/*
  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, 5, -4, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([9, 3, w^3 - w^2 - 4*w])

primes_array = [
[5, 5, w + 1],\
[5, 5, -w + 2],\
[7, 7, -w^2 + 2*w + 1],\
[7, 7, -w^2 + 2],\
[9, 3, w^3 - w^2 - 4*w],\
[16, 2, 2],\
[17, 17, -w^3 + 2*w^2 + 3*w - 2],\
[17, 17, -w^3 + w^2 + 4*w - 2],\
[25, 5, w^2 - w - 3],\
[37, 37, 2*w - 1],\
[43, 43, -w^3 + 2*w^2 + 2*w - 2],\
[43, 43, w^3 - w^2 - 3*w + 1],\
[59, 59, 2*w - 5],\
[59, 59, -2*w - 3],\
[79, 79, -w^3 + 2*w^2 + 5*w - 4],\
[79, 79, -w^3 + w^2 + 6*w - 2],\
[83, 83, -w^3 + 7*w],\
[83, 83, -w^3 + 2*w^2 + 4*w - 2],\
[83, 83, -w^3 + w^2 + 5*w - 3],\
[83, 83, w^2 - 2*w - 6],\
[89, 89, w^2 - 2*w - 4],\
[89, 89, w^2 - 5],\
[101, 101, -2*w^3 + 5*w^2 + 5*w - 11],\
[101, 101, w^2 + w - 4],\
[101, 101, w^2 - 3*w - 2],\
[101, 101, 2*w^3 - w^2 - 9*w - 3],\
[109, 109, w^3 - w^2 - 6*w - 3],\
[109, 109, -w^3 + 2*w^2 + 5*w - 9],\
[121, 11, w^3 - 8*w],\
[121, 11, w^3 - 3*w^2 - 5*w + 7],\
[131, 131, w^3 - 5*w - 6],\
[131, 131, -w^3 + 3*w^2 + 2*w - 10],\
[163, 163, 2*w^2 - 3*w - 6],\
[163, 163, 2*w^2 - w - 7],\
[167, 167, w^3 - w^2 - 3*w - 4],\
[167, 167, -w^3 + 2*w^2 + 2*w - 7],\
[193, 193, 2*w^3 - 3*w^2 - 7*w + 2],\
[193, 193, 2*w^3 - 3*w^2 - 7*w + 6],\
[227, 227, 2*w^3 - 3*w^2 - 8*w + 1],\
[227, 227, -2*w^3 + 3*w^2 + 8*w - 8],\
[251, 251, 2*w^2 - w - 9],\
[251, 251, 2*w^2 - 3*w - 8],\
[257, 257, w^3 + w^2 - 8*w - 7],\
[257, 257, -4*w^3 + 5*w^2 + 17*w - 1],\
[269, 269, 2*w^3 - 2*w^2 - 10*w + 3],\
[269, 269, 2*w^3 - 3*w^2 - 9*w + 2],\
[269, 269, 2*w^3 - 3*w^2 - 9*w + 8],\
[269, 269, -2*w^3 + 4*w^2 + 8*w - 7],\
[277, 277, w^3 - w^2 - 4*w - 4],\
[277, 277, -w^3 + 2*w^2 + 3*w - 8],\
[289, 17, 2*w^2 - 2*w - 3],\
[293, 293, -w^2 - 2*w + 5],\
[293, 293, -w^3 + 3*w^2 + 3*w - 4],\
[293, 293, w^3 - 6*w + 1],\
[293, 293, -2*w^3 + 4*w^2 + 7*w - 6],\
[311, 311, -w^3 + 3*w^2 + w - 7],\
[311, 311, w^3 - 4*w - 4],\
[331, 331, -2*w^3 + 4*w^2 + 9*w - 10],\
[331, 331, 2*w^3 - 2*w^2 - 11*w + 1],\
[337, 337, 2*w^2 - 3*w - 4],\
[337, 337, -w^3 + 2*w^2 + 6*w - 3],\
[337, 337, w^3 - w^2 - 7*w + 4],\
[337, 337, 2*w^2 - w - 5],\
[353, 353, -3*w^3 + 4*w^2 + 13*w - 2],\
[353, 353, 3*w^3 - 5*w^2 - 12*w + 12],\
[373, 373, -2*w^3 + 6*w^2 + 3*w - 11],\
[373, 373, -w^3 - w^2 + 6*w + 7],\
[373, 373, -w^3 + 4*w^2 + w - 11],\
[373, 373, 2*w^3 - 9*w - 4],\
[379, 379, w^3 - w^2 - 7*w + 1],\
[379, 379, 3*w^3 - 7*w^2 - 7*w + 11],\
[379, 379, 3*w^3 - 2*w^2 - 12*w],\
[379, 379, -w^3 + 2*w^2 + 6*w - 6],\
[383, 383, -3*w^3 + 4*w^2 + 12*w - 8],\
[383, 383, 3*w^3 - 5*w^2 - 11*w + 5],\
[421, 421, 2*w^3 - 2*w^2 - 9*w - 4],\
[421, 421, -2*w^3 + 4*w^2 + 7*w - 13],\
[457, 457, -w^3 + 2*w^2 + 6*w - 5],\
[457, 457, w^3 - w^2 - 7*w + 2],\
[461, 461, -w^3 + 3*w^2 + 4*w - 4],\
[461, 461, -w^3 + 7*w - 2],\
[463, 463, -w^3 + 4*w^2 + 3*w - 10],\
[463, 463, w^3 + w^2 - 8*w - 4],\
[467, 467, -w^3 + 6*w - 2],\
[467, 467, -w^3 + 3*w^2 + 3*w - 3],\
[479, 479, -w^3 + w^2 + w - 4],\
[479, 479, w^3 - 2*w^2 - 3],\
[487, 487, -3*w^3 + 4*w^2 + 12*w - 3],\
[487, 487, -3*w^3 + 5*w^2 + 11*w - 10],\
[499, 499, 3*w^3 - 4*w^2 - 11*w + 8],\
[499, 499, 3*w^3 - 5*w^2 - 10*w + 4],\
[503, 503, -w^3 + 2*w^2 + w - 5],\
[503, 503, w^3 - w^2 - 2*w - 3],\
[521, 521, 2*w^3 - 4*w^2 - 6*w + 3],\
[521, 521, -w^3 + 10*w - 8],\
[521, 521, w^3 - 3*w^2 - 7*w + 1],\
[521, 521, -2*w^3 + 2*w^2 + 8*w - 5],\
[541, 541, 2*w - 7],\
[541, 541, 2*w + 5],\
[547, 547, w^3 - 4*w^2 + 7],\
[547, 547, w^3 + w^2 - 5*w - 4],\
[563, 563, -2*w^3 + 4*w^2 + 7*w - 5],\
[563, 563, -2*w^3 + 2*w^2 + 9*w - 4],\
[587, 587, -w^3 - w^2 + 4*w + 6],\
[587, 587, w^3 - 4*w^2 + w + 8],\
[593, 593, w^2 + w - 7],\
[593, 593, 2*w^3 - 5*w^2 - 4*w + 5],\
[593, 593, -2*w^3 + w^2 + 8*w - 2],\
[593, 593, w^2 - 3*w - 5],\
[613, 613, 2*w^3 - 3*w^2 - 11*w + 2],\
[613, 613, w^3 + w^2 - 6*w - 3],\
[613, 613, 3*w^3 - 4*w^2 - 12*w + 4],\
[613, 613, 2*w^3 - 3*w^2 - 11*w + 10],\
[631, 631, -w^3 - w^2 + 7*w + 6],\
[631, 631, -w^3 + 4*w^2 + 2*w - 11],\
[647, 647, w^2 - 4*w - 3],\
[647, 647, w^2 + 2*w - 6],\
[677, 677, w^2 + w - 8],\
[677, 677, -w^3 + 7*w - 3],\
[677, 677, -w^3 + 3*w^2 + 4*w - 3],\
[677, 677, w^2 - 3*w - 6],\
[709, 709, w^3 - 7*w - 8],\
[709, 709, w^3 - 3*w^2 - 4*w + 14],\
[739, 739, w^3 - w^2 - 4*w - 5],\
[739, 739, -3*w^3 + 3*w^2 + 16*w - 3],\
[739, 739, -3*w^3 + 6*w^2 + 13*w - 13],\
[739, 739, -w^3 + 2*w^2 + 3*w - 9],\
[751, 751, -w - 5],\
[751, 751, w^3 + w^2 - 7*w - 4],\
[751, 751, -w^3 + 4*w^2 + 2*w - 9],\
[751, 751, w - 6],\
[757, 757, -w^3 + 4*w^2 + 2*w - 10],\
[757, 757, w^3 + w^2 - 7*w - 5],\
[761, 761, -3*w^3 + 2*w^2 + 17*w - 1],\
[761, 761, -3*w^3 + 6*w^2 + 9*w - 17],\
[761, 761, 2*w^3 - 5*w^2 - 9*w + 9],\
[761, 761, 2*w^3 - 2*w^2 - 7*w - 6],\
[773, 773, -3*w^3 + 8*w^2 + 6*w - 12],\
[773, 773, w^3 - 4*w - 6],\
[773, 773, -w^3 + 3*w^2 + w - 9],\
[773, 773, -3*w^3 + w^2 + 13*w + 1],\
[797, 797, 3*w^3 - 2*w^2 - 13*w + 1],\
[797, 797, 3*w^3 - 7*w^2 - 8*w + 11],\
[823, 823, 2*w^3 - 3*w^2 - 6*w - 4],\
[823, 823, -2*w^3 + 3*w^2 + 7*w + 3],\
[823, 823, w^3 - 2*w^2 - 7*w - 3],\
[823, 823, -3*w^3 + 5*w^2 + 9*w - 2],\
[857, 857, 2*w^3 - w^2 - 10*w + 1],\
[857, 857, -2*w^3 + 5*w^2 + 6*w - 8],\
[883, 883, 3*w^3 - 3*w^2 - 12*w + 1],\
[883, 883, 3*w^3 - 6*w^2 - 9*w + 11],\
[887, 887, -2*w^3 + 5*w^2 + 7*w - 9],\
[887, 887, -4*w^3 + 6*w^2 + 17*w - 7],\
[887, 887, -2*w^3 + 5*w^2 + 9*w - 16],\
[887, 887, 2*w^3 - w^2 - 11*w + 1],\
[907, 907, -3*w^3 + 3*w^2 + 16*w - 2],\
[907, 907, -3*w^3 + 6*w^2 + 13*w - 14],\
[919, 919, 2*w^3 - 2*w^2 - 7*w + 9],\
[919, 919, -2*w^3 + 2*w^2 + 12*w - 5],\
[929, 929, -2*w^3 + 4*w^2 + 8*w - 5],\
[929, 929, 3*w^3 - 4*w^2 - 11*w + 12],\
[929, 929, 3*w^3 - 5*w^2 - 10*w],\
[929, 929, -2*w^3 + 2*w^2 + 10*w - 5],\
[967, 967, 3*w^3 - 5*w^2 - 9*w + 11],\
[967, 967, -3*w^3 + 7*w^2 + 6*w - 10],\
[971, 971, 2*w^3 - 2*w^2 - 7*w - 5],\
[971, 971, -2*w^3 + w^2 + 8*w - 3],\
[971, 971, 2*w^3 - 5*w^2 - 4*w + 4],\
[971, 971, -2*w^3 + 4*w^2 + 5*w - 12],\
[983, 983, 4*w - 7],\
[983, 983, 2*w^2 - 4*w - 7],\
[983, 983, 2*w^2 - 9],\
[983, 983, 4*w + 3],\
[991, 991, 2*w^3 - 6*w^2 - 5*w + 14],\
[991, 991, -2*w^3 + 11*w + 5]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - 36*x^6 + 432*x^4 - 2020*x^2 + 3008
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, e, 1/37*e^6 - 53/74*e^4 + 171/37*e^2 - 192/37, 1/37*e^6 - 53/74*e^4 + 171/37*e^2 - 192/37, -1, 7/74*e^6 - 102/37*e^4 + 839/37*e^2 - 1819/37, -3/148*e^7 + 49/74*e^5 - 230/37*e^3 + 551/37*e, -3/148*e^7 + 49/74*e^5 - 230/37*e^3 + 551/37*e, 2/37*e^6 - 53/37*e^4 + 379/37*e^2 - 606/37, -11/74*e^6 + 155/37*e^4 - 1218/37*e^2 + 2462/37, -3/37*e^6 + 159/74*e^4 - 587/37*e^2 + 1316/37, -3/37*e^6 + 159/74*e^4 - 587/37*e^2 + 1316/37, 1/37*e^7 - 53/74*e^5 + 171/37*e^3 - 118/37*e, 1/37*e^7 - 53/74*e^5 + 171/37*e^3 - 118/37*e, 1/37*e^6 - 45/37*e^4 + 504/37*e^2 - 1080/37, 1/37*e^6 - 45/37*e^4 + 504/37*e^2 - 1080/37, -1/37*e^7 + 53/74*e^5 - 171/37*e^3 + 266/37*e, 3/74*e^7 - 49/37*e^5 + 460/37*e^3 - 1102/37*e, 3/74*e^7 - 49/37*e^5 + 460/37*e^3 - 1102/37*e, -1/37*e^7 + 53/74*e^5 - 171/37*e^3 + 266/37*e, 3/148*e^7 - 49/74*e^5 + 230/37*e^3 - 625/37*e, 3/148*e^7 - 49/74*e^5 + 230/37*e^3 - 625/37*e, -3*e, 3/148*e^7 - 49/74*e^5 + 230/37*e^3 - 551/37*e, 3/148*e^7 - 49/74*e^5 + 230/37*e^3 - 551/37*e, -3*e, -7/74*e^6 + 102/37*e^4 - 876/37*e^2 + 1930/37, -7/74*e^6 + 102/37*e^4 - 876/37*e^2 + 1930/37, 7/74*e^6 - 102/37*e^4 + 876/37*e^2 - 2226/37, 7/74*e^6 - 102/37*e^4 + 876/37*e^2 - 2226/37, -2/37*e^7 + 53/37*e^5 - 342/37*e^3 + 310/37*e, -2/37*e^7 + 53/37*e^5 - 342/37*e^3 + 310/37*e, 1/37*e^6 - 8/37*e^4 - 236/37*e^2 + 1436/37, 1/37*e^6 - 8/37*e^4 - 236/37*e^2 + 1436/37, -3/74*e^7 + 49/37*e^5 - 460/37*e^3 + 1176/37*e, -3/74*e^7 + 49/37*e^5 - 460/37*e^3 + 1176/37*e, 2/37*e^6 - 53/37*e^4 + 342/37*e^2 - 458/37, 2/37*e^6 - 53/37*e^4 + 342/37*e^2 - 458/37, 3/74*e^7 - 49/37*e^5 + 497/37*e^3 - 1546/37*e, 3/74*e^7 - 49/37*e^5 + 497/37*e^3 - 1546/37*e, 6/37*e^7 - 355/74*e^5 + 1507/37*e^3 - 3594/37*e, 6/37*e^7 - 355/74*e^5 + 1507/37*e^3 - 3594/37*e, -7/74*e^7 + 102/37*e^5 - 839/37*e^3 + 1819/37*e, -7/74*e^7 + 102/37*e^5 - 839/37*e^3 + 1819/37*e, e^3 - 11*e, 5/148*e^7 - 57/74*e^5 + 112/37*e^3 + 389/37*e, 5/148*e^7 - 57/74*e^5 + 112/37*e^3 + 389/37*e, e^3 - 11*e, 8/37*e^6 - 249/37*e^4 + 2145/37*e^2 - 4718/37, 8/37*e^6 - 249/37*e^4 + 2145/37*e^2 - 4718/37, -1/37*e^6 + 8/37*e^4 + 236/37*e^2 - 918/37, -7/74*e^7 + 102/37*e^5 - 839/37*e^3 + 2041/37*e, -9/148*e^7 + 147/74*e^5 - 690/37*e^3 + 1653/37*e, -9/148*e^7 + 147/74*e^5 - 690/37*e^3 + 1653/37*e, -7/74*e^7 + 102/37*e^5 - 839/37*e^3 + 2041/37*e, -1/74*e^7 + 4/37*e^5 + 118/37*e^3 - 940/37*e, -1/74*e^7 + 4/37*e^5 + 118/37*e^3 - 940/37*e, 7/74*e^6 - 241/74*e^4 + 1209/37*e^2 - 3188/37, 7/74*e^6 - 241/74*e^4 + 1209/37*e^2 - 3188/37, -11/37*e^6 + 310/37*e^4 - 2362/37*e^2 + 4554/37, -9/74*e^6 + 147/37*e^4 - 1380/37*e^2 + 3306/37, -9/74*e^6 + 147/37*e^4 - 1380/37*e^2 + 3306/37, -11/37*e^6 + 310/37*e^4 - 2362/37*e^2 + 4554/37, -5/148*e^7 + 57/74*e^5 - 112/37*e^3 - 241/37*e, -5/148*e^7 + 57/74*e^5 - 112/37*e^3 - 241/37*e, -2/37*e^6 + 53/37*e^4 - 416/37*e^2 + 1198/37, -16/37*e^6 + 461/37*e^4 - 3735/37*e^2 + 8178/37, -16/37*e^6 + 461/37*e^4 - 3735/37*e^2 + 8178/37, -2/37*e^6 + 53/37*e^4 - 416/37*e^2 + 1198/37, -3/74*e^6 + 61/74*e^4 + 21/37*e^2 - 1340/37, 15/74*e^6 - 379/74*e^4 + 1153/37*e^2 - 996/37, 15/74*e^6 - 379/74*e^4 + 1153/37*e^2 - 996/37, -3/74*e^6 + 61/74*e^4 + 21/37*e^2 - 1340/37, -7/74*e^7 + 102/37*e^5 - 839/37*e^3 + 1856/37*e, -7/74*e^7 + 102/37*e^5 - 839/37*e^3 + 1856/37*e, 7/37*e^6 - 204/37*e^4 + 1752/37*e^2 - 4526/37, 7/37*e^6 - 204/37*e^4 + 1752/37*e^2 - 4526/37, 2/37*e^6 - 90/37*e^4 + 1156/37*e^2 - 3122/37, 2/37*e^6 - 90/37*e^4 + 1156/37*e^2 - 3122/37, 4/37*e^7 - 106/37*e^5 + 684/37*e^3 - 583/37*e, 4/37*e^7 - 106/37*e^5 + 684/37*e^3 - 583/37*e, -11/37*e^6 + 310/37*e^4 - 2288/37*e^2 + 3592/37, -11/37*e^6 + 310/37*e^4 - 2288/37*e^2 + 3592/37, 7/74*e^7 - 102/37*e^5 + 876/37*e^3 - 2374/37*e, 7/74*e^7 - 102/37*e^5 + 876/37*e^3 - 2374/37*e, 1/74*e^7 - 4/37*e^5 - 118/37*e^3 + 644/37*e, 1/74*e^7 - 4/37*e^5 - 118/37*e^3 + 644/37*e, -9/74*e^6 + 257/74*e^4 - 1121/37*e^2 + 3528/37, -9/74*e^6 + 257/74*e^4 - 1121/37*e^2 + 3528/37, -11/74*e^6 + 273/74*e^4 - 1033/37*e^2 + 3572/37, -11/74*e^6 + 273/74*e^4 - 1033/37*e^2 + 3572/37, 11/74*e^7 - 347/74*e^5 + 1625/37*e^3 - 4164/37*e, 11/74*e^7 - 347/74*e^5 + 1625/37*e^3 - 4164/37*e, -11/148*e^7 + 155/74*e^5 - 572/37*e^3 + 935/37*e, -2/37*e^7 + 53/37*e^5 - 305/37*e^3 - 97/37*e, -2/37*e^7 + 53/37*e^5 - 305/37*e^3 - 97/37*e, -11/148*e^7 + 155/74*e^5 - 572/37*e^3 + 935/37*e, 1/37*e^6 - 45/37*e^4 + 615/37*e^2 - 2042/37, 1/37*e^6 - 45/37*e^4 + 615/37*e^2 - 2042/37, 5/37*e^6 - 114/37*e^4 + 670/37*e^2 - 1700/37, 5/37*e^6 - 114/37*e^4 + 670/37*e^2 - 1700/37, -5/74*e^7 + 57/37*e^5 - 224/37*e^3 - 630/37*e, -5/74*e^7 + 57/37*e^5 - 224/37*e^3 - 630/37*e, 11/74*e^7 - 155/37*e^5 + 1218/37*e^3 - 2610/37*e, 11/74*e^7 - 155/37*e^5 + 1218/37*e^3 - 2610/37*e, 9/148*e^7 - 147/74*e^5 + 764/37*e^3 - 2541/37*e, -e^3 + 15*e, -e^3 + 15*e, 9/148*e^7 - 147/74*e^5 + 764/37*e^3 - 2541/37*e, -1/37*e^6 + 45/37*e^4 - 652/37*e^2 + 1746/37, 14/37*e^6 - 371/37*e^4 + 2579/37*e^2 - 4094/37, 14/37*e^6 - 371/37*e^4 + 2579/37*e^2 - 4094/37, -1/37*e^6 + 45/37*e^4 - 652/37*e^2 + 1746/37, -7/37*e^6 + 167/37*e^4 - 1012/37*e^2 + 1936/37, -7/37*e^6 + 167/37*e^4 - 1012/37*e^2 + 1936/37, -10/37*e^7 + 302/37*e^5 - 2598/37*e^3 + 6212/37*e, -10/37*e^7 + 302/37*e^5 - 2598/37*e^3 + 6212/37*e, -3/37*e^7 + 98/37*e^5 - 920/37*e^3 + 2241/37*e, -5/148*e^7 + 57/74*e^5 - 112/37*e^3 - 463/37*e, -5/148*e^7 + 57/74*e^5 - 112/37*e^3 - 463/37*e, -3/37*e^7 + 98/37*e^5 - 920/37*e^3 + 2241/37*e, 7/74*e^6 - 102/37*e^4 + 876/37*e^2 - 2670/37, 7/74*e^6 - 102/37*e^4 + 876/37*e^2 - 2670/37, -6/37*e^6 + 196/37*e^4 - 1840/37*e^2 + 4260/37, -18/37*e^6 + 514/37*e^4 - 4188/37*e^2 + 8932/37, -18/37*e^6 + 514/37*e^4 - 4188/37*e^2 + 8932/37, -6/37*e^6 + 196/37*e^4 - 1840/37*e^2 + 4260/37, 1/37*e^6 - 127/74*e^4 + 763/37*e^2 - 784/37, -5/74*e^6 + 151/74*e^4 - 705/37*e^2 + 2256/37, -5/74*e^6 + 151/74*e^4 - 705/37*e^2 + 2256/37, 1/37*e^6 - 127/74*e^4 + 763/37*e^2 - 784/37, -13/37*e^6 + 363/37*e^4 - 2852/37*e^2 + 5678/37, -13/37*e^6 + 363/37*e^4 - 2852/37*e^2 + 5678/37, -17/148*e^7 + 253/74*e^5 - 1106/37*e^3 + 2999/37*e, -5/74*e^7 + 57/37*e^5 - 261/37*e^3 - 297/37*e, -5/74*e^7 + 57/37*e^5 - 261/37*e^3 - 297/37*e, -17/148*e^7 + 253/74*e^5 - 1106/37*e^3 + 2999/37*e, 23/148*e^7 - 351/74*e^5 + 1566/37*e^3 - 4027/37*e, 1/37*e^7 - 45/37*e^5 + 578/37*e^3 - 1931/37*e, 1/37*e^7 - 45/37*e^5 + 578/37*e^3 - 1931/37*e, 23/148*e^7 - 351/74*e^5 + 1566/37*e^3 - 4027/37*e, 1/148*e^7 - 41/74*e^5 + 348/37*e^3 - 1343/37*e, 1/148*e^7 - 41/74*e^5 + 348/37*e^3 - 1343/37*e, 5/37*e^6 - 151/37*e^4 + 1114/37*e^2 - 960/37, 4/37*e^6 - 143/37*e^4 + 1572/37*e^2 - 4320/37, 4/37*e^6 - 143/37*e^4 + 1572/37*e^2 - 4320/37, 5/37*e^6 - 151/37*e^4 + 1114/37*e^2 - 960/37, -17/148*e^7 + 253/74*e^5 - 1106/37*e^3 + 2851/37*e, -17/148*e^7 + 253/74*e^5 - 1106/37*e^3 + 2851/37*e, 10/37*e^6 - 567/74*e^4 + 1969/37*e^2 - 2660/37, 10/37*e^6 - 567/74*e^4 + 1969/37*e^2 - 2660/37, 5/37*e^7 - 151/37*e^5 + 1299/37*e^3 - 3032/37*e, 3/74*e^7 - 61/74*e^5 + 53/37*e^3 + 452/37*e, 3/74*e^7 - 61/74*e^5 + 53/37*e^3 + 452/37*e, 5/37*e^7 - 151/37*e^5 + 1299/37*e^3 - 3032/37*e, 13/37*e^6 - 763/74*e^4 + 3111/37*e^2 - 7084/37, 13/37*e^6 - 763/74*e^4 + 3111/37*e^2 - 7084/37, -33/74*e^6 + 1041/74*e^4 - 4653/37*e^2 + 10864/37, -33/74*e^6 + 1041/74*e^4 - 4653/37*e^2 + 10864/37, 4/37*e^7 - 106/37*e^5 + 684/37*e^3 - 657/37*e, -17/148*e^7 + 253/74*e^5 - 1106/37*e^3 + 3295/37*e, -17/148*e^7 + 253/74*e^5 - 1106/37*e^3 + 3295/37*e, 4/37*e^7 - 106/37*e^5 + 684/37*e^3 - 657/37*e, -18/37*e^6 + 551/37*e^4 - 5002/37*e^2 + 12040/37, -18/37*e^6 + 551/37*e^4 - 5002/37*e^2 + 12040/37, -5/37*e^7 + 151/37*e^5 - 1299/37*e^3 + 2662/37*e, 1/74*e^7 - 4/37*e^5 - 118/37*e^3 + 718/37*e, 1/74*e^7 - 4/37*e^5 - 118/37*e^3 + 718/37*e, -5/37*e^7 + 151/37*e^5 - 1299/37*e^3 + 2662/37*e, -17/74*e^7 + 253/37*e^5 - 2138/37*e^3 + 5184/37*e, 5/74*e^7 - 57/37*e^5 + 261/37*e^3 - 36/37*e, 5/74*e^7 - 57/37*e^5 + 261/37*e^3 - 36/37*e, -17/74*e^7 + 253/37*e^5 - 2138/37*e^3 + 5184/37*e, -11/74*e^6 + 347/74*e^4 - 1477/37*e^2 + 3128/37, -11/74*e^6 + 347/74*e^4 - 1477/37*e^2 + 3128/37]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([9, 3, w^3 - w^2 - 4*w])] = 1

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