/*
  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([-49, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([23,23,-w + 9])

primes_array = [
[4, 2, 2],\
[7, 7, w - 7],\
[7, 7, w + 6],\
[9, 3, 3],\
[19, 19, w + 5],\
[19, 19, w - 6],\
[23, 23, w + 8],\
[23, 23, -w + 9],\
[25, 5, 5],\
[29, 29, -w - 4],\
[29, 29, w - 5],\
[37, 37, -w - 3],\
[37, 37, w - 4],\
[41, 41, -w - 9],\
[41, 41, w - 10],\
[43, 43, -w - 2],\
[43, 43, w - 3],\
[47, 47, -w - 1],\
[47, 47, w - 2],\
[53, 53, 2*w - 13],\
[53, 53, -2*w - 11],\
[59, 59, -4*w - 25],\
[59, 59, -4*w + 29],\
[61, 61, -w - 10],\
[61, 61, w - 11],\
[83, 83, -w - 11],\
[83, 83, w - 12],\
[97, 97, 2*w - 11],\
[97, 97, -2*w - 9],\
[101, 101, 3*w - 20],\
[101, 101, -3*w - 17],\
[107, 107, -w - 12],\
[107, 107, w - 13],\
[109, 109, -5*w - 31],\
[109, 109, -5*w + 36],\
[121, 11, -11],\
[127, 127, 2*w - 19],\
[127, 127, -2*w - 17],\
[137, 137, -3*w - 16],\
[137, 137, 3*w - 19],\
[157, 157, -3*w - 23],\
[157, 157, 3*w - 26],\
[163, 163, -4*w + 27],\
[163, 163, 4*w + 23],\
[169, 13, -13],\
[173, 173, -6*w - 37],\
[173, 173, -6*w + 43],\
[181, 181, 2*w - 5],\
[181, 181, -2*w - 3],\
[191, 191, -w - 15],\
[191, 191, w - 16],\
[193, 193, 2*w - 3],\
[193, 193, -2*w - 1],\
[197, 197, 2*w - 1],\
[223, 223, -w - 16],\
[223, 223, w - 17],\
[233, 233, -3*w - 13],\
[233, 233, 3*w - 16],\
[239, 239, -5*w + 34],\
[239, 239, -5*w - 29],\
[251, 251, 5*w - 41],\
[251, 251, 5*w + 36],\
[257, 257, -w - 17],\
[257, 257, w - 18],\
[289, 17, -17],\
[293, 293, -w - 18],\
[293, 293, w - 19],\
[311, 311, -3*w - 10],\
[311, 311, 3*w - 13],\
[313, 313, -3*w - 26],\
[313, 313, 3*w - 29],\
[331, 331, -w - 19],\
[331, 331, w - 20],\
[347, 347, 4*w - 23],\
[347, 347, -4*w - 19],\
[353, 353, 3*w - 11],\
[353, 353, -3*w - 8],\
[379, 379, 2*w - 25],\
[379, 379, -2*w - 23],\
[401, 401, 3*w - 8],\
[401, 401, -3*w - 5],\
[409, 409, 5*w - 43],\
[409, 409, 5*w + 38],\
[419, 419, -5*w - 26],\
[419, 419, 5*w - 31],\
[431, 431, 3*w - 5],\
[431, 431, -3*w - 2],\
[433, 433, -7*w + 48],\
[433, 433, -7*w - 41],\
[443, 443, 3*w - 2],\
[443, 443, 3*w - 1],\
[449, 449, -9*w - 55],\
[449, 449, -9*w + 64],\
[457, 457, -w - 22],\
[457, 457, w - 23],\
[479, 479, 2*w - 27],\
[479, 479, -2*w - 25],\
[487, 487, -3*w - 29],\
[487, 487, 3*w - 32],\
[491, 491, -5*w - 39],\
[491, 491, 5*w - 44],\
[499, 499, 4*w - 19],\
[499, 499, -4*w - 15],\
[503, 503, -w - 23],\
[503, 503, w - 24],\
[521, 521, 11*w - 86],\
[521, 521, -7*w + 47],\
[557, 557, 7*w + 51],\
[557, 557, 7*w - 58],\
[563, 563, -4*w - 13],\
[563, 563, 4*w - 17],\
[569, 569, -10*w - 61],\
[569, 569, -10*w + 71],\
[587, 587, 2*w - 29],\
[587, 587, -2*w - 27],\
[601, 601, -w - 25],\
[601, 601, w - 26],\
[607, 607, -7*w - 39],\
[607, 607, 7*w - 46],\
[613, 613, 3*w - 34],\
[613, 613, -3*w - 31],\
[617, 617, -6*w - 31],\
[617, 617, 6*w - 37],\
[619, 619, 4*w - 15],\
[619, 619, -4*w - 11],\
[631, 631, 5*w - 27],\
[631, 631, -5*w - 22],\
[653, 653, -w - 26],\
[653, 653, w - 27],\
[661, 661, 5*w - 46],\
[661, 661, -5*w - 41],\
[683, 683, -9*w + 62],\
[683, 683, -9*w - 53],\
[691, 691, 7*w - 45],\
[691, 691, -7*w - 38],\
[727, 727, -6*w - 47],\
[727, 727, 6*w - 53],\
[733, 733, 4*w - 41],\
[733, 733, -4*w - 37],\
[739, 739, -4*w - 5],\
[739, 739, 4*w - 9],\
[751, 751, 8*w - 53],\
[751, 751, -8*w - 45],\
[769, 769, 5*w - 24],\
[769, 769, -5*w - 19],\
[773, 773, 7*w - 44],\
[773, 773, -7*w - 37],\
[787, 787, 4*w - 3],\
[787, 787, 4*w - 1],\
[797, 797, -9*w - 52],\
[797, 797, -9*w + 61],\
[811, 811, -5*w - 18],\
[811, 811, 5*w - 23],\
[821, 821, -w - 29],\
[821, 821, w - 30],\
[827, 827, 2*w - 33],\
[827, 827, -2*w - 31],\
[829, 829, -10*w + 69],\
[829, 829, -10*w - 59],\
[839, 839, 5*w - 48],\
[839, 839, -5*w - 43],\
[853, 853, -7*w - 36],\
[853, 853, 7*w - 43],\
[881, 881, -w - 30],\
[881, 881, w - 31],\
[961, 31, -31],\
[991, 991, -5*w - 13],\
[991, 991, 5*w - 18]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^3 - x^2 - 6*x + 4
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/2*e^2 + 1/2*e - 2, -1/2*e^2 - 1/2*e + 4, -1/2*e^2 - 1/2*e + 2, -3/2*e^2 + 1/2*e + 2, -e - 2, e^2 - e - 2, 1, e^2 - 2*e - 5, -2*e^2 + 5, e^2 - 2*e, 2*e^2 + 2*e - 11, -1/2*e^2 + 1/2*e + 7, e^2 + e - 1, 1/2*e^2 - 3/2*e - 4, 1/2*e^2 - 1/2*e - 5, -6, -e^2 + 10, -3/2*e^2 + 3/2*e + 5, -3/2*e^2 + 7/2*e + 12, -1/2*e^2 - 7/2*e + 3, e^2 + 2*e - 6, 2*e^2 - 3*e - 9, 5/2*e^2 + 3/2*e - 11, 4*e - 2, -e^2 + e - 7, -1/2*e^2 + 3/2*e - 3, 3/2*e^2 - 7/2*e - 15, 3*e^2 - e - 14, e^2 - 6*e - 10, -e^2 + 2*e - 3, 1/2*e^2 - 3/2*e - 5, -3/2*e^2 + 5/2*e + 4, 2*e^2 - e - 9, -3/2*e^2 - 1/2*e + 10, -e^2 + e - 1, -e^2 - 3*e + 1, 3/2*e^2 - 1/2*e, -5/2*e^2 + 7/2*e + 1, -3*e^2 + e + 12, -e^2 + 2*e + 1, 3/2*e^2 - 7/2*e - 10, -2*e^2 - 4*e + 10, 4*e^2 - e - 21, -e^2 - 4*e + 2, 3*e^2 - 2*e - 13, -5*e^2 - 3*e + 28, 7/2*e^2 - 13/2*e - 14, 1/2*e^2 + 7/2*e - 6, -11/2*e^2 + 9/2*e + 24, 1/2*e^2 + 3/2*e - 11, 2, -4*e^2 + 3*e + 19, e + 12, 5/2*e^2 + 19/2*e - 17, -5*e + 4, -1/2*e^2 - 5/2*e, e^2 + 4*e + 6, 5/2*e^2 - 9/2*e - 17, e^2 - 6*e - 8, -3*e^2 - 4*e + 15, 4*e^2 + e - 5, -6*e^2 + 19, -1/2*e^2 + 21/2*e + 1, 1/2*e^2 + 5/2*e + 16, -e^2 + 5*e - 2, 5*e^2 + 7*e - 29, -2*e^2 + 5*e + 22, 2*e^2 - 10*e - 10, 6*e^2 + e - 31, -5/2*e^2 - 13/2*e + 9, -e^2 - e - 11, 2*e - 4, -2*e^2 + 3*e + 3, -7/2*e^2 - 11/2*e + 26, -7/2*e^2 + 3/2*e + 25, e^2 + 15, -3*e^2 - 7*e + 33, 2*e^2 + 6*e - 15, 15/2*e^2 + 9/2*e - 30, 4*e^2 - 3*e - 21, -7/2*e^2 + 9/2*e + 21, -2*e^2 + 6*e - 2, -7*e - 2, 2*e^2 + 2*e - 28, 5*e^2 - e - 10, 2*e + 16, -7*e^2 + 4*e + 26, 3*e^2 + 6*e - 9, -3*e^2 + 9, 9/2*e^2 - 17/2*e - 14, 5*e^2 + 3*e - 6, -13/2*e^2 + 13/2*e + 31, -3/2*e^2 - 15/2*e - 6, 3*e^2 - 3*e - 5, -5/2*e^2 - 13/2*e - 1, -7*e^2 - 2*e + 46, 5/2*e^2 + 23/2*e - 25, -3*e^2 - 10*e + 16, 13/2*e^2 - 5/2*e - 18, -7/2*e^2 + 5/2*e - 4, 8*e^2 + 2*e - 34, -9/2*e^2 + 3/2*e + 28, 2*e^2 - 20, 11/2*e^2 - 9/2*e - 30, -8*e^2 - e + 34, e^2 + 2*e + 11, -4*e^2 + 2*e + 25, 11/2*e^2 - 9/2*e - 38, -13/2*e^2 + 9/2*e + 27, -6*e^2 + e + 5, -1/2*e^2 - 27/2*e + 2, 1/2*e^2 - 3/2*e - 20, 3*e^2 - 6*e - 45, 1/2*e^2 + 1/2*e - 10, e^2 - 7, e^2 + 2*e + 13, 1/2*e^2 + 21/2*e + 6, -3*e^2 + 6*e + 10, -e^2 - 10, -17/2*e^2 - 3/2*e + 39, -10*e^2 + 3*e + 49, 5*e^2 - e - 28, -8*e^2 + 7*e + 27, -3*e^2 - 5*e - 5, 1/2*e^2 - 3/2*e - 32, 7/2*e^2 + 11/2*e + 4, -3/2*e^2 + 17/2*e - 6, -8*e^2 + 7*e + 27, -3/2*e^2 - 3/2*e - 23, 5/2*e^2 - 3/2*e - 10, -5/2*e^2 + 7/2*e + 42, 13/2*e^2 + 5/2*e - 49, -e^2 - 4*e + 25, 7/2*e^2 + 15/2*e - 30, -5*e^2 - 7*e + 54, 4*e^2 + 5*e - 47, 7/2*e^2 - 7/2*e - 27, 5/2*e^2 + 7/2*e + 3, -2*e^2 + 3*e - 11, -5/2*e^2 + 13/2*e + 18, -15/2*e^2 - 1/2*e + 25, 3/2*e^2 + 1/2*e - 11, -e^2 - 8*e - 17, -19/2*e^2 + 3/2*e + 32, 3*e^2 - 2*e - 26, -4*e^2 + 36, -e - 6, -11/2*e^2 + 9/2*e + 39, -19/2*e^2 + 1/2*e + 33, -e^2 - 4*e - 1, 2*e^2 + 3*e - 11, 11/2*e^2 - 3/2*e - 28, 25/2*e^2 + 7/2*e - 43, -3/2*e^2 + 15/2*e + 25, -5/2*e^2 + 9/2*e + 23, -1/2*e^2 + 11/2*e + 22, e^2 - 8*e + 5, 4*e^2 + 14*e - 33, -6*e^2 + 5*e + 48, -17/2*e^2 - 15/2*e + 33, -4*e^2 + 4*e + 13, 7/2*e^2 + 5/2*e - 10, -1/2*e^2 + 9/2*e - 5, -4*e^2 + 4*e - 3, -4*e + 50, 4*e^2 - e - 27, -2*e^2 + 7*e - 19]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([23,23,-w + 9])] = -1

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