/*
  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([-50, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([32, 16, -2*w + 14])

primes_array = [
[2, 2, -17*w - 112],\
[2, 2, -17*w + 129],\
[3, 3, -124*w + 941],\
[5, 5, -2*w + 15],\
[5, 5, -2*w - 13],\
[11, 11, 12*w + 79],\
[11, 11, -12*w + 91],\
[19, 19, -90*w - 593],\
[19, 19, 90*w - 683],\
[37, 37, -4*w - 27],\
[37, 37, -4*w + 31],\
[41, 41, 158*w + 1041],\
[41, 41, 158*w - 1199],\
[49, 7, -7],\
[53, 53, 46*w - 349],\
[53, 53, 46*w + 303],\
[67, 67, 586*w - 4447],\
[73, 73, -32*w - 211],\
[73, 73, 32*w - 243],\
[101, 101, 2*w - 11],\
[101, 101, -2*w - 9],\
[103, 103, 18*w - 137],\
[103, 103, -18*w - 119],\
[113, 113, 26*w + 171],\
[113, 113, 26*w - 197],\
[127, 127, 6*w + 41],\
[127, 127, 6*w - 47],\
[137, 137, 2*w - 9],\
[137, 137, -2*w - 7],\
[151, 151, 14*w + 93],\
[151, 151, 14*w - 107],\
[157, 157, 4*w - 33],\
[157, 157, -4*w - 29],\
[163, 163, -42*w - 277],\
[163, 163, 42*w - 319],\
[169, 13, -13],\
[179, 179, 4*w - 27],\
[179, 179, -4*w - 23],\
[181, 181, -100*w + 759],\
[181, 181, -100*w - 659],\
[191, 191, 8*w + 51],\
[191, 191, 8*w - 59],\
[193, 193, 1792*w - 13599],\
[193, 193, -552*w + 4189],\
[197, 197, 2*w - 3],\
[197, 197, -2*w - 1],\
[199, 199, 2*w - 21],\
[199, 199, -2*w - 19],\
[211, 211, -134*w - 883],\
[211, 211, -134*w + 1017],\
[223, 223, 202*w - 1533],\
[223, 223, 202*w + 1331],\
[233, 233, 1826*w - 13857],\
[233, 233, -654*w + 4963],\
[239, 239, 440*w - 3339],\
[239, 239, 440*w + 2899],\
[241, 241, -800*w + 6071],\
[241, 241, 1544*w - 11717],\
[251, 251, 260*w + 1713],\
[251, 251, 260*w - 1973],\
[277, 277, -76*w - 501],\
[277, 277, -76*w + 577],\
[281, 281, -30*w + 227],\
[281, 281, 30*w + 197],\
[283, 283, 2*w - 23],\
[283, 283, -2*w - 21],\
[289, 17, -17],\
[307, 307, 6*w - 49],\
[307, 307, -6*w - 43],\
[311, 311, 40*w + 263],\
[311, 311, -40*w + 303],\
[347, 347, 12*w + 77],\
[347, 347, -12*w + 89],\
[349, 349, 20*w + 133],\
[349, 349, 20*w - 153],\
[353, 353, 294*w + 1937],\
[353, 353, 294*w - 2231],\
[383, 383, -24*w + 181],\
[383, 383, 24*w + 157],\
[397, 397, 484*w - 3673],\
[397, 397, 484*w + 3189],\
[401, 401, 10*w - 73],\
[401, 401, -10*w - 63],\
[421, 421, 4*w - 37],\
[421, 421, -4*w - 33],\
[439, 439, -62*w - 409],\
[439, 439, 62*w - 471],\
[443, 443, -4*w - 17],\
[443, 443, 4*w - 21],\
[457, 457, -144*w + 1093],\
[457, 457, -144*w - 949],\
[503, 503, 216*w - 1639],\
[503, 503, 216*w + 1423],\
[521, 521, 2322*w - 17621],\
[521, 521, 1150*w - 8727],\
[523, 523, -178*w + 1351],\
[523, 523, -178*w - 1173],\
[529, 23, -23],\
[563, 563, -44*w + 333],\
[563, 563, 44*w + 289],\
[571, 571, 30*w + 199],\
[571, 571, 30*w - 229],\
[587, 587, 28*w - 211],\
[587, 587, 28*w + 183],\
[593, 593, -74*w - 487],\
[593, 593, 74*w - 561],\
[599, 599, 936*w - 7103],\
[599, 599, 3280*w - 24891],\
[601, 601, -120*w - 791],\
[601, 601, -120*w + 911],\
[607, 607, -246*w - 1621],\
[607, 607, -246*w + 1867],\
[613, 613, 348*w - 2641],\
[613, 613, 348*w + 2293],\
[619, 619, -18*w + 139],\
[619, 619, -18*w - 121],\
[641, 641, 250*w - 1897],\
[641, 641, 250*w + 1647],\
[643, 643, 22*w - 169],\
[643, 643, -22*w - 147],\
[647, 647, 128*w - 971],\
[647, 647, 128*w + 843],\
[653, 653, -6*w - 31],\
[653, 653, 6*w - 37],\
[677, 677, 542*w - 4113],\
[677, 677, 542*w + 3571],\
[683, 683, -4*w - 9],\
[683, 683, 4*w - 13],\
[691, 691, -6*w - 47],\
[691, 691, 6*w - 53],\
[701, 701, 2570*w - 19503],\
[701, 701, 1398*w - 10609],\
[709, 709, 3708*w - 28139],\
[709, 709, -980*w + 7437],\
[751, 751, 10*w - 81],\
[751, 751, -10*w - 71],\
[809, 809, 206*w + 1357],\
[809, 809, 206*w - 1563],\
[823, 823, 2*w - 33],\
[823, 823, -2*w - 31],\
[829, 829, 3460*w - 26257],\
[829, 829, -1228*w + 9319],\
[841, 29, -29],\
[853, 853, -188*w + 1427],\
[853, 853, -188*w - 1239],\
[857, 857, 162*w + 1067],\
[857, 857, 162*w - 1229],\
[859, 859, 130*w + 857],\
[859, 859, -130*w + 987],\
[877, 877, -4*w - 39],\
[877, 877, 4*w - 43],\
[907, 907, 946*w - 7179],\
[907, 907, 946*w + 6233],\
[929, 929, -10*w + 69],\
[929, 929, 10*w + 59],\
[941, 941, -58*w + 439],\
[941, 941, 58*w + 381],\
[961, 31, -31],\
[967, 967, -14*w - 97],\
[967, 967, 14*w - 111],\
[983, 983, 16*w - 117],\
[983, 983, -16*w - 101],\
[997, 997, -1724*w + 13083],\
[997, 997, 2964*w - 22493]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^3 - x^2 - 4*x + 3
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, 0, e, e^2 - e - 3, -e^2 + e + 3, e^2 + 2*e - 6, e^2 + 2*e - 6, -2*e^2 + 2*e + 6, 2*e^2 - 2*e - 6, -4*e^2 - 2*e + 12, -4*e^2 - 2*e + 12, -6, 6, -4*e^2 + 4*e + 10, -3*e - 6, 3*e + 6, 0, e^2 - 4*e - 6, e^2 - 4*e - 6, -4*e^2 - 5*e + 18, 4*e^2 + 5*e - 18, 6*e^2 + 3*e - 24, -6*e^2 - 3*e + 24, -4*e^2 + 4*e + 6, 4*e^2 - 4*e - 6, e^2 - 7*e + 3, -e^2 + 7*e - 3, -8*e^2 + 2*e + 12, 8*e^2 - 2*e - 12, e^2 + 2*e + 4, -e^2 - 2*e - 4, 4*e^2 + 2*e - 2, 4*e^2 + 2*e - 2, -6*e^2 + 16, 6*e^2 - 16, -5*e^2 - e + 29, -4*e^2 - 5*e + 12, -4*e^2 - 5*e + 12, -2*e^2 - 4*e + 10, -2*e^2 - 4*e + 10, -2*e^2 - 4*e, -2*e^2 - 4*e, 2*e^2 + e + 2, 2*e^2 + e + 2, -3*e^2, 3*e^2, 5*e^2 + e - 9, -5*e^2 - e + 9, -6*e^2 + 6, 6*e^2 - 6, -7*e^2 + e + 23, 7*e^2 - e - 23, 4*e^2 - 4*e, -4*e^2 + 4*e, -6*e^2 + 6*e + 12, -6*e^2 + 6*e + 12, 5*e^2 + 4*e - 22, 5*e^2 + 4*e - 22, 3*e^2 - 3*e + 3, 3*e^2 - 3*e + 3, 6*e^2 - 30, 6*e^2 - 30, -6*e^2 - 6*e + 30, 6*e^2 + 6*e - 30, 4*e^2 - 4*e - 2, -4*e^2 + 4*e + 2, -2*e^2 - e - 18, -6*e - 16, 6*e + 16, 6*e^2 - 6*e - 12, 6*e^2 - 6*e - 12, 9*e^2 + 3*e - 39, 9*e^2 + 3*e - 39, 6*e^2 - 6*e - 18, 6*e^2 - 6*e - 18, -6*e^2 + 12, 6*e^2 - 12, -6*e^2 - 6*e + 24, -6*e^2 - 6*e + 24, -8*e^2 - 4*e + 24, -8*e^2 - 4*e + 24, 2*e^2 - 2*e - 30, -2*e^2 + 2*e + 30, -2*e^2 + 8*e + 12, -2*e^2 + 8*e + 12, 2*e^2 + 7*e - 24, -2*e^2 - 7*e + 24, 7*e^2 - 10*e - 18, 7*e^2 - 10*e - 18, -3*e^2 - 3*e - 17, -3*e^2 - 3*e - 17, 8*e^2 + 4*e - 24, 8*e^2 + 4*e - 24, -14*e^2 + 8*e + 42, 14*e^2 - 8*e - 42, -2*e^2 + 8*e + 18, 2*e^2 - 8*e - 18, -e^2 + 4*e + 30, 3*e^2 - 6*e - 30, 3*e^2 - 6*e - 30, 10*e^2 + 2*e - 38, -10*e^2 - 2*e + 38, -3*e, -3*e, -12*e^2 - 6*e + 42, 12*e^2 + 6*e - 42, 2*e^2 + 10*e + 12, 2*e^2 + 10*e + 12, 2*e^2 + 13*e - 18, 2*e^2 + 13*e - 18, -e^2 - 2*e - 16, e^2 + 2*e + 16, -12*e + 16, -12*e + 16, -10*e^2 - 2*e + 34, 10*e^2 + 2*e - 34, -6*e^2 + 18*e + 24, 6*e^2 - 18*e - 24, 12*e + 6, -12*e - 6, 6*e^2 - 6*e - 6, 6*e^2 - 6*e - 6, 12*e^2 - 42, -12*e^2 + 42, -5*e^2 - 16*e + 24, 5*e^2 + 16*e - 24, -3*e^2 + 3*e + 21, -3*e^2 + 3*e + 21, 14*e^2 - 2*e - 30, -14*e^2 + 2*e + 30, -8*e^2 + 8*e + 30, 8*e^2 - 8*e - 30, -2*e^2 + 14*e + 6, -2*e^2 + 14*e + 6, 10*e^2 - 13*e - 20, -10*e^2 + 13*e + 20, 10*e^2 - 10*e - 30, -10*e^2 + 10*e + 30, 13*e^2 + 2*e - 60, -13*e^2 - 2*e + 60, 4*e^2 + 2*e - 6, 4*e^2 + 2*e - 6, 16*e^2 - 16*e - 54, 4*e^2 + 2*e + 4, 4*e^2 + 2*e + 4, 2*e^2 + 4*e - 6, -2*e^2 - 4*e + 6, -8*e^2 + 8*e + 26, 8*e^2 - 8*e - 26, 4*e^2 + 2*e - 36, 4*e^2 + 2*e - 36, 6*e^2 - 18*e - 28, -6*e^2 + 18*e + 28, 2*e^2 + 28*e - 12, -2*e^2 - 28*e + 12, -8*e^2 - 4*e + 30, 8*e^2 + 4*e - 30, -4*e^2 + 4*e - 38, -e^2 + 7*e - 15, e^2 - 7*e + 15, 6*e^2 - 12, 6*e^2 - 12, 8*e^2 - 2*e + 6, 8*e^2 - 2*e + 6]
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, -17*w - 112])] = 1
AL_eigenvalues[ZF.ideal([2, 2, -17*w + 129])] = -1

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