/*
  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([-28, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([8, 8, -w + 5])

primes_array = [
[2, 2, -w + 6],\
[2, 2, w + 5],\
[7, 7, 6*w - 35],\
[7, 7, -6*w - 29],\
[9, 3, 3],\
[11, 11, 4*w + 19],\
[11, 11, 4*w - 23],\
[13, 13, -2*w + 11],\
[13, 13, 2*w + 9],\
[25, 5, -5],\
[31, 31, 2*w - 13],\
[31, 31, -2*w - 11],\
[41, 41, -8*w - 39],\
[41, 41, 8*w - 47],\
[53, 53, -26*w - 125],\
[53, 53, 26*w - 151],\
[61, 61, -14*w + 81],\
[61, 61, -14*w - 67],\
[83, 83, 2*w - 15],\
[83, 83, -2*w - 13],\
[97, 97, 2*w - 5],\
[97, 97, -2*w - 3],\
[109, 109, 2*w - 3],\
[109, 109, -2*w - 1],\
[113, 113, 2*w - 1],\
[127, 127, 8*w - 45],\
[127, 127, 8*w + 37],\
[131, 131, -50*w + 291],\
[131, 131, 50*w + 241],\
[139, 139, 6*w - 37],\
[139, 139, -6*w - 31],\
[149, 149, 20*w + 97],\
[149, 149, 20*w - 117],\
[157, 157, -12*w - 59],\
[157, 157, 12*w - 71],\
[163, 163, 4*w - 19],\
[163, 163, 4*w + 15],\
[173, 173, 4*w + 23],\
[173, 173, 4*w - 27],\
[211, 211, 2*w - 19],\
[211, 211, -2*w - 17],\
[227, 227, -4*w - 13],\
[227, 227, 4*w - 17],\
[233, 233, 6*w + 25],\
[233, 233, -6*w + 31],\
[239, 239, -14*w - 69],\
[239, 239, 14*w - 83],\
[241, 241, 46*w + 221],\
[241, 241, -46*w + 267],\
[251, 251, 22*w - 129],\
[251, 251, 22*w + 107],\
[257, 257, -34*w + 197],\
[257, 257, -34*w - 163],\
[277, 277, 4*w - 29],\
[277, 277, -4*w - 25],\
[283, 283, 4*w - 15],\
[283, 283, -4*w - 11],\
[289, 17, -17],\
[307, 307, 68*w - 395],\
[307, 307, 68*w + 327],\
[311, 311, 10*w - 61],\
[311, 311, -10*w - 51],\
[313, 313, -32*w - 155],\
[313, 313, 32*w - 187],\
[317, 317, -18*w - 85],\
[317, 317, 18*w - 103],\
[331, 331, -4*w - 9],\
[331, 331, 4*w - 13],\
[337, 337, -16*w - 79],\
[337, 337, 16*w - 95],\
[347, 347, -12*w + 67],\
[347, 347, 12*w + 55],\
[353, 353, 14*w - 79],\
[353, 353, 14*w + 65],\
[361, 19, -19],\
[367, 367, -32*w - 153],\
[367, 367, -32*w + 185],\
[383, 383, 56*w + 269],\
[383, 383, 56*w - 325],\
[389, 389, -4*w - 27],\
[389, 389, 4*w - 31],\
[401, 401, 8*w - 51],\
[401, 401, -8*w - 43],\
[421, 421, 12*w - 73],\
[421, 421, -12*w - 61],\
[439, 439, -8*w - 33],\
[439, 439, 8*w - 41],\
[443, 443, -4*w - 1],\
[443, 443, 4*w - 5],\
[461, 461, -30*w + 173],\
[461, 461, 30*w + 143],\
[463, 463, 2*w - 25],\
[463, 463, -2*w - 23],\
[467, 467, 34*w + 165],\
[467, 467, 34*w - 199],\
[503, 503, -26*w - 127],\
[503, 503, 26*w - 153],\
[509, 509, 4*w - 33],\
[509, 509, -4*w - 29],\
[521, 521, -10*w + 53],\
[521, 521, 10*w + 43],\
[529, 23, -23],\
[547, 547, 14*w - 85],\
[547, 547, -14*w - 71],\
[557, 557, 66*w + 317],\
[557, 557, 66*w - 383],\
[563, 563, 2*w - 27],\
[563, 563, -2*w - 25],\
[569, 569, -64*w + 373],\
[569, 569, 64*w + 309],\
[587, 587, 12*w + 53],\
[587, 587, -12*w + 65],\
[593, 593, 8*w + 45],\
[593, 593, 8*w - 53],\
[601, 601, -26*w - 123],\
[601, 601, 26*w - 149],\
[617, 617, 6*w - 23],\
[617, 617, -6*w - 17],\
[647, 647, 24*w - 137],\
[647, 647, -24*w - 113],\
[653, 653, 28*w - 165],\
[653, 653, -28*w - 137],\
[677, 677, -22*w - 103],\
[677, 677, 22*w - 125],\
[691, 691, 20*w - 113],\
[691, 691, 20*w + 93],\
[709, 709, -10*w - 41],\
[709, 709, 10*w - 51],\
[719, 719, -8*w + 37],\
[719, 719, -8*w - 29],\
[727, 727, -22*w - 109],\
[727, 727, 22*w - 131],\
[739, 739, 46*w - 269],\
[739, 739, -46*w - 223],\
[761, 761, -6*w - 13],\
[761, 761, 6*w - 19],\
[769, 769, 110*w - 639],\
[769, 769, 110*w + 529],\
[773, 773, 4*w - 37],\
[773, 773, -4*w - 33],\
[787, 787, 2*w - 31],\
[787, 787, -2*w - 29],\
[809, 809, 56*w + 271],\
[809, 809, -56*w + 327],\
[821, 821, 6*w - 17],\
[821, 821, -6*w - 11],\
[823, 823, 38*w - 223],\
[823, 823, -38*w - 185],\
[827, 827, 132*w - 767],\
[827, 827, 132*w + 635],\
[841, 29, -29],\
[853, 853, -76*w + 443],\
[853, 853, 76*w + 367],\
[863, 863, 14*w - 87],\
[863, 863, -14*w - 73],\
[911, 911, 2*w - 33],\
[911, 911, -2*w - 31],\
[919, 919, -6*w - 41],\
[919, 919, 6*w - 47],\
[929, 929, 50*w + 239],\
[929, 929, 50*w - 289],\
[953, 953, 6*w - 11],\
[953, 953, -6*w - 5],\
[967, 967, -8*w - 25],\
[967, 967, 8*w - 33],\
[991, 991, 16*w + 71],\
[991, 991, -16*w + 87]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^3 - 2*x^2 - 3*x + 5
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 0, -e^2 - e + 6, -e^2 + e + 2, -e^2 - e + 3, -e^2, e^2 - 6, e^2 + 2*e - 6, e^2 - 2*e - 6, 2*e^2 - 2*e - 7, 5*e^2 - 3*e - 13, -e^2 + e + 3, 6*e^2 - 3*e - 15, -6*e^2 + 5*e + 13, 4*e^2 - 3*e - 11, -4*e^2 + e + 9, -e^2 + 2*e + 9, -5*e^2 + 6*e + 9, -e - 6, 2*e^2 + e - 12, e^2 - 3*e + 2, -3*e^2 - 3*e + 18, -4*e^2 + 6*e + 13, 4*e^2 + 2*e - 27, -6*e^2 + 4*e + 22, 5*e - 8, -2*e^2 + 7*e + 10, -6*e^2 + 7*e + 7, 2*e^2 + 7*e - 7, -3*e^2 + 5*e + 8, -3*e^2 - e + 12, 2*e^2 - 7*e + 1, -6*e^2 + 9*e + 17, -3*e^2 - 2*e + 11, -3*e^2 - 2*e - 1, 5*e^2 - 9*e - 21, 3*e^2 - 5*e - 13, -2*e + 1, 4*e^2 + 2*e - 15, -e^2 - 3*e + 12, -5*e^2 - e + 8, 10*e^2 - 40, -6*e^2 + 24, -2*e^2 + e - 1, -2*e^2 - 3*e + 15, e^2 - 4*e - 5, e^2 + 2*e - 3, -2*e^2 + 8*e + 2, 2*e^2 - 8*e - 10, -e^2 - 3*e + 13, -7*e^2 + 5*e + 5, -5*e^2 + 23, 7*e^2 + 8*e - 29, -7*e^2 + 11*e + 13, 5*e^2 + 3*e - 19, 2*e^2 - 12*e - 2, 10*e^2 - 34, -6*e^2 + 11*e + 20, 11*e^2 - 7*e - 29, 5*e^2 - 7*e - 5, 5*e^2 + 8*e - 27, 13*e^2 - 2*e - 45, 10*e^2 - 10*e - 26, -2*e^2 + 2*e + 6, -6*e^2 - 7*e + 26, 2*e^2 + 9*e - 10, 9*e^2 - 7*e - 23, 3*e^2 - 3*e - 11, -15*e^2 + 10*e + 38, e^2 - 10*e - 6, 2*e^2 - 11*e - 3, -6*e^2 + 13*e + 7, -11*e^2 + 3*e + 27, 13*e^2 - e - 37, 16*e^2 - 7*e - 46, -8*e^2 + 5*e + 26, -2*e^2 - 5*e + 28, 5*e^2 - 8*e - 6, 7*e^2 - 4*e - 12, e^2 - 5*e - 4, 5*e^2 - 9*e - 28, 16*e^2 - 15*e - 40, -4*e^2 - 3*e - 8, -2*e^2 - 6*e + 29, 2*e^2 - 10*e - 3, -12*e^2 + 8*e + 29, -18*e^2 + 18*e + 41, -9*e^2 + 4*e + 19, -5*e^2 + 10*e + 21, e^2 + 3*e - 13, -7*e^2 + 3*e + 7, -11*e^2 + 4*e + 53, 9*e^2 + 6*e - 29, -3*e^2 - 7*e - 4, 9*e^2 - e - 40, 17*e^2 - 8*e - 54, -e^2 + 32, 4*e^2 + 2*e - 16, 12*e^2 - 6*e - 48, -2*e^2 + 4*e + 15, -2*e^2 + 4*e - 9, 7*e^2 + 8*e - 42, 4*e^2 - 5*e + 17, -12*e^2 + 7*e + 15, -17*e^2 + 12*e + 51, -5*e^2 + 4*e - 17, -3*e^2 + 16*e - 1, 9*e^2 - 14*e - 7, 15*e^2 - 9*e - 57, -13*e^2 + 11*e + 43, 4*e^2 - 9*e - 1, 8*e^2 - 13*e - 27, -8*e^2 + 11*e - 3, -8*e^2 - 5*e + 41, -e^2 - 12*e - 1, -9*e^2 - 4*e + 31, -9*e^2 + 47, -e^2 - 8*e + 3, -12*e^2 - 4*e + 27, 2*e^2 - 10*e - 25, -6*e^2 - 7*e + 3, -2*e^2 + 9*e - 21, 13*e^2 - 6*e - 61, -11*e^2 - 6*e + 47, -12*e^2 + 3*e + 63, 4*e^2 - 5*e - 35, e^2 - 3*e - 14, e^2 + 5*e + 14, 2*e^2 + 6*e - 9, -16*e^2 + 16*e + 55, -12*e^2 + 5*e + 48, -6*e^2 - e + 6, 17*e^2 - 5*e - 35, 3*e^2 - e + 5, -13*e^2 + 9*e + 8, -13*e^2 - 11*e + 60, -7*e^2 - 7*e + 44, e^2 + 9*e - 20, 11*e^2 - 27*e - 24, 7*e^2 + 9*e - 44, -13*e^2 + 2*e + 48, -3*e^2 - 10*e + 30, -7*e^2 - 16*e + 47, -3*e^2 + 20*e - 1, 16*e^2 - 22*e - 28, 28*e^2 - 14*e - 72, 2*e^2 - 11*e + 21, -14*e^2 + 9*e + 11, -9*e^2 + 4*e + 8, -3*e^2 - 8*e - 18, 25*e^2 - 17*e - 53, 12*e^2 - 6*e - 39, 6*e + 5, e^2 - 2*e - 4, 3*e^2 - 6*e - 22, 2*e^2 + e + 34, 4*e^2 - 9*e + 16, 7*e^2 - 5*e - 27, -7*e^2 + 19*e + 37, -2*e^2 + 8*e - 11, -14*e^2 + 4*e + 41, -10*e^2 + 9*e + 34, 6*e^2 + 13*e - 54, -5*e^2 + 10*e - 28, 9*e^2 + 10*e - 18, -20*e^2 + 2*e + 89, -2*e^2 + 12*e + 17]
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 + 5])] = -1

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