/*
  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, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

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

primes_array = [
[5, 5, -w - 1],\
[5, 5, w + 2],\
[7, 7, w + 3],\
[7, 7, -w + 2],\
[7, 7, -w + 1],\
[8, 2, 2],\
[13, 13, -w^2 + w + 4],\
[19, 19, -w^2 + 5],\
[23, 23, -w^2 - w + 3],\
[27, 3, 3],\
[29, 29, w^2 - w - 3],\
[31, 31, w^2 - w - 8],\
[37, 37, -w - 4],\
[43, 43, 2*w^2 - 4*w - 3],\
[47, 47, w^2 - 3],\
[53, 53, 2*w^2 - w - 11],\
[59, 59, w^2 - 2*w - 4],\
[67, 67, w^2 + w - 8],\
[71, 71, w^2 + w - 11],\
[73, 73, -w^2 + 4*w - 2],\
[89, 89, 2*w^2 + w - 12],\
[89, 89, w^2 - 10],\
[89, 89, w - 5],\
[97, 97, w^2 - 2*w - 5],\
[101, 101, 2*w^2 - w - 17],\
[103, 103, -2*w^2 - 2*w + 7],\
[109, 109, w^2 - 3*w - 3],\
[127, 127, 2*w^2 + w - 9],\
[137, 137, 2*w^2 + w - 13],\
[137, 137, -2*w^2 + 3*w + 8],\
[137, 137, w^2 - 2*w - 10],\
[139, 139, 2*w - 7],\
[163, 163, -3*w - 5],\
[163, 163, 2*w^2 - 3*w - 3],\
[163, 163, 2*w^2 + w - 14],\
[169, 13, -w^2 + 5*w - 5],\
[173, 173, w - 6],\
[179, 179, -2*w^2 + 6*w - 3],\
[181, 181, 2*w^2 - w - 9],\
[193, 193, w^2 + 2*w - 6],\
[193, 193, -w^2 - 2*w - 3],\
[193, 193, w^2 + 2*w - 11],\
[229, 229, w^2 - 3*w - 13],\
[233, 233, w^2 + 2*w - 7],\
[241, 241, -w^2 + 2*w - 3],\
[251, 251, 2*w^2 - 2*w - 13],\
[263, 263, -w^2 + 3*w - 4],\
[269, 269, 2*w^2 - 2*w - 5],\
[269, 269, 3*w^2 + w - 26],\
[271, 271, 2*w^2 + w - 7],\
[281, 281, 2*w^2 - 2*w - 15],\
[283, 283, 2*w^2 + 2*w - 3],\
[293, 293, w - 7],\
[307, 307, -w^2 - 4*w - 6],\
[311, 311, 2*w^2 + 3*w - 8],\
[313, 313, w^2 - 3*w - 6],\
[347, 347, w^2 + 3*w - 5],\
[353, 353, 3*w^2 - 5*w - 6],\
[359, 359, 2*w^2 + w - 5],\
[361, 19, 2*w^2 - w - 4],\
[367, 367, 4*w^2 - 3*w - 20],\
[367, 367, 2*w^2 + w - 4],\
[367, 367, -w^2 - 3*w - 5],\
[373, 373, w^2 - 3*w - 7],\
[373, 373, 4*w - 3],\
[373, 373, 3*w^2 - 16],\
[379, 379, -w^2 + 4*w - 6],\
[397, 397, -3*w^2 + 4*w + 9],\
[397, 397, -3*w - 10],\
[397, 397, 2*w^2 - 5],\
[401, 401, -3*w^2 + 2*w + 14],\
[409, 409, w^2 - w - 13],\
[419, 419, w^2 - 3*w - 8],\
[419, 419, 3*w^2 - 5*w - 4],\
[419, 419, 3*w^2 + 2*w - 17],\
[421, 421, 4*w^2 + w - 22],\
[421, 421, 2*w^2 - w - 19],\
[421, 421, 3*w^2 - 6*w - 8],\
[431, 431, -w^2 + 5*w - 8],\
[433, 433, w^2 + 3*w - 6],\
[439, 439, -w^2 + 6*w - 7],\
[439, 439, 3*w^2 + 3*w - 14],\
[439, 439, -w^2 - w - 4],\
[457, 457, -w - 8],\
[461, 461, 2*w^2 - 3*w - 11],\
[467, 467, 2*w^2 - 19],\
[467, 467, w^2 - 13],\
[467, 467, 2*w^2 + 2*w - 13],\
[479, 479, 2*w^2 + w - 20],\
[487, 487, 2*w^2 + 2*w - 17],\
[499, 499, 4*w - 5],\
[509, 509, 2*w^2 - 5*w - 6],\
[521, 521, 4*w^2 - 4*w - 17],\
[529, 23, 3*w^2 - 4*w - 8],\
[541, 541, -w^2 - 4*w - 7],\
[547, 547, -3*w^2 + 5*w + 11],\
[557, 557, 3*w^2 - 2*w - 13],\
[557, 557, 3*w^2 - 2*w - 27],\
[557, 557, 2*w^2 - 3*w - 12],\
[563, 563, -w^2 + 6*w - 6],\
[569, 569, 2*w^2 + 4*w - 7],\
[571, 571, w^2 + 3*w - 12],\
[587, 587, 2*w^2 - 3*w - 18],\
[593, 593, 3*w^2 - 4*w - 14],\
[601, 601, 2*w^2 + 3*w - 10],\
[613, 613, 3*w^2 - w - 26],\
[613, 613, 2*w^2 + 5*w - 5],\
[613, 613, 3*w^2 + 2*w - 29],\
[617, 617, -w^2 + 2*w - 5],\
[619, 619, w^2 + 3*w - 9],\
[619, 619, -3*w^2 + 8*w + 5],\
[619, 619, 4*w^2 + 3*w - 17],\
[643, 643, 3*w^2 + 4*w - 12],\
[653, 653, 4*w^2 - 3*w - 19],\
[659, 659, -3*w^2 - 2*w + 25],\
[659, 659, 3*w^2 - 14],\
[659, 659, 3*w^2 + w - 13],\
[661, 661, -3*w^2 + 3*w + 10],\
[677, 677, -4*w + 13],\
[677, 677, 4*w^2 + w - 21],\
[677, 677, 2*w^2 - 3*w - 17],\
[691, 691, w^2 - 5*w - 5],\
[701, 701, -2*w^2 + 9*w - 8],\
[709, 709, -5*w - 6],\
[719, 719, 5*w - 11],\
[727, 727, 4*w^2 - w - 22],\
[739, 739, -2*w^2 + 5*w - 4],\
[743, 743, 2*w^2 + 3*w - 11],\
[757, 757, w^2 - 4*w - 8],\
[757, 757, -5*w - 7],\
[757, 757, w^2 + 2*w - 16],\
[761, 761, 5*w - 4],\
[769, 769, 4*w^2 - 7*w - 7],\
[769, 769, 3*w^2 - w - 13],\
[769, 769, 4*w^2 - 5*w - 18],\
[773, 773, 2*w^2 + 5*w + 5],\
[787, 787, w^2 - 3*w - 17],\
[797, 797, 3*w^2 - 3*w - 19],\
[797, 797, w^2 - 4*w - 13],\
[797, 797, 3*w^2 + 2*w - 24],\
[809, 809, 3*w^2 + 2*w - 20],\
[823, 823, 4*w^2 - 3*w - 25],\
[827, 827, 3*w^2 + 5*w - 10],\
[829, 829, w^2 - 4*w - 9],\
[839, 839, 2*w^2 + 5*w - 6],\
[841, 29, 3*w^2 + 2*w - 10],\
[863, 863, w^2 + 4*w - 20],\
[877, 877, 3*w^2 + 3*w - 7],\
[881, 881, 7*w^2 + w - 42],\
[887, 887, -w^2 + 7*w - 9],\
[907, 907, 3*w^2 - w - 12],\
[911, 911, 3*w^2 - 3*w - 5],\
[919, 919, 5*w^2 - 29],\
[929, 929, w - 10],\
[937, 937, w^2 + 4*w - 15],\
[937, 937, w^2 - 2*w - 16],\
[937, 937, 3*w^2 - w - 27],\
[941, 941, 4*w^2 - 3*w - 18],\
[947, 947, 4*w^2 + w - 20],\
[947, 947, 4*w^2 - 7*w - 13],\
[947, 947, 3*w^2 - 2*w - 28],\
[961, 31, 5*w^2 - 2*w - 28],\
[971, 971, 4*w^2 - 3*w - 26],\
[971, 971, -4*w^2 - 7*w + 3],\
[971, 971, 5*w - 9],\
[977, 977, 5*w^2 - w - 29],\
[983, 983, 2*w^2 + 2*w - 23],\
[991, 991, 2*w^2 + 3*w - 13],\
[997, 997, -w^2 + w - 6]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - x - 7
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, -e - 1, -e, e - 2, -1, 0, 2*e - 2, e - 2, 4, -e + 1, 4*e - 2, 2*e - 6, e - 3, 3*e - 1, 2, -2*e + 2, -e + 7, -2*e + 6, -2*e + 4, -e + 8, -e + 7, -e - 8, 2*e - 2, 3*e + 6, 3*e + 5, -4*e + 2, -e - 11, 2*e - 6, -12, 2*e + 4, -6*e + 2, 5*e - 6, e + 3, -e + 1, e - 7, -6*e + 10, 2*e + 2, 3*e + 6, -2*e + 6, 2*e + 4, 20, -5*e + 15, -4*e, -3*e + 20, -14, 5*e + 14, 9*e - 2, -3*e - 13, -2*e + 28, 26, -e - 22, -6*e, 4*e - 16, 2*e, -6*e + 8, -4*e - 12, 8*e, -6*e - 14, 5*e + 14, -5*e + 12, 4*e - 4, -e + 20, -10*e + 4, 2*e - 18, 8*e - 8, 12, 4*e + 10, -4*e - 20, 6*e + 10, -e + 32, 8*e + 10, 22, -8*e - 2, 4*e - 2, 5*e + 1, -3*e + 33, 3*e - 6, -6*e - 12, 4*e - 2, -8*e + 22, 4*e + 4, 2*e + 16, 34, 3*e - 7, -9*e - 12, 8*e, 7*e + 8, 6*e + 4, 9*e + 12, 2*e + 10, 3*e - 13, -3*e + 5, 3*e + 22, -3*e - 27, 16, -8*e + 24, 6*e - 20, -8*e - 18, 5*e + 2, -7*e + 21, 10, 0, -2*e + 38, 3*e - 9, -4*e - 14, -14*e + 12, 6*e + 26, 8*e - 30, 4*e + 32, -6*e - 4, -2*e - 6, 8*e - 20, -8*e - 2, -10*e + 18, 6*e - 12, -8*e + 8, 3*e + 17, 12*e, -6*e - 22, -6*e + 20, -14*e, -46, -5*e - 11, -6*e - 18, e - 5, -4*e + 12, -11*e + 5, 6*e + 18, 8*e - 30, -4*e - 12, 7*e + 27, e + 28, -3*e + 25, -e - 7, 10*e - 6, -e + 32, 6*e - 16, 10*e, 6*e - 36, e + 18, e + 39, 8*e - 36, -5*e + 36, 6*e + 18, 7*e - 23, 15*e - 11, 4*e + 22, 3*e - 24, -15*e + 5, -4*e - 16, 14*e - 26, 8*e - 36, 3*e - 21, -6*e + 24, 6*e - 26, -32, -7*e + 25, -7*e + 12, -e - 42, 8*e, -7*e - 17, -6*e + 14, -4*e + 2, -8*e - 6, -2*e + 32, -e - 43, -10*e - 4, -6*e - 42]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([5, 5, -w - 1])] = -1

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