/*
  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([-55, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([5, 5, -2*w + 15])

primes_array = [
[2, 2, w + 1],\
[3, 3, w + 1],\
[3, 3, w + 2],\
[5, 5, -2*w + 15],\
[11, 11, 3*w - 22],\
[13, 13, w + 4],\
[13, 13, w + 9],\
[17, 17, w + 2],\
[17, 17, w + 15],\
[19, 19, -w - 6],\
[19, 19, w - 6],\
[23, 23, w + 3],\
[23, 23, w + 20],\
[47, 47, w + 14],\
[47, 47, w + 33],\
[49, 7, -7],\
[67, 67, w + 16],\
[67, 67, w + 51],\
[73, 73, w + 36],\
[73, 73, w + 37],\
[79, 79, 5*w + 36],\
[79, 79, 5*w - 36],\
[89, 89, -w - 12],\
[89, 89, w - 12],\
[103, 103, w + 40],\
[103, 103, w + 63],\
[131, 131, -6*w - 43],\
[131, 131, -6*w + 43],\
[139, 139, 2*w - 9],\
[139, 139, -2*w - 9],\
[151, 151, 4*w - 27],\
[151, 151, 4*w + 27],\
[163, 163, w + 50],\
[163, 163, w + 113],\
[173, 173, w + 48],\
[173, 173, w + 125],\
[181, 181, -3*w - 26],\
[181, 181, 3*w - 26],\
[193, 193, w + 21],\
[193, 193, w + 172],\
[197, 197, w + 45],\
[197, 197, w + 152],\
[211, 211, 2*w - 3],\
[211, 211, -2*w - 3],\
[223, 223, w + 72],\
[223, 223, w + 151],\
[229, 229, 6*w + 47],\
[229, 229, 6*w - 47],\
[233, 233, w + 88],\
[233, 233, w + 145],\
[239, 239, -3*w - 16],\
[239, 239, 3*w - 16],\
[269, 269, -w - 18],\
[269, 269, w - 18],\
[271, 271, -8*w - 57],\
[271, 271, -8*w + 57],\
[277, 277, w + 71],\
[277, 277, w + 206],\
[293, 293, w + 73],\
[293, 293, w + 220],\
[337, 337, w + 27],\
[337, 337, w + 310],\
[359, 359, 9*w + 64],\
[359, 359, 9*w - 64],\
[367, 367, w + 34],\
[367, 367, w + 333],\
[373, 373, w + 146],\
[373, 373, w + 227],\
[383, 383, w + 173],\
[383, 383, w + 210],\
[389, 389, -5*w - 42],\
[389, 389, 5*w - 42],\
[401, 401, 29*w - 216],\
[401, 401, 11*w - 84],\
[421, 421, -6*w + 49],\
[421, 421, -6*w - 49],\
[431, 431, 3*w - 8],\
[431, 431, -3*w - 8],\
[439, 439, -4*w - 21],\
[439, 439, 4*w - 21],\
[443, 443, w + 99],\
[443, 443, w + 344],\
[449, 449, -8*w - 63],\
[449, 449, -8*w + 63],\
[457, 457, w + 91],\
[457, 457, w + 366],\
[463, 463, w + 38],\
[463, 463, w + 425],\
[467, 467, w + 191],\
[467, 467, w + 276],\
[479, 479, -3*w - 4],\
[479, 479, 3*w - 4],\
[487, 487, w + 223],\
[487, 487, w + 264],\
[491, 491, 3*w - 2],\
[491, 491, -3*w - 2],\
[509, 509, 2*w - 27],\
[509, 509, -2*w - 27],\
[521, 521, -w - 24],\
[521, 521, w - 24],\
[557, 557, w + 75],\
[557, 557, w + 482],\
[571, 571, 11*w + 78],\
[571, 571, 11*w - 78],\
[587, 587, w + 246],\
[587, 587, w + 341],\
[593, 593, w + 184],\
[593, 593, w + 409],\
[613, 613, w + 235],\
[613, 613, w + 378],\
[641, 641, -4*w - 39],\
[641, 641, 4*w - 39],\
[643, 643, w + 174],\
[643, 643, w + 469],\
[647, 647, w + 257],\
[647, 647, w + 390],\
[659, 659, -18*w + 131],\
[659, 659, 30*w - 221],\
[661, 661, 3*w - 34],\
[661, 661, -3*w - 34],\
[673, 673, w + 196],\
[673, 673, w + 477],\
[677, 677, w + 240],\
[677, 677, w + 437],\
[683, 683, w + 136],\
[683, 683, w + 547],\
[709, 709, 21*w - 158],\
[709, 709, 27*w - 202],\
[727, 727, w + 339],\
[727, 727, w + 388],\
[733, 733, w + 39],\
[733, 733, w + 694],\
[739, 739, 10*w - 69],\
[739, 739, 10*w + 69],\
[811, 811, 35*w - 258],\
[811, 811, -19*w + 138],\
[823, 823, w + 177],\
[823, 823, w + 646],\
[829, 829, -6*w - 53],\
[829, 829, 6*w - 53],\
[841, 29, -29],\
[853, 853, w + 316],\
[853, 853, w + 537],\
[857, 857, w + 270],\
[857, 857, w + 587],\
[863, 863, w + 405],\
[863, 863, w + 458],\
[877, 877, w + 377],\
[877, 877, w + 500],\
[881, 881, -19*w + 144],\
[881, 881, -37*w + 276],\
[883, 883, w + 52],\
[883, 883, w + 831],\
[907, 907, w + 350],\
[907, 907, w + 557],\
[919, 919, -8*w - 51],\
[919, 919, 8*w - 51],\
[929, 929, 5*w - 48],\
[929, 929, -5*w - 48],\
[937, 937, w + 176],\
[937, 937, w + 761],\
[947, 947, w + 252],\
[947, 947, w + 695],\
[953, 953, w + 334],\
[953, 953, w + 619],\
[961, 31, -31],\
[983, 983, w + 277],\
[983, 983, w + 706],\
[997, 997, w + 371],\
[997, 997, w + 626]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^4 - 7*x^2 + 8
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -1/2*e^3 + 3/2*e, -1/2*e^3 + 7/2*e, -1, 2, 3/2*e^3 - 13/2*e, -1/2*e^3 + 7/2*e, 1/2*e^3 + 1/2*e, -3/2*e^3 + 13/2*e, -2*e^2 + 6, 2*e^2 - 10, -1/2*e^3 + 7/2*e, -1/2*e^3 + 11/2*e, -3/2*e^3 + 13/2*e, -3/2*e^3 + 9/2*e, 4*e^2 - 14, -3/2*e^3 + 29/2*e, -3/2*e^3 + 17/2*e, 5/2*e^3 - 35/2*e, 1/2*e^3 + 1/2*e, 6, 4*e^2 - 10, 2*e^2 + 4, 2*e^2 - 12, 1/2*e^3 - 15/2*e, -7/2*e^3 + 29/2*e, 4*e^2 - 12, -12, 6*e^2 - 20, 6*e^2 - 20, -2*e^2 + 8, 2*e^2 + 8, 9/2*e^3 - 47/2*e, 1/2*e^3 - 11/2*e, -1/2*e^3 + 23/2*e, 3/2*e^3 - 29/2*e, 6*e^2 - 16, 2*e^2 - 16, -1/2*e^3 - 1/2*e, -5/2*e^3 + 27/2*e, 3/2*e^3 - 29/2*e, -1/2*e^3 + 7/2*e, -4*e^2 + 4, 8*e^2 - 28, -7/2*e^3 + 49/2*e, 1/2*e^3 - 19/2*e, 4*e^2 - 26, 6, 1/2*e^3 - 7/2*e, 13/2*e^3 - 67/2*e, 4*e^2 - 14, 2, -2*e^2 + 12, 6*e^2 - 4, 2*e^2 - 24, -2*e^2 + 8, -13/2*e^3 + 67/2*e, -17/2*e^3 + 71/2*e, -11/2*e^3 + 37/2*e, 9/2*e^3 - 47/2*e, -7/2*e^3 + 49/2*e, -11/2*e^3 + 53/2*e, 4*e^2 - 18, 8*e^2 - 34, 7/2*e^3 - 37/2*e, 15/2*e^3 - 73/2*e, -9/2*e^3 + 47/2*e, -5/2*e^3 + 19/2*e, 7/2*e^3 - 13/2*e, 7/2*e^3 - 17/2*e, 6*e^2 + 4, 6*e^2 - 12, -2*e^2 + 12, 6*e^2 - 20, -4*e^2 - 10, -4*e^2 + 22, -2*e^2 - 14, 6*e^2 - 46, -8*e^2 + 16, 16, -1/2*e^3 - 9/2*e, -1/2*e^3 - 13/2*e, -4*e^2 + 2, 4*e^2 - 30, -3/2*e^3 - 19/2*e, -7/2*e^3 + 9/2*e, -7/2*e^3 + 37/2*e, 1/2*e^3 - 7/2*e, 3/2*e^3 - 33/2*e, -5/2*e^3 + 51/2*e, 18, -12*e^2 + 34, 7/2*e^3 - 13/2*e, -1/2*e^3 - 17/2*e, 4*e^2 - 22, -4*e^2 + 42, -8*e^2 + 6, 4*e^2 + 6, 14*e^2 - 52, -10*e^2 + 44, -19/2*e^3 + 85/2*e, 1/2*e^3 - 39/2*e, -16*e^2 + 66, -8*e^2 + 2, -11/2*e^3 + 53/2*e, 5/2*e^3 - 55/2*e, -17/2*e^3 + 79/2*e, -5/2*e^3 + 43/2*e, 1/2*e^3 + 25/2*e, 5/2*e^3 - 35/2*e, -12*e^2 + 50, -14, 1/2*e^3 + 13/2*e, -7/2*e^3 + 73/2*e, -1/2*e^3 + 35/2*e, 23/2*e^3 - 113/2*e, 6*e^2 - 20, -10*e^2 + 44, -6*e^2 + 28, 2*e^2 + 28, 11/2*e^3 - 53/2*e, 7/2*e^3 - 25/2*e, 5/2*e^3 - 35/2*e, 17/2*e^3 - 103/2*e, 11/2*e^3 - 93/2*e, 11/2*e^3 - 49/2*e, -10*e^2 + 24, 6*e^2 - 24, 27/2*e^3 - 117/2*e, -13/2*e^3 + 79/2*e, -3/2*e^3 + 5/2*e, -7/2*e^3 + 49/2*e, -18*e^2 + 52, 14*e^2 - 44, 4*e^2 + 10, -4*e^2 - 22, -21/2*e^3 + 83/2*e, -5/2*e^3 + 23/2*e, -18, -8*e^2 + 46, -20*e^2 + 58, -27/2*e^3 + 125/2*e, 17/2*e^3 - 47/2*e, -7/2*e^3 + 17/2*e, 21/2*e^3 - 123/2*e, -33/2*e^3 + 143/2*e, 15/2*e^3 - 77/2*e, -11/2*e^3 + 93/2*e, -15/2*e^3 + 89/2*e, -18*e^2 + 64, 6*e^2, 13/2*e^3 - 47/2*e, 5/2*e^3 - 51/2*e, -9/2*e^3 + 31/2*e, -1/2*e^3 + 11/2*e, 8*e^2 - 64, -32, 2*e^2 - 48, 14*e^2 - 32, -9/2*e^3 + 7/2*e, -13/2*e^3 + 51/2*e, -7/2*e^3 - 3/2*e, 9/2*e^3 - 23/2*e, -21/2*e^3 + 107/2*e, 7/2*e^3 - 49/2*e, -8*e^2 + 22, 9/2*e^3 - 63/2*e, -31/2*e^3 + 141/2*e, -1/2*e^3 + 23/2*e, -5/2*e^3 + 19/2*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([5, 5, -2*w + 15])] = 1

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