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\\ charpoly_s3g1.gp
\\ This is a table of characteristic polynomials of the
\\ Hecke operators T_p acting on the space S_3(Gamma_1(N)) 
\\ of weight 3 cusp forms for Gamma_1(N).
\\ William Stein ([email protected]), September, 1998.

{
T=matrix(20,97,m,n,0);
T[7,2]=x + 3;
T[7,3]=x ;
T[7,5]=x ;
T[7,7]=x + 7;
T[7,11]=x + 6;
T[7,13]=x ;
T[7,17]=x ;
T[7,19]=x ;
T[7,23]=x -18;
T[7,29]=x + 54;
T[7,31]=x ;
T[7,37]=x + 38;
T[7,41]=x ;
T[7,43]=x -58;
T[7,47]=x ;
T[7,53]=x + 6;
T[7,59]=x ;
T[7,61]=x ;
T[7,67]=x + 118;
T[7,71]=x -114;
T[7,73]=x ;
T[7,79]=x + 94;
T[7,83]=x ;
T[7,89]=x ;
T[7,97]=x ;

T[8,2]=x + 2;
T[8,3]=x + 2;
T[8,5]=x ;
T[8,7]=x ;
T[8,11]=x -14;
T[8,13]=x ;
T[8,17]=x -2;
T[8,19]=x + 34;
T[8,23]=x ;
T[8,29]=x ;
T[8,31]=x ;
T[8,37]=x ;
T[8,41]=x + 46;
T[8,43]=x -14;
T[8,47]=x ;
T[8,53]=x ;
T[8,59]=x + 82;
T[8,61]=x ;
T[8,67]=x -62;
T[8,71]=x ;
T[8,73]=x + 142;
T[8,79]=x ;
T[8,83]=x -158;
T[8,89]=x -146;
T[8,97]=x + 94;

T[9,2]=x^2 + 3*x + 3;
T[9,3]=x^2 + 3*x + 9;
T[9,5]=x^2 -6*x + 12;
T[9,7]=x^2 + 2*x + 4;
T[9,11]=x^2 + 3*x + 3;
T[9,13]=x^2 -4*x + 16;
T[9,17]=x^2 + 243;
T[9,19]=(x -11)^2;
T[9,23]=x^2 + 48*x + 768;
T[9,29]=x^2 -78*x + 2028;
T[9,31]=x^2 + 32*x + 1024;
T[9,37]=(x + 34)^2;
T[9,41]=x^2 + 21*x + 147;
T[9,43]=x^2 -61*x + 3721;
T[9,47]=x^2 + 84*x + 2352;
T[9,53]=(x )^2;
T[9,59]=x^2 -87*x + 2523;
T[9,61]=x^2 + 56*x + 3136;
T[9,67]=x^2 -31*x + 961;
T[9,71]=x^2 + 972;
T[9,73]=(x -65)^2;
T[9,79]=x^2 + 38*x + 1444;
T[9,83]=x^2 + 84*x + 2352;
T[9,89]=x^2 + 15552;
T[9,97]=x^2 -115*x + 13225;

T[10,2]=x^2 + 2*x + 2;
T[10,3]=x^2 + 4*x + 8;
T[10,5]=x^2 + 25;
T[10,7]=x^2 -4*x + 8;
T[10,11]=(x + 8)^2;
T[10,13]=x^2 -6*x + 18;
T[10,17]=x^2 -14*x + 98;
T[10,19]=x^2 + 400;
T[10,23]=x^2 + 4*x + 8;
T[10,29]=x^2 + 1600;
T[10,31]=(x -52)^2;
T[10,37]=x^2 + 6*x + 18;
T[10,41]=(x + 8)^2;
T[10,43]=x^2 + 84*x + 3528;
T[10,47]=x^2 + 36*x + 648;
T[10,53]=x^2 -106*x + 5618;
T[10,59]=x^2 + 400;
T[10,61]=(x + 48)^2;
T[10,67]=x^2 -124*x + 7688;
T[10,71]=(x + 28)^2;
T[10,73]=x^2 + 94*x + 4418;
T[10,79]=(x )^2;
T[10,83]=x^2 -36*x + 648;
T[10,89]=x^2 + 6400;
T[10,97]=x^2 + 126*x + 7938;

T[11,2]=(x^4 + 5*x^3 + 15*x^2 + 15*x + 5)*(x );
T[11,3]=(x + 5)*(x^4 + 10*x^2 + 25*x + 25);
T[11,5]=(x + 1)*(x^4 + 4*x^3 + 16*x^2 + 64*x + 256);
T[11,7]=(x^4 -10*x^3 + 80*x^2 + 160*x + 80)*(x );
T[11,11]=(x + 11)*(x^4 -x^3 -209*x^2 -121*x + 14641);
T[11,13]=(x^4 + 20*x^3 + 200*x^2 + 1000*x + 2000)*(x );
T[11,17]=(x^4 -10985*x + 142805)*(x );
T[11,19]=(x^4 -25*x^3 + 200*x^2 -440*x + 605)*(x );
T[11,23]=(x -35)*(x^2 + 10*x + 20)^2;
T[11,29]=(x^4 + 40*x^3 + 1040*x^2 + 5720*x + 9680)*(x );
T[11,31]=(x + 37)*(x^4 + 58*x^3 + 1384*x^2 + 7552*x + 55696);
T[11,37]=(x + 25)*(x^4 -90*x^3 + 4860*x^2 -145800*x + 2624400);
T[11,41]=(x^4 + 80*x^3 + 4720*x^2 -12095*x + 8405)*(x );
T[11,43]=(x^4 + 1625*x^2 + 581405)*(x );
T[11,47]=(x -50)*(x^4 + 30*x^3 + 640*x^2 + 12400*x + 384400);
T[11,53]=(x + 70)*(x^4 -120*x^3 + 5400*x^2 + 27000*x + 810000);
T[11,59]=(x -107)*(x^4 -23*x^3 + 1054*x^2 -3692*x + 5041);
T[11,61]=(x^4 -10*x^3 -120*x^2 -17040*x + 403280)*(x );
T[11,67]=(x -35)*(x^2 + 115*x + 2945)^2;
T[11,71]=(x + 133)*(x^4 -148*x^3 + 14464*x^2 -770472*x + 22619536);
T[11,73]=(x^4 -300*x^3 + 41100*x^2 -2966735*x + 93787805)*(x );
T[11,79]=(x^4 -70*x^3 + 3780*x^2 + 31320*x + 67280)*(x );
T[11,83]=(x^4 -225*x^3 + 20700*x^2 -971060*x + 22281605)*(x );
T[11,89]=(x + 97)*(x^2 -61*x -7681)^2;
T[11,97]=(x -95)*(x^4 + 165*x^3 + 16840*x^2 + 952850*x + 31416025);

T[12,2]=(x^2 + 2*x + 4)*(x );
T[12,3]=(x + 3)*(x^2 + 3);
T[12,5]=(x )*(x + 2)^2;
T[12,7]=(x -2)*(x^2 + 48);
T[12,11]=(x^2 + 48)*(x );
T[12,13]=(x + 22)*(x -2)^2;
T[12,17]=(x )*(x -10)^2;
T[12,19]=(x -26)*(x^2 + 432);
T[12,23]=(x^2 + 768)*(x );
T[12,29]=(x )*(x + 26)^2;
T[12,31]=(x + 46)*(x^2 + 48);
T[12,37]=(x -26)^3;
T[12,41]=(x )*(x -58)^2;
T[12,43]=(x + 22)*(x^2 + 2352);
T[12,47]=(x^2 + 4800)*(x );
T[12,53]=(x )*(x + 74)^2;
T[12,59]=(x^2 + 8112)*(x );
T[12,61]=(x -74)*(x -26)^2;
T[12,67]=(x -122)*(x^2 + 48);
T[12,71]=(x )^3;
T[12,73]=(x + 46)^3;
T[12,79]=(x + 142)*(x^2 + 13872);
T[12,83]=(x^2 + 2352)*(x );
T[12,89]=(x )*(x -82)^2;
T[12,97]=(x -2)^3;

T[13,2]=(x^4 + 2*x^3 + 5*x^2 + 4*x + 1)*(x^4 + 4*x^3 + 8*x^2 -12*x + 9);
T[13,3]=(x^4 + 2*x^3 + 6*x^2 -4*x + 4)*(x^2 + 2*x -9)^2;
T[13,5]=(x^4 -8*x^3 + 32*x^2 -24*x + 9)*(x^4 + 14*x^3 + 98*x^2 + 322*x + 529);
T[13,7]=(x^4 -16*x^3 + 164*x^2 -1040*x + 2704)*(x^4 + 12*x^3 + 72*x^2 + 156*x + 169);
T[13,11]=(x^4 + 4*x^3 + 8*x^2 -312*x + 6084)*(x^4 -4*x^3 + 200*x^2 -2912*x + 10816);
T[13,13]=(x^4 -8*x^3 + 104*x^2 -1352*x + 28561)*(x^2 + 13*x + 169)^2;
T[13,17]=(x^4 + 12*x^3 -165*x^2 -2556*x + 45369)*(x^4 + 738*x^2 + 123201);
T[13,19]=(x^4 -10*x^3 + 74*x^2 -308*x + 484)*(x^4 + 400);
T[13,23]=(x^4 + 828*x^2 + 54756)*(x^4 -18*x^3 -90*x^2 + 3564*x + 39204);
T[13,29]=(x^4 -2*x^3 + 111*x^2 + 214*x + 11449)*(x^2 -20*x -150)^2;
T[13,31]=(x^4 -40*x^3 + 800*x^2 -800*x + 400)*(x^4 + 20*x^3 + 200*x^2 -920*x + 2116);
T[13,37]=(x^4 + 68*x^3 + 1517*x^2 + 51946*x + 1868689)*(x^4 -40*x^3 + 800*x^2 + 8200*x + 42025);
T[13,41]=(x^4 -100*x^3 + 3461*x^2 -56606*x + 833569)*(x^4 -32*x^3 + 512*x^2 -3456*x + 11664);
T[13,43]=(x^4 + 1062*x^2 + 123201)*(x^2 -90*x + 2700)^2;
T[13,47]=(x^4 + 68*x^3 + 2312*x^2 -1496*x + 484)*(x^4 + 4*x^3 + 8*x^2 -10572*x + 6985449);
T[13,53]=(x^2 -64*x -1163)^2*(x^2 + 40*x + 150)^2;
T[13,59]=(x^4 + 164*x^3 + 6980*x^2 + 130432*x + 16613776)*(x^4 -56*x^3 + 1568*x^2 + 197568*x + 12446784);
T[13,61]=(x^4 + 124*x^3 + 12855*x^2 + 312604*x + 6355441)*(x^2 + 148*x + 5436)^2;
T[13,67]=(x^4 -118*x^3 + 10706*x^2 -530060*x + 9721924)*(x^4 + 84*x^3 + 3528*x^2 -532392*x + 40170244);
T[13,71]=(x^4 -284*x^3 + 40328*x^2 -2623308*x + 85322169)*(x^4 + 86*x^3 + 4658*x^2 + 157516*x + 2208196);
T[13,73]=(x^4 + 4000000)*(x^4 -58*x^3 + 1682*x^2 + 107938*x + 3463321);
T[13,79]=(x^2 -32*x -954)^2*(x^2 + 20*x -5192)^2;
T[13,83]=(x^4 + 188*x^3 + 17672*x^2 + 639952*x + 11587216)*(x^4 + 52*x^3 + 1352*x^2 -86424*x + 2762244);
T[13,89]=(x^4 -200*x^3 + 20000*x^2 -324000*x + 2624400)*(x^4 + 110*x^3 + 12050*x^2 + 560500*x + 8702500);
T[13,97]=(x^4 -178*x^3 + 13250*x^2 -619916*x + 18028516)*(x^4 + 68*x^3 + 2312*x^2 -1441736*x + 449524804);

T[14,2]=(x^2 + 3*x + 4)*(x^4 + 2*x^2 + 4);
T[14,3]=(x^4 + 6*x^3 + 9*x^2 -18*x + 9)*(x )^2;
T[14,5]=(x^4 + 6*x^3 -9*x^2 -126*x + 441)*(x )^2;
T[14,7]=(x^4 -8*x^3 + 42*x^2 -392*x + 2401)*(x + 7)^2;
T[14,11]=(x^4 -18*x^3 + 261*x^2 -1134*x + 3969)*(x + 6)^2;
T[14,13]=(x^4 + 264*x^2 + 7056)*(x )^2;
T[14,17]=(x^4 + 30*x^3 + 351*x^2 + 1530*x + 2601)*(x )^2;
T[14,19]=(x^4 -6*x^3 + 9*x^2 + 18*x + 9)*(x )^2;
T[14,23]=(x^4 -30*x^3 + 837*x^2 -1890*x + 3969)*(x -18)^2;
T[14,29]=(x + 54)^2*(x^2 -24*x + 72)^2;
T[14,31]=(x^4 + 42*x^3 -615*x^2 -50526*x + 1447209)*(x )^2;
T[14,37]=(x^4 + 62*x^3 + 4035*x^2 -11842*x + 36481)*(x + 38)^2;
T[14,41]=(x^4 + 1224*x^2 + 345744)*(x )^2;
T[14,43]=(x -58)^2*(x^2 + 4*x -68)^2;
T[14,47]=(x^4 -174*x^3 + 12609*x^2 -437958*x + 6335289)*(x )^2;
T[14,53]=(x^4 + 78*x^3 + 4851*x^2 + 96174*x + 1520289)*(x + 6)^2;
T[14,59]=(x^4 + 78*x^3 -1215*x^2 -252954*x + 10517049)*(x )^2;
T[14,61]=(x^4 + 42*x^3 -5409*x^2 -251874*x + 35964009)*(x )^2;
T[14,67]=(x^4 + 58*x^3 + 6573*x^2 -186122*x + 10297681)*(x + 118)^2;
T[14,71]=(x -114)^2*(x^2 + 12*x -1764)^2;
T[14,73]=(x^4 -318*x^3 + 40599*x^2 -2191338*x + 47485881)*(x )^2;
T[14,79]=(x^4 -110*x^3 + 9525*x^2 -283250*x + 6630625)*(x + 94)^2;
T[14,83]=(x^4 + 27936*x^2 + 189778176)*(x )^2;
T[14,89]=(x^4 + 378*x^3 + 56079*x^2 + 3194478*x + 71419401)*(x )^2;
T[14,97]=(x^4 + 11016*x^2 + 6780816)*(x )^2;

T[15,2]=(x + 1)*(x -1)*(x^2 + 5)*(x^4 + 4*x^3 + 8*x^2 -4*x + 1);
T[15,3]=(x + 3)*(x -3)*(x^2 + 4*x + 9)*(x^4 + 9);
T[15,5]=(x + 5)*(x -5)*(x^2 + 5)*(x^4 + 4*x^3 + 100*x + 625);
T[15,7]=(x^4 -4*x^3 + 8*x^2 + 40*x + 100)*(x + 6)^2*(x )^2;
T[15,11]=(x^2 + 20)*(x^2 -8*x -38)^2*(x )^2;
T[15,13]=(x^4 + 32*x^3 + 512*x^2 + 3712*x + 13456)*(x -16)^2*(x )^2;
T[15,17]=(x + 14)*(x -14)*(x^2 + 20)*(x^4 + 40*x^3 + 800*x^2 + 3680*x + 8464);
T[15,19]=(x^4 + 504*x^2 + 32400)*(x + 2)^2*(x + 22)^2;
T[15,23]=(x -34)*(x + 34)*(x^2 + 180)*(x^4 -56*x^3 + 1568*x^2 -21280*x + 144400);
T[15,29]=(x^2 + 980)*(x^4 + 1236*x^2 + 900)*(x )^2;
T[15,31]=(x -2)^2*(x + 18)^2*(x^2 + 8*x -200)^2;
T[15,37]=(x^4 -64*x^3 + 2048*x^2 + 29440*x + 211600)*(x + 16)^2*(x )^2;
T[15,41]=(x^2 + 3920)*(x^2 + 28*x -20)^2*(x )^2;
T[15,43]=(x^4 + 8*x^3 + 32*x^2 -9536*x + 1420864)*(x -16)^2*(x )^2;
T[15,47]=(x -14)*(x + 14)*(x^2 + 2420)*(x^4 -128*x^3 + 8192*x^2 -223744*x + 3055504);
T[15,53]=(x + 86)*(x -86)*(x^2 + 20)*(x^4 -56*x^3 + 1568*x^2 + 2240*x + 1600);
T[15,59]=(x^2 + 20)*(x^4 + 14124*x^2 + 19980900)*(x )^2;
T[15,61]=(x + 118)^2*(x -82)^2*(x^2 -100*x + 556)^2;
T[15,67]=(x^4 + 200*x^3 + 20000*x^2 + 990400*x + 24522304)*(x -24)^2*(x )^2;
T[15,71]=(x^2 + 15680)*(x )^2*(x + 68)^4;
T[15,73]=(x^4 -76*x^3 + 2888*x^2 + 470440*x + 38316100)*(x + 74)^2*(x )^2;
T[15,79]=(x -138)^2*(x -98)^2*(x^2 + 600)^2;
T[15,83]=(x -154)*(x + 154)*(x^2 + 8820)*(x^4 + 16*x^3 + 128*x^2 -8896*x + 309136);
T[15,89]=(x^2 + 11520)*(x^4 + 15624*x^2 + 59907600)*(x )^2;
T[15,97]=(x^4 + 20*x^3 + 200*x^2 -14360*x + 515524)*(x + 166)^2*(x )^2;

T[16,2]=(x + 2)*(x^6 + 2*x^5 + 6*x^4 + 8*x^3 + 24*x^2 + 32*x + 64)*(x )^2;
T[16,3]=(x^6 + 2*x^5 + 2*x^4 -32*x^3 + 196*x^2 -56*x + 8)*(x )*(x + 2)^2;
T[16,5]=(x + 6)*(x^6 + 2*x^5 + 2*x^4 -64*x^3 + 1156*x^2 + 136*x + 8)*(x )^2;
T[16,7]=(x^3 + 2*x^2 -60*x + 136)^2*(x )^3;
T[16,11]=(x^6 + 18*x^5 + 162*x^4 -32*x^3 + 3844*x^2 + 67208*x + 587528)*(x )*(x -14)^2;
T[16,13]=(x -10)*(x^6 + 2*x^5 + 2*x^4 + 1216*x^3 + 37636*x^2 + 311176*x + 1286408)*(x )^2;
T[16,17]=(x + 30)*(x -2)^2*(x^3 + 2*x^2 -260*x -1544)^2;
T[16,19]=(x^6 -30*x^5 + 450*x^4 -1184*x^3 + 1156*x^2 + 5576*x + 13448)*(x )*(x + 34)^2;
T[16,23]=(x^3 -30*x^2 + 164*x + 968)^2*(x )^3;
T[16,29]=(x -42)*(x^6 + 18*x^5 + 162*x^4 -20032*x^3 + 592900*x^2 -4752440*x + 19046792)*(x )^2;
T[16,31]=(x^6 + 1920*x^4 + 659456*x^2 + 16777216)*(x )^3;
T[16,37]=(x + 70)*(x^6 -46*x^5 + 1058*x^4 + 69568*x^3 + 2268036*x^2 + 439752*x + 42632)*(x )^2;
T[16,41]=(x -18)*(x^6 + 4992*x^4 + 6230016*x^2 + 67108864)*(x + 46)^2;
T[16,43]=(x^6 + 114*x^5 + 6498*x^4 + 30944*x^3 + 75076*x^2 + 80008*x + 42632)*(x )*(x -14)^2;
T[16,47]=(x^6 + 8576*x^4 + 15044608*x^2 + 6056574976)*(x )^3;
T[16,53]=(x -90)*(x^6 -78*x^5 + 3042*x^4 -51008*x^3 + 448900*x^2 -838840*x + 783752)*(x )^2;
T[16,59]=(x^6 -206*x^5 + 21218*x^4 -1225376*x^3 + 43270084*x^2 -853113976*x + 8410007432)*(x )*(x + 82)^2;
T[16,61]=(x + 22)*(x^6 -30*x^5 + 450*x^4 -64*x^3 + 334084*x^2 -10059512*x + 151449608)*(x )^2;
T[16,67]=(x^6 + 226*x^5 + 25538*x^4 + 1069024*x^3 + 8305924*x^2 -1203788344*x + 87233303432)*(x )*(x -62)^2;
T[16,71]=(x^3 + 130*x^2 -3548*x -391864)^2*(x )^3;
T[16,73]=(x + 110)*(x^6 + 18848*x^4 + 79362304*x^2 + 7310934016)*(x + 142)^2;
T[16,79]=(x^6 + 37376*x^4 + 433127424*x^2 + 1550483193856)*(x )^3;
T[16,83]=(x^6 -318*x^5 + 50562*x^4 -4522144*x^3 + 245423556*x^2 -7200782904*x + 105636303368)*(x )*(x -158)^2;
T[16,89]=(x + 78)*(x^6 + 16288*x^4 + 41113856*x^2 + 25681985536)*(x -146)^2;
T[16,97]=(x -130)*(x + 94)^2*(x^3 + 2*x^2 -17540*x + 519928)^2;

T[17,2]=(x^8 + 8*x^7 + 32*x^6 + 72*x^5 + 64*x^4 -120*x^3 -192*x^2 -248*x + 961)*(x^8 + 4*x^6 + 16*x^5 + 8*x^4 -8*x^3 + 20*x^2 -8*x + 1);
T[17,3]=(x^8 + 8*x^7 + 40*x^6 + 136*x^5 + 242*x^4 + 176*x^3 + 44*x^2 -8*x + 2)*(x^8 -4*x^6 -128*x^5 + 172*x^4 + 560*x^3 + 912*x^2 + 1088*x + 2312);
T[17,5]=(x^8 -16*x^7 + 96*x^6 -512*x^5 + 2848*x^4 -5632*x^3 + 7424*x^2 -3072*x + 512)*(x^8 + 24*x^7 + 280*x^6 + 1968*x^5 + 8530*x^4 + 24480*x^3 + 49524*x^2 + 23688*x + 4418);
T[17,7]=(x^8 + 16*x^7 + 124*x^6 + 512*x^5 + 1516*x^4 + 1584*x^3 + 1296*x^2 -11904*x + 7688)*(x^8 -8*x^7 + 24*x^6 + 832*x^5 -5872*x^4 + 17024*x^3 + 189952*x^2 -1579008*x + 8454272);
T[17,11]=(x^8 + 8*x^7 + 12*x^6 -432*x^5 + 12502*x^4 -130472*x^3 + 1210100*x^2 -9416168*x + 27572738)*(x^8 -40*x^7 + 700*x^6 -7600*x^5 + 58372*x^4 -308368*x^3 + 1142080*x^2 -2344096*x + 2221832);
T[17,13]=(x^8 -16*x^7 + 128*x^6 + 2688*x^5 + 129408*x^4 -1129472*x^3 + 5120000*x^2 + 9625600*x + 9048064)*(x^8 + 784*x^5 + 33548*x^4 + 159936*x^3 + 307328*x^2 -3162656*x + 16273156);
T[17,17]=(x^8 + 6975757441)*(x^8 + 16*x^7 + 240*x^6 -784*x^5 -11934*x^4 -226576*x^3 + 20045040*x^2 + 386201104*x + 6975757441);
T[17,19]=(x^8 + 368*x^6 -9888*x^5 + 67712*x^4 -20544*x^3 + 154432*x^2 + 925440*x + 929296)*(x^8 + 32*x^7 + 544*x^6 -18272*x^5 -731648*x^4 + 3772224*x^3 + 425576576*x^2 + 3674994944*x + 34090452496);
T[17,23]=(x^8 + 8*x^7 + 732*x^6 -4880*x^5 -155004*x^4 + 3797840*x^3 + 62607552*x^2 + 234152672*x + 564614408)*(x^8 + 56*x^7 + 1032*x^6 + 10912*x^5 + 193840*x^4 + 2371328*x^3 + 25926272*x^2 + 191029248*x + 859299968);
T[17,29]=(x^8 -48*x^7 + 624*x^6 -50688*x^5 + 2924096*x^4 -55948800*x^3 + 407177216*x^2 -17682432*x + 4240836608)*(x^8 -24*x^7 + 684*x^6 + 37368*x^5 -367578*x^4 + 9970776*x^3 + 194435964*x^2 -5811173928*x + 55846825218);
T[17,31]=(x^8 -24*x^7 + 232*x^6 -4512*x^5 + 46000*x^4 -407808*x^3 + 8906112*x^2 + 19152384*x + 14536832)*(x^8 -32*x^7 + 1988*x^6 -112*x^5 + 425124*x^4 + 15913520*x^3 + 1016546272*x^2 -29668074720*x + 182700453128);
T[17,37]=(x^8 + 168*x^7 + 13240*x^6 + 617328*x^5 + 18122514*x^4 + 331893280*x^3 + 3781969588*x^2 + 36497243576*x + 368317129538)*(x^8 -32*x^7 + 1024*x^6 -88192*x^5 + 4247072*x^4 -110329856*x^3 + 1831515392*x^2 -20619873280*x + 120057840128);
T[17,41]=(x^8 + 5396*x^6 + 188016*x^5 + 3219782*x^4 + 88327912*x^3 + 9430528292*x^2 + 66724395288*x + 126445152962)*(x^8 -48*x^7 + 1824*x^6 -56704*x^5 + 1267458*x^4 -34847696*x^3 + 851345876*x^2 -10891969944*x + 59058658562);
T[17,43]=(x^8 + 232*x^7 + 27932*x^6 + 2135880*x^5 + 106466248*x^4 + 3383205408*x^3 + 70877592744*x^2 + 937586073968*x + 6201305218564)*(x^8 -96*x^7 + 6096*x^6 -202080*x^5 + 3033216*x^4 -23148480*x^3 + 627412416*x^2 -3626059776*x + 6626611216);
T[17,47]=(x^8 + 80*x^7 + 3200*x^6 + 52224*x^5 + 454448*x^4 + 1132928*x^3 + 73728*x^2 + 6632448*x + 298321984)*(x^8 -192*x^7 + 18432*x^6 -907072*x^5 + 25209440*x^4 -277465600*x^3 + 2803712*x^2 -3559691264*x + 2259754549504);
T[17,53]=(x^8 -96*x^7 + 3844*x^6 -2888*x^5 -6527224*x^4 + 166007600*x^3 + 10152093336*x^2 -15284081296*x + 41458660996)*(x^8 + 32*x^7 + 2272*x^6 -76032*x^5 -1916416*x^4 + 38105088*x^3 + 1142718976*x^2 + 5213239296*x + 26754490624);
T[17,59]=(x^8 + 48*x^7 + 5988*x^6 -167784*x^5 -2594808*x^4 + 145724880*x^3 -682934952*x^2 -57746117328*x + 2675455605124)*(x^8 -8*x^7 -1064*x^6 + 336*x^5 + 632480*x^4 + 10633056*x^3 + 135774688*x^2 + 560492736*x + 2347596304);
T[17,61]=(x^8 -264*x^7 + 33304*x^6 -2572800*x^5 + 135893650*x^4 -5097119184*x^3 + 135419278356*x^2 -2424960371688*x + 22880163635522)*(x^8 + 160*x^7 + 8384*x^6 + 480256*x^5 + 53458432*x^4 + 2998558720*x^3 + 96984055808*x^2 + 3040094060544*x + 106680004247552);
T[17,67]=(x^8 + 21304*x^6 + 118064724*x^4 + 200330319344*x^2 + 83643718741636)*(x^8 + 5648*x^6 + 8900944*x^4 + 5129355392*x^2 + 883915868224);
T[17,71]=(x^8 -40*x^7 -12216*x^6 + 1432352*x^5 + 43290416*x^4 -6737847296*x^3 + 458184132736*x^2 -3272841105408*x + 71246079996032)*(x^8 -32*x^7 -2196*x^6 + 135024*x^5 + 42479948*x^4 + 3199372144*x^3 + 135768730928*x^2 + 3895168393024*x + 53847249369608);
T[17,73]=(x^8 -48*x^7 -4096*x^6 + 449272*x^5 + 5936898*x^4 -577515296*x^3 + 27962577292*x^2 + 13800580712*x + 51301810562)*(x^8 -24*x^7 + 3500*x^6 -666472*x^5 + 36581382*x^4 -2545401688*x^3 + 73884514684*x^2 + 2164179191800*x + 18825456624578);
T[17,79]=(x^8 + 96*x^7 -11292*x^6 -460080*x^5 + 155506340*x^4 + 14586463536*x^3 + 753162518240*x^2 + 605065512288*x + 376288804594952)*(x^8 + 136*x^7 + 3800*x^6 + 741152*x^5 + 121806000*x^4 + 5217092480*x^3 + 94955734144*x^2 + 467240282112*x + 3948319764608);
T[17,83]=(x^8 + 88*x^7 + 12840*x^6 + 2699248*x^5 + 235526048*x^4 + 15373798880*x^3 + 1840271092512*x^2 + 107151246314048*x + 2213513927616016)*(x^8 + 264*x^7 + 35100*x^6 + 5125992*x^5 + 737320392*x^4 + 61237522464*x^3 + 2706769838376*x^2 + 65499066502320*x + 1042256526864004);
T[17,89]=(x^8 -160*x^7 + 12800*x^6 + 64128*x^5 + 72896012*x^4 -9469447872*x^3 + 584098906112*x^2 -11720367113216*x + 117588822570244)*(x^8 -288*x^7 + 41472*x^6 -2375728*x^5 + 64339340*x^4 + 68856320*x^3 + 133930036352*x^2 -5877071051936*x + 128947789048324);
T[17,97]=(x^8 + 344*x^7 + 70152*x^6 + 9217176*x^5 + 1115831762*x^4 + 80979007328*x^3 + 4623209175980*x^2 -208389281287432*x + 1837260172011842)*(x^8 -48*x^7 -4444*x^6 + 520800*x^5 + 3432614*x^4 -652549016*x^3 + 50830789412*x^2 -852254254440*x + 21682310986562);

T[18,2]=(x^2 + 2)*(x^4 + 3*x^3 + 7*x^2 + 12*x + 16)*(x^4 -2*x^2 + 4);
T[18,3]=(x^4 -6*x^2 + 81)*(x^2 + 3*x + 9)^2*(x )^2;
T[18,5]=(x^2 + 18)*(x^2 -6*x + 12)^2*(x^2 + 9*x + 27)^2;
T[18,7]=(x^4 -2*x^3 + 57*x^2 + 106*x + 2809)*(x + 4)^2*(x^2 + 2*x + 4)^2;
T[18,11]=(x^2 + 288)*(x^4 -18*x^3 + 117*x^2 -162*x + 81)*(x^2 + 3*x + 3)^2;
T[18,13]=(x^4 + 10*x^3 + 291*x^2 -1910*x + 36481)*(x -8)^2*(x^2 -4*x + 16)^2;
T[18,17]=(x^2 + 162)*(x^4 + 360*x^2 + 1296)*(x^2 + 243)^2;
T[18,19]=(x + 16)^2*(x^2 + 20*x -116)^2*(x -11)^4;
T[18,23]=(x^2 + 288)*(x^4 -18*x^3 + 117*x^2 -162*x + 81)*(x^2 + 48*x + 768)^2;
T[18,29]=(x^2 + 18)*(x^4 -18*x^3 + 63*x^2 + 810*x + 2025)*(x^2 -78*x + 2028)^2;
T[18,31]=(x^4 -38*x^3 + 1569*x^2 + 4750*x + 15625)*(x -44)^2*(x^2 + 32*x + 1024)^2;
T[18,37]=(x^2 -64*x + 808)^2*(x + 34)^6;
T[18,41]=(x^2 + 2178)*(x^4 + 126*x^3 + 5967*x^2 + 85050*x + 455625)*(x^2 + 21*x + 147)^2;
T[18,43]=(x^4 + 46*x^3 + 2073*x^2 + 1978*x + 1849)*(x + 40)^2*(x^2 -61*x + 3721)^2;
T[18,47]=(x^2 + 7200)*(x^4 -54*x^3 + 333*x^2 + 34506*x + 408321)*(x^2 + 84*x + 2352)^2;
T[18,53]=(x^2 + 1458)*(x^4 + 9000*x^2 + 810000)*(x )^4;
T[18,59]=(x^2 + 1152)*(x^4 -126*x^3 + 3573*x^2 + 216594*x + 2954961)*(x^2 -87*x + 2523)^2;
T[18,61]=(x^4 -62*x^3 + 4827*x^2 + 60946*x + 966289)*(x -50)^2*(x^2 + 56*x + 3136)^2;
T[18,67]=(x^4 + 106*x^3 + 8913*x^2 + 246238*x + 5396329)*(x -8)^2*(x^2 -31*x + 961)^2;
T[18,71]=(x^2 + 2592)*(x^4 + 7704*x^2 + 2396304)*(x^2 + 972)^2;
T[18,73]=(x + 16)^2*(x^2 + 104*x + 760)^2*(x -65)^4;
T[18,79]=(x^4 -14*x^3 + 1497*x^2 + 18214*x + 1692601)*(x + 76)^2*(x^2 + 38*x + 1444)^2;
T[18,83]=(x^2 + 14112)*(x^4 + 378*x^3 + 59085*x^2 + 4330746*x + 131262849)*(x^2 + 84*x + 2352)^2;
T[18,89]=(x^2 + 162)*(x^4 + 22824*x^2 + 36144144)*(x^2 + 15552)^2;
T[18,97]=(x^4 -14*x^3 + 10731*x^2 + 147490*x + 110986225)*(x -176)^2*(x^2 -115*x + 13225)^2;

T[19,2]=(x^2 + 13)*(x^6 + 3*x^5 -4*x^4 -21*x^3 + 40*x^2 + 63*x + 27)*(x^12 + 6*x^11 + 18*x^10 + 39*x^9 + 48*x^8 + 57*x^7 + 74*x^6 -120*x^5 -171*x^4 -381*x^3 + 1110*x^2 -969*x + 361)*(x );
T[19,3]=(x^2 + 13)*(x^6 + 9*x^5 + 20*x^4 -63*x^3 -194*x^2 + 567*x + 2187)*(x^12 + 12*x^10 + 63*x^9 + 375*x^8 + 1395*x^7 + 2699*x^6 + 4905*x^5 + 8913*x^4 + 9657*x^3 + 6270*x^2 + 2142*x + 289)*(x );
T[19,5]=(x + 9)*(x^6 + 2*x^5 + 48*x^4 + 164*x^3 + 2188*x^2 + 5544*x + 15876)*(x^12 + 6*x^11 + 96*x^10 + 542*x^9 + 3060*x^8 + 12501*x^7 + 19875*x^6 -16974*x^5 + 18792*x^4 + 402464*x^3 + 644736*x^2 -483072*x + 87616)*(x -4)^2;
T[19,7]=(x^12 -6*x^11 + 177*x^10 -568*x^9 + 21825*x^8 -72927*x^7 + 816363*x^6 + 1402398*x^5 + 5673852*x^4 -31312*x^3 + 3662448*x^2 + 1064064*x + 1700416)*(x^3 -78*x -94)^2*(x + 5)^3;
T[19,11]=(x -3)*(x^12 + 18*x^11 + 498*x^10 + 3160*x^9 + 86157*x^8 + 645732*x^7 + 8499348*x^6 + 47760624*x^5 + 457663347*x^4 + 2377579384*x^3 + 15408882171*x^2 + 45455736540*x + 131774082049)*(x + 10)^2*(x^3 -13*x^2 -83*x -3)^2;
T[19,13]=(x^2 + 13)*(x^6 -30*x^5 + 272*x^4 + 840*x^3 -9536*x^2 -28896*x + 355008)*(x^12 -21*x^11 + 114*x^10 -6*x^9 -13908*x^8 + 747984*x^7 -17442205*x^6 + 108643920*x^5 + 1513037544*x^4 -28517583432*x^3 + 271049605152*x^2 -1250371517568*x + 3568865052736)*(x );
T[19,17]=(x^6 + 42*x^5 + 1200*x^4 + 18864*x^3 + 216792*x^2 + 1360368*x + 5817744)*(x^12 + 3*x^11 -84*x^10 -5835*x^9 + 140733*x^8 -3169872*x^7 + 42151440*x^6 + 134521551*x^5 -42311340*x^4 -5490473751*x^3 + 16088647032*x^2 -15053468544*x + 21556993329)*(x -15)^3;
T[19,19]=(x + 19)*(x^2 + 12*x + 361)*(x^6 -25*x^5 + 1026*x^4 -16967*x^3 + 370386*x^2 -3258025*x + 47045881)*(x^12 + 24*x^11 -234*x^10 -22458*x^9 -279414*x^8 + 4979634*x^7 + 206298143*x^6 + 1797647874*x^5 -36413511894*x^4 -1056556395498*x^3 -3974153751594*x^2 + 147145590187224*x + 2213314919066161);
T[19,23]=(x + 30)*(x^6 -8*x^5 + 174*x^4 -356*x^3 + 17044*x^2 -67980*x + 381924)*(x^12 + 102*x^11 + 5880*x^10 + 273784*x^9 + 10391760*x^8 + 292678560*x^7 + 6330373440*x^6 + 111502541952*x^5 + 1611787315968*x^4 + 13951271732224*x^3 + 68945393206272*x^2 + 146423489488896*x + 114585206984704)*(x -35)^2;
T[19,29]=(x^2 + 325)*(x^6 + 12*x^5 -1432*x^4 -17760*x^3 + 2241448*x^2 -18887760*x + 54289548)*(x^12 -147*x^11 + 10638*x^10 -495825*x^9 + 16448439*x^8 -407498262*x^7 + 7707315827*x^6 -111829141632*x^5 + 1234406252448*x^4 -10135043629824*x^3 + 59687422722048*x^2 -234855910394880*x + 484594358358016)*(x );
T[19,31]=(x^2 + 1300)*(x^6 + 4544*x^4 + 6412156*x^2 + 2642351052)*(x^12 -99*x^11 + 2961*x^10 + 30294*x^9 -2336403*x^8 -24699258*x^7 + 2537545199*x^6 -35287784172*x^5 + 130776490692*x^4 + 733017675600*x^3 -3715410684720*x^2 -19515803015520*x + 125789503910464)*(x );
T[19,37]=(x^2 + 468)*(x^6 + 3024*x^4 + 1967760*x^2 + 38988)*(x^12 + 7554*x^10 + 19173357*x^8 + 19392783351*x^6 + 6439801106628*x^4 + 49576343261472*x^2 + 58527273697344)*(x );
T[19,41]=(x^2 + 1300)*(x^6 -63*x^5 -304*x^4 + 102501*x^3 + 1834996*x^2 -62920971*x + 498533643)*(x^12 + 144*x^11 + 11163*x^10 + 537300*x^9 + 10784265*x^8 + 285844698*x^7 + 30757459193*x^6 + 799236717768*x^5 + 2841780178866*x^4 + 366249480780096*x^3 + 14496905319694035*x^2 + 148886418653773083*x + 1764172716994959769)*(x );
T[19,43]=(x + 85)*(x^6 + 34*x^5 + 2072*x^4 + 31528*x^3 + 1904480*x^2 + 28703776*x + 981944896)*(x^12 + 27*x^11 + 1068*x^10 + 32441*x^9 + 565380*x^8 + 16261317*x^7 + 452183766*x^6 + 8021235294*x^5 + 260261248977*x^4 + 3695565302087*x^3 + 25080864893577*x^2 + 85380845950785*x + 126559282520449)*(x + 20)^2;
T[19,47]=(x -75)*(x^6 -58*x^5 + 3198*x^4 -29056*x^3 + 590968*x^2 + 1612524*x + 94361796)*(x^12 + 99*x^11 + 6018*x^10 + 545900*x^9 + 21089358*x^8 -860318676*x^7 -26488542927*x^6 + 880962311304*x^5 + 48915724837824*x^4 -2093652566478400*x^3 + 23764014523054080*x^2 -16482130242902016*x + 51107507449532416)*(x -10)^2;
T[19,53]=(x^2 + 5733)*(x^6 + 12*x^5 -768*x^4 -9792*x^3 + 714240*x^2 -9870336*x + 48771072)*(x^12 -111*x^11 + 13224*x^10 -759030*x^9 + 54000135*x^8 -2236069071*x^7 + 72459909303*x^6 + 1311297014772*x^5 -198134250122232*x^4 -6124775763576312*x^3 + 139255277278786560*x^2 + 10531681076371220352*x + 143672891830751209536)*(x );
T[19,59]=(x^2 + 325)*(x^6 + 147*x^5 + 6458*x^4 -109515*x^3 -3033392*x^2 + 54558585*x + 1787690763)*(x^12 -3*x^11 -5478*x^10 + 170481*x^9 + 5105817*x^8 -709880586*x^7 -15953982352*x^6 + 1947351120693*x^5 + 113589671554704*x^4 -13709960216610501*x^3 + 665474506911671994*x^2 -4717178364676477758*x + 48598825300947064441)*(x );
T[19,61]=(x -103)*(x^6 -58*x^5 + 6152*x^4 + 213140*x^3 + 6281300*x^2 + 71701784*x + 661415524)*(x^12 -150*x^11 + 9552*x^10 + 23971*x^9 + 18260208*x^8 -1793646162*x^7 + 116380895793*x^6 -5154652604772*x^5 + 118058816917584*x^4 -1105033309337192*x^3 + 4290305499715008*x^2 -5851238461128384*x + 11772463528968256)*(x + 40)^2;
T[19,67]=(x^2 + 1573)*(x^6 -201*x^5 + 15182*x^4 -344715*x^3 + 2458624*x^2 + 12353145*x + 17294403)*(x^12 -135*x^11 -4890*x^10 + 73566*x^9 + 77517759*x^8 + 2845329903*x^7 + 105279919091*x^6 + 1299965734872*x^5 + 13626071201904*x^4 + 49196971997496*x^3 -29884036858080*x^2 + 189790627169088*x + 2263368445816384)*(x );
T[19,71]=(x^2 + 11700)*(x^6 + 102*x^5 + 4272*x^4 + 82008*x^3 + 712512*x^2 + 1562976*x + 1259712)*(x^12 + 168*x^11 + 7788*x^10 -97296*x^9 -13446288*x^8 + 768302208*x^7 + 39956011584*x^6 -3238391075328*x^5 + 85451574670848*x^4 -1376405107845120*x^3 + 11200687733947392*x^2 + 5231233176496128*x + 426631027998560256)*(x );
T[19,73]=(x + 25)*(x^6 -7*x^5 + 3274*x^4 -14343*x^3 + 10529838*x^2 -59530275*x + 340734681)*(x^12 + 90*x^11 -1881*x^10 -407115*x^9 -1795068*x^8 + 368250381*x^7 + 21718449513*x^6 + 3495933887544*x^5 + 254936506257504*x^4 -2354692496860296*x^3 + 105514942443289056*x^2 -634328099451521856*x + 1713970642862984256)*(x -105)^2;
T[19,79]=(x^2 + 1300)*(x^6 -6688*x^4 + 44729344*x^2 -2436251136*x + 44231363328)*(x^12 + 75*x^11 -2808*x^10 -1772211*x^9 -126894525*x^8 -394261176*x^7 + 937750422287*x^6 + 87287584862334*x^5 + 4128528610399896*x^4 + 101215054086396744*x^3 + 914131204085785296*x^2 -1217574818755284864*x + 30592994553513538624)*(x );
T[19,83]=(x -90)*(x^12 + 156*x^11 + 19440*x^10 + 1130752*x^9 + 59044293*x^8 + 1190227050*x^7 + 55848167622*x^6 + 632010719844*x^5 + 49439492501049*x^4 -30122656543898*x^3 + 13963617671247183*x^2 + 96276580750699470*x + 1588538503497182689)*(x + 40)^2*(x^3 -73*x^2 -5585*x + 397611)^2;
T[19,89]=(x^6 + 72*x^5 -14040*x^4 -1135296*x^3 + 260737056*x^2 -7954451424*x + 84829321008)*(x^12 + 558*x^11 + 156564*x^10 + 26603523*x^9 + 2934784926*x^8 + 209976419475*x^7 + 9470718256302*x^6 + 277313704883010*x^5 + 5585723277827445*x^4 + 29457764357281677*x^3 -75914916763074660*x^2 -22678618180055776479*x + 145912156022328113889)*(x )^3;
T[19,97]=(x^2 + 15028)*(x^6 -21*x^5 -15532*x^4 + 329259*x^3 + 247598380*x^2 + 3958586883*x + 21248211843)*(x^12 -465*x^11 + 120888*x^10 -15773727*x^9 + 981371550*x^8 + 69576778509*x^7 -14403696791830*x^6 + 1088121328485132*x^5 + 11099343945869775*x^4 -4421941171346667993*x^3 + 69710338525615487157*x^2 -14140453495929595146561*x + 1169324461779991579870201)*(x );

T[20,2]=(x + 2)*(x -2)*(x^2 + 2*x + 2)*(x^2 + 4)*(x^4 + 2*x^3 + 4*x^2 + 8*x + 16)*(x )^4;
T[20,3]=(x + 4)*(x -4)*(x^2 -2*x + 2)*(x^4 + 20*x^2 + 80)*(x^2 + 4*x + 8)^2*(x )^2;
T[20,5]=(x^2 + 6*x + 25)*(x^2 -6*x + 25)*(x + 5)^2*(x^2 + 25)^2*(x^2 -5)^2;
T[20,7]=(x -4)*(x + 4)*(x^2 + 14*x + 98)*(x^4 + 100*x^2 + 2000)*(x^2 -4*x + 8)^2*(x )^2;
T[20,11]=(x^4 + 400*x^2 + 1280)*(x -10)^2*(x + 8)^4*(x )^4;
T[20,13]=(x^2 -18*x + 162)*(x^2 + 576)*(x^2 + 8*x -4)^2*(x^2 -6*x + 18)^2*(x )^2;
T[20,17]=(x^2 -2*x + 2)*(x^2 + 256)*(x^2 + 12*x -284)^2*(x^2 -14*x + 98)^2*(x )^2;
T[20,19]=(x^2 + 64)*(x^4 + 320*x^2 + 20480)*(x^2 + 400)^2*(x )^4;
T[20,23]=(x -44)*(x + 44)*(x^2 + 46*x + 1058)*(x^4 + 260*x^2 + 80)*(x^2 + 4*x + 8)^2*(x )^2;
T[20,29]=(x^2 + 64)*(x -42)^2*(x + 22)^2*(x^2 + 4*x -76)^2*(x^2 + 1600)^2;
T[20,31]=(x^4 + 2320*x^2 + 154880)*(x + 14)^2*(x -52)^4*(x )^4;
T[20,37]=(x^2 + 576)*(x^2 -66*x + 2178)*(x^2 + 6*x + 18)^2*(x^2 -8*x -484)^2*(x )^2;
T[20,41]=(x + 18)^2*(x + 14)^2*(x -62)^2*(x^2 + 56*x + 604)^2*(x + 8)^4;
T[20,43]=(x -76)*(x + 76)*(x^2 + 30*x + 450)*(x^4 + 500*x^2 + 2000)*(x^2 + 84*x + 3528)^2*(x )^2;
T[20,47]=(x -4)*(x + 4)*(x^2 + 78*x + 3042)*(x^4 + 4100*x^2 + 3561680)*(x^2 + 36*x + 648)^2*(x )^2;
T[20,53]=(x^2 + 3136)*(x^2 + 14*x + 98)*(x^2 -106*x + 5618)^2*(x^2 + 88*x + 1436)^2*(x )^2;
T[20,59]=(x^2 + 3136)*(x^4 + 5760*x^2 + 1658880)*(x^2 + 400)^2*(x )^4;
T[20,61]=(x -42)^2*(x + 58)^2*(x -22)^2*(x^2 -64*x -2356)^2*(x + 48)^4;
T[20,67]=(x -116)*(x + 116)*(x^2 + 14*x + 98)*(x^4 + 10420*x^2 + 19920080)*(x^2 -124*x + 7688)^2*(x )^2;
T[20,71]=(x^4 + 8080*x^2 + 10138880)*(x -98)^2*(x + 28)^4*(x )^4;
T[20,73]=(x^2 -98*x + 4802)*(x^2 + 9216)*(x^2 + 94*x + 4418)^2*(x^2 -132*x -764)^2*(x )^2;
T[20,79]=(x^2 + 9216)*(x^4 + 13120*x^2 + 2478080)*(x )^8;
T[20,83]=(x + 76)*(x -76)*(x^2 + 126*x + 7938)*(x^4 + 6260*x^2 + 2620880)*(x^2 -36*x + 648)^2*(x )^2;
T[20,89]=(x^2 + 12544)*(x + 142)^2*(x + 78)^2*(x^2 + 44*x -7516)^2*(x^2 + 6400)^2;
T[20,97]=(x^2 -66*x + 2178)*(x^2 + 20736)*(x^2 + 126*x + 7938)^2*(x^2 + 132*x + 3636)^2*(x )^2;

}