/*
  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, 3, 4, -5, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([27, 27, w^4 - w^3 - 5*w^2 + 4*w + 1])

primes_array = [
[3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[9, 3, -w^4 + 5*w^2 - 3],\
[9, 3, -w^4 + w^3 + 5*w^2 - 3*w - 2],\
[13, 13, -w^4 + w^3 + 4*w^2 - 3*w - 1],\
[17, 17, w^4 - w^3 - 5*w^2 + 3*w + 1],\
[19, 19, -w^3 + w^2 + 4*w - 2],\
[23, 23, -w^2 + 3],\
[31, 31, w^3 - 4*w + 2],\
[32, 2, 2],\
[37, 37, w^3 - 3*w - 1],\
[53, 53, -2*w^4 + w^3 + 9*w^2 - 3*w - 2],\
[59, 59, -w^4 + 5*w^2 + w - 4],\
[61, 61, -w^4 + w^3 + 5*w^2 - 4*w],\
[67, 67, -w^4 + 6*w^2 + 2*w - 4],\
[71, 71, 2*w^4 - w^3 - 9*w^2 + 4*w + 5],\
[79, 79, 2*w^4 - w^3 - 10*w^2 + 2*w + 7],\
[83, 83, -w^4 + 2*w^3 + 5*w^2 - 7*w - 2],\
[83, 83, -w^4 + w^3 + 4*w^2 - 3*w + 3],\
[83, 83, w^4 - w^3 - 5*w^2 + 4*w - 1],\
[83, 83, -w^4 + w^3 + 4*w^2 - 4*w - 2],\
[83, 83, -2*w^4 + w^3 + 9*w^2 - 3*w - 5],\
[97, 97, -w^4 - w^3 + 6*w^2 + 4*w - 4],\
[101, 101, -w^4 + 4*w^2 + 2*w - 2],\
[107, 107, -2*w^4 + w^3 + 11*w^2 - 3*w - 7],\
[127, 127, w^3 - w^2 - 4*w],\
[131, 131, w^4 - w^3 - 4*w^2 + 2*w - 1],\
[137, 137, w^4 - w^3 - 6*w^2 + 3*w + 3],\
[139, 139, -2*w^4 + w^3 + 9*w^2 - 3*w + 1],\
[157, 157, 2*w^4 - w^3 - 9*w^2 + 4*w + 2],\
[163, 163, -w^2 - 2*w + 3],\
[167, 167, w^4 - 5*w^2 + 2*w + 1],\
[169, 13, -2*w^4 + 2*w^3 + 9*w^2 - 7*w - 5],\
[169, 13, w^4 - 2*w^3 - 5*w^2 + 8*w + 2],\
[191, 191, 2*w^4 - w^3 - 9*w^2 + 3*w + 4],\
[193, 193, 2*w^4 - 2*w^3 - 8*w^2 + 7*w],\
[199, 199, -w^4 + 2*w^3 + 5*w^2 - 9*w - 3],\
[211, 211, -3*w^4 + w^3 + 13*w^2 - 2*w - 1],\
[227, 227, 2*w^3 - w^2 - 9*w + 1],\
[233, 233, -w^3 + w^2 + 4*w + 1],\
[251, 251, -3*w^4 + 14*w^2 + w - 2],\
[257, 257, -2*w^4 + 2*w^3 + 10*w^2 - 6*w - 5],\
[257, 257, -w^4 + w^3 + 5*w^2 - 6*w - 1],\
[257, 257, 2*w^4 - 2*w^3 - 11*w^2 + 9*w + 9],\
[257, 257, -2*w^4 + 2*w^3 + 9*w^2 - 6*w - 3],\
[257, 257, 2*w^4 - w^3 - 10*w^2 + 5*w + 5],\
[269, 269, -w^4 + 2*w^3 + 4*w^2 - 6*w - 2],\
[271, 271, -w^4 + 4*w^2 + w - 3],\
[277, 277, -2*w^4 + 9*w^2 + w - 4],\
[281, 281, w^4 - w^3 - 3*w^2 + 3*w - 4],\
[283, 283, 2*w^4 - 3*w^3 - 8*w^2 + 13*w],\
[289, 17, -w^4 + w^3 + 7*w^2 - 5*w - 5],\
[289, 17, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 6],\
[293, 293, -2*w^4 + 11*w^2 - 7],\
[317, 317, w^3 - 6*w],\
[337, 337, -w^4 + 2*w^3 + 5*w^2 - 9*w - 1],\
[337, 337, w^4 - 2*w^3 - 5*w^2 + 6*w + 3],\
[337, 337, -w^4 + w^3 + 5*w^2 - 4*w - 6],\
[337, 337, -2*w^3 + 8*w + 1],\
[337, 337, w^2 + w - 5],\
[347, 347, -2*w^4 + w^3 + 9*w^2 - 5*w - 3],\
[349, 349, 3*w^4 - 2*w^3 - 13*w^2 + 8*w + 2],\
[353, 353, w^4 - 3*w^3 - 4*w^2 + 12*w + 2],\
[359, 359, 2*w^3 - w^2 - 7*w + 3],\
[361, 19, w^4 - 2*w^3 - 4*w^2 + 7*w + 3],\
[361, 19, w^4 - w^3 - 3*w^2 + 3*w - 3],\
[367, 367, -2*w^4 + w^3 + 9*w^2 - w - 2],\
[379, 379, -2*w^3 + w^2 + 7*w + 2],\
[379, 379, -2*w^4 + w^3 + 10*w^2 - 4*w],\
[379, 379, 2*w^3 - w^2 - 6*w - 2],\
[379, 379, -2*w^3 + 2*w^2 + 6*w - 3],\
[379, 379, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 6],\
[383, 383, 2*w^4 + w^3 - 10*w^2 - 7*w + 4],\
[383, 383, -2*w^3 + w^2 + 10*w],\
[383, 383, w^3 + w^2 - 5*w - 1],\
[383, 383, 3*w^4 + 3*w^3 - 15*w^2 - 15*w + 4],\
[383, 383, -2*w^4 + 3*w^3 + 10*w^2 - 10*w - 2],\
[389, 389, 3*w^4 - w^3 - 14*w^2 + 3*w + 3],\
[397, 397, w^4 - 6*w^2 - 2*w + 5],\
[397, 397, w^4 - 2*w^3 - 2*w^2 + 6*w - 5],\
[397, 397, 2*w^4 - 2*w^3 - 11*w^2 + 10*w + 6],\
[397, 397, w^4 - w^3 - 3*w^2 + 4*w - 6],\
[397, 397, w^3 + w^2 - 3*w - 4],\
[401, 401, w^3 - w^2 - 6*w + 3],\
[401, 401, -w^4 + 4*w^2 + 2*w - 3],\
[401, 401, -w^4 + 6*w^2 - w - 7],\
[421, 421, -w^4 - w^3 + 5*w^2 + 5*w - 4],\
[421, 421, -w^4 + w^3 + 6*w^2 - 3*w - 2],\
[421, 421, -w^4 - w^3 + 6*w^2 + 6*w - 5],\
[421, 421, 3*w^4 - w^3 - 15*w^2 + w + 10],\
[421, 421, 2*w^4 - 9*w^2 + 2*w + 4],\
[431, 431, 2*w^4 - 11*w^2 - 2*w + 11],\
[439, 439, 2*w^4 - 3*w^3 - 9*w^2 + 10*w + 6],\
[443, 443, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 2],\
[449, 449, -w^4 + 2*w^3 + 5*w^2 - 6*w - 4],\
[461, 461, 3*w^4 - 4*w^3 - 14*w^2 + 14*w + 5],\
[463, 463, w^3 - 6*w - 1],\
[467, 467, 3*w^4 - 3*w^3 - 13*w^2 + 10*w],\
[487, 487, 3*w^4 - w^3 - 14*w^2 + w + 3],\
[487, 487, 2*w^2 - w - 4],\
[487, 487, -2*w^4 + 2*w^3 + 9*w^2 - 8*w - 5],\
[487, 487, 2*w^4 - 10*w^2 - 3*w + 4],\
[487, 487, -2*w^4 + w^3 + 8*w^2 - 3*w - 1],\
[499, 499, -w^4 + 2*w^3 + 4*w^2 - 8*w - 2],\
[499, 499, -2*w^4 + w^3 + 10*w^2 - w - 9],\
[499, 499, -w^3 - 2*w^2 + 2*w + 5],\
[499, 499, -w^4 + 4*w^2 + 4*w],\
[499, 499, -2*w^4 + w^3 + 12*w^2 - 4*w - 9],\
[509, 509, 3*w^4 - 2*w^3 - 16*w^2 + 6*w + 9],\
[521, 521, -2*w^4 + w^3 + 10*w^2 - 5*w - 4],\
[523, 523, w - 4],\
[529, 23, -w^3 + 2*w^2 + 4*w - 4],\
[529, 23, w^4 + 2*w^3 - 6*w^2 - 11*w + 4],\
[569, 569, -2*w^4 + 11*w^2 - 10],\
[571, 571, -2*w^4 + w^3 + 10*w^2 - 3*w - 2],\
[593, 593, -2*w^4 + 3*w^3 + 10*w^2 - 11*w - 8],\
[613, 613, -2*w^3 + 2*w^2 + 9*w - 5],\
[617, 617, -2*w^4 + 10*w^2 - w - 7],\
[631, 631, -2*w^4 + 2*w^3 + 7*w^2 - 8*w + 3],\
[641, 641, -2*w^4 + 2*w^3 + 8*w^2 - 9*w + 3],\
[643, 643, -3*w^4 + w^3 + 13*w^2 - w + 1],\
[643, 643, w^4 + w^3 - 3*w^2 - 6*w - 2],\
[643, 643, -w^4 - w^3 + 6*w^2 + 3*w - 4],\
[643, 643, 2*w^4 - w^3 - 10*w^2 + 4*w + 1],\
[643, 643, 2*w^4 - 2*w^3 - 8*w^2 + 6*w + 5],\
[647, 647, -2*w^3 + w^2 + 6*w - 4],\
[659, 659, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 10],\
[661, 661, 2*w^4 + 3*w^3 - 11*w^2 - 14*w + 6],\
[673, 673, w^4 - 3*w^3 - 3*w^2 + 10*w - 1],\
[683, 683, w^4 - 2*w^3 - 4*w^2 + 6*w - 4],\
[701, 701, w^3 - w^2 - 2*w + 4],\
[727, 727, -w^4 + 6*w^2 + 2*w - 7],\
[743, 743, w^4 - w^3 - 7*w^2 + 5*w + 9],\
[769, 769, w^4 + 2*w^3 - 5*w^2 - 9*w + 4],\
[787, 787, w^4 + w^3 - 7*w^2 - 3*w + 5],\
[797, 797, -2*w^4 - w^3 + 10*w^2 + 4*w - 4],\
[797, 797, w^4 - 3*w^3 - 5*w^2 + 12*w + 5],\
[797, 797, -3*w^4 + 2*w^3 + 13*w^2 - 8*w],\
[797, 797, -w^4 + w^3 + 3*w^2 - 5*w - 1],\
[797, 797, 2*w^4 - 11*w^2 + 2*w + 7],\
[809, 809, -4*w^4 + 2*w^3 + 18*w^2 - 6*w + 1],\
[809, 809, 3*w^4 - 3*w^3 - 14*w^2 + 11*w + 8],\
[809, 809, w^4 - 2*w^3 - 2*w^2 + 8*w - 4],\
[809, 809, 2*w^4 - 8*w^2 - 2*w + 3],\
[809, 809, 2*w^4 - 3*w^3 - 9*w^2 + 13*w + 4],\
[821, 821, -2*w^4 + 2*w^3 + 8*w^2 - 6*w + 3],\
[823, 823, -2*w^4 + 3*w^3 + 8*w^2 - 12*w - 1],\
[829, 829, 2*w^4 - 3*w^3 - 10*w^2 + 13*w + 4],\
[839, 839, -2*w^4 + 12*w^2 - w - 10],\
[863, 863, 2*w^4 - w^3 - 9*w^2 + 5],\
[877, 877, -w^4 + w^3 + 5*w^2 - 5*w - 7],\
[881, 881, 2*w^4 - w^3 - 9*w^2 + w - 1],\
[887, 887, 3*w^4 - 3*w^3 - 15*w^2 + 11*w + 6],\
[907, 907, -3*w^4 + w^3 + 13*w^2 - w - 5],\
[919, 919, w^4 + w^3 - 3*w^2 - 5*w - 3],\
[929, 929, 2*w^4 - 3*w^3 - 10*w^2 + 9*w + 4],\
[937, 937, -2*w^4 + 10*w^2 + 3*w - 7],\
[941, 941, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\
[961, 31, 2*w^4 + 2*w^3 - 10*w^2 - 12*w + 5],\
[961, 31, -w^4 + 5*w^2 - w - 7],\
[967, 967, -2*w^4 + w^3 + 9*w^2 - 3*w + 2],\
[991, 991, -3*w^4 + w^3 + 15*w^2 - 4*w - 5],\
[997, 997, -3*w^4 + 15*w^2 - 5],\
[997, 997, 2*w^4 - w^3 - 9*w^2 + 6*w + 2],\
[997, 997, 2*w^4 - w^3 - 11*w^2 + w + 7],\
[997, 997, 2*w^3 - 5*w - 1],\
[997, 997, 2*w^4 - 3*w^3 - 6*w^2 + 5*w + 1]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - 48*x^6 + 716*x^4 - 3952*x^2 + 6400
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, -5/272*e^6 + 12/17*e^4 - 441/68*e^2 + 231/17, e, -49/5440*e^7 + 259/680*e^5 - 5811/1360*e^3 + 4093/340*e, -1/272*e^6 + 13/68*e^4 - 197/68*e^2 + 206/17, 21/5440*e^7 - 111/680*e^5 + 2539/1360*e^3 - 1827/340*e, -43/5440*e^7 + 203/680*e^5 - 3337/1360*e^3 + 511/340*e, 3/136*e^6 - 61/68*e^4 + 319/34*e^2 - 335/17, 19/5440*e^7 - 8/85*e^5 - 99/1360*e^3 + 2257/340*e, 1/136*e^6 - 13/34*e^4 + 197/34*e^2 - 344/17, 5/1088*e^7 - 3/17*e^5 + 475/272*e^3 - 333/68*e, -43/2720*e^7 + 203/340*e^5 - 3677/680*e^3 + 1871/170*e, -11/2720*e^7 + 23/170*e^5 - 569/680*e^3 - 63/170*e, 21/1360*e^7 - 111/170*e^5 + 2539/340*e^3 - 1827/85*e, 3/136*e^6 - 61/68*e^4 + 151/17*e^2 - 216/17, 11/5440*e^7 - 23/340*e^5 + 229/1360*e^3 + 913/340*e, 1/16*e^6 - 5/2*e^4 + 103/4*e^2 - 64, -1/272*e^7 + 13/68*e^5 - 107/34*e^3 + 497/34*e, 1/5440*e^7 + 19/680*e^5 - 1401/1360*e^3 + 1953/340*e, -1/68*e^6 + 13/17*e^4 - 197/17*e^2 + 722/17, 1/85*e^7 - 157/340*e^5 + 1639/340*e^3 - 2699/170*e, 3/136*e^6 - 61/68*e^4 + 134/17*e^2 - 12/17, 23/1360*e^7 - 231/340*e^5 + 2287/340*e^3 - 1236/85*e, -1/17*e^6 + 157/68*e^4 - 743/34*e^2 + 712/17, 1/4*e^3 - 9/2*e, -101/5440*e^7 + 273/340*e^5 - 12859/1360*e^3 + 9297/340*e, -5/544*e^7 + 6/17*e^5 - 475/136*e^3 + 333/34*e, -1/34*e^6 + 87/68*e^4 - 241/17*e^2 + 611/17, e^2 - 12, 7/2720*e^7 - 37/340*e^5 + 733/680*e^3 + 71/170*e, -5/272*e^6 + 12/17*e^4 - 407/68*e^2 + 112/17, 1/34*e^6 - 87/68*e^4 + 465/34*e^2 - 390/17, 9/680*e^7 - 83/170*e^5 + 651/170*e^3 - 376/85*e, 13/272*e^6 - 135/68*e^4 + 1473/68*e^2 - 1012/17, 1/34*e^6 - 26/17*e^4 + 377/17*e^2 - 1257/17, -131/5440*e^7 + 82/85*e^5 - 13669/1360*e^3 + 9867/340*e, 7/5440*e^7 - 37/680*e^5 + 53/1360*e^3 + 3301/340*e, -13/136*e^6 + 253/68*e^4 - 1201/34*e^2 + 1293/17, -1/34*e^6 + 87/68*e^4 - 533/34*e^2 + 798/17, -1/68*e^6 + 35/68*e^4 - 173/34*e^2 + 501/17, 63/2720*e^7 - 333/340*e^5 + 7617/680*e^3 - 6501/170*e, 11/2720*e^7 - 23/170*e^5 + 399/680*e^3 + 669/85*e, -5/68*e^6 + 209/68*e^4 - 1171/34*e^2 + 1706/17, -11/272*e^6 + 63/34*e^4 - 1487/68*e^2 + 889/17, -5/272*e^7 + 12/17*e^5 - 475/68*e^3 + 384/17*e, -1/40*e^7 + 19/20*e^5 - 79/10*e^3 + 24/5*e, 7/340*e^7 - 74/85*e^5 + 1721/170*e^3 - 3286/85*e, -147/5440*e^7 + 173/170*e^5 - 11653/1360*e^3 + 4459/340*e, 83/5440*e^7 - 463/680*e^5 + 11557/1360*e^3 - 9601/340*e, -7/68*e^6 + 131/34*e^4 - 563/17*e^2 + 940/17, -33/2720*e^7 + 69/170*e^5 - 1197/680*e^3 - 817/85*e, 3/136*e^6 - 61/68*e^4 + 168/17*e^2 - 624/17, -5/272*e^7 + 12/17*e^5 - 441/68*e^3 + 197/17*e, 77/2720*e^7 - 407/340*e^5 + 9083/680*e^3 - 6189/170*e, -5/272*e^6 + 12/17*e^4 - 543/68*e^2 + 486/17, -253/5440*e^7 + 1313/680*e^5 - 28727/1360*e^3 + 19461/340*e, -3/136*e^7 + 61/68*e^5 - 151/17*e^3 + 284/17*e, 3/160*e^7 - 9/10*e^5 + 497/40*e^3 - 471/10*e, -11/544*e^7 + 63/68*e^5 - 1623/136*e^3 + 623/17*e, 9/68*e^6 - 349/68*e^4 + 1659/34*e^2 - 1772/17, -1/17*e^6 + 157/68*e^4 - 380/17*e^2 + 1137/17, 3/136*e^6 - 95/68*e^4 + 406/17*e^2 - 1508/17, 23/1360*e^7 - 231/340*e^5 + 2287/340*e^3 - 726/85*e, 11/272*e^7 - 109/68*e^5 + 1079/68*e^3 - 566/17*e, 29/272*e^6 - 73/17*e^4 + 2993/68*e^2 - 1843/17, 13/136*e^6 - 253/68*e^4 + 558/17*e^2 - 698/17, -211/5440*e^7 + 1091/680*e^5 - 23309/1360*e^3 + 15637/340*e, 11/136*e^6 - 109/34*e^4 + 1045/34*e^2 - 911/17, -9/272*e^6 + 83/68*e^4 - 855/68*e^2 + 783/17, -2/17*e^6 + 157/34*e^4 - 760/17*e^2 + 1832/17, -3/68*e^7 + 61/34*e^5 - 655/34*e^3 + 976/17*e, 7/136*e^6 - 37/17*e^4 + 767/34*e^2 - 623/17, -1/68*e^6 + 35/68*e^4 - 173/34*e^2 + 552/17, -1/68*e^6 + 13/17*e^4 - 214/17*e^2 + 994/17, -1/34*e^6 + 35/34*e^4 - 139/17*e^2 + 254/17, 157/5440*e^7 - 757/680*e^5 + 14643/1360*e^3 - 10259/340*e, 39/5440*e^7 - 97/340*e^5 + 3841/1360*e^3 + 177/340*e, -2/17*e^6 + 157/34*e^4 - 743/17*e^2 + 1492/17, 11/272*e^6 - 23/17*e^4 + 603/68*e^2 + 131/17, -1/136*e^7 + 13/34*e^5 - 107/17*e^3 + 565/17*e, 1/2*e^3 - 7*e, 2/17*e^6 - 157/34*e^4 + 726/17*e^2 - 1322/17, 67/2720*e^7 - 171/170*e^5 + 7453/680*e^3 - 6509/170*e, -5/136*e^6 + 24/17*e^4 - 509/34*e^2 + 734/17, 9/136*e^6 - 183/68*e^4 + 470/17*e^2 - 1022/17, 3/136*e^7 - 61/68*e^5 + 353/34*e^3 - 760/17*e, -23/272*e^6 + 107/34*e^4 - 1777/68*e^2 + 658/17, 9/136*e^6 - 183/68*e^4 + 889/34*e^2 - 801/17, 133/5440*e^7 - 703/680*e^5 + 15967/1360*e^3 - 12761/340*e, 9/136*e^6 - 149/68*e^4 + 232/17*e^2 - 70/17, -7/680*e^7 + 37/85*e^5 - 409/85*e^3 + 623/85*e, 129/5440*e^7 - 347/340*e^5 + 17151/1360*e^3 - 16493/340*e, 21, 9/136*e^6 - 83/34*e^4 + 651/34*e^2 - 512/17, -5/136*e^6 + 113/68*e^4 - 679/34*e^2 + 955/17, -1/34*e^6 + 26/17*e^4 - 394/17*e^2 + 1512/17, -5/68*e^6 + 175/68*e^4 - 559/34*e^2 - 96/17, -7/68*e^6 + 279/68*e^4 - 1449/34*e^2 + 1926/17, -13/272*e^6 + 135/68*e^4 - 1575/68*e^2 + 995/17, 3/272*e^7 - 11/34*e^5 + 15/34*e^3 + 447/34*e, -15/272*e^6 + 36/17*e^4 - 1187/68*e^2 + 523/17, -61/2720*e^7 + 371/340*e^5 - 10419/680*e^3 + 9557/170*e, -21/272*e^6 + 205/68*e^4 - 1791/68*e^2 + 603/17, -1/1360*e^7 - 19/170*e^5 + 1401/340*e^3 - 1783/85*e, 127/2720*e^7 - 647/340*e^5 + 13493/680*e^3 - 8329/170*e, -1/68*e^6 + 69/68*e^4 - 615/34*e^2 + 1368/17, 13/136*e^6 - 253/68*e^4 + 609/17*e^2 - 1565/17, -43/272*e^6 + 423/68*e^4 - 4289/68*e^2 + 2823/17, 5/136*e^6 - 113/68*e^4 + 365/17*e^2 - 1312/17, 57/1088*e^7 - 277/136*e^5 + 5211/272*e^3 - 2817/68*e, 13/136*e^6 - 135/34*e^4 + 1439/34*e^2 - 1718/17, 3/17*e^6 - 471/68*e^4 + 2331/34*e^2 - 2663/17, -3/2720*e^7 + 7/85*e^5 - 1067/680*e^3 + 513/85*e, -5/68*e^6 + 48/17*e^4 - 475/17*e^2 + 1468/17, 333/5440*e^7 - 437/170*e^5 + 39387/1360*e^3 - 30161/340*e, -93/5440*e^7 + 613/680*e^5 - 19307/1360*e^3 + 19991/340*e, -141/5440*e^7 + 403/340*e^5 - 20739/1360*e^3 + 17537/340*e, -23/680*e^7 + 231/170*e^5 - 2287/170*e^3 + 2302/85*e, -23/136*e^6 + 231/34*e^4 - 2355/34*e^2 + 3220/17, 3/136*e^7 - 61/68*e^5 + 151/17*e^3 - 233/17*e, -3/17*e^6 + 471/68*e^4 - 1123/17*e^2 + 2561/17, -43/2720*e^7 + 203/340*e^5 - 3337/680*e^3 + 681/170*e, 299/5440*e^7 - 1459/680*e^5 + 27181/1360*e^3 - 11733/340*e, -23/1360*e^7 + 231/340*e^5 - 1271/170*e^3 + 4087/170*e, 23/544*e^7 - 31/17*e^5 + 2865/136*e^3 - 2001/34*e, -39/2720*e^7 + 97/170*e^5 - 3501/680*e^3 + 503/170*e, 1/136*e^6 - 9/68*e^4 - 29/17*e^2 + 64/17, -9/68*e^6 + 349/68*e^4 - 1727/34*e^2 + 2299/17, 101/2720*e^7 - 461/340*e^5 + 7079/680*e^3 - 1137/170*e, 21/272*e^6 - 205/68*e^4 + 2097/68*e^2 - 1334/17, -7/1360*e^7 + 37/170*e^5 - 733/340*e^3 - 836/85*e, 91/2720*e^7 - 481/340*e^5 + 10889/680*e^3 - 9277/170*e, -13/680*e^7 + 287/340*e^5 - 1847/170*e^3 + 4302/85*e, 1/272*e^7 - 13/68*e^5 + 129/68*e^3 + 151/17*e, 5/136*e^6 - 79/68*e^4 + 59/17*e^2 + 694/17, 13/544*e^7 - 59/68*e^5 + 827/136*e^3 + 433/34*e, 21/544*e^7 - 111/68*e^5 + 2573/136*e^3 - 1177/17*e, 53/5440*e^7 - 353/680*e^5 + 11087/1360*e^3 - 12261/340*e, -5/136*e^6 + 65/34*e^4 - 985/34*e^2 + 1958/17, 21/272*e^6 - 171/68*e^4 + 839/68*e^2 + 655/17, -19/1088*e^7 + 49/68*e^5 - 2213/272*e^3 + 1415/68*e, 37/272*e^6 - 181/34*e^4 + 3719/68*e^2 - 2794/17, -21/272*e^6 + 47/17*e^4 - 1247/68*e^2 + 42/17, -19/136*e^6 + 375/68*e^4 - 945/17*e^2 + 2252/17, -19/272*e^6 + 179/68*e^4 - 1703/68*e^2 + 922/17, -37/544*e^7 + 181/68*e^5 - 3515/136*e^3 + 1995/34*e, 93/5440*e^7 - 443/680*e^5 + 7067/1360*e^3 - 951/340*e, 13/68*e^6 - 489/68*e^4 + 2113/34*e^2 - 1566/17, 21/272*e^6 - 47/17*e^4 + 1553/68*e^2 - 705/17, 223/2720*e^7 - 559/170*e^5 + 22477/680*e^3 - 12941/170*e, 103/2720*e^7 - 593/340*e^5 + 15327/680*e^3 - 6393/85*e, 1/68*e^6 - 35/68*e^4 + 78/17*e^2 + 145/17, -3/136*e^6 + 95/68*e^4 - 727/34*e^2 + 947/17, 5/136*e^6 - 24/17*e^4 + 475/34*e^2 - 530/17, -49/680*e^7 + 259/85*e^5 - 2948/85*e^3 + 8781/85*e, -9/136*e^6 + 50/17*e^4 - 1127/34*e^2 + 1294/17, -1/34*e^6 + 87/68*e^4 - 207/17*e^2 - 205/17, -121/1360*e^7 + 591/170*e^5 - 11359/340*e^3 + 6192/85*e, -393/5440*e^7 + 246/85*e^5 - 41007/1360*e^3 + 28241/340*e, 1/1360*e^7 - 47/340*e^5 + 436/85*e^3 - 8419/170*e, 197/5440*e^7 - 1017/680*e^5 + 22523/1360*e^3 - 17819/340*e, 59/680*e^7 - 1211/340*e^5 + 6591/170*e^3 - 9841/85*e, 71/5440*e^7 - 521/680*e^5 + 17829/1360*e^3 - 18587/340*e, -39/2720*e^7 + 97/170*e^5 - 3501/680*e^3 - 857/170*e, 7/160*e^7 - 8/5*e^5 + 483/40*e^3 - 2/5*e, -7/272*e^6 + 37/34*e^4 - 767/68*e^2 + 269/17]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3])] = -1

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