\\ ap_s2_401-500.gp \\ This is a table of eigenforms for the action of \\ the Hecke operators on S_2^{new}(Gamma_0(N)). \\ William Stein (was@math.berkeley.edu), October, 1998. \\ 401<=N<=500 \\ E=matrix(500,?,i,j,0); \\ E[N,ith eigenform]=[[a_2,...,a_97], f(x)] \\ where the a_i are defined over Q[x]/f(x). \\ missing: only goes through 402. E[401,1]=[[x,-2*x^11-4*x^10+21*x^9+43*x^8-66*x^7-151*x^6+63*x^5+211*x^4+5*x^3-114*x^2-17*x+13,11/2*x^11+23/2*x^10-60*x^9-124*x^8+417/2*x^7+863/2*x^6-274*x^5-1151/2*x^4+231/2*x^3+265*x^2+25/2*x-23,-2*x^11-4*x^10+23*x^9+43*x^8-89*x^7-147*x^6+145*x^5+183*x^4-94*x^3-64*x^2+5*x+1,-11/2*x^11-11/2*x^10+70*x^9+53*x^8-629/2*x^7-289/2*x^6+630*x^5+151/2*x^4-1093/2*x^3+101*x^2+253/2*x-36,11/2*x^11+15/2*x^10-65*x^9-76*x^8+521/2*x^7+473/2*x^6-446*x^5-487/2*x^4+643/2*x^3+41*x^2-111/2*x+7,1/2*x^11-9/2*x^10-12*x^9+54*x^8+171/2*x^7-435/2*x^6-239*x^5+733/2*x^4+521/2*x^3-251*x^2-167/2*x+39,13/2*x^11+13/2*x^10-84*x^9-66*x^8+767/2*x^7+409/2*x^6-773*x^5-379/2*x^4+1313/2*x^3-27*x^2-283/2*x+26,-5*x^11-10*x^10+54*x^9+107*x^8-183*x^7-369*x^6+226*x^5+487*x^4-80*x^3-220*x^2-13*x+13,-3*x^11-13*x^10+24*x^9+149*x^8-23*x^7-571*x^6-150*x^5+899*x^4+297*x^3-551*x^2-129*x+71,3*x^11+10*x^10-28*x^9-110*x^8+67*x^7+393*x^6-7*x^5-552*x^4-90*x^3+289*x^2+58*x-37,-13/2*x^11-13/2*x^10+84*x^9+62*x^8-777/2*x^7-325/2*x^6+817*x^5+115/2*x^4-1521/2*x^3+160*x^2+399/2*x-50,9/2*x^11-3/2*x^10-68*x^9+27*x^8+745/2*x^7-325/2*x^6-910*x^5+839/2*x^4+1879/2*x^3-432*x^2-543/2*x+85,-15/2*x^11-37/2*x^10+78*x^9+202*x^8-489/2*x^7-1435/2*x^6+240*x^5+1999/2*x^4+21/2*x^3-511*x^2-157/2*x+53,-x^11+4*x^10+21*x^9-51*x^8-147*x^7+227*x^6+428*x^5-441*x^4-502*x^3+352*x^2+166*x-55,x^11+9*x^10-4*x^9-103*x^8-29*x^7+387*x^6+149*x^5-583*x^4-180*x^3+338*x^2+57*x-45,3/2*x^11+29/2*x^10+4*x^9-165*x^8-313/2*x^7+1257/2*x^6+626*x^5-2011/2*x^4-1577/2*x^3+671*x^2+523/2*x-103,-9/2*x^11-3/2*x^10+61*x^9+12*x^8-583/2*x^7-43/2*x^6+604*x^5-57/2*x^4-1015/2*x^3+86*x^2+207/2*x-23,5*x^11+13*x^10-55*x^9-145*x^8+197*x^7+527*x^6-280*x^5-739*x^4+145*x^3+349*x^2+2*x-27,21/2*x^11+43/2*x^10-116*x^9-234*x^8+823/2*x^7+1661/2*x^6-555*x^5-2309/2*x^4+459/2*x^3+578*x^2+71/2*x-58,14*x^11+28*x^10-154*x^9-302*x^8+542*x^7+1055*x^6-724*x^5-1425*x^4+302*x^3+682*x^2+48*x-68,-8*x^11-17*x^10+89*x^9+186*x^8-321*x^7-663*x^6+449*x^5+920*x^4-203*x^3-448*x^2-24*x+35,-3/2*x^11+1/2*x^10+18*x^9-9*x^8-139/2*x^7+89/2*x^6+101*x^5-141/2*x^4-91/2*x^3+15*x^2+7/2*x+9,1/2*x^11-11/2*x^10-20*x^9+65*x^8+351/2*x^7-537/2*x^6-556*x^5+1011/2*x^4+1311/2*x^3-437*x^2-415/2*x+86,-11/2*x^11-21/2*x^10+61*x^9+109*x^8-447/2*x^7-703/2*x^6+351*x^5+789/2*x^4-523/2*x^3-113*x^2+115/2*x+4], 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]; 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