/*
  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([-39, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([1, 1, 1])

primes_array = [
[3, 3, w + 6],\
[3, 3, -w + 7],\
[4, 2, 2],\
[11, 11, -3*w - 17],\
[11, 11, 3*w - 20],\
[13, 13, 2*w - 13],\
[13, 13, 2*w + 11],\
[17, 17, w + 7],\
[17, 17, -w + 8],\
[19, 19, -w - 4],\
[19, 19, -w + 5],\
[25, 5, 5],\
[31, 31, -6*w - 35],\
[31, 31, -6*w + 41],\
[37, 37, -w - 1],\
[37, 37, w - 2],\
[47, 47, 3*w + 16],\
[47, 47, -3*w + 19],\
[49, 7, -7],\
[67, 67, 3*w - 22],\
[67, 67, -3*w - 19],\
[71, 71, -w - 10],\
[71, 71, w - 11],\
[89, 89, -8*w - 47],\
[89, 89, 8*w - 55],\
[101, 101, 4*w - 29],\
[101, 101, -4*w - 25],\
[109, 109, -3*w - 20],\
[109, 109, 3*w - 23],\
[113, 113, 3*w - 17],\
[113, 113, -3*w - 14],\
[127, 127, -9*w - 53],\
[127, 127, 9*w - 62],\
[157, 157, 2*w - 1],\
[167, 167, 2*w - 19],\
[167, 167, -2*w - 17],\
[173, 173, 13*w - 89],\
[173, 173, -13*w - 76],\
[193, 193, 11*w - 73],\
[193, 193, -11*w - 62],\
[197, 197, 3*w - 14],\
[197, 197, -3*w - 11],\
[199, 199, 3*w - 25],\
[199, 199, -3*w - 22],\
[233, 233, -w - 16],\
[233, 233, w - 17],\
[239, 239, 7*w - 50],\
[239, 239, -7*w - 43],\
[257, 257, 6*w + 31],\
[257, 257, -6*w + 37],\
[263, 263, 3*w - 11],\
[263, 263, -3*w - 8],\
[277, 277, -12*w - 71],\
[277, 277, 12*w - 83],\
[281, 281, -3*w - 7],\
[281, 281, 3*w - 10],\
[283, 283, -7*w + 44],\
[283, 283, 7*w + 37],\
[311, 311, 3*w - 8],\
[311, 311, -3*w - 5],\
[313, 313, -13*w - 73],\
[313, 313, 13*w - 86],\
[317, 317, -9*w + 58],\
[317, 317, 9*w + 49],\
[331, 331, -5*w - 23],\
[331, 331, 5*w - 28],\
[347, 347, -3*w - 1],\
[347, 347, 3*w - 4],\
[349, 349, 3*w - 28],\
[349, 349, -3*w - 25],\
[353, 353, 3*w - 2],\
[353, 353, 3*w - 1],\
[389, 389, 6*w - 35],\
[389, 389, 6*w + 29],\
[419, 419, 2*w - 25],\
[419, 419, -2*w - 23],\
[431, 431, 10*w - 71],\
[431, 431, -10*w - 61],\
[457, 457, 27*w + 157],\
[457, 457, 27*w - 184],\
[461, 461, -4*w - 31],\
[461, 461, 4*w - 35],\
[467, 467, -w - 22],\
[467, 467, w - 23],\
[487, 487, 8*w + 41],\
[487, 487, -8*w + 49],\
[523, 523, -6*w - 41],\
[523, 523, 6*w - 47],\
[529, 23, -23],\
[547, 547, 4*w - 11],\
[547, 547, -4*w - 7],\
[557, 557, 28*w - 191],\
[557, 557, -28*w - 163],\
[571, 571, 20*w - 133],\
[571, 571, -20*w - 113],\
[577, 577, -3*w - 29],\
[577, 577, 3*w - 32],\
[593, 593, 19*w - 131],\
[593, 593, -19*w - 112],\
[601, 601, 5*w - 22],\
[601, 601, -5*w - 17],\
[617, 617, -18*w - 101],\
[617, 617, 18*w - 119],\
[619, 619, -4*w - 1],\
[619, 619, 4*w - 5],\
[631, 631, 17*w - 112],\
[631, 631, -17*w - 95],\
[641, 641, 15*w + 83],\
[641, 641, 15*w - 98],\
[647, 647, -17*w - 101],\
[647, 647, 17*w - 118],\
[653, 653, -11*w - 68],\
[653, 653, 11*w - 79],\
[659, 659, 5*w - 43],\
[659, 659, -5*w - 38],\
[661, 661, -25*w - 142],\
[661, 661, 25*w - 167],\
[677, 677, 13*w - 92],\
[677, 677, -13*w - 79],\
[709, 709, 5*w - 19],\
[709, 709, -5*w - 14],\
[727, 727, -9*w - 58],\
[727, 727, 9*w - 67],\
[733, 733, 7*w - 38],\
[733, 733, -7*w - 31],\
[739, 739, -18*w - 107],\
[739, 739, 18*w - 125],\
[743, 743, 2*w - 31],\
[743, 743, -2*w - 29],\
[769, 769, -3*w - 32],\
[769, 769, 3*w - 35],\
[773, 773, -w - 28],\
[773, 773, w - 29],\
[797, 797, 21*w - 139],\
[797, 797, -21*w - 118],\
[821, 821, -15*w + 97],\
[821, 821, 15*w + 82],\
[827, 827, 9*w - 53],\
[827, 827, -9*w - 44],\
[829, 829, -19*w - 106],\
[829, 829, 19*w - 125],\
[841, 29, -29],\
[853, 853, 9*w - 68],\
[853, 853, -9*w - 59],\
[907, 907, 3*w - 37],\
[907, 907, -3*w - 34],\
[911, 911, 5*w - 46],\
[911, 911, -5*w - 41],\
[929, 929, -6*w - 19],\
[929, 929, 6*w - 25],\
[941, 941, -20*w - 119],\
[941, 941, 20*w - 139],\
[953, 953, -w - 31],\
[953, 953, w - 32],\
[967, 967, 11*w + 56],\
[967, 967, -11*w + 67],\
[977, 977, 16*w - 113],\
[977, 977, -16*w - 97],\
[991, 991, -8*w - 35],\
[991, 991, 8*w - 43]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-2, -2, 3, 6, 6, -5, -5, 3, 3, 0, 0, -6, 0, 0, -3, -3, 6, 6, 5, 4, 4, 6, 6, 9, 9, -15, -15, -3, -3, 9, 9, 6, 6, -22, -18, -18, -6, -6, -14, -14, 15, 15, -2, -2, -3, -3, 0, 0, 18, 18, 24, 24, -9, -9, -27, -27, -6, -6, 6, 6, -21, -21, -27, -27, -8, -8, 12, 12, -1, -1, -6, -6, -15, -15, -24, -24, -18, -18, 17, 17, 27, 27, -24, -24, 2, 2, -6, -6, 21, 18, 18, -6, -6, -4, -4, 45, 45, -9, -9, -17, -17, 39, 39, -24, -24, -16, -16, 30, 30, 48, 48, 30, 30, 24, 24, -3, -3, 42, 42, -26, -26, -28, -28, 30, 30, 42, 42, 12, 12, -45, -45, -21, -21, -30, -30, 3, 3, -54, -54, -33, -33, 42, -42, -42, 28, 28, 12, 12, -27, -27, 18, 18, 39, 39, -50, -50, -45, -45, -34, -34]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}

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