/*
  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([1, 7, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16, 4, w^3 + w^2 - 5*w - 2])

primes_array = [
[2, 2, -w + 1],\
[4, 2, -w^2 - w + 3],\
[5, 5, w^3 - 5*w + 1],\
[11, 11, -w^3 + 6*w - 2],\
[13, 13, -w^2 + 4],\
[17, 17, 2*w^3 + w^2 - 10*w - 2],\
[37, 37, w^3 + w^2 - 6*w - 3],\
[37, 37, -w^3 + 6*w - 4],\
[41, 41, -w^3 + 5*w - 5],\
[43, 43, w^3 - 4*w + 4],\
[43, 43, -2*w^3 + 11*w - 2],\
[47, 47, -2*w^3 - w^2 + 12*w],\
[47, 47, 2*w - 1],\
[61, 61, -w^3 + w^2 + 6*w - 5],\
[71, 71, w^3 + w^2 - 4*w - 3],\
[71, 71, 2*w^3 + 2*w^2 - 9*w - 2],\
[79, 79, w^3 + w^2 - 6*w - 5],\
[81, 3, -3],\
[83, 83, -3*w^3 - w^2 + 16*w + 3],\
[97, 97, w^3 + w^2 - 6*w + 1],\
[103, 103, -2*w^3 - 2*w^2 + 7*w - 2],\
[103, 103, -3*w^3 + 14*w - 12],\
[107, 107, -w^3 + 3*w + 3],\
[125, 5, -2*w^3 - w^2 + 8*w - 2],\
[127, 127, w^3 - w^2 - 4*w + 1],\
[131, 131, 2*w^3 - 10*w + 3],\
[137, 137, -5*w^3 - 2*w^2 + 26*w + 2],\
[137, 137, w^3 - 7*w + 1],\
[139, 139, -2*w^3 - w^2 + 8*w],\
[149, 149, w^3 - 2*w^2 - 7*w + 9],\
[149, 149, -2*w^3 + 11*w],\
[151, 151, 2*w^2 + 2*w - 9],\
[151, 151, -5*w^3 - 2*w^2 + 27*w + 1],\
[151, 151, w^3 - 7*w + 3],\
[151, 151, 2*w^3 + 2*w^2 - 11*w - 8],\
[157, 157, w^3 - 7*w - 3],\
[169, 13, 6*w^3 + 4*w^2 - 32*w - 11],\
[173, 173, w^3 + w^2 - 4*w - 7],\
[191, 191, -3*w^3 + 14*w - 10],\
[193, 193, 2*w^3 - 12*w + 3],\
[197, 197, w + 4],\
[197, 197, w^3 + 2*w^2 - 6*w - 6],\
[197, 197, 2*w^3 + w^2 - 10*w + 2],\
[197, 197, 2*w^2 - 3],\
[199, 199, w^3 + 2*w^2 - 4*w - 4],\
[223, 223, -w^3 - 2*w^2 + 5*w + 7],\
[229, 229, 5*w^3 + 3*w^2 - 26*w - 5],\
[233, 233, 2*w + 3],\
[241, 241, 2*w^3 + 2*w^2 - 10*w - 3],\
[251, 251, w^3 - 2*w^2 - 5*w + 7],\
[263, 263, 2*w^3 + w^2 - 12*w + 2],\
[269, 269, 2*w^3 + 3*w^2 - 14*w - 4],\
[271, 271, 3*w^3 + 2*w^2 - 15*w - 7],\
[281, 281, 2*w^2 + w - 4],\
[281, 281, w^2 - 8],\
[283, 283, -3*w^3 + 18*w - 2],\
[283, 283, -w^3 - w^2 + 4*w - 3],\
[283, 283, -w^3 + w^2 + 6*w - 3],\
[283, 283, w^3 + 2*w^2 - 5*w - 3],\
[293, 293, -4*w^3 + 19*w - 16],\
[307, 307, -w^3 + 2*w^2 + 6*w - 8],\
[311, 311, 3*w^3 + 2*w^2 - 17*w - 9],\
[311, 311, w^3 + 2*w^2 - 6*w - 8],\
[313, 313, -4*w^3 - 2*w^2 + 17*w - 6],\
[317, 317, 2*w^3 - 9*w + 2],\
[317, 317, 3*w^2 + 2*w - 10],\
[331, 331, 5*w^3 + 4*w^2 - 26*w - 12],\
[337, 337, 2*w^3 + w^2 - 8*w + 6],\
[347, 347, 2*w^3 - 9*w + 4],\
[353, 353, w^3 - 5*w - 3],\
[359, 359, -w^3 + w + 3],\
[367, 367, -2*w^3 + 12*w - 7],\
[367, 367, 2*w^3 + 4*w^2 - 6*w - 7],\
[379, 379, -w^3 - 2*w^2 + w + 3],\
[379, 379, -3*w^2 - 2*w + 12],\
[397, 397, -2*w^3 - w^2 + 6*w + 2],\
[397, 397, -w^3 + 3*w - 7],\
[397, 397, -2*w^3 - 2*w^2 + 9*w + 6],\
[397, 397, w^3 + 2*w^2 - 5*w - 5],\
[401, 401, 3*w^3 + 3*w^2 - 16*w - 13],\
[401, 401, w^3 + 2*w^2 - 6*w - 4],\
[431, 431, 3*w^3 + 2*w^2 - 14*w - 4],\
[431, 431, 2*w^3 + w^2 - 10*w + 4],\
[433, 433, -2*w^3 + 2*w^2 + 13*w - 12],\
[433, 433, -w^3 + 4*w^2 + 8*w - 18],\
[439, 439, 2*w^3 + 2*w^2 - 8*w + 3],\
[439, 439, -w^3 + 3*w^2 + 6*w - 11],\
[443, 443, -7*w^3 - 2*w^2 + 39*w + 1],\
[457, 457, w^3 + 2*w^2 - 3*w - 7],\
[461, 461, w^2 - 2*w - 4],\
[461, 461, 4*w^3 + 2*w^2 - 20*w - 5],\
[463, 463, 3*w^3 + 2*w^2 - 13*w - 3],\
[467, 467, -3*w^3 + 15*w - 11],\
[467, 467, -4*w^3 + 18*w + 1],\
[479, 479, 2*w^2 + 2*w - 11],\
[487, 487, -3*w^3 - 2*w^2 + 19*w + 1],\
[487, 487, 4*w^3 + 2*w^2 - 19*w],\
[491, 491, 3*w^3 + 2*w^2 - 18*w],\
[499, 499, -w^3 + 3*w - 5],\
[499, 499, -6*w^3 - 2*w^2 + 31*w - 2],\
[523, 523, 2*w^2 + 3*w - 10],\
[541, 541, 2*w^3 + 3*w^2 - 8*w - 6],\
[547, 547, -3*w^3 - w^2 + 16*w - 3],\
[563, 563, -w^3 + 5*w - 7],\
[563, 563, 2*w^2 + w - 2],\
[571, 571, 3*w^3 + 2*w^2 - 12*w + 6],\
[577, 577, -2*w^3 + w^2 + 8*w - 6],\
[577, 577, -2*w^3 - 2*w^2 + 12*w + 11],\
[587, 587, -5*w^3 - w^2 + 26*w - 5],\
[593, 593, -w^3 + 8*w - 4],\
[599, 599, -w^3 + w^2 + 4*w - 9],\
[601, 601, 3*w^3 + w^2 - 14*w + 1],\
[607, 607, 2*w^2 + 2*w - 3],\
[607, 607, 4*w^3 - 24*w + 1],\
[613, 613, -3*w^3 - 3*w^2 + 16*w + 9],\
[617, 617, -2*w^3 + 13*w - 6],\
[619, 619, -4*w^3 + 20*w - 1],\
[631, 631, -5*w^3 - 2*w^2 + 29*w + 5],\
[643, 643, -w^3 - 2*w^2 + 6*w + 10],\
[647, 647, -5*w^3 - 4*w^2 + 20*w - 4],\
[647, 647, -3*w^3 - 3*w^2 + 18*w + 7],\
[653, 653, 4*w^3 - 20*w + 3],\
[653, 653, w^3 - 8*w + 2],\
[659, 659, -9*w^3 - 4*w^2 + 48*w + 4],\
[659, 659, -5*w^3 - 2*w^2 + 25*w - 1],\
[661, 661, 4*w^3 + 2*w^2 - 21*w],\
[673, 673, -3*w^3 + w^2 + 18*w - 9],\
[683, 683, 2*w^3 + 2*w^2 - 7*w - 4],\
[691, 691, -5*w^3 - 3*w^2 + 28*w + 7],\
[691, 691, 3*w^3 - 15*w + 5],\
[701, 701, -2*w^3 + 2*w^2 + 11*w - 10],\
[701, 701, -w^3 + 8*w - 10],\
[709, 709, -4*w^3 - w^2 + 20*w - 4],\
[709, 709, w^3 + 4*w^2 - w - 13],\
[719, 719, -2*w^3 + 12*w - 9],\
[739, 739, -6*w^3 - 4*w^2 + 29*w + 6],\
[739, 739, -w^3 + w^2 + 8*w - 7],\
[769, 769, -w^3 + w^2 + 8*w - 5],\
[769, 769, 3*w^3 - 2*w^2 - 15*w + 19],\
[773, 773, -4*w^3 + 22*w - 9],\
[797, 797, -2*w^3 + 13*w - 2],\
[827, 827, -w^3 + 6*w - 8],\
[827, 827, -4*w^2 - 3*w + 14],\
[839, 839, w^2 + 4*w - 6],\
[857, 857, 7*w^3 + 2*w^2 - 37*w + 1],\
[863, 863, 3*w^3 - 14*w + 2],\
[881, 881, -3*w^3 + 2*w^2 + 15*w - 13],\
[883, 883, 2*w^3 - w^2 - 10*w + 14],\
[887, 887, -5*w^3 - 4*w^2 + 25*w + 11],\
[887, 887, 3*w^3 - 14*w + 8],\
[907, 907, 4*w^3 - 20*w + 13],\
[907, 907, 2*w^2 + 4*w - 5],\
[907, 907, -3*w^3 + 18*w - 4],\
[907, 907, w - 6],\
[947, 947, 3*w^3 + 3*w^2 - 12*w - 5],\
[947, 947, 2*w^3 + 3*w^2 - 10*w - 10],\
[961, 31, 2*w^3 - w^2 - 12*w + 4],\
[961, 31, -w^3 + 2*w^2 + 5*w - 5],\
[971, 971, -4*w^3 - w^2 + 20*w - 2],\
[991, 991, -2*w^3 + 3*w^2 + 14*w - 18],\
[997, 997, 7*w^3 + 2*w^2 - 36*w + 6]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^12 - 4*x^11 - 10*x^10 + 51*x^9 + 25*x^8 - 222*x^7 - 7*x^6 + 430*x^5 - 19*x^4 - 374*x^3 - 10*x^2 + 112*x + 16
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 0, 3/10*e^10 - 6/5*e^9 - 13/5*e^8 + 137/10*e^7 + 37/10*e^6 - 48*e^5 + 13/2*e^4 + 62*e^3 - 87/10*e^2 - 116/5*e - 8/5, -2/5*e^11 + 12/5*e^10 + 3/5*e^9 - 131/5*e^8 + 138/5*e^7 + 431/5*e^6 - 122*e^5 - 112*e^4 + 798/5*e^3 + 317/5*e^2 - 282/5*e - 68/5, 1/2*e^11 - 5/2*e^10 - 2*e^9 + 53/2*e^8 - 20*e^7 - 161/2*e^6 + 201/2*e^5 + 167/2*e^4 - 265/2*e^3 - 53/2*e^2 + 50*e + 6, -3/10*e^11 + 17/10*e^10 + 3/5*e^9 - 177/10*e^8 + 89/5*e^7 + 103/2*e^6 - 147/2*e^5 - 95/2*e^4 + 797/10*e^3 + 77/10*e^2 - 77/5*e + 2, 1/10*e^11 - 7/10*e^10 + 15/2*e^8 - 39/5*e^7 - 227/10*e^6 + 57/2*e^5 + 39/2*e^4 - 279/10*e^3 + 53/10*e^2 + 8*e - 22/5, -3/5*e^11 + 29/10*e^10 + 16/5*e^9 - 162/5*e^8 + 161/10*e^7 + 221/2*e^6 - 100*e^5 - 289/2*e^4 + 712/5*e^3 + 669/10*e^2 - 274/5*e - 8, -7/10*e^11 + 41/10*e^10 + 6/5*e^9 - 439/10*e^8 + 232/5*e^7 + 1367/10*e^6 - 413/2*e^5 - 305/2*e^4 + 2733/10*e^3 + 671/10*e^2 - 504/5*e - 98/5, -6/5*e^11 + 27/5*e^10 + 8*e^9 - 61*e^8 + 68/5*e^7 + 1062/5*e^6 - 133*e^5 - 289*e^4 + 974/5*e^3 + 762/5*e^2 - 72*e - 116/5, -1/10*e^11 + 6/5*e^10 - 2*e^9 - 23/2*e^8 + 303/10*e^7 + 126/5*e^6 - 211/2*e^5 + 2*e^4 + 1249/10*e^3 - 129/5*e^2 - 43*e + 2/5, 1/10*e^11 - 14/5*e^9 + 21/10*e^8 + 45/2*e^7 - 107/5*e^6 - 131/2*e^5 + 59*e^4 + 631/10*e^3 - 48*e^2 - 29/5*e + 46/5, -1/2*e^11 + 13/5*e^10 + 13/5*e^9 - 297/10*e^8 + 129/10*e^7 + 532/5*e^6 - 145/2*e^5 - 155*e^4 + 165/2*e^3 + 468/5*e^2 - 87/5*e - 86/5, 1/2*e^11 - 2*e^10 - 5*e^9 + 49/2*e^8 + 27/2*e^7 - 98*e^6 - 23/2*e^5 + 160*e^4 - 1/2*e^3 - 98*e^2 + 7*e + 14, -3/5*e^10 + 7/5*e^9 + 41/5*e^8 - 87/5*e^7 - 197/5*e^6 + 70*e^5 + 84*e^4 - 108*e^3 - 373/5*e^2 + 262/5*e + 96/5, -4/5*e^11 + 17/5*e^10 + 29/5*e^9 - 193/5*e^8 + 23/5*e^7 + 674/5*e^6 - 77*e^5 - 179*e^4 + 576/5*e^3 + 417/5*e^2 - 176/5*e - 32/5, 1/5*e^11 - 6/5*e^10 - 4/5*e^9 + 73/5*e^8 - 49/5*e^7 - 283/5*e^6 + 57*e^5 + 82*e^4 - 454/5*e^3 - 166/5*e^2 + 216/5*e + 4/5, -1/2*e^11 + 17/10*e^10 + 26/5*e^9 - 189/10*e^8 - 91/5*e^7 + 633/10*e^6 + 87/2*e^5 - 153/2*e^4 - 143/2*e^3 + 197/10*e^2 + 196/5*e + 58/5, -2/5*e^11 + 2*e^10 + 11/5*e^9 - 112/5*e^8 + 10*e^7 + 373/5*e^6 - 64*e^5 - 83*e^4 + 443/5*e^3 + 15*e^2 - 154/5*e + 36/5, 1/5*e^11 - 3/10*e^10 - 17/5*e^9 + 24/5*e^8 + 193/10*e^7 - 51/2*e^6 - 40*e^5 + 101/2*e^4 + 96/5*e^3 - 353/10*e^2 + 58/5*e + 8, e^11 - 26/5*e^10 - 21/5*e^9 + 282/5*e^8 - 184/5*e^7 - 904/5*e^6 + 184*e^5 + 211*e^4 - 228*e^3 - 386/5*e^2 + 324/5*e - 8/5, -7/10*e^11 + 8/5*e^10 + 51/5*e^9 - 199/10*e^8 - 561/10*e^7 + 396/5*e^6 + 305/2*e^5 - 117*e^4 - 1967/10*e^3 + 263/5*e^2 + 421/5*e - 38/5, -3/5*e^11 + 11/5*e^10 + 5*e^9 - 22*e^8 - 41/5*e^7 + 276/5*e^6 + 7*e^5 - 17*e^4 - 148/5*e^3 - 209/5*e^2 + 20*e + 32/5, 1/5*e^11 - 3/2*e^10 + 2/5*e^9 + 81/5*e^8 - 39/2*e^7 - 533/10*e^6 + 65*e^5 + 151/2*e^4 - 239/5*e^3 - 107/2*e^2 - 38/5*e + 52/5, -9/10*e^11 + 23/5*e^10 + 19/5*e^9 - 491/10*e^8 + 329/10*e^7 + 150*e^6 - 329/2*e^5 - 149*e^4 + 2021/10*e^3 + 133/5*e^2 - 291/5*e + 2, 1/10*e^11 - 11/5*e^10 + 6*e^9 + 43/2*e^8 - 783/10*e^7 - 266/5*e^6 + 575/2*e^5 + 32*e^4 - 3819/10*e^3 - 36/5*e^2 + 149*e + 58/5, -3/5*e^11 + 18/5*e^10 + 2/5*e^9 - 194/5*e^8 + 242/5*e^7 + 619/5*e^6 - 215*e^5 - 150*e^4 + 1477/5*e^3 + 368/5*e^2 - 598/5*e - 62/5, -9/10*e^11 + 31/10*e^10 + 49/5*e^9 - 381/10*e^8 - 158/5*e^7 + 305/2*e^6 + 75/2*e^5 - 493/2*e^4 - 179/10*e^3 + 1531/10*e^2 + 29/5*e - 22, 9/10*e^11 - 26/5*e^10 - 12/5*e^9 + 583/10*e^8 - 513/10*e^7 - 1012/5*e^6 + 485/2*e^5 + 288*e^4 - 3211/10*e^3 - 921/5*e^2 + 513/5*e + 186/5, -3/2*e^11 + 57/10*e^10 + 66/5*e^9 - 649/10*e^8 - 96/5*e^7 + 2283/10*e^6 - 85/2*e^5 - 617/2*e^4 + 189/2*e^3 + 1457/10*e^2 - 204/5*e - 22/5, -1/10*e^11 + 17/10*e^10 - 4*e^9 - 33/2*e^8 + 269/5*e^7 + 397/10*e^6 - 383/2*e^5 - 35/2*e^4 + 2389/10*e^3 - 113/10*e^2 - 79*e + 2/5, 13/10*e^11 - 27/5*e^10 - 49/5*e^9 + 601/10*e^8 - 1/10*e^7 - 1014/5*e^6 + 163/2*e^5 + 260*e^4 - 1067/10*e^3 - 632/5*e^2 + 141/5*e + 82/5, -3/5*e^11 + 9/5*e^10 + 38/5*e^9 - 111/5*e^8 - 174/5*e^7 + 443/5*e^6 + 81*e^5 - 137*e^4 - 453/5*e^3 + 329/5*e^2 + 148/5*e - 4/5, 7/10*e^11 - 26/5*e^10 + 16/5*e^9 + 521/10*e^8 - 933/10*e^7 - 693/5*e^6 + 703/2*e^5 + 108*e^4 - 4313/10*e^3 - 166/5*e^2 + 751/5*e + 134/5, 1/5*e^11 - 6/5*e^10 - 4/5*e^9 + 68/5*e^8 - 34/5*e^7 - 243/5*e^6 + 29*e^5 + 75*e^4 - 144/5*e^3 - 301/5*e^2 + 86/5*e + 104/5, -9/10*e^11 + 21/10*e^10 + 69/5*e^9 - 301/10*e^8 - 378/5*e^7 + 291/2*e^6 + 363/2*e^5 - 543/2*e^4 - 1859/10*e^3 + 1581/10*e^2 + 304/5*e - 2, -9/10*e^11 + 31/10*e^10 + 44/5*e^9 - 331/10*e^8 - 133/5*e^7 + 201/2*e^6 + 121/2*e^5 - 189/2*e^4 - 1249/10*e^3 + 51/10*e^2 + 424/5*e + 10, 1/10*e^11 - 19/10*e^10 + 24/5*e^9 + 179/10*e^8 - 303/5*e^7 - 85/2*e^6 + 403/2*e^5 + 73/2*e^4 - 2309/10*e^3 - 369/10*e^2 + 359/5*e + 22, -2/5*e^11 + 19/5*e^10 - 5*e^9 - 36*e^8 + 431/5*e^7 + 399/5*e^6 - 296*e^5 - 14*e^4 + 1678/5*e^3 - 266/5*e^2 - 112*e + 28/5, -1/5*e^10 + 4/5*e^9 + 12/5*e^8 - 54/5*e^7 - 39/5*e^6 + 45*e^5 + 2*e^4 - 56*e^3 + 64/5*e^2 + 4/5*e - 48/5, -9/10*e^11 + 22/5*e^10 + 23/5*e^9 - 487/10*e^8 + 261/10*e^7 + 816/5*e^6 - 315/2*e^5 - 210*e^4 + 2381/10*e^3 + 512/5*e^2 - 567/5*e - 58/5, -1/5*e^10 + 4/5*e^9 + 7/5*e^8 - 39/5*e^7 - 4/5*e^6 + 20*e^5 + 3*e^4 - 17*e^3 - 136/5*e^2 + 54/5*e + 92/5, 1/10*e^11 - 21/10*e^10 + 28/5*e^9 + 193/10*e^8 - 347/5*e^7 - 403/10*e^6 + 457/2*e^5 + 31/2*e^4 - 2509/10*e^3 - 251/10*e^2 + 328/5*e + 142/5, 7/10*e^11 - 39/10*e^10 - 2*e^9 + 85/2*e^8 - 188/5*e^7 - 1379/10*e^6 + 357/2*e^5 + 331/2*e^4 - 2473/10*e^3 - 649/10*e^2 + 104*e + 86/5, -7/5*e^10 + 28/5*e^9 + 54/5*e^8 - 298/5*e^7 - 33/5*e^6 + 183*e^5 - 43*e^4 - 193*e^3 + 163/5*e^2 + 238/5*e + 4/5, 2/5*e^10 - 8/5*e^9 - 29/5*e^8 + 113/5*e^7 + 153/5*e^6 - 104*e^5 - 73*e^4 + 169*e^3 + 367/5*e^2 - 348/5*e - 104/5, -13/10*e^11 + 57/10*e^10 + 48/5*e^9 - 657/10*e^8 + 24/5*e^7 + 473/2*e^6 - 223/2*e^5 - 665/2*e^4 + 1617/10*e^3 + 1727/10*e^2 - 217/5*e - 22, -13/5*e^11 + 23/2*e^10 + 84/5*e^9 - 623/5*e^8 + 59/2*e^7 + 3949/10*e^6 - 251*e^5 - 869/2*e^4 + 1542/5*e^3 + 269/2*e^2 - 406/5*e - 56/5, -5/2*e^11 + 25/2*e^10 + 12*e^9 - 271/2*e^8 + 75*e^7 + 865/2*e^6 - 803/2*e^5 - 993/2*e^4 + 1001/2*e^3 + 373/2*e^2 - 154*e - 14, -2/5*e^11 + 12/5*e^10 + 3/5*e^9 - 131/5*e^8 + 138/5*e^7 + 436/5*e^6 - 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520*e^5 - 386*e^4 + 715*e^3 + 649/5*e^2 - 1376/5*e + 12/5, 7/5*e^11 - 36/5*e^10 - 27/5*e^9 + 394/5*e^8 - 314/5*e^7 - 1287/5*e^6 + 335*e^5 + 310*e^4 - 2498/5*e^3 - 576/5*e^2 + 1068/5*e - 24/5, 7/5*e^11 - 63/10*e^10 - 10*e^9 + 72*e^8 - 77/10*e^7 - 2543/10*e^6 + 127*e^5 + 679/2*e^4 - 1053/5*e^3 - 1423/10*e^2 + 112*e + 12/5, 13/10*e^11 - 67/10*e^10 - 33/5*e^9 + 757/10*e^8 - 184/5*e^7 - 527/2*e^6 + 427/2*e^5 + 711/2*e^4 - 2947/10*e^3 - 1717/10*e^2 + 592/5*e + 18, -4/5*e^11 + 24/5*e^10 + 6/5*e^9 - 277/5*e^8 + 301/5*e^7 + 1037/5*e^6 - 294*e^5 - 349*e^4 + 2281/5*e^3 + 1419/5*e^2 - 1124/5*e - 436/5, 3/5*e^11 - 4/5*e^10 - 58/5*e^9 + 71/5*e^8 + 394/5*e^7 - 403/5*e^6 - 228*e^5 + 154*e^4 + 1413/5*e^3 - 264/5*e^2 - 578/5*e - 196/5, -e^11 + 14/5*e^10 + 64/5*e^9 - 178/5*e^8 - 274/5*e^7 + 741/5*e^6 + 94*e^5 - 239*e^4 - 36*e^3 + 594/5*e^2 - 196/5*e - 48/5, -9/10*e^11 + 14/5*e^10 + 13*e^9 - 79/2*e^8 - 683/10*e^7 + 954/5*e^6 + 329/2*e^5 - 378*e^4 - 1679/10*e^3 + 1384/5*e^2 + 49*e - 142/5, 1/5*e^11 - 18/5*e^10 + 39/5*e^9 + 177/5*e^8 - 507/5*e^7 - 441/5*e^6 + 333*e^5 + 46*e^4 - 1739/5*e^3 + 112/5*e^2 + 374/5*e - 32/5, 7/2*e^11 - 191/10*e^10 - 53/5*e^9 + 2057/10*e^8 - 892/5*e^7 - 6509/10*e^6 + 1669/2*e^5 + 1523/2*e^4 - 2159/2*e^3 - 3691/10*e^2 + 1887/5*e + 466/5, -19/10*e^11 + 109/10*e^10 + 23/5*e^9 - 1167/10*e^8 + 538/5*e^7 + 3637/10*e^6 - 961/2*e^5 - 813/2*e^4 + 6241/10*e^3 + 1659/10*e^2 - 1172/5*e - 218/5, -7/2*e^11 + 91/5*e^10 + 76/5*e^9 - 1999/10*e^8 + 1253/10*e^7 + 3294/5*e^6 - 1285/2*e^5 - 817*e^4 + 1615/2*e^3 + 1826/5*e^2 - 1269/5*e - 162/5, 3/10*e^11 - 37/5*e^9 + 33/10*e^8 + 123/2*e^7 - 191/5*e^6 - 433/2*e^5 + 132*e^4 + 3273/10*e^3 - 148*e^2 - 827/5*e + 138/5, -7/2*e^11 + 199/10*e^10 + 32/5*e^9 - 2113/10*e^8 + 1148/5*e^7 + 6451/10*e^6 - 2075/2*e^5 - 1367/2*e^4 + 2807/2*e^3 + 2509/10*e^2 - 2773/5*e - 274/5, 9/10*e^11 - 73/10*e^10 + 6*e^9 + 149/2*e^8 - 706/5*e^7 - 2103/10*e^6 + 1041/2*e^5 + 413/2*e^4 - 6161/10*e^3 - 1123/10*e^2 + 192*e + 302/5, -13/5*e^11 + 67/5*e^10 + 61/5*e^9 - 752/5*e^8 + 438/5*e^7 + 518*e^6 - 490*e^5 - 698*e^4 + 3432/5*e^3 + 1872/5*e^2 - 1364/5*e - 52, -13/5*e^11 + 51/5*e^10 + 22*e^9 - 114*e^8 - 146/5*e^7 + 1926/5*e^6 - 47*e^5 - 478*e^4 + 177/5*e^3 + 951/5*e^2 + 36*e - 128/5, -1/10*e^11 - 8/5*e^10 + 41/5*e^9 + 121/10*e^8 - 799/10*e^7 - 2*e^6 + 485/2*e^5 - 86*e^4 - 2611/10*e^3 + 562/5*e^2 + 461/5*e - 14, 9/5*e^11 - 69/10*e^10 - 89/5*e^9 + 418/5*e^8 + 459/10*e^7 - 3313/10*e^6 - 31*e^5 + 1091/2*e^4 - 16/5*e^3 - 3469/10*e^2 - 44/5*e + 272/5, -43/10*e^10 + 76/5*e^9 + 203/5*e^8 - 1687/10*e^7 - 967/10*e^6 + 566*e^5 + 169/2*e^4 - 707*e^3 - 933/10*e^2 + 1396/5*e + 268/5, 2*e^11 - 103/10*e^10 - 39/5*e^9 + 563/5*e^8 - 837/10*e^7 - 3707/10*e^6 + 418*e^5 + 951/2*e^4 - 524*e^3 - 2493/10*e^2 + 686/5*e + 208/5, -1/2*e^11 + 3*e^10 - e^9 - 55/2*e^8 + 103/2*e^7 + 55*e^6 - 393/2*e^5 - 3*e^4 + 485/2*e^3 - 2*e^2 - 95*e - 26, -3*e^11 + 73/5*e^10 + 78/5*e^9 - 786/5*e^8 + 372/5*e^7 + 2472/5*e^6 - 417*e^5 - 552*e^4 + 509*e^3 + 1013/5*e^2 - 812/5*e - 176/5, 4*e^11 - 22*e^10 - 11*e^9 + 233*e^8 - 211*e^7 - 710*e^6 + 948*e^5 + 767*e^4 - 1185*e^3 - 331*e^2 + 392*e + 108, -19/5*e^11 + 20*e^10 + 72/5*e^9 - 1089/5*e^8 + 162*e^7 + 3536/5*e^6 - 802*e^5 - 871*e^4 + 5231/5*e^3 + 435*e^2 - 1788/5*e - 428/5, 4/5*e^11 - 3/5*e^10 - 15*e^9 + 7*e^8 + 538/5*e^7 - 118/5*e^6 - 361*e^5 + 17*e^4 + 2679/5*e^3 + 142/5*e^2 - 270*e - 126/5, -7/5*e^11 + 21/10*e^10 + 119/5*e^9 - 138/5*e^8 - 1521/10*e^7 + 229/2*e^6 + 453*e^5 - 303/2*e^4 - 3037/5*e^3 - 49/10*e^2 + 1384/5*e + 60, 1/10*e^11 - 13/10*e^10 + 12/5*e^9 + 147/10*e^8 - 191/5*e^7 - 551/10*e^6 + 309/2*e^5 + 217/2*e^4 - 2319/10*e^3 - 1363/10*e^2 + 512/5*e + 354/5, -13/10*e^11 + 53/10*e^10 + 66/5*e^9 - 669/10*e^8 - 164/5*e^7 + 2759/10*e^6 - 13/2*e^5 - 885/2*e^4 + 977/10*e^3 + 2223/10*e^2 - 404/5*e - 26/5, -19/5*e^11 + 81/5*e^10 + 143/5*e^9 - 916/5*e^8 + 14/5*e^7 + 638*e^6 - 260*e^5 - 856*e^4 + 1816/5*e^3 + 1996/5*e^2 - 512/5*e - 16, -19/10*e^11 + 34/5*e^10 + 19*e^9 - 159/2*e^8 - 513/10*e^7 + 1459/5*e^6 + 105/2*e^5 - 413*e^4 - 689/10*e^3 + 1029/5*e^2 + 75*e - 122/5, -e^8 + 2*e^7 + 14*e^6 - 24*e^5 - 61*e^4 + 85*e^3 + 82*e^2 - 82*e - 20, 3/10*e^11 + 1/5*e^10 - 36/5*e^9 - 11/10*e^8 + 563/10*e^7 - 2/5*e^6 - 351/2*e^5 - 14*e^4 + 2123/10*e^3 + 356/5*e^2 - 421/5*e - 234/5, 3/5*e^11 - 24/5*e^10 + 22/5*e^9 + 231/5*e^8 - 476/5*e^7 - 538/5*e^6 + 326*e^5 + 31*e^4 - 1617/5*e^3 + 371/5*e^2 + 292/5*e - 176/5, 9/5*e^11 - 47/5*e^10 - 39/5*e^9 + 513/5*e^8 - 318/5*e^7 - 1654/5*e^6 + 317*e^5 + 384*e^4 - 1796/5*e^3 - 812/5*e^2 + 316/5*e + 252/5, 17/5*e^11 - 81/5*e^10 - 92/5*e^9 + 874/5*e^8 - 389/5*e^7 - 2757/5*e^6 + 456*e^5 + 613*e^4 - 2728/5*e^3 - 1076/5*e^2 + 748/5*e + 196/5, -9/2*e^11 + 19*e^10 + 31*e^9 - 413/2*e^8 + 71/2*e^7 + 658*e^6 - 843/2*e^5 - 731*e^4 + 1211/2*e^3 + 250*e^2 - 241*e - 42, -2/5*e^11 + 31/5*e^10 - 68/5*e^9 - 299/5*e^8 + 929/5*e^7 + 722/5*e^6 - 656*e^5 - 85*e^4 + 4153/5*e^3 + 36/5*e^2 - 1598/5*e - 56/5, -13/5*e^11 + 67/5*e^10 + 66/5*e^9 - 762/5*e^8 + 388/5*e^7 + 537*e^6 - 464*e^5 - 745*e^4 + 3337/5*e^3 + 2107/5*e^2 - 1304/5*e - 92, 3*e^11 - 88/5*e^10 - 33/5*e^9 + 956/5*e^8 - 902/5*e^7 - 3082/5*e^6 + 811*e^5 + 743*e^4 - 1072*e^3 - 1783/5*e^2 + 2132/5*e + 376/5, 11/5*e^11 - 42/5*e^10 - 21*e^9 + 100*e^8 + 217/5*e^7 - 1882/5*e^6 + 30*e^5 + 537*e^4 - 649/5*e^3 - 1127/5*e^2 + 56*e - 124/5, -31/5*e^11 + 139/5*e^10 + 207/5*e^9 - 1564/5*e^8 + 326/5*e^7 + 1085*e^6 - 645*e^5 - 1481*e^4 + 4604/5*e^3 + 3884/5*e^2 - 1708/5*e - 120, 8/5*e^11 - 54/5*e^10 + 17/5*e^9 + 571/5*e^8 - 901/5*e^7 - 1743/5*e^6 + 759*e^5 + 384*e^4 - 5307/5*e^3 - 819/5*e^2 + 2232/5*e + 224/5, -13/5*e^11 + 66/5*e^10 + 15*e^9 - 153*e^8 + 284/5*e^7 + 2781/5*e^6 - 388*e^5 - 787*e^4 + 2757/5*e^3 + 1871/5*e^2 - 188*e - 48/5, -e^11 + 13/5*e^10 + 73/5*e^9 - 186/5*e^8 - 363/5*e^7 + 907/5*e^6 + 137*e^5 - 358*e^4 - 44*e^3 + 1328/5*e^2 - 412/5*e - 286/5, 5/2*e^11 - 131/10*e^10 - 38/5*e^9 + 1367/10*e^8 - 617/5*e^7 - 4019/10*e^6 + 1113/2*e^5 + 781/2*e^4 - 1321/2*e^3 - 901/10*e^2 + 902/5*e + 6/5, 29/10*e^11 - 89/5*e^10 - 2*e^9 + 377/2*e^8 - 2197/10*e^7 - 2889/5*e^6 + 1821/2*e^5 + 643*e^4 - 11241/10*e^3 - 1344/5*e^2 + 375*e + 222/5, 7/5*e^11 - 36/5*e^10 - 22/5*e^9 + 359/5*e^8 - 304/5*e^7 - 922/5*e^6 + 234*e^5 + 99*e^4 - 753/5*e^3 + 369/5*e^2 - 282/5*e - 244/5, 23/10*e^11 - 13/2*e^10 - 152/5*e^9 + 833/10*e^8 + 142*e^7 - 3497/10*e^6 - 613/2*e^5 + 1121/2*e^4 + 2923/10*e^3 - 489/2*e^2 - 447/5*e - 162/5]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([4, 2, -w^2 - w + 3])] = 1

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