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

NN = ZF.ideal([7, 7, w + 1])

primes_array = [
[2, 2, -w + 2],\
[4, 2, -w^2 - w + 3],\
[7, 7, w + 1],\
[7, 7, -w + 3],\
[11, 11, -w^2 + 3],\
[17, 17, w + 3],\
[19, 19, w^2 - 7],\
[27, 3, 3],\
[43, 43, -2*w - 5],\
[47, 47, 2*w + 3],\
[53, 53, 3*w^2 + 2*w - 9],\
[59, 59, 2*w^2 + w - 5],\
[61, 61, 3*w - 1],\
[61, 61, 2*w^2 + w - 9],\
[61, 61, 2*w^2 - w - 7],\
[67, 67, -2*w^2 + 13],\
[67, 67, -3*w - 7],\
[73, 73, w^2 + 2*w - 5],\
[79, 79, w - 5],\
[83, 83, -2*w^2 + 4*w + 3],\
[89, 89, w^2 + 2*w - 9],\
[97, 97, -w^2 + 2*w - 3],\
[97, 97, w^2 - 2*w - 7],\
[97, 97, w^2 - 2*w - 5],\
[103, 103, 2*w^2 - 2*w - 9],\
[107, 107, 3*w^2 + 2*w - 11],\
[107, 107, 3*w^2 + 4*w - 3],\
[107, 107, 2*w^2 - 5],\
[109, 109, -3*w^2 + 2*w + 11],\
[113, 113, w^2 + 2*w - 7],\
[121, 11, 2*w^2 - w - 5],\
[125, 5, -5],\
[131, 131, 2*w^2 - 2*w - 3],\
[137, 137, 4*w^2 + 7*w - 5],\
[149, 149, -3*w - 1],\
[149, 149, 5*w - 11],\
[149, 149, 4*w^2 + 3*w - 11],\
[157, 157, -2*w^2 - 6*w - 3],\
[167, 167, 2*w^2 + 3*w - 7],\
[173, 173, 3*w^2 - 11],\
[179, 179, 2*w^2 + 2*w - 9],\
[181, 181, 3*w^2 - 6*w - 1],\
[191, 191, 4*w^2 + w - 15],\
[197, 197, 2*w^2 - 3*w - 7],\
[199, 199, -3*w^2 + 4*w + 9],\
[223, 223, -2*w^2 - 5*w + 1],\
[227, 227, 5*w - 13],\
[233, 233, -w^2 - 2*w - 3],\
[239, 239, -2*w^2 - 4*w + 7],\
[241, 241, -w^2 - 3],\
[257, 257, 2*w^2 + 2*w - 11],\
[263, 263, 2*w^2 + 2*w - 13],\
[263, 263, 4*w^2 - 7*w - 5],\
[263, 263, w - 7],\
[269, 269, -2*w^2 - 5*w + 7],\
[277, 277, 5*w - 7],\
[277, 277, -4*w - 7],\
[277, 277, 3*w^2 - 2*w - 9],\
[281, 281, 2*w^2 - 4*w - 5],\
[283, 283, 3*w^2 + 2*w - 13],\
[289, 17, w^2 - 4*w + 7],\
[293, 293, 6*w - 13],\
[307, 307, 2*w^2 + 3*w - 17],\
[331, 331, -4*w - 1],\
[337, 337, 4*w^2 + w - 21],\
[347, 347, w^2 - 11],\
[349, 349, 4*w^2 + 5*w - 11],\
[353, 353, -w - 7],\
[353, 353, 4*w^2 - 2*w - 15],\
[353, 353, 2*w^2 - 3*w - 13],\
[361, 19, 4*w^2 + 2*w - 17],\
[373, 373, 3*w^2 - 7],\
[379, 379, 7*w^2 + 4*w - 25],\
[389, 389, w^2 - 4*w - 3],\
[389, 389, -5*w^2 - 10*w + 1],\
[389, 389, 5*w^2 + 2*w - 21],\
[397, 397, 2*w^2 - 3*w - 11],\
[401, 401, 4*w^2 + 2*w - 11],\
[419, 419, 2*w - 9],\
[431, 431, 4*w^2 + w - 13],\
[431, 431, -4*w - 5],\
[431, 431, -w^2 - 6*w - 7],\
[433, 433, 4*w^2 - w - 15],\
[433, 433, -4*w - 3],\
[433, 433, w^2 + 4*w - 9],\
[439, 439, -6*w^2 - 3*w + 23],\
[443, 443, -4*w^2 + 4*w + 11],\
[461, 461, 5*w^2 - 4*w - 21],\
[463, 463, 2*w^2 + 3*w - 11],\
[467, 467, 5*w^2 + 10*w - 3],\
[479, 479, -2*w^2 - 6*w - 1],\
[487, 487, -3*w^2 + 8*w + 1],\
[491, 491, 3*w^2 + 2*w - 17],\
[491, 491, 5*w + 9],\
[491, 491, -6*w^2 - 10*w + 5],\
[499, 499, 4*w^2 - 5*w - 13],\
[503, 503, 2*w^2 - 4*w - 7],\
[503, 503, 2*w^2 + 3*w - 15],\
[503, 503, 7*w - 15],\
[509, 509, 4*w^2 - 10*w - 1],\
[523, 523, 6*w^2 + 6*w - 17],\
[541, 541, 6*w^2 + 5*w - 19],\
[547, 547, -4*w^2 - 6*w + 11],\
[593, 593, 2*w^2 + 5*w - 9],\
[593, 593, 4*w^2 + 2*w - 25],\
[593, 593, -w^2 - 2*w - 5],\
[599, 599, 4*w^2 + 2*w - 19],\
[601, 601, 4*w^2 - 13],\
[607, 607, w - 9],\
[619, 619, -5*w - 1],\
[631, 631, 2*w^2 + 2*w - 19],\
[641, 641, w^2 - 4*w - 9],\
[643, 643, 2*w^2 - 5*w - 5],\
[653, 653, w^2 - 4*w - 7],\
[673, 673, 4*w^2 - w - 13],\
[683, 683, -2*w^2 - 8*w - 9],\
[691, 691, 2*w^2 + 4*w - 11],\
[701, 701, 2*w^2 - 4*w - 9],\
[719, 719, 4*w^2 + w - 9],\
[739, 739, 5*w^2 - 2*w - 19],\
[751, 751, 3*w^2 - 4*w - 13],\
[751, 751, w^2 + 6*w - 1],\
[751, 751, w^2 - 13],\
[757, 757, -3*w^2 - 8*w - 1],\
[761, 761, -w - 9],\
[769, 769, 6*w^2 + 3*w - 19],\
[769, 769, -w^2 + 2*w - 7],\
[769, 769, 4*w^2 - 4*w - 9],\
[773, 773, 6*w^2 - 2*w - 25],\
[787, 787, 5*w^2 + 2*w - 15],\
[787, 787, 6*w + 11],\
[787, 787, -5*w - 7],\
[797, 797, 6*w^2 + 2*w - 21],\
[809, 809, w^2 - 6*w - 1],\
[827, 827, 3*w^2 - 6*w - 7],\
[827, 827, 2*w^2 - 4*w - 11],\
[827, 827, -2*w^2 - 3*w - 3],\
[829, 829, 2*w^2 + 4*w - 17],\
[839, 839, 6*w^2 + 13*w - 1],\
[853, 853, -2*w^2 - w - 3],\
[857, 857, 2*w^2 + 4*w - 13],\
[857, 857, 7*w^2 + 6*w - 17],\
[857, 857, 4*w^2 - 7*w - 9],\
[859, 859, 4*w^2 - 7],\
[881, 881, 4*w^2 - w - 11],\
[883, 883, -2*w^2 + 9*w - 13],\
[887, 887, -2*w^2 - 2*w - 3],\
[919, 919, 2*w^2 + 4*w - 15],\
[941, 941, 6*w^2 - 9*w - 11],\
[941, 941, 6*w^2 - 4*w - 29],\
[941, 941, 4*w^2 - 5*w - 3],\
[971, 971, 4*w^2 - 3*w - 9],\
[983, 983, 6*w - 17],\
[983, 983, 3*w^2 - 4*w - 17],\
[983, 983, -2*w^2 + 10*w - 15],\
[991, 991, 4*w^2 - 4*w - 7],\
[997, 997, 5*w^2 - 6*w - 17]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - 3
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e + 2, 1, 2, 2*e, -2*e, 2*e - 4, -2*e + 4, 4*e - 4, 2*e, -2*e - 6, 2*e, 2*e + 2, 4*e + 2, -4, 4*e - 4, 4*e + 2, -2*e + 2, -2*e - 4, -2*e - 12, 2*e - 6, -4, -4, -4*e - 10, -16, -2*e, 2*e, -4*e, 2*e - 4, -2*e + 12, 14, -4*e + 6, -8*e - 6, -2*e + 6, 4*e + 6, -2*e, -10*e + 6, 10*e - 4, 4*e + 12, 0, 4*e, -12*e + 2, 8*e + 12, -8*e + 12, 6*e - 16, 2, 4*e - 12, 2*e + 18, 4*e + 18, 6*e + 8, -6*e + 18, 12, 4*e + 12, -4*e - 6, -4*e + 12, -12*e - 4, 2*e + 26, -6*e - 10, -8*e + 6, -2*e + 20, 12*e - 4, -6*e - 18, -16*e - 4, 12*e + 8, -8*e + 2, -6*e - 12, 8*e + 20, 4*e + 12, 4*e - 12, -4*e - 18, -4*e - 10, 16*e + 8, 12*e + 8, 14*e - 12, -10*e + 6, 6, -2*e + 32, -4*e - 12, 4*e + 24, 0, -16*e + 12, -14*e - 12, -2*e + 2, -10*e + 2, -22, -6*e - 28, 16*e, 16*e + 6, 6*e - 4, -12, 2*e - 12, -18*e + 8, 8*e + 12, -4*e - 24, 10*e + 12, -4, -6*e, -4*e + 12, 8*e - 18, 4*e + 18, -16, 18*e + 2, -6*e - 28, -10*e + 30, 8*e - 30, -8*e - 30, -2*e, -2*e - 10, -18*e - 4, 20, 22*e - 4, -10*e - 18, 12*e - 28, 8*e + 36, -6*e + 38, 14*e, 2*e + 8, 12*e - 6, 16*e, -4*e - 4, -4*e + 8, -6*e + 8, 18*e + 20, -12*e + 14, 8*e - 6, 8*e + 20, -20*e - 16, -18*e + 2, 24*e + 6, -4*e - 4, -12*e + 2, -2*e + 32, 16*e - 6, 16*e + 18, 8*e - 6, 0, -8*e, 12*e + 2, -28*e + 6, 18*e - 10, -18, 22*e + 6, -12*e - 18, 16*e + 8, -6*e + 18, 8*e + 8, 6*e, 2*e + 8, -2*e + 12, -12*e + 6, 16*e + 24, 12*e + 12, 4*e + 36, -8*e + 24, 18*e - 24, -12*e - 16, -46]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([7, 7, w + 1])] = -1

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