Sharedwww / Tables / ap_s4new_1-100.gpOpen in CoCalc
\\ ap_s4new_1-100.gp
\\ This is a table of eigenforms for the action of 
\\ the Hecke operators on S_4^{new}(Gamma_0(N)).
\\ William Stein ([email protected]), October, 1998.
\\ 1<=N<=100
\\ E=matrix(100,?,i,j,0);
\\ E[N,ith eigenform]=[[a_2,...,a_97],  f(x)]
\\ where the a_i are defined over Q[x]/f(x).

E[5,1]=[[-4,2,-5,6,32,-38,26,100,-78,-50,-108,266,22,442,-514,2,500,-518,126,412,-878,600,282,-150,386], x-1];
E[6,1]=[[-2,-3,6,-16,12,38,-126,20,168,30,-88,254,42,-52,-96,198,-660,-538,884,792,218,-520,-492,810,1154], x-1];
E[7,1]=[[-1,-2,16,-7,-8,28,54,-110,48,-110,12,-246,182,128,324,-162,810,-488,244,-768,-702,440,-1302,730,294], x-1];
E[8,1]=[[0,-4,-2,24,-44,22,50,44,-56,198,-160,-162,-198,52,528,-242,-668,550,188,728,154,-656,236,714,-478], x-1];
E[9,1]=[[0,0,0,20,0,-70,0,56,0,0,308,110,0,-520,0,0,0,182,-880,0,1190,884,0,0,-1330], x-1];
E[10,1]=[[2,-8,5,-4,12,-58,66,-100,132,-90,152,-34,-438,32,-204,222,420,902,-1024,432,362,-160,72,810,1106], x-1];
E[11,1]=[[x,-4*x+3,8*x-7,-4*x+14,-11,-20*x+60,12*x-74,60*x-24,-36*x-13,-56*x+128,28*x-45,-8*x+35,-4*x+272,-16*x-14,-120*x-16,-56*x-190,-132*x+449,184*x+236,-20*x+397,76*x-415,-468*x+268,656*x-498,120*x+114,-328*x-593,144*x+953], x^2-2*x-2];
E[12,1]=[[0,3,-18,8,36,-10,18,-100,72,-234,-16,-226,90,452,432,414,-684,422,332,-360,26,512,-1188,-630,-1054], x-1];
E[13,1]=[[-5,-7,-7,-13,-26,13,77,-126,-96,-82,196,-131,336,-201,-105,-432,-294,-56,478,9,98,1304,-308,-1190,70], x-1];
E[13,2]=[[x,-3*x+4,x-2,11*x-10,12*x+34,-13,-17*x+18,-32*x-26,-12*x+104,96*x-70,-34*x-26,5*x+102,22*x-126,143*x+72,-121*x+278,30*x-74,124*x-246,-190*x-434,-232*x+150,-231*x+50,260*x+98,40*x-524,-182*x+1070,-388*x-166,508*x-718], x^2-x-4];
E[14,1]=[[-2,8,-14,-7,-28,18,74,80,-112,190,72,-346,162,-412,24,318,-200,-198,-716,392,538,240,-1072,810,1354], x-1];
E[14,2]=[[2,-2,-12,7,48,56,-114,2,-120,-54,236,146,126,-376,-12,174,138,380,-484,576,-1150,776,378,-390,-1330], x-1];
E[15,1]=[[1,3,5,-24,52,22,-14,-20,-168,230,-288,-34,122,-188,256,-338,100,742,-84,-328,-38,-240,1212,330,866], x-1];
E[15,2]=[[3,-3,-5,20,-24,74,54,-124,-120,-78,200,-70,330,92,-24,450,24,-322,-196,-288,-430,-520,156,1026,-286], x-1];
E[16,1]=[[0,4,-2,-24,44,22,50,-44,56,198,160,-162,-198,-52,-528,-242,668,550,-188,-728,154,656,-236,714,-478], x-1];
E[17,1]=[[-3,-8,6,-28,-24,-58,17,116,-60,30,-172,-58,-342,-148,288,318,252,110,-484,-708,362,-484,756,-774,-382], x-1];
E[17,2]=[[x,-1/4*x^2-7/4*x+6,-1/2*x^2-3/2*x+6,5/4*x^2+11/4*x-14,-9/4*x^2+17/4*x+26,-7/2*x^2-5/2*x+68,-17,-7/2*x^2+23/2*x+80,43/4*x^2-27/4*x-126,-7/2*x^2-53/2*x-86,-55/4*x^2-9/4*x+302,39/2*x^2+61/2*x-210,28*x^2+32*x-566,-29/2*x^2-83/2*x+436,x^2-45*x+212,-27*x^2+35*x+530,65/2*x^2-65/2*x-308,-7/2*x^2-149/2*x+54,27*x^2+105*x-140,-257/4*x^2-31/4*x+918,16*x+274,87/4*x^2-807/4*x-486,-105/2*x^2-151/2*x+84,83/2*x^2-303/2*x-684,-65*x^2-55*x+990], x^3-x^2-24*x+32];
E[18,1]=[[2,0,-6,-16,-12,38,126,20,-168,-30,-88,254,-42,-52,96,-198,660,-538,884,-792,218,-520,492,-810,1154], x-1];
E[19,1]=[[-3,-5,-12,11,-54,11,-93,19,183,-249,56,-250,240,-196,-168,435,195,-358,-961,-246,353,-34,234,-168,758], x-1];
E[19,2]=[[x,-1/3*x^2-4/3*x+20/3,1/3*x^2-8/3*x+7/3,-4/3*x^2+8/3*x+17/3,-1/3*x^2+8/3*x+23/3,1/3*x^2+16/3*x+34/3,-26/3*x^2+40/3*x+379/3,-19,-25/3*x^2+8/3*x+266/3,55/3*x^2-20/3*x-428/3,44/3*x^2-124/3*x-676/3,-76/3*x^2+20/3*x+830/3,-14/3*x^2+4/3*x+1162/3,27*x^2+56*x-651,17*x^2-16*x-217,-19/3*x^2+68/3*x+1034/3,119/3*x^2-40/3*x-1480/3,-133/3*x^2-64/3*x+3047/3,-25*x^2+4*x+302,-12*x^2-40*x+502,56*x^2-120*x-511,-214/3*x^2+404/3*x+3188/3,70/3*x^2-320/3*x-1496/3,52/3*x^2+556/3*x-1508/3,-106/3*x^2-376/3*x-484/3], x^3-3*x^2-18*x+38];
E[20,1]=[[0,4,5,-16,-60,86,18,44,48,-186,176,254,186,-100,168,-498,-252,-58,-1036,168,506,272,948,-1014,-766], x-1];
E[21,1]=[[4,-3,-4,-7,62,-62,84,100,-42,-10,-48,-246,-248,68,324,258,120,622,904,-678,-642,740,468,200,-1266], x-1];
E[21,2]=[[-3,-3,-18,7,-36,-34,42,-124,0,102,-160,398,-318,-268,240,-498,-132,398,92,-720,-502,-1024,-204,354,-286], x-1];
E[21,3]=[[x,3,-2*x,7,-10*x-18,12*x+26,2*x,24*x+68,34*x+54,-24*x-162,-72*x-88,36*x-70,30*x-180,48*x+260,-68*x-108,-4*x-558,116*x+576,-72*x-322,-108*x-88,30*x+522,-12*x+518,108*x-124,-96*x+828,142*x+396,-276*x-10], x^2+3*x-12];
E[22,1]=[[-2,4,14,-8,-11,-50,130,-108,-96,142,40,382,-118,220,520,238,-852,190,-12,-112,-6,304,820,202,-1406], x-1];
E[22,2]=[[2,1,-3,-10,11,-16,42,116,189,-120,-163,-409,468,110,144,90,-453,20,-97,-465,848,-742,438,-273,761], x-1];
E[22,3]=[[-2,-7,-19,14,11,-72,-46,-20,-107,120,117,-201,-228,-242,-96,458,435,-668,439,-1113,-72,-70,358,895,409], x-1];
E[23,1]=[[-2,-5,-6,-8,34,-57,-80,-70,23,245,103,-298,95,88,-357,-414,-408,822,926,335,-899,-1322,-36,-460,-964], x-1];
E[23,2]=[[x,-1/11*x^3-5/11*x^2+x+71/11,10/11*x^3+6/11*x^2-20*x+148/11,-20/11*x^3-12/11*x^2+34*x-142/11,-12/11*x^3+28/11*x^2+30*x-600/11,x^3+5*x^2-21*x-19,14/11*x^3+26/11*x^2-12*x+106/11,-8/11*x^3-128/11*x^2+16*x+1778/11,-23,1/11*x^3-127/11*x^2-51*x+1997/11,-65/11*x^3-17/11*x^2+133*x-1545/11,222/11*x^3+186/11*x^2-380*x+1860/11,63/11*x^3+7/11*x^2-137*x+807/11,98/11*x^3-126/11*x^2-182*x+3404/11,-181/11*x^3+19/11*x^2+385*x-5629/11,106/11*x^3+90/11*x^2-306*x+702/11,-108/11*x^3-276/11*x^2+184*x-1396/11,106/11*x^3+90/11*x^2-150*x+2550/11,-68/11*x^3-428/11*x^2+162*x+5488/11,47/11*x^3+587/11*x^2+85*x-8837/11,257/11*x^3-123/11*x^2-579*x+10925/11,-46/11*x^3+298/11*x^2+10*x-6590/11,-310/11*x^3+122/11*x^2+592*x-6854/11,-82/11*x^3-410/11*x^2+242*x+9804/11,-526/11*x^3-562/11*x^2+1184*x-362/11], x^4-2*x^3-24*x^2+61*x+2];
E[24,1]=[[0,3,14,-24,-28,-74,82,92,8,-138,80,30,282,4,240,-130,596,-218,-436,856,-998,-32,-1508,-246,866], x-1];
E[25,1]=[[1,7,0,6,-43,-28,91,-35,162,160,42,-314,-203,92,196,82,-280,-518,141,412,-763,510,777,-945,1246], x-1];
E[25,2]=[[4,-2,0,-6,32,38,-26,100,78,-50,-108,-266,22,-442,514,-2,500,-518,-126,412,878,600,-282,-150,-386], x-1];
E[25,3]=[[-1,-7,0,-6,-43,28,-91,-35,-162,160,42,314,-203,-92,-196,-82,-280,-518,-141,412,763,510,-777,-945,-1246], x-1];
E[26,1]=[[2,4,-18,20,-48,13,66,-16,168,6,20,254,-390,-124,-468,558,-96,-826,-160,-420,362,776,0,1626,-1294], x-1];
E[26,2]=[[2,-1,17,-35,2,13,-19,94,-72,246,-100,-11,-280,241,137,-232,-386,64,-670,55,-838,1016,420,-934,-1154], x-1];
E[26,3]=[[-2,3,11,19,-38,-13,-51,90,-52,-190,292,-441,312,373,-41,468,530,592,-206,-863,-322,-460,528,870,-346], x-1];
E[27,1]=[[3,0,15,-25,-15,20,72,2,114,30,101,-430,-30,110,-330,621,-660,-376,-250,-360,785,488,489,-450,-1105], x-1];
E[27,2]=[[-3,0,-15,-25,15,20,-72,2,-114,-30,101,-430,30,110,330,-621,660,-376,-250,360,785,488,-489,450,-1105], x-1];
E[27,3]=[[x,0,-4*x,11,4*x,29,-12*x,29,20*x,64*x,-268,83,-64*x,-232,-92*x,72*x,68*x,767,-511,168*x,137,-475,136*x,-60*x,821], x^2-18];
E[28,1]=[[0,4,6,7,-12,-82,-30,68,216,246,-112,110,-246,-172,192,558,540,110,140,-840,-550,-208,516,-1398,1586], x-1];
E[28,2]=[[0,-10,-8,-7,-40,-12,-58,26,-64,-62,252,26,6,416,-396,-450,274,-576,-476,-448,-158,-936,530,-390,214], x-1];
E[29,1]=[[x,-3*x-8,4*x-1,10*x+2,-37*x-50,-26*x-39,18*x+48,32*x-78,48*x+74,29,-63*x-210,-56*x+100,138*x+158,171*x+10,-207*x-272,-122*x+379,248*x-202,-178*x-652,484*x+644,-34*x-364,-640*x-316,-341*x-212,64*x+670,522*x+902,-578*x-566], x^2+2*x-1];
E[29,2]=[[x,1/8*x^4+1/4*x^3-33/8*x^2-15/4*x+25,-11/16*x^4-5/4*x^3+315/16*x^2+16*x-85,3/8*x^4+x^3-83/8*x^2-37/2*x+56,-x^4-13/4*x^3+29*x^2+217/4*x-153,25/16*x^4+17/4*x^3-649/16*x^2-125/2*x+169,9/8*x^4+x^3-265/8*x^2-7/2*x+150,-5/4*x^4-5/2*x^3+141/4*x^2+55/2*x-112,-35/8*x^4-17/2*x^3+1075/8*x^2+140*x-650,-29,-5/4*x^4-3/4*x^3+173/4*x^2+107/4*x-147,49/8*x^4+17/2*x^3-1569/8*x^2-149*x+1080,-29/4*x^4-33/2*x^3+869/4*x^2+527/2*x-1332,29/4*x^4+47/4*x^3-813/4*x^2-423/4*x+795,-35/8*x^4-27/4*x^3+883/8*x^2-107/4*x-287,23/16*x^4+3/4*x^3-551/16*x^2-101/2*x-49,59/8*x^4+31/2*x^3-1579/8*x^2-259*x+874,69/8*x^4+9*x^3-1893/8*x^2-11/2*x+966,-57/4*x^4-11*x^3+1705/4*x^2+104*x-1560,-91/4*x^4-67/2*x^3+2491/4*x^2+733/2*x-2506,-7/8*x^4+13/2*x^3+183/8*x^2-79*x-336,221/8*x^4+291/4*x^3-6381/8*x^2-4481/4*x+4015,-127/8*x^4-53/2*x^3+3823/8*x^2+476*x-2174,-61/2*x^4-147/2*x^3+1729/2*x^2+2243/2*x-3872,83/4*x^4+71/2*x^3-2299/4*x^2-905/2*x+2644], x^5-33*x^3+28*x^2+192*x-256];
E[30,1]=[[2,3,-5,-4,-48,2,-114,140,72,210,272,-334,-198,-268,216,-78,240,302,596,-768,-478,-640,-348,210,-1534], x-1];
E[30,2]=[[-2,3,5,32,-60,-34,42,-76,0,6,-232,134,234,-412,-360,222,660,-490,812,120,746,152,-804,-678,194], x-1];
E[31,1]=[[x,-2*x-6,3*x-5,5*x+3,6*x+2,-20*x-18,-8*x-62,13*x+7,-54*x-130,-62*x-312,31,156*x+406,93*x-59,188*x+580,16*x+296,-106*x-292,-49*x-427,16*x+226,-240*x-388,-229*x-731,124*x-610,132*x-236,130*x+1054,222*x+764,247*x+1299], x^2+5*x+2];
E[31,2]=[[x,5/104*x^4+1/26*x^3-109/52*x^2-59/104*x+867/52,-1/4*x^4+15/2*x^2-5/4*x-65/2,-1/13*x^4+7/13*x^3+15/13*x^2-126/13*x+77/13,93/104*x^4-23/26*x^3-1237/52*x^2+941/104*x+5747/52,-63/104*x^4-23/26*x^3+1103/52*x^2+2033/104*x-7097/52,-51/52*x^4+21/13*x^3+883/26*x^2-1291/52*x-4725/26,8/13*x^4-43/13*x^3-237/13*x^2+813/13*x+1035/13,3/13*x^4+18/13*x^3-240/13*x^2-389/13*x+3058/13,-81/104*x^4-37/26*x^3+1433/52*x^2+5199/104*x-4623/52,-31,-633/104*x^4+71/26*x^3+9369/52*x^2+647/104*x-51335/52,391/52*x^4+8/13*x^3-6033/26*x^2-3085/52*x+33859/26,439/104*x^4-89/26*x^3-6055/52*x^2-3641/104*x+26889/52,-45/13*x^4-62/13*x^3+1572/13*x^2+1545/13*x-11446/13,-131/104*x^4-151/26*x^3+1067/52*x^2+13485/104*x+6363/52,-123/52*x^4-152/13*x^3+1709/26*x^2+16417/52*x-11131/26,-271/104*x^4+289/26*x^3+2767/52*x^2-28127/104*x+4343/52,38/13*x^4+124/13*x^3-1220/13*x^2-1634/13*x+1208/13,35/13*x^4+171/13*x^3-889/13*x^2-5262/13*x+5235/13,-99/13*x^4+212/13*x^3+3006/13*x^2-4271/13*x-14048/13,609/52*x^4-159/13*x^3-7369/26*x^2+12553/52*x+13363/26,375/104*x^4+179/26*x^3-4847/52*x^2-22521/104*x+34969/52,-193/13*x^4+246/13*x^3+5248/13*x^2-1633/13*x-14532/13,-413/52*x^4+518/13*x^3+4391/26*x^2-31849/52*x-4893/26], x^5-3*x^4-30*x^3+79*x^2+167*x-386];
E[32,1]=[[0,-8,-10,-16,40,-50,-30,-40,-48,-34,-320,310,410,-152,416,-410,200,30,-776,-400,-630,1120,-552,-326,-110], x-1];
E[32,2]=[[0,8,-10,16,-40,-50,-30,40,48,-34,320,310,410,152,-416,-410,-200,30,776,400,-630,-1120,552,-326,-110], x-1];
E[32,3]=[[0,0,22,0,0,-18,-94,0,0,-130,0,214,-230,0,0,518,0,830,0,0,1098,0,0,-1670,594], x-1];
E[33,1]=[[-5,3,-14,-32,-11,-38,-2,72,68,-54,-152,174,94,-528,-340,-438,20,570,-460,-1092,562,-16,372,-966,-526], x-1];
E[33,2]=[[-1,-3,-4,-26,11,-32,74,-60,-182,-90,-8,-66,422,408,-506,348,-200,132,-1036,762,-542,-550,-132,570,14], x-1];
E[33,3]=[[x,-3,-2*x-6,-4*x+14,-11,2*x+14,-14*x+60,-2*x+26,-10*x+72,-6*x-96,8*x+176,52*x-190,-14*x-384,-26*x+206,74*x+96,-54*x-234,-100*x-36,34*x-406,-96*x-340,54*x+288,-28*x+662,144*x+254,156*x-240,72*x-414,192*x-322], x^2-x-24];
E[33,4]=[[x,3,-4*x+10,-2*x+2,11,8*x-42,30*x-28,-18*x-18,112,46*x+88,104*x-72,44*x-46,2*x-248,-86*x+10,-48*x-8,-128*x+22,196,-52*x-526,152*x+388,184*x+136,-252*x-170,-74*x-78,-324*x+336,8*x+482,420*x-802], x^2-x-8];
E[34,1]=[[-2,-2,16,24,62,-62,-17,-20,-12,80,-208,-356,22,-312,24,-462,240,812,-216,732,178,700,-992,-390,-146], x-1];
E[34,2]=[[-2,-2,-18,-10,-6,74,17,-88,-114,-90,-310,86,90,368,-384,-258,240,302,-964,-390,722,-898,912,1446,-1438], x-1];
E[34,3]=[[2,-1/4*x+5/2,x,1/4*x-5/2,-15/4*x-21/2,7/2*x-25,17,-7/2*x-25,9/4*x+51/2,-5*x+204,23/4*x+109/2,-6*x+158,22*x+246,-9/2*x-319,-37*x-102,38*x+90,15/2*x+153,-12*x-142,32*x+332,39/4*x+1581/2,-39*x-160,109/4*x-1745/2,33/2*x-153,-5/2*x-993,20*x-70], x^2+4*x-204];
E[35,1]=[[1,-8,-5,7,12,-78,-94,40,32,-50,-248,-434,402,-68,536,22,-560,-278,-164,672,82,-1000,-448,-870,1026], x-1];
E[35,2]=[[x,-4*x+17,-5,-7,-32*x+121,4*x+9,44*x-201,44*x-158,-68*x+394,24*x-109,-180*x+660,-60*x+522,124*x-660,68*x-402,-132*x+353,128*x-540,-616,-108*x+600,-64*x+180,-952,-344*x+1714,248*x-485,600*x-2588,44*x-284,220*x+491], x^2-8*x+14];
E[35,3]=[[x,-x^2+13,5,7,x^2+4*x-33,5*x^2-8*x-55,11*x^2+24*x-129,6*x^2-4*x-22,2*x^2-12*x-78,17*x^2+36*x-63,-4*x^2+20*x+176,-12*x^2+4*x+134,2*x^2+12*x+108,-34*x^2-4*x+410,-13*x^2-64*x-147,-22*x^2-152*x+156,48*x^2-128*x-780,-26*x^2-60*x+668,108*x^2+96*x-1168,-40*x^2+32*x+480,76*x^2+200*x-634,-89*x^2-172*x+581,8*x^2-152*x-804,-82*x^2-180*x+912,-65*x^2-152*x+683], x^3+3*x^2-14*x-30];
E[36,1]=[[0,0,18,8,-36,-10,-18,-100,-72,234,-16,-226,-90,452,-432,-414,684,422,332,360,26,512,1188,630,-1054], x-1];
E[37,1]=[[x,-1/8*x^3-9/8*x^2-13/4*x-11/4,13/8*x^3+85/8*x^2+25/4*x-93/4,-19/4*x^3-119/4*x^2-15/2*x+85/2,17/8*x^3+145/8*x^2+109/4*x-141/4,27/8*x^3+91/8*x^2-145/4*x-67/4,-2*x^3-10*x^2+12*x+6,8*x^3+32*x^2-76*x-82,-55/8*x^3-263/8*x^2+37/4*x-249/4,39/8*x^3+343/8*x^2+123/4*x-567/4,101/8*x^3+829/8*x^2+449/4*x-805/4,37,-27/8*x^3-435/8*x^2-639/4*x+471/4,-73/4*x^3-369/4*x^2+187/2*x+241/2,219/4*x^3+1471/4*x^2+487/2*x-1401/2,15*x^2+20*x-33,-201/4*x^3-1353/4*x^2-333/2*x+489/2,-161/8*x^3-1545/8*x^2-1757/4*x+929/4,405/8*x^3+2621/8*x^2+849/4*x-1765/4,-72*x^3-381*x^2+244*x+735,225/8*x^3+2001/8*x^2+1085/4*x-3613/4,-75/8*x^3-891/8*x^2-255/4*x+2123/4,-179/2*x^3-1233/2*x^2-363*x+366,273/2*x^3+1733/2*x^2+97*x-1683,-65*x^3-463*x^2-358*x+206], x^4+6*x^3-x^2-16*x+6];
E[37,2]=[[x,-1/8*x^4+3/8*x^3+3/2*x^2-13/4*x+3,3/8*x^4-5/8*x^3-8*x^2+15/4*x+37,1/4*x^4-1/4*x^3-11/2*x^2-3/2*x+30,-7/8*x^4-3/8*x^3+49/2*x^2+29/4*x-115,-3/8*x^4-19/8*x^3+14*x^2+153/4*x-89,-3/2*x^4+7/2*x^3+39*x^2-39*x-194,3/2*x^4-3/2*x^3-25*x^2+11*x+38,27/8*x^4-117/8*x^3-46*x^2+607/4*x+101,17/8*x^4+49/8*x^3-84*x^2-339/4*x+603,15/8*x^4-49/8*x^3-23*x^2+299/4*x+61,-37,-15/8*x^4+85/8*x^3-41/2*x^2-355/4*x+519,19/4*x^4+43/4*x^3-170*x^2-233/2*x+936,1/4*x^4+23/4*x^3-59/2*x^2-203/2*x+326,-5*x^4-3/2*x^3+413/2*x^2+10*x-1454,-31/4*x^4+85/4*x^3+109*x^2-211/2*x-180,73/8*x^4-279/8*x^3-147*x^2+1197/4*x+155,-103/8*x^4+161/8*x^3+286*x^2-1379/4*x-971,1/2*x^4-13*x^3-21/2*x^2+361*x+304,-139/8*x^4+241/8*x^3+627/2*x^2-999/4*x-973,-9/8*x^4-33/8*x^3+71*x^2-245/4*x-383,-5*x^4-61/2*x^3+391/2*x^2+470*x-696,-5/2*x^4+37/2*x^3-3*x^2-9*x-354,-19/2*x^4+111/2*x^3+179*x^2-675*x-1370], x^5-4*x^4-21*x^3+74*x^2+102*x-296];
E[38,1]=[[-2,-2,-9,-31,57,-52,69,19,-72,-150,32,-226,-258,-67,579,-432,-330,-13,-856,642,-487,-700,-12,-600,1424], x-1];
E[38,2]=[[2,x,-3*x+9,-4*x+9,x-13,13*x-50,-2*x-31,19,13*x-22,-21*x+96,-44*x+304,-28*x+222,10*x-70,7*x+307,-71*x+125,17*x-686,25*x-256,111*x-343,-77*x+958,116*x-422,-184*x+1017,-58*x+936,194*x-1208,-188*x+728,102*x+188], x^2-9*x+2];
E[38,3]=[[-2,x,-2*x+6,x+28,2*x+4,-7*x+10,-15*x-18,-19,13*x-84,29*x-54,-16*x,-16*x+198,6*x-398,48*x+124,40*x-120,9*x+194,-71*x+136,44*x-362,-43*x-448,22*x+192,-x+62,58*x+24,-6*x+1116,-10*x-430,-76*x-894], x^2-x-44];
E[39,1]=[[x,-3,-2*x+14,-2*x+2,-12*x-10,-13,4*x+78,2*x+22,48*x-44,-24*x+226,-26*x+46,28*x-78,94*x+6,52*x-360,32*x-194,-120*x+38,40*x+30,136*x+178,-170*x-66,-84*x+298,76*x-526,-88*x-128,64*x-758,-190*x+670,-220*x-46], x^2-2*x-13];
E[39,2]=[[x,3,-2*x^2+24,-6*x+14,6*x^2-2*x-72,13,8*x-54,16*x^2+6*x-154,-8*x^2-32*x+96,8*x^2-20*x-78,-4*x^2+54*x+110,-28*x^2+48*x+410,34*x^2+4*x-228,4*x^2+60*x-172,-42*x^2-54*x+504,-12*x^2+108*x-162,2*x^2-82*x-564,-28*x^2-24*x+410,-76*x^2-42*x+914,14*x^2+134*x-564,12*x^2+240*x-370,-24*x^2-48*x+296,-10*x^2-30*x-132,30*x^2-116*x+216,-4*x^2+48*x+1094], x^3-2*x^2-15*x+24];
E[39,3]=[[0,-3,-12,2,-36,13,-78,74,-96,18,-214,-286,-384,524,300,558,576,74,38,-456,-682,704,-888,-1020,110], x-1];
E[40,1]=[[0,10,-5,-18,-16,-6,-6,-124,42,142,-188,202,54,66,38,738,564,-262,-554,140,882,-1160,642,-854,-478], x-1];
E[40,2]=[[0,4,5,16,36,-42,-110,-116,16,198,240,-258,442,-292,392,142,-348,-570,692,168,-134,784,564,1034,-382], x-1];
E[40,3]=[[0,-6,-5,-34,16,58,-70,4,-134,-242,100,-438,-138,178,22,162,-268,250,422,-852,306,-456,434,-726,1378], x-1];
E[41,1]=[[x,-1/2*x^2-3*x-5/2,2*x^2+5*x-11,-7/2*x^2-5*x+1/2,-13/2*x^2-13*x+31/2,15*x^2+48*x-37,-12*x^2-56*x+34,-35/2*x^2-59*x+5/2,34*x^2+82*x-116,-15*x^2-82*x-5,28*x^2+78*x-254,30*x^2+87*x-145,41,45*x^2-353,-37/2*x^2+47*x+611/2,-111*x^2-146*x+703,-30*x^2+66*x+240,23*x^2+334*x+213,-323/2*x^2-435*x+593/2,-51/2*x^2-197*x-831/2,-30*x^2-253*x+283,-39/2*x^2-59*x-1711/2,154*x^2+772*x-158,-12*x^2-110*x-516,-182*x^2-852*x+388], x^3+3*x^2-5*x-3];
E[41,2]=[[x,-1/64*x^6+1/64*x^5+37/64*x^4-17/64*x^3-81/16*x^2+3/4*x+8,1/32*x^6+1/32*x^5-39/32*x^4-49/32*x^3+147/16*x^2+27/2*x+12,1/32*x^6+3/32*x^5-47/32*x^4-123/32*x^3+263/16*x^2+115/4*x-18,-1/16*x^6-3/16*x^5+11/4*x^4+135/16*x^3-459/16*x^2-305/4*x+46,-1/8*x^6-3/8*x^5+37/8*x^4+135/8*x^3-65/2*x^2-301/2*x-30,3/32*x^6+21/32*x^5-147/32*x^4-853/32*x^3+107/2*x^2+229*x-114,9/64*x^6-41/64*x^5-333/64*x^4+1369/64*x^3+857/16*x^2-629/4*x-128,9/32*x^6+7/32*x^5-333/32*x^4-487/32*x^3+665/8*x^2+166*x-20,-15/32*x^6-69/32*x^5+667/32*x^4+2773/32*x^3-1659/8*x^2-1383/2*x+214,1/16*x^6+11/16*x^5-43/16*x^4-379/16*x^3+101/8*x^2+157*x+220,-3/16*x^6+3/4*x^5+15/2*x^4-113/4*x^3-1157/16*x^2+521/2*x+176,-41,-1/32*x^6-39/32*x^5+97/32*x^4+1175/32*x^3-64*x^2-365/2*x+420,-21/64*x^6-19/64*x^5+745/64*x^4+739/64*x^3-861/16*x^2-203/4*x-380,-1/4*x^6+21/8*x^5+75/8*x^4-745/8*x^3-953/8*x^2+1373/2*x+342,27/32*x^6+69/32*x^5-999/32*x^4-3045/32*x^3+1547/8*x^2+802*x+388,3/8*x^6-11/8*x^5-95/8*x^4+303/8*x^3+167/2*x^2-477/2*x-176,1/16*x^6-5/16*x^5-1/4*x^4-31/16*x^3-285/16*x^2+921/4*x-38,13/64*x^6+155/64*x^5-401/64*x^4-6347/64*x^3-183/16*x^2+2785/4*x+564,11/8*x^6-27/16*x^5-861/16*x^4+611/16*x^3+7863/16*x^2-383/2*x-340,-111/64*x^6-153/64*x^5+4587/64*x^4+6793/64*x^3-10839/16*x^2-3033/4*x+1092,53/32*x^6+51/32*x^5-2245/32*x^4-2963/32*x^3+1427/2*x^2+858*x-792,-47/32*x^6-69/32*x^5+1787/32*x^4+3525/32*x^3-3371/8*x^2-1137*x-522,25/16*x^6+83/16*x^5-1033/16*x^4-3027/16*x^3+537*x^2+1286*x-154], x^7-x^6-49*x^5+33*x^4+720*x^3-320*x^2-3200*x+512];
E[42,1]=[[2,3,2,-7,-8,-42,-2,-124,76,254,-72,398,462,212,-264,-162,-772,30,-764,-236,418,552,1036,30,-1190], x-1];
E[42,2]=[[2,-3,18,7,-72,-34,6,92,-180,-114,56,-34,6,164,168,654,-492,-250,-124,36,1010,56,228,390,-70], x-1];
E[43,1]=[[x,1/8*x^5-7/8*x^4-3/4*x^3+43/4*x^2-7/2*x-17/2,-1/8*x^5+7/8*x^4+7/4*x^3-59/4*x^2-17/2*x+101/2,-1/2*x^5+2*x^4+25/2*x^3-40*x^2-86*x+178,-2*x^4+11*x^3+14*x^2-120*x+91,x^5-3*x^4-33*x^3+80*x^2+256*x-435,-7/8*x^5+53/8*x^4-9/4*x^3-257/4*x^2+225/2*x-123/2,-7/8*x^5+37/8*x^4+55/4*x^3-273/4*x^2-103/2*x+295/2,7/8*x^5-21/8*x^4-139/4*x^3+401/4*x^2+567/2*x-1265/2,-7/8*x^5+81/8*x^4-99/4*x^3-349/4*x^2+681/2*x-201/2,27/8*x^5-185/8*x^4-71/4*x^3+1173/4*x^2-277/2*x-757/2,-25/8*x^5+211/8*x^4-175/4*x^3-727/4*x^2+1695/2*x-1715/2,-29/8*x^5+191/8*x^4+21/4*x^3-987/4*x^2+771/2*x+79/2,-43,21/8*x^5-239/8*x^4+295/4*x^3+955/4*x^2-2075/2*x+1643/2,17/4*x^5-171/4*x^4+205/2*x^3+495/2*x^2-1575*x+2070,-x^5+12*x^4-21*x^3-106*x^2+248*x-210,3/2*x^5-17*x^4+23/2*x^3+250*x^2-290*x-668,6*x^5-14*x^4-163*x^3+310*x^2+992*x-1947,-1/2*x^5+53/2*x^4-120*x^3-273*x^2+1394*x-368,-19/2*x^5+62*x^4+279/2*x^3-996*x^2-850*x+2952,-21/8*x^5+287/8*x^4-483/4*x^3-1115/4*x^2+3099/2*x-2267/2,-99/4*x^5+565/4*x^4+671/2*x^3-4025/2*x^2-1063*x+4152,-5/4*x^5+1/4*x^4-22*x^3+387/2*x^2+531*x-851,-123/8*x^5+329/8*x^4+2243/4*x^3-5413/4*x^2-9219/2*x+17269/2], x^6-6*x^5-17*x^4+124*x^3+26*x^2-608*x+540];
E[43,2]=[[x,1/8*x^3+1/8*x^2-7/2*x-13/4,-9/8*x^3-33/8*x^2+19/2*x+5/4,5/2*x^3+21/2*x^2-16*x-29,-13/2*x^3-51/2*x^2+60*x+50,5/2*x^3+19/2*x^2-24*x-24,83/8*x^3+203/8*x^2-285/2*x-291/4,-63/8*x^3-231/8*x^2+113/2*x+283/4,-47/8*x^3-143/8*x^2+197/2*x+135/4,21/8*x^3+357/8*x^2+117/2*x-1041/4,229/8*x^3+861/8*x^2-515/2*x-837/4,-33/8*x^3-209/8*x^2+3/2*x-91/4,-207/8*x^3-735/8*x^2+317/2*x-97/4,43,147/8*x^3+931/8*x^2-177/2*x-1903/4,-97/4*x^3-493/4*x^2+141*x+191/2,-65/2*x^3-253/2*x^2+286*x+509,-15*x^3-65*x^2+186*x+344,49*x^3+138*x^2-638*x-191,113/2*x^3+297/2*x^2-646*x+45,-6*x^3-100*x^2-126*x+686,-243/8*x^3-475/8*x^2+1253/2*x+1671/4,-107/4*x^3-271/4*x^2+95*x-887/2,273/4*x^3+1065/4*x^2-345*x-1149/2,447/8*x^3+1807/8*x^2-1357/2*x-4895/4], x^4+4*x^3-9*x^2-14*x+2];
E[44,1]=[[0,-5,-7,-26,-11,52,46,-96,27,16,-293,-29,-472,-110,-224,754,825,-548,-123,1001,-1020,526,-158,-1217,-263], x-1];
E[44,2]=[[0,x,-x+10,-6*x+32,11,-2*x-2,-4*x-62,20*x-84,-23*x+44,42*x-258,x+196,-23*x+274,-18*x-78,26*x+108,72*x-480,20*x-290,51*x-240,38*x-402,95*x-264,-69*x+612,58*x-158,42*x+824,82*x-892,-179*x+1166,-217*x+1710], x^2-9*x-4];
E[45,1]=[[-3,0,5,20,24,74,-54,-124,120,78,200,-70,-330,92,24,-450,-24,-322,-196,288,-430,-520,-156,-1026,-286], x-1];
E[45,2]=[[-1,0,-5,-24,-52,22,14,-20,168,-230,-288,-34,-122,-188,-256,338,-100,742,-84,328,-38,-240,-1212,-330,866], x-1];
E[45,3]=[[5,0,-5,-30,50,-20,-10,-44,120,-50,108,-40,400,280,-280,-610,50,-518,-180,700,-410,-516,660,-1500,-1630], x-1];
E[45,4]=[[4,0,5,6,-32,-38,-26,100,78,50,-108,266,-22,442,514,-2,-500,-518,126,-412,-878,600,-282,150,386], x-1];
E[45,5]=[[-5,0,5,-30,-50,-20,10,-44,-120,50,108,-40,-400,280,280,610,-50,-518,-180,-700,-410,-516,-660,1500,-1630], x-1];
E[46,1]=[[-2,-1,-10,-12,-42,7,20,106,23,-227,67,74,-497,-88,215,314,176,-298,266,-981,-411,806,-952,-1332,-1328], x-1];
E[46,2]=[[2,-9,-20,2,-52,43,-50,-74,-23,-7,-273,-4,123,-152,75,86,-444,262,764,-21,681,426,902,-1272,-342], x-1];
E[46,3]=[[-2,x,-2/3*x+14/3,-2/3*x+8/3,8/3*x+112/3,-7/3*x-170/3,-8*x+58,-6*x+8,-23,-65/3*x-10/3,-17/3*x+92/3,70/3*x+62/3,7*x+246,-56/3*x-688/3,-31*x+92,124/3*x+422/3,32/3*x+1204/3,212/3*x+790/3,-16*x+112,91/3*x-1012/3,-29/3*x+26/3,74/3*x+928/3,178/3*x+680/3,94/3*x-682/3,164/3*x+3310/3], x^2+x-92];
E[46,4]=[[2,x,-2*x+8,-4*x+12,-6,11*x-42,6*x-42,-20*x+22,23,33*x-78,69*x-112,-38*x+160,-29*x+230,82*x+34,25*x+392,38*x-32,-60*x+396,-58*x-444,-56*x-338,21*x+168,-3*x-634,-26*x+100,-22*x+934,-18*x+1050,274*x-866], x^2-3*x-16];
E[47,1]=[[x,-1/2*x^2-5/2*x-1,x^2+x-10,-1/2*x^2+5/2*x-6,6*x^2+20*x-24,-2*x^2+2*x-4,-21/2*x^2-57/2*x+41,-5*x^2-17*x+12,-10*x^2-64*x+30,-34*x^2-98*x+104,48*x^2+152*x-212,-7/2*x^2-27/2*x-185,21*x^2+19*x-202,-22*x^2-158*x-134,47,161/2*x^2+503/2*x-206,-29/2*x^2+337/2*x+614,49/2*x^2-65/2*x-202,75*x^2+513*x-50,-135/2*x^2-35/2*x+873,-81*x^2-205*x-200,-7/2*x^2-467/2*x-87,-48*x^2-356*x+108,181/2*x^2+699/2*x-14,259/2*x^2+933/2*x-1222], x^3+5*x^2-2*x-12];
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