Sharedwww / Tables / an_s6g0new_1-50.gpOpen in CoCalc
Author: William A. Stein
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\\ an_s6g0new_1-50.gp
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\\ This is a PARI readable nonnormalized basis for S_k(Gamma_0(N)) for N
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\\ in the range: 1 <= N <= 50.
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\\ The number of a_n computed is sufficient to satisfy Sturm's bound.
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\\ William Stein ([email protected])
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E[3,1] = [x, [1,-6]];
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E[4,1] = [x, [1,0,-12]];
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E[5,1] = [x, [1,2,-4]];
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E[6,1] = [x, [1,4,-9,16,-66,-36]];
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E[7,1] = [x, [1,-10,-14,68]];
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E[7,2] = [x^2-9*x+6, [1,x,-6*x+24,9*x-38]];
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E[8,1] = [x, [1,0,20,0,-74,0]];
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E[9,1] = [x, [1,6,0,4,-6,0]];
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E[10,1] = [x, [1,4,6,16,-25,24,-118,64,-207]];
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E[10,2] = [x, [1,-4,24,16,25,-96,-172,-64,333]];
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E[10,3] = [x, [1,-4,-26,16,-25,104,-22,-64,433]];
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E[11,1] = [x, [1,-4,-15,-16,-19,60]];
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E[11,2] = [x^3-90*x+188, [6,6*x,-x^2-10*x+128,6*x^2-192,-9*x^2-42*x+588,-10*x^2+38*x+188]];
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E[13,1] = [x^2+5*x+2, [1,x,-6*x-29,-5*x-34,40*x+79,x+12,-70*x-193]];
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E[13,2] = [x^3-7*x^2-84*x+444, [4,4*x,-x^2-3*x+90,4*x^2-128,-x^2-27*x+210,-10*x^2+6*x+444,-3*x^2-9*x+158]];
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E[14,1] = [x, [1,4,8,16,10,32,-49,64,-179,40,-340,128]];
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E[14,2] = [x, [1,-4,10,16,84,-40,49,-64,-143,-336,-336,160]];
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E[15,1] = [x, [1,-2,-9,-28,-25,18,-132,120,81,50,472,252]];
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E[15,2] = [x, [1,7,9,17,-25,63,12,-105,81,-175,112,153]];
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E[15,3] = [x^2+x-102, [1,x,-9,-x+70,25,-9*x,-16*x-64,39*x-102,81,25*x,-32*x+108,9*x-630]];
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E[16,1] = [x, [1,0,12,0,54,0,88,0,-99,0,-540,0]];
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E[16,2] = [x, [1,0,-20,0,-74,0,24,0,157,0,-124,0]];
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E[17,1] = [x, [1,-6,10,4,-72,-60,-196,168,-143]];
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E[17,2] = [x, [1,1,-18,-31,-16,-18,28,-63,81]];
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E[17,3] = [x^4-3*x^3-94*x^2+284*x+968, [24,24*x,-x^3-11*x^2+84*x+652,24*x^2-768,12*x^3+12*x^2-936*x+528,-14*x^3-10*x^2+936*x+968,-15*x^3-45*x^2+804*x+3396,24*x^3-1536*x,-30*x^3-162*x^2+2112*x+6960]];
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E[18,1] = [x, [1,4,0,16,96,0,-148,64,0,384,-384,0,-334,-592,0,256,-576,0]];
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E[18,2] = [x, [1,-4,0,16,66,0,176,-64,0,-264,60,0,-658,-704,0,256,414,0]];
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E[18,3] = [x, [1,-4,0,16,-96,0,-148,-64,0,384,384,0,-334,592,0,256,576,0]];
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E[19,1] = [x, [1,-6,4,4,54,-24,248,168,-227,-324]];
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E[19,2] = [x, [1,-2,-1,-28,-24,2,-167,120,-242,48]];
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E[19,3] = [x^2+7*x-32, [1,x,-3*x-14,-7*x,5*x-49,7*x-96,14*x+85,17*x-224,21*x+241,-84*x+160]];
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E[19,4] = [x^4-9*x^3-72*x^2+774*x-1140, [22,22*x,3*x^3-15*x^2-210*x+1086,22*x^2-704,-23*x^3+27*x^2+1786*x-3024,12*x^3+6*x^2-1236*x+3420,18*x^3-46*x^2-1260*x+2798,22*x^3-1408*x,45*x^3-225*x^2-4734*x+24012,-180*x^3+130*x^2+14778*x-26220]];
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E[20,1] = [x, [1,0,22,0,-25,0,218,0,241,0,-480,0,-622,0,-550,0,186,0]];
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E[21,1] = [x, [1,10,9,68,-106,90,-49,360,81,-1060,92,612,670,-490,-954,1424]];
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E[21,2] = [x, [1,5,9,-7,94,45,-49,-195,81,470,52,-63,-770,-245,846,-751]];
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E[21,3] = [x, [1,-6,-9,4,78,54,49,168,81,-468,444,-36,-442,-294,-702,-1136]];
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E[21,4] = [x, [1,1,-9,-31,-34,-9,-49,-63,81,-34,-340,279,454,-49,306,929]];
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E[22,1] = [x, [1,-4,1,16,-51,-4,-166,-64,-242,204,-121,16,692,664,-51,256,-738,968]];
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E[22,2] = [x, [1,-4,-21,16,81,84,98,-64,198,-324,121,-336,824,-392,-1701,256,978,-792]];
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E[22,3] = [x, [1,4,-29,16,-31,-116,-230,64,598,-124,121,-464,112,-920,899,256,-1142,2392]];
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E[22,4] = [x^2-29*x+12, [1,4,x,16,-5*x+66,4*x,-6*x+80,64,29*x-255,-20*x+264,-121,16*x,-10*x-178,-24*x+320,-79*x+60,256,124*x-1902,116*x-1020]];
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E[23,1] = [x^3+4*x^2-48*x-8, [4,4*x,-x^2-14*x-8,4*x^2-128,2*x^2-152,-10*x^2-56*x-8,-4*x^2+44*x-168,-16*x^2-64*x+32,41*x^2+346*x-908,-8*x^2-56*x+16,28*x^2+180*x-624,16*x^2-40*x+176]];
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E[23,2] = [x^6-4*x^5-144*x^4+381*x^3+5928*x^2-7784*x-77528, [1236,1236*x,-27*x^5+142*x^4+2992*x^3-12483*x^2-58778*x+199328,1236*x^2-39552,90*x^5-336*x^4-10248*x^3+21834*x^2+219960*x-112896,34*x^5-896*x^4-2196*x^3+101278*x^2-10840*x-2093256,-6*x^5+1176*x^4-2448*x^3-135438*x^2+143544*x+3027816,1236*x^3-79104*x,-353*x^5-234*x^4+44672*x^3+84271*x^2-1110962*x-2827076,24*x^5+2712*x^4-12456*x^3-313560*x^2+587664*x+6977520,-108*x^5+156*x^4+12792*x^3-10380*x^2-277548*x+158712,104*x^5-1844*x^4-7420*x^3+187064*x^2+52296*x-3742544]];
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E[24,1] = [x, [1,0,9,0,38,0,120,0,81,0,524,0,-962,0,342,0,-1358,0,-2284,0,1080,0,2552,0]];
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E[24,2] = [x, [1,0,-9,0,-34,0,-240,0,81,0,-124,0,46,0,306,0,1954,0,-1924,0,2160,0,2840,0]];
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E[24,3] = [x, [1,0,-9,0,94,0,144,0,81,0,-380,0,814,0,-846,0,-862,0,-1156,0,-1296,0,-488,0]];
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E[25,1] = [x, [1,-2,4,-28,0,-8,-192,120,-227,0,-148,-112,-286,384,0]];
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E[25,2] = [x^2+5*x-54, [1,x,-2*x-15,-5*x+22,0,-5*x-108,-4*x-110,15*x-270,40*x+198,0,50*x+27,-19*x+210,-32*x+100,-90*x-216,0]];
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E[25,3] = [x^2-5*x-54, [1,x,-2*x+15,5*x+22,0,5*x-108,-4*x+110,15*x+270,-40*x+198,0,-50*x+27,-19*x-210,-32*x-100,90*x-216,0]];
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E[25,4] = [x^2-44, [1,x,3*x,12,0,132,-9*x,-20*x,153,0,252,36*x,18*x,-396,0]];
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E[26,1] = [x^2-9*x-192, [1,4,x,16,-3*x+50,4*x,-9*x+118,64,9*x-51,-12*x+200,24*x-218,16*x,-169,-36*x+472,23*x-576,256,-129*x+486,36*x-204,60*x-1518,-48*x+800,37*x-1728]];
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E[26,2] = [x^2-9*x-676, [1,-4,x,16,-x-14,-4*x,-x+168,-64,9*x+433,4*x+56,-10*x+88,16*x,169,4*x-672,-23*x-676,256,11*x-290,-36*x-1732,-70*x+936,-16*x-224,159*x-676]];
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E[26,3] = [x, [1,-4,0,16,-14,0,-170,-64,-243,56,-250,0,-169,680,0,256,1062,972,-78,-224,0]];
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E[27,1] = [x^2+9*x-18, [1,x,0,-9*x-14,-10*x-81,0,18*x+77,35*x-162,0,9*x-180,-32*x-405,0,72*x-28,-85*x+324,0,-189*x+1078,168*x+648,0]];
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E[27,2] = [x^2-9*x-18, [1,x,0,9*x-14,-10*x+81,0,-18*x+77,35*x+162,0,-9*x-180,-32*x+405,0,-72*x-28,-85*x-324,0,189*x+1078,168*x-648,0]];
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E[27,3] = [x^2-54, [1,x,0,22,8*x,0,167,-10*x,0,432,-104*x,0,-235,167*x,0,-1244,24*x,0]];
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E[27,4] = [x, [1,0,0,-32,0,0,-211,0,0,0,0,0,-775,0,0,1024,0,0]];
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E[28,1] = [x, [1,0,26,0,16,0,-49,0,433,0,8,0,684,0,416,0,-2218,0,-2698,0,-1274,0,3344,0]];
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E[28,2] = [x, [1,0,-2,0,-96,0,49,0,-239,0,-720,0,572,0,192,0,1254,0,-94,0,-98,0,96,0]];
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E[29,1] = [x^4-69*x^2+168*x+196, [14,14*x,x^3-83*x+28,14*x^2-448,-14*x^3-56*x^2+602*x-70,-14*x^2-140*x-196,36*x^3+168*x^2-1588*x-1988,14*x^3-896*x,-8*x^3+832*x-1988,-56*x^3-364*x^2+2282*x+2744,39*x^3+280*x^2-885*x-5180,-46*x^3-140*x^2+2460*x-896,-190*x^3-840*x^2+9442*x+3430,168*x^3+896*x^2-8036*x-7056,191*x^3+1120*x^2-7173*x-11312]];
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E[29,2] = [x^7-4*x^6-181*x^5+346*x^4+10616*x^3+2416*x^2-186896*x-351200, [960,960*x,x^6-16*x^5-153*x^4+1846*x^3+8756*x^2-43720*x-148640,960*x^2-30720,3*x^6+6*x^5-363*x^4-1044*x^3+6432*x^2+30864*x+101040,-12*x^6+28*x^5+1500*x^4-1860*x^3-46136*x^2+38256*x+351200,72*x^5+288*x^4-10056*x^3-39408*x^2+282912*x+972480,960*x^3-61440*x,15*x^6-106*x^5-2439*x^4+13188*x^3+122144*x^2-385296*x-1568720,18*x^6+180*x^5-2082*x^4-25416*x^3+23616*x^2+661728*x+1053600,-9*x^6-216*x^5+1137*x^4+27426*x^3+876*x^2-704280*x-1023840,-52*x^6-160*x^5+7188*x^4+22184*x^3-212944*x^2-492512*x+542080,-15*x^6-114*x^5+1959*x^4+13272*x^3-36264*x^2-287424*x-324240,72*x^6+288*x^5-10056*x^4-39408*x^3+282912*x^2+972480*x,53*x^6-296*x^5-9501*x^4+39782*x^3+491620*x^2-1198088*x-6249760]];
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E[30,1] = [x, [1,-4,9,16,-25,-36,164,-64,81,100,720,144,698,-656,-225,256,-2226,-324,356,-400,1476,-2880,-1800,-576,625,-2792,729,2624,714,900,848,-1024,6480,8904,-4100,1296]];
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E[30,2] = [x, [1,4,9,16,25,36,32,64,81,100,12,144,-154,128,225,256,-918,324,-1060,400,288,48,-4224,576,625,-616,729,512,-7890,900,5192,1024,108,-3672,800,1296]];
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E[31,1] = [x^8-7*x^7-178*x^6+903*x^5+10963*x^4-30550*x^3-240688*x^2+115128*x+420336, [24864768,24864768*x,-4621*x^7+43273*x^6+571764*x^5-4457235*x^4-24531877*x^3+114846748*x^2+439195464*x-265445640,24864768*x^2-795672576,-150*x^7+38622*x^6-240168*x^5-3714858*x^4+18056730*x^3+42552840*x^2-74068752*x+1899615888,10926*x^7-250774*x^6-284472*x^5+26128146*x^4-26324802*x^3-673023784*x^2+266560848*x+1942372656,3078*x^7+160626*x^6-1785240*x^5-19997766*x^4+134852310*x^3+604611768*x^2-1818950256*x+1532545776,24864768*x^3-1591345152*x,31836*x^7-558124*x^6-2651760*x^5+70927140*x^4+22300284*x^3-2324005456*x^2-69438816*x+11516146272,37572*x^7-266868*x^6-3579408*x^5+19701180*x^4+37970340*x^3-110171952*x^2+1916885088*x+63050400,-74271*x^7+1054899*x^6+7852092*x^5-127684161*x^4-263084583*x^3+4130697204*x^2+3881112216*x-14162653656,-26420*x^7+275620*x^6-2034480*x^5-3475020*x^4+445785580*x^3-778778000*x^2-13369770720*x+3901669344,-197673*x^7+1457397*x^6+26096868*x^5-142116471*x^4-965437665*x^3+2765470572*x^2+6824317608*x+4713154200,182172*x^7-1237356*x^6-22777200*x^5+101108196*x^4+698644668*x^3-1078112592*x^2+1178181792*x-1293794208,-7822*x^7-831626*x^6+15296952*x^5+47802318*x^4-1529545246*x^3+521692072*x^2+36238851504*x-7802179632,24864768*x^4-2387017728*x^2+25461522432]];
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E[31,2] = [x^5+9*x^4-66*x^3-416*x^2+1064*x+1360, [704,704*x,5*x^4+43*x^3-488*x^2-3152*x+5736,704*x^2-22528,-62*x^4-498*x^3+3552*x^2+13952*x-46064,-2*x^4-158*x^3-1072*x^2+416*x-6800,136*x^4+1064*x^3-6480*x^2-32160*x-2240,704*x^3-45056*x,78*x^4+882*x^3-1488*x^2-14112*x-84688,60*x^4-540*x^3-11840*x^2+19904*x+84320,-291*x^4-3629*x^3+9112*x^2+164720*x-168536,-300*x^4-2580*x^3+15200*x^2+96192*x-180832,207*x^4+2977*x^3+4648*x^2-52912*x-286024,-160*x^4+2496*x^3+24416*x^2-146944*x-184960,-218*x^4+26*x^3+37680*x^2+72096*x-624336,704*x^4-67584*x^2+720896]];
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E[32,1] = [x, [1,0,-8,0,14,0,-208,0,-179,0,-536,0,694,0,-112,0,-1278,0,1112,0,1664,0,3216,0]];
101
E[32,2] = [x, [1,0,8,0,14,0,208,0,-179,0,536,0,694,0,112,0,-1278,0,-1112,0,1664,0,-3216,0]];
102
E[32,3] = [x^2-768, [1,0,x,0,46,0,-6*x,0,525,0,3*x,0,-42,0,46*x,0,962,0,-75*x,0,-4608,0,-114*x,0]];
103
E[32,4] = [x, [1,0,0,0,-82,0,0,0,-243,0,0,0,-1194,0,0,0,2242,0,0,0,0,0,0,0]];
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E[33,1] = [x, [1,1,9,-31,-92,9,-26,-63,81,-92,121,-279,-692,-26,-828,929,-1442,81,2160,2852,-234,121,-1582,-567]];
106
E[33,2] = [x, [1,-2,-9,-28,46,18,148,120,81,-92,121,252,574,-296,-414,656,-722,-162,2160,-1288,-1332,-242,-2536,-1080]];
107
E[33,3] = [x^2-13*x+34, [1,x,9,13*x-66,-10*x+94,9*x,-62*x+476,71*x-442,81,-36*x+340,-121,117*x-594,74*x-546,-330*x+2108,-90*x+846,65*x-302,-372*x+2054,81*x,852*x-5952,192*x-1784,-558*x+4284,-121*x,330*x-2264,639*x-3978]];
108
E[33,4] = [x^2-x-78, [1,x,-9,x+46,10*x-24,-9*x,2*x-10,15*x+78,81,-14*x+780,121,-9*x-414,-106*x+20,-8*x+156,-90*x+216,61*x-302,4*x-462,81*x,4*x-1468,446*x-324,-18*x+90,121*x,26*x+2610,-135*x-702]];
109
E[33,5] = [x^2+5*x-38, [1,x,-9,-5*x+6,-10*x+4,-9*x,10*x-118,-x-190,81,54*x-380,-121,45*x-54,38*x+12,-168*x+380,90*x-36,-25*x-230,60*x-250,81*x,-12*x-768,-330*x+1924,-90*x+1062,-121*x,366*x-770,9*x+1710]];
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E[34,1] = [x, [1,4,-14,16,-74,-56,-78,64,-47,-296,-250,-224,130,-312,1036,256,289,-188,424,-1184,1092,-1000,-1734,-896,2351,520,4060]];
112
E[34,2] = [x^3-4*x^2-798*x+6228, [15,60,15*x,240,x^2-16*x+204,60*x,-7*x^2-113*x+3822,960,15*x^2-3645,4*x^2-64*x+816,-14*x^2-181*x+6864,240*x,11*x^2+184*x-4566,-28*x^2-452*x+15288,-12*x^2+1002*x-6228,3840,-4335,60*x^2-14580,82*x^2+398*x-35352,16*x^2-256*x+3264,-141*x^2-1764*x+43596,-56*x^2-724*x+27456,-53*x^2-727*x+3678,960*x,90*x^2-2340*x-32475,44*x^2+736*x-18264,60*x^2+4680*x-93420]];
113
E[34,3] = [x^2+6*x-34, [1,-4,x,16,-10*x-14,-4*x,23*x,-64,-6*x-209,40*x+56,-15*x-564,16*x,-86*x-608,-92*x,46*x-340,256,-289,24*x+836,446*x+1140,-160*x-224,-138*x+782,60*x+2256,-183*x-660,-64*x,-320*x+471,344*x+2432,-416*x-204]];
114
E[34,4] = [x^2+6*x-612, [3,-12,3*x,48,4*x-42,-12*x,x,-192,-18*x+1107,-16*x+168,-11*x+1776,48*x,82*x-90,-4*x,-66*x+2448,768,867,72*x-4428,-22*x-3516,64*x-672,-6*x+612,44*x-7104,-311*x+1488,-192*x,-144*x-5523,-328*x+360,486*x-11016]];
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E[35,1] = [x, [1,-8,1,32,25,-8,49,0,-242,-200,-453,32,-969,-392,25,-1024,1637,1936,-1550,800,49,3624,-1654,0]];
117
E[35,2] = [x^2-x-16, [1,x,-3*x+3,x-16,-25,-48,-49,-47*x+16,-9*x-90,-25*x,97*x-349,48*x-96,53*x-315,-49*x,75*x-75,-63*x-240,251*x-105,-99*x-144,-86*x+358,-25*x+400,147*x-147,-252*x+1552,-902*x+230,-48*x+2304]];
118
E[35,3] = [x^3+6*x^2-86*x-420, [2,2*x,x^2-52,2*x^2-64,-50,-6*x^2+34*x+420,98,-12*x^2+44*x+840,9*x^2-48*x-394,-50*x,-7*x^2-16*x+324,38*x^2-96*x-856,-5*x^2-64*x+1480,98*x,-25*x^2+1300,52*x^2-192*x-2992,x^2-192*x-576,-102*x^2+380*x+3780,42*x^2+304*x-1496,-50*x^2+1600,49*x^2-2548,26*x^2-278*x-2940,58*x^2-336*x-2568,-132*x^2+1324*x+2520]];
119
E[35,4] = [x^4-7*x^3-64*x^2+250*x+964, [6,6*x,-x^3+7*x^2+42*x-128,6*x^2-192,150,-22*x^2+122*x+964,-294,6*x^3-384*x,x^3-87*x^2+166*x+4486,150*x,9*x^3+81*x^2-1002*x-2784,10*x^3-102*x^2-380*x+4096,-39*x^3+273*x^2+1158*x-4884,-294*x,-25*x^3+175*x^2+1050*x-3200,42*x^3-192*x^2-1500*x+360,-9*x^3-225*x^2+1434*x+12564,-80*x^3+230*x^2+4236*x-964,18*x^3-78*x^2-2244*x+4008,150*x^2-4800,49*x^3-343*x^2-2058*x+6272,144*x^3-426*x^2-5034*x-8676,30*x^3-66*x^2-156*x-13344,-32*x^3+964*x^2-2308*x-40488]];
120
121
E[36,1] = [x, [1,0,0,0,-54,0,-88,0,0,0,-540,0,-418,0,0,0,-594,0,836,0,0,0,4104,0,-209,0,0,0,594,0,4256,0,0,0,4752,0]];
122
E[36,2] = [x, [1,0,0,0,0,0,236,0,0,0,0,0,1202,0,0,0,0,0,-1432,0,0,0,0,0,-3125,0,0,0,0,0,-10324,0,0,0,0,0]];
123
124
E[37,1] = [x^7+8*x^6-133*x^5-906*x^4+4326*x^3+19928*x^2-40920*x-109600, [3673920,3673920*x,-589*x^6+3618*x^5+134377*x^4-402716*x^3-9004094*x^2+1179788*x+102104240,3673920*x^2-117565440,3117*x^6-51114*x^5-978561*x^4+5787948*x^3+67006542*x^2-124161324*x-721682160,8330*x^6+56040*x^5-936350*x^4-6456080*x^3+12917380*x^2+78002360*x-64554400,-6114*x^6+57828*x^5+1273242*x^4-7596936*x^3-63266124*x^2+171837528*x+245728800,3673920*x^3-235130880*x,-36345*x^6-329550*x^5+4720125*x^4+35853780*x^3-121504950*x^2-490251300*x+228630960,-76050*x^6-564000*x^5+8611950*x^4+53522400*x^3-186276900*x^2-594134520*x+341623200,192669*x^6+2099022*x^5-17727417*x^4-217028724*x^3+3333054*x^2+3048864852*x+3172044240,8248*x^6+55764*x^5-3209164*x^4-10231288*x^3+200133128*x^2+238555984*x-2354367680,-200949*x^6-2250102*x^5+19450377*x^4+227209284*x^3-98674014*x^2-2668726932*x-3933177360,106740*x^6+460080*x^5-13136220*x^4-36816960*x^3+293677320*x^2-4456080*x-670094400,148958*x^6+1341444*x^5-18131174*x^4-130079528*x^3+539410228*x^2+1885652504*x-5033883040,3673920*x^4-352696320*x^2+3762094080,-408060*x^6-5159400*x^5+30711660*x^4+531016080*x^3+632506200*x^2-6983371440*x-15795122880,-38790*x^6-113760*x^5+2925210*x^4+35723520*x^3+234031860*x^2-1258606440*x-3983412000,478740*x^6+6562200*x^5-37652100*x^4-695777520*x^3-554995080*x^2+10354064400*x+13712024640]];
125
E[37,2] = [x^8-12*x^7-133*x^6+1754*x^5+4422*x^4-71652*x^3-24744*x^2+654576*x+724608, [4888320,4888320*x,-893*x^7+342*x^6+168245*x^5+147668*x^4-10150902*x^3-16534560*x^2+193205832*x+314351808,4888320*x^2-156426240,4683*x^7-19242*x^6-769395*x^5+2342052*x^4+35352282*x^3-65612160*x^2-330895032*x-37274688,-10374*x^7+49476*x^6+1713990*x^5-6202056*x^4-80519796*x^3+171109440*x^2+898888176*x+647074944,2538*x^7-33132*x^6-413850*x^5+4629432*x^4+20359692*x^3-166613760*x^2-214904592*x+876922752,4888320*x^3-312852480*x,-7049*x^7+100206*x^6+769025*x^5-13661836*x^4-14642046*x^3+475699200*x^2-229632024*x-1520913216,36954*x^7-146556*x^6-5871930*x^5+14644056*x^4+269934156*x^3-215018880*x^2-3102654096*x-3393339264,30009*x^7-180846*x^6-4522065*x^5+22302156*x^4+187630686*x^3-638317440*x^2-1694797416*x+917568576,-46436*x^7+323304*x^6+6610100*x^5-39371344*x^4-247379544*x^3+1171299840*x^2+1255059744*x-2542174464,1545*x^7-103230*x^6+265215*x^5+17249820*x^4-50018850*x^3-782215200*x^2+1331426520*x+6837983040,-2676*x^7-76296*x^6+177780*x^5+9136656*x^4+15239016*x^3-152104320*x^2-784391136*x-1839055104,-56586*x^7+200604*x^6+10186170*x^5-21439464*x^4-558660204*x^3+292537440*x^2+8368764624*x+11805100416,4888320*x^4-469278720*x^2+5005639680,-26832*x^7-129312*x^6+5958480*x^5+19591872*x^4-389386848*x^3-864817920*x^2+6922831488*x+12450949632,15618*x^7-168492*x^6-1297890*x^5+16528632*x^4-29375748*x^3-404052480*x^2+3093193008*x+5107761792,-53112*x^7+790128*x^6+5528760*x^5-104481408*x^4-84043728*x^3+3476667840*x^2-2138162112*x-13846391808]];
126
127
E[38,1] = [x, [1,-4,-6,16,31,24,-27,-64,-207,-124,-323,-96,-676,108,-186,256,-1107,828,-361,496,162,1292,1384,384,-2164,2704,2700,-432,2870,744]];
128
E[38,2] = [x^2-3*x-358, [1,-4,x,16,3*x-27,-4*x,-4*x+63,-64,3*x+115,-12*x+108,x+329,16*x,-5*x+814,16*x-252,-18*x+1074,256,10*x+17,-12*x-460,361,48*x-432,51*x-1432,-4*x-1316,49*x-1666,-64*x,-135*x+826,20*x-3256,-119*x+1074,-64*x+1008,-315*x-768,72*x-4296]];
129
E[38,3] = [x, [1,4,-14,16,-45,-56,-121,64,-47,-180,-381,-224,-100,-484,630,256,933,-188,361,-720,1694,-1524,-552,-896,-1100,-400,4060,-1936,2394,2520]];
130
E[38,4] = [x^3-13*x^2-398*x+5496, [2,8,2*x,32,x^2+x-272,8*x,-5*x^2-23*x+1860,128,2*x^2-486,4*x^2+4*x-1088,17*x^2+17*x-5300,32*x,-28*x^2-94*x+9748,-20*x^2-92*x+7440,14*x^2+126*x-5496,512,21*x^2+183*x-8352,8*x^2-1944,-722,16*x^2+16*x-4352,-88*x^2-130*x+27480,68*x^2+68*x-21200,34*x^2-212*x-10736,128*x,25*x^2-35*x-10478,-112*x^2-376*x+38992,26*x^2-176*x-10992,-80*x^2-368*x+29760,62*x^2+428*x-27364,56*x^2+504*x-21984]];
131
132
E[39,1] = [x, [1,2,9,-28,-74,18,-112,-120,81,-148,164,-252,169,-224,-666,656,-1646,162,-2052,2072,-1008,328,4152,-1080,2351,338,729,3136]];
133
E[39,2] = [x^2+4*x-52, [1,x,-9,-4*x+20,-5*x-34,-9*x,-11*x+14,4*x-208,81,-14*x-260,42*x-214,36*x-180,-169,58*x-572,45*x+306,-96*x-432,106*x+78,81*x,-73*x+418,-44*x+360,99*x-126,-382*x+2184,-168*x-1220,-36*x+1872,240*x-669,-169*x,-729,-452*x+2568]];
134
E[39,3] = [x^3-55*x-78, [1,x,-9,x^2-32,8*x+18,-9*x,-6*x^2+30*x+248,-9*x+78,81,8*x^2+18*x,6*x^2-38*x+72,-9*x^2+288,169,30*x^2-82*x-468,-72*x-162,-41*x^2+78*x+1024,-48*x^2-112*x+1794,81*x,70*x^2-222*x-2572,18*x^2+184*x+48,54*x^2-270*x-2232,-38*x^2+402*x+468,-144*x^2+192*x+5280,81*x-702,64*x^2+288*x-2801,169*x,-729,110*x^2+222*x-5596]];
135
E[39,4] = [x^4-6*x^3-117*x^2+780*x+292, [1,x,9,x^2-32,-11*x^3-30*x^2+1037*x+426,9*x,51*x^3+134*x^2-4797*x-1602,x^3-64*x,81,-96*x^3-250*x^2+9006*x+3212,-80*x^3-216*x^2+7480*x+3270,9*x^2-288,-169,440*x^3+1170*x^2-41382*x-14892,-99*x^3-270*x^2+9333*x+3834,6*x^3+21*x^2-780*x+732,-306*x^3-804*x^2+28750*x+10062,81*x,285*x^3+730*x^2-27027*x-7278,-474*x^3-1266*x^2+44908*x+14400,459*x^3+1206*x^2-43173*x-14418,-696*x^3-1880*x^2+65670*x+23360,464*x^3+1296*x^2-43600*x-19620,9*x^3-576*x,-456*x^3-1200*x^2+42792*x+15123,-169*x,729,2178*x^3+5810*x^2-204588*x-77216]];
136
137
E[40,1] = [x, [1,0,-2,0,-25,0,-62,0,-239,0,-144,0,-654,0,50,0,-1190,0,556,0,124,0,2182,0,625,0,964,0,-1578,0,9660,0,288,0,1550,0]];
138
E[40,2] = [x, [1,0,-18,0,-25,0,242,0,81,0,656,0,-206,0,450,0,1690,0,-1364,0,-4356,0,2198,0,625,0,2916,0,-2218,0,-1700,0,-11808,0,-6050,0]];
139
E[40,3] = [x, [1,0,-8,0,25,0,-108,0,-179,0,-604,0,-306,0,-200,0,930,0,-1324,0,864,0,-852,0,625,0,3376,0,5902,0,-3320,0,4832,0,-2700,0]];
140
E[40,4] = [x^2+12*x-480, [1,0,x,0,25,0,3*x+44,0,-12*x+237,0,-6*x+244,0,-12*x+622,0,25*x,0,84*x+578,0,-36*x-716,0,8*x+1440,0,-123*x-1964,0,625,0,138*x-5760,0,-312*x-1202,0,-54*x-1448,0,316*x-2880,0,75*x+1100,0]];
141
142
E[41,1] = [x^6+5*x^5-91*x^4-345*x^3+1618*x^2+2548*x-1176, [448,448*x,-3*x^5-15*x^4+287*x^3+811*x^2-6268*x+644,448*x^2-14336,22*x^5+110*x^4-2030*x^3-7142*x^2+35288*x+23800,14*x^4-224*x^3-1414*x^2+8288*x-3528,7*x^5-21*x^4-819*x^3+2569*x^2+18060*x-70420,448*x^3-28672*x,-76*x^5-212*x^4+7644*x^3+13732*x^2-154832*x-46928,-28*x^4+448*x^3-308*x^2-32256*x+25872,-81*x^5-517*x^4+6405*x^3+35001*x^2-75604*x-313684,110*x^5+256*x^4-10598*x^3-17664*x^2+197048*x-20608,-72*x^5-24*x^4+6440*x^3-3720*x^2-86368*x+49952,-56*x^5-182*x^4+4984*x^3+6734*x^2-88256*x+8232,280*x^5+840*x^4-26488*x^3-41832*x^2+542304*x-326368,448*x^4-43008*x^2+458752,-68*x^5+220*x^4+7252*x^3-10700*x^2-105488*x-59024,168*x^5+728*x^4-12488*x^3-31864*x^2+146720*x-89376,299*x^5+1159*x^4-25319*x^3-67203*x^2+423708*x+76636,-732*x^5-3072*x^4+64652*x^3+196288*x^2-1103344*x-761600,710*x^5+2430*x^4-66206*x^3-131382*x^2+1270104*x-232904]];
143
E[41,2] = [x^10-3*x^9-259*x^8+639*x^7+22422*x^6-38356*x^5-735592*x^4+422608*x^3+8253728*x^2-28352*x-24923264, [1408819607040,1408819607040*x,8287374*x^9-67294246*x^8-1816611830*x^7+15349996966*x^6+117591801552*x^5-1082581480416*x^4-2046626379232*x^3+23279936537504*x^2+12073773626368*x-125518560024576,1408819607040*x^2-45082227425280,40236126*x^9-247651734*x^8-9586290390*x^7+52747572294*x^6+729356877408*x^5-3334222701264*x^4-18784182068448*x^3+55461507496416*x^2+135792001527552*x-210806828557824,-42432124*x^9+329818036*x^8+10054364980*x^7-68227698276*x^6-764710963272*x^5+4049499636176*x^4+19777625986112*x^3-56327957203904*x^2-125283596396928*x+206548410068736,-44145483*x^9+64946247*x^8+10998615195*x^7-14744129667*x^6-892406755524*x^5+1176277377132*x^4+25381438783824*x^3-37074453648528*x^2-159060584876736*x+450858054080832,1408819607040*x^3-90164454850560*x,-33767122*x^9+339599858*x^8+8760469730*x^7-86614312098*x^6-646851900776*x^5+6451767092528*x^4+10085149853856*x^3-127795271923232*x^2+40384898494336*x+900950015784448,-126943356*x^9+834866244*x^8+27036687780*x^7-172817539764*x^6-1790925852408*x^5+10813190328144*x^4+38457398759808*x^3-196306038250176*x^2-209666053913472*x+1002815590635264,368238327*x^9-1730183523*x^8-91846092615*x^7+390695623503*x^6+7344341610516*x^5-26117900738268*x^4-199144446425616*x^3+446104005538512*x^2+1386962527825344*x-1767353278498368,-62674304*x^9+1217860736*x^8+17018007520*x^7-304497781856*x^6-1340964561632*x^5+23207502402016*x^4+27096241990912*x^3-520018355638784*x^2-181015381554688*x+2959046892253696,-84546822*x^9-432172482*x^8+22330926150*x^7+101617294122*x^6-2057694114216*x^5-7247601706632*x^4+75869667337056*x^3+162491039285088*x^2-831867298287744*x-760393537594752,-67490202*x^9-435064902*x^8+13464833970*x^7+97423264302*x^6-516966768816*x^5-7091625347112*x^4-18418219368864*x^3+205304224233888*x^2+449606441346816*x-1100249527216512,-338315879*x^9+967042491*x^8+90771829735*x^7-229957889311*x^6-7900138692132*x^5+14367653128756*x^4+239884661649872*x^3-91739438049744*x^2-2003093938022848*x-282960988302144,1408819607040*x^4-135246682275840*x^2+1442631277608960,694785726*x^9-2810607534*x^8-164244804870*x^7+659430613254*x^6+11808028853328*x^5-45059660287704*x^4-247883564506848*x^3+705738892975776*x^2+1091614086830592*x-2074661709362304,238298492*x^9+14785132*x^8-65037121140*x^7+110274508708*x^6+5156595361096*x^5-14753674952368*x^4-113525016029056*x^3+319089538825152*x^2+899992650341504*x-841586896126208,-25237242*x^9+491860578*x^8+5341901010*x^7-87902394978*x^6-152245819536*x^5+2582347006368*x^4-21837706594464*x^3+138016671425568*x^2+642485359178496*x-988255291471872,-833519856*x^9+2083214064*x^8+215060557200*x^7-632524237584*x^6-17395269111648*x^5+51774008073504*x^4+458435065732608*x^3-936678361967616*x^2-3346127556275712*x+3581975739216384,-1234412*x^9-3282140092*x^8-7405476180*x^7+906229247492*x^6+1480644089744*x^5-80482327809512*x^4-85127289012224*x^3+2437330656799488*x^2+1593459941502976*x-15806879888351872]];
144
145
E[42,1] = [x, [1,4,9,16,24,36,49,64,81,96,66,144,98,196,216,256,-216,324,-340,384,441,264,-1038,576,-2549,392,729,784,-2490,864,-7048,1024,594,-864,1176,1296,-12238,-1360,882,1536,6468,1764,-15412,1056,1944,-4152,20604,2304]];
146
E[42,2] = [x, [1,4,-9,16,76,-36,-49,64,81,304,650,-144,762,-196,-684,256,-556,324,-2452,1216,441,2600,-2950,-576,2651,3048,-729,-784,-674,-2736,-3024,1024,-5850,-2224,-3724,1296,7730,-9808,-6858,4864,-17016,1764,21836,10400,6156,-11800,-23940,-2304]];
147
E[42,3] = [x, [1,-4,9,16,26,-36,-49,-64,81,-104,664,144,318,196,234,256,1582,-324,236,416,-441,-2656,2212,-576,-2449,-1272,729,-784,-4954,-936,-7128,-1024,5976,-6328,-1274,1296,4358,-944,2862,-1664,10542,1764,-8452,10624,2106,-8848,5352,2304]];
148
E[42,4] = [x, [1,-4,9,16,-72,-36,49,-64,81,288,-414,144,-1054,-196,-648,256,-1848,-324,236,-1152,441,1656,2898,-576,2059,4216,729,784,-6522,2592,6200,-1024,-3726,7392,-3528,1296,9650,-944,-9486,4608,8484,-1764,-10804,-6624,-5832,-11592,60,2304]];
149
E[42,5] = [x, [1,-4,-9,16,44,36,-49,-64,81,-176,-470,-144,-1158,196,-396,256,1204,-324,-2644,704,441,1880,-1190,576,-1189,4632,-729,-784,3614,1584,5616,-1024,4230,-4816,-2156,1296,-6478,10576,10422,-2816,2856,-1764,-13492,-7520,3564,4760,-18372,-2304]];
150
E[42,6] = [x, [1,-4,-9,16,-54,36,49,-64,81,216,216,-144,998,-196,486,256,1302,-324,884,-864,-441,-864,-2268,576,-209,-3992,-729,784,-1482,-1944,8360,-1024,-1944,-5208,-2646,1296,-4714,-3536,-8982,3456,-9786,1764,19436,3456,-4374,9072,22200,-2304]];
151
152
E[43,1] = [x^8+12*x^7-117*x^6-1502*x^5+3358*x^4+49104*x^3-39464*x^2-439936*x+259776, [1094531712,1094531712*x,204587*x^7+1548278*x^6-26986075*x^5-158154500*x^4+940523682*x^3+2735439756*x^2-11646685072*x+9039530784,1094531712*x^2-35025014784,-1189197*x^7-10029498*x^6+147793677*x^5+1039401996*x^4-4441231854*x^3-21326022708*x^2+32103840624*x+19609896480,-906766*x^7-3049396*x^6+149135174*x^5+253520536*x^4-7310600292*x^3-3572863704*x^2+99044717216*x-53146792512,467088*x^7+1103952*x^6-67466832*x^5-63821328*x^4+1833842592*x^3+1377991968*x^2+8806917312*x-119443298304,1094531712*x^3-70050029568*x,1796579*x^7+15047366*x^6-267733555*x^5-1651350788*x^4+12883539282*x^3+40957782636*x^2-223065314896*x-141992554080,4240866*x^7+8657628*x^6-746771898*x^5-447908328*x^4+37068306780*x^3-14826629784*x^2-503560674912*x+308924839872,708792*x^7+36171072*x^6+167176680*x^5-3979539600*x^4-21248024592*x^3+87977593152*x^2+367995796992*x-412966261632,1285012*x^7-6501344*x^6-244887596*x^5+795263936*x^4+10856216136*x^3-24273968400*x^2-79371877184*x-53708940672,2814288*x^7+38258064*x^6-178983024*x^5-4292106384*x^4-10996319040*x^3+106065046368*x^2+487572925056*x-951076874880,-4501104*x^7-12817536*x^6+637744848*x^5+265361088*x^4-21557897184*x^3+27240078144*x^2+86045528064*x-121338252288,-6475298*x^7-71291156*x^6+730657378*x^5+8202434888*x^4-17727297132*x^3-196635763752*x^2+226881512032*x+29828345664,1094531712*x^4-105075044352*x^2+1120800473088,-8011299*x^7-94992198*x^6+708150963*x^5+10430324484*x^4+1608268398*x^3-239843093868*x^2-301069496112*x+533205424224,-6511582*x^7-57533812*x^6+1047110870*x^5+6850627000*x^4-47261432580*x^3-152165121240*x^2+648387224864*x-466708106304,-4367337*x^7-42388242*x^6-64593927*x^5+485072172*x^4+50325302346*x^3+231982105212*x^2-1198376944272*x-2775281451360,-4178460*x^7+70353360*x^6+1192474740*x^5-10433385120*x^4-80950694520*x^3+346233587568*x^2+1147311564480*x-1729191893376,-3729462*x^7-69695436*x^6+620580246*x^5+9504583464*x^4-39082240068*x^3-249310773336*x^2+1098106992672*x-895761049920,27665568*x^7+250105344*x^6-2914934016*x^5-23628148128*x^4+53173070784*x^3+395967564480*x^2-101143144320*x-184127150592]];
153
E[43,2] = [x^10-8*x^9-229*x^8+1734*x^7+16722*x^6-112716*x^5-450596*x^4+2163208*x^3+5497616*x^2-9477216*x-20373120, [197066179584,197066179584*x,1424751*x^9-16257690*x^8-271658943*x^7+3501326364*x^6+12364905798*x^5-223061293032*x^4+46320128916*x^3+4040062615968*x^2-2439196568784*x-18367317414720,197066179584*x^2-6306117746688,6235841*x^9-56170134*x^8-1328023089*x^7+11885203508*x^6+81781082490*x^5-732336840824*x^4-1326051976084*x^3+11944644227360*x^2+7575197956944*x-34095937777344,-4859682*x^9+54609036*x^8+1030808130*x^7-11459780424*x^6-62469059316*x^5+688307230512*x^4+958029854760*x^3-10271930462400*x^2-4864644441504*x+29026623093120,-8421400*x^9+40144432*x^8+1923386392*x^7-8608410624*x^6-137302958896*x^5+557003562240*x^4+3226668303456*x^3-11070821603456*x^2-17317026889344*x+57634891034112,197066179584*x^3-12612235493376*x,1744107*x^9-8050578*x^8-523672251*x^7+2836057500*x^6+53700929214*x^5-286537981032*x^4-2213195750748*x^3+8208000242400*x^2+30690304643952*x+14608711931328,-6283406*x^9+99984500*x^8+1072255214*x^7-22494650712*x^6-29457786668*x^5+1483793035152*x^4-1544776910568*x^3-26707061298112*x^2+25002474321312*x+127043536993920,-4873660*x^9+73608360*x^8+1029539964*x^7-17948954800*x^6-61518297624*x^5+1370442147616*x^4+678779158448*x^3-34074962010496*x^2+10051487302464*x+210102689362176,-29860452*x^9+438187032*x^8+5659994340*x^7-93247900560*x^6-255133671336*x^5+5906237961312*x^4-1241671607856*x^3-107429982634368*x^2+61024657288896*x+488747272723200,88669012*x^9-831998392*x^8-18840644500*x^7+177533859216*x^6+1163991069064*x^5-11160501527136*x^4-18876891416976*x^3+194359642125440*x^2+62270203719744*x-649077581746944,-27226768*x^9-5114208*x^8+5994296976*x^7+3519691904*x^6-392222960160*x^5-567980850944*x^4+7146418247744*x^3+28980596493056*x^2-22176535788288*x-171570192768000,-20609940*x^9+160440360*x^8+4883431956*x^7-32379266688*x^6-400079008680*x^5+1783462104960*x^4+14072771031888*x^3-15717667276224*x^2-215281792541376*x-160291110055680,197066179584*x^4-18918353240064*x^2+201795767894016,-19075837*x^9+160958478*x^8+4758956781*x^7-35429761588*x^6-375993332466*x^5+2404585758712*x^4+9583294280324*x^3-51057404600416*x^2-49631267072400*x+274931172347328,5902278*x^9-124271748*x^8-188224038*x^7+24535971960*x^6-89949216420*x^5-1427308112976*x^4+4435134027144*x^3+21101874095040*x^2+31137990697440*x+35532901203840,49883429*x^9-324470222*x^8-9360107093*x^7+63895065252*x^6+408025355234*x^5-3419955060504*x^4+3310032614940*x^3+32972147386144*x^2-148561270223472*x-55092858291648,-149829660*x^9+1430799528*x^8+30897514140*x^7-304713183792*x^6-1841441995224*x^5+19058724385824*x^4+29318916063024*x^3-322682387594112*x^2-174911993505984*x+963057424428288,103016982*x^9-1384371012*x^8-20866179126*x^7+310780901592*x^6+1154308993212*x^5-21465583416720*x^4-11762701789752*x^3+462881019483456*x^2-25771627379232*x-2051800257144960,34619080*x^9-86528176*x^8-9498028360*x^7+19979044896*x^6+821102687056*x^5-1517272542912*x^4-23532221709216*x^3+36844998497024*x^2+163913960831616*x-99291660019200]];
154
155
E[44,1] = [x, [1,0,7,0,-79,0,-50,0,-194,0,121,0,-380,0,-553,0,-1154,0,-1824,0,-350,0,3591,0,3116,0,-3059,0,8032,0,-2945,0,847,0,3950,0]];
156
E[44,2] = [x^2+6*x-487, [1,0,x,0,2*x-5,0,-3*x+125,0,-6*x+244,0,-121,0,-5*x+601,0,-17*x+974,0,47*x+79,0,-31*x+879,0,143*x-1461,0,-59*x+1496,0,-44*x-1152,0,37*x-2922,0,-78*x-3522,0,-371*x+136,0,-121*x,0,301*x-3547,0]];
157
158
E[45,1] = [x, [1,2,0,-28,25,0,-132,-120,0,50,-472,0,-686,-264,0,656,1562,0,-2180,-700,0,-944,-264,0,625,-1372,0,3696,-170,0,7272,5152,0,3124,-3300,0]];
159
E[45,2] = [x, [1,-2,0,-28,-25,0,192,120,0,50,148,0,286,-384,0,656,1678,0,1060,700,0,-296,-2976,0,625,-572,0,-5376,3410,0,-2448,-5152,0,-3356,-4800,0]];
160
E[45,3] = [x, [1,-7,0,17,25,0,12,105,0,-175,-112,0,-974,-84,0,-1279,-2182,0,1420,425,0,784,-3216,0,625,6818,0,204,4150,0,-5688,5593,0,15274,300,0]];
161
E[45,4] = [x^2-x-102, [1,x,0,x+70,-25,0,16*x-64,39*x+102,0,-25*x,-32*x-108,0,-16*x+446,-48*x+1632,0,109*x+1738,-80*x-978,0,-208*x+836,-25*x-1750,0,-140*x-3264,-48*x+1632,0,625,430*x-1632,0,1072*x-2848,-64*x-942,0,-176*x+1424,599*x+7854,0,-1058*x-8160,-400*x+1600,0]];
162
E[45,5] = [x^2-5*x-30, [1,x,0,5*x-2,25,0,20*x-10,-9*x+150,0,25*x,-20*x+450,0,-80*x+140,90*x+600,0,-55*x-206,-32*x+1050,0,-320*x+44,125*x-50,0,350*x-600,-504*x+600,0,625,-260*x-2400,0,410*x+3020,1280*x-2550,0,440*x-4012,-193*x-6450,0,890*x-960,500*x-250,0]];
163
E[45,6] = [x^2+5*x-30, [1,x,0,-5*x-2,-25,0,-20*x-10,-9*x-150,0,-25*x,-20*x-450,0,80*x+140,90*x-600,0,55*x-206,-32*x-1050,0,320*x+44,125*x+50,0,-350*x-600,-504*x-600,0,625,-260*x+2400,0,-410*x+3020,1280*x+2550,0,-440*x-4012,-193*x+6450,0,-890*x-960,500*x+250,0]];
164
165
E[46,1] = [x^2-6*x-211, [1,-4,x,16,-5*x-19,-4*x,-x+51,-64,6*x-32,20*x+76,-3*x-333,16*x,20*x-309,4*x-204,-49*x-1055,256,-15*x-1407,-24*x+128,-32*x-1118,-80*x-304,45*x-211,12*x+1332,-529,-64*x,340*x+2511,-80*x+1236,-239*x+1266,-16*x+816,378*x-21,196*x+4220,-45*x+746,-1024,-351*x-633,60*x+5628,-206*x+86,96*x-512]];
166
E[46,2] = [x^3-6*x^2-579*x+3312, [87,-348,87*x,1392,5*x^2+225*x-1512,-348*x,-27*x^2+351*x+4476,-5568,87*x^2-21141,-20*x^2-900*x+6048,-161*x^2-1503*x+80946,1392*x,73*x^2-630*x+28002,108*x^2-1404*x-17904,255*x^2+1383*x-16560,22272,-85*x^2+3483*x+99306,-348*x^2+84564,-632*x^2+1836*x+233886,80*x^2+3600*x-24192,189*x^2-11157*x+89424,644*x^2+6012*x-323784,46023,-5568*x,740*x^2+7200*x-336963,-292*x^2+2520*x-112008,522*x^2+8091*x-288144,-432*x^2+5616*x+71616,-1235*x^2-14076*x+483606,-1020*x^2-5532*x+66240,1862*x^2-6255*x-815856,-89088,-2469*x^2-12273*x+533232,340*x^2-13932*x-397224,382*x^2-23526*x+117504,1392*x^2-338256]];
167
E[46,3] = [x^2+22*x+49, [3,12,3*x,48,-25*x-377,12*x,17*x-281,192,-66*x-876,-100*x-1508,247*x+2699,48*x,-8*x-2311,68*x-1124,173*x+1225,768,-339*x-1077,-264*x-3504,-204*x-3930,-400*x-6032,-655*x-833,988*x+10796,1587,192*x,1700*x+27793,-32*x-9244,-153*x+3234,272*x-4496,-1954*x-29171,692*x+4900,749*x+3574,3072,-2735*x-12103,-1356*x-4308,3322*x+42254,-1056*x-14016]];
168
E[46,4] = [x^3-14*x^2-375*x+4860, [3,12,3*x,48,-x^2-x+402,12*x,3*x^2-9*x-732,192,3*x^2-729,-4*x^2-4*x+1608,-5*x^2-47*x+2316,48*x,-7*x^2-70*x+3234,12*x^2-36*x-2928,-15*x^2+27*x+4860,768,35*x^2+17*x-11046,12*x^2-2916,-22*x^2+140*x+5664,-16*x^2-16*x+6432,33*x^2+393*x-14580,-20*x^2-188*x+9264,-1587,192*x,-68*x^2+112*x+18573,-28*x^2-280*x+12936,42*x^2-333*x-14580,48*x^2-144*x-11712,85*x^2-176*x-30894,-60*x^2+108*x+19440,-62*x^2-983*x+21420,3072,-117*x^2+441*x+24300,140*x^2+68*x-44184,106*x^2-602*x-39768,48*x^2-11664]];
169
170
E[47,1] = [x^7+9*x^6-98*x^5-824*x^4+2576*x^3+16160*x^2-26272*x+2112, [10240,10240*x,-30*x^6-130*x^5+3120*x^4+8880*x^3-77760*x^2-86080*x+200000,10240*x^2-327680,129*x^6+687*x^5-12904*x^4-49832*x^3+289056*x^2+508384*x-499552,140*x^6+180*x^5-15840*x^4-480*x^3+398720*x^2-588160*x+63360,110*x^6+690*x^5-12080*x^4-62000*x^3+344000*x^2+1092160*x-2399040,10240*x^3-655360*x,-320*x^6-1600*x^5+35200*x^4+125440*x^3-901120*x^2-1725440*x+1269760,-474*x^6-262*x^5+56464*x^4-43248*x^3-1576256*x^2+2889536*x-272448,-497*x^6-3391*x^5+48872*x^4+270376*x^3-1078048*x^2-3871712*x+1255776,-120*x^6+2040*x^5+15040*x^4-246080*x^3-362240*x^2+6496000*x-6695680,393*x^6-3801*x^5-60328*x^4+479256*x^3+1917472*x^2-13428512*x+5330336,-300*x^6-1300*x^5+28640*x^4+60640*x^3-685440*x^2+490880*x-232320,716*x^6+3188*x^5-76256*x^4-225248*x^3+1966464*x^2+2907776*x-8786048,10240*x^4-983040*x^2+10485760,-344*x^6+5848*x^5+54464*x^4-783168*x^3-1520896*x^2+24230656*x-24848128,1280*x^6+3840*x^5-138240*x^4-76800*x^3+3445760*x^2-7137280*x+675840,1003*x^6+4389*x^5-82808*x^4-214584*x^3+1012832*x^2-356192*x+6841056,-124*x^6-11972*x^5-20896*x^4+1239392*x^3+1299584*x^2-28993664*x+16986752,1220*x^6+17020*x^5-100640*x^4-1596320*x^3+2524800*x^2+34218880*x-46151040,1082*x^6+166*x^5-139152*x^4+202224*x^3+4159808*x^2-11801408*x+1049664,590*x^6+3410*x^5-70320*x^4-211760*x^3+2509760*x^2+1583680*x-19218240,-1360*x^6-2480*x^5+161920*x^4-37760*x^3-4323840*x^2+8972800*x-1774080]];
171
E[47,2] = [x^12-7*x^11-274*x^10+1736*x^9+26508*x^8-138509*x^7-1138205*x^6+3941618*x^5+22596696*x^4-24468848*x^3-184114592*x^2-201624416*x-45475136, 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172
173
E[48,1] = [x, [1,0,-9,0,6,0,40,0,81,0,564,0,638,0,-54,0,882,0,556,0,-360,0,840,0,-3089,0,-729,0,4638,0,-4400,0,-5076,0,240,0,-2410,0,-5742,0,-6870,0,-9644,0,486,0,18672,0]];
174
E[48,2] = [x, [1,0,-9,0,38,0,-120,0,81,0,-524,0,-962,0,-342,0,-1358,0,2284,0,1080,0,-2552,0,-1681,0,-729,0,3966,0,2992,0,4716,0,-4560,0,13206,0,8658,0,-15126,0,7316,0,3078,0,6960,0]];
175
E[48,3] = [x, [1,0,9,0,-66,0,-176,0,81,0,60,0,-658,0,-594,0,-414,0,-956,0,-1584,0,-600,0,1231,0,729,0,5574,0,3592,0,540,0,11616,0,-8458,0,-5922,0,19194,0,-13316,0,-5346,0,19680,0]];
176
E[48,4] = [x, [1,0,9,0,94,0,-144,0,81,0,380,0,814,0,846,0,-862,0,1156,0,-1296,0,488,0,5711,0,729,0,-5466,0,-9560,0,3420,0,-13536,0,-10506,0,7326,0,-5190,0,17084,0,7614,0,-3168,0]];
177
E[48,5] = [x, [1,0,9,0,-34,0,240,0,81,0,124,0,46,0,-306,0,1954,0,1924,0,2160,0,-2840,0,-1969,0,729,0,-8922,0,4648,0,1116,0,-8160,0,-4362,0,414,0,-2886,0,-11332,0,-2754,0,-7008,0]];
178
179
E[49,1] = [x, [1,-10,14,68,56,-140,0,-360,-47,-560,232,952,140,0,784,1424,1722,470,98,3808,0,-2320,1824,-5040,11,-1400,-4060,0]];
180
E[49,2] = [x, [1,11,0,89,0,0,0,627,-243,0,-76,0,0,0,0,4049,0,-2673,0,0,0,-836,-4952,0,-3125,0,0,0]];
181
E[49,3] = [x^2-9*x+6, [1,x,6*x-24,9*x-38,-10*x+54,30*x-36,0,11*x-54,36*x+117,-36*x+60,-124*x+756,42*x+588,-126*x+742,0,24*x-936,-243*x+1150,76*x-1242,441*x-216,18*x+1552,56*x-1512,0,-360*x+744,568*x-1512,6*x+900,-180*x-809,-392*x+756,324*x+1728,0]];
182
E[49,4] = [x^2-624, [1,-2,x,-28,3*x,-2*x,0,120,381,-6*x,-284,-28*x,21*x,0,1872,656,-6*x,-762,87*x,-84*x,0,568,1496,120*x,2491,-42*x,138*x,0]];
183
E[49,5] = [x^2-8*x-21, [1,x-3,x,2*x-2,10*x-21,5*x+21,0,-24*x+144,8*x-222,29*x+273,23*x+120,14*x+42,-28*x+574,0,59*x+210,-40*x-872,-132*x+1701,-182*x+834,-277*x+1288,98*x+462,0,235*x+123,-69*x+270,-48*x-504,380*x-584,434*x-2310,-401*x+168,0]];
184
E[49,6] = [x^2+8*x-21, [1,-x-3,x,-2*x-2,10*x+21,5*x-21,0,24*x+144,-8*x-222,29*x-273,-23*x+120,14*x-42,-28*x-574,0,-59*x+210,40*x-872,-132*x-1701,182*x+834,-277*x-1288,98*x-462,0,-235*x+123,69*x+270,-48*x+504,-380*x-584,434*x+2310,-401*x-168,0]];
185
E[49,7] = [x^4-596*x^2+23716, [528,-11*x^2+1958,528*x,55*x^2-15070,4*x^3-3880*x,-11*x^3+1958*x,0,187*x^2-91366,528*x^2-128304,46*x^3-12412*x,132*x^2-297000,55*x^3-15070*x,-184*x^3+96112*x,0,-1496*x^2-94864,-1485*x^2+235818,138*x^3-101124*x,-1925*x^2-214918,184*x^3-101920*x,-270*x^3+100860*x,0,5038*x^2-1036156,-3784*x^2+185680,187*x^3-91366*x,3520*x^2-684112,-400*x^3+265504*x,528*x^3-256608*x,0]];
186
187
E[50,1] = [x, [1,-4,-11,16,0,44,-142,-64,-122,0,777,-176,884,568,0,256,-27,488,1145,0,1562,-3108,1854,704,0,-3536,4015,-2272,-4920,0,1802,-1024,-8547,108,0,-1952,13178,-4580,-9724,0,-15123,-6248,7844,12432,0]];
188
E[50,2] = [x, [1,-4,-6,16,0,24,118,-64,-207,0,192,-96,-1106,-472,0,256,-762,828,-2740,0,-708,-768,-1566,384,0,4424,2700,1888,5910,0,-6868,-1024,-1152,3048,0,-3312,5518,10960,6636,0,-378,2832,2434,3072,0]];
189
E[50,3] = [x, [1,-4,14,16,0,-56,158,-64,-47,0,-148,224,684,-632,0,256,2048,188,2220,0,2212,592,-1246,-896,0,-2736,-4060,2528,-270,0,-2048,-1024,-2072,-8192,0,-752,-4372,-8880,9576,0,-2398,-8848,2294,-2368,0]];
190
E[50,4] = [x, [1,4,-14,16,0,-56,-158,64,-47,0,-148,-224,-684,-632,0,256,-2048,-188,2220,0,2212,-592,1246,-896,0,-2736,4060,-2528,-270,0,-2048,1024,2072,-8192,0,-752,4372,8880,9576,0,-2398,8848,-2294,-2368,0]];
191
E[50,5] = [x, [1,4,-24,16,0,-96,172,64,333,0,132,-384,946,688,0,256,222,1332,500,0,-4128,528,-3564,-1536,0,3784,-2160,2752,2190,0,2312,1024,-3168,888,0,5328,11242,2000,-22704,0,1242,-16512,-20624,2112,0]];
192
E[50,6] = [x, [1,4,11,16,0,44,142,64,-122,0,777,176,-884,568,0,256,27,-488,1145,0,1562,3108,-1854,704,0,-3536,-4015,2272,-4920,0,1802,1024,8547,108,0,-1952,-13178,4580,-9724,0,-15123,6248,-7844,12432,0]];
193
E[50,7] = [x, [1,4,26,16,0,104,22,64,433,0,-768,416,46,88,0,256,-378,1732,1100,0,572,-3072,1986,1664,0,184,4940,352,-5610,0,-3988,1024,-19968,-1512,0,6928,142,4400,1196,0,1542,2288,5026,-12288,0]];
194
195