/*
  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([9, 6, -7, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([23,23,-2/3*w^3 + 4/3*w^2 + 11/3*w - 4])

primes_array = [
[4, 2, -1/3*w^3 + 2/3*w^2 + 4/3*w - 1],\
[7, 7, 1/3*w^3 - 2/3*w^2 - 7/3*w + 1],\
[7, 7, w - 2],\
[7, 7, w - 1],\
[9, 3, w],\
[9, 3, -1/3*w^3 + 2/3*w^2 + 7/3*w - 2],\
[23, 23, -1/3*w^3 + 2/3*w^2 + 1/3*w - 2],\
[23, 23, -2/3*w^3 + 4/3*w^2 + 11/3*w - 4],\
[31, 31, -2/3*w^3 + 1/3*w^2 + 14/3*w + 2],\
[41, 41, -1/3*w^3 + 5/3*w^2 + 4/3*w - 7],\
[41, 41, -1/3*w^3 + 5/3*w^2 + 4/3*w - 4],\
[47, 47, 1/3*w^3 - 5/3*w^2 - 1/3*w + 5],\
[47, 47, w^2 - w - 4],\
[73, 73, -w^3 + 3*w^2 + 4*w - 8],\
[73, 73, -2/3*w^3 + 7/3*w^2 - 1/3*w - 4],\
[73, 73, -w^3 + w^2 + 7*w + 1],\
[73, 73, 2/3*w^3 - 4/3*w^2 - 14/3*w + 5],\
[79, 79, w^2 - 5],\
[79, 79, -2/3*w^3 + 7/3*w^2 + 8/3*w - 6],\
[97, 97, -2/3*w^3 + 7/3*w^2 + 5/3*w - 4],\
[97, 97, 1/3*w^3 + 1/3*w^2 - 7/3*w - 5],\
[103, 103, w^3 - 3*w^2 - 2*w + 5],\
[103, 103, -4/3*w^3 + 11/3*w^2 + 13/3*w - 10],\
[113, 113, -1/3*w^3 + 5/3*w^2 + 4/3*w - 3],\
[113, 113, w^3 - 2*w^2 - 5*w + 1],\
[113, 113, -1/3*w^3 + 5/3*w^2 + 4/3*w - 1],\
[113, 113, -1/3*w^3 + 5/3*w^2 + 4/3*w - 10],\
[127, 127, -2/3*w^3 + 1/3*w^2 + 14/3*w + 1],\
[127, 127, -2/3*w^3 + 7/3*w^2 + 2/3*w - 6],\
[137, 137, -1/3*w^3 + 5/3*w^2 - 2/3*w - 6],\
[137, 137, 1/3*w^3 + 1/3*w^2 - 10/3*w - 1],\
[151, 151, -w^3 + 2*w^2 + 3*w - 5],\
[151, 151, 1/3*w^3 + 1/3*w^2 - 10/3*w - 7],\
[169, 13, -2/3*w^3 + 7/3*w^2 + 5/3*w - 2],\
[169, 13, 1/3*w^3 + 1/3*w^2 - 7/3*w - 7],\
[191, 191, 1/3*w^3 - 2/3*w^2 + 2/3*w - 2],\
[191, 191, 2*w - 5],\
[191, 191, -w^3 + 2*w^2 + 6*w - 2],\
[191, 191, 2/3*w^3 - 4/3*w^2 - 14/3*w - 1],\
[239, 239, 1/3*w^3 - 2/3*w^2 - 7/3*w - 3],\
[239, 239, w - 5],\
[241, 241, 1/3*w^3 + 1/3*w^2 - 10/3*w],\
[241, 241, 4/3*w^3 - 17/3*w^2 + 2/3*w + 9],\
[241, 241, -1/3*w^3 + 5/3*w^2 - 2/3*w - 7],\
[241, 241, -4/3*w^3 + 14/3*w^2 + 13/3*w - 14],\
[257, 257, -w - 4],\
[257, 257, -1/3*w^3 + 2/3*w^2 + 7/3*w - 6],\
[263, 263, -4/3*w^3 + 11/3*w^2 + 16/3*w - 8],\
[263, 263, 2/3*w^3 - 1/3*w^2 - 8/3*w - 3],\
[281, 281, -1/3*w^3 - 1/3*w^2 + 10/3*w - 2],\
[281, 281, -1/3*w^3 + 5/3*w^2 - 5/3*w - 5],\
[281, 281, -1/3*w^3 + 5/3*w^2 - 2/3*w - 9],\
[281, 281, -2/3*w^3 + 1/3*w^2 + 17/3*w],\
[289, 17, -w^3 + 2*w^2 + 4*w - 4],\
[289, 17, w^3 - 2*w^2 - 4*w + 2],\
[311, 311, -2/3*w^3 + 10/3*w^2 - 4/3*w - 9],\
[311, 311, -2/3*w^3 - 2/3*w^2 + 20/3*w + 5],\
[313, 313, -1/3*w^3 + 5/3*w^2 - 2/3*w - 8],\
[313, 313, -1/3*w^3 - 1/3*w^2 + 10/3*w - 1],\
[313, 313, w^3 - 4*w^2 - 2*w + 10],\
[313, 313, 1/3*w^3 + 4/3*w^2 - 10/3*w - 8],\
[337, 337, -4/3*w^3 + 5/3*w^2 + 19/3*w + 4],\
[337, 337, 5/3*w^3 - 13/3*w^2 - 17/3*w + 5],\
[353, 353, -4/3*w^3 + 8/3*w^2 + 25/3*w - 3],\
[353, 353, -1/3*w^3 - 1/3*w^2 + 16/3*w + 6],\
[353, 353, -2/3*w^3 + 10/3*w^2 + 2/3*w - 13],\
[353, 353, -5/3*w^3 + 7/3*w^2 + 29/3*w - 3],\
[367, 367, -5/3*w^3 + 4/3*w^2 + 35/3*w + 4],\
[367, 367, 2/3*w^3 - 7/3*w^2 - 8/3*w + 4],\
[367, 367, -4/3*w^3 + 14/3*w^2 + 1/3*w - 8],\
[367, 367, w^2 - 7],\
[383, 383, 4/3*w^3 - 14/3*w^2 - 10/3*w + 15],\
[383, 383, -5/3*w^3 + 13/3*w^2 + 20/3*w - 12],\
[383, 383, 2*w^2 - 2*w - 13],\
[383, 383, w^3 - w^2 - 8*w - 1],\
[401, 401, -4/3*w^3 + 11/3*w^2 + 22/3*w - 11],\
[401, 401, 5/3*w^3 - 10/3*w^2 - 29/3*w + 5],\
[409, 409, -w^3 + 2*w^2 + 3*w - 2],\
[409, 409, -1/3*w^3 + 8/3*w^2 - 2/3*w - 6],\
[409, 409, 1/3*w^3 - 8/3*w^2 + 2/3*w + 12],\
[409, 409, 4/3*w^3 - 8/3*w^2 - 19/3*w + 4],\
[433, 433, -w^3 + 3*w^2 - 1],\
[433, 433, -1/3*w^3 + 5/3*w^2 - 8/3*w - 5],\
[433, 433, -w^3 + w^2 + 8*w - 2],\
[433, 433, 5/3*w^3 - 7/3*w^2 - 32/3*w - 2],\
[439, 439, w^2 - 10],\
[439, 439, -2/3*w^3 + 4/3*w^2 + 17/3*w - 7],\
[449, 449, -2/3*w^3 + 4/3*w^2 + 11/3*w - 8],\
[449, 449, -4/3*w^3 + 5/3*w^2 + 22/3*w + 2],\
[457, 457, 2/3*w^3 - 7/3*w^2 - 14/3*w + 6],\
[457, 457, 2/3*w^3 - 7/3*w^2 - 14/3*w + 9],\
[463, 463, w^3 - 3*w^2 - 6*w + 11],\
[463, 463, -1/3*w^3 + 5/3*w^2 + 10/3*w - 4],\
[479, 479, -1/3*w^3 + 5/3*w^2 - 2/3*w + 1],\
[479, 479, 5/3*w^3 - 10/3*w^2 - 23/3*w + 9],\
[487, 487, -2/3*w^3 + 7/3*w^2 + 2/3*w - 8],\
[487, 487, -2/3*w^3 + 1/3*w^2 + 14/3*w - 1],\
[503, 503, w^3 - 4*w^2 - 2*w + 16],\
[503, 503, -1/3*w^3 + 5/3*w^2 - 2/3*w - 11],\
[521, 521, -4/3*w^3 + 11/3*w^2 + 10/3*w - 7],\
[521, 521, 4/3*w^3 - 5/3*w^2 - 22/3*w],\
[529, 23, -1/3*w^3 + 2/3*w^2 + 4/3*w - 6],\
[569, 569, -1/3*w^3 + 8/3*w^2 + 1/3*w - 10],\
[569, 569, -2/3*w^3 + 10/3*w^2 + 5/3*w - 10],\
[577, 577, -2/3*w^3 + 10/3*w^2 + 5/3*w - 12],\
[577, 577, -1/3*w^3 + 8/3*w^2 + 1/3*w - 8],\
[593, 593, w^3 - w^2 - 5*w - 5],\
[593, 593, 4/3*w^3 - 11/3*w^2 - 13/3*w + 4],\
[599, 599, 2*w^2 - 3*w - 7],\
[599, 599, 2/3*w^3 - 1/3*w^2 - 8/3*w - 4],\
[599, 599, -1/3*w^3 + 8/3*w^2 - 5/3*w - 9],\
[599, 599, -4/3*w^3 + 11/3*w^2 + 16/3*w - 7],\
[607, 607, 4/3*w^3 - 8/3*w^2 - 22/3*w + 9],\
[607, 607, -2/3*w^3 + 4/3*w^2 + 2/3*w - 5],\
[625, 5, -5],\
[631, 631, -1/3*w^3 + 2/3*w^2 + 13/3*w - 5],\
[631, 631, -2/3*w^3 + 4/3*w^2 + 17/3*w - 1],\
[641, 641, -2/3*w^3 + 7/3*w^2 + 14/3*w - 7],\
[641, 641, 2/3*w^3 - 7/3*w^2 - 14/3*w + 8],\
[647, 647, -2/3*w^3 - 5/3*w^2 + 26/3*w + 8],\
[647, 647, -1/3*w^3 + 8/3*w^2 + 1/3*w - 9],\
[647, 647, -2/3*w^3 + 10/3*w^2 + 5/3*w - 11],\
[647, 647, -2/3*w^3 + 13/3*w^2 - 10/3*w - 13],\
[673, 673, -4/3*w^3 + 5/3*w^2 + 25/3*w - 2],\
[673, 673, -w^3 + 3*w^2 + w - 7],\
[727, 727, -2/3*w^3 + 7/3*w^2 + 2/3*w - 11],\
[727, 727, -2/3*w^3 + 1/3*w^2 + 14/3*w - 4],\
[743, 743, w^2 - w - 10],\
[743, 743, 1/3*w^3 - 5/3*w^2 - 1/3*w - 1],\
[769, 769, -w^3 + 2*w^2 + 7*w - 4],\
[769, 769, 3*w - 2],\
[809, 809, -1/3*w^3 + 8/3*w^2 - 2/3*w - 8],\
[809, 809, -1/3*w^3 + 8/3*w^2 - 2/3*w - 10],\
[823, 823, -w^3 + 2*w^2 + 7*w - 5],\
[823, 823, 3*w - 1],\
[839, 839, 4/3*w^3 - 2/3*w^2 - 25/3*w - 8],\
[839, 839, 2/3*w^3 - 7/3*w^2 - 14/3*w + 12],\
[857, 857, -1/3*w^3 + 5/3*w^2 - 5/3*w - 7],\
[857, 857, -2/3*w^3 + 1/3*w^2 + 17/3*w - 2],\
[863, 863, -2/3*w^3 + 7/3*w^2 - 7/3*w - 2],\
[863, 863, 5/3*w^3 - 7/3*w^2 - 35/3*w + 1],\
[881, 881, -2/3*w^3 + 1/3*w^2 + 14/3*w + 8],\
[881, 881, -2/3*w^3 + 13/3*w^2 - 4/3*w - 18],\
[881, 881, -5/3*w^3 + 7/3*w^2 + 35/3*w + 3],\
[881, 881, -2/3*w^3 + 7/3*w^2 + 2/3*w + 1],\
[887, 887, -1/3*w^3 + 11/3*w^2 - 8/3*w - 7],\
[887, 887, -1/3*w^3 + 11/3*w^2 - 8/3*w - 18],\
[911, 911, 5/3*w^3 - 4/3*w^2 - 29/3*w - 3],\
[911, 911, 2*w^3 - 6*w^2 - 5*w + 13],\
[929, 929, 2*w^3 - 4*w^2 - 9*w + 2],\
[929, 929, 5/3*w^3 - 10/3*w^2 - 17/3*w],\
[929, 929, -4/3*w^3 + 14/3*w^2 + 13/3*w - 11],\
[929, 929, 1/3*w^3 + 4/3*w^2 - 7/3*w - 9],\
[937, 937, -w^3 + 4*w^2 + w - 13],\
[937, 937, 2/3*w^3 + 2/3*w^2 - 17/3*w - 3],\
[953, 953, -2*w^3 + w^2 + 15*w + 8],\
[953, 953, -5/3*w^3 + 19/3*w^2 - 1/3*w - 11],\
[961, 31, 4/3*w^3 - 8/3*w^2 - 16/3*w + 5],\
[967, 967, -4/3*w^3 + 2/3*w^2 + 31/3*w + 11],\
[967, 967, 7/3*w^3 - 5/3*w^2 - 46/3*w - 9],\
[977, 977, 2*w^3 - 5*w^2 - 8*w + 10],\
[977, 977, -w^3 + 3*w^2 + 2*w - 14],\
[977, 977, -4/3*w^3 + 8/3*w^2 + 25/3*w - 11],\
[977, 977, -w^3 + w^2 + 6*w - 7],\
[983, 983, -5/3*w^3 + 16/3*w^2 + 8/3*w - 12],\
[983, 983, -1/3*w^3 + 11/3*w^2 - 11/3*w - 15],\
[983, 983, 3*w^2 - 2*w - 16],\
[983, 983, -5/3*w^3 + 16/3*w^2 + 11/3*w - 14],\
[991, 991, 4/3*w^3 - 8/3*w^2 - 22/3*w + 1],\
[991, 991, 2/3*w^3 - 4/3*w^2 - 2/3*w - 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^4 - 6*x^3 - 3*x^2 + 36*x - 27
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [2/9*e^3 - e^2 - 8/3*e + 4, 2/9*e^3 - e^2 - 5/3*e + 4, -1/3*e^3 + 4/3*e^2 + 3*e - 5, -2/9*e^3 + e^2 + 5/3*e - 4, 1/9*e^3 - 2/3*e^2 - 1/3*e + 3, 1/3*e^2 - e - 2, -2/9*e^3 + e^2 + 8/3*e - 1, 1, -5, -1/3*e^3 + 2*e^2 + e - 9, 4/9*e^3 - 2*e^2 - 10/3*e + 8, 7/9*e^3 - 3*e^2 - 22/3*e + 11, 4/3*e^3 - 6*e^2 - 10*e + 24, 2/9*e^3 - 14/3*e - 2, 4/9*e^3 - 2*e^2 - 16/3*e + 8, -10/9*e^3 + 5*e^2 + 40/3*e - 26, 2/9*e^3 - 2*e^2 + 4/3*e + 10, -1/3*e^3 + 2/3*e^2 + 5*e - 1, e^3 - 16/3*e^2 - 5*e + 23, -2/3*e^3 + 7/3*e^2 + 7*e - 8, e^3 - 14/3*e^2 - 7*e + 19, -4/9*e^3 + 2*e^2 + 16/3*e - 11, -2/9*e^3 + e^2 + 8/3*e - 22, 2/3*e^3 - 3*e^2 - 5*e + 12, -e^3 + 3*e^2 + 12*e - 9, 2/3*e^3 - 3*e^2 - 5*e + 12, -e^3 + 5*e^2 + 6*e - 21, -4/9*e^3 + 2*e^2 + 16/3*e - 26, -4/3*e^3 + 6*e^2 + 16*e - 33, 2/3*e^3 - 3*e^2 - 8*e + 9, 2/3*e^3 - 3*e^2 - 8*e + 6, 4/3*e^3 - 6*e^2 - 16*e + 39, 4/9*e^3 - 2*e^2 - 16/3*e + 14, -2*e^3 + 10*e^2 + 12*e - 42, -16/9*e^3 + 8*e^2 + 40/3*e - 32, 3*e^2 - 9*e - 18, -4/3*e^3 + 7*e^2 + 7*e - 30, -2*e^2 + 6*e + 12, -4/3*e^3 + 6*e^2 + 10*e - 24, 21, -12, -4/3*e^3 + 6*e^2 + 16*e - 23, -2*e^3 + 8*e^2 + 18*e - 30, 4/3*e^3 - 6*e^2 - 16*e + 43, -4/3*e^3 + 5*e^2 + 13*e - 18, -2*e^3 + 9*e^2 + 24*e - 54, 10/9*e^3 - 5*e^2 - 40/3*e + 32, -4/3*e^3 + 7*e^2 + 7*e - 30, 4/3*e^3 - 5*e^2 - 13*e + 18, 2*e^3 - 9*e^2 - 24*e + 39, 8/9*e^3 - 4*e^2 - 32/3*e + 10, -4/9*e^3 + 2*e^2 + 16/3*e - 2, -2/3*e^3 + 3*e^2 + 8*e - 36, 3, 2/3*e^3 - 3*e^2 - 8*e + 9, 14/9*e^3 - 7*e^2 - 56/3*e + 43, 2/3*e^3 - 3*e^2 - 8*e + 36, -2/3*e^3 + 3*e^2 + 8*e - 12, -20/9*e^3 + 10*e^2 + 80/3*e - 55, e^3 - 20/3*e^2 - e + 31, -8/3*e^3 + 31/3*e^2 + 25*e - 38, 14/9*e^3 - 6*e^2 - 44/3*e + 22, -e^3 + 8*e^2 - 3*e - 39, -4/3*e^3 + 3*e^2 + 19*e - 6, 14/9*e^3 - 7*e^2 - 56/3*e + 46, 8/9*e^3 - 3*e^2 - 29/3*e + 10, -24, 4/9*e^3 - 2*e^2 - 16/3*e - 19, -7/3*e^2 + 7*e + 14, -3, 2/3*e^3 - 1/3*e^2 - 13*e - 4, -20/9*e^3 + 10*e^2 + 80/3*e - 61, 4/3*e^3 - 6*e^2 - 16*e + 21, 1/3*e^3 - 7*e - 3, -e^3 + e^2 + 18*e + 3, -11/3*e^3 + 17*e^2 + 26*e - 69, -19/9*e^3 + 7*e^2 + 70/3*e - 23, -8/9*e^3 + 4*e^2 + 32/3*e - 40, 23/9*e^3 - 11*e^2 - 62/3*e + 43, -11/9*e^3 + 6*e^2 + 23/3*e - 25, 4/3*e^3 - 6*e^2 - 16*e + 45, 2/3*e^3 - 13/3*e^2 - e + 20, -8/3*e^3 + 12*e^2 + 32*e - 54, 4/3*e^3 - 6*e^2 - 16*e + 21, -2/3*e^3 + 8/3*e^2 + 6*e - 10, -1/3*e^3 + 11/3*e^2 - 4*e - 19, 14/3*e^3 - 61/3*e^2 - 37*e + 80, -27, -10/9*e^3 + 5*e^2 + 40/3*e - 26, -e^3 + 25/3*e^2 - 4*e - 41, -4/3*e^3 + 25/3*e^2 + 3*e - 38, 8/3*e^3 - 11*e^2 - 23*e + 42, 4/3*e^3 - 7*e^2 - 7*e + 30, 4/3*e^3 - 6*e^2 - 16*e + 12, 2*e^3 - 9*e^2 - 24*e + 63, -8/3*e^3 + 12*e^2 + 32*e - 77, 4*e^3 - 18*e^2 - 48*e + 97, -2/3*e^3 + 3*e^2 + 8*e - 39, 8/9*e^3 - 4*e^2 - 32/3*e + 40, -16/9*e^3 + 8*e^2 + 64/3*e - 53, -4/3*e^3 + 6*e^2 + 16*e - 36, 14/9*e^3 - 7*e^2 - 56/3*e + 40, 11/3*e^3 - 16*e^2 - 29*e + 63, 16/9*e^3 - 7*e^2 - 49/3*e + 26, 19/9*e^3 - 6*e^2 - 79/3*e + 17, -8/3*e^3 + 10*e^2 + 26*e - 36, -1/3*e^3 + 7*e + 3, -4/9*e^3 - 2*e^2 + 46/3*e + 16, -e^2 + 3*e + 6, 4/3*e^3 - 8*e^2 - 4*e + 36, -26/9*e^3 + 11*e^2 + 83/3*e - 40, 4/9*e^3 - 4*e^2 + 8/3*e + 20, -23, 2*e^3 - 9*e^2 - 24*e + 25, -2/3*e^3 + 3*e^2 + 8*e - 7, -e^3 + 25/3*e^2 - 4*e - 41, 11/3*e^3 - 50/3*e^2 - 27*e + 67, 4/3*e^3 - 4*e^2 - 16*e + 12, 20/9*e^3 - 13*e^2 - 23/3*e + 58, 2*e^3 - 9*e^2 - 24*e + 51, 38/9*e^3 - 21*e^2 - 77/3*e + 88, 3*e^3 - 12*e^2 - 27*e + 45, -8/9*e^3 + 4*e^2 + 32/3*e - 37, -2*e^3 + 9*e^2 + 24*e - 26, 10/3*e^3 - 15*e^2 - 40*e + 79, -8/3*e^3 + 12*e^2 + 32*e - 82, 2*e^3 - 9*e^2 - 24*e + 71, 14/3*e^3 - 21*e^2 - 56*e + 114, 2*e^3 - 9*e^2 - 24*e + 42, 4/3*e^3 - 4*e^2 - 16*e + 12, -26/9*e^3 + 12*e^2 + 74/3*e - 46, -4/3*e^3 + 11*e^2 - 5*e - 54, -4/3*e^3 + 4*e^2 + 16*e - 12, -4/9*e^3 + e^2 + 19/3*e - 2, 23/9*e^3 - 10*e^2 - 71/3*e + 37, -4/3*e^3 + 8*e^2 + 4*e - 36, -8/3*e^3 + 16*e^2 + 8*e - 72, -2*e^3 + 9*e^2 + 24*e - 27, -2/3*e^3 + 3*e^2 + 8*e - 18, 34/9*e^3 - 20*e^2 - 58/3*e + 86, 1/3*e^3 - 6*e^2 + 11*e + 33, 2/3*e^3 - 3*e^2 - 8*e + 6, 13/9*e^3 - e^2 - 82/3*e - 7, -3*e^3 + 17*e^2 + 12*e - 75, -4/3*e^3 + 6*e^2 + 16*e - 42, -4*e^3 + 20*e^2 + 24*e - 84, 31/9*e^3 - 15*e^2 - 82/3*e + 59, 15, -2/9*e^3 + e^2 + 8/3*e - 13, -38/9*e^3 + 19*e^2 + 152/3*e - 115, -2*e^3 + 9*e^2 + 24*e - 24, 1/3*e^3 - e^2 - 4*e + 3, 5/3*e^3 - 4*e^2 - 23*e + 9, 2*e^3 - 9*e^2 - 24*e + 79, 4/3*e^3 - 6*e^2 - 16*e + 58, -40/9*e^3 + 20*e^2 + 160/3*e - 104, -9, 2*e^3 - 9*e^2 - 24*e + 47, -4/3*e^3 + 6*e^2 + 16*e - 50, 7, 10/9*e^3 - 5*e^2 - 40/3*e + 32, -4/3*e^3 + 6*e^2 + 16*e + 15, 4/3*e^3 - 6*e^2 - 16*e + 9, 28/9*e^3 - 14*e^2 - 112/3*e + 71, 10/9*e^3 - 5*e^2 - 40/3*e - 16, -20/9*e^3 + 15*e^2 + 5/3*e - 70, 2/3*e^3 - 5*e^2 + e + 24, -3, -14/3*e^3 + 20*e^2 + 38*e - 78, -4/9*e^3 + e^2 + 19/3*e - 2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([23,23,-2/3*w^3 + 4/3*w^2 + 11/3*w - 4])] = -1

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