/*
  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([1, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([25, 5, w^2 - 6])

primes_array = [
[5, 5, w + 1],\
[5, 5, w - 1],\
[7, 7, -w + 2],\
[8, 2, 2],\
[11, 11, -w^2 + 2*w + 2],\
[17, 17, -w - 3],\
[17, 17, -w^2 + 2*w + 1],\
[17, 17, -w^2 + w + 4],\
[23, 23, -w^2 + 3],\
[27, 3, -3],\
[29, 29, w^2 - w - 8],\
[29, 29, w^2 - w - 3],\
[29, 29, w^2 - w - 1],\
[31, 31, w^2 - 2],\
[37, 37, 2*w - 5],\
[43, 43, w^2 - 2*w - 5],\
[47, 47, w^2 - 3*w - 2],\
[49, 7, w^2 + w - 4],\
[53, 53, w^2 - 2*w - 6],\
[71, 71, w - 5],\
[79, 79, w^2 - 10],\
[83, 83, -2*w^2 + 3*w + 7],\
[89, 89, 2*w^2 - w - 9],\
[97, 97, 3*w^2 - 4*w - 15],\
[107, 107, w^2 - 2*w - 10],\
[121, 11, w^2 - 5*w + 3],\
[127, 127, 2*w^2 - 3*w - 13],\
[131, 131, 3*w + 4],\
[137, 137, 2*w^2 - 3*w - 12],\
[139, 139, 2*w^2 - 3*w - 6],\
[149, 149, w^2 + w - 9],\
[151, 151, 2*w^2 - 11],\
[157, 157, w^2 + w - 8],\
[163, 163, 2*w^2 + w - 4],\
[173, 173, 3*w - 4],\
[179, 179, -w^2 + 2*w - 3],\
[193, 193, 3*w - 5],\
[197, 197, -w^2 + 3*w - 4],\
[197, 197, w^2 - 3*w - 7],\
[199, 199, 2*w^2 - w - 7],\
[211, 211, w^2 + 2*w - 5],\
[223, 223, 2*w^2 - 3*w - 3],\
[227, 227, w^2 - 2*w - 11],\
[227, 227, 2*w^2 + w - 9],\
[227, 227, 2*w^2 - 5],\
[229, 229, 2*w^2 - 13],\
[233, 233, 4*w - 3],\
[241, 241, 3*w^2 - w - 18],\
[257, 257, 2*w^2 + 2*w - 7],\
[269, 269, w^2 - w - 11],\
[271, 271, 2*w^2 - 2*w - 3],\
[277, 277, 2*w^2 - 4*w - 9],\
[277, 277, 2*w^2 - w - 5],\
[277, 277, w^2 + 2*w - 6],\
[281, 281, w^2 + 4*w - 3],\
[293, 293, 2*w^2 - 3*w - 17],\
[311, 311, w^2 - 12],\
[311, 311, 2*w^2 - 5*w - 6],\
[311, 311, 3*w^2 - 6*w - 10],\
[313, 313, -w^2 + 2*w - 4],\
[337, 337, -w^2 - 2*w - 4],\
[337, 337, w^2 + 2*w - 7],\
[337, 337, w^2 + 2*w - 12],\
[347, 347, -w^2 + 6*w - 6],\
[349, 349, -w - 7],\
[353, 353, 2*w^2 - 19],\
[359, 359, 2*w - 9],\
[383, 383, w^2 + 2*w - 16],\
[383, 383, w^2 + 3*w - 16],\
[383, 383, w^2 + 3*w - 5],\
[389, 389, -3*w^2 + 6*w + 5],\
[397, 397, 3*w^2 - 2*w - 13],\
[397, 397, 2*w^2 - 2*w - 17],\
[397, 397, w^2 + 2*w - 11],\
[401, 401, 3*w - 11],\
[401, 401, w^2 + w - 14],\
[401, 401, w - 8],\
[409, 409, -w^2 - w - 4],\
[409, 409, w^2 - 4*w - 6],\
[409, 409, 3*w^2 - 5*w - 14],\
[421, 421, w^2 + 2*w - 10],\
[433, 433, 4*w^2 - 3*w - 20],\
[439, 439, w^2 - 4*w - 9],\
[443, 443, 3*w^2 - 16],\
[457, 457, w^2 - 4*w - 8],\
[461, 461, 4*w - 7],\
[487, 487, w^2 - 5*w - 13],\
[491, 491, 4*w^2 - 6*w - 19],\
[491, 491, 4*w^2 - 4*w - 19],\
[491, 491, 3*w^2 + w - 8],\
[503, 503, -5*w - 3],\
[509, 509, 2*w^2 + w - 12],\
[523, 523, w^2 - 5*w - 4],\
[523, 523, 2*w^2 - 6*w - 5],\
[523, 523, 2*w^2 - 3*w - 18],\
[529, 23, 3*w^2 - 5*w - 7],\
[541, 541, -w^2 - 2*w - 5],\
[557, 557, 3*w^2 - w - 11],\
[563, 563, 3*w^2 - 5*w - 21],\
[571, 571, 3*w^2 - 17],\
[587, 587, -5*w - 7],\
[599, 599, w^2 + 3*w - 7],\
[607, 607, 3*w^2 - 5*w - 6],\
[613, 613, 4*w^2 - 3*w - 19],\
[617, 617, 2*w^2 + w - 14],\
[631, 631, w^2 - 5*w - 5],\
[631, 631, 4*w^2 - 8*w - 13],\
[631, 631, 2*w^2 + w - 22],\
[641, 641, -w^2 - 5],\
[647, 647, 4*w^2 - w - 17],\
[647, 647, 2*w^2 - 5*w - 9],\
[647, 647, 5*w^2 - 6*w - 23],\
[653, 653, 3*w^2 - 5*w - 5],\
[659, 659, w^2 - 5*w - 12],\
[661, 661, w^2 - 6*w - 3],\
[661, 661, 3*w^2 - 5*w - 4],\
[661, 661, 3*w^2 + w - 6],\
[683, 683, 3*w^2 + w - 5],\
[691, 691, 2*w^2 + 2*w - 21],\
[691, 691, 3*w^2 - 5*w - 17],\
[691, 691, 3*w^2 + 2*w - 12],\
[701, 701, 3*w^2 - 4*w - 8],\
[709, 709, 3*w^2 - 7*w - 9],\
[719, 719, -2*w^2 - w - 3],\
[727, 727, w^2 - 14],\
[733, 733, -3*w - 10],\
[739, 739, 2*w^2 + 3*w - 8],\
[739, 739, 5*w - 6],\
[739, 739, 2*w^2 - w - 19],\
[743, 743, 4*w^2 - 5*w - 16],\
[743, 743, 5*w^2 - 3*w - 25],\
[743, 743, 2*w^2 - 5*w - 10],\
[761, 761, w^2 + 4*w - 6],\
[773, 773, -5*w^2 + 7*w + 25],\
[787, 787, 3*w^2 - 20],\
[797, 797, 3*w^2 + w - 15],\
[809, 809, 4*w^2 - 3*w - 18],\
[821, 821, 2*w^2 - 5*w - 11],\
[821, 821, 2*w^2 + 2*w - 11],\
[821, 821, 3*w^2 - 4*w - 6],\
[827, 827, 5*w - 7],\
[853, 853, -w^2 + w - 6],\
[859, 859, w^2 + 3*w - 12],\
[863, 863, 3*w^2 - 3*w - 8],\
[863, 863, w^2 + 3*w - 11],\
[863, 863, w^2 - 5*w - 9],\
[881, 881, w^2 + 4*w - 18],\
[881, 881, w^2 - 5*w - 17],\
[881, 881, 4*w^2 - 4*w - 17],\
[883, 883, 5*w - 8],\
[883, 883, 3*w^2 - 3*w - 4],\
[883, 883, 4*w^2 - 6*w - 27],\
[887, 887, w^2 - w - 14],\
[887, 887, 3*w^2 - w - 26],\
[887, 887, 2*w^2 - 5*w - 14],\
[911, 911, 2*w^2 + 4*w - 7],\
[919, 919, 3*w^2 - 3*w - 7],\
[929, 929, 3*w^2 - w - 5],\
[941, 941, 5*w^2 - 24],\
[947, 947, 3*w^2 - w - 6],\
[947, 947, 3*w^2 + 2*w - 13],\
[947, 947, 3*w^2 - 5*w - 26],\
[961, 31, 4*w^2 - 5*w - 15],\
[967, 967, -5*w - 13],\
[967, 967, 4*w^2 - 21],\
[967, 967, 3*w^2 - 2*w - 7],\
[971, 971, w^2 + w - 16]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 + x - 7
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, -1, e, -e - 2, 1, 3, -3, -1, -e - 7, -2*e - 6, -e + 5, e - 1, -1, -e + 3, 3*e + 1, 3*e, 5, 2*e + 7, 2*e + 2, -2*e + 3, -2*e + 5, -4*e - 6, -2*e + 6, 4*e + 3, -3*e - 14, -4*e - 11, 5*e, 2*e - 1, -13, 7*e + 5, -4*e - 14, 3*e + 4, -2*e - 4, -5*e - 2, 4, e - 2, -5*e - 3, -7*e - 1, 2*e + 15, 3*e + 7, 2*e + 3, -6*e + 3, 7*e + 5, 2*e - 19, -2*e + 16, -21, -e - 15, -2*e - 3, -6*e - 13, -13, -18, 5*e + 7, -2*e + 8, 5*e - 4, -6*e - 5, -e, -3*e - 15, 3*e + 4, e - 8, 3*e - 23, -10*e - 2, 6*e - 15, -10*e - 5, 2*e - 12, 10*e + 8, 4*e - 7, 2*e - 1, -8*e - 7, -10, -6*e + 17, -2*e - 25, 3*e - 12, 14, -7, 3*e + 8, 5*e - 10, 2*e - 31, -4*e - 5, 4*e + 29, -4*e + 5, -9*e - 10, 3*e - 24, e - 7, 2*e - 19, -33, e + 19, 3*e + 30, -5*e - 20, 5*e - 10, 10*e + 1, 10*e - 1, -4*e - 2, 12, 2*e + 15, -2*e, e + 33, -e - 20, -8, 10*e + 6, -6*e + 8, -4*e - 8, -5*e - 18, e + 23, 6*e + 2, e + 24, e + 44, 16*e + 11, -9*e - 8, -7*e + 5, -4*e - 38, -6*e - 2, -2*e + 3, e + 3, -7*e - 8, -12*e - 24, -11*e + 2, 4*e - 4, 2*e + 20, 2*e - 19, 6*e + 1, 4*e - 22, -6*e - 19, 5*e + 27, 10*e + 25, 8*e - 12, -2*e + 23, -2*e - 12, 5*e - 24, 4*e - 12, -9*e - 7, -12*e - 4, -6*e + 3, -22, -4*e - 13, 35, -8*e - 19, -2*e - 16, 18, -7*e - 22, -16*e + 2, e - 15, 5*e - 16, 3*e - 14, -2*e + 2, 7*e + 24, 2*e - 15, -4*e + 17, 7*e + 5, 10*e + 26, 4*e - 6, -12*e - 27, -6*e + 22, e + 5, -9*e - 19, -e + 10, 15*e + 3, 10*e, 6*e + 34, -e + 55, -3*e - 33, 5*e - 5, -38, -e + 17, 8*e + 22, -6*e - 37, 18*e + 9, -22]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([5, 5, w + 1])] = 1
AL_eigenvalues[ZF.ideal([5, 5, w - 1])] = 1

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