/*
  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, 4, 5, -4, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([49, 7, w^5 - 4*w^4 + 11*w^2 - 3*w - 4])

primes_array = [
[13, 13, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 + w + 4],\
[13, 13, -w^2 + w + 2],\
[27, 3, 2*w^5 - 4*w^4 - 7*w^3 + 9*w^2 + 4*w - 2],\
[27, 3, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - w + 5],\
[29, 29, w^3 - 2*w^2 - 2*w + 3],\
[29, 29, 2*w^5 - 4*w^4 - 7*w^3 + 8*w^2 + 4*w - 2],\
[43, 43, -w^5 + 3*w^4 + w^3 - 6*w^2 + 3*w + 1],\
[43, 43, -w^4 + w^3 + 5*w^2 - 4],\
[49, 7, w^5 - 4*w^4 + 11*w^2 - 3*w - 4],\
[64, 2, -2],\
[71, 71, 2*w^5 - 6*w^4 - 4*w^3 + 17*w^2 - w - 6],\
[71, 71, 2*w^4 - 4*w^3 - 6*w^2 + 7*w + 2],\
[71, 71, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 - w],\
[71, 71, -2*w^5 + 5*w^4 + 6*w^3 - 14*w^2 - 3*w + 5],\
[83, 83, -3*w^5 + 7*w^4 + 9*w^3 - 17*w^2 - 5*w + 5],\
[83, 83, 3*w^5 - 6*w^4 - 10*w^3 + 12*w^2 + 5*w - 2],\
[83, 83, -2*w^5 + 5*w^4 + 5*w^3 - 11*w^2 - 3*w + 3],\
[83, 83, 3*w^5 - 7*w^4 - 8*w^3 + 15*w^2 + 2*w - 4],\
[97, 97, -3*w^5 + 6*w^4 + 10*w^3 - 12*w^2 - 5*w + 3],\
[97, 97, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 5*w - 3],\
[97, 97, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 5*w - 1],\
[97, 97, -3*w^5 + 7*w^4 + 8*w^3 - 15*w^2 - 2*w + 3],\
[113, 113, -3*w^5 + 6*w^4 + 11*w^3 - 14*w^2 - 7*w + 3],\
[113, 113, 2*w^5 - 5*w^4 - 5*w^3 + 12*w^2 - 6],\
[113, 113, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 - 1],\
[113, 113, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 2*w + 5],\
[125, 5, 3*w^5 - 6*w^4 - 10*w^3 + 11*w^2 + 6*w - 1],\
[125, 5, -2*w^5 + 4*w^4 + 6*w^3 - 6*w^2 - 3*w - 1],\
[127, 127, -2*w^5 + 6*w^4 + 3*w^3 - 15*w^2 + 2*w + 5],\
[127, 127, 2*w^5 - 3*w^4 - 9*w^3 + 6*w^2 + 7*w - 2],\
[127, 127, -3*w^5 + 7*w^4 + 9*w^3 - 17*w^2 - 4*w + 4],\
[127, 127, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 - w + 3],\
[139, 139, 3*w^5 - 7*w^4 - 9*w^3 + 16*w^2 + 6*w - 4],\
[139, 139, -w^5 + w^4 + 5*w^3 - 6*w - 1],\
[167, 167, -2*w^5 + 5*w^4 + 6*w^3 - 12*w^2 - 5*w + 4],\
[167, 167, w^5 - 4*w^4 - w^3 + 13*w^2 - 2*w - 4],\
[169, 13, -w^5 + 4*w^4 - 11*w^2 + 3*w + 5],\
[169, 13, 2*w^5 - 5*w^4 - 6*w^3 + 13*w^2 + 3*w - 3],\
[181, 181, 2*w^5 - 4*w^4 - 6*w^3 + 6*w^2 + 2*w + 1],\
[197, 197, -w^4 + 3*w^3 + 2*w^2 - 6*w - 1],\
[197, 197, -3*w^5 + 6*w^4 + 11*w^3 - 14*w^2 - 6*w + 4],\
[211, 211, 2*w^5 - 5*w^4 - 6*w^3 + 12*w^2 + 6*w - 1],\
[211, 211, -2*w^5 + 4*w^4 + 8*w^3 - 9*w^2 - 8*w + 2],\
[211, 211, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 3*w + 3],\
[211, 211, -2*w^4 + 5*w^3 + 5*w^2 - 9*w - 3],\
[223, 223, -w^5 + 8*w^3 + w^2 - 11*w + 1],\
[223, 223, 2*w^5 - 5*w^4 - 5*w^3 + 12*w^2 + w - 1],\
[239, 239, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 2*w + 3],\
[239, 239, 2*w^5 - 5*w^4 - 4*w^3 + 9*w^2 + w],\
[239, 239, -3*w^5 + 7*w^4 + 10*w^3 - 18*w^2 - 7*w + 5],\
[239, 239, w^5 - w^4 - 6*w^3 + 2*w^2 + 5*w - 2],\
[251, 251, w^5 - w^4 - 6*w^3 + 3*w^2 + 6*w - 2],\
[251, 251, -w^5 + 4*w^4 - 12*w^2 + 3*w + 6],\
[281, 281, -5*w^5 + 11*w^4 + 17*w^3 - 27*w^2 - 10*w + 9],\
[281, 281, 2*w^5 - 5*w^4 - 5*w^3 + 10*w^2 + 3*w + 1],\
[293, 293, -2*w^5 + 4*w^4 + 7*w^3 - 7*w^2 - 7*w + 2],\
[293, 293, -w^4 + 2*w^3 + 2*w^2 - 3*w + 3],\
[293, 293, -2*w^5 + 7*w^4 + w^3 - 19*w^2 + 7*w + 9],\
[293, 293, -2*w^5 + 3*w^4 + 9*w^3 - 5*w^2 - 7*w + 2],\
[307, 307, 2*w^2 - 3*w - 4],\
[307, 307, -w^5 + 4*w^4 - 13*w^2 + 6*w + 6],\
[337, 337, 4*w^5 - 9*w^4 - 12*w^3 + 20*w^2 + 6*w - 5],\
[337, 337, -2*w^5 + 3*w^4 + 10*w^3 - 6*w^2 - 12*w + 2],\
[349, 349, 4*w^5 - 9*w^4 - 11*w^3 + 19*w^2 + 2*w - 4],\
[349, 349, 5*w^5 - 11*w^4 - 15*w^3 + 24*w^2 + 5*w - 7],\
[379, 379, -2*w^5 + 5*w^4 + 4*w^3 - 10*w^2 + w + 5],\
[379, 379, -2*w^5 + 5*w^4 + 6*w^3 - 12*w^2 - 5*w + 5],\
[379, 379, -4*w^5 + 8*w^4 + 14*w^3 - 17*w^2 - 10*w + 4],\
[379, 379, -5*w^5 + 12*w^4 + 13*w^3 - 27*w^2 - 2*w + 7],\
[421, 421, 2*w^5 - 6*w^4 - 4*w^3 + 15*w^2 + w - 3],\
[421, 421, 3*w^5 - 9*w^4 - 6*w^3 + 25*w^2 - w - 9],\
[433, 433, -5*w^5 + 10*w^4 + 18*w^3 - 21*w^2 - 13*w + 4],\
[433, 433, 5*w^5 - 12*w^4 - 15*w^3 + 30*w^2 + 7*w - 9],\
[433, 433, -3*w^5 + 8*w^4 + 8*w^3 - 22*w^2 - w + 8],\
[433, 433, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 9*w - 3],\
[449, 449, 3*w^5 - 9*w^4 - 6*w^3 + 24*w^2 + w - 9],\
[449, 449, 3*w^5 - 6*w^4 - 11*w^3 + 15*w^2 + 6*w - 5],\
[449, 449, 2*w^5 - 3*w^4 - 8*w^3 + 3*w^2 + 7*w],\
[449, 449, 4*w^5 - 8*w^4 - 14*w^3 + 17*w^2 + 8*w - 2],\
[449, 449, -3*w^4 + 5*w^3 + 12*w^2 - 9*w - 6],\
[449, 449, -3*w^5 + 8*w^4 + 7*w^3 - 20*w^2 - 2*w + 6],\
[461, 461, 2*w^4 - 4*w^3 - 7*w^2 + 7*w + 2],\
[461, 461, -4*w^5 + 10*w^4 + 11*w^3 - 24*w^2 - 6*w + 8],\
[463, 463, 4*w^5 - 8*w^4 - 14*w^3 + 18*w^2 + 6*w - 5],\
[463, 463, w^5 - w^4 - 5*w^3 + w^2 + 4*w - 3],\
[491, 491, -3*w^5 + 7*w^4 + 8*w^3 - 15*w^2 + 5],\
[491, 491, -2*w^5 + 6*w^4 + 3*w^3 - 14*w^2 + 3],\
[547, 547, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 10*w - 5],\
[547, 547, w^5 - 4*w^4 + 12*w^2 - 2*w - 5],\
[547, 547, -3*w^5 + 5*w^4 + 13*w^3 - 11*w^2 - 11*w + 3],\
[547, 547, -2*w^5 + 6*w^4 + 3*w^3 - 15*w^2 + w + 6],\
[547, 547, -2*w^5 + 6*w^4 + 4*w^3 - 15*w^2 - w + 4],\
[547, 547, 4*w^5 - 8*w^4 - 15*w^3 + 18*w^2 + 12*w - 6],\
[587, 587, -5*w^5 + 12*w^4 + 14*w^3 - 28*w^2 - 6*w + 7],\
[587, 587, 5*w^5 - 12*w^4 - 14*w^3 + 27*w^2 + 6*w - 6],\
[601, 601, -3*w^5 + 9*w^4 + 5*w^3 - 24*w^2 + 5*w + 10],\
[601, 601, -3*w^5 + 8*w^4 + 8*w^3 - 23*w^2 - w + 9],\
[601, 601, -w^5 + 8*w^3 + 2*w^2 - 11*w - 1],\
[601, 601, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 10*w - 4],\
[617, 617, w^5 - w^4 - 7*w^3 + 4*w^2 + 10*w - 3],\
[617, 617, -5*w^5 + 11*w^4 + 16*w^3 - 26*w^2 - 7*w + 8],\
[617, 617, 3*w^5 - 7*w^4 - 9*w^3 + 15*w^2 + 7*w - 2],\
[617, 617, -2*w^5 + 2*w^4 + 11*w^3 - w^2 - 13*w - 2],\
[631, 631, 2*w^4 - 4*w^3 - 7*w^2 + 8*w + 2],\
[631, 631, w^5 - w^4 - 5*w^3 - w^2 + 4*w + 5],\
[631, 631, 4*w^5 - 9*w^4 - 11*w^3 + 19*w^2 + 2*w - 6],\
[631, 631, -3*w^5 + 7*w^4 + 9*w^3 - 15*w^2 - 7*w + 3],\
[643, 643, -2*w^5 + 3*w^4 + 9*w^3 - 6*w^2 - 8*w + 4],\
[643, 643, 3*w^5 - 8*w^4 - 7*w^3 + 20*w^2 + 2*w - 5],\
[659, 659, 3*w^5 - 9*w^4 - 5*w^3 + 23*w^2 - 3*w - 10],\
[659, 659, -2*w^4 + 3*w^3 + 7*w^2 - 3*w - 5],\
[673, 673, 3*w^5 - 6*w^4 - 11*w^3 + 14*w^2 + 8*w - 2],\
[673, 673, 3*w^5 - 8*w^4 - 6*w^3 + 19*w^2 - 3*w - 8],\
[673, 673, 3*w^5 - 6*w^4 - 10*w^3 + 13*w^2 + 3*w - 2],\
[673, 673, 2*w^5 - 3*w^4 - 10*w^3 + 6*w^2 + 11*w - 2],\
[701, 701, 2*w^5 - 5*w^4 - 6*w^3 + 13*w^2 + 6*w - 4],\
[701, 701, 2*w^5 - 5*w^4 - 5*w^3 + 11*w^2 + 2*w - 6],\
[701, 701, -w^5 + w^4 + 5*w^3 - 5*w - 5],\
[701, 701, -w^5 + w^4 + 6*w^3 - 2*w^2 - 9*w + 2],\
[727, 727, -w^5 + 5*w^4 - w^3 - 16*w^2 + 4*w + 8],\
[727, 727, w^5 - w^4 - 4*w^3 - 2*w^2 + 4*w + 4],\
[727, 727, -3*w^5 + 9*w^4 + 5*w^3 - 22*w^2 + 2*w + 7],\
[727, 727, -w^5 + 2*w^4 + 3*w^3 - 5*w^2 + 5],\
[727, 727, -5*w^5 + 11*w^4 + 16*w^3 - 24*w^2 - 10*w + 6],\
[727, 727, 4*w^5 - 8*w^4 - 14*w^3 + 17*w^2 + 7*w - 4],\
[743, 743, 5*w^5 - 11*w^4 - 16*w^3 + 26*w^2 + 6*w - 8],\
[743, 743, -4*w^5 + 7*w^4 + 16*w^3 - 14*w^2 - 12*w + 1],\
[743, 743, -4*w^5 + 9*w^4 + 14*w^3 - 23*w^2 - 10*w + 7],\
[743, 743, w^5 - 3*w^4 + 6*w^2 - 6*w - 2],\
[757, 757, -w^5 + 7*w^3 + 3*w^2 - 7*w - 6],\
[757, 757, 5*w^5 - 11*w^4 - 16*w^3 + 24*w^2 + 11*w - 5],\
[769, 769, -3*w^5 + 4*w^4 + 14*w^3 - 6*w^2 - 12*w + 1],\
[769, 769, 4*w^5 - 7*w^4 - 17*w^3 + 16*w^2 + 14*w - 5],\
[797, 797, -5*w^5 + 12*w^4 + 14*w^3 - 27*w^2 - 7*w + 7],\
[797, 797, 2*w^5 - 7*w^4 - w^3 + 17*w^2 - 4*w - 7],\
[811, 811, 5*w^5 - 13*w^4 - 13*w^3 + 33*w^2 + 3*w - 10],\
[811, 811, -4*w^5 + 10*w^4 + 9*w^3 - 22*w^2 + w + 6],\
[841, 29, 3*w^5 - 6*w^4 - 9*w^3 + 10*w^2 + 4*w - 1],\
[841, 29, -w^5 + w^4 + 4*w^3 + 3*w^2 - 3*w - 7],\
[853, 853, -4*w^5 + 9*w^4 + 12*w^3 - 21*w^2 - 4*w + 5],\
[853, 853, -3*w^5 + 6*w^4 + 10*w^3 - 13*w^2 - 4*w + 2],\
[853, 853, -w^5 + w^4 + 5*w^3 + w^2 - 4*w - 6],\
[853, 853, -3*w^5 + 7*w^4 + 8*w^3 - 16*w^2 - w + 7],\
[853, 853, -4*w^5 + 10*w^4 + 10*w^3 - 24*w^2 - w + 10],\
[853, 853, -w^4 + 3*w^3 + 3*w^2 - 8*w - 2],\
[883, 883, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - 4*w + 6],\
[883, 883, -w^5 + 5*w^4 - 3*w^3 - 12*w^2 + 9*w + 3],\
[883, 883, 5*w^5 - 12*w^4 - 14*w^3 + 27*w^2 + 7*w - 6],\
[883, 883, 2*w^5 - 6*w^4 - 3*w^3 + 16*w^2 - 3*w - 9],\
[937, 937, 5*w^5 - 11*w^4 - 16*w^3 + 26*w^2 + 8*w - 7],\
[937, 937, -w^5 + 2*w^4 + 4*w^3 - 3*w^2 - 6*w],\
[937, 937, 2*w^5 - 6*w^4 - 4*w^3 + 18*w^2 - 3*w - 10],\
[937, 937, 2*w^5 - 7*w^4 - 3*w^3 + 22*w^2 - 2*w - 10],\
[953, 953, 4*w^5 - 7*w^4 - 16*w^3 + 14*w^2 + 13*w - 3],\
[953, 953, 5*w^5 - 11*w^4 - 15*w^3 + 23*w^2 + 7*w - 3],\
[953, 953, w^5 + w^4 - 9*w^3 - 6*w^2 + 12*w + 3],\
[953, 953, -3*w^5 + 7*w^4 + 10*w^3 - 17*w^2 - 9*w + 5],\
[953, 953, w^5 - 4*w^4 + w^3 + 8*w^2 - 5*w + 1],\
[953, 953, -2*w^5 + 6*w^4 + 3*w^3 - 15*w^2 + 4*w + 7],\
[967, 967, 4*w^5 - 10*w^4 - 11*w^3 + 26*w^2 + w - 9],\
[967, 967, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 3*w - 8]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 33*x^4 + 16*x^3 + 292*x^2 - 248*x - 272
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, e, 1/10*e^5 + 3/10*e^4 - 19/10*e^3 - 51/10*e^2 + 32/5*e + 72/5, 1/10*e^5 + 3/10*e^4 - 19/10*e^3 - 51/10*e^2 + 32/5*e + 72/5, 1/40*e^5 + 1/5*e^4 - 29/40*e^3 - 17/5*e^2 + 38/5*e + 28/5, 1/40*e^5 + 1/5*e^4 - 29/40*e^3 - 17/5*e^2 + 38/5*e + 28/5, -3/8*e^5 - 3/2*e^4 + 59/8*e^3 + 47/2*e^2 - 69/2*e - 33, -3/8*e^5 - 3/2*e^4 + 59/8*e^3 + 47/2*e^2 - 69/2*e - 33, -1, -1/5*e^5 - 3/5*e^4 + 19/5*e^3 + 46/5*e^2 - 74/5*e - 44/5, 3/8*e^5 + 5/4*e^4 - 55/8*e^3 - 73/4*e^2 + 24*e + 24, -7/40*e^5 - 3/20*e^4 + 143/40*e^3 + 31/20*e^2 - 137/10*e - 16/5, 3/8*e^5 + 5/4*e^4 - 55/8*e^3 - 73/4*e^2 + 24*e + 24, -7/40*e^5 - 3/20*e^4 + 143/40*e^3 + 31/20*e^2 - 137/10*e - 16/5, -2/5*e^5 - 6/5*e^4 + 43/5*e^3 + 92/5*e^2 - 213/5*e - 128/5, 1/10*e^5 + 3/10*e^4 - 29/10*e^3 - 51/10*e^2 + 107/5*e + 22/5, -2/5*e^5 - 6/5*e^4 + 43/5*e^3 + 92/5*e^2 - 213/5*e - 128/5, 1/10*e^5 + 3/10*e^4 - 29/10*e^3 - 51/10*e^2 + 107/5*e + 22/5, 1/10*e^5 + 4/5*e^4 - 19/10*e^3 - 68/5*e^2 + 57/5*e + 112/5, -3/20*e^5 - 7/10*e^4 + 67/20*e^3 + 99/10*e^2 - 108/5*e + 12/5, -3/20*e^5 - 7/10*e^4 + 67/20*e^3 + 99/10*e^2 - 108/5*e + 12/5, 1/10*e^5 + 4/5*e^4 - 19/10*e^3 - 68/5*e^2 + 57/5*e + 112/5, 7/40*e^5 + 13/20*e^4 - 103/40*e^3 - 181/20*e^2 + 27/10*e + 56/5, -19/40*e^5 - 41/20*e^4 + 371/40*e^3 + 637/20*e^2 - 439/10*e - 202/5, -19/40*e^5 - 41/20*e^4 + 371/40*e^3 + 637/20*e^2 - 439/10*e - 202/5, 7/40*e^5 + 13/20*e^4 - 103/40*e^3 - 181/20*e^2 + 27/10*e + 56/5, -3/10*e^5 - 7/5*e^4 + 57/10*e^3 + 109/5*e^2 - 121/5*e - 146/5, -3/10*e^5 - 7/5*e^4 + 57/10*e^3 + 109/5*e^2 - 121/5*e - 146/5, 3/8*e^5 + 5/4*e^4 - 63/8*e^3 - 73/4*e^2 + 39*e + 14, 3/8*e^5 + 5/4*e^4 - 63/8*e^3 - 73/4*e^2 + 39*e + 14, 19/40*e^5 + 13/10*e^4 - 371/40*e^3 - 191/10*e^2 + 379/10*e + 147/5, 19/40*e^5 + 13/10*e^4 - 371/40*e^3 - 191/10*e^2 + 379/10*e + 147/5, 1/4*e^5 + 3/2*e^4 - 21/4*e^3 - 51/2*e^2 + 30*e + 44, 1/4*e^5 + 3/2*e^4 - 21/4*e^3 - 51/2*e^2 + 30*e + 44, -1/5*e^5 - 11/10*e^4 + 14/5*e^3 + 167/10*e^2 - 29/5*e - 124/5, -1/5*e^5 - 11/10*e^4 + 14/5*e^3 + 167/10*e^2 - 29/5*e - 124/5, 3/40*e^5 + 7/20*e^4 - 67/40*e^3 - 79/20*e^2 + 123/10*e + 4/5, -1/40*e^5 - 9/20*e^4 + 29/40*e^3 + 173/20*e^2 - 38/5*e - 28/5, 1/5*e^5 + 3/5*e^4 - 19/5*e^3 - 31/5*e^2 + 74/5*e - 36/5, -23/40*e^5 - 47/20*e^4 + 467/40*e^3 + 719/20*e^2 - 289/5*e - 194/5, -23/40*e^5 - 47/20*e^4 + 467/40*e^3 + 719/20*e^2 - 289/5*e - 194/5, 5/8*e^5 + 2*e^4 - 105/8*e^3 - 31*e^2 + 65*e + 46, 5/8*e^5 + 2*e^4 - 105/8*e^3 - 31*e^2 + 65*e + 46, -1/40*e^5 - 1/5*e^4 - 11/40*e^3 + 22/5*e^2 + 37/5*e - 128/5, -1/40*e^5 - 1/5*e^4 - 11/40*e^3 + 22/5*e^2 + 37/5*e - 128/5, 17/20*e^5 + 23/10*e^4 - 333/20*e^3 - 331/10*e^2 + 347/5*e + 202/5, 17/20*e^5 + 23/10*e^4 - 333/20*e^3 - 331/10*e^2 + 347/5*e + 202/5, 13/40*e^5 + 37/20*e^4 - 297/40*e^3 - 629/20*e^2 + 234/5*e + 254/5, 19/40*e^5 + 21/20*e^4 - 411/40*e^3 - 317/20*e^2 + 469/10*e + 132/5, 13/40*e^5 + 37/20*e^4 - 297/40*e^3 - 629/20*e^2 + 234/5*e + 254/5, 19/40*e^5 + 21/20*e^4 - 411/40*e^3 - 317/20*e^2 + 469/10*e + 132/5, -7/10*e^5 - 8/5*e^4 + 143/10*e^3 + 116/5*e^2 - 319/5*e - 194/5, -7/10*e^5 - 8/5*e^4 + 143/10*e^3 + 116/5*e^2 - 319/5*e - 194/5, 13/40*e^5 + 7/20*e^4 - 257/40*e^3 - 39/20*e^2 + 129/5*e - 76/5, 13/40*e^5 + 7/20*e^4 - 257/40*e^3 - 39/20*e^2 + 129/5*e - 76/5, -1/10*e^5 + 1/5*e^4 + 19/10*e^3 - 27/5*e^2 - 17/5*e + 78/5, 3/5*e^5 + 14/5*e^4 - 57/5*e^3 - 208/5*e^2 + 272/5*e + 142/5, 3/5*e^5 + 14/5*e^4 - 57/5*e^3 - 208/5*e^2 + 272/5*e + 142/5, -1/10*e^5 + 1/5*e^4 + 19/10*e^3 - 27/5*e^2 - 17/5*e + 78/5, 9/10*e^5 + 16/5*e^4 - 171/10*e^3 - 242/5*e^2 + 343/5*e + 318/5, 9/10*e^5 + 16/5*e^4 - 171/10*e^3 - 242/5*e^2 + 343/5*e + 318/5, 19/40*e^5 + 9/5*e^4 - 371/40*e^3 - 133/5*e^2 + 399/10*e + 117/5, 19/40*e^5 + 9/5*e^4 - 371/40*e^3 - 133/5*e^2 + 399/10*e + 117/5, -7/10*e^5 - 13/5*e^4 + 133/10*e^3 + 191/5*e^2 - 299/5*e - 134/5, -7/10*e^5 - 13/5*e^4 + 133/10*e^3 + 191/5*e^2 - 299/5*e - 134/5, 7/40*e^5 + 9/10*e^4 - 63/40*e^3 - 133/10*e^2 - 123/10*e + 111/5, 7/40*e^5 + 9/10*e^4 - 63/40*e^3 - 133/10*e^2 - 123/10*e + 111/5, -9/40*e^5 - 3/10*e^4 + 261/40*e^3 + 41/10*e^2 - 212/5*e + 28/5, -9/40*e^5 - 3/10*e^4 + 261/40*e^3 + 41/10*e^2 - 212/5*e + 28/5, 13/40*e^5 + 27/20*e^4 - 257/40*e^3 - 379/20*e^2 + 179/5*e + 4/5, 13/40*e^5 + 27/20*e^4 - 257/40*e^3 - 379/20*e^2 + 179/5*e + 4/5, -3/4*e^5 - 7/2*e^4 + 63/4*e^3 + 115/2*e^2 - 88*e - 98, -1/4*e^5 - e^4 + 25/4*e^3 + 17*e^2 - 40*e - 16, -1/4*e^5 - e^4 + 25/4*e^3 + 17*e^2 - 40*e - 16, -3/4*e^5 - 7/2*e^4 + 63/4*e^3 + 115/2*e^2 - 88*e - 98, 9/40*e^5 + 4/5*e^4 - 121/40*e^3 - 58/5*e^2 - 31/10*e + 97/5, 29/40*e^5 + 51/20*e^4 - 601/40*e^3 - 787/20*e^2 + 362/5*e + 322/5, 9/40*e^5 + 4/5*e^4 - 121/40*e^3 - 58/5*e^2 - 31/10*e + 97/5, 29/40*e^5 + 51/20*e^4 - 601/40*e^3 - 787/20*e^2 + 362/5*e + 322/5, -9/40*e^5 + 1/5*e^4 + 161/40*e^3 - 22/5*e^2 - 39/10*e + 23/5, -9/40*e^5 + 1/5*e^4 + 161/40*e^3 - 22/5*e^2 - 39/10*e + 23/5, 3/10*e^5 + 9/10*e^4 - 47/10*e^3 - 133/10*e^2 + 11/5*e + 116/5, 3/10*e^5 + 9/10*e^4 - 47/10*e^3 - 133/10*e^2 + 11/5*e + 116/5, 3/40*e^5 + 3/5*e^4 - 47/40*e^3 - 41/5*e^2 + 29/5*e - 36/5, 3/40*e^5 + 3/5*e^4 - 47/40*e^3 - 41/5*e^2 + 29/5*e - 36/5, -33/40*e^5 - 31/10*e^4 + 717/40*e^3 + 477/10*e^2 - 504/5*e - 264/5, -33/40*e^5 - 31/10*e^4 + 717/40*e^3 + 477/10*e^2 - 504/5*e - 264/5, 21/40*e^5 + 7/10*e^4 - 429/40*e^3 - 99/10*e^2 + 391/10*e + 133/5, 21/40*e^5 + 7/10*e^4 - 429/40*e^3 - 99/10*e^2 + 391/10*e + 133/5, -37/40*e^5 - 63/20*e^4 + 813/40*e^3 + 951/20*e^2 - 1167/10*e - 236/5, -37/40*e^5 - 63/20*e^4 + 813/40*e^3 + 951/20*e^2 - 1167/10*e - 236/5, -17/40*e^5 - 19/10*e^4 + 393/40*e^3 + 303/10*e^2 - 667/10*e - 181/5, -17/40*e^5 - 19/10*e^4 + 393/40*e^3 + 303/10*e^2 - 667/10*e - 181/5, 9/20*e^5 + 8/5*e^4 - 201/20*e^3 - 126/5*e^2 + 279/5*e + 134/5, 9/20*e^5 + 8/5*e^4 - 201/20*e^3 - 126/5*e^2 + 279/5*e + 134/5, -11/20*e^5 - 29/10*e^4 + 199/20*e^3 + 473/10*e^2 - 226/5*e - 446/5, 19/20*e^5 + 31/10*e^4 - 371/20*e^3 - 447/10*e^2 + 374/5*e + 174/5, -11/20*e^5 - 29/10*e^4 + 199/20*e^3 + 473/10*e^2 - 226/5*e - 446/5, 19/20*e^5 + 31/10*e^4 - 371/20*e^3 - 447/10*e^2 + 374/5*e + 174/5, -17/40*e^5 - 19/10*e^4 + 373/40*e^3 + 333/10*e^2 - 251/5*e - 316/5, 17/40*e^5 + 12/5*e^4 - 393/40*e^3 - 184/5*e^2 + 707/10*e + 61/5, -17/40*e^5 - 19/10*e^4 + 373/40*e^3 + 333/10*e^2 - 251/5*e - 316/5, 17/40*e^5 + 12/5*e^4 - 393/40*e^3 - 184/5*e^2 + 707/10*e + 61/5, -29/40*e^5 - 61/20*e^4 + 501/40*e^3 + 957/20*e^2 - 379/10*e - 442/5, -9/40*e^5 - 3/10*e^4 + 261/40*e^3 + 31/10*e^2 - 252/5*e + 78/5, -9/40*e^5 - 3/10*e^4 + 261/40*e^3 + 31/10*e^2 - 252/5*e + 78/5, -29/40*e^5 - 61/20*e^4 + 501/40*e^3 + 957/20*e^2 - 379/10*e - 442/5, -13/20*e^5 - 11/5*e^4 + 257/20*e^3 + 177/5*e^2 - 288/5*e - 388/5, -13/20*e^5 - 11/5*e^4 + 257/20*e^3 + 177/5*e^2 - 288/5*e - 388/5, -39/40*e^5 - 61/20*e^4 + 671/40*e^3 + 897/20*e^2 - 449/10*e - 402/5, -39/40*e^5 - 61/20*e^4 + 671/40*e^3 + 897/20*e^2 - 449/10*e - 402/5, 57/40*e^5 + 27/5*e^4 - 1113/40*e^3 - 429/5*e^2 + 1277/10*e + 721/5, -1/40*e^5 + 1/20*e^4 + 29/40*e^3 - 17/20*e^2 - 18/5*e - 18/5, -1/40*e^5 + 1/20*e^4 + 29/40*e^3 - 17/20*e^2 - 18/5*e - 18/5, 57/40*e^5 + 27/5*e^4 - 1113/40*e^3 - 429/5*e^2 + 1277/10*e + 721/5, -1/8*e^5 - 1/2*e^4 + 21/8*e^3 + 13/2*e^2 - 19*e + 2, 17/40*e^5 + 7/5*e^4 - 313/40*e^3 - 104/5*e^2 + 287/10*e + 131/5, 17/40*e^5 + 7/5*e^4 - 313/40*e^3 - 104/5*e^2 + 287/10*e + 131/5, -1/8*e^5 - 1/2*e^4 + 21/8*e^3 + 13/2*e^2 - 19*e + 2, 19/20*e^5 + 13/5*e^4 - 371/20*e^3 - 211/5*e^2 + 349/5*e + 494/5, -3/20*e^5 - 6/5*e^4 + 67/20*e^3 + 92/5*e^2 - 148/5*e - 68/5, 19/20*e^5 + 13/5*e^4 - 371/20*e^3 - 211/5*e^2 + 349/5*e + 494/5, 2/5*e^5 + 7/10*e^4 - 38/5*e^3 - 59/10*e^2 + 118/5*e - 162/5, -3/20*e^5 - 6/5*e^4 + 67/20*e^3 + 92/5*e^2 - 148/5*e - 68/5, 2/5*e^5 + 7/10*e^4 - 38/5*e^3 - 59/10*e^2 + 118/5*e - 162/5, -31/40*e^5 - 49/20*e^4 + 619/40*e^3 + 753/20*e^2 - 343/5*e - 178/5, -23/40*e^5 - 27/20*e^4 + 447/40*e^3 + 339/20*e^2 - 493/10*e - 34/5, -23/40*e^5 - 27/20*e^4 + 447/40*e^3 + 339/20*e^2 - 493/10*e - 34/5, -31/40*e^5 - 49/20*e^4 + 619/40*e^3 + 753/20*e^2 - 343/5*e - 178/5, -9/8*e^5 - 4*e^4 + 185/8*e^3 + 62*e^2 - 233/2*e - 77, -9/8*e^5 - 4*e^4 + 185/8*e^3 + 62*e^2 - 233/2*e - 77, -7/20*e^5 - 4/5*e^4 + 143/20*e^3 + 58/5*e^2 - 147/5*e - 52/5, -7/20*e^5 - 4/5*e^4 + 143/20*e^3 + 58/5*e^2 - 147/5*e - 52/5, 11/10*e^5 + 19/5*e^4 - 229/10*e^3 - 283/5*e^2 + 567/5*e + 372/5, 11/10*e^5 + 19/5*e^4 - 229/10*e^3 - 283/5*e^2 + 567/5*e + 372/5, -1/20*e^5 - 7/5*e^4 - 31/20*e^3 + 109/5*e^2 + 104/5*e - 176/5, -1/20*e^5 - 7/5*e^4 - 31/20*e^3 + 109/5*e^2 + 104/5*e - 176/5, 1/2*e^5 + e^4 - 21/2*e^3 - 14*e^2 + 52*e + 42, 1/2*e^5 + 3*e^4 - 17/2*e^3 - 48*e^2 + 30*e + 94, 1/4*e^5 + 3/2*e^4 - 17/4*e^3 - 51/2*e^2 + 17*e + 46, 1/2*e^5 + 5/2*e^4 - 25/2*e^3 - 81/2*e^2 + 89*e + 44, -19/20*e^5 - 31/10*e^4 + 391/20*e^3 + 467/10*e^2 - 499/5*e - 324/5, 1/4*e^5 + 3/2*e^4 - 17/4*e^3 - 51/2*e^2 + 17*e + 46, 1/2*e^5 + 5/2*e^4 - 25/2*e^3 - 81/2*e^2 + 89*e + 44, -19/20*e^5 - 31/10*e^4 + 391/20*e^3 + 467/10*e^2 - 499/5*e - 324/5, -1/8*e^5 - 3/4*e^4 + 25/8*e^3 + 39/4*e^2 - 43/2*e + 14, -1/8*e^5 - 3/4*e^4 + 25/8*e^3 + 39/4*e^2 - 43/2*e + 14, -33/40*e^5 - 31/10*e^4 + 557/40*e^3 + 457/10*e^2 - 174/5*e - 334/5, -33/40*e^5 - 31/10*e^4 + 557/40*e^3 + 457/10*e^2 - 174/5*e - 334/5, 1/20*e^5 + 19/10*e^4 - 9/20*e^3 - 283/10*e^2 + 71/5*e - 4/5, 2*e^5 + 13/2*e^4 - 38*e^3 - 193/2*e^2 + 150*e + 122, 2*e^5 + 13/2*e^4 - 38*e^3 - 193/2*e^2 + 150*e + 122, 1/20*e^5 + 19/10*e^4 - 9/20*e^3 - 283/10*e^2 + 71/5*e - 4/5, -19/40*e^5 - 41/20*e^4 + 371/40*e^3 + 717/20*e^2 - 439/10*e - 422/5, -1/40*e^5 + 3/10*e^4 - 11/40*e^3 - 41/10*e^2 + 37/5*e - 128/5, 7/8*e^5 + 3*e^4 - 123/8*e^3 - 44*e^2 + 44*e + 82, 7/8*e^5 + 3*e^4 - 123/8*e^3 - 44*e^2 + 44*e + 82, -19/40*e^5 - 41/20*e^4 + 371/40*e^3 + 717/20*e^2 - 439/10*e - 422/5, -1/40*e^5 + 3/10*e^4 - 11/40*e^3 - 41/10*e^2 + 37/5*e - 128/5, 7/8*e^5 + 5*e^4 - 131/8*e^3 - 80*e^2 + 77*e + 102, 7/8*e^5 + 5*e^4 - 131/8*e^3 - 80*e^2 + 77*e + 102]
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^5 - 4*w^4 + 11*w^2 - 3*w - 4])] = 1

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