/*
  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, -6, 3, 10, -3, -3, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([17,17,w^3 - w^2 - 4*w])

primes_array = [
[3, 3, w - 1],\
[17, 17, -w^2 + 2*w + 1],\
[17, 17, -w^3 + w^2 + 4*w],\
[19, 19, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + w - 4],\
[19, 19, w^2 - w - 1],\
[37, 37, w^4 - 2*w^3 - 3*w^2 + 3*w + 2],\
[37, 37, w^4 - 4*w^3 + w^2 + 7*w - 3],\
[53, 53, 2*w^5 - 6*w^4 - 6*w^3 + 18*w^2 + 9*w - 6],\
[53, 53, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - 3*w + 2],\
[64, 2, -2],\
[71, 71, -w^5 + 4*w^4 - w^3 - 8*w^2 + 3*w - 1],\
[71, 71, 2*w^5 - 5*w^4 - 8*w^3 + 15*w^2 + 12*w - 6],\
[71, 71, 2*w^5 - 6*w^4 - 6*w^3 + 18*w^2 + 9*w - 7],\
[73, 73, -2*w^5 + 6*w^4 + 5*w^3 - 16*w^2 - 7*w + 3],\
[73, 73, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 6*w + 6],\
[89, 89, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 8*w - 4],\
[89, 89, w^5 - w^4 - 9*w^3 + 7*w^2 + 16*w - 6],\
[89, 89, 2*w^5 - 6*w^4 - 4*w^3 + 15*w^2 + 3*w - 3],\
[89, 89, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 10*w - 6],\
[107, 107, w^5 - 2*w^4 - 7*w^3 + 10*w^2 + 12*w - 6],\
[107, 107, 2*w^5 - 5*w^4 - 7*w^3 + 14*w^2 + 9*w - 5],\
[107, 107, w^5 - 3*w^4 - 3*w^3 + 9*w^2 + 6*w - 3],\
[107, 107, w^4 - 2*w^3 - 3*w^2 + 4*w + 1],\
[109, 109, 2*w^5 - 5*w^4 - 8*w^3 + 15*w^2 + 13*w - 6],\
[109, 109, -w^4 + 4*w^3 - w^2 - 9*w + 3],\
[127, 127, w^4 - 3*w^3 + 5*w - 4],\
[127, 127, -w^5 + 3*w^4 + w^3 - 6*w^2 + w + 3],\
[127, 127, 2*w^5 - 5*w^4 - 8*w^3 + 16*w^2 + 11*w - 6],\
[127, 127, w^5 - 4*w^4 + 2*w^3 + 7*w^2 - 7*w],\
[163, 163, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w + 5],\
[163, 163, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 2*w + 5],\
[163, 163, -w^5 + 3*w^4 + 4*w^3 - 10*w^2 - 8*w + 4],\
[163, 163, w^5 - 4*w^4 + 10*w^2 - w - 4],\
[179, 179, -w^5 + 3*w^4 + 3*w^3 - 7*w^2 - 7*w - 1],\
[179, 179, 2*w^5 - 6*w^4 - 5*w^3 + 18*w^2 + 5*w - 7],\
[179, 179, -2*w^5 + 5*w^4 + 10*w^3 - 19*w^2 - 18*w + 10],\
[179, 179, -2*w^5 + 5*w^4 + 9*w^3 - 17*w^2 - 14*w + 9],\
[197, 197, 2*w^5 - 6*w^4 - 5*w^3 + 18*w^2 + 3*w - 7],\
[197, 197, -w^5 + 4*w^4 - w^3 - 7*w^2 + 3*w - 2],\
[197, 197, w^5 - w^4 - 7*w^3 + 4*w^2 + 10*w - 3],\
[197, 197, -2*w^5 + 8*w^4 - 2*w^3 - 17*w^2 + 10*w + 1],\
[197, 197, -w^4 + 3*w^3 + 2*w^2 - 6*w - 2],\
[197, 197, w^5 - 4*w^4 + w^3 + 9*w^2 - 4*w - 2],\
[199, 199, -w^5 + 2*w^4 + 6*w^3 - 9*w^2 - 10*w + 4],\
[199, 199, -w^4 + 3*w^3 + 2*w^2 - 9*w + 1],\
[233, 233, 2*w^5 - 4*w^4 - 12*w^3 + 17*w^2 + 19*w - 9],\
[233, 233, -w^5 + w^4 + 8*w^3 - 6*w^2 - 13*w + 6],\
[233, 233, 2*w^5 - 6*w^4 - 6*w^3 + 19*w^2 + 9*w - 7],\
[233, 233, w^5 - 4*w^4 + 11*w^2 - 4*w - 2],\
[251, 251, -2*w^5 + 5*w^4 + 10*w^3 - 18*w^2 - 18*w + 7],\
[251, 251, w^3 - w^2 - 3*w - 2],\
[251, 251, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 3*w - 3],\
[251, 251, -w^5 + 4*w^4 - 11*w^2 + 4*w + 3],\
[269, 269, w^5 - 3*w^4 - w^3 + 6*w^2 - 2*w - 3],\
[269, 269, 2*w^5 - 7*w^4 - 3*w^3 + 20*w^2 + 3*w - 8],\
[271, 271, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 2*w - 7],\
[271, 271, -w^4 + 4*w^3 - w^2 - 10*w + 6],\
[289, 17, -w^5 + 3*w^4 + w^3 - 5*w^2 - 2],\
[289, 17, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 6*w - 4],\
[307, 307, 2*w^5 - 5*w^4 - 10*w^3 + 19*w^2 + 16*w - 8],\
[307, 307, w^5 - 4*w^4 + 2*w^3 + 7*w^2 - 6*w - 1],\
[307, 307, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 3*w + 2],\
[307, 307, w^5 - 2*w^4 - 6*w^3 + 10*w^2 + 7*w - 9],\
[361, 19, 2*w^5 - 6*w^4 - 6*w^3 + 18*w^2 + 8*w - 5],\
[361, 19, w^5 - 3*w^4 - w^3 + 5*w^2 + 3],\
[379, 379, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 9*w - 5],\
[379, 379, -2*w + 3],\
[397, 397, -w^5 + 5*w^4 - 6*w^3 - 6*w^2 + 14*w - 5],\
[397, 397, -w^5 + 3*w^4 + w^3 - 4*w^2 - w - 5],\
[397, 397, 3*w^5 - 9*w^4 - 7*w^3 + 23*w^2 + 9*w - 6],\
[397, 397, -w^4 + 5*w^3 - 2*w^2 - 10*w + 1],\
[431, 431, -3*w^5 + 8*w^4 + 11*w^3 - 24*w^2 - 18*w + 9],\
[431, 431, 2*w^5 - 6*w^4 - 3*w^3 + 13*w^2 + w - 3],\
[431, 431, -3*w^5 + 8*w^4 + 10*w^3 - 23*w^2 - 14*w + 8],\
[431, 431, -2*w^5 + 6*w^4 + 4*w^3 - 14*w^2 - 5*w],\
[433, 433, -3*w^5 + 9*w^4 + 8*w^3 - 25*w^2 - 11*w + 9],\
[433, 433, -2*w^5 + 6*w^4 + 4*w^3 - 16*w^2 - 3*w + 7],\
[433, 433, 2*w^5 - 5*w^4 - 7*w^3 + 13*w^2 + 11*w - 4],\
[433, 433, -w^4 + 4*w^3 + w^2 - 10*w - 2],\
[449, 449, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 + w + 3],\
[449, 449, -w^4 + 4*w^3 - 2*w^2 - 5*w + 5],\
[449, 449, -w^5 + 4*w^4 - w^3 - 8*w^2 + 3*w - 2],\
[449, 449, -w^3 + 5*w + 3],\
[449, 449, w^3 - 5*w],\
[449, 449, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - w - 6],\
[467, 467, -2*w^4 + 7*w^3 - 16*w + 7],\
[467, 467, -2*w^4 + 6*w^3 + w^2 - 10*w + 3],\
[487, 487, -w^5 + 2*w^4 + 6*w^3 - 10*w^2 - 8*w + 9],\
[487, 487, 2*w^5 - 6*w^4 - 5*w^3 + 15*w^2 + 7*w - 3],\
[487, 487, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 8*w - 6],\
[487, 487, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 8*w + 1],\
[503, 503, 2*w^5 - 7*w^4 - 3*w^3 + 19*w^2 + 3*w - 6],\
[503, 503, 2*w^5 - 6*w^4 - 5*w^3 + 18*w^2 + 4*w - 6],\
[503, 503, 2*w^5 - 5*w^4 - 9*w^3 + 17*w^2 + 13*w - 7],\
[503, 503, -w^5 + 4*w^4 - 10*w^2 + 3*w - 1],\
[521, 521, w^5 - 4*w^4 + 11*w^2 - w - 6],\
[521, 521, w^5 - w^4 - 9*w^3 + 8*w^2 + 15*w - 6],\
[521, 521, -w^5 + 4*w^4 - 2*w^3 - 8*w^2 + 9*w],\
[521, 521, -2*w^5 + 4*w^4 + 11*w^3 - 15*w^2 - 17*w + 9],\
[523, 523, 3*w^5 - 8*w^4 - 10*w^3 + 24*w^2 + 12*w - 10],\
[523, 523, -w^4 + 3*w^3 - w^2 - 4*w + 5],\
[523, 523, -2*w^5 + 4*w^4 + 11*w^3 - 14*w^2 - 17*w + 7],\
[523, 523, -w^5 + 5*w^4 - 4*w^3 - 9*w^2 + 9*w + 1],\
[577, 577, -3*w^5 + 8*w^4 + 10*w^3 - 22*w^2 - 14*w + 7],\
[577, 577, -2*w^5 + 7*w^4 + w^3 - 15*w^2 + 2*w + 2],\
[593, 593, 2*w^5 - 5*w^4 - 9*w^3 + 17*w^2 + 15*w - 10],\
[593, 593, w^3 - w^2 - 2*w - 2],\
[593, 593, -3*w^5 + 9*w^4 + 9*w^3 - 27*w^2 - 14*w + 10],\
[593, 593, 2*w^5 - 6*w^4 - 6*w^3 + 19*w^2 + 8*w - 7],\
[613, 613, w^5 - 2*w^4 - 7*w^3 + 9*w^2 + 12*w - 5],\
[613, 613, w^5 - w^4 - 9*w^3 + 8*w^2 + 13*w - 7],\
[613, 613, w^5 - 5*w^4 + 3*w^3 + 11*w^2 - 6*w - 2],\
[613, 613, -w^4 + 3*w^3 + w^2 - 5*w + 4],\
[613, 613, w^5 - w^4 - 9*w^3 + 7*w^2 + 14*w - 4],\
[613, 613, w^5 - 2*w^4 - 7*w^3 + 11*w^2 + 12*w - 8],\
[631, 631, 2*w^5 - 7*w^4 + 15*w^2 - 6*w - 2],\
[631, 631, -3*w^5 + 8*w^4 + 10*w^3 - 23*w^2 - 12*w + 10],\
[631, 631, w^5 - 3*w^4 + w^3 + 3*w^2 - 6*w + 3],\
[631, 631, -3*w^5 + 8*w^4 + 13*w^3 - 29*w^2 - 21*w + 15],\
[683, 683, -w^5 + 4*w^4 - w^3 - 8*w^2 + 2*w - 1],\
[683, 683, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 11*w - 4],\
[701, 701, -w^5 + 3*w^4 + w^3 - 7*w^2 + 3*w + 2],\
[701, 701, 2*w^2 - 3*w - 4],\
[719, 719, 2*w^5 - 5*w^4 - 8*w^3 + 16*w^2 + 13*w - 8],\
[719, 719, w^5 - 5*w^4 + 4*w^3 + 10*w^2 - 10*w - 1],\
[719, 719, w^5 - w^4 - 9*w^3 + 6*w^2 + 16*w - 2],\
[719, 719, 2*w^5 - 5*w^4 - 9*w^3 + 18*w^2 + 15*w - 10],\
[739, 739, -2*w^5 + 9*w^4 - 6*w^3 - 15*w^2 + 16*w - 7],\
[739, 739, 4*w^5 - 9*w^4 - 19*w^3 + 30*w^2 + 28*w - 14],\
[757, 757, 2*w^5 - 5*w^4 - 9*w^3 + 16*w^2 + 17*w - 7],\
[757, 757, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 6*w - 6],\
[757, 757, 2*w^5 - 6*w^4 - 7*w^3 + 20*w^2 + 11*w - 6],\
[757, 757, -2*w^4 + 5*w^3 + 4*w^2 - 10*w - 1],\
[773, 773, 2*w^5 - 8*w^4 + 3*w^3 + 16*w^2 - 11*w],\
[773, 773, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 12*w - 6],\
[809, 809, 2*w^5 - 6*w^4 - 3*w^3 + 13*w^2 + 2*w - 3],\
[809, 809, -2*w^3 + 5*w^2 + 4*w - 6],\
[811, 811, -w^4 + 3*w^3 + 3*w^2 - 7*w - 3],\
[811, 811, 2*w^5 - 7*w^4 - w^3 + 17*w^2 - 3*w - 6],\
[827, 827, w^5 - 4*w^4 + w^3 + 10*w^2 - 5*w - 4],\
[827, 827, w^5 - 4*w^4 + w^3 + 10*w^2 - 5*w - 5],\
[829, 829, 2*w^5 - 4*w^4 - 11*w^3 + 15*w^2 + 18*w - 9],\
[829, 829, 2*w^5 - 6*w^4 - 7*w^3 + 19*w^2 + 13*w - 7],\
[829, 829, -2*w^5 + 9*w^4 - 5*w^3 - 18*w^2 + 15*w],\
[829, 829, 3*w^5 - 9*w^4 - 9*w^3 + 28*w^2 + 11*w - 11],\
[829, 829, w^3 - 2*w^2 - 3*w - 1],\
[829, 829, -2*w^5 + 4*w^4 + 12*w^3 - 17*w^2 - 20*w + 10],\
[863, 863, -w^4 + 4*w^3 + w^2 - 11*w],\
[863, 863, w^4 - 4*w^3 - w^2 + 11*w + 1],\
[919, 919, -w^5 + 5*w^4 - 3*w^3 - 11*w^2 + 4*w + 1],\
[919, 919, -w^5 + 4*w^4 - w^3 - 8*w^2 + 6*w - 4],\
[919, 919, -w^4 + 5*w^3 - w^2 - 12*w + 1],\
[919, 919, -2*w^5 + 5*w^4 + 7*w^3 - 13*w^2 - 11*w + 6],\
[937, 937, 2*w^5 - 6*w^4 - 3*w^3 + 12*w^2 + 3*w],\
[937, 937, 2*w^5 - 4*w^4 - 10*w^3 + 12*w^2 + 16*w - 5],\
[937, 937, w^5 - 4*w^4 + 8*w^2 + w + 1],\
[937, 937, 2*w^4 - 8*w^3 + 2*w^2 + 16*w - 5],\
[953, 953, -w^5 + 4*w^4 - 11*w^2 + 3*w + 7],\
[953, 953, w^5 - 2*w^4 - 7*w^3 + 9*w^2 + 13*w - 7],\
[953, 953, -w^5 + 3*w^4 + w^3 - 7*w^2 + 4*w + 1],\
[953, 953, 2*w^5 - 8*w^4 + 3*w^3 + 16*w^2 - 11*w - 1],\
[971, 971, w^4 - w^3 - 5*w^2 + 2*w + 4],\
[971, 971, -w^4 + w^3 + 4*w^2 - w + 1],\
[971, 971, -2*w^5 + 5*w^4 + 10*w^3 - 20*w^2 - 15*w + 9],\
[971, 971, w^4 - 2*w^3 - 4*w^2 + 6*w + 1],\
[991, 991, -w - 3],\
[991, 991, -2*w^5 + 7*w^4 + 3*w^3 - 19*w^2 - 5*w + 6],\
[991, 991, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - 5*w + 7],\
[991, 991, 2*w^5 - 7*w^4 - 2*w^3 + 16*w^2 + 2*w],\
[1009, 1009, 2*w^4 - 6*w^3 - 2*w^2 + 11*w],\
[1009, 1009, -w^5 + w^4 + 9*w^3 - 7*w^2 - 15*w + 6],\
[1061, 1061, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 4*w + 2],\
[1061, 1061, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + 2*w - 7],\
[1063, 1063, 2*w^5 - 5*w^4 - 10*w^3 + 18*w^2 + 18*w - 9],\
[1063, 1063, -2*w^5 + 5*w^4 + 8*w^3 - 15*w^2 - 14*w + 8],\
[1063, 1063, -w^5 + 4*w^4 - 11*w^2 + 4*w + 5],\
[1063, 1063, w^5 - 2*w^4 - 7*w^3 + 10*w^2 + 14*w - 5],\
[1117, 1117, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 7*w + 5],\
[1117, 1117, -w^5 + 2*w^4 + 3*w^3 - 2*w^2 - 3*w - 3],\
[1117, 1117, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 5*w - 8],\
[1117, 1117, w^5 - 4*w^4 + 3*w^3 + 4*w^2 - 7*w + 4],\
[1151, 1151, -w^4 + 4*w^3 - 10*w - 1],\
[1151, 1151, w^5 - 3*w^4 - w^3 + 8*w^2 - 3*w - 3],\
[1151, 1151, 3*w^5 - 8*w^4 - 8*w^3 + 19*w^2 + 8*w - 3],\
[1151, 1151, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 12*w - 5],\
[1171, 1171, w^5 - 2*w^4 - 5*w^3 + 5*w^2 + 7*w + 1],\
[1171, 1171, 3*w^5 - 10*w^4 - 4*w^3 + 25*w^2 + 3*w - 7],\
[1171, 1171, -w^5 + 5*w^4 - 3*w^3 - 11*w^2 + 8*w + 3],\
[1171, 1171, -2*w^5 + 5*w^4 + 7*w^3 - 16*w^2 - 7*w + 6],\
[1187, 1187, -3*w^5 + 8*w^4 + 12*w^3 - 27*w^2 - 18*w + 11],\
[1187, 1187, w^4 - 2*w^3 - 2*w^2 + 4*w - 3],\
[1259, 1259, 2*w^5 - 6*w^4 - 5*w^3 + 16*w^2 + 9*w - 5],\
[1259, 1259, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 9*w - 7],\
[1277, 1277, -3*w^5 + 11*w^4 + w^3 - 25*w^2 + 2*w + 3],\
[1277, 1277, -w^4 + w^3 + 5*w^2 - w - 6],\
[1277, 1277, 2*w^5 - 6*w^4 - 4*w^3 + 13*w^2 + 5*w + 1],\
[1277, 1277, w^4 - 5*w^3 + 3*w^2 + 9*w - 7],\
[1277, 1277, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 - 4*w - 1],\
[1277, 1277, 3*w^5 - 9*w^4 - 6*w^3 + 22*w^2 + 5*w - 4],\
[1279, 1279, -2*w^5 + 4*w^4 + 12*w^3 - 17*w^2 - 18*w + 11],\
[1279, 1279, -3*w^5 + 11*w^4 - 23*w^2 + 5*w + 2],\
[1279, 1279, w^3 + w^2 - 5*w - 2],\
[1279, 1279, -2*w^5 + 6*w^4 + 7*w^3 - 21*w^2 - 9*w + 9],\
[1279, 1279, -w^5 + 3*w^4 + 5*w^3 - 12*w^2 - 9*w + 4],\
[1279, 1279, -2*w^3 + 5*w^2 + 3*w - 8],\
[1297, 1297, -2*w^5 + 4*w^4 + 11*w^3 - 14*w^2 - 19*w + 7],\
[1297, 1297, -w^5 + w^4 + 10*w^3 - 9*w^2 - 19*w + 7],\
[1331, 11, -3*w^5 + 7*w^4 + 16*w^3 - 26*w^2 - 28*w + 9],\
[1331, 11, w^3 - w^2 - w - 3],\
[1367, 1367, 2*w^5 - 6*w^4 - 4*w^3 + 13*w^2 + 5*w],\
[1367, 1367, w^3 - 6*w],\
[1367, 1367, 3*w^5 - 9*w^4 - 6*w^3 + 22*w^2 + 5*w - 5],\
[1367, 1367, w^3 - 6*w - 2],\
[1369, 37, 2*w^5 - 6*w^4 - 7*w^3 + 20*w^2 + 10*w - 8],\
[1369, 37, 3*w^5 - 9*w^4 - 8*w^3 + 25*w^2 + 10*w - 8],\
[1423, 1423, 3*w^5 - 10*w^4 - 5*w^3 + 26*w^2 + 6*w - 3],\
[1423, 1423, -2*w^4 + 7*w^3 - w^2 - 13*w + 4],\
[1459, 1459, -w^5 + 4*w^4 - 3*w^3 - 4*w^2 + 8*w - 5],\
[1459, 1459, 2*w^5 - 5*w^4 - 6*w^3 + 11*w^2 + 8*w],\
[1459, 1459, -2*w^5 + 7*w^4 + 4*w^3 - 22*w^2 - 2*w + 7],\
[1459, 1459, -3*w^5 + 8*w^4 + 14*w^3 - 29*w^2 - 24*w + 11],\
[1493, 1493, -3*w^5 + 9*w^4 + 9*w^3 - 25*w^2 - 16*w + 6],\
[1493, 1493, -2*w^5 + 3*w^4 + 15*w^3 - 14*w^2 - 27*w + 9],\
[1493, 1493, w^5 - 4*w^4 + 2*w^3 + 5*w^2 - 5*w + 3],\
[1493, 1493, -3*w^5 + 8*w^4 + 9*w^3 - 21*w^2 - 11*w + 7],\
[1531, 1531, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 + w + 4],\
[1531, 1531, 2*w^5 - 6*w^4 - 6*w^3 + 17*w^2 + 11*w - 7],\
[1549, 1549, w^5 - 4*w^4 - 3*w^3 + 14*w^2 + 7*w - 4],\
[1549, 1549, -4*w^5 + 10*w^4 + 18*w^3 - 34*w^2 - 28*w + 15],\
[1567, 1567, -3*w^5 + 6*w^4 + 17*w^3 - 23*w^2 - 25*w + 9],\
[1567, 1567, -w^5 + 3*w^4 + 6*w^3 - 13*w^2 - 12*w + 4],\
[1583, 1583, w^5 - 2*w^4 - 8*w^3 + 11*w^2 + 15*w - 7],\
[1583, 1583, w^5 - 4*w^4 - w^3 + 13*w^2 - w - 7],\
[1601, 1601, -w^4 + 4*w^3 - 3*w^2 - 6*w + 7],\
[1601, 1601, 3*w^5 - 8*w^4 - 9*w^3 + 22*w^2 + 10*w - 8],\
[1619, 1619, 2*w^5 - 5*w^4 - 11*w^3 + 19*w^2 + 21*w - 6],\
[1619, 1619, w^5 - 2*w^4 - 8*w^3 + 13*w^2 + 12*w - 12],\
[1619, 1619, -4*w^5 + 9*w^4 + 20*w^3 - 32*w^2 - 31*w + 13],\
[1619, 1619, w^5 - 2*w^4 - 6*w^3 + 10*w^2 + 10*w - 12],\
[1637, 1637, -w^5 + 2*w^4 + 4*w^3 - 4*w^2 - 5*w - 3],\
[1637, 1637, w^5 - 4*w^4 + 2*w^3 + 6*w^2 - 5*w + 4],\
[1637, 1637, 4*w^5 - 10*w^4 - 17*w^3 + 31*w^2 + 29*w - 12],\
[1637, 1637, -w^5 + 5*w^4 - 5*w^3 - 8*w^2 + 15*w - 1],\
[1657, 1657, w^4 - 2*w^3 - w^2 + w - 4],\
[1657, 1657, 2*w^5 - 5*w^4 - 8*w^3 + 17*w^2 + 9*w - 7],\
[1693, 1693, w^5 - 2*w^4 - 9*w^3 + 14*w^2 + 15*w - 8],\
[1693, 1693, w^5 - 3*w^4 - 3*w^3 + 9*w^2 + w],\
[1709, 1709, 2*w^5 - 7*w^4 - 3*w^3 + 18*w^2 + 4*w - 3],\
[1709, 1709, 3*w^5 - 8*w^4 - 11*w^3 + 25*w^2 + 14*w - 9],\
[1709, 1709, -w^5 + w^4 + 11*w^3 - 11*w^2 - 20*w + 9],\
[1709, 1709, -w^5 + w^4 + 7*w^3 - 3*w^2 - 12*w + 1],\
[1747, 1747, -w^5 + 5*w^4 - 3*w^3 - 9*w^2 + 7*w - 4],\
[1747, 1747, -3*w^5 + 11*w^4 - 24*w^2 + 5*w + 3],\
[1783, 1783, -w^4 + 3*w^3 + 2*w^2 - 5*w - 4],\
[1783, 1783, -2*w^5 + 7*w^4 + 2*w^3 - 18*w^2 - w + 4],\
[1871, 1871, -w^5 + 3*w^4 + 4*w^3 - 11*w^2 - 9*w + 6],\
[1871, 1871, 2*w^5 - 8*w^4 + w^3 + 17*w^2 - 3*w - 2],\
[1871, 1871, 2*w^5 - 6*w^4 - 5*w^3 + 16*w^2 + 9*w - 6],\
[1871, 1871, -3*w^5 + 11*w^4 - w^3 - 23*w^2 + 12*w - 3],\
[1873, 1873, -w^5 + w^4 + 8*w^3 - 5*w^2 - 11*w + 4],\
[1873, 1873, 3*w^5 - 6*w^4 - 15*w^3 + 19*w^2 + 22*w - 9],\
[1889, 1889, 2*w^5 - 5*w^4 - 8*w^3 + 14*w^2 + 13*w - 5],\
[1889, 1889, -2*w^5 + 5*w^4 + 8*w^3 - 15*w^2 - 12*w + 8],\
[1889, 1889, 2*w^5 - 7*w^4 - w^3 + 16*w^2 - 3*w - 5],\
[1889, 1889, w^5 - 4*w^4 + w^3 + 8*w^2 - 4*w - 3],\
[1907, 1907, -3*w^5 + 6*w^4 + 18*w^3 - 25*w^2 - 28*w + 12],\
[1907, 1907, 2*w^5 - 5*w^4 - 7*w^3 + 14*w^2 + 8*w - 1],\
[1979, 1979, 2*w^4 - 9*w^3 + 5*w^2 + 18*w - 11],\
[1979, 1979, 4*w^5 - 10*w^4 - 14*w^3 + 27*w^2 + 20*w - 8],\
[1997, 1997, 3*w^5 - 8*w^4 - 11*w^3 + 25*w^2 + 14*w - 10],\
[1997, 1997, -4*w^5 + 13*w^4 + 5*w^3 - 32*w^2 + w + 4],\
[1997, 1997, 2*w^5 - 7*w^4 - 3*w^3 + 18*w^2 + 4*w - 4],\
[1997, 1997, -4*w^5 + 11*w^4 + 15*w^3 - 35*w^2 - 24*w + 11]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - x - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -2*e, 1, -2*e + 4, -2*e - 4, 2*e - 2, -e, -3*e - 8, -4, -6*e - 3, -8*e + 2, 9*e - 9, -3*e + 9, -5*e + 4, 9*e - 3, 6*e - 6, 3*e - 13, -4*e, 5*e - 13, -e - 8, 8*e + 2, 7*e + 7, 6*e + 2, -4, 12*e - 4, 5*e - 5, 4*e - 8, 3*e + 9, 2*e + 14, 4*e, -5*e + 2, 8*e - 10, -5*e - 11, -6*e - 14, 5*e - 10, -15*e - 2, e + 7, -12*e + 2, -15*e + 6, 8*e - 6, 8*e, -5*e + 11, 7*e - 14, -7*e + 4, -8*e + 6, -11*e + 3, -4*e - 10, e - 23, -4*e + 14, -4*e + 8, -16, -18*e + 4, 5*e - 7, -e - 18, 17*e + 1, 6*e - 24, 16*e - 20, 5*e - 10, 18*e - 4, -3*e + 12, -13*e + 17, 9*e - 17, 14*e - 18, 6*e + 6, -7*e - 11, -18*e + 16, -7*e - 5, 2*e + 6, -9*e + 2, -17*e + 10, 9*e - 24, 7*e - 6, 21*e - 8, -17*e - 12, 26*e - 6, -24*e + 18, 32*e - 16, 3*e - 5, -9*e - 2, 17*e - 6, -26*e + 16, 24*e - 14, 9*e - 13, -18*e + 30, -10*e + 16, 16*e - 14, 17*e - 29, 22*e - 10, 13*e + 1, -25*e + 3, 17*e + 7, 31*e - 12, -11*e + 15, -15*e + 4, -22*e, -5*e + 4, -28*e + 14, -8*e - 18, 18*e - 20, -8*e + 20, 4*e - 10, -12*e + 12, -12*e - 8, -13*e - 3, 11*e - 14, 26*e - 26, 8*e - 42, 6*e - 6, -14*e + 14, 22*e - 4, -36*e + 24, 40, -22*e + 32, 27*e - 31, -8*e + 30, -11*e - 8, -2*e - 4, 18*e - 28, 30*e - 6, 6*e - 40, 6*e - 18, 15*e - 22, -17*e + 33, 21*e - 14, -11*e + 10, -9*e - 15, -4*e - 34, -12*e + 4, -5*e + 34, 20, 22*e - 12, -26*e - 2, 8*e + 34, -26*e - 4, -34*e + 26, -2, -9*e - 6, 22*e + 16, -30*e + 10, -9*e + 15, 4*e - 10, -29*e + 20, -6*e - 4, 45*e - 21, -26*e + 26, -23*e - 12, -20*e - 22, -14*e + 40, 17*e - 1, -10*e, 21*e + 16, -3*e + 34, -17*e + 23, -22*e + 20, -28*e + 14, 18*e - 20, -16*e - 16, 31*e - 8, -12*e - 6, -23*e - 17, 32*e - 4, 16*e + 4, 8*e - 12, -9*e + 8, -10*e - 6, -19*e + 33, -16*e - 36, 15*e - 16, 14*e + 2, 4*e + 54, -3*e - 15, 3*e - 36, 8*e, 2*e + 6, -22*e - 26, 22*e - 32, 26*e - 46, -15*e + 31, -12*e + 20, -23*e - 8, 14*e + 40, -18*e - 30, -15*e + 38, 9*e - 47, 14*e - 14, 16*e - 20, 28*e + 20, -11*e + 45, 29*e - 18, 23*e - 37, -52, 20*e - 46, -26*e + 12, 44*e - 16, -20*e - 16, 38*e - 32, -42*e + 42, -10*e + 30, -26*e + 32, -15*e + 56, -14*e + 12, 20*e + 4, 37*e - 38, -15*e + 53, -26*e - 8, -5*e + 4, -3*e + 21, -4*e - 52, -56*e + 32, -38*e + 26, 28*e - 22, -34*e + 8, -25*e + 11, 30, -16*e - 24, -16*e + 12, -4*e - 16, 24*e - 36, 8*e + 26, e - 8, -25*e - 16, -29*e + 30, -26, 4*e + 30, 6*e - 6, -15*e - 15, -34*e + 38, 4*e - 26, -11*e - 45, -2*e + 46, 9*e + 28, -10*e - 6, -14*e - 8, e + 19, 27*e - 18, -20*e + 10, -38*e + 16, 25*e + 36, -12*e + 24, -12*e + 54, -34*e + 14, 6*e - 14, 12*e + 46, 8*e - 54, -28*e + 26, 49*e - 13, -36*e - 2, -23*e + 14, -30*e + 40, -18*e + 44, -59*e + 38, e - 19, -8*e - 22, -38*e + 38, -11*e + 63, 46*e - 30, -16*e + 16, -21*e + 20, -6*e + 36, 7*e - 53, 8*e - 34, 44*e + 12, 28*e - 30, -39*e + 43, 36*e - 18, -36*e + 50, 17*e - 47, 10*e - 6, -3*e + 43, 15*e + 56, 60*e - 38, 51*e - 48, -8*e - 58]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([17,17,w^3 - w^2 - 4*w])] = -1

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