/*
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
*/

P.<x> = PolynomialRing(QQ)
g = P([1, -4, -1, 9, -2, -3, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([49, 7, w^4 - 2*w^3 - 3*w^2 + 4*w + 2])

primes_array = [
[3, 3, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 5*w + 1],\
[7, 7, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 3*w + 5],\
[25, 5, -w^3 + 2*w^2 + 2*w - 3],\
[37, 37, w^3 - w^2 - 4*w + 2],\
[37, 37, w^3 - 2*w^2 - 3*w + 2],\
[49, 7, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 5*w - 3],\
[49, 7, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - 3*w + 4],\
[53, 53, w^4 - 2*w^3 - 3*w^2 + 3*w + 1],\
[53, 53, w^4 - 2*w^3 - 3*w^2 + 5*w],\
[61, 61, -3*w^5 + 6*w^4 + 12*w^3 - 16*w^2 - 12*w + 5],\
[61, 61, 2*w^5 - 5*w^4 - 7*w^3 + 16*w^2 + 7*w - 7],\
[61, 61, -2*w^5 + 5*w^4 + 7*w^3 - 15*w^2 - 8*w + 6],\
[61, 61, -w^3 + 2*w^2 + 4*w - 3],\
[64, 2, -2],\
[67, 67, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 2*w - 3],\
[67, 67, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 4*w + 5],\
[71, 71, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + 2*w - 4],\
[71, 71, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 - w],\
[81, 3, -w^4 + 2*w^3 + 2*w^2 - 3*w + 2],\
[101, 101, w^5 - 3*w^4 - 3*w^3 + 9*w^2 + 4*w - 3],\
[101, 101, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 4*w + 3],\
[103, 103, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - 2*w + 3],\
[103, 103, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + w - 3],\
[107, 107, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 4*w - 3],\
[107, 107, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - w - 1],\
[113, 113, -2*w^5 + 4*w^4 + 9*w^3 - 12*w^2 - 10*w + 6],\
[113, 113, -3*w^5 + 9*w^4 + 7*w^3 - 27*w^2 - 2*w + 12],\
[113, 113, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 4*w + 6],\
[113, 113, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 + 2],\
[149, 149, 3*w^5 - 8*w^4 - 8*w^3 + 22*w^2 + 4*w - 7],\
[149, 149, 3*w^5 - 7*w^4 - 10*w^3 + 20*w^2 + 7*w - 6],\
[151, 151, -w^5 + 4*w^4 - 12*w^2 + 3*w + 3],\
[151, 151, -w^5 + w^4 + 6*w^3 - 3*w^2 - 6*w + 3],\
[163, 163, 2*w^5 - 5*w^4 - 5*w^3 + 14*w^2 - 4],\
[163, 163, 2*w^5 - 5*w^4 - 5*w^3 + 11*w^2 + 3*w - 2],\
[167, 167, -w^4 + 3*w^3 - 6*w + 2],\
[167, 167, -2*w^5 + 6*w^4 + 5*w^3 - 19*w^2 - w + 7],\
[193, 193, 4*w^5 - 10*w^4 - 11*w^3 + 27*w^2 + 4*w - 7],\
[193, 193, 4*w^5 - 10*w^4 - 11*w^3 + 26*w^2 + 5*w - 7],\
[197, 197, w^5 - 4*w^4 - 2*w^3 + 15*w^2 + 3*w - 8],\
[197, 197, -2*w^5 + 5*w^4 + 7*w^3 - 16*w^2 - 4*w + 8],\
[197, 197, -w^3 + w^2 + w - 2],\
[197, 197, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + 2*w - 4],\
[227, 227, -w^4 + 3*w^3 + 2*w^2 - 6*w - 3],\
[227, 227, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 2*w - 4],\
[241, 241, -2*w^5 + 6*w^4 + 5*w^3 - 20*w^2 - w + 9],\
[241, 241, -w^4 + w^3 + 4*w^2 - 3*w - 1],\
[241, 241, -4*w^5 + 11*w^4 + 10*w^3 - 31*w^2 - 2*w + 11],\
[241, 241, -2*w^5 + 4*w^4 + 9*w^3 - 11*w^2 - 12*w + 3],\
[257, 257, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 3*w - 1],\
[257, 257, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - 2*w - 4],\
[263, 263, -3*w^5 + 8*w^4 + 8*w^3 - 21*w^2 - 6*w + 5],\
[263, 263, -3*w^5 + 7*w^4 + 10*w^3 - 21*w^2 - 7*w + 9],\
[271, 271, 2*w^5 - 6*w^4 - 6*w^3 + 21*w^2 + 6*w - 11],\
[271, 271, w^5 - 3*w^4 - 4*w^3 + 12*w^2 + 6*w - 7],\
[277, 277, 4*w^5 - 9*w^4 - 15*w^3 + 27*w^2 + 13*w - 9],\
[277, 277, -4*w^5 + 11*w^4 + 11*w^3 - 32*w^2 - 6*w + 11],\
[281, 281, -w^5 + 3*w^4 + 3*w^3 - 11*w^2 - 3*w + 5],\
[281, 281, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 9*w + 4],\
[311, 311, -w^4 + w^3 + 3*w^2 + w + 1],\
[311, 311, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 5*w + 5],\
[353, 353, w^5 - 4*w^4 - w^3 + 14*w^2 - 3*w - 6],\
[353, 353, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w - 1],\
[359, 359, -4*w^5 + 10*w^4 + 11*w^3 - 28*w^2 - 4*w + 11],\
[359, 359, -2*w^2 + w + 5],\
[361, 19, -3*w^5 + 9*w^4 + 6*w^3 - 25*w^2 + 8],\
[361, 19, 3*w^5 - 6*w^4 - 12*w^3 + 17*w^2 + 11*w - 5],\
[361, 19, -w^4 + 2*w^3 + 4*w^2 - 5*w - 2],\
[367, 367, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 6*w - 8],\
[367, 367, w^5 - 3*w^4 - 2*w^3 + 10*w^2 - 7],\
[383, 383, -2*w^5 + 6*w^4 + 6*w^3 - 20*w^2 - 5*w + 8],\
[383, 383, 4*w^5 - 10*w^4 - 11*w^3 + 28*w^2 + 3*w - 12],\
[419, 419, -w^4 + 5*w^2 + 3*w - 3],\
[419, 419, -2*w^5 + 6*w^4 + 6*w^3 - 20*w^2 - 6*w + 11],\
[443, 443, w^5 - 3*w^4 - w^3 + 8*w^2 - 3*w - 4],\
[443, 443, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 3*w - 2],\
[461, 461, -w^5 + 2*w^4 + 4*w^3 - 4*w^2 - 4*w - 3],\
[461, 461, w^5 - 3*w^4 - 2*w^3 + 10*w^2 - 3*w - 6],\
[463, 463, -3*w^5 + 7*w^4 + 10*w^3 - 21*w^2 - 5*w + 8],\
[463, 463, -3*w^5 + 8*w^4 + 8*w^3 - 21*w^2 - 4*w + 4],\
[499, 499, w^5 - 2*w^4 - 2*w^3 + 2*w^2 - w + 2],\
[499, 499, w^5 - 4*w^4 + 11*w^2 - 4*w - 5],\
[509, 509, -2*w^5 + 5*w^4 + 8*w^3 - 18*w^2 - 8*w + 10],\
[509, 509, w^5 - w^4 - 6*w^3 + 4*w^2 + 7*w - 3],\
[541, 541, -2*w^5 + 6*w^4 + 6*w^3 - 20*w^2 - 5*w + 9],\
[541, 541, -2*w^5 + 4*w^4 + 10*w^3 - 14*w^2 - 13*w + 6],\
[557, 557, -w^5 + 2*w^4 + 6*w^3 - 9*w^2 - 9*w + 4],\
[557, 557, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 6*w - 7],\
[577, 577, 2*w^5 - 5*w^4 - 6*w^3 + 16*w^2 + 2*w - 9],\
[577, 577, -3*w^5 + 7*w^4 + 10*w^3 - 19*w^2 - 9*w + 8],\
[587, 587, -w^4 + 3*w^3 + w^2 - 6*w - 1],\
[587, 587, 2*w^5 - 4*w^4 - 9*w^3 + 14*w^2 + 8*w - 7],\
[587, 587, -w^5 + 4*w^4 - 12*w^2 + 6*w + 3],\
[587, 587, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 5*w - 7],\
[587, 587, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 3*w + 4],\
[587, 587, -w^4 + w^3 + 4*w^2 - w - 4],\
[625, 5, -2*w^5 + 6*w^4 + 3*w^3 - 16*w^2 + 3*w + 6],\
[631, 631, 3*w^5 - 8*w^4 - 8*w^3 + 22*w^2 + 5*w - 4],\
[631, 631, -3*w^5 + 7*w^4 + 10*w^3 - 20*w^2 - 8*w + 10],\
[641, 641, -3*w^5 + 7*w^4 + 11*w^3 - 21*w^2 - 10*w + 10],\
[641, 641, 3*w^5 - 8*w^4 - 9*w^3 + 24*w^2 + 6*w - 6],\
[643, 643, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 6*w - 5],\
[643, 643, 3*w^5 - 6*w^4 - 13*w^3 + 16*w^2 + 15*w - 3],\
[643, 643, 3*w^5 - 8*w^4 - 8*w^3 + 24*w^2 + 5*w - 11],\
[643, 643, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 6*w - 6],\
[653, 653, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w + 4],\
[653, 653, 2*w^5 - 6*w^4 - 5*w^3 + 19*w^2 + 2*w - 6],\
[653, 653, -2*w^5 + 4*w^4 + 9*w^3 - 12*w^2 - 11*w + 6],\
[653, 653, -w^5 + 3*w^4 + 4*w^3 - 12*w^2 - 4*w + 6],\
[659, 659, 2*w^5 - 4*w^4 - 8*w^3 + 12*w^2 + 8*w - 7],\
[659, 659, -2*w^5 + 6*w^4 + 4*w^3 - 16*w^2 - 2*w + 3],\
[661, 661, 2*w^5 - 5*w^4 - 6*w^3 + 13*w^2 + 6*w - 1],\
[661, 661, -w^5 + w^4 + 5*w^3 - w^2 - 6*w - 1],\
[691, 691, -w^5 + 2*w^4 + 6*w^3 - 9*w^2 - 8*w + 6],\
[691, 691, 4*w^5 - 11*w^4 - 11*w^3 + 32*w^2 + 7*w - 11],\
[733, 733, -4*w^5 + 10*w^4 + 13*w^3 - 30*w^2 - 8*w + 14],\
[733, 733, -2*w^5 + 6*w^4 + 4*w^3 - 17*w^2 - w + 5],\
[739, 739, -w^2 + 5],\
[739, 739, w^2 - 2*w - 4],\
[757, 757, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 - 2*w],\
[757, 757, -w^4 + w^3 + 5*w^2 - w - 6],\
[821, 821, -3*w^5 + 7*w^4 + 9*w^3 - 17*w^2 - 7*w + 2],\
[821, 821, -2*w^5 + 3*w^4 + 10*w^3 - 9*w^2 - 11*w + 4],\
[821, 821, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\
[821, 821, -3*w^5 + 8*w^4 + 7*w^3 - 22*w^2 - w + 9],\
[823, 823, 3*w^5 - 7*w^4 - 10*w^3 + 19*w^2 + 10*w - 7],\
[823, 823, 3*w^5 - 8*w^4 - 8*w^3 + 23*w^2 + 5*w - 8],\
[827, 827, w^5 - w^4 - 7*w^3 + 4*w^2 + 9*w - 2],\
[827, 827, -w^5 + 4*w^4 + w^3 - 13*w^2 + 3*w + 4],\
[853, 853, -5*w^5 + 13*w^4 + 12*w^3 - 33*w^2 - 2*w + 9],\
[853, 853, 2*w^4 - 6*w^3 - 4*w^2 + 16*w - 1],\
[857, 857, 3*w^5 - 6*w^4 - 11*w^3 + 16*w^2 + 8*w - 8],\
[857, 857, 2*w^5 - 7*w^4 - 3*w^3 + 21*w^2 - 2*w - 6],\
[859, 859, -3*w^5 + 7*w^4 + 11*w^3 - 20*w^2 - 12*w + 8],\
[859, 859, -3*w^5 + 7*w^4 + 12*w^3 - 23*w^2 - 12*w + 9],\
[859, 859, 3*w^5 - 8*w^4 - 10*w^3 + 25*w^2 + 9*w - 10],\
[859, 859, -2*w^5 + 7*w^4 + 2*w^3 - 20*w^2 + 5*w + 7],\
[863, 863, w^3 - 6*w],\
[863, 863, 3*w^5 - 7*w^4 - 11*w^3 + 21*w^2 + 9*w - 8],\
[863, 863, -3*w^5 + 8*w^4 + 9*w^3 - 24*w^2 - 5*w + 7],\
[863, 863, -w^3 + 3*w^2 + 3*w - 5],\
[877, 877, 2*w^5 - 6*w^4 - 4*w^3 + 15*w^2 + 2*w - 1],\
[877, 877, -2*w^5 + 4*w^4 + 8*w^3 - 13*w^2 - 6*w + 8],\
[881, 881, -4*w^5 + 10*w^4 + 13*w^3 - 29*w^2 - 9*w + 8],\
[881, 881, -4*w^5 + 10*w^4 + 13*w^3 - 30*w^2 - 8*w + 11],\
[883, 883, -4*w^5 + 9*w^4 + 16*w^3 - 30*w^2 - 14*w + 12],\
[883, 883, w^5 - w^4 - 8*w^3 + 7*w^2 + 10*w - 5],\
[907, 907, -2*w^5 + 4*w^4 + 9*w^3 - 14*w^2 - 9*w + 7],\
[907, 907, -w^4 + 3*w^3 + w^2 - 7*w],\
[907, 907, w^5 - 4*w^4 - w^3 + 12*w^2 - 2*w - 2],\
[907, 907, -w^4 + 3*w^3 + 3*w^2 - 9*w - 1],\
[907, 907, -w^4 + w^3 + 4*w^2 - 4],\
[907, 907, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 4*w + 5],\
[919, 919, -4*w^5 + 10*w^4 + 12*w^3 - 28*w^2 - 6*w + 9],\
[919, 919, 4*w^5 - 10*w^4 - 12*w^3 + 28*w^2 + 6*w - 7],\
[929, 929, -w^5 + 4*w^4 + 2*w^3 - 14*w^2 - 2*w + 8],\
[929, 929, -2*w^5 + 5*w^4 + 5*w^3 - 14*w^2 + w + 5],\
[937, 937, -w^5 + 2*w^4 + 6*w^3 - 9*w^2 - 8*w + 5],\
[937, 937, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 5*w - 5],\
[941, 941, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 5*w + 5],\
[941, 941, -w^5 + 3*w^4 + 2*w^3 - 9*w^2],\
[947, 947, 3*w^5 - 6*w^4 - 12*w^3 + 16*w^2 + 12*w - 6],\
[947, 947, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 5*w + 6],\
[947, 947, 2*w^4 - 4*w^3 - 5*w^2 + 6*w + 1],\
[947, 947, -3*w^5 + 9*w^4 + 6*w^3 - 26*w^2 + w + 7],\
[953, 953, -3*w^5 + 6*w^4 + 12*w^3 - 18*w^2 - 10*w + 10],\
[953, 953, 2*w^5 - 7*w^4 - 3*w^3 + 22*w^2 - w - 7],\
[971, 971, -w^5 + w^4 + 5*w^3 - 7*w - 3],\
[971, 971, -w^5 + 4*w^4 - w^3 - 11*w^2 + 7*w + 5],\
[997, 997, -4*w^5 + 9*w^4 + 14*w^3 - 25*w^2 - 12*w + 10],\
[997, 997, -3*w^5 + 8*w^4 + 9*w^3 - 23*w^2 - 6*w + 5],\
[997, 997, -2*w^4 + 4*w^3 + 6*w^2 - 9*w - 1],\
[997, 997, 4*w^5 - 11*w^4 - 10*w^3 + 31*w^2 + 4*w - 8],\
[1021, 1021, 3*w^5 - 7*w^4 - 11*w^3 + 23*w^2 + 10*w - 15],\
[1021, 1021, -4*w^5 + 11*w^4 + 10*w^3 - 32*w^2 - 4*w + 12],\
[1031, 1031, -2*w^5 + 6*w^4 + 4*w^3 - 17*w^2 - 2*w + 6],\
[1031, 1031, 2*w^5 - 4*w^4 - 8*w^3 + 11*w^2 + 10*w - 5],\
[1039, 1039, -w^4 + 7*w^2 + 2*w - 6],\
[1039, 1039, w^5 - 4*w^4 + w^3 + 10*w^2 - 7*w - 4],\
[1039, 1039, w^5 - 2*w^4 - 3*w^3 + 5*w^2 + 2*w - 4],\
[1039, 1039, -3*w^5 + 8*w^4 + 7*w^3 - 21*w^2 + w + 7],\
[1051, 1051, -w^4 + 3*w^3 + 2*w^2 - 5*w - 2],\
[1051, 1051, w^4 - 2*w^3 - 2*w^2 + 4*w - 4],\
[1061, 1061, 4*w^5 - 10*w^4 - 11*w^3 + 26*w^2 + 4*w - 6],\
[1061, 1061, 4*w^5 - 10*w^4 - 11*w^3 + 27*w^2 + 3*w - 7],\
[1087, 1087, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + w - 4],\
[1087, 1087, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + w - 2],\
[1097, 1097, -2*w^5 + 6*w^4 + 4*w^3 - 17*w^2 - w + 4],\
[1097, 1097, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 9*w + 6],\
[1103, 1103, 4*w^5 - 10*w^4 - 13*w^3 + 30*w^2 + 8*w - 10],\
[1103, 1103, 4*w^5 - 10*w^4 - 13*w^3 + 29*w^2 + 9*w - 9],\
[1129, 1129, 3*w^5 - 9*w^4 - 4*w^3 + 24*w^2 - 8*w - 7],\
[1129, 1129, 3*w^5 - 6*w^4 - 10*w^3 + 12*w^2 + 7*w + 1],\
[1181, 1181, 4*w^5 - 10*w^4 - 14*w^3 + 32*w^2 + 9*w - 13],\
[1181, 1181, 3*w^5 - 7*w^4 - 12*w^3 + 22*w^2 + 13*w - 7],\
[1181, 1181, -4*w^5 + 10*w^4 + 12*w^3 - 29*w^2 - 5*w + 9],\
[1181, 1181, 4*w^5 - 10*w^4 - 12*w^3 + 27*w^2 + 7*w - 7],\
[1181, 1181, 3*w^5 - 8*w^4 - 10*w^3 + 26*w^2 + 8*w - 12],\
[1181, 1181, -5*w^5 + 13*w^4 + 16*w^3 - 40*w^2 - 11*w + 19],\
[1187, 1187, 2*w^5 - 7*w^4 - 4*w^3 + 22*w^2 + w - 11],\
[1187, 1187, 3*w^5 - 7*w^4 - 10*w^3 + 21*w^2 + 7*w - 12],\
[1187, 1187, 2*w^5 - 4*w^4 - 7*w^3 + 11*w^2 + 4*w - 7],\
[1187, 1187, 6*w^5 - 14*w^4 - 22*w^3 + 41*w^2 + 21*w - 14],\
[1217, 1217, 3*w^5 - 6*w^4 - 12*w^3 + 17*w^2 + 12*w - 7],\
[1217, 1217, 3*w^5 - 9*w^4 - 6*w^3 + 25*w^2 + w - 7],\
[1229, 1229, -2*w^5 + 5*w^4 + 8*w^3 - 17*w^2 - 8*w + 8],\
[1229, 1229, -2*w^5 + 5*w^4 + 8*w^3 - 17*w^2 - 8*w + 6],\
[1231, 1231, -6*w^5 + 16*w^4 + 17*w^3 - 47*w^2 - 8*w + 18],\
[1231, 1231, -6*w^5 + 14*w^4 + 21*w^3 - 40*w^2 - 17*w + 10],\
[1237, 1237, -3*w^5 + 8*w^4 + 8*w^3 - 22*w^2 - 2*w + 6],\
[1237, 1237, 3*w^5 - 7*w^4 - 10*w^3 + 20*w^2 + 5*w - 5],\
[1279, 1279, 3*w^5 - 8*w^4 - 8*w^3 + 23*w^2 + w - 6],\
[1279, 1279, 2*w^5 - 5*w^4 - 7*w^3 + 16*w^2 + 8*w - 9],\
[1291, 1291, -2*w^5 + 4*w^4 + 9*w^3 - 13*w^2 - 9*w + 8],\
[1291, 1291, -2*w^5 + 6*w^4 + 5*w^3 - 18*w^2 - 2*w + 3],\
[1297, 1297, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + w - 6],\
[1297, 1297, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 - 3],\
[1303, 1303, -w^4 + w^3 + 6*w^2 - 3*w - 3],\
[1303, 1303, -w^4 + 3*w^3 + 3*w^2 - 8*w],\
[1319, 1319, -2*w^5 + 5*w^4 + 7*w^3 - 16*w^2 - 8*w + 7],\
[1319, 1319, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 9*w - 7],\
[1369, 37, 2*w^5 - 6*w^4 - 5*w^3 + 19*w^2 + 4*w - 13],\
[1369, 37, 2*w^5 - 4*w^4 - 9*w^3 + 12*w^2 + 13*w - 1],\
[1373, 1373, w^5 - 3*w^4 - 4*w^3 + 10*w^2 + 6*w - 6],\
[1373, 1373, 2*w^5 - 5*w^4 - 8*w^3 + 17*w^2 + 9*w - 8],\
[1373, 1373, 2*w^5 - 5*w^4 - 8*w^3 + 17*w^2 + 9*w - 7],\
[1373, 1373, 4*w^5 - 10*w^4 - 13*w^3 + 31*w^2 + 8*w - 17],\
[1381, 1381, -w^4 + 3*w^3 + 2*w^2 - 5*w - 1],\
[1381, 1381, w^5 - 2*w^4 - 5*w^3 + 5*w^2 + 9*w + 1],\
[1423, 1423, -3*w^5 + 8*w^4 + 9*w^3 - 24*w^2 - 5*w + 6],\
[1423, 1423, 3*w^5 - 7*w^4 - 11*w^3 + 21*w^2 + 9*w - 9],\
[1427, 1427, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 - 2],\
[1427, 1427, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 3*w - 6],\
[1433, 1433, w^5 - w^4 - 7*w^3 + 4*w^2 + 9*w - 1],\
[1433, 1433, w^5 - 4*w^4 - w^3 + 13*w^2 - 3*w - 5],\
[1439, 1439, 3*w^5 - 7*w^4 - 9*w^3 + 17*w^2 + 5*w - 4],\
[1439, 1439, 4*w^5 - 11*w^4 - 11*w^3 + 32*w^2 + 6*w - 9],\
[1451, 1451, -w^5 + w^4 + 6*w^3 - w^2 - 9*w - 2],\
[1451, 1451, -w^5 + 4*w^4 - 13*w^2 + 6*w + 6],\
[1471, 1471, 5*w^5 - 14*w^4 - 15*w^3 + 46*w^2 + 11*w - 23],\
[1471, 1471, -5*w^5 + 14*w^4 + 11*w^3 - 38*w^2 + w + 11],\
[1489, 1489, 4*w^5 - 10*w^4 - 13*w^3 + 30*w^2 + 10*w - 9],\
[1489, 1489, 4*w^5 - 10*w^4 - 13*w^3 + 29*w^2 + 11*w - 12],\
[1499, 1499, w^5 - 3*w^4 - w^3 + 7*w^2 - 4*w - 3],\
[1499, 1499, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 - 3],\
[1511, 1511, 4*w^5 - 12*w^4 - 9*w^3 + 35*w^2 + 2*w - 13],\
[1511, 1511, -2*w^5 + 6*w^4 + 3*w^3 - 18*w^2 + 4*w + 10],\
[1549, 1549, -2*w^5 + 6*w^4 + 4*w^3 - 16*w^2 + 3*w + 1],\
[1549, 1549, 2*w^5 - 4*w^4 - 8*w^3 + 12*w^2 + 3*w - 4],\
[1579, 1579, 3*w^5 - 9*w^4 - 6*w^3 + 24*w^2 - w - 6],\
[1579, 1579, 5*w^5 - 12*w^4 - 15*w^3 + 32*w^2 + 7*w - 13],\
[1607, 1607, -w^5 + 4*w^4 - 3*w^3 - 7*w^2 + 12*w - 2],\
[1607, 1607, -w^5 + w^4 + 3*w^3 + 2*w^2 - 3],\
[1613, 1613, -w^4 + 3*w^3 + w^2 - 6*w - 2],\
[1613, 1613, -w^4 + w^3 + 4*w^2 - w - 5],\
[1619, 1619, 4*w^5 - 10*w^4 - 12*w^3 + 29*w^2 + 6*w - 8],\
[1619, 1619, -2*w^5 + 6*w^4 + 3*w^3 - 17*w^2 + 5*w + 6],\
[1627, 1627, 4*w^5 - 11*w^4 - 9*w^3 + 29*w^2 - w - 4],\
[1627, 1627, 4*w^5 - 11*w^4 - 12*w^3 + 35*w^2 + 10*w - 18],\
[1637, 1637, w^5 - 4*w^4 + w^3 + 11*w^2 - 7*w - 4],\
[1637, 1637, w^5 - w^4 - 5*w^3 + 7*w + 2],\
[1657, 1657, 4*w^5 - 10*w^4 - 14*w^3 + 31*w^2 + 15*w - 15],\
[1657, 1657, -4*w^5 + 10*w^4 + 14*w^3 - 31*w^2 - 15*w + 11],\
[1681, 41, 2*w^4 - 4*w^3 - 7*w^2 + 9*w + 3],\
[1693, 1693, w^5 - 4*w^4 - w^3 + 15*w^2 - w - 10],\
[1693, 1693, -5*w^5 + 12*w^4 + 17*w^3 - 35*w^2 - 16*w + 11],\
[1697, 1697, -7*w^5 + 17*w^4 + 21*w^3 - 48*w^2 - 9*w + 19],\
[1697, 1697, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 - w - 7],\
[1709, 1709, -3*w^5 + 9*w^4 + 7*w^3 - 27*w^2 - 3*w + 14],\
[1709, 1709, -4*w^5 + 10*w^4 + 11*w^3 - 30*w^2 - 3*w + 14],\
[1721, 1721, -w^5 + 9*w^3 - 17*w + 2],\
[1721, 1721, -w^5 + 5*w^4 - w^3 - 17*w^2 + 5*w + 7],\
[1723, 1723, -w^5 + 2*w^4 + 2*w^3 - 2*w^2 + w - 3],\
[1723, 1723, w^5 - 3*w^4 + 6*w^2 - 6*w - 1],\
[1759, 1759, w^4 - 4*w^3 - w^2 + 8*w - 1],\
[1759, 1759, -3*w^5 + 9*w^4 + 7*w^3 - 27*w^2 - 4*w + 14],\
[1777, 1777, 3*w^5 - 9*w^4 - 7*w^3 + 29*w^2 - 13],\
[1777, 1777, 3*w^5 - 8*w^4 - 8*w^3 + 26*w^2 + 3*w - 13],\
[1777, 1777, -3*w^5 + 9*w^4 + 6*w^3 - 25*w^2 + 11],\
[1777, 1777, 3*w^5 - 6*w^4 - 13*w^3 + 16*w^2 + 16*w - 3],\
[1783, 1783, 3*w^5 - 7*w^4 - 10*w^3 + 19*w^2 + 10*w - 8],\
[1783, 1783, -6*w^5 + 15*w^4 + 17*w^3 - 42*w^2 - 7*w + 15],\
[1783, 1783, 7*w^5 - 18*w^4 - 20*w^3 + 52*w^2 + 8*w - 20],\
[1783, 1783, -3*w^5 + 8*w^4 + 8*w^3 - 23*w^2 - 5*w + 7],\
[1801, 1801, -2*w^5 + 6*w^4 + 3*w^3 - 15*w^2 + 4*w + 4],\
[1801, 1801, -2*w^5 + 4*w^4 + 7*w^3 - 10*w^2 - 3*w],\
[1811, 1811, -2*w^5 + 4*w^4 + 8*w^3 - 12*w^2 - 9*w + 7],\
[1811, 1811, 3*w^5 - 10*w^4 - 7*w^3 + 33*w^2 + 3*w - 14],\
[1823, 1823, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 9*w - 5],\
[1823, 1823, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 5*w + 5],\
[1847, 1847, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + w - 6],\
[1847, 1847, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 4*w - 1],\
[1849, 43, -2*w^4 + 4*w^3 + 6*w^2 - 8*w - 3],\
[1901, 1901, -5*w^5 + 13*w^4 + 13*w^3 - 37*w^2 - 3*w + 13],\
[1901, 1901, -5*w^5 + 12*w^4 + 15*w^3 - 30*w^2 - 11*w + 6],\
[1913, 1913, 3*w^5 - 9*w^4 - 7*w^3 + 29*w^2 + w - 13],\
[1913, 1913, -w^5 + 4*w^4 + w^3 - 12*w^2 + 3*w + 1],\
[1913, 1913, 2*w^5 - 3*w^4 - 10*w^3 + 7*w^2 + 14*w + 1],\
[1913, 1913, -2*w^4 + 2*w^3 + 9*w^2 + w - 5],\
[1931, 1931, -3*w^5 + 6*w^4 + 13*w^3 - 16*w^2 - 17*w + 5],\
[1931, 1931, 4*w^5 - 9*w^4 - 15*w^3 + 26*w^2 + 17*w - 10],\
[1949, 1949, -3*w^5 + 8*w^4 + 9*w^3 - 23*w^2 - 10*w + 10],\
[1949, 1949, 2*w^5 - 7*w^4 - 3*w^3 + 20*w^2 - w - 8],\
[1973, 1973, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 3*w + 9],\
[1973, 1973, -5*w^5 + 13*w^4 + 13*w^3 - 34*w^2 - 7*w + 11],\
[1979, 1979, 6*w^5 - 15*w^4 - 18*w^3 + 43*w^2 + 8*w - 13],\
[1979, 1979, -2*w^5 + 3*w^4 + 11*w^3 - 11*w^2 - 12*w + 7],\
[1987, 1987, -5*w^5 + 13*w^4 + 13*w^3 - 35*w^2 - 3*w + 7],\
[1987, 1987, -w^5 + 2*w^4 + 6*w^3 - 6*w^2 - 11*w]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-3, 0, -9, 10, 10, -6, -6, -2, -2, -8, -1, -1, -8, 9, -2, -2, 9, 9, -2, -3, -3, 6, 6, -4, -4, 2, 16, 16, 2, 10, 10, -16, -16, -4, -4, -7, -7, 12, 12, 2, 2, 2, 2, 18, 18, 4, -10, -10, 4, 6, 6, -16, -16, 20, 20, -9, -9, -26, -26, 4, 4, -3, -3, -18, -18, -16, -16, -37, 25, 25, -1, -1, -28, -28, 24, 24, -7, -7, -26, -26, 3, 3, 34, 34, 10, 10, -9, -9, 32, 32, 28, 28, -21, -21, 28, 28, -46, 23, 23, -30, -30, -14, 28, 28, -14, -11, 38, 38, -11, -12, -12, -10, -10, -29, -29, 6, 6, -37, -37, -26, -26, -11, 10, 10, -11, 40, 40, -54, -54, -56, -56, 32, 32, 6, 41, 41, 6, -39, -25, -25, -39, -11, -11, 35, 35, -5, -5, -2, 26, 12, 12, 26, -2, 10, 10, 20, 20, -56, -56, -24, -24, -32, 24, 24, -32, 51, 51, 27, 27, 32, 46, 46, 32, 14, 14, 3, 3, 32, 39, 39, 32, -26, -26, 40, 40, -25, -25, 55, 55, -51, -51, 45, 45, 6, -8, 27, 27, -8, 6, 33, 68, 68, 33, 63, 63, 54, 54, -56, -56, -50, -50, 41, 41, -66, -66, 38, 38, -12, -12, -24, -24, 54, 54, -5, 58, 58, -5, 10, 10, -4, -4, 42, 42, 6, 6, -37, -37, 31, 31, -47, -47, -1, -1, -68, -68, 35, 35, 10, 10, 47, 47, 75, 75, 46, 46, -25, -25, -38, -38, -42, -42, 6, 6, -82, 28, 28, -17, -17, -19, -19, 0, 0, 51, 51, -4, -4, 0, 14, 14, 0, -36, -64, -64, -36, 31, 31, -15, -15, -31, -31, 21, 21, -82, -72, -72, -46, -18, -18, -46, -63, -63, 25, 25, 0, 0, 6, 6, 70, 70]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([7, 7, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 3*w + 5])] = 1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]