/*
  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([49, 7, w^2 - 4*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 - 3*x^4 - 14*x^3 + 38*x^2 + 17*x - 35
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/11*e^4 - 5/22*e^3 - 25/22*e^2 + 47/22*e + 41/22, 1/11*e^4 - 5/22*e^3 - 25/22*e^2 + 47/22*e + 41/22, -1/11*e^4 - 3/11*e^3 + 18/11*e^2 + 37/11*e - 37/11, -1/11*e^4 - 3/11*e^3 + 18/11*e^2 + 37/11*e - 37/11, -1/22*e^4 + 4/11*e^3 - 2/11*e^2 - 42/11*e + 117/22, -1/22*e^4 + 4/11*e^3 - 2/11*e^2 - 42/11*e + 117/22, 5/11*e^4 - 7/11*e^3 - 79/11*e^2 + 57/11*e + 152/11, 3/11*e^4 - 2/11*e^3 - 43/11*e^2 + 21/11*e + 23/11, 3/11*e^4 - 2/11*e^3 - 43/11*e^2 + 21/11*e + 23/11, -1, -5/11*e^4 + 7/11*e^3 + 57/11*e^2 - 57/11*e + 2/11, -5/11*e^4 + 7/11*e^3 + 57/11*e^2 - 57/11*e + 2/11, -4/11*e^4 + 10/11*e^3 + 61/11*e^2 - 138/11*e - 71/11, -4/11*e^4 + 10/11*e^3 + 61/11*e^2 - 138/11*e - 71/11, 3/22*e^4 + 9/22*e^3 - 43/22*e^2 - 155/22*e + 39/11, 3/22*e^4 + 9/22*e^3 - 43/22*e^2 - 155/22*e + 39/11, -9/22*e^4 + 3/11*e^3 + 81/11*e^2 - 15/11*e - 465/22, -9/22*e^4 + 3/11*e^3 + 81/11*e^2 - 15/11*e - 465/22, -6/11*e^4 + 15/11*e^3 + 86/11*e^2 - 141/11*e - 68/11, -6/11*e^4 + 19/22*e^3 + 183/22*e^2 - 249/22*e - 125/22, -6/11*e^4 + 19/22*e^3 + 183/22*e^2 - 249/22*e - 125/22, -5/11*e^4 + 25/22*e^3 + 125/22*e^2 - 279/22*e - 249/22, -5/11*e^4 + 25/22*e^3 + 125/22*e^2 - 279/22*e - 249/22, 9/22*e^4 - 3/11*e^3 - 59/11*e^2 + 15/11*e + 113/22, 9/22*e^4 - 3/11*e^3 - 59/11*e^2 + 15/11*e + 113/22, -2/11*e^4 + 5/11*e^3 + 36/11*e^2 - 47/11*e - 96/11, -2/11*e^4 + 5/11*e^3 + 36/11*e^2 - 47/11*e - 96/11, 6/11*e^4 - 4/11*e^3 - 108/11*e^2 + 42/11*e + 244/11, 6/11*e^4 - 4/11*e^3 - 108/11*e^2 + 42/11*e + 244/11, 5/22*e^4 - 9/11*e^3 - 45/11*e^2 + 111/11*e + 273/22, 5/22*e^4 - 9/11*e^3 - 45/11*e^2 + 111/11*e + 273/22, -5/11*e^4 + 7/11*e^3 + 79/11*e^2 - 112/11*e - 97/11, -5/11*e^4 + 7/11*e^3 + 79/11*e^2 - 112/11*e - 97/11, 2/11*e^4 - 5/11*e^3 - 36/11*e^2 + 58/11*e + 107/11, 2/11*e^4 - 5/11*e^3 - 36/11*e^2 + 58/11*e + 107/11, 3/22*e^4 + 10/11*e^3 - 16/11*e^2 - 138/11*e + 1/22, 3/22*e^4 + 10/11*e^3 - 16/11*e^2 - 138/11*e + 1/22, 9/22*e^4 - 39/22*e^3 - 151/22*e^2 + 525/22*e + 62/11, 9/22*e^4 - 39/22*e^3 - 151/22*e^2 + 525/22*e + 62/11, -7/22*e^4 + 1/22*e^3 + 93/22*e^2 - 71/22*e + 74/11, -7/22*e^4 + 1/22*e^3 + 93/22*e^2 - 71/22*e + 74/11, -5/11*e^4 + 7/11*e^3 + 68/11*e^2 - 57/11*e + 35/11, -5/11*e^4 + 7/11*e^3 + 68/11*e^2 - 57/11*e + 35/11, -1/2*e^4 + 2*e^3 + 6*e^2 - 22*e - 7/2, 2/11*e^4 - 5/11*e^3 - 14/11*e^2 + 25/11*e - 36/11, 2/11*e^4 - 5/11*e^3 - 14/11*e^2 + 25/11*e - 36/11, -1/2*e^4 + 2*e^3 + 6*e^2 - 22*e - 7/2, 1/11*e^4 - 8/11*e^3 + 4/11*e^2 + 62/11*e - 161/11, 1/11*e^4 - 8/11*e^3 + 4/11*e^2 + 62/11*e - 161/11, 9/11*e^4 - 17/11*e^3 - 129/11*e^2 + 217/11*e + 80/11, 9/11*e^4 - 17/11*e^3 - 129/11*e^2 + 217/11*e + 80/11, 9/22*e^4 - 14/11*e^3 - 70/11*e^2 + 114/11*e + 311/22, 9/22*e^4 - 14/11*e^3 - 70/11*e^2 + 114/11*e + 311/22, 27/22*e^4 - 51/22*e^3 - 387/22*e^2 + 629/22*e + 219/11, 27/22*e^4 - 51/22*e^3 - 387/22*e^2 + 629/22*e + 219/11, -4*e + 2, -4*e + 2, -3/11*e^4 + 13/11*e^3 + 54/11*e^2 - 175/11*e + 65/11, -2*e^2 + e + 7, -2*e^2 + e + 7, 5/11*e^4 + 4/11*e^3 - 79/11*e^2 - 53/11*e + 119/11, 5/11*e^4 + 4/11*e^3 - 79/11*e^2 - 53/11*e + 119/11, 3/11*e^4 - 13/11*e^3 - 21/11*e^2 + 153/11*e - 230/11, -3*e^2 + 35, -3*e^2 + 35, 3/11*e^4 - 13/11*e^3 - 21/11*e^2 + 153/11*e - 230/11, 1/22*e^4 + 3/22*e^3 + 15/22*e^2 + 51/22*e - 141/11, 1/22*e^4 + 3/22*e^3 + 15/22*e^2 + 51/22*e - 141/11, -2/11*e^4 - 1/22*e^3 + 83/22*e^2 + 203/22*e - 621/22, 5/11*e^4 - 47/22*e^3 - 103/22*e^2 + 565/22*e - 81/22, 5/11*e^4 - 47/22*e^3 - 103/22*e^2 + 565/22*e - 81/22, -2/11*e^4 - 1/22*e^3 + 83/22*e^2 + 203/22*e - 621/22, 8/11*e^4 - 9/11*e^3 - 144/11*e^2 + 45/11*e + 340/11, 8/11*e^4 - 9/11*e^3 - 144/11*e^2 + 45/11*e + 340/11, -17/11*e^4 + 26/11*e^3 + 229/11*e^2 - 218/11*e - 310/11, -e^3 + 13*e + 10, -e^3 + 13*e + 10, -17/11*e^4 + 26/11*e^3 + 229/11*e^2 - 218/11*e - 310/11, -3/11*e^4 + 2/11*e^3 + 76/11*e^2 + 12/11*e - 397/11, -3/11*e^4 + 2/11*e^3 + 76/11*e^2 + 12/11*e - 397/11, 3/11*e^4 - 2/11*e^3 - 10/11*e^2 - 56/11*e - 241/11, 3/11*e^4 - 2/11*e^3 - 10/11*e^2 - 56/11*e - 241/11, -14/11*e^4 + 24/11*e^3 + 208/11*e^2 - 252/11*e - 210/11, -14/11*e^4 + 24/11*e^3 + 208/11*e^2 - 252/11*e - 210/11, 2/11*e^4 - 27/11*e^3 - 3/11*e^2 + 322/11*e + 8/11, 2/11*e^4 - 27/11*e^3 - 3/11*e^2 + 322/11*e + 8/11, 19/11*e^4 - 31/11*e^3 - 254/11*e^2 + 353/11*e + 153/11, 19/11*e^4 - 31/11*e^3 - 254/11*e^2 + 353/11*e + 153/11, -15/22*e^4 + 43/22*e^3 + 171/22*e^2 - 325/22*e + 69/11, -15/22*e^4 + 43/22*e^3 + 171/22*e^2 - 325/22*e + 69/11, -e^3 + 2*e^2 + 14*e - 23, -e^3 + 2*e^2 + 14*e - 23, -3/11*e^4 + 13/11*e^3 + 10/11*e^2 - 54/11*e + 450/11, e^4 - e^3 - 13*e^2 + 5*e + 30, -2/11*e^4 - 17/11*e^3 + 25/11*e^2 + 239/11*e + 25/11, -10/11*e^4 + 36/11*e^3 + 136/11*e^2 - 356/11*e - 150/11, -2/11*e^4 - 17/11*e^3 + 25/11*e^2 + 239/11*e + 25/11, -10/11*e^4 + 36/11*e^3 + 136/11*e^2 - 356/11*e - 150/11, 6/11*e^4 - 4/11*e^3 - 86/11*e^2 + 97/11*e + 123/11, 6/11*e^4 - 4/11*e^3 - 86/11*e^2 + 97/11*e + 123/11, -19/22*e^4 + 21/11*e^3 + 127/11*e^2 - 237/11*e - 87/22, -19/22*e^4 + 21/11*e^3 + 127/11*e^2 - 237/11*e - 87/22, 14/11*e^4 - 24/11*e^3 - 230/11*e^2 + 274/11*e + 452/11, 14/11*e^4 - 24/11*e^3 - 230/11*e^2 + 274/11*e + 452/11, -9/11*e^4 + 23/22*e^3 + 203/22*e^2 - 137/22*e + 181/22, 19/22*e^4 - 53/22*e^3 - 265/22*e^2 + 375/22*e + 148/11, 19/22*e^4 - 53/22*e^3 - 265/22*e^2 + 375/22*e + 148/11, -9/11*e^4 + 23/22*e^3 + 203/22*e^2 - 137/22*e + 181/22, 19/22*e^4 - 31/22*e^3 - 243/22*e^2 + 485/22*e + 27/11, e^4 - e^3 - 15*e^2 + 7*e + 22, e^4 - e^3 - 15*e^2 + 7*e + 22, 19/22*e^4 - 31/22*e^3 - 243/22*e^2 + 485/22*e + 27/11, 9/22*e^4 - 61/22*e^3 - 85/22*e^2 + 591/22*e - 103/11, 9/22*e^4 - 61/22*e^3 - 85/22*e^2 + 591/22*e - 103/11, -9/11*e^4 + 17/11*e^3 + 96/11*e^2 - 107/11*e + 63/11, 9/22*e^4 + 8/11*e^3 - 92/11*e^2 - 84/11*e + 971/22, 9/22*e^4 + 8/11*e^3 - 92/11*e^2 - 84/11*e + 971/22, -9/11*e^4 + 17/11*e^3 + 96/11*e^2 - 107/11*e + 63/11, 13/11*e^4 - 5/11*e^3 - 201/11*e^2 + 25/11*e + 514/11, 13/11*e^4 - 5/11*e^3 - 201/11*e^2 + 25/11*e + 514/11, 1/11*e^4 - 27/22*e^3 - 3/22*e^2 + 245/22*e - 685/22, 1/11*e^4 - 27/22*e^3 - 3/22*e^2 + 245/22*e - 685/22, -23/22*e^4 + 37/11*e^3 + 163/11*e^2 - 339/11*e - 719/22, -23/22*e^4 + 37/11*e^3 + 163/11*e^2 - 339/11*e - 719/22, 3/11*e^4 + 9/11*e^3 - 65/11*e^2 - 45/11*e + 34/11, 5/11*e^4 + 4/11*e^3 - 90/11*e^2 - 86/11*e + 339/11, 3/11*e^4 + 9/11*e^3 - 65/11*e^2 - 45/11*e + 34/11, 5/11*e^4 + 4/11*e^3 - 90/11*e^2 - 86/11*e + 339/11, 2/11*e^4 + 17/11*e^3 - 14/11*e^2 - 239/11*e - 58/11, 2/11*e^4 + 17/11*e^3 - 14/11*e^2 - 239/11*e - 58/11, -12/11*e^4 + 8/11*e^3 + 227/11*e^2 - 51/11*e - 488/11, 7/22*e^4 + 5/11*e^3 - 107/11*e^2 - 25/11*e + 1139/22, 7/22*e^4 + 5/11*e^3 - 107/11*e^2 - 25/11*e + 1139/22, -12/11*e^4 + 8/11*e^3 + 227/11*e^2 - 51/11*e - 488/11, -13/22*e^4 + 5/22*e^3 + 245/22*e^2 - 179/22*e - 345/11, 1/11*e^4 + 3/11*e^3 - 40/11*e^2 - 37/11*e + 455/11, -13/22*e^4 + 5/22*e^3 + 245/22*e^2 - 179/22*e - 345/11, 1/11*e^4 + 3/11*e^3 - 40/11*e^2 - 37/11*e + 455/11, -31/22*e^4 + 36/11*e^3 + 202/11*e^2 - 334/11*e - 465/22, -31/22*e^4 + 36/11*e^3 + 202/11*e^2 - 334/11*e - 465/22, -9/11*e^4 + 39/11*e^3 + 129/11*e^2 - 371/11*e - 256/11, -9/11*e^4 + 39/11*e^3 + 129/11*e^2 - 371/11*e - 256/11, 25/11*e^4 - 35/11*e^3 - 362/11*e^2 + 329/11*e + 595/11, 25/11*e^4 - 35/11*e^3 - 362/11*e^2 + 329/11*e + 595/11, -5/11*e^4 - 4/11*e^3 + 112/11*e^2 + 42/11*e - 317/11, -5/11*e^4 - 4/11*e^3 + 112/11*e^2 + 42/11*e - 317/11, -20/11*e^4 + 17/11*e^3 + 283/11*e^2 - 195/11*e - 355/11, -20/11*e^4 + 17/11*e^3 + 283/11*e^2 - 195/11*e - 355/11, 17/22*e^4 - 15/22*e^3 - 163/22*e^2 + 185/22*e - 120/11, 17/22*e^4 - 15/22*e^3 - 163/22*e^2 + 185/22*e - 120/11, 12/11*e^4 - 71/22*e^3 - 399/22*e^2 + 773/22*e + 921/22, 12/11*e^4 - 71/22*e^3 - 399/22*e^2 + 773/22*e + 921/22, -1/11*e^4 - 3/11*e^3 + 18/11*e^2 + 37/11*e + 447/11, -7/11*e^4 + 1/11*e^3 + 49/11*e^2 - 5/11*e + 632/11, -9/11*e^4 + 28/11*e^3 + 107/11*e^2 - 360/11*e - 102/11, -9/11*e^4 + 28/11*e^3 + 107/11*e^2 - 360/11*e - 102/11, -1/11*e^4 - 14/11*e^3 + 62/11*e^2 + 92/11*e - 477/11, -1/11*e^4 - 14/11*e^3 + 62/11*e^2 + 92/11*e - 477/11, 9/22*e^4 - 39/22*e^3 - 107/22*e^2 + 525/22*e + 62/11, 9/22*e^4 - 39/22*e^3 - 107/22*e^2 + 525/22*e + 62/11]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([49, 7, w^2 - 4*w - 1])] = 1

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