/*
  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, 1, 9, 2, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([25, 25, w^4 - 2*w^3 - 3*w^2 + 3*w + 1])

primes_array = [
[5, 5, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 5*w],\
[11, 11, w^5 - 2*w^4 - 3*w^3 + 4*w^2 + w + 1],\
[11, 11, w^2 - w - 2],\
[17, 17, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 3*w - 3],\
[27, 3, w^5 - w^4 - 5*w^3 + w^2 + 6*w + 1],\
[27, 3, w^4 - 2*w^3 - 3*w^2 + 5*w],\
[37, 37, -w^2 + 2*w + 2],\
[47, 47, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 2*w - 1],\
[53, 53, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 + 3],\
[59, 59, w^4 - 2*w^3 - 2*w^2 + 3*w - 2],\
[64, 2, -2],\
[67, 67, w^5 - 2*w^4 - 3*w^3 + 4*w^2 + w - 2],\
[67, 67, -w^5 + 3*w^4 + w^3 - 7*w^2 + 3*w + 2],\
[71, 71, w^4 - w^3 - 4*w^2 + 2*w + 1],\
[71, 71, w^4 - w^3 - 5*w^2 + 2*w + 4],\
[73, 73, 2*w^5 - 4*w^4 - 7*w^3 + 10*w^2 + 5*w - 3],\
[83, 83, w^4 - 2*w^3 - 4*w^2 + 5*w + 2],\
[83, 83, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - 3],\
[89, 89, -w^5 + w^4 + 6*w^3 - 2*w^2 - 8*w + 1],\
[97, 97, 2*w^5 - 4*w^4 - 7*w^3 + 8*w^2 + 7*w],\
[103, 103, -w^5 + w^4 + 6*w^3 - 2*w^2 - 9*w + 1],\
[107, 107, w^5 - 2*w^4 - 3*w^3 + 3*w^2 + 2*w + 2],\
[113, 113, w^5 - w^4 - 5*w^3 + w^2 + 4*w + 2],\
[127, 127, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 12*w],\
[127, 127, -2*w^5 + 3*w^4 + 9*w^3 - 6*w^2 - 9*w - 1],\
[131, 131, w^4 - 3*w^3 - 2*w^2 + 7*w + 1],\
[137, 137, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 - 2*w - 2],\
[137, 137, w^2 - 2*w - 3],\
[149, 149, -w^4 + 3*w^3 + w^2 - 7*w + 1],\
[151, 151, -w^5 + w^4 + 6*w^3 - 3*w^2 - 8*w + 4],\
[163, 163, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w + 5],\
[173, 173, -2*w^5 + 3*w^4 + 9*w^3 - 7*w^2 - 10*w + 1],\
[179, 179, w^5 - 2*w^4 - 3*w^3 + 5*w^2 + w - 3],\
[191, 191, -w^5 + w^4 + 6*w^3 - 2*w^2 - 7*w - 1],\
[193, 193, 2*w^5 - 4*w^4 - 8*w^3 + 10*w^2 + 9*w],\
[193, 193, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 7*w],\
[211, 211, -w^5 + w^4 + 6*w^3 - 2*w^2 - 8*w - 4],\
[211, 211, -3*w^5 + 5*w^4 + 13*w^3 - 13*w^2 - 12*w + 3],\
[223, 223, 3*w^5 - 4*w^4 - 15*w^3 + 9*w^2 + 17*w - 1],\
[227, 227, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 5*w - 3],\
[229, 229, 2*w^5 - 4*w^4 - 9*w^3 + 12*w^2 + 11*w - 5],\
[229, 229, -w^5 + w^4 + 6*w^3 - 2*w^2 - 10*w],\
[233, 233, -w^5 + w^4 + 7*w^3 - 3*w^2 - 12*w + 1],\
[239, 239, 2*w^5 - 4*w^4 - 8*w^3 + 11*w^2 + 9*w - 2],\
[239, 239, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + 2*w - 6],\
[241, 241, -2*w^5 + 3*w^4 + 10*w^3 - 6*w^2 - 14*w - 3],\
[251, 251, -2*w^5 + 3*w^4 + 11*w^3 - 8*w^2 - 17*w],\
[251, 251, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - 2*w],\
[251, 251, -3*w^5 + 6*w^4 + 11*w^3 - 15*w^2 - 10*w + 2],\
[257, 257, 2*w^5 - 3*w^4 - 9*w^3 + 8*w^2 + 9*w - 1],\
[257, 257, -w^5 + 9*w^3 - 16*w - 3],\
[263, 263, -2*w^5 + 3*w^4 + 9*w^3 - 8*w^2 - 11*w + 2],\
[269, 269, 2*w^5 - 4*w^4 - 8*w^3 + 10*w^2 + 9*w - 1],\
[271, 271, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 11*w - 2],\
[271, 271, 3*w^5 - 6*w^4 - 11*w^3 + 14*w^2 + 11*w],\
[277, 277, -w^5 + 3*w^4 + w^3 - 7*w^2 + 4*w + 3],\
[293, 293, w^5 - w^4 - 7*w^3 + 3*w^2 + 12*w - 2],\
[293, 293, -w^5 + w^4 + 6*w^3 - 2*w^2 - 10*w - 1],\
[307, 307, w^5 - 7*w^3 - 2*w^2 + 9*w + 5],\
[313, 313, -3*w^5 + 4*w^4 + 15*w^3 - 9*w^2 - 17*w - 1],\
[313, 313, -w^3 + 6*w + 1],\
[317, 317, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 8*w - 1],\
[317, 317, -3*w^5 + 4*w^4 + 15*w^3 - 9*w^2 - 19*w],\
[317, 317, 2*w^4 - 3*w^3 - 8*w^2 + 5*w + 5],\
[337, 337, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 5*w - 3],\
[337, 337, 3*w^5 - 5*w^4 - 14*w^3 + 14*w^2 + 17*w - 4],\
[347, 347, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + 2*w - 3],\
[347, 347, w^5 - 7*w^3 - w^2 + 9*w],\
[353, 353, 3*w^5 - 5*w^4 - 13*w^3 + 12*w^2 + 14*w - 2],\
[361, 19, -w^5 + w^4 + 7*w^3 - 3*w^2 - 10*w - 1],\
[367, 367, 2*w^5 - 4*w^4 - 7*w^3 + 11*w^2 + 3*w - 3],\
[389, 389, -2*w^5 + 3*w^4 + 9*w^3 - 5*w^2 - 10*w - 2],\
[389, 389, 2*w^5 - 4*w^4 - 9*w^3 + 13*w^2 + 10*w - 6],\
[397, 397, 2*w^5 - 4*w^4 - 8*w^3 + 9*w^2 + 9*w + 1],\
[401, 401, -3*w^5 + 4*w^4 + 15*w^3 - 9*w^2 - 18*w],\
[401, 401, -2*w^4 + 4*w^3 + 6*w^2 - 8*w - 1],\
[401, 401, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 6*w - 3],\
[401, 401, -2*w^3 + 3*w^2 + 6*w - 4],\
[419, 419, w^5 - 2*w^4 - 3*w^3 + 6*w^2 - 3],\
[433, 433, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + w + 1],\
[443, 443, 2*w^5 - 3*w^4 - 11*w^3 + 8*w^2 + 16*w + 1],\
[443, 443, w^3 - w^2 - 4*w + 3],\
[461, 461, -w^5 + 3*w^4 - 6*w^2 + 6*w + 2],\
[479, 479, 3*w^5 - 5*w^4 - 13*w^3 + 12*w^2 + 12*w],\
[479, 479, 2*w^5 - 4*w^4 - 9*w^3 + 11*w^2 + 12*w],\
[487, 487, 2*w^5 - 2*w^4 - 12*w^3 + 6*w^2 + 15*w - 2],\
[491, 491, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 4],\
[491, 491, -2*w^5 + 4*w^4 + 8*w^3 - 10*w^2 - 10*w - 1],\
[499, 499, w^4 - w^3 - 4*w^2 + 2*w - 1],\
[499, 499, w^5 - 8*w^3 + 10*w],\
[499, 499, -2*w^5 + 3*w^4 + 8*w^3 - 4*w^2 - 8*w - 4],\
[503, 503, -2*w^4 + 4*w^3 + 5*w^2 - 7*w - 2],\
[509, 509, 2*w^5 - 4*w^4 - 9*w^3 + 11*w^2 + 13*w - 2],\
[509, 509, w^5 - 9*w^3 + 15*w + 2],\
[509, 509, -w^5 + 9*w^3 - 16*w - 1],\
[521, 521, w^5 - w^4 - 5*w^3 + 5*w + 6],\
[523, 523, -2*w^4 + 5*w^3 + 4*w^2 - 10*w + 1],\
[523, 523, -w^5 + 7*w^3 + 2*w^2 - 11*w - 3],\
[563, 563, -w^5 + w^4 + 5*w^3 - w^2 - 7*w],\
[571, 571, -3*w^5 + 4*w^4 + 15*w^3 - 8*w^2 - 18*w - 2],\
[577, 577, w^5 - 3*w^4 - w^3 + 7*w^2 - 4*w - 2],\
[587, 587, w^5 - w^4 - 5*w^3 - w^2 + 7*w + 5],\
[593, 593, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - w - 2],\
[593, 593, -w^5 + 9*w^3 - w^2 - 16*w + 1],\
[607, 607, w^5 - 2*w^4 - 3*w^3 + 5*w^2 + 2*w - 4],\
[607, 607, -2*w^5 + 3*w^4 + 9*w^3 - 5*w^2 - 11*w - 1],\
[613, 613, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 9*w - 4],\
[619, 619, -w^5 + 4*w^4 - 11*w^2 + 4*w + 3],\
[619, 619, w^2 - 5],\
[631, 631, -w^3 + 2*w^2 + w - 5],\
[631, 631, -2*w^3 + 3*w^2 + 6*w - 5],\
[641, 641, w^5 - 8*w^3 + 13*w + 2],\
[643, 643, -w^5 + w^4 + 4*w^3 - 2*w - 4],\
[647, 647, -w^5 + w^4 + 6*w^3 - 3*w^2 - 10*w + 1],\
[647, 647, -w^4 + 6*w^2 + w - 5],\
[653, 653, 2*w^4 - 3*w^3 - 8*w^2 + 6*w + 7],\
[659, 659, w^5 - 7*w^3 + 7*w - 4],\
[659, 659, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 8*w + 6],\
[673, 673, w^5 - 3*w^4 - 2*w^3 + 10*w^2 - 5],\
[673, 673, w^5 - 2*w^4 - 2*w^3 + 3*w^2 - 2*w + 3],\
[677, 677, -3*w^5 + 5*w^4 + 13*w^3 - 12*w^2 - 13*w + 3],\
[691, 691, -2*w^5 + 3*w^4 + 10*w^3 - 9*w^2 - 12*w + 2],\
[691, 691, -w^5 + 2*w^4 + 5*w^3 - 5*w^2 - 11*w - 3],\
[709, 709, w^4 - 3*w^3 - 2*w^2 + 9*w + 2],\
[719, 719, -2*w^5 + 3*w^4 + 9*w^3 - 7*w^2 - 7*w + 1],\
[719, 719, -2*w^5 + 3*w^4 + 11*w^3 - 9*w^2 - 14*w + 2],\
[719, 719, 2*w^5 - 2*w^4 - 12*w^3 + 5*w^2 + 15*w - 1],\
[727, 727, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 2*w - 4],\
[727, 727, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 5*w - 4],\
[733, 733, w^5 - w^4 - 5*w^3 + 2*w^2 + 5*w - 4],\
[733, 733, 2*w^5 - 4*w^4 - 6*w^3 + 8*w^2 + 3*w + 1],\
[739, 739, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + w - 5],\
[739, 739, -2*w^5 + 4*w^4 + 6*w^3 - 7*w^2 - 4*w - 3],\
[751, 751, -2*w^5 + 5*w^4 + 5*w^3 - 11*w^2 - 3*w - 1],\
[751, 751, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 3*w - 7],\
[757, 757, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 7*w],\
[761, 761, 3*w^5 - 4*w^4 - 15*w^3 + 10*w^2 + 17*w - 2],\
[769, 769, -w^5 + 2*w^4 + 4*w^3 - 3*w^2 - 6*w - 4],\
[773, 773, 2*w^4 - 4*w^3 - 5*w^2 + 9*w],\
[787, 787, -2*w^5 + 2*w^4 + 11*w^3 - 5*w^2 - 12*w + 2],\
[787, 787, 2*w^5 - 4*w^4 - 7*w^3 + 10*w^2 + 7*w - 1],\
[787, 787, 3*w^5 - 5*w^4 - 12*w^3 + 11*w^2 + 10*w - 1],\
[797, 797, -w^4 + 2*w^3 + 4*w^2 - 6*w],\
[809, 809, -3*w^5 + 5*w^4 + 13*w^3 - 13*w^2 - 12*w + 2],\
[809, 809, 3*w^5 - 4*w^4 - 14*w^3 + 8*w^2 + 14*w],\
[809, 809, -3*w^5 + 6*w^4 + 11*w^3 - 14*w^2 - 10*w + 2],\
[821, 821, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + w + 4],\
[823, 823, -w^4 + 2*w^3 + 4*w^2 - 3*w - 5],\
[823, 823, -2*w^5 + 4*w^4 + 7*w^3 - 9*w^2 - 6*w - 3],\
[827, 827, -w^3 + 3*w^2 + 3*w - 4],\
[839, 839, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 7*w],\
[839, 839, -2*w^5 + 4*w^4 + 9*w^3 - 11*w^2 - 13*w + 1],\
[839, 839, -2*w^5 + 3*w^4 + 10*w^3 - 7*w^2 - 11*w - 1],\
[841, 29, -w^3 + 3*w^2 + w - 2],\
[857, 857, -2*w^5 + 4*w^4 + 8*w^3 - 9*w^2 - 10*w - 3],\
[859, 859, 3*w^5 - 4*w^4 - 15*w^3 + 9*w^2 + 17*w + 2],\
[859, 859, -2*w^5 + 2*w^4 + 11*w^3 - 3*w^2 - 15*w],\
[863, 863, 2*w^5 - 4*w^4 - 7*w^3 + 8*w^2 + 6*w + 4],\
[863, 863, 3*w^5 - 5*w^4 - 14*w^3 + 12*w^2 + 18*w - 1],\
[881, 881, w^5 - 3*w^4 - w^3 + 6*w^2 - 3*w - 1],\
[887, 887, 2*w^5 - 5*w^4 - 5*w^3 + 11*w^2 + 2*w + 1],\
[907, 907, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 8*w - 2],\
[919, 919, w^5 - w^4 - 7*w^3 + 3*w^2 + 10*w + 2],\
[929, 929, 2*w^5 - 4*w^4 - 7*w^3 + 10*w^2 + 4*w - 4],\
[937, 937, 3*w^5 - 5*w^4 - 12*w^3 + 10*w^2 + 11*w],\
[953, 953, -3*w^5 + 5*w^4 + 14*w^3 - 12*w^2 - 17*w - 1],\
[953, 953, -2*w^5 + 2*w^4 + 11*w^3 - 4*w^2 - 13*w - 2],\
[967, 967, -w^5 + 3*w^4 - 6*w^2 + 6*w],\
[967, 967, 3*w^5 - 6*w^4 - 11*w^3 + 14*w^2 + 9*w - 1],\
[977, 977, -w^5 + 3*w^4 - 6*w^2 + 5*w + 2],\
[991, 991, -w^3 + 3*w^2 + 2*w - 3],\
[997, 997, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 10*w - 1],\
[1009, 1009, w^5 - 2*w^4 - 2*w^3 + 3*w^2 - w + 2],\
[1013, 1013, 3*w^5 - 5*w^4 - 14*w^3 + 14*w^2 + 14*w - 4],\
[1019, 1019, -3*w^5 + 5*w^4 + 14*w^3 - 13*w^2 - 18*w + 2],\
[1031, 1031, -2*w^5 + 2*w^4 + 11*w^3 - 3*w^2 - 15*w - 1],\
[1039, 1039, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 3],\
[1049, 1049, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 5*w - 4],\
[1063, 1063, -w^4 + 2*w^3 + 3*w^2 - 2*w - 4],\
[1069, 1069, 2*w^5 - 3*w^4 - 8*w^3 + 4*w^2 + 7*w + 4],\
[1069, 1069, w^5 - w^4 - 5*w^3 + 2*w^2 + 3*w + 2],\
[1091, 1091, -2*w^5 + 2*w^4 + 11*w^3 - 4*w^2 - 15*w],\
[1117, 1117, -w^4 + w^3 + 6*w^2 - 3*w - 5],\
[1117, 1117, -3*w^5 + 4*w^4 + 16*w^3 - 11*w^2 - 20*w + 1],\
[1123, 1123, 2*w^5 - 2*w^4 - 14*w^3 + 7*w^2 + 21*w - 3],\
[1129, 1129, w^5 - w^4 - 5*w^3 + 3*w^2 + 3*w - 3],\
[1129, 1129, w^4 - 3*w^3 - w^2 + 6*w - 4],\
[1151, 1151, 2*w^5 - 3*w^4 - 8*w^3 + 5*w^2 + 7*w + 4],\
[1151, 1151, -2*w^5 + 3*w^4 + 10*w^3 - 9*w^2 - 10*w + 5],\
[1151, 1151, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 10*w + 2],\
[1153, 1153, -w^3 + 2*w^2 - 3],\
[1171, 1171, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 13*w + 1],\
[1187, 1187, -w^5 + 3*w^4 + 4*w^3 - 10*w^2 - 4*w + 5],\
[1193, 1193, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - 3*w],\
[1193, 1193, -w^3 + 3*w^2 - 6],\
[1201, 1201, -w^4 + 3*w^3 + w^2 - 5*w + 3],\
[1201, 1201, 2*w^4 - 5*w^3 - 4*w^2 + 9*w],\
[1213, 1213, -2*w^5 + 3*w^4 + 11*w^3 - 8*w^2 - 16*w - 2],\
[1213, 1213, 2*w^5 - w^4 - 13*w^3 + w^2 + 17*w - 2],\
[1213, 1213, 3*w^5 - 5*w^4 - 12*w^3 + 13*w^2 + 10*w - 2],\
[1213, 1213, -2*w^5 + 4*w^4 + 7*w^3 - 11*w^2 - 5*w + 5],\
[1217, 1217, -w^5 + 4*w^4 + w^3 - 13*w^2 + 3*w + 9],\
[1229, 1229, -w^5 + 2*w^4 + 3*w^3 - 6*w^2 + w + 4],\
[1229, 1229, -w^5 + w^4 + 4*w^3 + w^2 - 3*w - 6],\
[1231, 1231, 2*w^5 - 4*w^4 - 9*w^3 + 13*w^2 + 9*w - 5],\
[1277, 1277, -w^5 + 2*w^4 + 5*w^3 - 5*w^2 - 9*w],\
[1277, 1277, w^5 - 9*w^3 + 15*w],\
[1301, 1301, 2*w^4 - 4*w^3 - 5*w^2 + 8*w + 1],\
[1301, 1301, 2*w^5 - 4*w^4 - 8*w^3 + 9*w^2 + 9*w + 3],\
[1307, 1307, 2*w^5 - 4*w^4 - 9*w^3 + 13*w^2 + 9*w - 8],\
[1307, 1307, 3*w^5 - 6*w^4 - 12*w^3 + 14*w^2 + 13*w - 1],\
[1319, 1319, w^3 - 2*w - 3],\
[1319, 1319, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 7*w - 8],\
[1321, 1321, 3*w^5 - 5*w^4 - 14*w^3 + 12*w^2 + 18*w],\
[1327, 1327, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 4*w - 5],\
[1327, 1327, -w^5 + 7*w^3 + 3*w^2 - 10*w - 3],\
[1327, 1327, -w^4 + 4*w^3 + w^2 - 10*w - 2],\
[1361, 1361, -2*w^5 + 3*w^4 + 11*w^3 - 9*w^2 - 16*w],\
[1361, 1361, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 3*w - 6],\
[1367, 1367, w^5 - 2*w^4 - 2*w^3 + 2*w^2 + 4],\
[1367, 1367, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 - w - 3],\
[1369, 37, -w^5 + 7*w^3 + w^2 - 10*w + 1],\
[1399, 1399, -w^4 + w^3 + 4*w^2 - 4*w - 4],\
[1427, 1427, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 + w + 3],\
[1429, 1429, -3*w^5 + 6*w^4 + 12*w^3 - 15*w^2 - 14*w],\
[1429, 1429, -2*w^5 + 5*w^4 + 7*w^3 - 15*w^2 - 7*w + 5],\
[1433, 1433, -w^5 + 4*w^4 - w^3 - 8*w^2 + 4*w - 2],\
[1439, 1439, -w^5 + w^4 + 8*w^3 - 6*w^2 - 12*w + 2],\
[1439, 1439, -w^4 - w^3 + 5*w^2 + 7*w - 1],\
[1447, 1447, 2*w^5 - 2*w^4 - 11*w^3 + 6*w^2 + 11*w - 3],\
[1471, 1471, -w^5 + 2*w^4 + 2*w^3 - 4*w^2 + 3],\
[1483, 1483, 2*w^5 - 4*w^4 - 9*w^3 + 12*w^2 + 10*w - 2],\
[1483, 1483, -w^4 + 2*w^3 + 2*w^2 - w - 4],\
[1487, 1487, -3*w^5 + 4*w^4 + 14*w^3 - 7*w^2 - 16*w - 3],\
[1489, 1489, -2*w^3 + 3*w^2 + 5*w - 5],\
[1493, 1493, -3*w^5 + 3*w^4 + 18*w^3 - 6*w^2 - 25*w - 1],\
[1499, 1499, 3*w^5 - 5*w^4 - 16*w^3 + 15*w^2 + 23*w - 3],\
[1511, 1511, 2*w^5 - 4*w^4 - 8*w^3 + 10*w^2 + 11*w],\
[1511, 1511, -2*w^5 + 2*w^4 + 11*w^3 - 2*w^2 - 15*w - 3],\
[1511, 1511, -2*w^5 + 2*w^4 + 11*w^3 - 3*w^2 - 14*w],\
[1571, 1571, -2*w^5 + 4*w^4 + 6*w^3 - 9*w^2 - 2*w + 4],\
[1571, 1571, 2*w^5 - w^4 - 12*w^3 + w^2 + 14*w - 1],\
[1571, 1571, -3*w^5 + 5*w^4 + 13*w^3 - 13*w^2 - 13*w],\
[1579, 1579, -2*w^5 + 3*w^4 + 10*w^3 - 9*w^2 - 10*w - 1],\
[1583, 1583, -2*w^5 + 4*w^4 + 6*w^3 - 6*w^2 - 6*w - 5],\
[1607, 1607, -w^4 + 4*w^3 + w^2 - 11*w],\
[1607, 1607, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 10*w],\
[1613, 1613, 2*w^5 - 5*w^4 - 5*w^3 + 10*w^2 + 2*w + 2],\
[1619, 1619, -w^5 + w^4 + 8*w^3 - 4*w^2 - 17*w],\
[1637, 1637, 2*w^4 - 5*w^3 - 5*w^2 + 11*w],\
[1663, 1663, w^5 - 4*w^4 + 2*w^3 + 9*w^2 - 8*w - 2],\
[1669, 1669, -w^5 + 2*w^4 + 7*w^3 - 10*w^2 - 13*w + 7],\
[1697, 1697, -2*w^5 + 5*w^4 + 3*w^3 - 9*w^2 + 4*w - 2],\
[1709, 1709, 2*w^4 - 4*w^3 - 4*w^2 + 10*w - 1],\
[1733, 1733, 2*w^5 - 2*w^4 - 14*w^3 + 8*w^2 + 23*w - 4],\
[1753, 1753, -w^5 + w^4 + 5*w^3 - 4*w - 4],\
[1777, 1777, -4*w^5 + 9*w^4 + 12*w^3 - 22*w^2 - 7*w + 6],\
[1783, 1783, w^5 - 2*w^4 - 6*w^3 + 6*w^2 + 11*w - 1],\
[1801, 1801, -2*w^5 + 4*w^4 + 7*w^3 - 11*w^2 - 5*w + 8],\
[1811, 1811, 2*w^5 - 15*w^3 - 3*w^2 + 22*w + 5],\
[1811, 1811, w^2 + w - 5],\
[1811, 1811, w^2 - 3*w - 4],\
[1823, 1823, -4*w^5 + 7*w^4 + 18*w^3 - 20*w^2 - 20*w + 5],\
[1831, 1831, 3*w^5 - 5*w^4 - 14*w^3 + 11*w^2 + 19*w + 4],\
[1831, 1831, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 + w - 2],\
[1847, 1847, w^5 - 2*w^4 - w^3 + 3*w^2 - 7*w - 2],\
[1849, 43, w^3 - 3*w - 4],\
[1861, 1861, -w^5 + 3*w^4 + 4*w^3 - 12*w^2 - 6*w + 10],\
[1861, 1861, w^4 - 4*w^3 - 3*w^2 + 10*w + 3],\
[1861, 1861, -w^5 + 4*w^4 - 2*w^3 - 10*w^2 + 9*w + 3],\
[1861, 1861, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 4*w - 2],\
[1867, 1867, -w^5 + 7*w^3 - w^2 - 7*w + 3],\
[1873, 1873, -3*w^5 + 5*w^4 + 12*w^3 - 11*w^2 - 11*w],\
[1877, 1877, 4*w^5 - 8*w^4 - 13*w^3 + 17*w^2 + 8*w + 1],\
[1889, 1889, -w^4 + 5*w^2 + 3*w - 4],\
[1901, 1901, -2*w^5 + 3*w^4 + 10*w^3 - 6*w^2 - 15*w - 1],\
[1949, 1949, -w^5 + 2*w^4 + 2*w^3 - 2*w^2 + w - 5],\
[1951, 1951, -2*w^5 + 4*w^4 + 6*w^3 - 7*w^2 - 3*w - 2],\
[1973, 1973, w^5 - 9*w^3 + w^2 + 16*w],\
[1987, 1987, -3*w^5 + 6*w^4 + 12*w^3 - 16*w^2 - 14*w + 3],\
[1999, 1999, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 4*w + 6]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^3 + 3*x^2 - 16*x - 24
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e + 3, e, e, 2, -2, -e^2 - e + 10, 1/2*e^2 - 1/2*e - 3, 3, -e^2 - 2*e + 12, 1/2*e^2 - 1/2*e - 1, -1/2*e^2 - 1/2*e + 5, -e + 4, -1/2*e^2 + 3/2*e + 9, e + 9, 1/2*e^2 + 5/2*e - 7, -1/2*e^2 + 1/2*e + 3, e^2 + e - 15, -1/2*e^2 + 1/2*e + 9, 2*e + 2, -e^2 - e + 16, -e^2 - 2*e + 12, 1/2*e^2 + 1/2*e - 9, -2*e^2 - 2*e + 22, e^2 + 3*e - 8, -e^2 - 2*e + 6, e + 6, -1/2*e^2 - 5/2*e + 15, e^2 - 2*e - 18, -e^2 - 2*e + 19, 2*e + 1, 4*e, -2*e - 3, 3/2*e^2 + 3/2*e - 21, e^2 + 3*e - 10, -e^2 - e + 8, -1/2*e^2 - 13/2*e + 1, -e^2 + 10, -3*e - 2, e^2 - 30, e^2 + e - 4, e^2 + e - 22, e^2 + e, e^2 + 2*e - 3, e^2 - 3*e - 18, 1/2*e^2 + 13/2*e - 7, 2*e^2 + 3*e - 18, -e^2 - 7*e + 9, -2*e^2 - 4*e + 18, -e^2 - 4*e + 18, -2*e^2 - 4*e + 12, -e^2 + 2*e + 6, -e^2 - 3*e + 12, 5/2*e^2 + 9/2*e - 29, e^2 - 4*e - 22, -2*e + 10, e^2 - e - 12, e + 12, 1/2*e^2 + 3/2*e - 25, -e^2 - 7*e + 4, e^2 + 2*e + 2, -3*e - 3, 1/2*e^2 + 3/2*e - 15, -3/2*e^2 - 15/2*e + 21, 3*e - 11, e^2 + e - 34, -1/2*e^2 - 7/2*e + 27, e^2 + 7*e - 12, e^2 - 2*e - 15, 3/2*e^2 - 1/2*e - 29, -1/2*e^2 - 3/2*e - 5, -e^2 - 4*e + 15, -e^2 + 2*e + 15, -e^2 + 2*e + 22, 6*e - 3, 2*e^2 + 4*e - 18, -12, -e^2 + e + 12, e + 12, -e^2 - 2*e + 13, -3/2*e^2 - 11/2*e + 9, -2*e^2 - 8*e + 30, -e^2 - 3*e + 18, -3/2*e^2 + 9/2*e + 39, -e^2 + 5*e + 24, 1/2*e^2 - 3/2*e - 29, 0, -3*e^2 - 9*e + 30, -2*e^2 + 23, 2*e^2 + 8*e - 20, 5*e + 1, 2*e + 24, -3*e^2 - 6*e + 27, -e^2 - 2*e + 12, 2*e^2 + 7*e - 12, 2*e^2 + 4*e - 18, 3/2*e^2 + 3/2*e + 7, -2*e^2 - 3*e + 34, 12, e^2 - 3*e - 23, -2*e^2 - 4*e + 20, 3*e^2 + 2*e - 36, 6*e + 12, 7/2*e^2 + 11/2*e - 45, -3/2*e^2 + 5/2*e + 41, -6*e - 2, -e^2 - 6*e + 26, -2*e^2 - 5*e + 8, 3/2*e^2 + 7/2*e - 25, -1/2*e^2 + 3/2*e - 11, -7*e - 1, e^2 - 5*e - 30, 3*e^2 + 7*e - 38, e^2 - 4*e - 48, -6*e + 9, -e^2 - 11*e + 18, -e^2 - 5*e + 30, -e + 6, -e - 32, -e^2 - e + 50, 2*e^2 + 7*e - 33, -3*e^2 + e + 44, -2*e + 8, -e^2 - e - 20, 2*e^2 + 2*e - 24, 2*e^2 + 5*e - 45, 3*e^2 + 6*e - 36, -e^2 + 2*e + 22, 1/2*e^2 + 7/2*e - 1, -2*e^2 - 9*e + 40, -4*e^2 - 5*e + 40, -3*e - 13, 1/2*e^2 + 1/2*e + 5, 2*e^2 - 2*e - 32, 2*e^2 - 40, -3*e^2 - 3*e + 28, -2*e^2 + 2*e + 27, 2*e^2 - 7*e - 41, -24, 2*e^2 + 8*e - 20, -2*e^2 + 34, 3*e^2 + 4*e - 32, 3*e^2 + 12*e - 39, e^2 + e - 30, -e, 2*e^2 + 3*e - 12, 6*e + 24, 2*e^2 + 4*e - 38, -e^2 - 13, 4*e^2 + 5*e - 33, e^2 + 4*e - 27, 3/2*e^2 + 3/2*e - 9, -4*e + 24, -e^2 - 5*e + 10, -2*e^2 - 2*e + 54, -4*e^2 - 5*e + 40, e^2 - 10*e - 35, 1/2*e^2 - 11/2*e + 15, -2*e^2 - 2*e + 36, -2*e^2 - 7*e + 39, 4*e^2 + 5*e - 54, e^2 + 4*e - 7, -e^2 + e + 4, 3*e - 24, -4*e^2 - 7*e + 41, -2*e^2 - 8*e + 36, -e^2 - 5*e + 36, 2*e^2 + e - 26, 2*e^2 + 8*e - 28, 2*e^2 + 6*e - 30, 2*e^2 - 2*e - 8, -3*e + 8, 3*e^2 + 6*e - 56, -2*e^2 + 2*e + 54, -4*e^2 - 7*e + 51, -24, 4*e^2 + 12*e - 44, e^2 + 7*e + 6, -4*e^2 - 6*e + 38, -4*e^2 - 6*e + 20, 2*e^2 + 4*e - 20, -e^2 - 7*e + 24, -3*e^2 - 4*e + 49, -2*e^2 - 9*e + 16, -4*e^2 - 6*e + 22, -2*e^2 - 10*e + 46, -e^2 + 7*e + 38, -3*e^2 - 14*e + 30, -5*e - 6, 1/2*e^2 - 19/2*e - 33, e^2 + 6*e - 25, 7/2*e^2 - 7/2*e - 73, -5/2*e^2 - 5/2*e + 69, 3/2*e^2 + 3/2*e + 3, -3/2*e^2 - 9/2*e + 21, e^2 + 10*e - 23, 1/2*e^2 - 3/2*e + 41, -3*e - 8, -3*e^2 - 10*e + 23, 2*e^2 - 5*e - 64, -5/2*e^2 + 9/2*e + 25, -6, -3*e^2 - 13*e + 18, 2*e^2 + 4*e - 24, -2*e^2 + 28, -3*e^2 + 3*e + 69, -e^2 + e + 60, -2*e^2 - 2*e + 9, -2*e^2 - 4*e + 60, -3*e^2 - 9*e + 30, e^2 - 5*e - 15, 3*e^2 - 30, 2*e^2 + 14*e - 12, 2*e^2 + e - 52, 1/2*e^2 - 19/2*e - 35, 2*e^2 + 3*e + 1, 2*e + 1, -3*e^2 - 3*e + 48, -2*e^2 + 72, -e^2 - 8*e, 2*e^2 - 4*e - 24, -e^2 - 8*e + 31, 6*e^2 + 8*e - 74, -5/2*e^2 - 3/2*e + 51, -3*e^2 + 19, -e^2 + 22, 1/2*e^2 + 5/2*e - 9, e^2 - 7*e - 18, 3*e^2 + 11*e - 30, 1/2*e^2 + 9/2*e - 7, -e^2 + 8*e + 16, -e^2 - 9*e - 19, 4*e^2 + 8*e - 52, e^2 + 10*e - 24, 11/2*e^2 + 21/2*e - 61, -e^2 - 7*e, 1/2*e^2 + 5/2*e + 9, -2*e^2 - 16*e + 42, 2*e^2 + e + 21, 7*e^2 + 10*e - 72, -e^2 - 2*e + 63, 5*e^2 - 72, -9/2*e^2 + 3/2*e + 81, e^2 + 11*e - 32, -4*e^2 + 4*e + 60, 3*e^2 + 3*e - 21, 3*e^2 + 18*e - 57, -e^2 - 3*e - 6, 3*e^2 + 3*e - 54, -e^2 - e + 30, e^2 + 46, -3*e^2 + 7*e + 56, 4*e^2 - 4*e - 66, 3/2*e^2 + 3/2*e + 21, -7/2*e^2 - 1/2*e + 27, -2*e^2 + 5*e + 50, -1/2*e^2 - 5/2*e - 19, -4*e^2 - 6*e + 38, -2*e^2 + 8*e + 29, 2*e^2 - 6*e - 12, 10*e - 9, -2*e^2 - 8*e - 18, -7/2*e^2 - 23/2*e + 27, 4*e^2 + 17*e - 64, -4*e^2 - 6*e - 4, 3*e^2 + 6*e - 60, -e^2 + e + 56, -e^2 - e - 2, 6*e^2 + 3*e - 80, 9/2*e^2 - 9/2*e - 85, -15/2*e^2 - 23/2*e + 71, 5*e^2 - 8*e - 92, -3/2*e^2 - 15/2*e + 43, 5*e^2 + 17*e - 60, -5*e^2 - 2*e + 39, -2*e^2 + 5*e + 6, -4*e^2 - 4*e + 54, -e^2 - e + 16, 7*e^2 + 7*e - 72, -5*e^2 - 9*e + 74, 3/2*e^2 - 5/2*e + 1]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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