/*
  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([-58, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([6,6,w - 8])

primes_array = [
[2, 2, w],\
[3, 3, w + 1],\
[3, 3, w + 2],\
[7, 7, -2*w + 15],\
[7, 7, -2*w - 15],\
[11, 11, w + 5],\
[11, 11, w + 6],\
[19, 19, w + 1],\
[19, 19, w + 18],\
[23, 23, w + 9],\
[23, 23, -w + 9],\
[25, 5, 5],\
[29, 29, w],\
[37, 37, w + 13],\
[37, 37, w + 24],\
[43, 43, w + 12],\
[43, 43, w + 31],\
[61, 61, w + 27],\
[61, 61, w + 34],\
[71, 71, 12*w - 91],\
[71, 71, 12*w + 91],\
[101, 101, w + 19],\
[101, 101, w + 82],\
[103, 103, -3*w + 25],\
[103, 103, -3*w - 25],\
[131, 131, w + 53],\
[131, 131, w + 78],\
[151, 151, 2*w - 9],\
[151, 151, -2*w - 9],\
[157, 157, w + 23],\
[157, 157, w + 134],\
[163, 163, w + 59],\
[163, 163, w + 104],\
[167, 167, -w - 15],\
[167, 167, w - 15],\
[169, 13, -13],\
[199, 199, -4*w + 27],\
[199, 199, -4*w - 27],\
[211, 211, w + 67],\
[211, 211, w + 144],\
[223, 223, 2*w - 3],\
[223, 223, -2*w - 3],\
[229, 229, w + 79],\
[229, 229, w + 150],\
[233, 233, 3*w - 17],\
[233, 233, -3*w - 17],\
[239, 239, 6*w + 43],\
[239, 239, 6*w - 43],\
[241, 241, -7*w + 51],\
[241, 241, -7*w - 51],\
[251, 251, w + 73],\
[251, 251, w + 178],\
[257, 257, -8*w - 63],\
[257, 257, -8*w + 63],\
[269, 269, w + 70],\
[269, 269, w + 199],\
[281, 281, 15*w + 113],\
[281, 281, 15*w - 113],\
[289, 17, -17],\
[293, 293, w + 75],\
[293, 293, w + 218],\
[307, 307, w + 66],\
[307, 307, w + 241],\
[313, 313, -6*w + 49],\
[313, 313, -6*w - 49],\
[317, 317, w + 117],\
[317, 317, w + 200],\
[331, 331, w + 148],\
[331, 331, w + 183],\
[353, 353, -3*w - 13],\
[353, 353, 3*w - 13],\
[379, 379, w + 171],\
[379, 379, w + 208],\
[383, 383, -w - 21],\
[383, 383, w - 21],\
[389, 389, w + 35],\
[389, 389, w + 354],\
[401, 401, 3*w - 11],\
[401, 401, -3*w - 11],\
[421, 421, w + 30],\
[421, 421, w + 391],\
[431, 431, -12*w - 89],\
[431, 431, -12*w + 89],\
[439, 439, 3*w - 31],\
[439, 439, -3*w - 31],\
[443, 443, w + 175],\
[443, 443, w + 268],\
[457, 457, -11*w - 81],\
[457, 457, -11*w + 81],\
[461, 461, w + 141],\
[461, 461, w + 320],\
[463, 463, 8*w + 57],\
[463, 463, 8*w - 57],\
[467, 467, w + 92],\
[467, 467, w + 375],\
[487, 487, -4*w - 21],\
[487, 487, 4*w - 21],\
[491, 491, w + 135],\
[491, 491, w + 356],\
[521, 521, -3*w - 1],\
[521, 521, 3*w - 1],\
[541, 541, w + 41],\
[541, 541, w + 500],\
[563, 563, w + 109],\
[563, 563, w + 454],\
[593, 593, -4*w - 39],\
[593, 593, 4*w - 39],\
[619, 619, w + 36],\
[619, 619, w + 583],\
[631, 631, -9*w + 73],\
[631, 631, -9*w - 73],\
[647, 647, 24*w - 181],\
[647, 647, 24*w + 181],\
[653, 653, w + 133],\
[653, 653, w + 520],\
[659, 659, w + 306],\
[659, 659, w + 353],\
[673, 673, 12*w + 95],\
[673, 673, 12*w - 95],\
[677, 677, w + 259],\
[677, 677, w + 418],\
[719, 719, -6*w - 37],\
[719, 719, 6*w - 37],\
[733, 733, w + 304],\
[733, 733, w + 429],\
[739, 739, w + 102],\
[739, 739, w + 637],\
[757, 757, w + 315],\
[757, 757, w + 442],\
[761, 761, -10*w + 81],\
[761, 761, -10*w - 81],\
[773, 773, w + 226],\
[773, 773, w + 547],\
[797, 797, w + 281],\
[797, 797, w + 516],\
[827, 827, w + 239],\
[827, 827, w + 588],\
[829, 829, w + 108],\
[829, 829, w + 721],\
[853, 853, w + 42],\
[853, 853, w + 811],\
[857, 857, 2*w - 33],\
[857, 857, -2*w - 33],\
[859, 859, w + 403],\
[859, 859, w + 456],\
[863, 863, 6*w - 35],\
[863, 863, -6*w - 35],\
[907, 907, w + 128],\
[907, 907, w + 779],\
[919, 919, 4*w - 3],\
[919, 919, -4*w - 3],\
[929, 929, 21*w - 157],\
[929, 929, 21*w + 157],\
[937, 937, 6*w - 55],\
[937, 937, -6*w - 55],\
[947, 947, w + 406],\
[947, 947, w + 541],\
[953, 953, 14*w + 111],\
[953, 953, 14*w - 111],\
[961, 31, -31],\
[971, 971, w + 143],\
[971, 971, w + 828],\
[977, 977, 9*w + 61],\
[977, 977, -9*w + 61],\
[991, 991, -21*w + 163],\
[991, 991, -21*w - 163],\
[997, 997, w + 105],\
[997, 997, w + 892]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 + 4
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1/2*e, -1/2*e, e, -2, -5, -1/2*e, e, -2*e, e, 9, 0, -3, e, 1/2*e, 2*e, 9/2*e, 0, 2*e, -11/2*e, -2, 4, -3*e, -9*e, -20, 13, 0, 15/2*e, -16, -16, 3/2*e, -6*e, 5/2*e, 11/2*e, 3, -21, -22, 4, -17, -23/2*e, 7/2*e, -21, -6, -12*e, -3*e, -4, 17, -18, -12, 4, 4, -12*e, 6*e, -22, -10, -5*e, 11/2*e, 23, -4, -18, 1/2*e, 11*e, 15/2*e, 9/2*e, -13, -10, 2*e, -4*e, -11*e, 4*e, 21, -24, 16*e, e, 24, -6, -15*e, -12*e, -11, -8, -e, 8*e, -17, -23, -6, -15, -10*e, -29/2*e, 18, 24, -7*e, -e, 14, 23, -9*e, 39/2*e, -4, 23, -3*e, -9/2*e, -10, -10, -23/2*e, 5*e, -10*e, -29/2*e, -31, 20, 10*e, 17/2*e, 4, -20, -28, -7, -12*e, 12*e, -23/2*e, -16*e, 25, -26, -29/2*e, -17/2*e, -11, -32, 9/2*e, 21*e, 21/2*e, -9/2*e, 17/2*e, -5*e, -49, -22, -31/2*e, -49/2*e, 5/2*e, 29/2*e, 18*e, 9*e, -17*e, 41/2*e, -28*e, 7/2*e, -20, 13, 35/2*e, 4*e, 0, 0, -26*e, 22*e, 52, -20, -5, 40, 2, 8, -12*e, -24*e, -14, -26, -26, 16*e, -31/2*e, -54, -9, -44, -17, 13*e, -23*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])] = 1/2*e
AL_eigenvalues[ZF.ideal([3,3,-w + 2])] = 1/2*e

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