/*
  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([47, 47, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 2*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
K = QQ
e = 1

hecke_eigenvalues_array = [0, -2, 0, 6, -1, 2, 3, -1, -2, 8, -1, -4, -5, 12, -13, -6, 12, -11, 4, 0, 9, 9, 14, -15, -2, 15, -10, -14, 2, 20, -4, 26, 17, 6, -14, -7, 10, -22, 0, 5, -5, 3, 13, -18, -12, 14, 16, -23, 12, -11, -5, -2, -14, -7, 5, 3, 19, 18, -21, -4, 4, 10, 34, -33, 13, -4, -3, -17, 9, 28, -7, -8, 16, 36, 24, 7, 30, -12, 0, -11, 16, 31, -4, 20, -10, -21, -18, 28, -9, -21, 15, 44, -2, 1, 24, -9, -19, 0, -9, 20, -2, -12, -2, 9, -2, -16, 42, 14, -12, -26, -28, 35, 34, -20, -24, -34, -21, 3, -41, 1, 7, -18, -8, 2, 25, 4, 34, -16, -8, -2, -30, 30, -26, 15, -46, 31, -42, -22, -24, 19, 22, 27, 14, 11, -30, 26, -10, 19, 50, 45, 14, -5, -30, -10, 30, 25, 15, -20, -12, -12, -32, -32, 5, -29, 50, 14, 7, 19, 46, 20, 36, 28, -26, 46, 49, -50, -10, -40, -32, 30, 46, -12, -53, 63, 36, -21, 48, -18, 43, 30, -24, 32, -37, -44, -40, 32, 16, -36, 65, -22, -21, -8, 14, -2, 12, -39, 58, -61, -15, -35, -50, -30, -32, 37, 48, -39, 43, 22, 18, 15, 63, 2, -26, -63, 52, 34, 6, 34, 40, 64, 31, -44, 70, -44, -70, 34, -34, -45, 38, 45, 20, -58, 22, 6, 36, 12, -36, -24, -67, 12, 71, -14, -3, 69, 72, 20, 27, -38, 48, -18, 60, 30, 44, 6, 50, 8, 62, 41, 54, 56, 13, 42, -31, -20, -12, 30, -36, 0, -7, -26, 59]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([47, 47, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 2*w - 1])] = 1

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