/*
  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([-82, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([2, 2, w])

primes_array = [
[2, 2, w],\
[3, 3, w + 1],\
[3, 3, w + 2],\
[11, 11, w + 4],\
[11, 11, w + 7],\
[13, 13, w + 2],\
[13, 13, w + 11],\
[19, 19, w + 5],\
[19, 19, w + 14],\
[23, 23, w + 6],\
[23, 23, w + 17],\
[25, 5, -5],\
[29, 29, w + 13],\
[29, 29, w + 16],\
[31, 31, w + 12],\
[31, 31, w + 19],\
[41, 41, w],\
[49, 7, -7],\
[53, 53, w + 20],\
[53, 53, w + 33],\
[67, 67, w + 22],\
[67, 67, w + 45],\
[73, 73, -w - 3],\
[73, 73, w - 3],\
[101, 101, w + 48],\
[101, 101, w + 53],\
[103, 103, 2*w - 15],\
[103, 103, -2*w - 15],\
[109, 109, w + 54],\
[109, 109, w + 55],\
[113, 113, 2*w - 21],\
[113, 113, -2*w - 21],\
[127, 127, w + 35],\
[127, 127, w + 92],\
[149, 149, w + 23],\
[149, 149, w + 126],\
[157, 157, w + 32],\
[157, 157, w + 125],\
[179, 179, w + 34],\
[179, 179, w + 145],\
[181, 181, w + 25],\
[181, 181, w + 156],\
[211, 211, w + 90],\
[211, 211, w + 121],\
[223, 223, -4*w - 33],\
[223, 223, 4*w - 33],\
[227, 227, w + 38],\
[227, 227, w + 189],\
[229, 229, w + 51],\
[229, 229, w + 178],\
[241, 241, w + 75],\
[241, 241, w + 166],\
[271, 271, w + 95],\
[271, 271, w + 176],\
[289, 17, -17],\
[293, 293, w + 31],\
[293, 293, w + 262],\
[317, 317, w + 84],\
[317, 317, w + 233],\
[331, 331, w + 134],\
[331, 331, w + 197],\
[337, 337, w + 115],\
[337, 337, w + 222],\
[347, 347, w + 155],\
[347, 347, w + 192],\
[353, 353, w + 105],\
[353, 353, w + 248],\
[359, 359, -w - 21],\
[359, 359, w - 21],\
[367, 367, w + 123],\
[367, 367, w + 244],\
[397, 397, w + 102],\
[397, 397, w + 295],\
[401, 401, 2*w - 27],\
[401, 401, -2*w - 27],\
[409, 409, w + 30],\
[409, 409, w + 379],\
[421, 421, w + 107],\
[421, 421, w + 314],\
[431, 431, w + 157],\
[431, 431, w + 274],\
[433, 433, w + 184],\
[433, 433, w + 249],\
[449, 449, 3*w - 17],\
[449, 449, -3*w - 17],\
[487, 487, -3*w - 35],\
[487, 487, 3*w - 35],\
[499, 499, w + 138],\
[499, 499, w + 361],\
[509, 509, w + 56],\
[509, 509, w + 453],\
[547, 547, w + 58],\
[547, 547, w + 489],\
[557, 557, w + 235],\
[557, 557, w + 322],\
[563, 563, w + 229],\
[563, 563, w + 334],\
[569, 569, -3*w - 13],\
[569, 569, 3*w - 13],\
[571, 571, w + 129],\
[571, 571, w + 442],\
[587, 587, w + 114],\
[587, 587, w + 473],\
[599, 599, w + 185],\
[599, 599, w + 414],\
[607, 607, w + 36],\
[607, 607, w + 571],\
[617, 617, 3*w - 11],\
[617, 617, -3*w - 11],\
[631, 631, 3*w - 37],\
[631, 631, -3*w - 37],\
[643, 643, w + 255],\
[643, 643, w + 388],\
[647, 647, -w - 27],\
[647, 647, w - 27],\
[653, 653, w + 188],\
[653, 653, w + 465],\
[659, 659, w + 93],\
[659, 659, w + 566],\
[683, 683, w + 273],\
[683, 683, w + 410],\
[691, 691, w + 321],\
[691, 691, w + 370],\
[709, 709, w + 47],\
[709, 709, w + 662],\
[743, 743, 6*w - 47],\
[743, 743, -6*w - 47],\
[757, 757, w + 68],\
[757, 757, w + 689],\
[761, 761, 2*w - 33],\
[761, 761, -2*w - 33],\
[769, 769, 7*w + 57],\
[769, 769, -7*w + 57],\
[773, 773, w + 49],\
[773, 773, w + 724],\
[827, 827, w + 387],\
[827, 827, w + 440],\
[857, 857, w + 238],\
[857, 857, w + 619],\
[863, 863, w + 169],\
[863, 863, w + 694],\
[881, 881, w + 277],\
[881, 881, w + 604],\
[883, 883, w + 247],\
[883, 883, w + 636],\
[911, 911, w + 91],\
[911, 911, w + 820],\
[953, 953, w + 193],\
[953, 953, w + 760],\
[971, 971, w + 259],\
[971, 971, w + 712],\
[983, 983, w + 345],\
[983, 983, w + 638],\
[997, 997, w + 413],\
[997, 997, w + 584]]
primes = [ZF.ideal(I) for I in primes_array]

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

hecke_eigenvalues_array = [1/2*e - 1, e, 1/2*e - 2, 1/2*e, e - 4, 3/2*e - 6, 3/2*e, -3/2*e, 0, 0, -3*e + 6, 4, e - 4, -e, -2*e + 4, 5*e - 10, -3*e + 6, 2, 2*e - 8, -2*e, -9/2*e, 3*e - 12, 2, -4, 11/2*e, 1/2*e - 2, 16, -2, 0, 6*e, -6, 6, 8*e - 16, 10*e - 20, 5/2*e, 13/2*e - 26, -3/2*e + 6, -3/2*e, -4*e, -13/2*e + 26, -3*e + 12, 9*e, 6*e - 24, -9/2*e, 2, -16, -e + 4, 11/2*e, -6*e, 0, -7*e + 14, -11*e + 22, -4*e + 8, e - 2, -20, 7*e - 28, 11*e, 5/2*e - 10, 7/2*e, 3*e, 21/2*e - 42, 11*e - 22, 7*e - 14, -19/2*e + 38, -e, -9*e + 18, -15*e + 30, 30, 12, 5*e - 10, -8*e + 16, 6*e, 0, 12, -18, 13*e - 26, -7*e + 14, -3/2*e + 6, -3/2*e, -6*e + 12, -12*e + 24, 17*e - 34, 7*e - 14, -30, 6, 16, -38, 9/2*e, -9*e + 36, 7/2*e - 14, -19/2*e, -6*e, -3/2*e + 6, 19/2*e, -13/2*e + 26, 29/2*e, 5*e - 20, -42, -18, -3*e, -33/2*e + 66, -13/2*e, -e + 4, 0, 0, 4*e - 8, -4*e + 8, 18, 18, 32, -16, 21/2*e, 3*e - 12, -24, -12, -13*e, e - 4, -29/2*e, e - 4, 11*e - 44, -31/2*e, -21/2*e + 42, -3*e, 33/2*e, 33/2*e - 66, 12, -48, -15*e + 60, 9*e, 42, -42, 14, 38, -8*e + 32, 8*e, 7*e, -23/2*e + 46, 21*e - 42, -21*e + 42, 18*e - 36, -24*e + 48, 9*e - 18, 15*e - 30, 12*e, 9/2*e - 18, 12*e - 24, -12*e + 24, 21*e - 42, 15*e - 30, -19/2*e, 11*e - 44, -12*e + 24, 12*e - 24, -3*e + 12, -3*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 + 1

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