/*
  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([44, 0, -14, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([25, 5, 1/2*w^2 - 1])

primes_array = [
[4, 2, -1/2*w^3 + w^2 + 4*w - 8],\
[11, 11, 1/2*w^3 - 3/2*w^2 - 4*w + 11],\
[11, 11, -1/2*w^2 - w + 2],\
[11, 11, -1/2*w^2 + w + 2],\
[19, 19, 1/2*w^3 - 1/2*w^2 - 4*w + 5],\
[19, 19, 1/2*w^3 + w^2 - 4*w - 9],\
[19, 19, 1/2*w^3 - w^2 - 4*w + 9],\
[19, 19, 1/2*w^3 + 1/2*w^2 - 4*w - 5],\
[25, 5, 1/2*w^2 - 1],\
[29, 29, 1/2*w^3 - 4*w - 1],\
[29, 29, -1/2*w^3 + 4*w - 1],\
[31, 31, -w - 1],\
[31, 31, w - 1],\
[41, 41, 1/2*w^3 + 1/2*w^2 - 4*w - 2],\
[41, 41, -1/2*w^3 + 1/2*w^2 + 4*w - 2],\
[49, 7, -1/2*w^3 + 1/2*w^2 + 5*w - 7],\
[49, 7, 3/2*w^3 - 7/2*w^2 - 13*w + 29],\
[59, 59, -1/2*w^3 - 3/2*w^2 + 3*w + 10],\
[59, 59, 1/2*w^3 - 3/2*w^2 - 3*w + 10],\
[61, 61, 1/2*w^2 + w - 6],\
[61, 61, 1/2*w^2 - w - 6],\
[71, 71, w^3 - 5/2*w^2 - 8*w + 20],\
[71, 71, -w^3 + 5/2*w^2 + 10*w - 24],\
[81, 3, -3],\
[101, 101, -1/2*w^3 + 1/2*w^2 + 4*w - 1],\
[101, 101, 1/2*w^3 + 1/2*w^2 - 4*w - 1],\
[109, 109, 3/2*w^2 + w - 12],\
[109, 109, 3/2*w^2 - w - 12],\
[149, 149, 1/2*w^3 + 2*w^2 - 4*w - 15],\
[149, 149, -1/2*w^3 + 2*w^2 + 4*w - 15],\
[151, 151, 1/2*w^3 - 1/2*w^2 - 4*w + 8],\
[151, 151, -w^3 + 5/2*w^2 + 8*w - 18],\
[151, 151, -w^3 + 3/2*w^2 + 10*w - 18],\
[151, 151, -1/2*w^3 - 1/2*w^2 + 4*w + 8],\
[179, 179, 1/2*w^3 + w^2 - 4*w - 5],\
[179, 179, -1/2*w^3 + w^2 + 4*w - 5],\
[181, 181, 1/2*w^3 - 5*w - 3],\
[181, 181, w^3 - 1/2*w^2 - 7*w - 1],\
[181, 181, -1/2*w^3 - 5/2*w^2 + 4*w + 15],\
[181, 181, 1/2*w^3 - 5*w + 3],\
[191, 191, w^3 - 2*w^2 - 7*w + 13],\
[191, 191, -w^3 - 2*w^2 + 7*w + 13],\
[199, 199, -5/2*w^2 - 2*w + 18],\
[199, 199, -5/2*w^2 + 2*w + 18],\
[241, 241, -3/2*w^3 + 7/2*w^2 + 14*w - 30],\
[241, 241, -3/2*w^3 + 5/2*w^2 + 16*w - 30],\
[251, 251, 3/2*w^2 - w - 13],\
[251, 251, 3/2*w^2 + w - 13],\
[269, 269, 1/2*w^3 + 1/2*w^2 - 3*w - 10],\
[269, 269, -w^3 + 1/2*w^2 + 7*w - 8],\
[269, 269, w^3 + 1/2*w^2 - 7*w - 8],\
[269, 269, -1/2*w^3 + 1/2*w^2 + 3*w - 10],\
[271, 271, -w^3 + 8*w + 5],\
[271, 271, -2*w^2 + 2*w + 15],\
[271, 271, 2*w^2 + 2*w - 15],\
[271, 271, w^3 - 8*w + 5],\
[281, 281, -2*w + 3],\
[281, 281, w^3 - 2*w^2 - 12*w + 25],\
[311, 311, 1/2*w^3 + 5/2*w^2 - 3*w - 17],\
[311, 311, -1/2*w^3 + 5/2*w^2 + 3*w - 17],\
[331, 331, -1/2*w^3 + 3/2*w^2 + 5*w - 10],\
[331, 331, 1/2*w^3 + 3/2*w^2 - 5*w - 10],\
[349, 349, -1/2*w^2 + 3*w - 3],\
[349, 349, -w^3 + 5/2*w^2 + 11*w - 25],\
[379, 379, 5/2*w^2 - w - 21],\
[379, 379, 5/2*w^2 + w - 21],\
[389, 389, 3/2*w^2 - w - 14],\
[389, 389, 1/2*w^3 - 5/2*w^2 - 3*w + 16],\
[389, 389, -1/2*w^3 - 5/2*w^2 + 3*w + 16],\
[389, 389, 3/2*w^2 + w - 14],\
[409, 409, w^3 + w^2 - 8*w - 7],\
[409, 409, -w^3 + w^2 + 8*w - 7],\
[419, 419, 3/2*w^3 - 5/2*w^2 - 15*w + 28],\
[419, 419, 3/2*w^3 - 7/2*w^2 - 13*w + 28],\
[439, 439, 1/2*w^2 + 2*w - 9],\
[439, 439, -3/2*w^2 + 2*w + 6],\
[439, 439, -3/2*w^2 - 2*w + 6],\
[439, 439, 1/2*w^2 - 2*w - 9],\
[449, 449, -w^3 + 1/2*w^2 + 6*w - 1],\
[449, 449, 1/2*w^2 + 2*w - 5],\
[449, 449, 1/2*w^2 - 2*w - 5],\
[449, 449, w^3 + 1/2*w^2 - 6*w - 1],\
[461, 461, w^3 + 3/2*w^2 - 7*w - 9],\
[461, 461, -w^3 + 3/2*w^2 + 7*w - 9],\
[491, 491, -1/2*w^3 - 1/2*w^2 + 6*w + 7],\
[491, 491, -5/2*w^2 + w + 16],\
[491, 491, 5/2*w^2 + w - 16],\
[491, 491, 1/2*w^3 - 1/2*w^2 - 6*w + 7],\
[499, 499, -1/2*w^3 + 5/2*w^2 + 4*w - 19],\
[499, 499, 1/2*w^3 + 5/2*w^2 - 4*w - 19],\
[541, 541, -1/2*w^3 + 3/2*w^2 + 4*w - 7],\
[541, 541, 1/2*w^3 + 3/2*w^2 - 4*w - 7],\
[569, 569, 1/2*w^2 + 2*w - 2],\
[569, 569, 1/2*w^2 - 2*w - 2],\
[571, 571, -2*w^3 + 9/2*w^2 + 17*w - 39],\
[571, 571, 1/2*w^3 - 1/2*w^2 - 5*w - 2],\
[571, 571, -1/2*w^3 - 1/2*w^2 + 5*w - 2],\
[571, 571, w^3 - 5/2*w^2 - 11*w + 27],\
[599, 599, -w^3 + 2*w^2 + 8*w - 13],\
[599, 599, w^3 + 2*w^2 - 8*w - 13],\
[601, 601, 1/2*w^2 + 2*w - 4],\
[601, 601, 1/2*w^2 - 2*w - 4],\
[619, 619, -1/2*w^3 + 2*w^2 + 6*w - 13],\
[619, 619, 1/2*w^3 + 2*w^2 - 6*w - 13],\
[631, 631, -w^3 - 1/2*w^2 + 6*w - 2],\
[631, 631, w^3 - 1/2*w^2 - 6*w - 2],\
[641, 641, w^3 - 8*w - 1],\
[641, 641, -1/2*w^3 - 1/2*w^2 + 5*w - 1],\
[641, 641, 1/2*w^3 - 1/2*w^2 - 5*w - 1],\
[641, 641, w^3 - 8*w + 1],\
[661, 661, -1/2*w^3 + 7/2*w^2 + 2*w - 25],\
[661, 661, 3/2*w^3 - 9/2*w^2 - 11*w + 32],\
[661, 661, -5/2*w^3 + 13/2*w^2 + 23*w - 56],\
[661, 661, 1/2*w^3 + 7/2*w^2 - 2*w - 25],\
[691, 691, 1/2*w^3 + 7/2*w^2 - 3*w - 28],\
[691, 691, -1/2*w^3 + 7/2*w^2 + 3*w - 28],\
[701, 701, -1/2*w^3 + 1/2*w^2 + 5*w - 10],\
[701, 701, 3/2*w^3 - 5/2*w^2 - 17*w + 34],\
[709, 709, 1/2*w^3 - 5/2*w^2 - 6*w + 17],\
[709, 709, w^3 + 5/2*w^2 - 7*w - 14],\
[709, 709, -w^3 + 5/2*w^2 + 7*w - 14],\
[709, 709, -1/2*w^3 - 5/2*w^2 + 6*w + 17],\
[719, 719, -w^3 + 7/2*w^2 + 8*w - 23],\
[719, 719, w^3 + 7/2*w^2 - 8*w - 23],\
[751, 751, 7/2*w^2 + 2*w - 27],\
[751, 751, 7/2*w^2 - 2*w - 27],\
[761, 761, -1/2*w^3 + 3/2*w^2 + 3*w - 13],\
[761, 761, 1/2*w^3 + 3/2*w^2 - 3*w - 13],\
[769, 769, -w^3 + 7/2*w^2 + 8*w - 25],\
[769, 769, w^3 + 7/2*w^2 - 8*w - 25],\
[809, 809, 2*w^3 - 7/2*w^2 - 20*w + 40],\
[809, 809, -1/2*w^2 + 2*w - 4],\
[811, 811, -1/2*w^2 - 3*w + 8],\
[811, 811, 1/2*w^3 + 3/2*w^2 - 3*w - 18],\
[811, 811, -1/2*w^3 + 3/2*w^2 + 3*w - 18],\
[811, 811, 1/2*w^2 - 3*w - 8],\
[821, 821, 3/2*w^3 - 7/2*w^2 - 16*w + 37],\
[821, 821, -3/2*w^3 + 7/2*w^2 + 12*w - 29],\
[839, 839, 3*w^2 - 2*w - 23],\
[839, 839, 3*w^2 + 2*w - 23],\
[841, 29, -5/2*w^2 + 16],\
[859, 859, 5/2*w^2 + 3*w - 16],\
[859, 859, 5/2*w^2 - 3*w - 16],\
[911, 911, 3*w^2 - 2*w - 17],\
[911, 911, 3*w^2 + 2*w - 17],\
[919, 919, 3*w^2 - w - 23],\
[919, 919, -2*w^2 + 3*w + 15],\
[919, 919, -2*w^2 - 3*w + 15],\
[919, 919, 3*w^2 + w - 23],\
[941, 941, 3/2*w^2 - 3*w - 2],\
[941, 941, 2*w^3 - 11/2*w^2 - 17*w + 42],\
[961, 31, -w^2 + 13],\
[971, 971, 1/2*w^3 + 1/2*w^2 - 6*w - 5],\
[971, 971, -1/2*w^3 + 1/2*w^2 + 6*w - 5],\
[991, 991, w^3 + 3/2*w^2 - 8*w - 8],\
[991, 991, -w^3 + 3/2*w^2 + 8*w - 8]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - 20
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, -2, 0, 0, 0, 0, 0, 0, 1, -e, e, 2*e, -2*e, 2*e, -2*e, -e, e, 0, 0, -2, -2, -2, -2, -2, -2*e, 2*e, 10, 10, 10, 10, -2, 2*e, -2*e, -2, 4*e, -4*e, -2*e, 2*e, -2*e, 2*e, 2*e, -2*e, -20, -20, -6*e, 6*e, 2, 2, -10, -30, -30, -10, 6*e, 22, 22, -6*e, -4*e, 4*e, -18, -18, 0, 0, e, -e, -20, -20, 30, -10, -10, 30, 5*e, -5*e, 6*e, -6*e, 20, 6*e, -6*e, 20, -e, -5*e, 5*e, e, -4*e, 4*e, 8*e, -2, -2, -8*e, -20, -20, -4*e, 4*e, 7*e, -7*e, -18, 0, 0, -18, 2*e, -2*e, -8*e, 8*e, 6*e, -6*e, -2, -2, -4*e, -2*e, 2*e, 4*e, -22, -18, -18, -22, -2, -2, 2, 2, -7*e, 7*e, -7*e, 7*e, 4*e, -4*e, 42, 42, 18, 18, 10, 10, -50, -50, 8*e, 38, 38, -8*e, 2, 2, 20, 20, 38, -10*e, 10*e, 10*e, -10*e, -40, 2*e, -2*e, -40, -10*e, 10*e, -58, 4*e, -4*e, 6*e, -6*e]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([25, 5, 1/2*w^2 - 1])] = -1

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