/*
  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([12, -9, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16, 4, 2*w - 4])

primes_array = [
[2, 2, w - 2],\
[3, 3, -w + 3],\
[3, 3, w - 1],\
[4, 2, w^2 + w - 7],\
[19, 19, w + 1],\
[23, 23, w^2 - 2*w - 1],\
[31, 31, -2*w^2 + 19],\
[31, 31, -w^2 + 5],\
[31, 31, -3*w + 5],\
[41, 41, w^2 + 2*w - 7],\
[43, 43, w^2 - 11],\
[47, 47, 3*w - 7],\
[53, 53, -3*w^2 - 6*w + 11],\
[59, 59, 2*w - 1],\
[67, 67, 2*w^2 + w - 19],\
[67, 67, 3*w^2 + 2*w - 25],\
[67, 67, w - 5],\
[73, 73, -4*w^2 - 3*w + 29],\
[73, 73, 2*w^2 - w - 11],\
[73, 73, w^2 + 2*w - 11],\
[79, 79, 2*w^2 + 2*w - 11],\
[83, 83, 2*w^2 - 13],\
[89, 89, -2*w + 7],\
[97, 97, -2*w^2 + 4*w - 1],\
[101, 101, -2*w - 5],\
[103, 103, 2*w^2 + w - 13],\
[107, 107, -2*w^2 - 2*w + 17],\
[109, 109, -4*w^2 - 2*w + 31],\
[113, 113, w^2 + 2*w - 1],\
[125, 5, -5],\
[127, 127, 2*w^2 + 3*w - 13],\
[137, 137, -2*w^2 + 7*w - 7],\
[139, 139, 2*w^2 + w - 7],\
[149, 149, -6*w^2 - 9*w + 31],\
[157, 157, w^2 - 4*w + 1],\
[163, 163, 2*w^2 + 5*w - 5],\
[173, 173, 5*w^2 + 4*w - 37],\
[179, 179, 2*w^2 + w - 11],\
[179, 179, 3*w^2 - 2*w - 17],\
[179, 179, -4*w^2 - w + 37],\
[191, 191, -6*w^2 - 9*w + 29],\
[193, 193, -2*w^2 - 4*w + 5],\
[223, 223, -2*w^2 + 2*w + 7],\
[227, 227, 6*w^2 + 4*w - 47],\
[233, 233, 2*w^2 + 4*w - 13],\
[233, 233, -4*w^2 - 4*w + 25],\
[233, 233, 4*w + 13],\
[239, 239, -4*w^2 - 8*w + 13],\
[239, 239, 2*w^2 + 2*w - 5],\
[239, 239, -w^2 + 8*w - 11],\
[241, 241, 3*w - 1],\
[251, 251, w^2 + 4*w - 19],\
[263, 263, -2*w^2 + 2*w + 25],\
[263, 263, -5*w^2 - 4*w + 35],\
[263, 263, 3*w^2 - 25],\
[269, 269, 6*w^2 + 3*w - 47],\
[269, 269, -w^2 - 1],\
[269, 269, 2*w^2 - 7],\
[277, 277, 2*w^2 - w - 5],\
[277, 277, -5*w^2 - 6*w + 31],\
[277, 277, 2*w^2 - 2*w - 11],\
[281, 281, 4*w^2 + 5*w - 25],\
[307, 307, 4*w^2 + 2*w - 37],\
[317, 317, -w - 7],\
[317, 317, 3*w^2 + 2*w - 19],\
[317, 317, -2*w^2 + 2*w + 5],\
[331, 331, 2*w^2 + 3*w - 19],\
[337, 337, w^2 - 4*w + 7],\
[343, 7, -7],\
[347, 347, 4*w^2 + 2*w - 29],\
[349, 349, 3*w^2 - 19],\
[361, 19, w^2 - 2*w - 7],\
[367, 367, 4*w^2 + 5*w - 19],\
[367, 367, -6*w + 11],\
[373, 373, -4*w^2 + w + 25],\
[379, 379, -5*w^2 - 10*w + 19],\
[383, 383, 4*w^2 + 6*w - 23],\
[401, 401, -3*w + 11],\
[401, 401, -3*w - 1],\
[401, 401, -3*w - 7],\
[409, 409, -w^2 - 4*w + 13],\
[419, 419, 2*w^2 - w - 17],\
[421, 421, -3*w^2 + 31],\
[431, 431, w^2 + 4*w - 1],\
[449, 449, -w^2 + 4*w + 1],\
[457, 457, -w^2 + 2*w + 13],\
[461, 461, 4*w^2 - 4*w - 19],\
[463, 463, 2*w^2 + 4*w - 23],\
[467, 467, 2*w^2 - 5*w + 5],\
[479, 479, 3*w + 11],\
[491, 491, 8*w^2 + 9*w - 49],\
[499, 499, -6*w^2 - 6*w + 41],\
[499, 499, 2*w^2 + 2*w - 23],\
[499, 499, 2*w^2 + 5*w - 29],\
[523, 523, -4*w^2 + w + 41],\
[529, 23, 6*w^2 + 7*w - 35],\
[547, 547, -2*w^2 + 6*w + 1],\
[557, 557, 3*w^2 + 2*w - 13],\
[563, 563, -w^2 + 4*w + 23],\
[569, 569, 10*w^2 + 8*w - 73],\
[587, 587, 2*w^2 - 2*w - 13],\
[593, 593, -6*w^2 - 8*w + 31],\
[601, 601, 4*w^2 + 5*w - 41],\
[601, 601, 10*w^2 + 16*w - 49],\
[601, 601, w^2 - 2*w + 5],\
[613, 613, -8*w^2 - 7*w + 55],\
[617, 617, -8*w^2 - 12*w + 37],\
[617, 617, 2*w^2 + 3*w - 25],\
[617, 617, 3*w^2 - 17],\
[641, 641, 4*w^2 - 35],\
[643, 643, 4*w^2 + 4*w - 37],\
[659, 659, -3*w^2 - 4*w + 23],\
[661, 661, -w^2 - 4*w - 5],\
[673, 673, 4*w^2 + 4*w - 31],\
[683, 683, 2*w^2 + 4*w - 19],\
[683, 683, 2*w^2 + w - 23],\
[683, 683, 3*w^2 + 6*w - 19],\
[701, 701, -6*w^2 - 12*w + 23],\
[701, 701, -2*w^2 + 7*w - 1],\
[701, 701, 3*w^2 + 2*w - 31],\
[709, 709, 5*w^2 + 4*w - 41],\
[719, 719, -6*w^2 - 2*w + 55],\
[719, 719, w^2 + 2*w - 17],\
[719, 719, 3*w^2 + 4*w - 29],\
[727, 727, -9*w^2 - 12*w + 49],\
[733, 733, 13*w^2 + 20*w - 65],\
[739, 739, 11*w^2 + 6*w - 91],\
[743, 743, -2*w^2 - 8*w + 35],\
[751, 751, 3*w^2 - 4*w - 13],\
[769, 769, 2*w^2 - 1],\
[797, 797, 2*w^2 - 8*w + 11],\
[811, 811, 4*w^2 - w - 29],\
[821, 821, 2*w^2 + 5*w - 17],\
[827, 827, -3*w^2 - 6*w + 7],\
[827, 827, -11*w^2 - 8*w + 83],\
[827, 827, -5*w^2 - 6*w + 25],\
[829, 829, -4*w^2 + 41],\
[829, 829, 4*w^2 + 8*w - 23],\
[829, 829, 8*w - 19],\
[839, 839, 2*w^2 + 6*w - 7],\
[853, 853, 10*w^2 + 6*w - 77],\
[859, 859, -5*w^2 - 2*w + 47],\
[863, 863, 12*w^2 + 19*w - 59],\
[877, 877, 8*w^2 + 6*w - 61],\
[907, 907, -4*w - 1],\
[907, 907, 9*w^2 + 4*w - 71],\
[907, 907, 2*w^2 + 7*w - 17],\
[919, 919, -10*w^2 - 5*w + 79],\
[929, 929, 2*w^2 + 7*w - 11],\
[937, 937, -4*w^2 + 6*w + 11],\
[941, 941, 3*w^2 - 11],\
[947, 947, 6*w - 5],\
[967, 967, -2*w^2 + 5*w + 5],\
[971, 971, 5*w^2 - 2*w - 29],\
[991, 991, 4*w^2 + 2*w - 25],\
[997, 997, 3*w^2 - 2*w - 11]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 + 3*x - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, -2, 1, 2, 3*e + 3, -3*e - 7, 3*e + 2, 2, -3*e - 6, 3*e + 2, 3*e - 3, -6*e - 6, -12, -10, -3*e - 1, 3*e + 11, -3*e - 10, 2, -6*e - 4, -4, -6*e - 6, -6*e - 6, 3*e - 1, -6, -3*e - 4, 6, -3*e - 1, -6*e - 6, 3*e - 12, -3*e - 4, 12*e + 18, 3*e - 1, 6, 9*e + 14, 6*e + 14, 3*e + 3, -6*e - 6, -3*e, 3*e, -12, -6*e - 4, 9*e + 8, -9*e - 15, -6*e, 9*e + 18, -24, 0, 6*e + 6, -3*e - 6, 6*e + 14, -3*e - 18, 3*e + 21, 6*e + 18, 0, 12*e + 18, -3*e + 9, -30, 3*e - 7, 26, -12*e - 28, 6*e + 12, -3*e - 10, -3*e - 12, 6*e - 6, 6, 2, -9*e - 4, 6*e - 4, -3*e + 9, -9*e - 25, -9*e - 4, -6*e - 34, -10, -15*e - 31, 6*e + 14, 9*e + 9, -9*e - 3, -12, 6*e, 12*e + 26, -3*e - 18, 6*e - 4, -6*e - 6, 9*e + 12, -12*e - 34, -12*e - 30, -6*e + 14, 12*e + 24, -12*e - 24, 36, 12*e + 2, 6*e + 2, 12*e + 2, 2, -6*e + 2, -6*e - 10, 3*e + 18, -12*e - 30, 9*e + 9, -9*e - 30, 3*e - 9, 6*e + 14, 15*e + 11, 6*e - 16, -9*e + 11, -6*e - 30, 9*e + 21, -6*e - 30, -12*e - 36, 6*e - 16, -15*e - 33, 6*e - 10, 26, -6*e + 12, 3*e - 3, -9*e - 12, 6*e - 6, -6*e + 6, -3*e + 9, 2, -3*e - 9, 9*e - 18, 6*e + 30, 6*e + 20, 6*e - 10, -3*e - 31, 15*e + 9, 6*e + 50, 9*e - 13, -9*e - 12, 3*e + 35, -6*e, 18*e + 48, -6*e - 42, -6*e - 24, 18*e + 50, -6*e - 28, 21*e + 14, 15*e + 21, -6*e - 52, -9*e - 40, -18*e - 30, -18*e - 4, -3*e + 8, -12*e - 16, 9*e + 44, -12*e - 34, -18*e - 36, -9*e - 7, 15*e + 51, -12, 9*e + 26, -9*e - 48, 12*e + 44, 6*e + 14]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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