/*
  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([-48, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([6, 6, -w - 6])

primes_array = [
[2, 2, -9*w - 58],\
[2, 2, -9*w + 67],\
[3, 3, -2*w + 15],\
[3, 3, 2*w + 13],\
[7, 7, 186*w - 1385],\
[7, 7, -186*w - 1199],\
[23, 23, -38*w - 245],\
[23, 23, 38*w - 283],\
[25, 5, 5],\
[31, 31, 16*w - 119],\
[31, 31, 16*w + 103],\
[43, 43, 4*w + 25],\
[43, 43, -4*w + 29],\
[59, 59, 12*w - 89],\
[59, 59, -12*w - 77],\
[67, 67, 92*w + 593],\
[67, 67, 92*w - 685],\
[83, 83, 204*w - 1519],\
[83, 83, 204*w + 1315],\
[97, 97, -24*w + 179],\
[97, 97, -24*w - 155],\
[101, 101, 428*w + 2759],\
[101, 101, 428*w - 3187],\
[107, 107, -298*w + 2219],\
[107, 107, -298*w - 1921],\
[109, 109, 818*w - 6091],\
[109, 109, 818*w + 5273],\
[121, 11, -11],\
[131, 131, 2*w - 19],\
[131, 131, -2*w - 17],\
[137, 137, 6*w + 37],\
[137, 137, -6*w + 43],\
[139, 139, 150*w + 967],\
[139, 139, 150*w - 1117],\
[151, 151, -42*w - 271],\
[151, 151, -42*w + 313],\
[157, 157, 2*w - 7],\
[157, 157, -2*w - 5],\
[169, 13, -13],\
[179, 179, 1692*w + 10907],\
[179, 179, 1692*w - 12599],\
[181, 181, 132*w - 983],\
[181, 181, 132*w + 851],\
[191, 191, 576*w + 3713],\
[191, 191, 576*w - 4289],\
[193, 193, 2*w - 1],\
[197, 197, 28*w - 209],\
[197, 197, -28*w - 181],\
[199, 199, 6*w + 41],\
[199, 199, 6*w - 47],\
[211, 211, -78*w + 581],\
[211, 211, -78*w - 503],\
[229, 229, 70*w - 521],\
[229, 229, 70*w + 451],\
[239, 239, 1320*w - 9829],\
[239, 239, 1320*w + 8509],\
[241, 241, 14*w + 89],\
[241, 241, -14*w + 103],\
[257, 257, 18*w - 133],\
[257, 257, 18*w + 115],\
[277, 277, -12*w - 79],\
[277, 277, 12*w - 91],\
[289, 17, -17],\
[293, 293, 6*w - 41],\
[293, 293, 6*w + 35],\
[311, 311, 240*w + 1547],\
[311, 311, 240*w - 1787],\
[317, 317, -4*w - 31],\
[317, 317, -4*w + 35],\
[331, 331, 4*w - 23],\
[331, 331, -4*w - 19],\
[337, 337, 2194*w + 14143],\
[337, 337, 2194*w - 16337],\
[359, 359, 10*w - 77],\
[359, 359, 10*w + 67],\
[361, 19, -19],\
[379, 379, -6*w + 49],\
[379, 379, -6*w - 43],\
[383, 383, 2*w - 25],\
[383, 383, -2*w - 23],\
[389, 389, -1804*w + 13433],\
[389, 389, -1804*w - 11629],\
[409, 409, 1078*w + 6949],\
[409, 409, 1078*w - 8027],\
[449, 449, 258*w - 1921],\
[449, 449, 258*w + 1663],\
[461, 461, 594*w - 4423],\
[461, 461, 594*w + 3829],\
[467, 467, -82*w - 529],\
[467, 467, -82*w + 611],\
[479, 479, -50*w - 323],\
[479, 479, 50*w - 373],\
[487, 487, 8*w - 55],\
[487, 487, 8*w + 47],\
[523, 523, -522*w + 3887],\
[523, 523, -522*w - 3365],\
[547, 547, -4*w - 13],\
[547, 547, 4*w - 17],\
[563, 563, 84*w + 541],\
[563, 563, 84*w - 625],\
[571, 571, 124*w - 923],\
[571, 571, 124*w + 799],\
[577, 577, 912*w + 5879],\
[577, 577, 912*w - 6791],\
[587, 587, 374*w + 2411],\
[587, 587, 374*w - 2785],\
[593, 593, -136*w + 1013],\
[593, 593, -136*w - 877],\
[607, 607, 1208*w - 8995],\
[607, 607, -1208*w - 7787],\
[641, 641, 40*w - 299],\
[641, 641, -40*w - 259],\
[643, 643, 2324*w - 17305],\
[643, 643, 2324*w + 14981],\
[677, 677, 966*w + 6227],\
[677, 677, 966*w - 7193],\
[691, 691, 4*w - 11],\
[691, 691, -4*w - 7],\
[709, 709, -58*w - 373],\
[709, 709, 58*w - 431],\
[751, 751, 18*w - 137],\
[751, 751, 18*w + 119],\
[769, 769, -24*w - 157],\
[769, 769, 24*w - 181],\
[773, 773, 294*w + 1895],\
[773, 773, 294*w - 2189],\
[797, 797, -3198*w - 20615],\
[797, 797, 3198*w - 23813],\
[821, 821, 54*w - 401],\
[821, 821, -54*w - 347],\
[827, 827, 1414*w + 9115],\
[827, 827, 1414*w - 10529],\
[839, 839, -634*w + 4721],\
[839, 839, -634*w - 4087],\
[841, 29, -29],\
[853, 853, -22*w + 161],\
[853, 853, 22*w + 139],\
[857, 857, -104*w + 775],\
[857, 857, -104*w - 671],\
[881, 881, -8*w + 67],\
[881, 881, -8*w - 59],\
[911, 911, 120*w - 893],\
[911, 911, 120*w + 773],\
[919, 919, 486*w + 3133],\
[919, 919, 486*w - 3619],\
[929, 929, 320*w - 2383],\
[929, 929, 320*w + 2063],\
[937, 937, 406*w + 2617],\
[937, 937, 406*w - 3023],\
[941, 941, 1710*w + 11023],\
[941, 941, 1710*w - 12733],\
[947, 947, 14*w + 95],\
[947, 947, 14*w - 109],\
[953, 953, -6*w - 25],\
[953, 953, 6*w - 31],\
[967, 967, 6*w - 55],\
[967, 967, -6*w - 49],\
[971, 971, -3050*w - 19661],\
[971, 971, 3050*w - 22711],\
[977, 977, 1024*w - 7625],\
[977, 977, -1024*w - 6601],\
[983, 983, -22*w - 145],\
[983, 983, 22*w - 167],\
[997, 997, 742*w - 5525],\
[997, 997, 742*w + 4783]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - x - 8
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, 0, -1, e, -e + 2, -e - 1, -3, -e - 1, 2*e - 1, 6, e - 8, 0, e + 4, -3, 6, -3*e + 1, -5, -3*e + 3, 12, -2*e + 4, 2*e + 8, -3*e + 9, e - 5, 6, 2*e + 11, -2, 6*e - 2, -4*e - 4, 2*e - 4, 3*e, -3*e + 9, -2*e + 16, -2, 3*e - 8, 6*e - 4, 3*e + 8, -3*e - 7, -6*e - 4, -3*e + 8, 2*e + 5, 18, 3*e - 15, 6*e, 3*e + 9, -3, -3*e + 10, -3*e, -e - 4, -2*e - 14, 2*e + 8, 3*e - 3, -e + 11, -3*e - 6, -2*e + 16, -4*e + 11, 9*e - 3, 6*e - 2, -3*e + 7, -e + 23, 3*e + 18, 20, 3*e - 19, 9*e - 6, -21, -9*e + 6, -8*e - 8, 3*e - 3, -24, -6*e + 18, 4*e - 20, 12, 18, 3, 9*e + 3, 6*e, 3*e - 13, 25, -3*e - 5, 7*e + 1, 9*e - 9, -3*e - 12, -3*e + 18, e - 17, 4*e - 2, -4*e + 26, -3*e + 9, e - 29, -3*e + 3, 9*e - 12, -6*e + 24, -6*e + 6, -3*e + 12, 6*e + 8, -3*e + 14, 9*e - 21, -8*e - 5, 7*e - 5, -7*e - 13, -9*e + 3, e - 2, 4*e + 16, -8*e - 11, -e + 29, -5*e + 1, -36, -e + 8, -9*e + 15, -5*e + 28, -12*e + 20, -12*e + 11, -6*e - 12, 2*e - 10, -3*e + 2, -12*e + 14, 33, -15*e + 6, -5*e + 37, 2*e + 11, 13*e - 11, -6*e + 24, 3*e + 36, -9*e + 21, -3*e - 26, -9*e + 28, 3*e + 18, -3*e + 6, 6, -6*e, 3*e - 21, -3*e + 21, -5*e - 5, -6*e + 18, 9*e, 10*e + 10, -9*e - 18, 11*e - 22, 3*e + 12, 8*e - 10, -6*e + 6, -e - 19, -12*e - 6, -9*e + 30, -8*e - 14, 6*e + 34, -9*e - 17, 12*e - 18, 3*e - 15, 2*e - 28, 2*e - 22, 3*e - 30, 3*e - 9, 6*e + 36, -7*e - 22, 6*e - 36, 10*e - 14, 4, -12*e - 17, 3*e - 39, -2*e + 52, -6*e + 24, -10*e - 1, 12*e - 21, 6*e, -5*e + 28, 7*e - 41]
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, -9*w - 58])] = 1
AL_eigenvalues[ZF.ideal([3, 3, -2*w + 15])] = 1

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