/*
  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([-95, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([2, 2, w + 1])

primes_array = [
[2, 2, w + 1],\
[5, 5, -w + 10],\
[7, 7, w + 2],\
[7, 7, w + 5],\
[9, 3, 3],\
[13, 13, w + 2],\
[13, 13, w + 11],\
[19, 19, 2*w - 19],\
[23, 23, w + 7],\
[23, 23, w + 16],\
[31, 31, -w - 8],\
[31, 31, w - 8],\
[37, 37, w + 13],\
[37, 37, w + 24],\
[43, 43, w + 3],\
[43, 43, w + 40],\
[47, 47, w + 1],\
[47, 47, w + 46],\
[53, 53, w + 25],\
[53, 53, w + 28],\
[59, 59, -w - 6],\
[59, 59, w - 6],\
[61, 61, 2*w - 21],\
[61, 61, 6*w - 59],\
[71, 71, 5*w - 48],\
[71, 71, -3*w + 28],\
[79, 79, -w - 4],\
[79, 79, w - 4],\
[83, 83, w + 26],\
[83, 83, w + 57],\
[97, 97, w + 17],\
[97, 97, w + 80],\
[101, 101, -w - 14],\
[101, 101, w - 14],\
[113, 113, w + 35],\
[113, 113, w + 78],\
[121, 11, -11],\
[149, 149, 2*w - 23],\
[149, 149, -2*w - 23],\
[151, 151, 8*w - 77],\
[151, 151, -4*w + 37],\
[163, 163, w + 62],\
[163, 163, w + 101],\
[173, 173, w + 21],\
[173, 173, w + 152],\
[179, 179, 3*w - 26],\
[179, 179, -13*w + 126],\
[193, 193, w + 45],\
[193, 193, w + 148],\
[211, 211, 2*w - 13],\
[211, 211, -2*w - 13],\
[229, 229, -w - 18],\
[229, 229, w - 18],\
[257, 257, w + 98],\
[257, 257, w + 159],\
[263, 263, w + 44],\
[263, 263, w + 219],\
[283, 283, w + 100],\
[283, 283, w + 183],\
[289, 17, -17],\
[293, 293, w + 55],\
[293, 293, w + 238],\
[317, 317, w + 27],\
[317, 317, w + 290],\
[331, 331, 2*w - 7],\
[331, 331, -2*w - 7],\
[337, 337, w + 134],\
[337, 337, w + 203],\
[347, 347, w + 147],\
[347, 347, w + 200],\
[349, 349, 2*w - 27],\
[349, 349, -2*w - 27],\
[367, 367, w + 126],\
[367, 367, w + 241],\
[373, 373, w + 29],\
[373, 373, w + 344],\
[379, 379, 2*w - 1],\
[379, 379, -2*w - 1],\
[389, 389, -w - 22],\
[389, 389, w - 22],\
[431, 431, -4*w - 33],\
[431, 431, 4*w - 33],\
[433, 433, w + 31],\
[433, 433, w + 402],\
[439, 439, 5*w - 44],\
[439, 439, -19*w + 184],\
[443, 443, w + 192],\
[443, 443, w + 251],\
[461, 461, 2*w - 29],\
[461, 461, -2*w - 29],\
[463, 463, w + 133],\
[463, 463, w + 330],\
[467, 467, w + 58],\
[467, 467, w + 409],\
[503, 503, w + 108],\
[503, 503, w + 395],\
[541, 541, 21*w - 206],\
[541, 541, 5*w - 54],\
[587, 587, w + 260],\
[587, 587, w + 327],\
[599, 599, -3*w - 16],\
[599, 599, 3*w - 16],\
[643, 643, w + 122],\
[643, 643, w + 521],\
[647, 647, w + 68],\
[647, 647, w + 579],\
[659, 659, 3*w - 14],\
[659, 659, -3*w - 14],\
[673, 673, w + 257],\
[673, 673, w + 416],\
[677, 677, w + 210],\
[677, 677, w + 467],\
[701, 701, 10*w - 101],\
[701, 701, 14*w - 139],\
[709, 709, 2*w - 33],\
[709, 709, -2*w - 33],\
[727, 727, w + 72],\
[727, 727, w + 655],\
[751, 751, 20*w - 193],\
[751, 751, -8*w + 73],\
[761, 761, -5*w + 56],\
[761, 761, 5*w + 56],\
[769, 769, 17*w - 168],\
[769, 769, 9*w - 92],\
[773, 773, w + 274],\
[773, 773, w + 499],\
[797, 797, w + 172],\
[797, 797, w + 625],\
[809, 809, 8*w - 83],\
[809, 809, 20*w - 197],\
[811, 811, 7*w - 62],\
[811, 811, 7*w + 62],\
[821, 821, -7*w + 74],\
[821, 821, -7*w - 74],\
[823, 823, w + 170],\
[823, 823, w + 653],\
[839, 839, -3*w - 4],\
[839, 839, 3*w - 4],\
[841, 29, -29],\
[857, 857, w + 106],\
[857, 857, w + 751],\
[877, 877, w + 43],\
[877, 877, w + 834],\
[881, 881, 4*w - 49],\
[881, 881, -4*w - 49],\
[883, 883, w + 401],\
[883, 883, w + 482],\
[911, 911, 16*w - 153],\
[911, 911, -12*w + 113],\
[929, 929, -w - 32],\
[929, 929, w - 32],\
[947, 947, w + 82],\
[947, 947, w + 865],\
[953, 953, w + 420],\
[953, 953, w + 533],\
[967, 967, w + 391],\
[967, 967, w + 576],\
[971, 971, 23*w - 222],\
[971, 971, -9*w + 82],\
[977, 977, w + 308],\
[977, 977, w + 669],\
[991, 991, 4*w - 23],\
[991, 991, -4*w - 23]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^4 - 26*x^2 + 61
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, 1/6*e^2 - 7/6, e, -e, -3, 1/3*e^2 - 4/3, 1/3*e^2 - 4/3, 0, e, -e, 1/6*e^3 - 31/6*e, -1/6*e^3 + 31/6*e, -1/3*e^2 + 31/3, -1/3*e^2 + 31/3, 1/6*e^3 - 31/6*e, -1/6*e^3 + 31/6*e, 1/3*e^3 - 19/3*e, -1/3*e^3 + 19/3*e, 1/3*e^2 - 4/3, 1/3*e^2 - 4/3, -1/3*e^3 + 22/3*e, 1/3*e^3 - 22/3*e, -1/6*e^2 - 5/6, -1/6*e^2 - 5/6, -1/2*e^3 + 19/2*e, 1/2*e^3 - 19/2*e, 0, 0, 2*e, -2*e, -4/3*e^2 + 52/3, -4/3*e^2 + 52/3, -1/2*e^2 + 15/2, -1/2*e^2 + 15/2, 7/6*e^2 - 109/6, 7/6*e^2 - 109/6, -1/3*e^2 - 41/3, -4/3*e^2 + 76/3, -4/3*e^2 + 76/3, 2/3*e^3 - 44/3*e, -2/3*e^3 + 44/3*e, 1/2*e^3 - 23/2*e, -1/2*e^3 + 23/2*e, -2/3*e^2 + 62/3, -2/3*e^2 + 62/3, -1/3*e^3 + 13/3*e, 1/3*e^3 - 13/3*e, -2/3*e^2 + 8/3, -2/3*e^2 + 8/3, -2/3*e^3 + 35/3*e, 2/3*e^3 - 35/3*e, -2/3*e^2 + 26/3, -2/3*e^2 + 26/3, 1/6*e^2 + 113/6, 1/6*e^2 + 113/6, 1/3*e^3 - 25/3*e, -1/3*e^3 + 25/3*e, -2/3*e^3 + 44/3*e, 2/3*e^3 - 44/3*e, 5/3*e^2 - 20/3, -1/3*e^2 + 40/3, -1/3*e^2 + 40/3, -e^2 + 28, -e^2 + 28, -3*e, 3*e, -1/6*e^2 - 41/6, -1/6*e^2 - 41/6, -2/3*e^3 + 38/3*e, 2/3*e^3 - 38/3*e, -2*e^2 + 34, -2*e^2 + 34, -e^3 + 19*e, e^3 - 19*e, -e^2 + 16, -e^2 + 16, 1/3*e^3 - 40/3*e, -1/3*e^3 + 40/3*e, -7/6*e^2 + 97/6, -7/6*e^2 + 97/6, -1/6*e^3 - 5/6*e, 1/6*e^3 + 5/6*e, -13/6*e^2 + 115/6, -13/6*e^2 + 115/6, -1/6*e^3 - 5/6*e, 1/6*e^3 + 5/6*e, -1/6*e^3 + 55/6*e, 1/6*e^3 - 55/6*e, 1/6*e^2 + 197/6, 1/6*e^2 + 197/6, 2/3*e^3 - 62/3*e, -2/3*e^3 + 62/3*e, 1/6*e^3 - 43/6*e, -1/6*e^3 + 43/6*e, -e^3 + 24*e, e^3 - 24*e, 5/2*e^2 - 75/2, 5/2*e^2 - 75/2, 1/6*e^3 + 29/6*e, -1/6*e^3 - 29/6*e, -1/6*e^3 - 5/6*e, 1/6*e^3 + 5/6*e, -4/3*e^3 + 88/3*e, 4/3*e^3 - 88/3*e, 1/3*e^3 - 34/3*e, -1/3*e^3 + 34/3*e, -2/3*e^3 + 53/3*e, 2/3*e^3 - 53/3*e, -2*e^2 + 14, -2*e^2 + 14, 45, 45, -20, -20, 20, 20, -5/3*e^3 + 92/3*e, 5/3*e^3 - 92/3*e, -5/6*e^3 + 119/6*e, 5/6*e^3 - 119/6*e, 5/3*e^2 - 104/3, 5/3*e^2 - 104/3, -5/3*e^2 + 92/3, -5/3*e^2 + 92/3, -9, -9, 2*e^2 - 53, 2*e^2 - 53, 4/3*e^2 - 13/3, 4/3*e^2 - 13/3, 5/3*e^3 - 110/3*e, -5/3*e^3 + 110/3*e, -2/3*e^2 - 4/3, -2/3*e^2 - 4/3, e^3 - 20*e, -e^3 + 20*e, -4/3*e^3 + 70/3*e, 4/3*e^3 - 70/3*e, -3*e^2 + 58, -2/3*e^2 - 46/3, -2/3*e^2 - 46/3, -4/3*e^2 - 11/3, -4/3*e^2 - 11/3, -8/3*e^2 + 164/3, -8/3*e^2 + 164/3, 8*e, -8*e, -4/3*e^3 + 70/3*e, 4/3*e^3 - 70/3*e, -2*e^2 + 63, -2*e^2 + 63, -2*e^3 + 36*e, 2*e^3 - 36*e, 13/6*e^2 - 187/6, 13/6*e^2 - 187/6, e^3 - 27*e, -e^3 + 27*e, 2*e^3 - 38*e, -2*e^3 + 38*e, -5/6*e^2 - 61/6, -5/6*e^2 - 61/6, -3/2*e^3 + 45/2*e, 3/2*e^3 - 45/2*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([2, 2, w + 1])] = 1

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