558*x + 2630917249966398919929776478702931933375084696407053148119307338250496192466883\ 730841591655 over GF(4074071952668972172536891376818756322102936787331872501272\ 280898708762599526673412366794779) Setting low_entropy to 8.1088 Setting max_entropy to 9.6088 ----------------------------------------- Computing trace mod 2. Prime 2 is Ramified Trace is 0 mod 2. ----------------------------------------- Computing trace mod 3 Computing x^q mod modular equation (degree 4). Time: 0.020 Number of roots: 2 Prime 3 is Elkies. Characterization time: 0.03 Processing Elkies prime 3 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 1). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..(match) Baby step time: 0 Found baby step match: 1 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 1 mod 3 Trace = 0 mod 3 Sign time: 0 Trace 0 mod 3. Trace computation time: 0.019 Total prime time = 0.049 ----------------------------------------- Current run time = 0.049 ----------------------------------------- CRT Moduli: Log(Elkies) = 0.77815125 Log(Atkin) = 0 Log(Total) = 0.77815125 Log(Weil) = 45.9071 Entropy: Absolute = -0.77815125 Relative = 0 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Processing prime power 3^2 Elkies: computing modular points. Time: 0.030 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 3) Time: 0.020 Doing eigenvalue loop Computing IsEigenvalue: 2 Time: 0 Eigenvalue = 2 mod 9 Trace = 3 mod 9 Trace computation time: 0.059 Total prime time = 0.059 ----------------------------------------- Current run time = 0.109 ----------------------------------------- CRT Moduli: Log(Elkies) = 1.2552 Log(Atkin) = 0 Log(Total) = 1.2553 Log(Weil) = 45.9071 Entropy: Absolute = -1.2553 Relative = 0 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Computing trace mod 5 Computing x^q mod modular equation (degree 6). Time: 0.040 Number of roots: 2 Prime 5 is Elkies. Characterization time: 0.051 Processing Elkies prime 5 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 2). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..(match) Baby step time: 0.001 Found baby step match: 1 Determining sign on y coordinate. Sign time: 0.011 Eigenvalue = 1 mod 5 Trace = 0 mod 5 Sign time: 0.011 Trace 0 mod 5. Trace computation time: 0.029 Total prime time = 0.08 ----------------------------------------- Current run time = 0.189 ----------------------------------------- CRT Moduli: Log(Elkies) = 1.9542 Log(Atkin) = 0 Log(Total) = 1.9542 Log(Weil) = 45.9071 Entropy: Absolute = -1.9542 Relative = 0 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Computing trace mod 7 Computing x^q mod modular equation (degree 8). Time: 0.060 Number of roots: 0 Prime 7 is Atkin. Characterization time: 0.07 Processing Atkin prime 7 Modular_eqn degree: 8 Possible r values: [ 2, 4 ] Performing Brent-Kung evaluations Total Brent-Kung time: 0 Found splitting degree r = 2 Possible values for t mod 7 are [ 0 ] Trace 0 mod 7. Trace computation time: 0.011 Total prime time = 0.091 ----------------------------------------- Current run time = 0.28 ----------------------------------------- CRT Moduli: Log(Elkies) = 2.7993 Log(Atkin) = 0 Log(Total) = 2.7993 Log(Weil) = 45.9071 Entropy: Absolute = -2.7993 Relative = 0 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Processing prime power 3^3 Elkies: computing modular points. Time: 0.030 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 9) Time: 0.140 Doing eigenvalue loop Computing IsEigenvalue: 2 Time: 0 Eigenvalue = 2 mod 27 Trace = 21 mod 27 Trace computation time: 0.179 Total prime time = 0.179 ----------------------------------------- Current run time = 0.459 ----------------------------------------- CRT Moduli: Log(Elkies) = 3.2765 Log(Atkin) = 0 Log(Total) = 3.2765 Log(Weil) = 45.9071 Entropy: Absolute = -3.2765 Relative = 0 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Computing trace mod 11 Computing x^q mod modular equation (degree 12). Time: 0.160 Number of roots: 0 Prime 11 is Atkin. Characterization time: 0.179 Processing Atkin prime 11 Modular_eqn degree: 12 Possible r values: [ 4, 12 ] Performing Brent-Kung evaluations Total Brent-Kung time: 0.01 Found splitting degree r = 4 Possible values for t mod 11 are [ 5, 6 ] Number of trace candidates: 2 Trace computation time: 0.01 Total prime time = 0.189 ----------------------------------------- Current run time = 0.649 ----------------------------------------- CRT Moduli: Log(Elkies) = 3.2765 Log(Atkin) = 1.0414 Log(Total) = 4.3179 Log(Weil) = 45.9071 Entropy: Absolute = -4.0168 Relative = 0.30103 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Processing prime power 5^2 Elkies: computing modular points. Time: 0.050 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 10) Time: 0.170 Doing eigenvalue loop Computing IsEigenvalue: 4..9 Time: 0.02 Eigenvalue = 9 mod 25 Trace = 15 mod 25 Trace computation time: 0.261 Total prime time = 0.261 ----------------------------------------- Current run time = 0.91 ----------------------------------------- CRT Moduli: Log(Elkies) = 3.9754 Log(Atkin) = 1.0414 Log(Total) = 5.0168 Log(Weil) = 45.9071 Entropy: Absolute = -4.7158 Relative = 0.30103 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Computing trace mod 13 Computing x^q mod modular equation (degree 14). Time: 0.220 Number of roots: 2 Prime 13 is Elkies. Characterization time: 0.229 Processing Elkies prime 13 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 6). Time: 0.070 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..3..4..(no match) Baby step time: 0.001 Doing giant steps... Looking for eigenvalue by giant steps... Computing multiplication maps from division polynomials. Multiplication map time: 0.001 Computing multiplicaton maps for x^q: j = 1..2..(no match) Giant step time: 0.011 Found giant step match: 5 Determining sign on y coordinate. Sign time: 0.07 Eigenvalue = 5 mod 13 Trace = 3 mod 13 Sign time: 0.07 Trace 3 mod 13. Trace computation time: 0.16 Total prime time = 0.399 ----------------------------------------- Current run time = 1.309 ----------------------------------------- CRT Moduli: Log(Elkies) = 5.0893 Log(Atkin) = 1.0414 Log(Total) = 6.1308 Log(Weil) = 45.9071 Entropy: Absolute = -5.8297 Relative = 0.30103 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Computing trace mod 17 Computing x^q mod modular equation (degree 18). Time: 0.400 Number of roots: 0 Prime 17 is Atkin. Characterization time: 0.4 Processing Atkin prime 17 Modular_eqn degree: 18 Possible r values: [ 3, 9 ] Performing Brent-Kung evaluations Total Brent-Kung time: 0.021 Found splitting degree r = 9 Possible values for t mod 17 are [ 1, 2, 3, 14, 15, 16 ] Number of trace candidates: 6 Trace computation time: 0.03 Total prime time = 0.431 ----------------------------------------- Current run time = 1.74 ----------------------------------------- CRT Moduli: Log(Elkies) = 5.0893 Log(Atkin) = 2.2718 Log(Total) = 7.3612 Log(Weil) = 45.9071 Entropy: Absolute = -6.282 Relative = 1.0792 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Computing trace mod 19 Computing x^q mod modular equation (degree 20). Time: 0.380 Number of roots: 2 Prime 19 is Elkies. Characterization time: 0.399 Processing Elkies prime 19 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 9). Time: 0.140 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..(match) Baby step time: 0 Found baby step match: 1 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 1 mod 19 Trace = 7 mod 19 Sign time: 0 Trace 7 mod 19. Trace computation time: 0.17 Total prime time = 0.579 ----------------------------------------- Current run time = 2.319 ----------------------------------------- CRT Moduli: Log(Elkies) = 6.3681 Log(Atkin) = 2.2718 Log(Total) = 8.64 Log(Weil) = 45.9071 Entropy: Absolute = -7.5608 Relative = 1.0792 Low exit = 8.1088 Max exit = 9.6088 ----------------------------------------- Computing trace mod 23 Computing x^q mod modular equation (degree 24). Time: 0.740 Number of roots: 0 Prime 23 is Atkin. Characterization time: 0.75 Processing Atkin prime 23 Modular_eqn degree: 24 Possible r values: [ 8, 24 ] Performing Brent-Kung evaluations Total Brent-Kung time: 0.09 Found splitting degree r = 8 Possible values for t mod 23 are [ 3, 5, 18, 20 ] Number of trace candidates: 4 Trace computation time: 0.09 Total prime time = 0.84 ----------- ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 20228 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:33:25 2003 Input: F:=GF(2); t:=2^101; K:=GF(NextPrime(t)); K; SetVerbose("SEA",5); SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:33:20 on modular [Seed = 2108071501] ------------------------------------- Finite field of size 2535301200456458802993406410833 Computing torsion data for Elliptic Curve defined by y^2 = x^3 + 615729128502160991176260984486*x + 2501094026650783192372503022806 over GF(2535301200456458802993406410833) Setting low_entropy to 4.8624 Setting max_entropy to 6.3624 ----------------------------------------- Computing trace mod 2. Prime 2 is Ramified Trace is 0 mod 2. ----------------------------------------- Computing trace mod 3 Computing x^q mod modular equation (degree 4). Time: 0.000 Number of roots: 2 Prime 3 is Elkies. Characterization time: 0 Processing Elkies prime 3 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 1). Time: 0.000 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..(match) Baby step time: 0 Found baby step match: 1 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 1 mod 3 Trace = 0 mod 3 Sign time: 0 Trace 0 mod 3. Trace computation time: 0.02 Total prime time = 0.02 ----------------------------------------- Current run time = 0.02 ----------------------------------------- CRT Moduli: Log(Elkies) = 0.77815125 Log(Atkin) = 0 Log(Total) = 0.77815125 Log(Weil) = 15.8041 Entropy: Absolute = -0.77815125 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Processing prime power 3^2 Elkies: computing modular points. Time: 0.010 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 3) Time: 0.000 Doing eigenvalue loop Computing IsEigenvalue: 1..4..7 Time: 0 Eigenvalue = 7 mod 9 Trace = 0 mod 9 Trace computation time: 0.02 Total prime time = 0.02 ----------------------------------------- Current run time = 0.04 ----------------------------------------- CRT Moduli: Log(Elkies) = 1.2552 Log(Atkin) = 0 Log(Total) = 1.2553 Log(Weil) = 15.8041 Entropy: Absolute = -1.2553 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 5 Computing x^q mod modular equation (degree 6). Time: 0.000 Number of roots: 2 Prime 5 is Elkies. Characterization time: 0.009 Processing Elkies prime 5 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 2). Time: 0.000 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..(match) Baby step time: 0 Found baby step match: 1 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 1 mod 5 Trace = 1 mod 5 Sign time: 0 Trace 1 mod 5. Trace computation time: 0.011 Total prime time = 0.02 ----------------------------------------- Current run time = 0.06 ----------------------------------------- CRT Moduli: Log(Elkies) = 1.9542 Log(Atkin) = 0 Log(Total) = 1.9542 Log(Weil) = 15.8041 Entropy: Absolute = -1.9542 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 7 Computing x^q mod modular equation (degree 8). Time: 0.010 Number of roots: 2 Prime 7 is Elkies. Characterization time: 0.02 Processing Elkies prime 7 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 3). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..(match) Baby step time: 0 Found baby step match: 2 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 2 mod 7 Trace = 1 mod 7 Sign time: 0 Trace 1 mod 7. Trace computation time: 0.009 Total prime time = 0.029 ----------------------------------------- Current run time = 0.09 ----------------------------------------- CRT Moduli: Log(Elkies) = 2.7993 Log(Atkin) = 0 Log(Total) = 2.7993 Log(Weil) = 15.8041 Entropy: Absolute = -2.7993 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Processing prime power 3^3 Elkies: computing modular points. Time: 0.010 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 9) Time: 0.010 Doing eigenvalue loop Computing IsEigenvalue: 7..16..25 Time: 0.009 Eigenvalue = 25 mod 27 Trace = 0 mod 27 Trace computation time: 0.04 Total prime time = 0.04 ----------------------------------------- Current run time = 0.13 ----------------------------------------- CRT Moduli: Log(Elkies) = 3.2765 Log(Atkin) = 0 Log(Total) = 3.2765 Log(Weil) = 15.8041 Entropy: Absolute = -3.2765 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 11 Computing x^q mod modular equation (degree 12). Time: 0.030 Number of roots: 2 Prime 11 is Elkies. Characterization time: 0.031 Processing Elkies prime 11 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 5). Time: 0.000 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..3..4..(no match) Baby step time: 0.011 Doing giant steps... Looking for eigenvalue by giant steps... Computing multiplication maps from division polynomials. Multiplication map time: 0 Computing multiplicaton maps for x^q: j = 1..(no match) Giant step time: 0 Found giant step match: 5 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 5 mod 11 Trace = 7 mod 11 Sign time: 0 Trace 7 mod 11. Trace computation time: 0.02 Total prime time = 0.051 ----------------------------------------- Current run time = 0.181 ----------------------------------------- CRT Moduli: Log(Elkies) = 4.3179 Log(Atkin) = 0 Log(Total) = 4.3179 Log(Weil) = 15.8041 Entropy: Absolute = -4.3179 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Processing prime power 5^2 Elkies: computing modular points. Time: 0.010 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 10) Time: 0.020 Doing eigenvalue loop Computing IsEigenvalue: 4..9 Time: 0 Eigenvalue = 9 mod 25 Trace = 21 mod 25 Trace computation time: 0.049 Total prime time = 0.049 ----------------------------------------- Current run time = 0.23 ----------------------------------------- CRT Moduli: Log(Elkies) = 5.0168 Log(Atkin) = 0 Log(Total) = 5.0168 Log(Weil) = 15.8041 Entropy: Absolute = -5.0168 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 13 Computing x^q mod modular equation (degree 14). Time: 0.030 Number of roots: 2 Prime 13 is Elkies. Characterization time: 0.031 Processing Elkies prime 13 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 6). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..3..4..(no match) Baby step time: 0 Doing giant steps... Looking for eigenvalue by giant steps... Computing multiplication maps from division polynomials. Multiplication map time: 0 Computing multiplicaton maps for x^q: j = 1..2..(no match) Giant step time: 0 Found giant step match: 5 Determining sign on y coordinate. Sign time: 0.011 Eigenvalue = 5 mod 13 Trace = 12 mod 13 Sign time: 0.011 Trace 12 mod 13. Trace computation time: 0.029 Total prime time = 0.06 ----------------------------------------- Current run time = 0.29 ----------------------------------------- CRT Moduli: Log(Elkies) = 6.1307 Log(Atkin) = 0 Log(Total) = 6.1308 Log(Weil) = 15.8041 Entropy: Absolute = -6.1308 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 17 Computing x^q mod modular equation (degree 18). Time: 0.040 Number of roots: 0 Prime 17 is Atkin. Characterization time: 0.049 Processing Atkin prime 17 Modular_eqn degree: 18 Possible r values: [ 2, 6, 18 ] Performing Brent-Kung evaluations Total Brent-Kung time: 0.009 Found splitting degree r = 18 Possible values for t mod 17 are [ 2, 15, 7, 8, 9, 10 ] Number of trace candidates: 6 Trace computation time: 0.02 Total prime time = 0.08 ----------------------------------------- Current run time = 0.37 ----------------------------------------- CRT Moduli: Log(Elkies) = 6.1307 Log(Atkin) = 1.2304 Log(Total) = 7.3612 Log(Weil) = 15.8041 Entropy: Absolute = -6.5831 Relative = 0.77815125 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 19 Computing x^q mod modular equation (degree 20). Time: 0.050 Number of roots: 2 Prime 19 is Elkies. Characterization time: 0.049 Processing Elkies prime 19 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 9). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..3..4..5..(match) Baby step time: 0.009 Found baby step match: 5 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 5 mod 19 Trace = 10 mod 19 Sign time: 0 Trace 10 mod 19. Trace computation time: 0.04 Total prime time = 0.089 ----------------------------------------- Current run time = 0.46 ----------------------------------------- CRT Moduli: Log(Elkies) = 7.4095 Log(Atkin) = 1.2304 Log(Total) = 8.64 Log(Weil) = 15.8041 Entropy: Absolute = -7.8618 Relative = 0.77815125 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 23 Computing x^q mod modular equation (degree 24). Time: 0.070 Number of roots: 1 Possible values for t mod 23 are [ 15, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:33:51 2003 Input: F:=GF(2); t:=2^101; K:=GF(NextPrime(t)); K; SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:33:47 on modular [Seed = 1723696461] ------------------------------------- Finite field of size 2535301200456458802993406410833 Computing torsion data for Elliptic Curve defined by y^2 = x^3 + 615729128502160991176260984486*x + 2501094026650783192372503022806 over GF(2535301200456458802993406410833) Setting low_entropy to 4.8624 Setting max_entropy to 6.3624 ----------------------------------------- Computing trace mod 2. Prime 2 is Ramified Trace is 0 mod 2. ----------------------------------------- Computing trace mod 3 Computing x^q mod modular equation (degree 4). Time: 0.000 Number of roots: 2 Prime 3 is Elkies. Characterization time: 0.011 Processing Elkies prime 3 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 1). Time: 0.000 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..(match) Baby step time: 0 Found baby step match: 1 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 1 mod 3 Trace = 0 mod 3 Sign time: 0 Trace 0 mod 3. Trace computation time: 0.009 Total prime time = 0.02 ----------------------------------------- Current run time = 0.02 ----------------------------------------- CRT Moduli: Log(Elkies) = 0.77815125 Log(Atkin) = 0 Log(Total) = 0.77815125 Log(Weil) = 15.8041 Entropy: Absolute = -0.77815125 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Processing prime power 3^2 Elkies: computing modular points. Time: 0.010 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 3) Time: 0.000 Doing eigenvalue loop Computing IsEigenvalue: 1..4..7 Time: 0 Eigenvalue = 7 mod 9 Trace = 0 mod 9 Trace computation time: 0.02 Total prime time = 0.02 ----------------------------------------- Current run time = 0.04 ----------------------------------------- CRT Moduli: Log(Elkies) = 1.2552 Log(Atkin) = 0 Log(Total) = 1.2553 Log(Weil) = 15.8041 Entropy: Absolute = -1.2553 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 5 Computing x^q mod modular equation (degree 6). Time: 0.000 Number of roots: 2 Prime 5 is Elkies. Characterization time: 0.011 Processing Elkies prime 5 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 2). Time: 0.000 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..(match) Baby step time: 0 Found baby step match: 1 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 1 mod 5 Trace = 1 mod 5 Sign time: 0 Trace 1 mod 5. Trace computation time: 0.009 Total prime time = 0.031 ----------------------------------------- Current run time = 0.071 ----------------------------------------- CRT Moduli: Log(Elkies) = 1.9542 Log(Atkin) = 0 Log(Total) = 1.9542 Log(Weil) = 15.8041 Entropy: Absolute = -1.9542 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 7 Computing x^q mod modular equation (degree 8). Time: 0.010 Number of roots: 2 Prime 7 is Elkies. Characterization time: 0.009 Processing Elkies prime 7 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 3). Time: 0.000 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..(match) Baby step time: 0 Found baby step match: 2 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 2 mod 7 Trace = 1 mod 7 Sign time: 0 Trace 1 mod 7. Trace computation time: 0.011 Total prime time = 0.02 ----------------------------------------- Current run time = 0.091 ----------------------------------------- CRT Moduli: Log(Elkies) = 2.7993 Log(Atkin) = 0 Log(Total) = 2.7993 Log(Weil) = 15.8041 Entropy: Absolute = -2.7993 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Processing prime power 3^3 Elkies: computing modular points. Time: 0.000 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 9) Time: 0.010 Doing eigenvalue loop Computing IsEigenvalue: 7..16..25 Time: 0.009 Eigenvalue = 25 mod 27 Trace = 0 mod 27 Trace computation time: 0.039 Total prime time = 0.039 ----------------------------------------- Current run time = 0.13 ----------------------------------------- CRT Moduli: Log(Elkies) = 3.2765 Log(Atkin) = 0 Log(Total) = 3.2765 Log(Weil) = 15.8041 Entropy: Absolute = -3.2765 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 11 Computing x^q mod modular equation (degree 12). Time: 0.020 Number of roots: 2 Prime 11 is Elkies. Characterization time: 0.031 Processing Elkies prime 11 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 5). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..3..4..(no match) Baby step time: 0 Doing giant steps... Looking for eigenvalue by giant steps... Computing multiplication maps from division polynomials. Multiplication map time: 0 Computing multiplicaton maps for x^q: j = 1..(no match) Giant step time: 0 Found giant step match: 5 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 5 mod 11 Trace = 7 mod 11 Sign time: 0 Trace 7 mod 11. Trace computation time: 0.02 Total prime time = 0.051 ----------------------------------------- Current run time = 0.181 ----------------------------------------- CRT Moduli: Log(Elkies) = 4.3179 Log(Atkin) = 0 Log(Total) = 4.3179 Log(Weil) = 15.8041 Entropy: Absolute = -4.3179 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Processing prime power 5^2 Elkies: computing modular points. Time: 0.000 In prime power Schoof algorithm... Computing x^q mod kernel polynomial (degree 10) Time: 0.010 Doing eigenvalue loop Computing IsEigenvalue: 4..9 Time: 0.011 Eigenvalue = 9 mod 25 Trace = 21 mod 25 Trace computation time: 0.04 Total prime time = 0.04 ----------------------------------------- Current run time = 0.221 ----------------------------------------- CRT Moduli: Log(Elkies) = 5.0168 Log(Atkin) = 0 Log(Total) = 5.0168 Log(Weil) = 15.8041 Entropy: Absolute = -5.0168 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 13 Computing x^q mod modular equation (degree 14). Time: 0.020 Number of roots: 2 Prime 13 is Elkies. Characterization time: 0.029 Processing Elkies prime 13 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 6). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..3..4..(no match) Baby step time: 0 Doing giant steps... Looking for eigenvalue by giant steps... Computing multiplication maps from division polynomials. Multiplication map time: 0 Computing multiplicaton maps for x^q: j = 1..2..(no match) Giant step time: 0.011 Found giant step match: 5 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 5 mod 13 Trace = 12 mod 13 Sign time: 0 Trace 12 mod 13. Trace computation time: 0.031 Total prime time = 0.069 ----------------------------------------- Current run time = 0.29 ----------------------------------------- CRT Moduli: Log(Elkies) = 6.1307 Log(Atkin) = 0 Log(Total) = 6.1308 Log(Weil) = 15.8041 Entropy: Absolute = -6.1308 Relative = 0 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 17 Computing x^q mod modular equation (degree 18). Time: 0.050 Number of roots: 0 Prime 17 is Atkin. Characterization time: 0.051 Processing Atkin prime 17 Modular_eqn degree: 18 Possible r values: [ 2, 6, 18 ] Performing Brent-Kung evaluations Total Brent-Kung time: 0.019 Found splitting degree r = 18 Possible values for t mod 17 are [ 2, 15, 7, 8, 9, 10 ] Number of trace candidates: 6 Trace computation time: 0.019 Total prime time = 0.07 ----------------------------------------- Current run time = 0.36 ----------------------------------------- CRT Moduli: Log(Elkies) = 6.1307 Log(Atkin) = 1.2304 Log(Total) = 7.3612 Log(Weil) = 15.8041 Entropy: Absolute = -6.5831 Relative = 0.77815125 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 19 Computing x^q mod modular equation (degree 20). Time: 0.040 Number of roots: 2 Prime 19 is Elkies. Characterization time: 0.06 Processing Elkies prime 19 Entering Schoof computation on kernel polynomial. Computing x^q modulo the kernel polynomial (degree 9). Time: 0.010 Doing baby steps... Looking for eigenvalue by baby steps... Computing division polynomials: 1..2..3..4..5..(match) Baby step time: 0 Found baby step match: 5 Determining sign on y coordinate. Sign time: 0 Eigenvalue = 5 mod 19 Trace = 10 mod 19 Sign time: 0 Trace 10 mod 19. Trace computation time: 0.031 Total prime time = 0.091 ----------------------------------------- Current run time = 0.46 ----------------------------------------- CRT Moduli: Log(Elkies) = 7.4095 Log(Atkin) = 1.2304 Log(Total) = 8.64 Log(Weil) = 15.8041 Entropy: Absolute = -7.8618 Relative = 0.77815125 Low exit = 4.8624 Max exit = 6.3624 ----------------------------------------- Computing trace mod 23 Computing x^q mod modular equation (degree 24). Time: 0.070 Number of roots: 1 Possible values for t mod 23 are [ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:34:29 2003 Input: F:=GF(2); t:=2^101; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:34:23 on modular [Seed = 1874103392] ------------------------------------- Finite field of size 2535301200456458802993406410833 2535301200456456074666252949588 Total time: 4.139 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:35:06 2003 Input: F:=GF(2); t:=2^201; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!3); Order(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 20 2003 18:34:43 on modular [Seed = 1501739706] ------------------------------------- Finite field of size 3213876088517980551083924184682325205044405987565585670603\ 103 Errors: /home/mfd/gomagma: line 2: 20265 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:43:20 2003 Input: F:=GF(2); t:=2^101; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!5); Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:43:16 on modular [Seed = 987880414] ------------------------------------- Finite field of size 2535301200456458802993406410833 2535301200456457409695713064512 Total time: 4.439 seconds, Total memory usage: 3.22MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:43:24 2003 Input: F:=GF(2); t:=2^201; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!5); Order(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Dec 20 2003 18:43:01 on modular [Seed = 938268354] ------------------------------------- Finite field of size 3213876088517980551083924184682325205044405987565585670603\ 103 Errors: /home/mfd/gomagma: line 2: 20295 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:43:42 2003 Input: F:=GF(2); t:=2^101; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!5); E; Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:43:37 on modular [Seed = 687065585] ------------------------------------- Finite field of size 2535301200456458802993406410833 Elliptic Curve defined by y^2 + x*y = x^3 + 1946722860246021472060520418765*x + 1955551535349178032024513708646 over GF(2535301200456458802993406410833) 2535301200456457409695713064512 Total time: 4.409 seconds, Total memory usage: 3.22MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:43:57 2003 Input: F:=GF(2); t:=2^101; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!7); E; Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:43:53 on modular [Seed = 298512600] ------------------------------------- Finite field of size 2535301200456458802993406410833 Elliptic Curve defined by y^2 + x*y = x^3 + 799923621062090139468576223755*x + 1501145800851325694509169745868 over GF(2535301200456458802993406410833) 2535301200456457604056092011064 Total time: 4.149 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:44:16 2003 Input: F:=GF(2); t:=2^141; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!7); E; Order(E); Output: Magma V2.10-6 Sat Dec 20 2003 18:44:06 on modular [Seed = 448920492] ------------------------------------- Finite field of size 2787593149816327892691964784081045188247557 Elliptic Curve defined by y^2 + x*y = x^3 + 1885391299469032926841049975985088087809504*x + 981569697146249101087350760693267509632783 over GF(2787593149816327892691964784081045188247557) 2787593149816327892690718026337817334298368 Total time: 9.449 seconds, Total memory usage: 3.55MB ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:44:52 2003 Input: F:=GF(2); t:=2^141; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!7); E; ShowMemoryUsage(); Order(E); ShowMemoryUsage(); Output: WARNING: MAGMA command contains unsafe command 'memory', so it will not be executed. ************** MAGMA ***************** Host 2(SERVFAIL) (62.248.73.142) Time: Sat Dec 20 18:45:09 2003 Input: F:=GF(2); t:=2^141; K:=GF(NextPrime(t)); K; //SetVerbose("SEA",5); //SetVerbose("ECPointCount",5); E:=EllipticCurveFromjInvariant(K!7); E; //ShowMemoryUsage(); Order(E); //ShowMemoryUsage(); Output: WARNING: MAGMA command contains unsafe command 'memory', so it will not be executed. ************** MAGMA ***************** Host wbar1.sjo1-4-4-001-026.sjo1.dsl-verizon.net. (4.4.1.26) Time: Sat Dec 20 19:49:42 2003 Input: (x+y)^100 Output: Magma V2.10-6 Sat Dec 20 2003 19:49:39 on modular [Seed = 1790032678] ------------------------------------- >> (x+y)^100; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ool-182dcc14.dyn.optonline.net. (24.45.204.20) Time: Sat Dec 20 21:05:47 2003 Input: 4x=9 Output: Magma V2.10-6 Sat Dec 20 2003 21:05:43 on modular [Seed = 3574469954] ------------------------------------- >> 4x=9 ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host saci.Berkeley.EDU. (128.32.183.35) Time: Sat Dec 20 23:01:26 2003 Input: F:= FreeGroup(16); Output: Magma V2.10-6 Sat Dec 20 2003 23:01:23 on modular [Seed = 3507221932] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host saci.Berkeley.EDU. (128.32.183.35) Time: Sat Dec 20 23:09:42 2003 Input: F:= FreeGroup(16); for i := 0 to 16 do rel :=s_i^3=Id(F) ; end for; Output: Magma V2.10-6 Sat Dec 20 2003 23:09:39 on modular [Seed = 3211107794] ------------------------------------- >> rel :=s_i^3=Id(F) ; ^ User error: Identifier 's_i' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host saci.Berkeley.EDU. (128.32.183.35) Time: Sat Dec 20 23:10:23 2003 Input: > G := Group< x, y, z, h, k, a | > x^2, y^2, z^2, (x,y), (y,z), (x,z), h^3, k^3, (h,k), > (x,k), (y,k), (z,k), x^h*y, y^h*z, z^h*x, a^2, a*x*a*y, > a*y*a*x, (a,z), (a,k), (a*h)^2 >; > for i := 0 to 1 do > for j := 0 to 1 do > for k := 0 to 1 do > for l := 0 to 2 do > rel := G.1^i*G.2^j*G.3^k*G.5^l*(G.6*G.4)^2 = Id(G); > K := ReplaceRelation(G, 21, rel); > print Order(K), Index(K, sub< K | K.6, K.4>); > end for; > end for; > end for; > end for; Output: Magma V2.10-6 Sat Dec 20 2003 23:10:15 on modular [Seed = 2404756934] ------------------------------------- 144 24 144 8 144 8 18 3 18 1 18 1 72 3 72 1 72 1 36 6 36 2 36 2 18 3 18 1 18 1 144 6 144 2 144 2 36 6 36 2 36 2 72 12 72 4 72 4 Total time: 7.949 seconds, Total memory usage: 17.72MB ************** MAGMA ***************** Host saci.Berkeley.EDU. (128.32.183.35) Time: Sat Dec 20 23:11:07 2003 Input: G := Group< x, y, z, h, k, a | x^2, y^2, z^2, (x,y), (y,z), (x,z), h^3, k^3, (h,k), (x,k), (y,k), (z,k), x^h*y, y^h*z, z^h*x, a^2, a*x*a*y, a*y*a*x, (a,z), (a,k), (a*h)^2 >; Output: Magma V2.10-6 Sat Dec 20 2003 23:11:04 on modular [Seed = 2220795570] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:48:17 2003 Input: c=1 Output: Magma V2.10-6 Sun Dec 21 2003 01:48:14 on modular [Seed = 2153446851] ------------------------------------- >> c=1; ^ User error: Identifier 'c' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:48:26 2003 Input: c:=1 Output: Magma V2.10-6 Sun Dec 21 2003 01:48:23 on modular [Seed = 2604787393] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:48:39 2003 Input: c:=1; print(c); Output: Magma V2.10-6 Sun Dec 21 2003 01:48:36 on modular [Seed = 2454253499] ------------------------------------- 1 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:51:14 2003 Input: P:= FunctionField(GF(5)); Output: Magma V2.10-6 Sun Dec 21 2003 01:51:11 on modular [Seed = 2124678093] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:51:49 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); Output: Magma V2.10-6 Sun Dec 21 2003 01:51:46 on modular [Seed = 2007829273] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:52:18 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^3+t*x+t^2; Output: Magma V2.10-6 Sun Dec 21 2003 01:52:15 on modular [Seed = 1217541179] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:52:28 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^3+t*x+t^2; print(t); Output: Magma V2.10-6 Sun Dec 21 2003 01:52:25 on modular [Seed = 1100692740] ------------------------------------- t Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (69.162.40.105) Time: Sun Dec 21 01:52:42 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^3+7*t*x+t^2; print(f); Output: Magma V2.10-6 Sun Dec 21 2003 01:52:39 on modular [Seed = 1518347777] ------------------------------------- x^3 + 2*t*x + t^2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:53:21 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^3+7*t*x+t^2; print(f); G, R:= GaloisGroup(f) Output: Magma V2.10-6 Sun Dec 21 2003 01:53:17 on modular [Seed = 1401499490] ------------------------------------- x^3 + 2*t*x + t^2 Total time: 3.389 seconds, Total memory usage: 6.52MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:53:43 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^3+7*t*x+t^2; print(f); G, R:= GaloisGroup(f); print(G); Output: Magma V2.10-6 Sun Dec 21 2003 01:53:39 on modular [Seed = 620648507] ------------------------------------- x^3 + 2*t*x + t^2 Permutation group G acting on a set of cardinality 3 (1, 3) (1, 2) Total time: 3.299 seconds, Total memory usage: 6.52MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:54:14 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+t*x+1; print(f); G, R:= GaloisGroup(f); print(G); Output: Magma V2.10-6 Sun Dec 21 2003 01:54:11 on modular [Seed = 1038565826] ------------------------------------- x^5 + t*x + 1 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 2, 4, 3) Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:54:49 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+t*x+1; print(f); G, R:= GaloisGroup(f); print(G); print(R); Output: Magma V2.10-6 Sun Dec 21 2003 01:54:46 on modular [Seed = 938298349] ------------------------------------- x^5 + t*x + 1 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 2, 4, 3) [ w^260*$.1^7 + $.1^6 + w^364*$.1^5 + w^338*$.1^4 + w^78*$.1^3 + w^442*$.1^2 + w^182*$.1 + w^546, w^581*$.1^7 + w^321*$.1^6 + w^61*$.1^5 + w^271*$.1^4 + w^11*$.1^3 + w^375*$.1^2 + w^115*$.1 + w^479, w^484*$.1^7 + w^224*$.1^6 + w^588*$.1^5 + w^72*$.1^4 + w^436*$.1^3 + w^176*$.1^2 + w^540*$.1 + w^280, w^244*$.1^7 + w^608*$.1^6 + w^348*$.1^5 + w^552*$.1^4 + w^292*$.1^3 + w^32*$.1^2 + w^396*$.1 + w^136, w^173*$.1^7 + w^537*$.1^6 + w^277*$.1^5 + w^535*$.1^4 + w^275*$.1^3 + w^15*$.1^2 + w^379*$.1 + w^119 ] Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:55:33 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+t*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 01:55:30 on modular [Seed = 81688714] ------------------------------------- x^5 + t*x + 1 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 2, 4, 3) 3 5 Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:57:01 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+t*x+T; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 01:56:58 on modular [Seed = 499607115] ------------------------------------- >> f:=x^5+t*x+T; ^ User error: Identifier 'T' has not been declared or assigned >> print(f); ^ User error: Identifier 'f' has not been declared or assigned >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:57:11 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+t*x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 01:57:08 on modular [Seed = 382496062] ------------------------------------- x^5 + t*x + t Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 2, 4, 3) 3 5 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:57:21 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 01:57:18 on modular [Seed = 4013266125] ------------------------------------- x^5 + x + t Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 01:57:31 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 01:57:28 on modular [Seed = 3761937364] ------------------------------------- x^5 + x + t^2 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 Total time: 2.949 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:00:06 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); TransitiveGroupDescription(t1,t2) Output: Magma V2.10-6 Sun Dec 21 2003 02:00:03 on modular [Seed = 4046162542] ------------------------------------- x^5 + x + t^2 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 TransitiveGroupDescription( d: 2, n: 5 ) In file "/usr/local/magma/package/Group/GrpData/trngps.m", line 333, column 43: >> return s where _, s is TransitiveGroup(d, n); ^ Runtime error in 'TransitiveGroup': The group number given (5) exceeds the number of transitive groups of degree 2 (1) Total time: 3.329 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:00:34 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); TransitiveGroupDescription(t2,t1) Output: Magma V2.10-6 Sun Dec 21 2003 02:00:29 on modular [Seed = 3390091432] ------------------------------------- x^5 + x + t^2 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 D(5) = 5:2 Total time: 3.289 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:01:02 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+t*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:00:59 on modular [Seed = 3273243012] ------------------------------------- x^5 + t*x + 1 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 2, 4, 3) 3 5 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:01:16 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+t^2*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:01:13 on modular [Seed = 2793200883] ------------------------------------- x^5 + t^2*x + 1 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 Total time: 3.309 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:01:28 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:01:25 on modular [Seed = 3211117974] ------------------------------------- x^5 + x + 1 >> G, R:= GaloisGroup(f); ^ Runtime error in 'GaloisGroup': Argument 1 is not irreducible >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2);; ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:01:39 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:01:36 on modular [Seed = 2959788684] ------------------------------------- x^5 + x + t Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:01:49 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:01:46 on modular [Seed = 2303980479] ------------------------------------- x^5 + x + t^2 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 Total time: 3.009 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:01:56 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:01:53 on modular [Seed = 2186868879] ------------------------------------- x^5 + x + t^2 Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 Total time: 2.959 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:02:09 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^5+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:02:06 on modular [Seed = 2604786073] ------------------------------------- x^5 + x + t Permutation group G acting on a set of cardinality 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) 2 5 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:05:45 2003 Input: Q:= PolynomialRing(Integers()); f:=x^6-10*x^5-3*x^4-14*x^3-70*x^2-64*x-19; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:05:41 on modular [Seed = 1857296192] ------------------------------------- x^6 - 10*x^5 - 3*x^4 - 14*x^3 - 70*x^2 - 64*x - 19 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:06:51 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+t; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:06:48 on modular [Seed = 1707023494] ------------------------------------- x^6 + x + t Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 2)(3, 4)(5, 6) 14 6 Total time: 3.289 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:07:05 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:07:02 on modular [Seed = 1267806902] ------------------------------------- x^6 + x + t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.279 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:07:49 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+t*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:07:46 on modular [Seed = 1117273067] ------------------------------------- x^6 + t*x + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.269 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:08:53 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+t*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); f^2 Output: Magma V2.10-6 Sun Dec 21 2003 02:08:49 on modular [Seed = 1501765939] ------------------------------------- x^6 + t*x + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 x^12 + 2*t*x^7 + 2*x^6 + t^2*x^2 + 2*t*x + 1 Total time: 3.359 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:10:43 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+2*t*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:10:39 on modular [Seed = 686968876] ------------------------------------- x^6 + 2*t*x + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.319 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:11:00 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+3*t*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:10:56 on modular [Seed = 1055147733] ------------------------------------- x^6 + 3*t*x + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.299 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:11:11 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+4*t*x+1; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:11:07 on modular [Seed = 904875477] ------------------------------------- x^6 + 4*t*x + 1 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.329 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:11:25 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+t*x+2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:11:22 on modular [Seed = 215381245] ------------------------------------- x^6 + t*x + 2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 2)(3, 4)(5, 6) 14 6 Total time: 3.349 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:11:36 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+t*x+3; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:11:32 on modular [Seed = 465658836] ------------------------------------- x^6 + t*x + 3 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 2)(3, 4)(5, 6) 14 6 Total time: 3.269 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:11:48 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+t*x+4; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:11:45 on modular [Seed = 315124424] ------------------------------------- x^6 + t*x + 4 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.339 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:12:46 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+2*t*x+4; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:12:42 on modular [Seed = 3912470888] ------------------------------------- x^6 + 2*t*x + 4 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.339 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:13:21 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+3*t*x+4; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:13:18 on modular [Seed = 3761936261] ------------------------------------- x^6 + 3*t*x + 4 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.329 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:13:51 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+4*t*x+4; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:13:47 on modular [Seed = 4130111926] ------------------------------------- x^6 + 4*t*x + 4 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.319 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:17:51 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+T^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:17:48 on modular [Seed = 3222976183] ------------------------------------- >> f:=x^6+x+T^2; ^ User error: Identifier 'T' has not been declared or assigned >> print(f); ^ User error: Identifier 'f' has not been declared or assigned >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2); ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:18:02 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+T^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:17:58 on modular [Seed = 3741690258] ------------------------------------- >> f:=x^6+x+T^2; ^ User error: Identifier 'T' has not been declared or assigned >> print(f); ^ User error: Identifier 'f' has not been declared or assigned >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2); ^ User error: Identifier 't2' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:18:15 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:18:11 on modular [Seed = 3591151758] ------------------------------------- x^6 + x + t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.309 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:18:27 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+x-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:18:24 on modular [Seed = 2910313350] ------------------------------------- x^6 + x + 4*t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.429 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:19:11 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+2x-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:19:08 on modular [Seed = 2759774883] ------------------------------------- >> f:=x^6+2x-t^2; ^ User error: bad syntax >> print(f); ^ User error: Identifier 'f' has not been declared or assigned >> G, R:= GaloisGroup(f); ^ User error: Identifier 'f' has not been declared or assigned >> print(G); ^ User error: Identifier 'G' has not been declared or assigned >> t1, t2:= TransitiveGroupIdentification(G); ^ User error: Identifier 'G' has not been declared or assigned >> print(t1); ^ User error: Identifier 't1' has not been declared or assigned >> print(t2); ^ User error: Identifier 't2' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:19:22 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+2*x-t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:19:18 on modular [Seed = 3010053550] ------------------------------------- x^6 + 2*x + 4*t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.339 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:19:32 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+2*x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:19:28 on modular [Seed = 2320563297] ------------------------------------- x^6 + 2*x + t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.349 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:19:42 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+3*x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:19:38 on modular [Seed = 2153444961] ------------------------------------- x^6 + 3*x + t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.339 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Sun Dec 21 02:20:04 2003 Input: P:= FunctionField(GF(5)); Q:= PolynomialRing(P); f:=x^6+4*x+t^2; print(f); G, R:= GaloisGroup(f); print(G); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2); Output: Magma V2.10-6 Sun Dec 21 2003 02:20:01 on modular [Seed = 2420827738] ------------------------------------- x^6 + 4*x + t^2 Permutation group G acting on a set of cardinality 6 (1, 2, 3, 4, 6) (1, 4)(5, 6) 12 6 Total time: 3.329 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host vkampen2.math.metro-u.ac.jp. (133.86.76.201) Time: Mon Dec 22 02:29:42 2003 Input: g:=; DerivedGroup(g); Output: Magma V2.10-6 Mon Dec 22 2003 02:29:39 on modular [Seed = 3356584585] ------------------------------------- >> g:=; ^ User error: bad syntax >> DerivedGroup(g); ^ User error: Identifier 'g' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host vkampen2.math.metro-u.ac.jp. (133.86.76.201) Time: Mon Dec 22 02:30:11 2003 Input: g:=; DerivedGroup(g); Output: Magma V2.10-6 Mon Dec 22 2003 02:30:08 on modular [Seed = 3725032572] ------------------------------------- >> g:=; ^ User error: bad syntax >> DerivedGroup(g); ^ User error: Identifier 'g' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host vkampen2.math.metro-u.ac.jp. (133.86.76.201) Time: Mon Dec 22 02:32:11 2003 Input: g:=; Output: Magma V2.10-6 Mon Dec 22 2003 02:32:08 on modular [Seed = 670991870] ------------------------------------- >> g:=;; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host www-cache1.usyd.edu.au. (129.78.64.101) Time: Mon Dec 22 02:47:21 2003 Input: SetRows(3); for k in [1..10] do print k; end for; Output: Magma V2.10-6 Mon Dec 22 2003 02:47:18 on modular [Seed = 64658852] ------------------------------------- 1 2 3 4 5 6 7 8 9 10 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 10:25:40 2003 Input: E=EllipticCurve([-30,133]); Q, reps := IntegralPoints(E); Q; reps; Output: Magma V2.10-6 Mon Dec 22 2003 10:25:37 on modular [Seed = 448932337] ------------------------------------- >> E=EllipticCurve([-30,133]); ^ User error: Identifier 'E' has not been declared or assigned >> Q, reps := IntegralPoints(E); ^ User error: Identifier 'E' has not been declared or assigned >> Q; ^ User error: Identifier 'Q' has not been declared or assigned >> reps;; ^ User error: Identifier 'reps' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 10:26:01 2003 Input: E:=EllipticCurve([-30,133]); Q, reps := IntegralPoints(E); Q; reps; Output: Magma V2.10-6 Mon Dec 22 2003 10:25:58 on modular [Seed = 315236366] ------------------------------------- [ (-7 : 0 : 1), (2 : -9 : 1), (6 : 13 : 1), (-3 : 14 : 1) ] [ [ <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 1> ], [ <(2 : -9 : 1), 1>, <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 2> ] ] Total time: 3.389 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 10:27:58 2003 Input: E:=EllipticCurve([-30,133]); time IntegralPoints(E); Output: Magma V2.10-6 Mon Dec 22 2003 10:27:55 on modular [Seed = 164707176] ------------------------------------- [ (-7 : 0 : 1), (2 : -9 : 1), (6 : 13 : 1), (-3 : 14 : 1) ] [ [ <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 1> ], [ <(2 : -9 : 1), 1>, <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 2> ] ] Time: 0.400 Total time: 3.659 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 11:28:46 2003 Input: E:=EllipticCurve([-16390332,0]); time IntegralPoints(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Dec 22 2003 11:28:22 on modular [Seed = 1284794610] ------------------------------------- Height bound (21.3584) on point search is too large -- reducing to 15.0000 This means that the computed group may only generate a group of finite index in the actual group. Errors: /home/mfd/gomagma: line 2: 9813 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (203.77.201.104) Time: Mon Dec 22 11:37:08 2003 Input: 123+12 Output: Magma V2.10-6 Mon Dec 22 2003 11:37:05 on modular [Seed = 2371202853] ------------------------------------- 135 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 11:46:40 2003 Input: E:=EllipticCurve([-30,133]); time MordellWeilGroup(E); Output: Magma V2.10-6 Mon Dec 22 2003 11:46:35 on modular [Seed = 4029206530] ------------------------------------- Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 Time: 0.250 Total time: 3.819 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 14:31:10 2003 Input: E=EllipticCurve([-30,133]); time IntegerPoints(E); Output: Magma V2.10-6 Mon Dec 22 2003 14:31:07 on modular [Seed = 1367943228] ------------------------------------- >> E=EllipticCurve([-30,133]); ^ User error: Identifier 'E' has not been declared or assigned >> time IntegerPoints(E);; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 14:31:48 2003 Input: E:=EllipticCurve([-30,133]); time IntegerPoints(E); Output: Magma V2.10-6 Mon Dec 22 2003 14:31:45 on modular [Seed = 1501634798] ------------------------------------- >> time IntegerPoints(E);; ^ User error: Identifier 'IntegerPoints' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 14:32:34 2003 Input: E:=EllipticCurve([-30,133]); time IntegralPoints(E); Output: Magma V2.10-6 Mon Dec 22 2003 14:32:30 on modular [Seed = 1100560537] ------------------------------------- [ (-7 : 0 : 1), (2 : -9 : 1), (6 : 13 : 1), (-3 : 14 : 1) ] [ [ <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 1> ], [ <(2 : -9 : 1), 1>, <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 2> ] ] Time: 0.400 Total time: 3.439 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host djbroadhurst.plus.com. (212.56.75.172) Time: Mon Dec 22 14:35:39 2003 Input: E:=EllipticCurve([-30,133]); IntegralPoints(E); Output: Magma V2.10-6 Mon Dec 22 2003 14:35:35 on modular [Seed = 1923746531] ------------------------------------- [ (-7 : 0 : 1), (2 : -9 : 1), (6 : 13 : 1), (-3 : 14 : 1) ] [ [ <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 1> ], [ <(2 : -9 : 1), 1>, <(-7 : 0 : 1), 1> ], [ <(2 : -9 : 1), 2> ] ] Total time: 3.409 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host ccd-mbras.uab.es. (158.109.70.154) Time: Tue Dec 23 08:31:22 2003 Input: Z:=function(x) return x+4; end function; Z(5); Output: Magma V2.10-6 Tue Dec 23 2003 08:31:16 on modular [Seed = 1468017547] ------------------------------------- 9 Total time: 4.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ccd-mbras.uab.es. (158.109.70.154) Time: Tue Dec 23 08:32:03 2003 Input: Z:=function(x) return x+4; end function; Z(5); Z(10); Z(15); Z(20); Z(25); Output: Magma V2.10-6 Tue Dec 23 2003 08:32:00 on modular [Seed = 1384460021] ------------------------------------- 9 14 19 24 29 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ccd-mbras.uab.es. (158.109.70.154) Time: Tue Dec 23 08:42:25 2003 Input: load "~/provamagma" Output: WARNING: MAGMA command contains unsafe command 'load', so it will not be executed. ************** MAGMA ***************** Host ccd-mbras.uab.es. (158.109.70.154) Time: Tue Dec 23 08:42:41 2003 Input: read "~/provamagma" Output: WARNING: MAGMA command contains unsafe command 'read', so it will not be executed. ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 09:08:19 2003 Input: H := HammingCode(FiniteField(2), 3); Output: Magma V2.10-6 Tue Dec 23 2003 09:08:15 on modular [Seed = 265845814] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 09:08:39 2003 Input: H := HammingCode(FiniteField(2), 3); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 09:08:36 on modular [Seed = 4095969254] ------------------------------------- [7, 4, 3] Hamming code (r = 3) over GF(2) Generator matrix: [1 0 0 0 1 1 0] [0 1 0 0 0 1 1] [0 0 1 0 1 1 1] [0 0 0 1 1 0 1] [1 0 0 1 0 1 1] [0 1 0 1 1 1 0] [0 0 1 0 1 1 1] Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 09:08:59 2003 Input: H := HammingCode(FiniteField(4), 3); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 09:08:56 on modular [Seed = 4247424755] ------------------------------------- [21, 18, 3] Hamming code (r = 3) over GF(2^2) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 $.1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 0 0 $.1 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 0 0 $.1^2 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1 0 0 1 $.1^2] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1 0 0 0 $.1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 0 0 $.1 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1 0 0 $.1^2 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1 0 0 1 $.1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1 0 0 0 $.1^2] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^2 0 0 $.1 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^2 0 0 $.1^2 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^2 0 0 1 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1^2 0 0 0 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 $.1 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 $.1^2 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^2 $.1] [1 0 $.1^2 $.1 1 0 $.1^2 $.1 1 $.1^2 0 1 $.1 $.1 1 0 $.1^2 1 $.1 $.1^2 0] [0 1 1 1 1 0 0 0 0 $.1^2 $.1^2 $.1^2 $.1^2 $.1 $.1 $.1 $.1 1 1 1 1] [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ccd-mbras.uab.es. (158.109.70.154) Time: Tue Dec 23 10:08:38 2003 Input: MAX:=6; c:=5; g:=3; semi:=[0,3]; i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; oplus:=func; inferior:=func; ominus:=func; I:=func; nu:=func; dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf,llista))); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..(#llista-1)]])+nu(llista[#llista])-interseccioinf(Lconjunts,Linterseccioinf,llista)); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({I(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Tue Dec 23 2003 10:08:35 on modular [Seed = 1857620840] ------------------------------------- CONJUNTS= <[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 ], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1, 5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ]> MCINF= <[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ]> INTERSECCIOINF= [ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] UNIOINF= [ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 10, 10, 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6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:16:46 2003 Input: BKLCLowerBound(GF(8),8,6); Output: Magma V2.10-6 Tue Dec 23 2003 14:16:43 on modular [Seed = 3441059370] ------------------------------------- Database does not exist for GF( 8 ) currently Total time: 3.059 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:17:01 2003 Input: BKLCLowerBound(GF(2),8,6); Output: Magma V2.10-6 Tue Dec 23 2003 14:16:58 on modular [Seed = 3323030800] ------------------------------------- 2 Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:18:24 2003 Input: HammingCode(GF(2),2); Output: Magma V2.10-6 Tue Dec 23 2003 14:18:21 on modular [Seed = 2487435026] ------------------------------------- [3, 1, 3] Hamming code (r = 2) over GF(2) Generator matrix: [1 1 1] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:18:38 2003 Input: HammingCode(GF(8),2); Output: Magma V2.10-6 Tue Dec 23 2003 14:18:35 on modular [Seed = 2203331059] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:19:54 2003 Input: HammingCode(GF(16),2); Output: Magma V2.10-6 Tue Dec 23 2003 14:19:51 on modular [Seed = 2074923350] ------------------------------------- [17, 15, 3] Hamming code (r = 2) over GF(2^4) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 2.909 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:20:28 2003 Input: HammingCode(GF(8),2); Output: Magma V2.10-6 Tue Dec 23 2003 14:20:25 on modular [Seed = 1807532392] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:21:36 2003 Input: H:=HammingCode(GF(8),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:21:33 on modular [Seed = 1639369638] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:22:37 2003 Input: H:=HammingCode(GF(8),2); H*5; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:22:34 on modular [Seed = 1586099422] ------------------------------------- >> H*5; ^ Runtime error in '*': Bad argument types Argument types given: Code, RngIntElt [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:22:55 2003 Input: H:=HammingCode(GF(8),2); H*[5]; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:22:52 on modular [Seed = 1468071457] ------------------------------------- >> H*[5]; ^ Runtime error in '*': Bad argument types Argument types given: Code, SeqEnum[RngIntElt] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:23:29 2003 Input: H:=HammingCode(GF(8),2); H; ParityCheckMatrix(H)*5; Output: Magma V2.10-6 Tue Dec 23 2003 14:23:26 on modular [Seed = 1285285144] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:24:12 2003 Input: H:=HammingCode(GF(8),2); H; ParityCheckMatrix(H); ParityCheckMatrix(H)*2; Output: Magma V2.10-6 Tue Dec 23 2003 14:24:09 on modular [Seed = 1167256678] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] [ 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:25:05 2003 Input: H:=HammingCode(GF(8),2); H; ParityCheckMatrix(H); ParityCheckMatrix(H)+ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:24:59 on modular [Seed = 1956896135] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] [ 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0] Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:25:41 2003 Input: H:=HammingCode(GF(8),2); H; ParityCheckMatrix(H); GF(8); Output: Magma V2.10-6 Tue Dec 23 2003 14:25:34 on modular [Seed = 1268572828] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] Finite field of size 2^3 Total time: 3.669 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:28:02 2003 Input: H:=HammingCode(GF(3),2); H; ParityCheckMatrix(H); GF(8); Output: Magma V2.10-6 Tue Dec 23 2003 14:27:59 on modular [Seed = 3094286578] ------------------------------------- [4, 2, 3] Hamming code (r = 2) over GF(3) Generator matrix: [1 0 1 2] [0 1 1 1] [1 0 1 2] [0 1 1 1] Finite field of size 2^3 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:28:31 2003 Input: H:=HammingCode(GF(4),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:28:28 on modular [Seed = 2742291338] ------------------------------------- [5, 3, 3] Hamming code (r = 2) over GF(2^2) Generator matrix: [ 1 0 0 1 $.1^2] [ 0 1 0 $.1^2 $.1^2] [ 0 0 1 $.1^2 1] [ 1 0 1 $.1^2 $.1^2] [ 0 1 $.1^2 $.1^2 1] Total time: 3.009 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:28:50 2003 Input: H:=HammingCode(GF(5),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:28:47 on modular [Seed = 2860319408] ------------------------------------- [6, 4, 3] Hamming code (r = 2) over GF(5) Generator matrix: [1 0 0 0 1 4] [0 1 0 0 1 3] [0 0 1 0 2 2] [0 0 0 1 3 1] [1 0 1 2 3 4] [0 1 1 1 1 1] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:29:01 2003 Input: H:=HammingCode(GF(9),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:28:58 on modular [Seed = 2638886290] ------------------------------------- [10, 8, 3] Hamming code (r = 2) over GF(3^2) Generator matrix: [ 1 0 0 0 0 0 0 0 $.1^5 $.1] [ 0 1 0 0 0 0 0 0 $.1^5 $.1^7] [ 0 0 1 0 0 0 0 0 $.1^6 $.1] [ 0 0 0 1 0 0 0 0 $.1^7 $.1^5] [ 0 0 0 0 1 0 0 0 1 1] [ 0 0 0 0 0 1 0 0 $.1 $.1^6] [ 0 0 0 0 0 0 1 0 $.1^2 $.1^3] [ 0 0 0 0 0 0 0 1 $.1^3 $.1^2] [ 1 0 $.1^7 $.1 $.1^5 1 $.1^6 $.1^3 $.1^2 2] [ 0 1 1 1 1 1 1 1 1 1] Total time: 2.889 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:29:11 2003 Input: H:=HammingCode(GF(6),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:29:08 on modular [Seed = 2220043381] ------------------------------------- >> H:=HammingCode(GF(6),2); ^ Runtime error in 'GF': Argument 1 (6) is not a prime power >> H; ^ User error: Identifier 'H' has not been declared or assigned >> ParityCheckMatrix(H); ^ User error: Identifier 'H' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:29:24 2003 Input: H:=HammingCode(GF(7),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:29:20 on modular [Seed = 2404919146] ------------------------------------- [8, 6, 3] Hamming code (r = 2) over GF(7) Generator matrix: [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] [1 0 1 2 3 4 5 6] [0 1 1 1 1 1 1 1] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:29:45 2003 Input: H:=HammingCode(GF(256),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:29:42 on modular [Seed = 2007031717] ------------------------------------- [257, 255, 3] Hamming code (r = 2) over GF(2^8) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^99] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^99 $.1^26] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^26 $.1^42] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 $.1^159 $.1^127] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^127 $.1^120] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^120 $.1^146] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^146 $.1^59] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^59 $.1^18] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^18 $.1^166] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^166 $.1^210] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^210 $.1^61] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^61 $.1^162] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:30:01 2003 Input: H:=HammingCode(GF(16),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:29:58 on modular [Seed = 2024788154] ------------------------------------- [17, 15, 3] Hamming code (r = 2) over GF(2^4) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] [1 0 1 $.1^3 $.1^13 $.1^9 $.1 $.1^14 $.1^5 $.1^6 $.1^6 $.1^5 $.1^14 $.1 $.1^9 $.1^13 $.1^3] [0 1 $.1^3 $.1^13 $.1^9 $.1 $.1^14 $.1^5 $.1^6 $.1^6 $.1^5 $.1^14 $.1 $.1^9 $.1^13 $.1^3 1] Total time: 3.089 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:31:10 2003 Input: H:=HammingCode(GF(8),2); H; ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:31:07 on modular [Seed = 1757397223] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:31:23 2003 Input: H:=HammingCode(GF(8),2); H; ParityCheckMatrix(H); H*GF(8) Output: Magma V2.10-6 Tue Dec 23 2003 14:31:20 on modular [Seed = 1384510766] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] >> H*GF(8) ^ Runtime error in '*': Bad argument types Argument types given: Code, FldFin Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:31:56 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); ParityCheckMatrix(H); GeneratorMatrix(H)*GF(8) Output: Magma V2.10-6 Tue Dec 23 2003 14:31:53 on modular [Seed = 1535966214] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] >> GeneratorMatrix(H)*GF(8) ^ Runtime error in '*': Bad argument types Argument types given: ModMatFldElt, FldFin Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:32:37 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); ParityCheckMatrix(H); GeneratorMatrix(H)*[0 0 0 0 0 0 0 0] Output: Magma V2.10-6 Tue Dec 23 2003 14:32:34 on modular [Seed = 1285286762] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] >> GeneratorMatrix(H)*[0 0 0 0 0 0 0 0] ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:33:01 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); ParityCheckMatrix(H); GeneratorMatrix(H)*[0,0,0,0,0,0,0,0] Output: Magma V2.10-6 Tue Dec 23 2003 14:32:58 on modular [Seed = 904041003] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] >> GeneratorMatrix(H)*[0,0,0,0,0,0,0,0] ^ Runtime error in '*': Bad argument types Argument types given: ModMatFldElt, SeqEnum[RngIntElt] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:33:21 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); ParityCheckMatrix(H); GeneratorMatrix(H)*(0,0,0,0,0,0,0,0) Output: Magma V2.10-6 Tue Dec 23 2003 14:33:18 on modular [Seed = 1055496500] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] >> GeneratorMatrix(H)*(0,0,0,0,0,0,0,0) ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:35:25 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); ParityCheckMatrix(H); GeneratorMatrix(H)*5; Output: Magma V2.10-6 Tue Dec 23 2003 14:35:22 on modular [Seed = 603227309] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:35:42 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); ParityCheckMatrix(H); 5*GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:35:39 on modular [Seed = 348369515] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:37:15 2003 Input: ScalarMatrix(2,1); Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed. ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:37:29 2003 Input: ScalarMatrix(2,1); Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed. ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:37:49 2003 Input: 2^100 Output: Magma V2.10-6 Tue Dec 23 2003 14:37:37 on modular [Seed = 249145596] ------------------------------------- 1267650600228229401496703205376 Total time: 4.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:39:39 2003 Input: S := ScalarMatrix(3, -4); Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed. ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:39:57 2003 Input: D := DiagonalMatrix(GF(23), [1, 2, -3]); D; Output: Magma V2.10-6 Tue Dec 23 2003 14:39:54 on modular [Seed = 2108348422] ------------------------------------- [ 1 0 0] [ 0 2 0] [ 0 0 20] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:40:14 2003 Input: D := DiagonalMatrix(GF(23), [1, 2, 3]); D; Output: Magma V2.10-6 Tue Dec 23 2003 14:40:11 on modular [Seed = 1840957447] ------------------------------------- [ 1 0 0] [ 0 2 0] [ 0 0 3] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:40:29 2003 Input: D := DiagonalMatrix(GF(2), [1, 2, 3]); D; Output: Magma V2.10-6 Tue Dec 23 2003 14:40:25 on modular [Seed = 1417933068] ------------------------------------- [1 0 0] [0 0 0] [0 0 1] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:40:44 2003 Input: D := DiagonalMatrix(GF(8), [1, 2, 3]); D; Output: Magma V2.10-6 Tue Dec 23 2003 14:40:39 on modular [Seed = 3523573652] ------------------------------------- [ 1 0 0] [ 0 0 0] [ 0 0 1] Total time: 3.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:41:01 2003 Input: D := DiagonalMatrix(GF(8), [1, 2, 3, 4]); D; Output: Magma V2.10-6 Tue Dec 23 2003 14:40:58 on modular [Seed = 1807535697] ------------------------------------- [ 1 0 0 0] [ 0 0 0 0] [ 0 0 1 0] [ 0 0 0 0] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:41:56 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:41:53 on modular [Seed = 1434644644] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] [ 1 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1] [ 0 1 $.1 $.1^6 $.1^3 $.1^3 $.1^6 $.1 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:42:39 2003 Input: H:=HammingCode(GF(8),2); DiagonalMatrix(GeneratorMatrix(H),[1]); Output: Magma V2.10-6 Tue Dec 23 2003 14:42:36 on modular [Seed = 1586101122] ------------------------------------- >> DiagonalMatrix(GeneratorMatrix(H),[1]); ^ Runtime error in 'DiagonalMatrix': Bad argument types Argument types given: ModMatFldElt, SeqEnum[RngIntElt] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:43:05 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:43:02 on modular [Seed = 1200677617] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:43:27 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); $.1 Output: Magma V2.10-6 Tue Dec 23 2003 14:43:24 on modular [Seed = 820483485] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] >> $.1; ^ Runtime error: Bad dollar structure Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:44:07 2003 Input: $.1; Output: Magma V2.10-6 Tue Dec 23 2003 14:44:04 on modular [Seed = 971939149] ------------------------------------- >> $.1;; ^ Runtime error: Bad dollar structure Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:44:51 2003 Input: Type($.1); Output: Magma V2.10-6 Tue Dec 23 2003 14:44:48 on modular [Seed = 586516066] ------------------------------------- >> Type($.1);; ^ Runtime error: Bad dollar structure Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:46:43 2003 Input: H:=HammingCode(GF(7),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:46:40 on modular [Seed = 281523392] ------------------------------------- [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:46:57 2003 Input: H:=HammingCode(GF(7),2); 5*GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:46:54 on modular [Seed = 449691332] ------------------------------------- [5 0 0 0 0 0 5 2] [0 5 0 0 0 0 5 4] [0 0 5 0 0 0 3 6] [0 0 0 5 0 0 1 1] [0 0 0 0 5 0 6 3] [0 0 0 0 0 5 4 5] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:47:20 2003 Input: H:=HammingCode(GF(7),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:47:16 on modular [Seed = 64268215] ------------------------------------- [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 14:49:18 2003 Input: H:=HammingCode(GF(7),2); ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 14:49:15 on modular [Seed = 215723847] ------------------------------------- [1 0 1 2 3 4 5 6] [0 1 1 1 1 1 1 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 15:04:04 2003 Input: H:=HammingCode(GF(15),2); ParityCheckMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 15:04:01 on modular [Seed = 2520856151] ------------------------------------- >> H:=HammingCode(GF(15),2); ^ Runtime error in 'GF': Argument 1 (15) is not a prime power >> ParityCheckMatrix(H); ^ User error: Identifier 'H' has not been declared or assigned Total time: 3.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:39:06 2003 Input: H:=HammingCode(GF(7),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:39:03 on modular [Seed = 1940191653] ------------------------------------- [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:39:14 2003 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:39:11 on modular [Seed = 2058219684] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:39:46 2003 Input: H:=HammingCode(GF(8),2); Rank(GeneratorMatrix(H)); Output: Magma V2.10-6 Tue Dec 23 2003 16:39:43 on modular [Seed = 1167248507] ------------------------------------- 7 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:40:20 2003 Input: H:=HammingCode(GF(16),2); Rank(GeneratorMatrix(H)); Output: Magma V2.10-6 Tue Dec 23 2003 16:40:17 on modular [Seed = 1417927988] ------------------------------------- 15 Total time: 2.929 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:40:32 2003 Input: H:=HammingCode(GF(16),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:40:29 on modular [Seed = 1602803251] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 2.949 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:43:35 2003 Input: H:=HammingCode(GF(16),2); print GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:43:32 on modular [Seed = 2992978583] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 3.329 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:45:16 2003 Input: H:=HammingCode(GF(16),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:45:12 on modular [Seed = 2354775237] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 2.979 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:45:35 2003 Input: H:=HammingCode(GF(16),2); GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:45:32 on modular [Seed = 2555318469] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 3.309 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:46:36 2003 Input: H:=HammingCode(GF(16),2); H<1,2,3>:=H; GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:46:33 on modular [Seed = 3811863419] ------------------------------------- >> H<1,2,3>:=H; ^ User error: bad syntax [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 3.229 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:46:53 2003 Input: H:=HammingCode(GF(16),2); H:=H; GeneratorMatrix(H); Output: Magma V2.10-6 Tue Dec 23 2003 16:46:50 on modular [Seed = 3929891329] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 3.339 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:47:13 2003 Input: H:=HammingCode(GF(16),2); G:=GeneratorMatrix(H); print G; Output: Magma V2.10-6 Tue Dec 23 2003 16:47:09 on modular [Seed = 4112678153] ------------------------------------- >> G:=GeneratorMatrix(H); ^ Runtime error in 'AssignNames': Bad argument types Argument types given: ModMatFldElt ~, SeqEnum[MonStgElt] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 3.339 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:47:50 2003 Input: PolynomialAlgebra(Integers(30), 3); Output: Magma V2.10-6 Tue Dec 23 2003 16:47:47 on modular [Seed = 3256174048] ------------------------------------- Polynomial ring of rank 3 over IntegerRing(30) Lexicographical Order Variables: $.1, $.2, $.3 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:48:13 2003 Input: D:=PolynomialAlgebra(Integers(30), 3); print D; Output: Magma V2.10-6 Tue Dec 23 2003 16:48:10 on modular [Seed = 3441052406] ------------------------------------- Polynomial ring of rank 3 over IntegerRing(30) Lexicographical Order Variables: r, s, t Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:48:45 2003 Input: HammingCode(GF(16),2); Output: Magma V2.10-6 Tue Dec 23 2003 16:48:38 on modular [Seed = 3658309069] ------------------------------------- [17, 15, 3] Hamming code (r = 2) over GF(2^4) Generator matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 3.269 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:49:12 2003 Input: HammingCode(GF(8),2); Output: Magma V2.10-6 Tue Dec 23 2003 16:49:08 on modular [Seed = 704556636] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 3.369 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Tue Dec 23 16:57:49 2003 Input: H:=GeneratorMatrix(HammingCode(GF(8),2)); Output: Magma V2.10-6 Tue Dec 23 2003 16:57:45 on modular [Seed = 1990325007] ------------------------------------- >> H:=GeneratorMatrix(HammingCode(GF(8),2)); ^ Runtime error in 'AssignNames': Bad argument types Argument types given: ModMatFldElt ~, SeqEnum[MonStgElt] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 18:54:12 2003 Input: 1+1; Output: Magma V2.10-6 Tue Dec 23 2003 18:54:09 on modular [Seed = 619957986] ------------------------------------- 2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 18:54:31 2003 Input: Factorial(10000); Output: Magma V2.10-6 Tue Dec 23 2003 18:54:27 on modular [Seed = 737985023] ------------------------------------- 2846259680917054518906413212119868890148051401702799230794179994274411340003764\ 4437729907867577847758158840621423175288300423399401535187390524211613827161748\ 1982419982759241828925978789812425312059465996259867065601615720360323979263287\ 3671705574197596209947972034615369811989709261127750048419884541047554464244213\ 6573303076703628825803548967461117097369578603670191071512730587281041158640561\ 2811653853259684258259955846881464304255898366493170592517172042765974074461334\ 0005419405246230343686915405940406622782824837151203832217864462718382292389963\ 8992827221879702459387693803094627332292570555459690027875282242544348021127559\ 0191694254290289169072190970836905398737474524833728995218023632827412170402680\ 8676921045155584056717255537201585213282903427998981844931361064038148930449962\ 1599999359670892980190336998484404665419236258424947163178961192041233108268651\ 0713545168455409360330096072103469443779823494307806260694223026818852275920570\ 2923084312618849760656074258627944882715595683153344053442544664841689458042570\ 9461673613187605234982286326452921529423479870603344290737158688499178932580691\ 4831688542519560061723726363239744207869246429560123062887201226529529640915083\ 0133663098273380635397290150658182257429547589439976511386554120812578868370423\ 9208764484761569001264889271590706306409661628038784044485191643790807186112370\ 6221334154150659918438759610239267132765469861636577066264386380298480519527695\ 3619525924093090861447190739076858575593478698172073437209310482547562856777769\ 4081564074962275254993384112809289637516990219870492405617531786346939798024619\ 7370790418683299310165541507423083931768783669236948490259996077296842939774275\ 3626311982541668153189176323483919082100014717893218422780513518173492190114624\ 6875769835373441456013122615221391178759688367364087207937002992038279198038702\ 3720780391403123689976081528403060511167094847222248703891999934420713958369830\ 6396223207911562404425080891991431983712044559834404755675948921210149815245454\ 3594285414390843564419984224855478532163624030098442855331829253154206551237079\ 7058163934602962476970103887422064415366267337154287007891227493406843364428898\ 4710084064160009362393526124803797529334392876439831639031277645072247926785170\ 0826669598389526150759007349215197592659192708873202594066382118801988854748266\ 0483422564577057439731222597006719360617635135795298217942907977053272832675014\ 8802444352868164502616566283754651900617187344226043891929850607151539003110668\ 4727360135816706437861756757439184376479658136100599638689552334648781746143243\ 5732248643267984819814584327030358955084205347884933645824825920332880890257823\ 8823326577020524897093704721021424841334246526820680673231421448385407418213962\ 1846870108359582946965235632764870475718351616879235068366271743711915723361143\ 0701211207676086978515597218464859859186436417168508996255168209107935702311185\ 1817477501080462258552131476489749066075287708289766751495100968232968973200062\ 2392888056658036140311285465929084078033974900664953205873164948093883816198658\ 8508273824680348978647571166798904235680183035041338757319726308979094357106877\ 9730163391808786847494363353389337358690640584841782806519627582643442925805842\ 2212947649402948622670761832988229004072390403733168207417413251656688443079339\ 4470192089056207883875853425128209573593070181977083401638176382785625395168254\ 2664461494104471157953326237281546879408042371858742302620026422182269418862621\ 2107297776657401018376182280136857586442185863011539843712299107010094061929413\ 2232027731939594670067136953770978977781182882424429208648161341795620174718316\ 0968766104314049795819823644580736820940402221118153005143338707660706314961610\ 7771117448059552764348333385744040212757031851527298377435921878558552795591028\ 6644579173620072218581433099772947789237207179428577562713009239823979219575811\ 9726474264287826668235391568785727162014619224426626670840076566562580710947439\ 8740110772811669918806268726626565583345665007890309050656074633078027158530817\ 6912237728135105845273265916262196476205714348802156308152590053437211410003030\ 3924286645720732847348171203416818632896886504828736793339844397123673508452734\ 0196309427697652684170174990756947982757825835229994315633322107439131550124459\ 0053247026803129123922979790304175878233986223735350546426469135025039510092392\ 8658510868208807066273473320035499572039708648806604092985460700633940988583634\ 9865466136727880748764700702458790118046518296111277090609016152022111461543158\ 3176699570609746180853593904000678928785488278509386373537039040494126846189912\ 7287156265500127083303995025787993170543188275265922581494895074663997600731692\ 7310831735883056612614782997663188070063044632429112260691931278881566221591523\ 2704576958675128219909389426866019639044897189185974729253103224802105438410443\ 2582847283058429780416240510811032691400190056878439634150269652104892027214023\ 2160234898588827371428695339681755106287470907473718188014223487248498558198439\ 0946517083643689943061896502432883532796671901845276205510857076262042445096233\ 2320474470783119043449935144262550170177101737955112474615947173186270156557126\ 6295855125077711738338208419705893367323724453280456537178514960308802580284067\ 8478094146418386592266528068679788432506605379430462502871051049293472674712674\ 9989263462735816714693506049511034075540465817039348104675848562596776795976829\ 9409334026387269378365320912287718077451152622642548771835461108886360843272806\ 2277766430972838790567286180360486334648933714394152502594596525015209595361579\ 7713559579496572977565090269442808847976127666484700361964890604376193469427044\ 4070215317943583831051404915462608728486678750541674146731648999356381312866931\ 4276168635373056345866269578945682750658102359508148887789550739393653419373657\ 0084831850447568221544406759920313807707353997803633926733454954929666875992253\ 0893898086430606532961793164029612492673080638031873912596151131890359351266480\ 8185683667702865377423907465823909109555171797705807977892897524902307378017531\ 4268036391424472025772889178495007811788933662975043680421466819782427298069757\ 9391742229456683185815676816288797870624531246651727622758295493421483658868919\ 2995874020956960002435603052898298663868920769928340305497102665143223061252319\ 1513184387690382370620539920693394371688046642971147674356448637502684769814885\ 3105354063328845062012173302630676481322931561043551941761050712449024873277273\ 1120919458651374931909651624976916575538121985664322079786663003989386602386073\ 5785811439471587280089337416503379296583261843607313332752602360511552422722844\ 7251463863269369763762510196714380125691227784428426999440829152215904694437282\ 4986580852051865762929927755088331286726384187132777808744466438753526447335624\ 4113944762878097465068395298210817496795883645227334469487379347179071006497823\ 6466016680572034297929207446822322848665839522211446859572858403863377278030227\ 5915304978658739195136502462741958990883743873315942873720297706202071202130385\ 7217593321116241333042277374241635355358797706530964768588607730143277829032889\ 4795818404378858567772932094476778669357537460048142376741194182671636870481056\ 9111562156143575162905273512243500806046536689174581965494826086122607502930627\ 6147881326895528073614902252581968281505103331813212965966495815903042123877564\ 5990973296728066683849166257949747922905361845563741034791430771561168650484292\ 4902811029925296787352987678292690407887784802624792227507359484058174390862518\ 7794689004594206016860514277224448627246991114620014988066272353883780938062854\ 4384763053235070132028029488392008132135446450056134987017834271106158177289819\ 2906564986880810455622337030672542512772773302834984335957725759562247037077933\ 8714659303308862969944031833266579751467650271734629888377739784821870071802674\ 1265997158728035440478432478674907127921672898523588486943546692255101337606377\ 9151645972542571169684773399511589983490818882812639844005055462100669887926145\ 5821456531969690982725393451576040861347625877816586729441077535882416231577908\ 2538054746933540582469717674324523451498483027170396543887737637358191736582454\ 2733474904242629460112998819165637138471118491569150547681404117498014542657123\ 9420442544102807580600138819865061375928853903892264432294799028648284009959867\ 5963580999112695367601527173086852756572147583507122298296529564917835071750835\ 7413622825450556202709694174767992592297748886274113145876761475314568953280931\ 1705269648641018740767329698664923643738256547502281647192681555988319662984830\ 7776666840622314315884384910519058281816740764463033300119710293036455866594651\ 8690744752508378419876229904159117936827997606541860887216266548864923443910309\ 2325691063377596973905178112276466848679173604940439370333935190060938726839729\ 9246478483727274770977466693599784857120156789000241947269220974984127323147401\ 5499809203814598214164811763571478015542315996678385348544864069364105569135313\ 3523118405358134894093819182189869482538396098994282202759933963520621770534357\ 2073396250574216769465101608495601439303244304271576099527308684609204422226103\ 1542299844448021100981613338248273752189987382053151649271344981059501599748005\ 7159191220215448774875010347324619063394130303089239941198500622590218416440998\ 8173214324422108554248620896250260604398180189026317781146617454999771440665232\ 8638463638470016556181538610981881111817341913055050248603458567555856375117297\ 7429932907494423657966833270091836733897734790175924888566037995277154056908301\ 7311723894140326159612292912225191095948743805673381278538616491842786938417556\ 8980471008598683720336151751580970225662752001609561922299254017598785220385459\ 1377178397638981119848580329104875166692119510451489667776159824946872742066343\ 7593207852618922687285527671324883267794152912839165407968344190239094803676688\ 70 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 19:00:34 2003 Input: ModularSymbols(1000); Output: Magma V2.10-6 Tue Dec 23 2003 19:00:29 on modular [Seed = 80997502] ------------------------------------- Full modular symbols space for Gamma_0(1000) of weight 2 and dimension 301 over Rational Field Total time: 4.359 seconds, Total memory usage: 17.90MB ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 19:01:08 2003 Input: ModularSymbols(1000); ModularSymbols(1001); ModularSymbols(1002); ModularSymbols(1003); Output: Magma V2.10-6 Tue Dec 23 2003 19:01:01 on modular [Seed = 432992579] ------------------------------------- Full modular symbols space for Gamma_0(1000) of weight 2 and dimension 301 over Rational Field Full modular symbols space for Gamma_0(1001) of weight 2 and dimension 225 over Rational Field Full modular symbols space for Gamma_0(1002) of weight 2 and dimension 337 over Rational Field Full modular symbols space for Gamma_0(1003) of weight 2 and dimension 181 over Rational Field Total time: 7.109 seconds, Total memory usage: 23.98MB ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 19:01:41 2003 Input: ModularSymbols(10000); ModularSymbols(1001); ModularSymbols(1002); ModularSymbols(1003); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Tue Dec 23 2003 19:01:25 on modular [Seed = 3761703122] ------------------------------------- Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Full modular symbols space for Gamma_0(1001) of weight 2 and dimension 225 over Rational Field Full modular symbols space for Gamma_0(1002) of weight 2 and dimension 337 over Rational Field Full modular symbols space for Gamma_0(1003) of weight 2 and dimension 181 over Rational Field Total time: 15.500 seconds, Total memory usage: 100.00MB ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 19:02:44 2003 Input: for a:=1000 to 1030 do M:=ModularSymbols(a); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 23 2003 19:02:21 on modular [Seed = 4146077469] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 22672 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 19:03:20 2003 Input: for a:=1000 to 1010 do M:=ModularSymbols(a); end for; Output: Magma V2.10-6 Tue Dec 23 2003 19:03:06 on modular [Seed = 4247393568] ------------------------------------- Total time: 14.479 seconds, Total memory usage: 28.41MB ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 19:03:52 2003 Input: for a:=1000 to 1020 do M:=ModularSymbols(a); end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Dec 23 2003 19:03:29 on modular [Seed = 3289590898] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 22691 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 82-35-66-245.cable.ubr01.dals.blueyonder.co.uk. (82.35.66.245) Time: Tue Dec 23 19:04:27 2003 Input: print "erdos"; for a:=1000 to 1020 do M:=ModularSymbols(a); end for; Output: Magma V2.10-6 Tue Dec 23 2003 19:04:02 on modular [Seed = 3407618910] ------------------------------------- erdos Total time: 25.649 seconds, Total memory usage: 35.41MB