Sharedwww / Tables / an_s2g0new_401-500.gpOpen in CoCalc
\\ an_s2g0new_401-500.gp
\\ This is a PARI readable nonnormalized basis for S_k(Gamma_0(N)) for N 
\\ in the range:  401 <= N <= 500.
\\ The number of a_n computed is sufficient to satisfy Sturm's bound.
\\ William Stein ([email protected])

E[401,1] = [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, [2,2*x,-4*x^11-8*x^10+42*x^9+86*x^8-132*x^7-302*x^6+126*x^5+422*x^4+10*x^3-228*x^2-34*x+26,2*x^2-4,11*x^11+23*x^10-120*x^9-248*x^8+417*x^7+863*x^6-548*x^5-1151*x^4+231*x^3+530*x^2+25*x-46,4*x^11+2*x^10-50*x^9-16*x^8+214*x^7+30*x^6-390*x^5+14*x^4+292*x^3-54*x^2-62*x+16,-4*x^11-8*x^10+46*x^9+86*x^8-178*x^7-294*x^6+290*x^5+366*x^4-188*x^3-128*x^2+10*x+2,2*x^3-8*x,-8*x^11-16*x^10+90*x^9+172*x^8-334*x^7-594*x^6+508*x^5+776*x^4-306*x^3-332*x^2+24*x+20,-10*x^11-10*x^10+126*x^9+98*x^8-556*x^7-284*x^6+1082*x^5+220*x^4-900*x^3+80*x^2+196*x-44,-11*x^11-11*x^10+140*x^9+106*x^8-629*x^7-289*x^6+1260*x^5+151*x^4-1093*x^3+202*x^2+253*x-72,-2*x^11+6*x^10+36*x^9-74*x^8-222*x^7+310*x^6+574*x^5-556*x^4-594*x^3+414*x^2+172*x-68,11*x^11+15*x^10-130*x^9-152*x^8+521*x^7+473*x^6-892*x^5-487*x^4+643*x^3+82*x^2-111*x+14,4*x^11+6*x^10-50*x^9-62*x^8+222*x^7+194*x^6-446*x^5-184*x^4+392*x^3-10*x^2-86*x+16,9*x^11+15*x^10-102*x^9-158*x^8+379*x^7+533*x^6-566*x^5-681*x^4+323*x^3+298*x^2-31*x-26,2*x^4-12*x^2+8,x^11-9*x^10-24*x^9+108*x^8+171*x^7-435*x^6-478*x^5+733*x^4+521*x^3-502*x^2-167*x+78,8*x^11+10*x^10-100*x^9-102*x^8+438*x^7+316*x^6-848*x^5-298*x^4+708*x^3-16*x^2-156*x+32,13*x^11+13*x^10-168*x^9-132*x^8+767*x^7+409*x^6-1546*x^5-379*x^4+1313*x^3-54*x^2-283*x+52,-2*x^11-20*x^10-2*x^9+230*x^8+172*x^7-884*x^6-714*x^5+1412*x^4+918*x^3-914*x^2-314*x+132,18*x^11+34*x^10-200*x^9-364*x^8+718*x^7+1256*x^6-1006*x^5-1654*x^4+498*x^3+744*x^2+4*x-62,22*x^11+30*x^10-268*x^9-310*x^8+1130*x^7+996*x^6-2082*x^5-1082*x^4+1632*x^3+198*x^2-314*x+44,-10*x^11-20*x^10+108*x^9+214*x^8-366*x^7-738*x^6+452*x^5+974*x^4-160*x^3-440*x^2-26*x+26,4*x^11+12*x^10-42*x^9-132*x^8+140*x^7+466*x^6-182*x^5-620*x^4+90*x^3+270*x^2+12*x-24,-11*x^11-9*x^10+140*x^9+84*x^8-625*x^7-219*x^6+1234*x^5+99*x^4-1055*x^3+158*x^2+259*x-54,-18*x^11-20*x^10+222*x^9+202*x^8-946*x^7-628*x^6+1746*x^5+632*x^4-1348*x^3-56*x^2+256*x-44,-4*x^11+6*x^10+68*x^9-76*x^8-406*x^7+334*x^6+1032*x^5-656*x^4-1052*x^3+558*x^2+286*x-98,2*x^11+6*x^10-18*x^9-66*x^8+34*x^7+238*x^6+48*x^5-344*x^4-154*x^3+190*x^2+84*x-20,-6*x^11-26*x^10+48*x^9+298*x^8-46*x^7-1142*x^6-300*x^5+1798*x^4+594*x^3-1102*x^2-258*x+142,-12*x^11-12*x^10+148*x^9+118*x^8-628*x^7-350*x^6+1146*x^5+314*x^4-872*x^3+14*x^2+172*x-36,6*x^11+20*x^10-56*x^9-220*x^8+134*x^7+786*x^6-14*x^5-1104*x^4-180*x^3+578*x^2+116*x-74,2*x^5-16*x^3+24*x,5*x^11+23*x^10-38*x^9-262*x^8+19*x^7+991*x^6+304*x^5-1525*x^4-537*x^3+914*x^2+223*x-124,-12*x^11-14*x^10+142*x^9+142*x^8-564*x^7-454*x^6+936*x^5+520*x^4-632*x^3-162*x^2+100*x-4,-29*x^11-67*x^10+304*x^9+728*x^8-967*x^7-2571*x^6+996*x^5+3551*x^4-61*x^3-1790*x^2-243*x+182,2*x^11+12*x^10-10*x^9-138*x^8-48*x^7+532*x^6+310*x^5-852*x^4-444*x^3+548*x^2+160*x-72,-13*x^11-13*x^10+168*x^9+124*x^8-777*x^7-325*x^6+1634*x^5+115*x^4-1521*x^3+320*x^2+399*x-100,-26*x^11-38*x^10+310*x^9+390*x^8-1268*x^7-1234*x^6+2260*x^5+1300*x^4-1744*x^3-218*x^2+338*x-52,3*x^11+7*x^10-34*x^9-76*x^8+129*x^7+263*x^6-206*x^5-337*x^4+141*x^3+132*x^2-23*x-6,6*x^11-2*x^10-90*x^9+34*x^8+486*x^7-194*x^6-1158*x^5+480*x^4+1146*x^3-484*x^2-304*x+96,9*x^11-3*x^10-136*x^9+54*x^8+745*x^7-325*x^6-1820*x^5+839*x^4+1879*x^3-864*x^2-543*x+170,-20*x^11-20*x^10+248*x^9+196*x^8-1066*x^7-574*x^6+2000*x^5+480*x^4-1596*x^3+94*x^2+334*x-72,-15*x^11-37*x^10+156*x^9+404*x^8-489*x^7-1435*x^6+480*x^5+1999*x^4+21*x^3-1022*x^2-157*x+106,-14*x^11-26*x^10+158*x^9+280*x^8-584*x^7-976*x^6+864*x^5+1308*x^4-476*x^3-608*x^2+22*x+56,16*x^11+12*x^10-206*x^9-112*x^8+932*x^7+294*x^6-1858*x^5-134*x^4+1578*x^3-226*x^2-362*x+76,10*x^11+8*x^10-126*x^9-76*x^8+552*x^7+212*x^6-1056*x^5-150*x^4+860*x^3-76*x^2-194*x+40,-2*x^11+8*x^10+42*x^9-102*x^8-294*x^7+454*x^6+856*x^5-882*x^4-1004*x^3+704*x^2+332*x-110,4*x^11-14*x^10-68*x^9+172*x^8+394*x^7-706*x^6-956*x^5+1198*x^4+938*x^3-796*x^2-280*x+120,10*x^11+30*x^10-98*x^9-332*x^8+266*x^7+1200*x^6-132*x^5-1708*x^4-224*x^3+886*x^2+172*x-92,24*x^11+30*x^10-290*x^9-306*x^8+1200*x^7+970*x^6-2134*x^5-1044*x^4+1588*x^3+204*x^2-296*x+44,-23*x^11-49*x^10+254*x^9+532*x^8-909*x^7-1869*x^6+1284*x^5+2521*x^4-657*x^3-1168*x^2-7*x+106,12*x^11+12*x^10-150*x^9-120*x^8+652*x^7+368*x^6-1238*x^5-356*x^4+998*x^3+2*x^2-218*x+44,2*x^11+18*x^10-8*x^9-206*x^8-58*x^7+774*x^6+298*x^5-1166*x^4-360*x^3+676*x^2+114*x-90,18*x^11+28*x^10-212*x^9-290*x^8+850*x^7+936*x^6-1468*x^5-1048*x^4+1078*x^3+266*x^2-186*x+16,-2*x^11-28*x^10-12*x^9+328*x^8+278*x^7-1296*x^6-1076*x^5+2152*x^4+1376*x^3-1458*x^2-478*x+218,-8*x^11-10*x^10+102*x^9+100*x^8-464*x^7-292*x^6+954*x^5+212*x^4-854*x^3+114*x^2+196*x-40,17*x^11+29*x^10-186*x^9-306*x^8+639*x^7+1045*x^6-788*x^5-1399*x^4+241*x^3+712*x^2+63*x-72,-8*x^11-12*x^10+94*x^9+128*x^8-368*x^7-444*x^6+580*x^5+600*x^4-322*x^3-288*x^2+10*x+24,3*x^11+29*x^10+8*x^9-330*x^8-313*x^7+1257*x^6+1252*x^5-2011*x^4-1577*x^3+1342*x^2+523*x-206,6*x^11-2*x^10-86*x^9+36*x^8+440*x^7-208*x^6-990*x^5+502*x^4+928*x^3-484*x^2-238*x+100,-9*x^11-3*x^10+122*x^9+24*x^8-583*x^7-43*x^6+1208*x^5-57*x^4-1015*x^3+172*x^2+207*x-46,2*x^11+4*x^10-16*x^9-40*x^8+12*x^7+130*x^6+114*x^5-186*x^4-202*x^3+146*x^2+58*x-24,18*x^11+40*x^10-192*x^9-434*x^8+634*x^7+1530*x^6-720*x^5-2108*x^4+128*x^3+1056*x^2+148*x-108,2*x^6-20*x^4+48*x^2-16,-9*x^11-15*x^10+100*x^9+154*x^8-359*x^7-493*x^6+510*x^5+561*x^4-285*x^3-184*x^2+37*x+8,8*x^11+12*x^10-92*x^9-126*x^8+346*x^7+424*x^6-510*x^5-542*x^4+264*x^3+248*x^2-14*x-20,10*x^11+26*x^10-110*x^9-290*x^8+394*x^7+1054*x^6-560*x^5-1478*x^4+290*x^3+698*x^2+4*x-54]];
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E[402,1] = [x, [1,-1,1,1,-3,-1,-1,-1,1,3,0,1,-4,1,-3,1,-6,-1,2,-3,-1,0,-9,-1,4,4,1,-1,0,3,5,-1,0,6,3,1,-7,-2,-4,3,3,1,-1,0,-3,9,0,1,-6,-4,-6,-4,9,-1,0,1,2,0,-3,-3,-10,-5,-1,1,12,0,1,-6,-9,-3,-12,-1,11,7,4,2,0,4,8,-3,1,-3,15,-1,18,1,0,0,0,3,4,-9,5,0,-6,-1,8,6,0,4,18,6,-4,4,3,-9,0,1,2,0,-7,-1,-6,-2,27,0,-4,3,6,3,-11,10,3,5,3,1,-16,-1,-1,-12,-3,0,-2,-1,-3,6]];
E[402,2] = [x, [1,-1,1,1,2,-1,0,-1,1,-2,4,1,-2,0,2,1,2,-1,-4,2,0,-4,4,-1,-1,2,1,0,-2,-2,0,-1,4,-2,0,1,6,4,-2,-2,-2,0,4,4,2,-4,12,1,-7,1,2,-2,2,-1,8,0,-4,2,0,2,-10,0,0,1,-4,-4,-1,2,4,0,-4,-1,-6,-6,-1,-4,0,2,0,2,1,2,-16,0,4,-4,-2,-4,-6,-2,0,4,0,-12,-8,-1,-6,7,4,-1,-6,-2,-16,2,0,-2,8,1,-2,-8,6,0,-2,4,8,-2,-2,0,0,-2,5,10,-2,0,-12,0,8,-1,4,4,0,4,0,1,2,-2]];
E[402,3] = [x, [1,-1,-1,1,1,1,-3,-1,1,-1,0,-1,-4,3,-1,1,2,-1,-2,1,3,0,-3,1,-4,4,-1,-3,0,1,-9,-1,0,-2,-3,1,-3,2,4,-1,3,-3,-7,0,1,3,-8,-1,2,4,-2,-4,-3,1,0,3,2,0,3,-1,6,9,-3,1,-4,0,-1,2,3,3,4,-1,11,3,4,-2,0,-4,0,1,1,-3,9,3,2,7,0,0,16,-1,12,-3,9,8,-2,1,0,-2,0,-4,-14,2,-4,4,3,3,0,-1,18,0,3,-3,-6,-2,-3,0,-4,-3,-6,1,-11,-6,-3,-9,-9,3,8,-1,7,4,11,0,6,1,-1,-2]];
E[402,4] = [x^2-12, [2,-2,-2,2,2*x,2,x+6,-2,2,-2*x,-4,-2,-x-2,-x-6,-2*x,2,-2*x,-2,4,2*x,-x-6,4,x+14,2,14,x+2,-2,x+6,-5*x-2,2*x,3*x+10,-2,4,2*x,6*x+12,2,-4,-4,x+2,-2*x,-2*x-4,x+6,-4*x+8,-4,2*x,-x-14,-5*x+2,-2,6*x+10,-14,2*x,-x-2,2*x+8,2,-4*x,-x-6,-4,5*x+2,2*x-12,-2*x,x-6,-3*x-10,x+6,2,-2*x-12,-4,2,-2*x,-x-14,-6*x-12,-3*x+6,-2,12,4,-14,4,-2*x-12,-x-2,-3*x+6,2*x,2,2*x+4,4*x+16,-x-6,-24,4*x-8,5*x+2,4,-20,-2*x,-4*x-12,x+14,-3*x-10,5*x-2,4*x,2,6*x,-6*x-10,-4,14,-20,-2*x,-2*x-20,x+2,-6*x-12,-2*x-8,6*x-4,-2,-x-18,4*x,4,x+6,2*x+20,4,14*x+12,-5*x-2,-x-2,-2*x+12,-6*x-12,2*x,-14,-x+6,2*x+4,3*x+10,4*x,-x-6,-10*x-4,-2,4*x-8,2*x+12,-8*x+8,4,2*x+12,-2,-2*x,2*x]];
E[402,5] = [x^3-3*x^2-4*x+4, [2,2,2,2,2*x,2,x^2-3*x-2,2,2,2*x,-4*x+4,2,-3*x^2+7*x+6,x^2-3*x-2,2*x,2,-2*x^2+2*x+8,2,-4,2*x,x^2-3*x-2,-4*x+4,3*x^2-9*x-6,2,2*x^2-10,-3*x^2+7*x+6,2,x^2-3*x-2,3*x^2-7*x-6,2*x,-x^2+3*x-6,2,-4*x+4,-2*x^2+2*x+8,2*x-4,2,2*x^2+4*x-20,-4,-3*x^2+7*x+6,2*x,-4*x^2+14*x+12,x^2-3*x-2,2*x^2-12*x,-4*x+4,2*x,3*x^2-9*x-6,-x^2+9*x-10,2,-2*x-6,2*x^2-10,-2*x^2+2*x+8,-3*x^2+7*x+6,2*x+8,2,-4*x^2+4*x,x^2-3*x-2,-4,3*x^2-7*x-6,6*x-4,2*x,3*x^2-11*x-6,-x^2+3*x-6,x^2-3*x-2,2,-2*x^2-6*x+12,-4*x+4,2,-2*x^2+2*x+8,3*x^2-9*x-6,2*x-4,-3*x^2+11*x+10,2,2*x^2-12,2*x^2+4*x-20,2*x^2-10,-4,2*x^2-10*x+4,-3*x^2+7*x+6,-5*x^2+13*x-2,2*x,2,-4*x^2+14*x+12,6*x^2-20*x-16,x^2-3*x-2,-4*x^2+8,2*x^2-12*x,3*x^2-7*x-6,-4*x+4,4*x^2-8*x-4,2*x,4*x-20,3*x^2-9*x-6,-x^2+3*x-6,-x^2+9*x-10,-4*x,2,-2*x^2-2*x+16,-2*x-6,-4*x+4,2*x^2-10,-4*x^2+12*x+12,-2*x^2+2*x+8,6*x^2-14*x-12,-3*x^2+7*x+6,2*x-4,2*x+8,-2*x^2+2*x+12,2,-3*x^2+11*x-2,-4*x^2+4*x,2*x^2+4*x-20,x^2-3*x-2,-6*x^2+18*x+28,-4,6*x-12,3*x^2-7*x-6,-3*x^2+7*x+6,6*x-4,2*x^2-6*x-12,2*x,8*x^2-16*x-14,3*x^2-11*x-6,-4*x^2+14*x+12,-x^2+3*x-6,6*x^2-12*x-8,x^2-3*x-2,-2*x^2+10*x+4,2,2*x^2-12*x,-2*x^2-6*x+12,-2*x^2+8*x+24,-4*x+4,-2*x^2+6*x+4,2,2*x,-2*x^2+2*x+8]];
E[402,6] = [x, [1,1,-1,1,2,-1,2,1,1,2,-4,-1,0,2,-2,1,6,1,4,2,-2,-4,-6,-1,-1,0,-1,2,8,-2,2,1,4,6,4,1,-2,4,0,2,-10,-2,4,-4,2,-6,-6,-1,-3,-1,-6,0,-6,-1,-8,2,-4,8,-8,-2,8,2,2,1,0,4,-1,6,6,4,-14,1,-6,-2,1,4,-8,0,-2,2,1,-10,-12,-2,12,4,-8,-4,-6,2,0,-6,-2,-6,8,-1,-2,-3,-4,-1,6,-6,4,0,-4,-6,16,-1,20,-8,2,2,6,-4,-12,8,0,-8,12,-2,5,8,10,2,-12,2,-4,1,-4,0,-12,4,8,-1,-2,6]];
E[402,7] = [x^2-x-10, [1,1,-1,1,x,-1,-x,1,1,x,4,-1,4,-x,-x,1,-2,1,-2*x,x,x,4,x+4,-1,x+5,4,-1,-x,-4,-x,x-4,1,-4,-2,-x-10,1,-x+8,-2*x,-4,x,-x,x,x-6,4,x,x+4,2*x-6,-1,x+3,x+5,2,4,-3*x,-1,4*x,-x,2*x,-4,-3*x-2,-x,2*x-8,x-4,-x,1,4*x,-4,-1,-2,-x-4,-x-10,-2*x-6,1,-3*x+8,-x+8,-x-5,-2*x,-4*x,-4,-2*x-2,x,1,-x,3*x+6,x,-2*x,x-6,4,4,2*x-10,x,-4*x,x+4,-x+4,2*x-6,-2*x-20,-1,-2*x-6,x+3,4,x+5,-10,2,4*x+4,4,x+10,-3*x,-8,-1,-2*x+4,4*x,x-8,-x,6,2*x,5*x+10,-4,4,-3*x-2,2*x,-x,5,2*x-8,x,x-4,x+10,-x,4*x-4,1,-x+6,4*x,x-6,-4,2*x+20,-1,-x,-2]];

E[403,1] = [x^2-3*x+1, [1,x,-2,3*x-3,2*x-3,-2*x,1,4*x-3,1,3*x-2,-4*x+6,-6*x+6,1,x,-4*x+6,3*x+2,-2*x+6,x,1,3*x+3,-2,-6*x+4,2*x-6,-8*x+6,0,x,4,3*x-3,2*x,-6*x+4,-1,3*x+3,8*x-12,2,2*x-3,3*x-3,-6*x+6,x,-2,6*x+1,-2*x+3,-2*x,-6*x+4,-6*x-6,2*x-3,-2,-8*x+12,-6*x-4,-6,0,4*x-12,3*x-3,-2*x+12,4*x,-10,4*x-3,-2,6*x-2,-4*x+3,-6*x-6,6*x-2,-x,1,6*x-7,2*x-3,12*x-8,-8,6*x-12,-4*x+12,3*x-2,3,4*x-3,14,-12*x+6]];
E[403,2] = [x^7-2*x^6-9*x^5+17*x^4+20*x^3-37*x^2+x+4, [1,x,x^5-3*x^4-3*x^3+13*x^2-6*x,x^2-2,-x^5+2*x^4+5*x^3-9*x^2-2*x+4,x^6-3*x^5-3*x^4+13*x^3-6*x^2,x^4-2*x^3-5*x^2+8*x+2,x^3-4*x,x^6-2*x^5-7*x^4+12*x^3+11*x^2-15*x+1,-x^6+2*x^5+5*x^4-9*x^3-2*x^2+4*x,-x^6+3*x^5+3*x^4-14*x^3+7*x^2+5*x-1,-x^6+4*x^5+2*x^4-20*x^3+11*x^2+11*x-4,-1,x^5-2*x^4-5*x^3+8*x^2+2*x,x^5-4*x^4+16*x^2-19*x+4,x^4-6*x^2+4,-x^5+4*x^4+x^3-17*x^2+14*x,2*x^5-5*x^4-9*x^3+22*x^2-4,-x^6+4*x^5+2*x^4-20*x^3+10*x^2+10*x,-2*x^5+4*x^4+8*x^3-15*x^2+5*x-4,x^5-3*x^4-4*x^3+14*x^2-x-4,x^6-6*x^5+3*x^4+27*x^3-32*x^2+4,-x^6+4*x^5+2*x^4-19*x^3+9*x^2+4*x+4,-x^5+3*x^4+5*x^3-14*x^2-3*x+4,-3*x^5+5*x^4+17*x^3-22*x^2-13*x+7,-x,x^6-4*x^5-2*x^4+20*x^3-12*x^2-10*x+8,x^6-2*x^5-7*x^4+12*x^3+12*x^2-16*x-4,x^6-4*x^5+x^4+13*x^3-23*x^2+19*x-2,x^6-4*x^5+16*x^3-19*x^2+4*x,1,x^5-8*x^3+12*x,x^5-2*x^4-6*x^3+10*x^2+5*x-4,-x^6+4*x^5+x^4-17*x^3+14*x^2,3*x^4-5*x^3-15*x^2+19*x+4,-x^5+5*x^4-2*x^3-22*x^2+26*x-2,-2*x^5+5*x^4+9*x^3-22*x^2-x+7,2*x^6-7*x^5-3*x^4+30*x^3-27*x^2+x+4,-x^5+3*x^4+3*x^3-13*x^2+6*x,-2*x^4+3*x^3+9*x^2-12*x,-x^6+4*x^5+x^4-16*x^3+14*x^2-9*x+2,x^6-3*x^5-4*x^4+14*x^3-x^2-4*x,x^5-4*x^4-x^3+20*x^2-16*x-8,-2*x^6+6*x^5+4*x^4-24*x^3+23*x^2-7*x-2,2*x^6-4*x^5-14*x^4+27*x^3+20*x^2-45*x+8,2*x^6-7*x^5-2*x^4+29*x^3-33*x^2+5*x+4,3*x^5-8*x^4-13*x^3+39*x^2-x-16,x^6-5*x^5+x^4+26*x^3-25*x^2-18*x+8,-x^6+x^5+11*x^4-11*x^3-31*x^2+30*x+5,-3*x^6+5*x^5+17*x^4-22*x^3-13*x^2+7*x,-2*x^6+7*x^5+6*x^4-36*x^3+14*x^2+25*x-12,-x^2+2,-3*x^4+5*x^3+14*x^2-22*x+4,-2*x^6+7*x^5+3*x^4-32*x^3+27*x^2+7*x-4,-2*x^6+3*x^5+13*x^4-15*x^3-16*x^2+15*x,-x^4+2*x^3+5*x^2-9*x-4,-x^3+2*x^2+3*x-4,-2*x^6+10*x^5-4*x^4-43*x^3+56*x^2-3*x-4,3*x^6-8*x^5-14*x^4+42*x^3+4*x^2-35*x-2,-2*x^6+7*x^5+7*x^4-39*x^3+9*x^2+37*x-12,-2*x^6+6*x^5+9*x^4-31*x^3-x^2+20*x,x,x^6-2*x^5-8*x^4+12*x^3+19*x^2-13*x-10,x^6-10*x^4+24*x^2-8,x^5-2*x^4-5*x^3+9*x^2+2*x-4,x^6-2*x^5-6*x^4+10*x^3+5*x^2-4*x,x^6-3*x^5-3*x^4+13*x^3-7*x^2-x-2,2*x^6-6*x^5-8*x^4+32*x^3-3*x^2-27*x+4,-x^6+3*x^5+x^4-8*x^3+15*x^2-23*x+4,3*x^5-5*x^4-15*x^3+19*x^2+4*x,x^6+x^5-15*x^4-2*x^3+50*x^2-13*x-14,-x^6+x^5+8*x^4-4*x^3-18*x^2-2*x+8,4*x^6-12*x^5-17*x^4+62*x^3-2*x^2-40*x-1,-2*x^6+5*x^5+9*x^4-22*x^3-x^2+7*x]];
E[403,3] = [x^8+x^7-11*x^6-10*x^5+37*x^4+33*x^3-36*x^2-33*x-4, [1,x,-x^5-x^4+7*x^3+5*x^2-10*x-4,x^2-2,-x^7+10*x^5-x^4-29*x^3+25*x+8,-x^6-x^5+7*x^4+5*x^3-10*x^2-4*x,2*x^6+2*x^5-15*x^4-10*x^3+25*x^2+10*x-2,x^3-4*x,-x^6-2*x^5+7*x^4+12*x^3-11*x^2-15*x+1,x^7-x^6-11*x^5+8*x^4+33*x^3-11*x^2-25*x-4,x^6+x^5-7*x^4-4*x^3+11*x^2+x-3,-x^7-x^6+9*x^5+7*x^4-24*x^3-14*x^2+20*x+8,1,2*x^7+2*x^6-15*x^5-10*x^4+25*x^3+10*x^2-2*x,-x^5-2*x^4+6*x^3+12*x^2-7*x-12,x^4-6*x^2+4,x^7-10*x^5+x^4+27*x^3-2*x^2-17*x,-x^7-2*x^6+7*x^5+12*x^4-11*x^3-15*x^2+x,-x^7-x^6+9*x^5+7*x^4-22*x^3-15*x^2+13*x+8,-2*x^5-2*x^4+14*x^3+11*x^2-21*x-12,x^7+2*x^6-6*x^5-12*x^4+4*x^3+13*x^2+8*x+8,x^7+x^6-7*x^5-4*x^4+11*x^3+x^2-3*x,x^7-x^6-11*x^5+9*x^4+35*x^3-16*x^2-33*x,-x^5-x^4+9*x^3+4*x^2-17*x-4,-2*x^7+21*x^5-x^4-65*x^3-6*x^2+59*x+23,x,x^7-x^6-11*x^5+9*x^4+34*x^3-15*x^2-31*x-4,3*x^6+6*x^5-19*x^4-36*x^3+20*x^2+46*x+12,-x^7-x^6+7*x^5+4*x^4-9*x^3-6*x-2,-x^6-2*x^5+6*x^4+12*x^3-7*x^2-12*x,-1,x^5-8*x^3+12*x,x^5+2*x^4-6*x^3-10*x^2+5*x+8,-x^7+x^6+11*x^5-10*x^4-35*x^3+19*x^2+33*x+4,2*x^6+2*x^5-17*x^4-11*x^3+37*x^2+11*x-12,-x^7-2*x^6+6*x^5+12*x^4-6*x^3-13*x^2-3*x-6,-2*x^6-2*x^5+15*x^4+9*x^3-26*x^2-5*x+5,-2*x^6-3*x^5+15*x^4+18*x^3-23*x^2-25*x-4,-x^5-x^4+7*x^3+5*x^2-10*x-4,-2*x^7+20*x^5-2*x^4-55*x^3+x^2+38*x+8,x^7+x^6-7*x^5-6*x^4+8*x^3+11*x^2+8*x-2,x^7+5*x^6-2*x^5-33*x^4-20*x^3+44*x^2+41*x+4,x^5-9*x^3-2*x^2+18*x+8,2*x^6+4*x^5-12*x^4-24*x^3+11*x^2+31*x+10,-2*x^6+18*x^4-5*x^3-40*x^2+15*x+16,-2*x^7+19*x^5-2*x^4-49*x^3+3*x^2+33*x+4,-2*x^7+21*x^5-63*x^3-9*x^2+51*x+20,2*x^7+x^6-19*x^5-5*x^4+52*x^3+11*x^2-44*x-16,-x^7-3*x^6+6*x^5+20*x^4-5*x^3-28*x^2-7*x+1,2*x^7-x^6-21*x^5+9*x^4+60*x^3-13*x^2-43*x-8,2*x^7+2*x^6-19*x^5-14*x^4+52*x^3+28*x^2-39*x-12,x^2-2,-2*x^6-2*x^5+15*x^4+11*x^3-22*x^2-16*x-4,-2*x^7+19*x^5-3*x^4-48*x^3+5*x^2+29*x+4,-x^5-x^4+9*x^3+8*x^2-21*x-16,-x^7+2*x^6+11*x^5-16*x^4-30*x^3+26*x^2+16*x,-2*x^6-4*x^5+12*x^4+27*x^3-8*x^2-41*x-20,-4*x^6-6*x^5+28*x^4+33*x^3-42*x^2-35*x-4,3*x^6+2*x^5-24*x^4-8*x^3+44*x^2+7*x-6,-x^7-2*x^6+8*x^5+16*x^4-19*x^3-36*x^2+14*x+24,x^7-4*x^6-17*x^5+28*x^4+69*x^3-36*x^2-71*x-16,-x,3*x^7+x^6-29*x^5-5*x^4+80*x^3+12*x^2-64*x-18,x^6-10*x^4+24*x^2-8,-x^7+10*x^5-x^4-29*x^3+25*x+8,x^6+2*x^5-6*x^4-10*x^3+5*x^2+8*x,-x^6+x^5+11*x^4-9*x^3-29*x^2+19*x+14,-2*x^3+x^2+5*x-4,x^7-x^6-16*x^5+4*x^4+72*x^3+8*x^2-90*x-24,2*x^7+2*x^6-17*x^5-11*x^4+37*x^3+11*x^2-12*x,3*x^6+5*x^5-19*x^4-30*x^3+18*x^2+41*x+14,x^7-x^6-12*x^5+7*x^4+42*x^3-9*x^2-41*x-4,-2*x^7+18*x^5-5*x^4-42*x^3+18*x^2+18*x-11,-2*x^7-2*x^6+15*x^5+9*x^4-26*x^3-5*x^2+5*x]];
E[403,4] = [x^6+2*x^5-7*x^4-13*x^3+6*x^2+7*x-3, [1,x,-x^5-3*x^4+5*x^3+19*x^2+6*x-8,x^2-2,3*x^5+8*x^4-17*x^3-51*x^2-8*x+18,-x^5-2*x^4+6*x^3+12*x^2-x-3,-2*x^5-5*x^4+12*x^3+31*x^2-10,x^3-4*x,-2*x^5-4*x^4+13*x^3+25*x^2-4*x-8,2*x^5+4*x^4-12*x^3-26*x^2-3*x+9,5*x^5+12*x^4-29*x^3-75*x^2-8*x+24,2*x^5+5*x^4-11*x^3-33*x^2-8*x+13,1,-x^5-2*x^4+5*x^3+12*x^2+4*x-6,3*x^5+8*x^4-16*x^3-50*x^2-11*x+18,x^4-6*x^2+4,-3*x^5-8*x^4+17*x^3+51*x^2+6*x-24,-x^4-x^3+8*x^2+6*x-6,-12*x^5-29*x^4+69*x^3+184*x^2+23*x-67,-6*x^5-14*x^4+34*x^3+87*x^2+11*x-30,x^5+x^4-8*x^3-4*x^2+13*x-4,2*x^5+6*x^4-10*x^3-38*x^2-11*x+15,4*x^5+11*x^4-22*x^3-71*x^2-13*x+27,3*x^5+7*x^4-19*x^3-44*x^2+x+12,-7*x^5-19*x^4+39*x^3+122*x^2+23*x-47,x,6*x^5+15*x^4-35*x^3-94*x^2-9*x+31,4*x^5+8*x^4-25*x^3-52*x^2+x+17,8*x^5+20*x^4-46*x^3-127*x^2-14*x+45,2*x^5+5*x^4-11*x^3-29*x^2-3*x+9,1,x^5-8*x^3+12*x,5*x^5+14*x^4-26*x^3-90*x^2-27*x+36,-2*x^5-4*x^4+12*x^3+24*x^2-3*x-9,x^4+x^3-5*x^2-x,3*x^5+7*x^4-18*x^3-44*x^2+2*x+16,-3*x^4-3*x^3+20*x^2+17*x-13,-5*x^5-15*x^4+28*x^3+95*x^2+17*x-36,-x^5-3*x^4+5*x^3+19*x^2+6*x-8,-6*x^5-16*x^4+33*x^3+99*x^2+18*x-36,-14*x^5-34*x^4+81*x^3+214*x^2+26*x-75,-x^5-x^4+9*x^3+7*x^2-11*x+3,7*x^5+20*x^4-37*x^3-128*x^2-32*x+50,-8*x^5-20*x^4+46*x^3+127*x^2+17*x-42,-4*x^5-12*x^4+21*x^3+76*x^2+17*x-30,3*x^5+6*x^4-19*x^3-37*x^2-x+12,-x^5-2*x^4+5*x^3+13*x^2+9*x-6,-3*x^5-8*x^4+17*x^3+49*x^2+7*x-17,x^5+4*x^4-2*x^3-25*x^2-21*x+12,-5*x^5-10*x^4+31*x^3+65*x^2+2*x-21,5*x^5+14*x^4-26*x^3-88*x^2-23*x+36,x^2-2,-2*x^5-5*x^4+11*x^3+30*x^2+6*x-12,3*x^5+7*x^4-16*x^3-45*x^2-11*x+18,-15*x^5-37*x^4+85*x^3+232*x^2+35*x-78,2*x^5+7*x^4-10*x^3-47*x^2-19*x+24,-6*x^5-16*x^4+33*x^3+100*x^2+21*x-34,4*x^5+10*x^4-23*x^3-62*x^2-11*x+24,16*x^5+39*x^4-93*x^3-246*x^2-26*x+87,-5*x^5-13*x^4+29*x^3+85*x^2+17*x-30,12*x^5+29*x^4-71*x^3-185*x^2-14*x+68,x,2*x^5+9*x^4-7*x^3-61*x^2-32*x+35,-2*x^5-3*x^4+13*x^3+18*x^2-7*x-5,3*x^5+8*x^4-17*x^3-51*x^2-8*x+18,4*x^5+9*x^4-25*x^3-57*x^2+x+15,-9*x^5-22*x^4+50*x^3+139*x^2+26*x-55,6*x^5+14*x^4-36*x^3-93*x^2-7*x+42,3*x^5+8*x^4-17*x^3-49*x^2-6*x+15,x^5+x^4-5*x^3-x^2,7*x^5+16*x^4-39*x^3-102*x^2-20*x+39,x^5+5*x^4-3*x^3-32*x^2-17*x+21,-8*x^5-21*x^4+44*x^3+134*x^2+28*x-55,-3*x^5-3*x^4+20*x^3+17*x^2-13*x]];
E[403,5] = [x^8+5*x^7-30*x^5-24*x^4+54*x^3+54*x^2-28*x-29, [1,x,-x^7-3*x^6+6*x^5+19*x^4-12*x^3-36*x^2+8*x+19,x^2-2,-x^5-2*x^4+5*x^3+7*x^2-6*x-6,2*x^7+6*x^6-11*x^5-36*x^4+18*x^3+62*x^2-9*x-29,x^4+2*x^3-3*x^2-4*x,x^3-4*x,x^7+3*x^6-5*x^5-18*x^4+6*x^3+34*x^2-2*x-19,-x^6-2*x^5+5*x^4+7*x^3-6*x^2-6*x,2*x^7+7*x^6-9*x^5-43*x^4+8*x^3+77*x^2+x-37,-2*x^7-5*x^6+12*x^5+28*x^4-22*x^3-45*x^2+11*x+20,-1,x^5+2*x^4-3*x^3-4*x^2,2*x^7+5*x^6-13*x^5-29*x^4+29*x^3+50*x^2-20*x-27,x^4-6*x^2+4,-x^6-x^5+9*x^4+4*x^3-25*x^2-x+17,-2*x^7-5*x^6+12*x^5+30*x^4-20*x^3-56*x^2+9*x+29,-x^6-4*x^5+16*x^3+14*x^2-14*x-16,-x^7-2*x^6+7*x^5+11*x^4-16*x^3-20*x^2+12*x+12,x^7+3*x^6-8*x^5-23*x^4+21*x^3+49*x^2-17*x-29,-3*x^7-9*x^6+17*x^5+56*x^4-31*x^3-107*x^2+19*x+58,x^7+4*x^6-3*x^5-22*x^4-2*x^3+32*x^2+8*x-11,x^7-10*x^5+2*x^4+27*x^3-5*x^2-18*x,x^7+3*x^6-2*x^5-11*x^4-8*x^3+7*x^2+15*x+2,-x,-2*x^7-6*x^6+10*x^5+33*x^4-13*x^3-48*x^2+3*x+17,x^6+2*x^5-5*x^4-8*x^3+6*x^2+8*x,-x^7-2*x^6+7*x^5+11*x^4-14*x^3-12*x^2+7*x-5,-5*x^7-13*x^6+31*x^5+77*x^4-58*x^3-128*x^2+29*x+58,-1,x^5-8*x^3+12*x,-2*x^7-7*x^6+11*x^5+47*x^4-19*x^3-94*x^2+16*x+51,-x^7-x^6+9*x^5+4*x^4-25*x^3-x^2+17*x,-x^7-3*x^6+7*x^5+19*x^4-22*x^3-40*x^2+23*x+29,3*x^7+6*x^6-20*x^5-32*x^4+40*x^3+49*x^2-23*x-20,2*x^7+8*x^6-6*x^5-45*x^4-x^3+74*x^2+5*x-33,-x^7-4*x^6+16*x^4+14*x^3-14*x^2-16*x,x^7+3*x^6-6*x^5-19*x^4+12*x^3+36*x^2-8*x-19,3*x^7+9*x^6-15*x^5-50*x^4+20*x^3+78*x^2-4*x-29,x^6-11*x^4-2*x^3+28*x^2+5*x-20,-2*x^7-8*x^6+7*x^5+45*x^4-5*x^3-71*x^2-x+29,-x^7-6*x^6+35*x^4+11*x^3-59*x^2-7*x+28,2*x^7+3*x^6-16*x^5-17*x^4+39*x^3+27*x^2-28*x-13,-x^7+9*x^5-3*x^4-21*x^3+7*x^2+14*x-2,-x^7-3*x^6+8*x^5+22*x^4-22*x^3-46*x^2+17*x+29,-x^7-5*x^6+4*x^5+38*x^4+2*x^3-84*x^2-13*x+47,-x^7+8*x^5-5*x^4-15*x^3+18*x^2+6*x-11,-x^7-2*x^6+10*x^5+17*x^4-30*x^3-38*x^2+28*x+22,-2*x^7-2*x^6+19*x^5+16*x^4-47*x^3-39*x^2+30*x+29,4*x^7+15*x^6-19*x^5-95*x^4+27*x^3+174*x^2-14*x-83,-x^2+2,-x^7-5*x^6+x^5+29*x^4+10*x^3-49*x^2-10*x+19,4*x^7+10*x^6-27*x^5-61*x^4+60*x^3+111*x^2-39*x-58,-x^7-2*x^6+6*x^5+10*x^4-5*x^3-5*x^2-8*x-10,x^7+2*x^6-7*x^5-12*x^4+12*x^3+16*x^2,-x^7-3*x^6+7*x^5+22*x^4-12*x^3-41*x^2+x+15,3*x^7+7*x^6-19*x^5-38*x^4+42*x^3+61*x^2-33*x-29,-3*x^7-11*x^6+11*x^5+61*x^4-6*x^3-95*x^2-2*x+36,8*x^7+21*x^6-47*x^5-120*x^4+84*x^3+199*x^2-42*x-91,-2*x^7-8*x^6+10*x^5+55*x^4-13*x^3-111*x^2+62,-x,2*x^7+6*x^6-12*x^5-37*x^4+23*x^3+63*x^2-10*x-29,x^6-10*x^4+24*x^2-8,x^5+2*x^4-5*x^3-7*x^2+6*x+6,3*x^7+11*x^6-13*x^5-67*x^4+14*x^3+124*x^2-5*x-58,2*x^7+7*x^6-9*x^5-41*x^4+11*x^3+69*x^2-5*x-30,4*x^7+11*x^6-24*x^5-67*x^4+45*x^3+121*x^2-26*x-63,2*x^7+8*x^6-9*x^5-50*x^4+11*x^3+85*x^2-35,2*x^7+7*x^6-11*x^5-46*x^4+14*x^3+77*x^2+x-29,3*x^7+10*x^6-18*x^5-69*x^4+35*x^3+145*x^2-23*x-87,-5*x^7-10*x^6+34*x^5+52*x^4-73*x^3-73*x^2+46*x+29,-x^7-3*x^6+5*x^5+17*x^4-7*x^3-31*x^2-2*x+22,-2*x^7-6*x^6+15*x^5+47*x^4-34*x^3-103*x^2+23*x+58]];

E[404,1] = [x, [1,0,-2,0,3,0,2,0,1,0,-6,0,5,0,-6,0,3,0,5,0,-4,0,3,0,4,0,4,0,0,0,5,0,12,0,6,0,-10,0,-10,0,12,0,8,0,3,0,-3,0,-3,0,-6,0,-6,0,-18,0,-10,0,-6,0,8,0,2,0,15,0,-10,0,-6,0,-9,0,-4,0,-8,0,-12,0,5,0,-11,0,-12,0,9,0,0,0,6,0,10,0,-10,0,15,0,2,0,-6,0,-1,0]];
E[404,2] = [x^7-2*x^6-17*x^5+36*x^4+64*x^3-148*x^2+11*x+58, [1,0,x,0,8*x^6+8*x^5-113*x^4-52*x^3+368*x^2-72*x-154,0,-18*x^6-17*x^5+256*x^4+105*x^3-844*x^2+189*x+360,0,x^2-3,0,-2*x^6-2*x^5+28*x^4+13*x^3-90*x^2+17*x+40,0,20*x^6+18*x^5-286*x^4-106*x^3+951*x^2-232*x-406,0,24*x^6+23*x^5-340*x^4-144*x^3+1112*x^2-242*x-464,0,21*x^6+20*x^5-298*x^4-124*x^3+977*x^2-220*x-406,0,-22*x^6-22*x^5+310*x^4+142*x^3-1004*x^2+206*x+412,0,-53*x^6-50*x^5+753*x^4+308*x^3-2475*x^2+558*x+1044,0,2*x^6+2*x^5-28*x^4-12*x^3+90*x^2-26*x-36,0,5*x^6+6*x^5-68*x^4-44*x^3+205*x^2-24*x-69,0,x^3-6*x,0,-6*x^6-6*x^5+84*x^4+38*x^3-268*x^2+60*x+106,0,-40*x^6-38*x^5+568*x^4+236*x^3-1866*x^2+412*x+788,0,-6*x^6-6*x^5+85*x^4+38*x^3-279*x^2+62*x+116,0,x^5+2*x^4-13*x^3-18*x^2+34*x+8,0,21*x^6+20*x^5-298*x^4-124*x^3+977*x^2-220*x-402,0,58*x^6+54*x^5-826*x^4-329*x^3+2728*x^2-626*x-1160,0,-20*x^6-18*x^5+286*x^4+106*x^3-952*x^2+232*x+410,0,22*x^6+22*x^5-310*x^4-142*x^3+1004*x^2-206*x-416,0,47*x^6+44*x^5-669*x^4-268*x^3+2206*x^2-512*x-930,0,14*x^6+12*x^5-202*x^4-68*x^3+684*x^2-170*x-308,0,-30*x^6-28*x^5+427*x^4+172*x^3-1408*x^2+314*x+601,0,62*x^6+59*x^5-880*x^4-367*x^3+2888*x^2-637*x-1218,0,-16*x^6-14*x^5+230*x^4+80*x^3-772*x^2+198*x+334,0,-26*x^6-24*x^5+370*x^4+144*x^3-1218*x^2+291*x+510,0,-66*x^6-64*x^5+934*x^4+404*x^3-3050*x^2+654*x+1276,0,18*x^6+17*x^5-256*x^4-105*x^3+844*x^2-189*x-364,0,24*x^6+22*x^5-342*x^4-132*x^3+1130*x^2-268*x-478,0,-102*x^6-97*x^5+1448*x^4+602*x^3-4754*x^2+1060*x+1994,0,15*x^6+12*x^5-218*x^4-62*x^3+748*x^2-208*x-348,0,20*x^6+20*x^5-282*x^4-130*x^3+914*x^2-179*x-376,0,6*x^6+6*x^5-84*x^4-38*x^3+270*x^2-58*x-116,0,-18*x^6-16*x^5+258*x^4+94*x^3-862*x^2+202*x+376,0,2*x^6-32*x^4+10*x^3+124*x^2-62*x-58,0,16*x^6+17*x^5-224*x^4-115*x^3+716*x^2-124*x-290,0,53*x^6+50*x^5-752*x^4-308*x^3+2464*x^2-556*x-1028,0,10*x^6+10*x^5-140*x^4-64*x^3+448*x^2-96*x-180,0,x^4-9*x^2+9,0,4*x^6+4*x^5-56*x^4-25*x^3+180*x^2-43*x-80,0,-18*x^6-16*x^5+257*x^4+92*x^3-849*x^2+222*x+348,0,-18*x^6-18*x^5+254*x^4+116*x^3-828*x^2+172*x+348,0,22*x^6+22*x^5-310*x^4-142*x^3+1004*x^2-204*x-414,0,2*x^6-32*x^4+11*x^3+124*x^2-73*x-58,0,-118*x^6-112*x^5+1676*x^4+694*x^3-5508*x^2+1228*x+2320,0,-20*x^6-22*x^5+278*x^4+154*x^3-880*x^2+128*x+352,0,-20*x^6-20*x^5+281*x^4+128*x^3-904*x^2+196*x+362,0,-12*x^6-11*x^5+170*x^4+66*x^3-556*x^2+131*x+228,0,-1,0]];
E[404,3] = [x, [1,0,0,0,-1,0,-2,0,-3,0,-2,0,-3,0,0,0,-1,0,1,0,0,0,3,0,-4,0,0,0,-2,0,-3,0,0,0,2,0,-2,0,0,0,2,0,4,0,3,0,-3,0,-3,0,0,0,0,0,2,0,0,0,12,0,-10,0,6,0,3,0,2,0,0,0,-1,0,2,0,0,0,4,0,1,0,9,0,4,0,1,0,0,0,-6,0,6,0,0,0,-1,0,-2,0,6,0,1,0]];

E[405,1] = [x, [1,-1,0,-1,1,0,-3,3,0,-1,2,0,-2,3,0,-1,-4,0,-8,-1,0,-2,-3,0,1,2,0,3,1,0,0,-5,0,4,-3,0,-4,8,0,3,-5,0,-8,-2,0,3,-7,0,2,-1,0,2,2,0,2,-9,0,-1,14,0,7,0,0,7,-2,0,-3,4,0,3,-2,0,4,4,0,8,-6,0,-6,-1,0,5,-9,0,-4,8,0,6,15,0,6,3,0,7,-8,0,2,-2,0,-1,18,0,8,-6,0,-2,-3,0]];
E[405,2] = [x, [1,2,0,2,1,0,0,0,0,2,5,0,4,0,0,-4,-4,0,-5,2,0,10,6,0,1,8,0,0,-5,0,-9,-8,0,-8,0,0,-10,-10,0,0,7,0,-2,10,0,12,2,0,-7,2,0,8,8,0,5,0,0,-10,-1,0,-2,-18,0,-8,4,0,6,-8,0,0,1,0,-8,-20,0,-10,0,0,12,-4,0,14,6,0,-4,-4,0,0,-9,0,0,12,0,4,-5,0,14,-14,0,2,-3,0,2,0,0,16,-6,0]];
E[405,3] = [x, [1,-2,0,2,-1,0,0,0,0,2,-5,0,4,0,0,-4,4,0,-5,-2,0,10,-6,0,1,-8,0,0,5,0,-9,8,0,-8,0,0,-10,10,0,0,-7,0,-2,-10,0,12,-2,0,-7,-2,0,8,-8,0,5,0,0,-10,1,0,-2,18,0,-8,-4,0,6,8,0,0,-1,0,-8,20,0,-10,0,0,12,4,0,14,-6,0,-4,4,0,0,9,0,0,-12,0,4,5,0,14,14,0,2,3,0,2,0,0,16,6,0]];
E[405,4] = [x, [1,1,0,-1,-1,0,-3,-3,0,-1,-2,0,-2,-3,0,-1,4,0,-8,1,0,-2,3,0,1,-2,0,3,-1,0,0,5,0,4,3,0,-4,-8,0,3,5,0,-8,2,0,3,7,0,2,1,0,2,-2,0,2,9,0,-1,-14,0,7,0,0,7,2,0,-3,-4,0,3,2,0,4,-4,0,8,6,0,-6,1,0,5,9,0,-4,-8,0,6,-15,0,6,-3,0,7,8,0,2,2,0,-1,-18,0,8,6,0,-2,3,0]];
E[405,5] = [x^2-2*x-2, [1,x,0,2*x,-1,0,x-4,2*x+4,0,-x,-x+5,0,-2*x,-2*x+2,0,4*x+4,-x+2,0,-2*x+3,-2*x,0,3*x-2,-2*x+2,0,1,-4*x-4,0,-4*x+4,3*x-1,0,-3,8*x,0,-2,-x+4,0,x-2,-x-4,0,-2*x-4,-3*x+5,0,-3*x-2,6*x-4,0,-2*x-4,-x+8,0,-6*x+11,x,0,-8*x-8,x-6,0,x-5,-12,0,5*x+6,x+9,0,4,-3*x,0,8*x+8,2*x,0,-2*x+2,-4,0,2*x-2,-x+3,0,5*x-4,2,0,-2*x-8,7*x-22,0,-2*x+14,-4*x-4,0,-x-6,3*x,0,x-2,-8*x-6,0,2*x+16,3*x-3,0,4*x-4,-4*x-8,0,6*x-2,2*x-3,0,5*x-6,-x-12,0,2*x,-5*x-1,0,-2*x-2,-16*x-8,0,-4*x+2,2*x+10,0]];
E[405,6] = [x^2+2*x-2, [1,x,0,-2*x,1,0,-x-4,2*x-4,0,x,-x-5,0,2*x,-2*x-2,0,-4*x+4,-x-2,0,2*x+3,-2*x,0,-3*x-2,-2*x-2,0,1,-4*x+4,0,4*x+4,3*x+1,0,-3,8*x,0,-2,-x-4,0,-x-2,-x+4,0,2*x-4,-3*x-5,0,3*x-2,6*x+4,0,2*x-4,-x-8,0,6*x+11,x,0,8*x-8,x+6,0,-x-5,12,0,-5*x+6,x-9,0,4,-3*x,0,-8*x+8,2*x,0,2*x+2,4,0,-2*x-2,-x-3,0,-5*x-4,-2,0,2*x-8,7*x+22,0,2*x+14,-4*x+4,0,x-6,3*x,0,-x-2,-8*x+6,0,-2*x+16,3*x+3,0,-4*x-4,-4*x+8,0,-6*x-2,2*x+3,0,-5*x-6,-x+12,0,-2*x,-5*x+1,0,2*x-2,-16*x+8,0,4*x+2,2*x-10,0]];
E[405,7] = [x^3-x^2-5*x+3, [1,x,0,x^2-2,1,0,-x+2,x^2+x-3,0,x,-x^2+3,0,-x^2+5,-x^2+2*x,0,2*x+1,-x^2+3,0,-x^2+5,x^2-2,0,-x^2-2*x+3,2*x^2-x-6,0,1,-x^2+3,0,x^2-3*x-1,2*x^2-2*x-9,0,-x^2+4*x+5,-x+6,0,-x^2-2*x+3,-x+2,0,x^2-2*x-1,-x^2+3,0,x^2+x-3,-x^2-2*x,0,x^2+2*x-1,-x^2-2*x-3,0,x^2+4*x-6,-x^2-3*x+9,0,x^2-4*x-3,x,0,x^2-2*x-7,-2*x,0,-x^2+3,-3,0,x-6,-2*x,0,x^2+2*x-4,3*x^2+3,0,-x^2+2*x-2,-x^2+5,0,3*x^2-x-7,-x^2-2*x-3,0,-x^2+2*x,3*x^2+2*x-15,0,4*x-4,-x^2+4*x-3,0,x^2-2*x-7,-x^2+2*x+3,0,-4*x+2,2*x+1,0,-3*x^2-5*x+3,3*x-6,0,-x^2+3,3*x^2+4*x-3,0,-x^2-4*x-3,-3,0,-x^2+7,x^2+x+9,0,-4*x^2+4*x+3,-x^2+5,0,-4*x^2+2*x+8,-3*x^2+2*x-3,0,x^2-2,2*x^2+2*x-6,0,x^2-2*x-1,x^2-2*x-9,0,-2*x^2,-2*x^2+x+12,0]];
E[405,8] = [x^3+x^2-5*x-3, [1,x,0,x^2-2,-1,0,x+2,-x^2+x+3,0,-x,x^2-3,0,-x^2+5,x^2+2*x,0,-2*x+1,x^2-3,0,-x^2+5,-x^2+2,0,-x^2+2*x+3,-2*x^2-x+6,0,1,x^2-3,0,x^2+3*x-1,-2*x^2-2*x+9,0,-x^2-4*x+5,-x-6,0,-x^2+2*x+3,-x-2,0,x^2+2*x-1,x^2-3,0,x^2-x-3,x^2-2*x,0,x^2-2*x-1,x^2-2*x+3,0,x^2-4*x-6,x^2-3*x-9,0,x^2+4*x-3,x,0,x^2+2*x-7,-2*x,0,-x^2+3,3,0,-x-6,-2*x,0,x^2-2*x-4,-3*x^2-3,0,-x^2-2*x-2,x^2-5,0,3*x^2+x-7,x^2-2*x+3,0,-x^2-2*x,-3*x^2+2*x+15,0,-4*x-4,x^2+4*x+3,0,x^2+2*x-7,x^2+2*x-3,0,4*x+2,2*x-1,0,-3*x^2+5*x+3,3*x+6,0,-x^2+3,-3*x^2+4*x+3,0,-x^2+4*x-3,3,0,-x^2+7,-x^2+x-9,0,-4*x^2-4*x+3,x^2-5,0,-4*x^2-2*x+8,3*x^2+2*x+3,0,x^2-2,-2*x^2+2*x+6,0,x^2+2*x-1,-x^2-2*x+9,0,-2*x^2,2*x^2+x-12,0]];
E[405,9] = [x, [1,0,0,-2,1,0,2,0,0,0,3,0,-4,0,0,4,6,0,-1,-2,0,0,6,0,1,0,0,-4,9,0,-1,0,0,0,2,0,8,0,0,0,-3,0,-4,-6,0,0,-12,0,-3,0,0,8,-6,0,3,0,0,0,-3,0,-10,0,0,-8,-4,0,14,-12,0,0,3,0,2,0,0,2,6,0,-16,4,0,0,12,0,6,0,0,0,-15,0,-8,-12,0,0,-1,0,-4,0,0,-2,-9,0,14,0,0,0,18,0]];
E[405,10] = [x, [1,0,0,-2,-1,0,2,0,0,0,-3,0,-4,0,0,4,-6,0,-1,2,0,0,-6,0,1,0,0,-4,-9,0,-1,0,0,0,-2,0,8,0,0,0,3,0,-4,6,0,0,12,0,-3,0,0,8,6,0,3,0,0,0,3,0,-10,0,0,-8,4,0,14,12,0,0,-3,0,2,0,0,2,-6,0,-16,-4,0,0,-12,0,6,0,0,0,15,0,-8,12,0,0,1,0,-4,0,0,-2,9,0,14,0,0,0,-18,0]];

E[406,1] = [x, [1,-1,1,1,-3,-1,1,-1,-2,3,-3,1,-1,-1,-3,1,0,2,-4,-3,1,3,-6,-1,4,1,-5,1,1,3,5,-1,-3,0,-3,-2,2,4,-1,3,0,-1,-7,-3,6,6,-3,1,1,-4,0,-1,-9,5,9,-1,-4,-1,12,-3,-10,-5,-2,1,3,3,2,0,-6,3,-12,2,8,-2,4,-4,-3,1,5,-3,1,0,12,1,0,7,1,3,6,-6,-1,-6,5,3,12,-1,8,-1,6,4,-12,0,8,1,-3,9,18,-5,-13,-9,2,1,12,4,18,1,2,-12,0,3]];
E[406,2] = [x, [1,-1,2,1,2,-2,1,-1,1,-2,4,2,-2,-1,4,1,-4,-1,2,2,2,-4,0,-2,-1,2,-4,1,-1,-4,-2,-1,8,4,2,1,2,-2,-4,-2,8,-2,-8,4,2,0,6,2,1,1,-8,-2,6,4,8,-1,4,1,-4,4,4,2,1,1,-4,-8,-4,-4,0,-2,8,-1,-12,-2,-2,2,4,4,-12,2,-11,-8,0,2,-8,8,-2,-4,4,-2,-2,0,-4,-6,4,-2,4,-1,4,-1,-12,8,-16,2,4,-6,-12,-4,-14,-8,4,1,18,-4,0,-1,-2,4,-4,-4]];
E[406,3] = [x^3-x^2-8*x+4, [2,-2,2*x,2,x^2-x-2,-2*x,-2,-2,2*x^2-6,-x^2+x+2,-2*x^2+12,2*x,-x^2+x+10,2,6*x-4,2,-x^2+3*x+10,-2*x^2+6,-4*x-4,x^2-x-2,-2*x,2*x^2-12,-2*x^2-2*x+16,-2*x,2*x^2-4*x-6,x^2-x-10,2*x^2+4*x-8,-2,2,-6*x+4,-x^2-3*x+10,-2,-2*x^2-4*x+8,x^2-3*x-10,-x^2+x+2,2*x^2-6,2*x^2-2*x-4,4*x+4,2*x+4,-x^2+x+2,-x^2-5*x+18,2*x,-2*x^2+4*x,-2*x^2+12,3*x^2-x+6,2*x^2+2*x-16,x^2-x-2,2*x,2,-2*x^2+4*x+6,2*x^2+2*x+4,-x^2+x+10,2*x^2-4,-2*x^2-4*x+8,-2*x-12,2,-4*x^2-4*x,-2,x^2-3*x+14,6*x-4,-2*x^2+2*x+4,x^2+3*x-10,-2*x^2+6,2,2*x^2-12,2*x^2+4*x-8,4*x^2-32,-x^2+3*x+10,-4*x^2+8,x^2-x-2,2*x^2+6*x-8,-2*x^2+6,-x^2+3*x-6,-2*x^2+2*x+4,-2*x^2+10*x-8,-4*x-4,2*x^2-12,-2*x-4,6*x-4,x^2-x-2,8*x+10,x^2+5*x-18,5*x^2-7*x-34,-2*x,2*x^2+6*x-16,2*x^2-4*x,2*x,2*x^2-12,-x^2-9*x+2,-3*x^2+x-6,x^2-x-10,-2*x^2-2*x+16,-4*x^2+2*x+4,-x^2+x+2,-2*x^2-10*x+12,-2*x,-5*x^2-x+18,-2,-8*x-28,2*x^2-4*x-6,-2*x^2+6*x+28,-2*x^2-2*x-4,2*x^2-6*x-4,x^2-x-10,-6*x+4,-2*x^2+4,-4*x^2+8,2*x^2+4*x-8,-2*x^2-12*x+20,2*x+12,12*x-8,-2,6*x^2+2*x-40,4*x^2+4*x,2*x^2-10*x-12,2,5*x^2+x-30,-x^2+3*x-14,x^2-3*x-10,-6*x+4]];
E[406,4] = [x, [1,-1,0,1,0,0,-1,-1,-3,0,-4,0,0,1,0,1,-4,3,4,0,0,4,0,0,-5,0,0,-1,-1,0,-6,-1,0,4,0,-3,-2,-4,0,0,-8,0,4,-4,0,0,2,0,1,5,0,0,-2,0,0,1,0,1,-10,0,-2,6,3,1,0,0,8,-4,0,0,16,3,0,2,0,4,4,0,-4,0,9,8,-6,0,0,-4,0,4,0,0,0,0,0,-2,0,0,12,-1,12,-5,-10,0,12,0,0,2,4,0,10,0,0,-1,-6,0,0,-1,0,10,4,0]];
E[406,5] = [x, [1,1,-1,1,-3,-1,-1,1,-2,-3,-1,-1,-1,-1,3,1,-4,-2,-4,-3,1,-1,-2,-1,4,-1,5,-1,1,3,-1,1,1,-4,3,-2,6,-4,1,-3,0,1,3,-1,6,-2,-9,-1,1,4,4,-1,3,5,3,-1,4,1,0,3,6,-1,2,1,3,1,2,-4,2,3,-8,-2,0,6,-4,-4,1,1,-13,-3,1,0,0,1,12,3,-1,-1,-14,6,1,-2,1,-9,12,-1,16,1,2,4,-4,4,4,-1,-3,3,-14,5,15,3,-6,-1,0,4,6,1,2,0,4,3]];
E[406,6] = [x^4-x^3-10*x^2+4*x+8, [4,4,4*x,4,x^3-3*x^2-8*x+12,4*x,4,4,4*x^2-12,x^3-3*x^2-8*x+12,-4*x+8,4*x,-3*x^3+x^2+24*x-4,4,-2*x^3+2*x^2+8*x-8,4,-x^3+3*x^2+4*x-12,4*x^2-12,2*x^3-2*x^2-20*x+8,x^3-3*x^2-8*x+12,4*x,-4*x+8,-2*x^3+2*x^2+20*x,4*x,4*x^3-4*x^2-36*x+20,-3*x^3+x^2+24*x-4,4*x^3-24*x,4,4,-2*x^3+2*x^2+8*x-8,x^3+x^2-20*x-12,4,-4*x^2+8*x,-x^3+3*x^2+4*x-12,x^3-3*x^2-8*x+12,4*x^2-12,2*x^3-2*x^2-12*x-8,2*x^3-2*x^2-20*x+8,-2*x^3-6*x^2+8*x+24,x^3-3*x^2-8*x+12,-3*x^3+9*x^2+28*x-36,4*x,-4*x^2+16,-4*x+8,-3*x^3-3*x^2+24*x-20,-2*x^3+2*x^2+20*x,-3*x^3+5*x^2+20*x-28,4*x,4,4*x^3-4*x^2-36*x+20,2*x^3-6*x^2-8*x+8,-3*x^3+x^2+24*x-4,-4*x^2+8*x+24,4*x^3-24*x,4*x^3-8*x^2-24*x+32,4,-16,4,5*x^3-3*x^2-48*x+20,-2*x^3+2*x^2+8*x-8,4*x^2+4*x-56,x^3+x^2-20*x-12,4*x^2-12,4,-4*x^3+12*x^2+44*x-56,-4*x^2+8*x,-8*x^3+8*x^2+56*x-16,-x^3+3*x^2+4*x-12,8*x+16,x^3-3*x^2-8*x+12,6*x^3+2*x^2-60*x,4*x^2-12,x^3+5*x^2-12*x-52,2*x^3-2*x^2-12*x-8,4*x^2+4*x-32,2*x^3-2*x^2-20*x+8,-4*x+8,-2*x^3-6*x^2+8*x+24,-2*x^3-6*x^2+32*x+24,x^3-3*x^2-8*x+12,4*x^3+4*x^2-16*x+4,-3*x^3+9*x^2+28*x-36,-9*x^3+7*x^2+72*x-20,4*x,-2*x^3+2*x^2+28*x-32,-4*x^2+16,4*x,-4*x+8,-3*x^3+9*x^2+20*x-36,-3*x^3-3*x^2+24*x-20,-3*x^3+x^2+24*x-4,-2*x^3+2*x^2+20*x,2*x^3-10*x^2-16*x-8,-3*x^3+5*x^2+20*x-28,6*x^3-10*x^2-48*x+56,4*x,3*x^3-9*x^2-28*x+36,4,-4*x^3+8*x^2+12*x-24,4*x^3-4*x^2-36*x+20,-4*x^2+4*x+8,2*x^3-6*x^2-8*x+8,2*x^3+2*x^2-24,-3*x^3+x^2+24*x-4,-2*x^3+2*x^2+8*x-8,-4*x^2+8*x+24,4*x^3-4*x^2-32*x+32,4*x^3-24*x,4*x^3-40*x+8,4*x^3-8*x^2-24*x+32,8*x^2-16*x-16,4,2*x^3-6*x^2+32,-16,-4*x^3+4*x^2+32*x-32,4,x^3-15*x^2-40*x+28,5*x^3-3*x^2-48*x+20,-x^3+3*x^2+4*x-12,-2*x^3+2*x^2+8*x-8]];
E[406,7] = [x^2-2*x-2, [1,1,2,1,x,2,-1,1,1,x,-2*x+2,2,-x,-1,2*x,1,-3*x+2,1,-2*x+2,x,-2,-2*x+2,4*x-6,2,2*x-3,-x,-4,-1,-1,2*x,3*x,1,-4*x+4,-3*x+2,-x,1,-4,-2*x+2,-2*x,x,5*x-6,-2,4*x,-2*x+2,x,4*x-6,5*x-4,2,1,2*x-3,-6*x+4,-x,-4*x+2,-4,-2*x-4,-1,-4*x+4,-1,-x+10,2*x,4,3*x,-1,1,-2*x-2,-4*x+4,4*x-4,-3*x+2,8*x-12,-x,-4*x+6,1,x+6,-4,4*x-6,-2*x+2,2*x-2,-2*x,-2*x-4,x,-11,5*x-6,-9*x+10,-2,-4*x-6,4*x,-2,-2*x+2,-3*x+14,x,x,4*x-6,6*x,5*x-4,-2*x-4,2,x-6,1,-2*x+2,2*x-3,4,-6*x+4,-2*x+4,-x,-2*x,-4*x+2,4,-4,-10,-2*x-4,-8,-1,2*x-2,-4*x+4,2*x+8,-1,-x,-x+10,3*x-2,2*x]];

E[407,1] = [x^4+x^3-4*x^2+1, [1,x,x^3+x^2-4*x,x^2-2,-x^3-x^2+3*x,-1,-2*x^3-3*x^2+6*x,x^3-4*x,-x^2-x+1,-x^2+1,-1,-2*x^3-2*x^2+7*x,x^3+x^2-2*x-2,-x^3-2*x^2+2,x^2+x-3,-x^3-2*x^2+3,x^3+3*x^2-x-6,-x^3-x^2+x,3*x^3+6*x^2-7*x-7,x^3+2*x^2-5*x,2*x^2+3*x-6,-x,-x^3+5*x-3,-x^2+4,-x-3,2*x^2-2*x-1,-2*x^3-2*x^2+9*x+1,3*x^3+2*x^2-10*x+1,x^3-6*x+2,x^3+x^2-3*x,3*x^3+2*x^2-11*x+4,-3*x^3-4*x^2+11*x+1,-x^3-x^2+4*x,2*x^3+3*x^2-6*x-1,x^3-3*x+4,-x^2+2*x-1,-1,3*x^3+5*x^2-7*x-3,-2*x^3-3*x^2+7*x+2,x^3+x^2-3,-x^3-x^2+2*x-2,2*x^3+3*x^2-6*x,-3*x^3-6*x^2+8*x+4,-x^2+2,2*x-1,x^3+x^2-3*x+1,2*x^3+2*x^2-6*x+1,3*x^3+4*x^2-10*x,3*x^3+4*x^2-8*x,-x^2-3*x,-6*x^3-7*x^2+21*x+1,-4*x^2+3*x+4,4*x^3+2*x^2-18*x+3,x^2+x+2,x^3+x^2-3*x,x^3+6*x^2+x-7,-7*x^3-10*x^2+22*x+7,-x^3-2*x^2+2*x-1,-3*x^3-7*x^2+2*x+9,-x^2-2*x+5,-8*x^3-10*x^2+24*x+2,-x^3+x^2+4*x-3,3*x^2+4*x-3,x^3+3*x^2+x-3,2*x^3+x^2-5*x-1,1,-6*x^3-6*x^2+25*x-1,-x^3-4*x^2+x+10,-3*x^3-2*x^2+12*x-5,-x^3+x^2+4*x-1,4*x^3+6*x^2-11*x+2,x^3+4*x^2-3*x,3*x^3+2*x^2-10*x-5,-x,-3*x^3-3*x^2+12*x+1,-4*x^3-7*x^2+11*x+11]];
E[407,2] = [x^4-x^3-4*x^2+2*x+3, [1,x,-x^3+x^2+2*x-2,x^2-2,x^3-x^2-3*x,-2*x^2+3,-x^2+2,x^3-4*x,2*x^3-x^2-5*x+1,x^2-2*x-3,1,-2*x^2-x+4,-x^3+x^2+2*x-4,-x^3+2*x,x^2+x-3,x^3-2*x^2-2*x+1,-x^3-x^2+3*x,x^3+3*x^2-3*x-6,3*x^3-4*x^2-7*x+5,-x^3+3*x,2*x^2+x-4,x,-x^3+4*x^2+x-9,-2*x^3+3*x^2+4*x-6,-2*x^3+7*x+1,-2*x^2-2*x+3,-2*x^2+x+1,-x^3+2*x-1,-3*x^3+4*x^2+10*x-6,x^3+x^2-3*x,x^3+x-4,-3*x^3+2*x^2+7*x-3,-x^3+x^2+2*x-2,-2*x^3-x^2+2*x+3,x^3-3*x,3*x^2+2*x-5,1,-x^3+5*x^2-x-9,4*x^3-3*x^2-9*x+8,-x^3-3*x^2+6*x+9,-x^3+3*x^2,2*x^3+x^2-4*x,x^3+6*x^2-4*x-16,x^2-2,-2*x^3-2*x^2+6*x+9,3*x^3-3*x^2-7*x+3,2*x^3-6*x^2-2*x+9,x^3-2,x^3-2*x-6,-2*x^3-x^2+5*x+6,4*x^3-x^2-7*x+3,-4*x^2-x+8,-6*x^2+2*x+15,-2*x^3+x^2+x,x^3-x^2-3*x,x^3-2*x^2-3*x+3,-3*x^3+4*x^2+10*x-13,x^3-2*x^2+9,-x^3-5*x^2+10*x+9,2*x^3-x^2-4*x+3,2*x^2-10,x^3+5*x^2-6*x-3,-3*x^2-2*x+5,-3*x^3-x^2+7*x+7,-2*x^3+3*x^2+7*x-3,-2*x^2+3,-4*x^3+2*x^2+9*x-1,-x^3-4*x^2+x+6,3*x^3-6*x^2-10*x+15,x^3+x^2-2*x-3,2*x^3-2*x^2-11*x+6,x^3-4*x^2+x+12,-x^3+2*x-7,x,3*x^3-3*x^2-6*x+7,-2*x^3+3*x^2+7*x-7]];
E[407,3] = [x^12-x^11-18*x^10+18*x^9+111*x^8-104*