/*
  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, 2, -3, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([71,71,2*w^3 - 4*w^2 - 6*w + 1])

primes_array = [
[4, 2, w^3 - 2*w^2 - 2*w + 1],\
[7, 7, -w^3 + 3*w^2 + w - 3],\
[7, 7, -w^2 + w + 2],\
[17, 17, -w^3 + 3*w^2 - 3],\
[17, 17, -w^3 + w^2 + 4*w],\
[25, 5, -w^3 + 3*w^2 + 2*w - 2],\
[25, 5, -2*w^3 + 4*w^2 + 5*w - 1],\
[41, 41, -w^3 + 2*w^2 + 4*w - 2],\
[47, 47, -2*w^3 + 5*w^2 + 4*w - 4],\
[47, 47, 2*w^3 - 4*w^2 - 5*w],\
[49, 7, w^2 - 4*w - 1],\
[71, 71, 2*w - 3],\
[71, 71, -w^3 + w^2 + 6*w - 2],\
[73, 73, -w^3 + 3*w^2 + 3*w - 5],\
[73, 73, 2*w^3 - 5*w^2 - 5*w + 4],\
[73, 73, -w^3 + 3*w^2 - 5],\
[73, 73, w^3 - w^2 - 4*w + 2],\
[79, 79, 2*w^3 - 3*w^2 - 6*w + 2],\
[79, 79, 2*w^3 - 3*w^2 - 5*w],\
[81, 3, -3],\
[89, 89, -w^3 + w^2 + 5*w - 3],\
[89, 89, w - 4],\
[97, 97, -3*w^3 + 7*w^2 + 6*w - 5],\
[97, 97, -2*w^3 + 3*w^2 + 7*w - 2],\
[103, 103, -w - 3],\
[103, 103, -w^3 + 2*w^2 + 3*w - 5],\
[103, 103, -w^3 + 4*w^2 - w - 5],\
[103, 103, -3*w^3 + 6*w^2 + 7*w - 3],\
[113, 113, w^3 - 4*w^2 + w + 4],\
[113, 113, 2*w^2 - 3*w - 4],\
[113, 113, 3*w^3 - 6*w^2 - 7*w + 4],\
[113, 113, -2*w^3 + 6*w^2 + 2*w - 7],\
[137, 137, -w^3 + 4*w^2 - 4],\
[137, 137, w^3 - 4*w^2 + 6],\
[151, 151, -3*w^3 + 8*w^2 + 3*w - 4],\
[151, 151, -2*w^3 + 2*w^2 + 7*w + 4],\
[167, 167, -2*w^3 + 3*w^2 + 6*w - 3],\
[167, 167, -2*w^3 + 5*w^2 + 2*w - 6],\
[191, 191, w^3 - 2*w^2 - w + 5],\
[191, 191, -w^3 + 5*w^2 - 3*w - 3],\
[193, 193, -w^3 + 2*w^2 + 5*w - 2],\
[193, 193, -2*w^3 + 4*w^2 + 7*w - 4],\
[199, 199, -2*w^3 + 5*w^2 + 4*w - 2],\
[199, 199, w^2 - 5],\
[223, 223, -w^3 + 8*w - 2],\
[223, 223, -2*w^3 + 2*w^2 + 9*w],\
[223, 223, -3*w^3 + 5*w^2 + 11*w - 1],\
[223, 223, -w^3 + 4*w^2 + w - 8],\
[233, 233, -3*w^3 + 7*w^2 + 6*w - 4],\
[233, 233, w^3 - w^2 - 2*w - 3],\
[239, 239, -w^3 + 6*w],\
[239, 239, 2*w^3 - 5*w^2 - 4*w + 1],\
[257, 257, -3*w^3 + 7*w^2 + 7*w - 5],\
[257, 257, 3*w^3 - 7*w^2 - 5*w + 1],\
[263, 263, w^3 - w^2 - 4*w - 5],\
[263, 263, -2*w^3 + 3*w^2 + 9*w - 4],\
[281, 281, -w^3 + 3*w^2 + 4*w - 6],\
[281, 281, 3*w^3 - 7*w^2 - 8*w + 5],\
[289, 17, -3*w^3 + 6*w^2 + 6*w - 4],\
[311, 311, -3*w^3 + 5*w^2 + 11*w - 3],\
[311, 311, w - 5],\
[313, 313, -2*w^3 + 6*w^2 + w - 9],\
[313, 313, -w^3 + 3*w^2 + 3*w - 7],\
[359, 359, 3*w^3 - 6*w^2 - 8*w],\
[359, 359, -w^2 + 3*w - 4],\
[359, 359, w^3 - w^2 - 5*w - 5],\
[359, 359, w^3 - 2*w^2 - 4],\
[383, 383, -4*w^3 + 8*w^2 + 9*w - 3],\
[383, 383, -w^3 + 5*w^2 - 3*w - 7],\
[401, 401, -3*w^3 + 8*w^2 + 3*w - 9],\
[401, 401, -3*w^3 + 7*w^2 + 6*w - 3],\
[401, 401, w^3 - w^2 - 2*w - 4],\
[401, 401, -2*w^3 + 2*w^2 + 7*w - 1],\
[439, 439, -4*w^3 + 9*w^2 + 7*w - 6],\
[439, 439, 3*w^3 - 5*w^2 - 7*w + 1],\
[449, 449, -4*w^3 + 9*w^2 + 9*w - 6],\
[449, 449, 2*w^3 - 2*w^2 - 11*w - 2],\
[449, 449, -w^3 + 5*w^2 - 3*w - 11],\
[449, 449, -3*w^3 + 5*w^2 + 10*w - 5],\
[457, 457, -2*w^3 + 2*w^2 + 9*w - 1],\
[457, 457, w^3 - 4*w^2 + 3*w + 5],\
[463, 463, 3*w^2 - 5*w - 6],\
[463, 463, -w^3 + 5*w^2 - 3*w - 5],\
[479, 479, -2*w^3 + 3*w^2 + 9*w - 2],\
[479, 479, -w^3 + w^2 + 7*w - 1],\
[487, 487, -2*w^2 + 5*w + 6],\
[487, 487, -w^3 + 7*w - 2],\
[487, 487, -w^3 + 6*w - 2],\
[487, 487, -w^3 + 4*w^2 - 2*w - 8],\
[503, 503, w^3 - 4*w - 6],\
[503, 503, -3*w^3 + 8*w^2 + 4*w - 4],\
[521, 521, 3*w^2 - 4*w - 7],\
[521, 521, 2*w^3 - 7*w^2 + 6],\
[529, 23, -w^3 + 2*w^2 + 2*w - 6],\
[529, 23, w^3 - 2*w^2 - 2*w - 4],\
[569, 569, 2*w^3 - 7*w^2 - 2*w + 7],\
[569, 569, 4*w^3 - 7*w^2 - 10*w + 4],\
[569, 569, 3*w^3 - 4*w^2 - 13*w],\
[569, 569, 4*w^3 - 8*w^2 - 11*w + 3],\
[577, 577, 4*w^2 - 7*w - 10],\
[577, 577, w^3 + w^2 - 6*w - 9],\
[593, 593, w^3 - 4*w^2 + 2*w - 2],\
[593, 593, 3*w^3 - 10*w^2 + w + 11],\
[601, 601, -2*w^3 + 4*w^2 + 8*w - 3],\
[601, 601, -2*w^3 + 4*w^2 + 8*w - 5],\
[617, 617, 5*w^3 - 12*w^2 - 11*w + 11],\
[617, 617, 3*w^2 - 4*w - 5],\
[617, 617, -2*w^3 + 7*w^2 - 8],\
[617, 617, 5*w^3 - 10*w^2 - 13*w + 11],\
[631, 631, -3*w^2 + 8*w + 5],\
[631, 631, 2*w^3 - 7*w^2 - w + 10],\
[631, 631, 5*w^3 - 11*w^2 - 10*w + 9],\
[631, 631, 2*w^3 - w^2 - 12*w],\
[641, 641, -3*w^3 + 8*w^2 + 5*w - 5],\
[641, 641, 2*w^2 - w - 7],\
[647, 647, -2*w^3 + 2*w^2 + 11*w - 1],\
[647, 647, 2*w^3 - 2*w^2 - 11*w - 1],\
[647, 647, -3*w^3 + 9*w^2 + 4*w - 10],\
[647, 647, w^3 - 5*w^2 + 6],\
[673, 673, -5*w^3 + 11*w^2 + 12*w - 8],\
[673, 673, 3*w^3 - 5*w^2 - 10*w + 6],\
[719, 719, -3*w^3 + 4*w^2 + 10*w - 2],\
[719, 719, -3*w^3 + 8*w^2 + 2*w - 8],\
[727, 727, -w^3 + 5*w^2 - 2*w - 6],\
[727, 727, -w^3 + 5*w^2 - 2*w - 7],\
[743, 743, -5*w^3 + 10*w^2 + 13*w - 4],\
[743, 743, -4*w^3 + 9*w^2 + 10*w - 6],\
[743, 743, 2*w^3 - 2*w^2 - 10*w + 3],\
[743, 743, w^2 + 2*w - 5],\
[751, 751, -w^3 + 4*w^2 - 3*w - 6],\
[751, 751, 2*w^3 - 2*w^2 - 9*w + 2],\
[761, 761, 4*w^3 - 9*w^2 - 6*w + 4],\
[761, 761, 3*w^3 - 3*w^2 - 12*w - 1],\
[761, 761, 3*w^3 - 9*w^2 + 8],\
[761, 761, 4*w^3 - 7*w^2 - 10*w + 1],\
[769, 769, 4*w^3 - 7*w^2 - 10*w + 3],\
[769, 769, -4*w^3 + 7*w^2 + 14*w - 5],\
[769, 769, 4*w^3 - 9*w^2 - 6*w + 6],\
[769, 769, -w^2 + 6*w],\
[809, 809, -2*w^3 + 2*w^2 + 7*w - 3],\
[809, 809, -3*w^3 + 8*w^2 + 3*w - 11],\
[823, 823, 3*w^3 - 8*w^2 - 7*w + 6],\
[823, 823, -2*w^3 + 6*w^2 + 5*w - 10],\
[839, 839, -3*w^3 + 5*w^2 + 12*w - 1],\
[839, 839, -w^3 + w^2 + 8*w - 4],\
[887, 887, -4*w^3 + 9*w^2 + 5*w - 6],\
[887, 887, -5*w^3 + 9*w^2 + 13*w - 5],\
[919, 919, -4*w^3 + 6*w^2 + 14*w - 3],\
[919, 919, -5*w^3 + 12*w^2 + 9*w - 8],\
[929, 929, -2*w^3 + 3*w^2 + 10*w - 5],\
[929, 929, -2*w^3 + 3*w^2 + 10*w],\
[937, 937, -3*w^3 + 7*w^2 + 8*w - 3],\
[937, 937, -w^3 + 3*w^2 + 4*w - 8],\
[961, 31, -4*w^3 + 8*w^2 + 8*w - 5],\
[961, 31, -4*w^3 + 8*w^2 + 8*w - 3],\
[967, 967, 4*w^3 - 8*w^2 - 7*w + 1],\
[967, 967, -5*w^3 + 10*w^2 + 11*w - 3],\
[977, 977, 3*w^3 - 8*w^2 - w + 7],\
[977, 977, -4*w^3 + 6*w^2 + 13*w - 3],\
[991, 991, w^2 - w - 8],\
[991, 991, -3*w^3 + 5*w^2 + 12*w - 5]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 - 4*x^4 - 8*x^3 + 38*x^2 - 9*x - 14
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 2, 1/4*e^4 - 3/4*e^3 - 9/4*e^2 + 25/4*e + 1/2, 3/4*e^4 - 1/4*e^3 - 31/4*e^2 - 5/4*e + 11/2, -3/4*e^4 + 3/4*e^3 + 31/4*e^2 - 21/4*e - 5/2, -e^4 + 11*e^2 + 2*e - 6, 3/2*e^4 - 3/2*e^3 - 31/2*e^2 + 21/2*e + 7, -2*e^4 + 2*e^3 + 20*e^2 - 14*e - 6, 1/4*e^4 + 3/4*e^3 - 13/4*e^2 - 41/4*e + 11/2, -1/2*e^4 - 1/2*e^3 + 13/2*e^2 + 11/2*e - 7, -2*e^4 + 3*e^3 + 20*e^2 - 23*e - 6, -9/4*e^4 + 5/4*e^3 + 93/4*e^2 - 35/4*e - 3/2, -1, -9/4*e^4 + 11/4*e^3 + 85/4*e^2 - 73/4*e - 5/2, 5/4*e^4 - 1/4*e^3 - 49/4*e^2 - 5/4*e + 11/2, 11/4*e^4 - 5/4*e^3 - 115/4*e^2 + 15/4*e + 31/2, -7/4*e^4 + 7/4*e^3 + 75/4*e^2 - 53/4*e - 29/2, 1/4*e^4 - 5/4*e^3 - 13/4*e^2 + 51/4*e + 15/2, 1/4*e^4 + 5/4*e^3 - 17/4*e^2 - 47/4*e + 9/2, 2*e^4 - e^3 - 22*e^2 + 5*e + 16, -3/2*e^4 - 1/2*e^3 + 31/2*e^2 + 19/2*e - 5, -2*e^4 + 3*e^3 + 20*e^2 - 25*e - 4, e^4 - e^3 - 9*e^2 + 5*e - 4, 9/4*e^4 - 15/4*e^3 - 89/4*e^2 + 125/4*e + 9/2, 2*e^4 - 2*e^3 - 20*e^2 + 12*e + 6, -2*e^2 + 16, -1/4*e^4 + 5/4*e^3 + 5/4*e^2 - 35/4*e + 17/2, 3/2*e^4 - 3/2*e^3 - 35/2*e^2 + 25/2*e + 17, e^4 - 2*e^3 - 9*e^2 + 18*e - 6, e^3 - 9*e - 2, 13/4*e^4 - 5/4*e^3 - 137/4*e^2 + 19/4*e + 27/2, 3/4*e^4 + 1/4*e^3 - 39/4*e^2 - 3/4*e + 29/2, 11/4*e^4 - 15/4*e^3 - 111/4*e^2 + 109/4*e + 13/2, 3/4*e^4 - 3/4*e^3 - 31/4*e^2 + 29/4*e - 3/2, 5/2*e^4 - 1/2*e^3 - 49/2*e^2 - 9/2*e + 1, -e^4 + 2*e^3 + 11*e^2 - 16*e - 4, -5/4*e^4 + 5/4*e^3 + 49/4*e^2 - 23/4*e - 19/2, 2*e^4 - e^3 - 20*e^2 + 3*e + 8, 7/4*e^4 - 9/4*e^3 - 59/4*e^2 + 67/4*e - 29/2, 1/4*e^4 + 1/4*e^3 - 9/4*e^2 - 11/4*e + 5/2, -3/4*e^4 + 3/4*e^3 + 31/4*e^2 - 37/4*e + 3/2, -3/2*e^4 + 3/2*e^3 + 27/2*e^2 - 21/2*e + 5, -e^4 + 4*e^3 + 9*e^2 - 34*e, -e^3 + 9*e - 8, -11/4*e^4 + 5/4*e^3 + 111/4*e^2 - 15/4*e - 15/2, -19/4*e^4 + 11/4*e^3 + 191/4*e^2 - 49/4*e - 17/2, -9/4*e^4 + 9/4*e^3 + 101/4*e^2 - 59/4*e - 55/2, 2*e^4 - 2*e^3 - 22*e^2 + 18*e + 20, -5/4*e^4 - 1/4*e^3 + 49/4*e^2 + 35/4*e - 5/2, 3/4*e^4 - 7/4*e^3 - 39/4*e^2 + 45/4*e + 37/2, -9/4*e^4 + 15/4*e^3 + 93/4*e^2 - 141/4*e - 21/2, 3/2*e^4 - 3/2*e^3 - 39/2*e^2 + 21/2*e + 33, 1/2*e^4 + 5/2*e^3 - 9/2*e^2 - 55/2*e + 3, 9/4*e^4 + 9/4*e^3 - 105/4*e^2 - 91/4*e + 37/2, -5/4*e^4 - 5/4*e^3 + 57/4*e^2 + 63/4*e - 9/2, -2*e^4 + 2*e^3 + 22*e^2 - 14*e - 20, -3/4*e^4 - 7/4*e^3 + 47/4*e^2 + 53/4*e - 47/2, -e^3 + 4*e^2 + 9*e - 20, -4*e^4 + 4*e^3 + 38*e^2 - 26*e - 6, 5*e^4 - 4*e^3 - 55*e^2 + 28*e + 44, 13/4*e^4 - 17/4*e^3 - 129/4*e^2 + 131/4*e + 19/2, -7/4*e^4 - 9/4*e^3 + 83/4*e^2 + 119/4*e - 33/2, 2*e^3 - 2*e^2 - 18*e + 6, -11/4*e^4 + 1/4*e^3 + 115/4*e^2 + 29/4*e - 19/2, -19/4*e^4 + 13/4*e^3 + 191/4*e^2 - 63/4*e - 39/2, -e^4 + 4*e^3 + 9*e^2 - 38*e - 6, 1/2*e^4 - 7/2*e^3 - 5/2*e^2 + 69/2*e - 3, -3*e^4 + 4*e^3 + 33*e^2 - 30*e - 32, 11/2*e^4 - 9/2*e^3 - 115/2*e^2 + 59/2*e + 29, -9/2*e^4 + 7/2*e^3 + 97/2*e^2 - 37/2*e - 35, 3*e^4 - 29*e^2 - 6*e - 10, 3*e^4 - 5*e^3 - 31*e^2 + 35*e + 28, -4*e^4 + 7*e^3 + 36*e^2 - 53*e, -11/4*e^4 + 13/4*e^3 + 119/4*e^2 - 111/4*e - 63/2, 1/4*e^4 + 7/4*e^3 + 3/4*e^2 - 77/4*e - 33/2, -2*e^3 - 2*e^2 + 24*e + 6, -e^4 - e^3 + 9*e^2 + 13*e + 4, 9/4*e^4 - 1/4*e^3 - 85/4*e^2 - 13/4*e - 5/2, 3/2*e^4 - 5/2*e^3 - 23/2*e^2 + 27/2*e - 15, -9/4*e^4 + 1/4*e^3 + 101/4*e^2 - 27/4*e - 43/2, 7*e^4 - 7*e^3 - 71*e^2 + 53*e + 10, -19/4*e^4 + 29/4*e^3 + 183/4*e^2 - 215/4*e - 39/2, -11/4*e^4 + 11/4*e^3 + 119/4*e^2 - 89/4*e - 65/2, -5/2*e^4 + 9/2*e^3 + 49/2*e^2 - 83/2*e + 7, 29/4*e^4 - 9/4*e^3 - 305/4*e^2 - 9/4*e + 99/2, -3/4*e^4 + 5/4*e^3 + 39/4*e^2 - 63/4*e - 55/2, -3/2*e^4 - 1/2*e^3 + 35/2*e^2 + 27/2*e - 25, 1/4*e^4 - 7/4*e^3 - 5/4*e^2 + 53/4*e - 19/2, -1/2*e^4 + 1/2*e^3 - 3/2*e^2 - 3/2*e + 33, -1/2*e^4 + 3/2*e^3 + 1/2*e^2 - 5/2*e + 35, 7/2*e^4 - 3/2*e^3 - 79/2*e^2 + 5/2*e + 37, -1/2*e^4 + 7/2*e^3 + 5/2*e^2 - 53/2*e - 7, -2*e^4 + e^3 + 22*e^2 - 15*e - 16, -15/4*e^4 - 7/4*e^3 + 159/4*e^2 + 101/4*e - 27/2, -9/4*e^4 + 1/4*e^3 + 101/4*e^2 + 41/4*e - 39/2, -11/4*e^4 + 9/4*e^3 + 103/4*e^2 - 67/4*e + 57/2, -3*e^4 + 4*e^3 + 33*e^2 - 38*e - 16, -7/4*e^4 - 7/4*e^3 + 79/4*e^2 + 133/4*e - 39/2, 2*e^4 - 2*e^3 - 22*e^2 + 12*e + 24, -3*e^4 + 3*e^3 + 31*e^2 - 23*e + 2, -3/2*e^4 + 1/2*e^3 + 35/2*e^2 - 19/2*e - 11, -3*e^4 + e^3 + 29*e^2 + 5*e - 2, -5/4*e^4 - 1/4*e^3 + 57/4*e^2 + 51/4*e - 37/2, -7/2*e^4 + 9/2*e^3 + 67/2*e^2 - 47/2*e - 11, -7/4*e^4 - 3/4*e^3 + 63/4*e^2 + 81/4*e + 33/2, 11/4*e^4 - 1/4*e^3 - 135/4*e^2 + 3/4*e + 111/2, 13/4*e^4 - 19/4*e^3 - 125/4*e^2 + 137/4*e - 35/2, 8*e^4 - 10*e^3 - 82*e^2 + 76*e + 38, -7*e^4 + e^3 + 71*e^2 + 15*e - 24, -5/4*e^4 + 17/4*e^3 + 57/4*e^2 - 175/4*e - 47/2, -5/2*e^4 + 7/2*e^3 + 49/2*e^2 - 49/2*e - 41, 11/2*e^4 - 9/2*e^3 - 103/2*e^2 + 39/2*e - 9, -25/4*e^4 + 17/4*e^3 + 229/4*e^2 - 83/4*e + 49/2, e^4 + 2*e^3 - 13*e^2 - 22*e + 22, -1/4*e^4 - 21/4*e^3 + 33/4*e^2 + 183/4*e - 37/2, 1/4*e^4 + 9/4*e^3 - 5/4*e^2 - 107/4*e - 11/2, -e^4 + 5*e^3 + 9*e^2 - 49*e + 2, e^4 - e^3 - 11*e^2 + e + 28, 11/2*e^4 - 7/2*e^3 - 119/2*e^2 + 41/2*e + 35, 4*e^4 - 3*e^3 - 42*e^2 + 23*e + 24, -e^4 - 3*e^3 + 13*e^2 + 23*e - 26, e^4 - 2*e^3 - 9*e^2 + 20*e - 28, 21/4*e^4 - 9/4*e^3 - 241/4*e^2 + 55/4*e + 115/2, 7/4*e^4 - 9/4*e^3 - 67/4*e^2 + 83/4*e + 11/2, 3/4*e^4 - 15/4*e^3 - 23/4*e^2 + 105/4*e - 19/2, -5/2*e^4 + 3/2*e^3 + 49/2*e^2 - 29/2*e + 7, 2*e^3 - 4*e^2 - 28*e + 20, -3/4*e^4 + 21/4*e^3 + 19/4*e^2 - 183/4*e - 23/2, 31/4*e^4 - 31/4*e^3 - 315/4*e^2 + 221/4*e + 69/2, -9/2*e^4 + 9/2*e^3 + 93/2*e^2 - 59/2*e - 23, -7/2*e^4 + 17/2*e^3 + 71/2*e^2 - 127/2*e - 25, -11/4*e^4 + 9/4*e^3 + 127/4*e^2 - 51/4*e - 67/2, 5*e^4 - 6*e^3 - 47*e^2 + 42*e - 6, -3/4*e^4 + 19/4*e^3 + 23/4*e^2 - 193/4*e + 23/2, 13/4*e^4 - 27/4*e^3 - 125/4*e^2 + 209/4*e + 33/2, -11/2*e^4 + 5/2*e^3 + 123/2*e^2 - 27/2*e - 35, -3/4*e^4 - 7/4*e^3 + 43/4*e^2 + 45/4*e - 3/2, 9/2*e^4 - 1/2*e^3 - 93/2*e^2 - 17/2*e + 29, 17/2*e^4 - 21/2*e^3 - 173/2*e^2 + 163/2*e + 31, -31/4*e^4 + 45/4*e^3 + 303/4*e^2 - 351/4*e - 55/2, 27/4*e^4 - 49/4*e^3 - 247/4*e^2 + 387/4*e + 27/2, -9/4*e^4 + 13/4*e^3 + 77/4*e^2 - 91/4*e - 3/2, -5/2*e^4 + 5/2*e^3 + 61/2*e^2 - 31/2*e - 51, 3*e^4 - e^3 - 27*e^2 - e - 20, -11/4*e^4 + 21/4*e^3 + 115/4*e^2 - 135/4*e - 31/2, -31/4*e^4 + 19/4*e^3 + 331/4*e^2 - 97/4*e - 105/2, 3*e^4 - e^3 - 29*e^2 + 5*e - 18, 19/4*e^4 - 13/4*e^3 - 195/4*e^2 + 31/4*e + 71/2, 13/4*e^4 - 5/4*e^3 - 129/4*e^2 + 23/4*e + 23/2, -3/2*e^4 + 7/2*e^3 + 27/2*e^2 - 57/2*e + 11, 17/4*e^4 - 15/4*e^3 - 185/4*e^2 + 141/4*e + 45/2, 19/4*e^4 - 35/4*e^3 - 199/4*e^2 + 285/4*e + 45/2, -5/2*e^4 + 17/2*e^3 + 37/2*e^2 - 163/2*e + 15, 4*e^4 - 6*e^3 - 38*e^2 + 38*e - 16, -1/4*e^4 - 11/4*e^3 + 13/4*e^2 + 113/4*e - 47/2, 15/2*e^4 - 13/2*e^3 - 159/2*e^2 + 83/2*e + 79, -1/2*e^4 + 5/2*e^3 + 17/2*e^2 - 59/2*e - 27, 1/2*e^4 + 9/2*e^3 - 13/2*e^2 - 107/2*e + 17, -7/2*e^4 + 1/2*e^3 + 71/2*e^2 + 9/2*e - 21, -2*e^4 - 3*e^3 + 24*e^2 + 35*e - 6, -21/4*e^4 + 27/4*e^3 + 193/4*e^2 - 233/4*e + 31/2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([71,71,2*w^3 - 4*w^2 - 6*w + 1])] = 1

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