/*
  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, 6, 4, -5, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([79,79,-w^3 + w^2 + 4*w - 1])

primes_array = [
[13, 13, w^5 - 5*w^3 + 4*w],\
[25, 5, w^5 - 5*w^3 + 6*w - 1],\
[25, 5, -w^3 + w^2 + 3*w - 1],\
[25, 5, w^5 - 4*w^3 - w^2 + 3*w + 2],\
[27, 3, w^4 - w^3 - 4*w^2 + 2*w + 2],\
[27, 3, w^4 - w^3 - 4*w^2 + 2*w + 3],\
[53, 53, -w^4 + w^3 + 3*w^2 - 2*w + 1],\
[53, 53, -w^4 + w^3 + 4*w^2 - 3*w - 4],\
[53, 53, -w^5 + w^4 + 4*w^3 - 4*w^2 - 3*w + 1],\
[53, 53, w^3 - 2*w - 2],\
[53, 53, w^5 - 5*w^3 - w^2 + 5*w],\
[53, 53, -w^4 + 4*w^2 + w - 4],\
[64, 2, -2],\
[79, 79, -2*w^5 + w^4 + 9*w^3 - 3*w^2 - 9*w + 2],\
[79, 79, -w^5 - w^4 + 5*w^3 + 4*w^2 - 6*w - 1],\
[79, 79, w^3 - w^2 - 4*w + 1],\
[79, 79, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 9*w + 3],\
[79, 79, -2*w^4 + w^3 + 7*w^2 - 3*w - 3],\
[79, 79, -w^5 + 6*w^3 - w^2 - 8*w + 1],\
[103, 103, 2*w^4 - 7*w^2 - w + 3],\
[103, 103, w^5 - w^4 - 4*w^3 + 5*w^2 + 2*w - 4],\
[103, 103, -w^5 - w^4 + 4*w^3 + 4*w^2 - 2*w - 3],\
[103, 103, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 4*w - 1],\
[103, 103, -w^4 + w^3 + 5*w^2 - 3*w - 4],\
[103, 103, 2*w^5 - w^4 - 10*w^3 + 3*w^2 + 10*w - 1],\
[131, 131, w^5 - w^4 - 5*w^3 + 3*w^2 + 4*w - 1],\
[131, 131, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 4*w + 2],\
[131, 131, w^5 - w^4 - 4*w^3 + 5*w^2 + 2*w - 5],\
[131, 131, 2*w^4 - 7*w^2 - w + 2],\
[131, 131, -2*w^5 + w^4 + 9*w^3 - 2*w^2 - 8*w],\
[131, 131, 2*w^5 - w^4 - 10*w^3 + 3*w^2 + 10*w],\
[157, 157, -w^5 - w^4 + 5*w^3 + 5*w^2 - 6*w - 3],\
[157, 157, -2*w^3 + w^2 + 5*w - 2],\
[157, 157, -w^5 - w^4 + 4*w^3 + 5*w^2 - 3*w - 3],\
[157, 157, -w^5 + 5*w^3 - 7*w],\
[157, 157, -2*w^5 + w^4 + 8*w^3 - 3*w^2 - 6*w + 2],\
[157, 157, -w^5 + w^4 + 5*w^3 - 4*w^2 - 7*w + 2],\
[181, 181, w^2 - 2*w - 2],\
[181, 181, 2*w^5 - 9*w^3 + 7*w],\
[181, 181, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 5*w + 4],\
[181, 181, -w^5 + w^4 + 6*w^3 - 3*w^2 - 9*w + 1],\
[181, 181, 2*w^5 - 2*w^4 - 8*w^3 + 6*w^2 + 5*w - 2],\
[181, 181, w^4 - 2*w^2 - 2],\
[233, 233, 2*w^3 - w^2 - 5*w + 1],\
[233, 233, -w^5 - w^4 + 6*w^3 + 3*w^2 - 8*w],\
[233, 233, w^5 - w^4 - 5*w^3 + 4*w^2 + 7*w - 3],\
[233, 233, w^5 + w^4 - 5*w^3 - 5*w^2 + 6*w + 4],\
[233, 233, -w^5 + 4*w^3 + 2*w^2 - 2*w - 3],\
[233, 233, 2*w^5 - w^4 - 8*w^3 + 3*w^2 + 6*w - 1],\
[311, 311, 2*w^5 - 2*w^4 - 9*w^3 + 6*w^2 + 8*w - 2],\
[311, 311, w^4 + w^3 - 3*w^2 - 4*w + 1],\
[311, 311, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w + 2],\
[311, 311, w^5 - w^4 - 4*w^3 + 4*w^2 + w - 3],\
[311, 311, w^4 - 2*w^2 - w - 2],\
[311, 311, -2*w^5 + w^4 + 9*w^3 - 4*w^2 - 7*w + 2],\
[313, 313, -w^5 + 5*w^3 + w^2 - 4*w - 3],\
[313, 313, -w^5 + 6*w^3 - 7*w + 1],\
[313, 313, -w^4 + w^3 + 5*w^2 - 3*w - 3],\
[313, 313, -w^5 + w^4 + 3*w^3 - 4*w^2 + 4],\
[313, 313, -w^5 + 2*w^4 + 4*w^3 - 7*w^2 - 4*w + 2],\
[313, 313, -2*w^4 + w^3 + 7*w^2 - 2*w - 4],\
[337, 337, 2*w^5 - w^4 - 7*w^3 + 2*w^2 + 2*w + 2],\
[337, 337, w^5 - 2*w^4 - 3*w^3 + 7*w^2 + 2*w - 3],\
[337, 337, 2*w^5 - w^4 - 9*w^3 + 2*w^2 + 10*w - 1],\
[337, 337, -2*w^5 - w^4 + 9*w^3 + 4*w^2 - 8*w],\
[337, 337, 3*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 11*w - 5],\
[337, 337, w^4 - w^3 - 2*w^2 + 4*w],\
[389, 389, 2*w^5 - w^4 - 9*w^3 + 4*w^2 + 7*w],\
[389, 389, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 7*w + 3],\
[389, 389, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w],\
[389, 389, -2*w^5 + 3*w^4 + 9*w^3 - 10*w^2 - 8*w + 2],\
[389, 389, -3*w^5 + w^4 + 14*w^3 - 2*w^2 - 12*w],\
[389, 389, -w^5 + w^4 + 5*w^3 - 3*w^2 - 3*w + 1],\
[443, 443, -2*w^5 + w^4 + 8*w^3 - w^2 - 7*w - 3],\
[443, 443, 2*w^5 - w^4 - 9*w^3 + 4*w^2 + 8*w],\
[443, 443, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 2*w - 4],\
[443, 443, 2*w^5 - w^4 - 9*w^3 + 2*w^2 + 8*w - 2],\
[443, 443, -2*w^4 + 2*w^3 + 7*w^2 - 4*w - 3],\
[443, 443, -3*w^5 + w^4 + 15*w^3 - 3*w^2 - 17*w + 2],\
[467, 467, 2*w^5 - 2*w^4 - 9*w^3 + 6*w^2 + 10*w - 1],\
[467, 467, w^5 + w^4 - 5*w^3 - 6*w^2 + 6*w + 5],\
[467, 467, -w^5 - 2*w^4 + 5*w^3 + 7*w^2 - 5*w - 3],\
[467, 467, -2*w^5 + w^4 + 11*w^3 - 4*w^2 - 13*w + 3],\
[467, 467, 3*w^5 - 2*w^4 - 13*w^3 + 6*w^2 + 11*w - 1],\
[467, 467, -2*w^5 + w^4 + 9*w^3 - w^2 - 8*w - 3],\
[521, 521, w^5 + 2*w^4 - 6*w^3 - 7*w^2 + 7*w + 3],\
[521, 521, 2*w^5 - 2*w^4 - 8*w^3 + 6*w^2 + 7*w - 1],\
[521, 521, -w^5 + w^4 + 6*w^3 - 4*w^2 - 10*w + 3],\
[521, 521, 2*w^5 - 3*w^4 - 9*w^3 + 10*w^2 + 9*w - 3],\
[521, 521, -2*w^5 + 11*w^3 - 13*w + 1],\
[521, 521, 3*w^5 - w^4 - 13*w^3 + 3*w^2 + 11*w - 1],\
[547, 547, w^4 + w^3 - 5*w^2 - 3*w + 1],\
[547, 547, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 10*w + 6],\
[547, 547, w^4 - w^3 - w^2 + 3*w - 3],\
[547, 547, 2*w^4 + w^3 - 9*w^2 - 2*w + 6],\
[547, 547, 3*w^5 - w^4 - 13*w^3 + 3*w^2 + 11*w - 2],\
[547, 547, -w^5 + w^4 + 6*w^3 - 4*w^2 - 10*w + 2],\
[571, 571, -w^5 + 4*w^3 + 3*w^2 - 3*w - 4],\
[571, 571, -w^5 - w^4 + 3*w^3 + 6*w^2 - 5],\
[571, 571, w^5 - 6*w^3 + 2*w^2 + 9*w - 4],\
[571, 571, 2*w^5 - 9*w^3 - w^2 + 10*w + 1],\
[571, 571, 2*w^5 - 11*w^3 + w^2 + 13*w - 3],\
[571, 571, -w^5 + 7*w^3 - w^2 - 12*w + 2],\
[599, 599, -2*w^5 + w^4 + 8*w^3 - 5*w^2 - 5*w + 5],\
[599, 599, w^5 - w^4 - 6*w^3 + 4*w^2 + 6*w - 2],\
[599, 599, w^4 - 2*w^3 - 5*w^2 + 7*w + 4],\
[599, 599, -2*w^5 + 10*w^3 - w^2 - 11*w + 3],\
[599, 599, w^5 - 3*w^4 - 5*w^3 + 11*w^2 + 7*w - 5],\
[599, 599, -w^5 + w^4 + 6*w^3 - 3*w^2 - 8*w + 3],\
[677, 677, -w^5 - 2*w^4 + 6*w^3 + 8*w^2 - 9*w - 4],\
[677, 677, -3*w^5 + 2*w^4 + 13*w^3 - 7*w^2 - 12*w + 4],\
[677, 677, w^4 + w^3 - 5*w^2 - 5*w + 4],\
[677, 677, -2*w^5 + 9*w^3 - w^2 - 7*w + 1],\
[677, 677, w^5 - 5*w^3 + 2*w^2 + 5*w - 5],\
[677, 677, -w^5 - w^4 + 7*w^3 + 2*w^2 - 10*w + 1],\
[701, 701, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 2*w - 6],\
[701, 701, w^5 + w^4 - 6*w^3 - 5*w^2 + 6*w + 4],\
[701, 701, -w^5 - w^4 + 3*w^3 + 4*w^2 + 2*w - 2],\
[701, 701, 3*w^5 - 2*w^4 - 14*w^3 + 5*w^2 + 14*w],\
[701, 701, 3*w^5 - 2*w^4 - 14*w^3 + 8*w^2 + 13*w - 5],\
[701, 701, -w^5 + 2*w^4 + 3*w^3 - 7*w^2 + 2*w + 3],\
[727, 727, w^5 + 2*w^4 - 5*w^3 - 8*w^2 + 6*w + 3],\
[727, 727, -w^5 + 4*w^3 + 3*w^2 - 3*w - 6],\
[727, 727, -w^5 - w^4 + 5*w^3 + 2*w^2 - 4*w + 2],\
[727, 727, 3*w^5 - 2*w^4 - 13*w^3 + 6*w^2 + 12*w - 3],\
[727, 727, -2*w^5 + 11*w^3 - w^2 - 13*w + 1],\
[727, 727, w^5 - 3*w^4 - 4*w^3 + 10*w^2 + 5*w - 4],\
[857, 857, -w^5 + 3*w^4 + 5*w^3 - 11*w^2 - 5*w + 5],\
[857, 857, -w^5 - 2*w^4 + 4*w^3 + 9*w^2 - 3*w - 7],\
[857, 857, 2*w^5 + w^4 - 9*w^3 - 4*w^2 + 6*w + 3],\
[857, 857, 2*w^5 - 3*w^4 - 7*w^3 + 10*w^2 + 2*w - 5],\
[857, 857, -w^5 + 6*w^3 - 2*w^2 - 8*w + 2],\
[857, 857, -3*w^3 + w^2 + 9*w],\
[859, 859, 2*w^4 - 2*w^3 - 5*w^2 + 5*w - 2],\
[859, 859, -2*w^5 + 9*w^3 - 6*w - 2],\
[859, 859, -w^4 - w^3 + 2*w^2 + 3*w + 4],\
[859, 859, -w^5 - 2*w^4 + 6*w^3 + 9*w^2 - 7*w - 7],\
[859, 859, -2*w^5 - w^4 + 10*w^3 + 4*w^2 - 9*w - 4],\
[859, 859, -w^5 - w^4 + 4*w^3 + 4*w^2 - 3*w + 1],\
[883, 883, 2*w^5 + w^4 - 10*w^3 - 4*w^2 + 11*w],\
[883, 883, -2*w^5 + w^4 + 9*w^3 - 3*w^2 - 10*w + 3],\
[883, 883, 3*w^5 - w^4 - 13*w^3 + 2*w^2 + 12*w + 1],\
[883, 883, 3*w^5 - 2*w^4 - 12*w^3 + 6*w^2 + 8*w - 3],\
[883, 883, w^5 - 6*w^3 + w^2 + 10*w - 3],\
[883, 883, -2*w^5 + 11*w^3 - w^2 - 14*w + 3],\
[911, 911, -3*w^5 + 15*w^3 - 15*w + 1],\
[911, 911, -2*w^5 + 2*w^4 + 8*w^3 - 8*w^2 - 6*w + 3],\
[911, 911, -2*w^5 + 11*w^3 - 13*w + 2],\
[911, 911, -2*w^5 + 10*w^3 + 2*w^2 - 10*w - 1],\
[911, 911, 2*w^4 - 2*w^3 - 8*w^2 + 6*w + 7],\
[911, 911, -3*w^4 + 12*w^2 - 7],\
[937, 937, 3*w^4 - w^3 - 10*w^2 + 2*w + 4],\
[937, 937, -w^5 + 2*w^4 + 5*w^3 - 9*w^2 - 6*w + 5],\
[937, 937, -w^5 + 2*w^4 + 2*w^3 - 6*w^2 + 3*w + 3],\
[937, 937, 2*w^5 - w^4 - 11*w^3 + 4*w^2 + 12*w - 3],\
[937, 937, -2*w^5 + 11*w^3 + w^2 - 14*w],\
[937, 937, 2*w^5 + w^4 - 9*w^3 - 5*w^2 + 7*w + 5],\
[961, 31, -3*w^5 + w^4 + 12*w^3 - 3*w^2 - 8*w + 2],\
[961, 31, -2*w^5 + 2*w^4 + 10*w^3 - 7*w^2 - 13*w + 3],\
[961, 31, -w^5 + w^4 + 7*w^3 - 5*w^2 - 10*w + 4]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 - 7*x^4 - 8*x^3 + 106*x^2 - 19*x - 361
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -7/38*e^4 + 15/19*e^3 + 47/19*e^2 - 124/19*e - 17/2, 17/38*e^4 - 31/19*e^3 - 163/19*e^2 + 312/19*e + 91/2, 5/19*e^4 - 16/19*e^3 - 116/19*e^2 + 188/19*e + 30, 4/19*e^4 - 9/19*e^3 - 108/19*e^2 + 101/19*e + 32, -7/38*e^4 + 15/19*e^3 + 66/19*e^2 - 162/19*e - 37/2, -17/38*e^4 + 31/19*e^3 + 163/19*e^2 - 312/19*e - 83/2, 3/19*e^4 - 21/19*e^3 - 24/19*e^2 + 204/19*e + 9, -17/38*e^4 + 31/19*e^3 + 163/19*e^2 - 312/19*e - 83/2, -17/38*e^4 + 31/19*e^3 + 163/19*e^2 - 312/19*e - 83/2, 3/38*e^4 - 1/19*e^3 - 31/19*e^2 - 50/19*e + 17/2, 7/38*e^4 - 15/19*e^3 - 47/19*e^2 + 124/19*e + 25/2, 12/19*e^4 - 46/19*e^3 - 229/19*e^2 + 436/19*e + 68, 5/19*e^4 - 16/19*e^3 - 116/19*e^2 + 226/19*e + 37, -21/38*e^4 + 45/19*e^3 + 160/19*e^2 - 410/19*e - 71/2, -1, -10/19*e^4 + 32/19*e^3 + 232/19*e^2 - 338/19*e - 74, -2/19*e^4 + 14/19*e^3 + 16/19*e^2 - 174/19*e, -5/38*e^4 + 8/19*e^3 + 39/19*e^2 - 94/19*e - 7/2, -5/19*e^4 + 16/19*e^3 + 116/19*e^2 - 188/19*e - 33, 4/19*e^4 - 9/19*e^3 - 108/19*e^2 + 101/19*e + 32, 15/19*e^4 - 48/19*e^3 - 348/19*e^2 + 564/19*e + 101, 12/19*e^4 - 46/19*e^3 - 210/19*e^2 + 474/19*e + 54, -1/38*e^4 - 6/19*e^3 + 23/19*e^2 + 118/19*e - 7/2, -5/19*e^4 + 16/19*e^3 + 116/19*e^2 - 188/19*e - 33, -10/19*e^4 + 32/19*e^3 + 232/19*e^2 - 376/19*e - 70, -7/19*e^4 + 30/19*e^3 + 94/19*e^2 - 248/19*e - 13, 2*e^2 - 6*e - 20, -41/38*e^4 + 77/19*e^3 + 411/19*e^2 - 843/19*e - 215/2, -1/38*e^4 - 6/19*e^3 + 61/19*e^2 - 34/19*e - 47/2, 14/19*e^4 - 41/19*e^3 - 340/19*e^2 + 477/19*e + 106, 15/19*e^4 - 67/19*e^3 - 234/19*e^2 + 678/19*e + 63, -12/19*e^4 + 46/19*e^3 + 210/19*e^2 - 398/19*e - 57, 5/19*e^4 - 16/19*e^3 - 78/19*e^2 + 74/19*e + 14, 25/38*e^4 - 59/19*e^3 - 195/19*e^2 + 584/19*e + 111/2, -5/38*e^4 + 8/19*e^3 + 77/19*e^2 - 113/19*e - 67/2, -17/38*e^4 + 31/19*e^3 + 163/19*e^2 - 274/19*e - 83/2, -11/38*e^4 + 29/19*e^3 + 63/19*e^2 - 298/19*e - 17/2, -9/38*e^4 + 3/19*e^3 + 131/19*e^2 - 40/19*e - 79/2, 27/38*e^4 - 47/19*e^3 - 279/19*e^2 + 538/19*e + 165/2, -1/19*e^4 - 12/19*e^3 + 65/19*e^2 + 160/19*e - 21, -2/19*e^4 - 5/19*e^3 + 92/19*e^2 + 54/19*e - 32, 7/19*e^4 - 30/19*e^3 - 94/19*e^2 + 286/19*e + 10, 18/19*e^4 - 69/19*e^3 - 372/19*e^2 + 711/19*e + 114, -17/19*e^4 + 62/19*e^3 + 364/19*e^2 - 624/19*e - 121, 51/38*e^4 - 93/19*e^3 - 470/19*e^2 + 898/19*e + 257/2, -5/19*e^4 + 16/19*e^3 + 116/19*e^2 - 112/19*e - 39, -21/38*e^4 + 45/19*e^3 + 217/19*e^2 - 543/19*e - 119/2, -12/19*e^4 + 46/19*e^3 + 248/19*e^2 - 512/19*e - 76, 25/38*e^4 - 59/19*e^3 - 176/19*e^2 + 508/19*e + 71/2, 25/19*e^4 - 80/19*e^3 - 542/19*e^2 + 902/19*e + 151, 5/19*e^4 - 16/19*e^3 - 154/19*e^2 + 226/19*e + 53, -2*e^2 + 2*e + 30, 1/38*e^4 - 13/19*e^3 + 15/19*e^2 + 186/19*e - 11/2, -27/38*e^4 + 47/19*e^3 + 279/19*e^2 - 557/19*e - 129/2, -2/19*e^4 + 14/19*e^3 + 16/19*e^2 - 98/19*e - 16, -1/19*e^4 - 12/19*e^3 + 46/19*e^2 + 160/19*e + 3, -31/38*e^4 + 61/19*e^3 + 295/19*e^2 - 636/19*e - 175/2, -12/19*e^4 + 46/19*e^3 + 248/19*e^2 - 512/19*e - 72, 23/38*e^4 - 33/19*e^3 - 225/19*e^2 + 288/19*e + 99/2, -10/19*e^4 + 32/19*e^3 + 232/19*e^2 - 224/19*e - 80, -1/19*e^4 + 26/19*e^3 - 106/19*e^2 - 125/19*e + 51, -7/19*e^4 + 11/19*e^3 + 170/19*e^2 - 134/19*e - 39, -15/38*e^4 + 5/19*e^3 + 231/19*e^2 - 92/19*e - 121/2, 12/19*e^4 - 46/19*e^3 - 191/19*e^2 + 398/19*e + 38, -27/38*e^4 + 47/19*e^3 + 241/19*e^2 - 424/19*e - 113/2, -3/38*e^4 + 1/19*e^3 - 7/19*e^2 + 88/19*e + 51/2, 7/38*e^4 - 15/19*e^3 - 47/19*e^2 + 10/19*e + 37/2, -29/38*e^4 + 35/19*e^3 + 363/19*e^2 - 416/19*e - 211/2, -69/38*e^4 + 137/19*e^3 + 675/19*e^2 - 1510/19*e - 347/2, -21/19*e^4 + 90/19*e^3 + 358/19*e^2 - 915/19*e - 79, -33/38*e^4 + 49/19*e^3 + 417/19*e^2 - 514/19*e - 279/2, 31/38*e^4 - 42/19*e^3 - 371/19*e^2 + 465/19*e + 201/2, -9/38*e^4 + 3/19*e^3 + 169/19*e^2 - 154/19*e - 117/2, -10/19*e^4 + 32/19*e^3 + 270/19*e^2 - 376/19*e - 108, -35/38*e^4 + 75/19*e^3 + 273/19*e^2 - 639/19*e - 121/2, -e^3 + 4*e^2 + 9*e - 24, 27/19*e^4 - 94/19*e^3 - 596/19*e^2 + 1038/19*e + 171, -41/38*e^4 + 77/19*e^3 + 373/19*e^2 - 805/19*e - 155/2, 25/38*e^4 - 59/19*e^3 - 157/19*e^2 + 432/19*e + 65/2, 2/19*e^4 + 5/19*e^3 - 54/19*e^2 - 73/19*e, -16/19*e^4 + 74/19*e^3 + 242/19*e^2 - 670/19*e - 62, 1/19*e^4 - 26/19*e^3 + 106/19*e^2 + 182/19*e - 47, 3/19*e^4 - 2/19*e^3 - 138/19*e^2 + 52/19*e + 49, 45/38*e^4 - 110/19*e^3 - 351/19*e^2 + 1074/19*e + 199/2, 25/38*e^4 - 59/19*e^3 - 233/19*e^2 + 774/19*e + 103/2, -2/19*e^4 + 14/19*e^3 + 73/19*e^2 - 326/19*e - 26, 61/38*e^4 - 109/19*e^3 - 605/19*e^2 + 1086/19*e + 359/2, -13/38*e^4 + 17/19*e^3 + 109/19*e^2 - 24/19*e - 59/2, -7/38*e^4 + 34/19*e^3 + 9/19*e^2 - 409/19*e + 19/2, -49/38*e^4 + 67/19*e^3 + 595/19*e^2 - 792/19*e - 351/2, -61/38*e^4 + 109/19*e^3 + 567/19*e^2 - 1181/19*e - 251/2, -e^4 + 4*e^3 + 18*e^2 - 40*e - 93, -1/19*e^4 - 12/19*e^3 + 84/19*e^2 + 198/19*e - 27, -7/19*e^4 + 30/19*e^3 + 132/19*e^2 - 438/19*e - 27, -29/19*e^4 + 108/19*e^3 + 574/19*e^2 - 1060/19*e - 161, 41/38*e^4 - 77/19*e^3 - 335/19*e^2 + 691/19*e + 179/2, -9/19*e^4 + 6/19*e^3 + 338/19*e^2 - 232/19*e - 117, -5/38*e^4 + 27/19*e^3 - 37/19*e^2 - 208/19*e + 35/2, 41/19*e^4 - 154/19*e^3 - 784/19*e^2 + 1686/19*e + 199, -17/38*e^4 + 12/19*e^3 + 239/19*e^2 - 84/19*e - 159/2, 23/38*e^4 - 52/19*e^3 - 149/19*e^2 + 592/19*e + 37/2, -11/19*e^4 + 58/19*e^3 + 126/19*e^2 - 558/19*e - 31, -23/38*e^4 + 33/19*e^3 + 263/19*e^2 - 364/19*e - 159/2, -37/19*e^4 + 145/19*e^3 + 714/19*e^2 - 1471/19*e - 191, 47/38*e^4 - 79/19*e^3 - 511/19*e^2 + 819/19*e + 329/2, -39/38*e^4 + 89/19*e^3 + 327/19*e^2 - 908/19*e - 195/2, 39/19*e^4 - 140/19*e^3 - 806/19*e^2 + 1588/19*e + 213, 35/38*e^4 - 75/19*e^3 - 368/19*e^2 + 924/19*e + 221/2, -43/38*e^4 + 65/19*e^3 + 495/19*e^2 - 759/19*e - 249/2, 23/19*e^4 - 66/19*e^3 - 564/19*e^2 + 690/19*e + 169, 7/19*e^4 - 30/19*e^3 - 170/19*e^2 + 324/19*e + 61, 5/38*e^4 - 8/19*e^3 - 77/19*e^2 + 18/19*e + 63/2, 11/19*e^4 - 20/19*e^3 - 316/19*e^2 + 216/19*e + 97, -17/19*e^4 + 62/19*e^3 + 364/19*e^2 - 586/19*e - 123, -21/19*e^4 + 90/19*e^3 + 358/19*e^2 - 1010/19*e - 77, 25/19*e^4 - 80/19*e^3 - 504/19*e^2 + 788/19*e + 119, 21/38*e^4 - 45/19*e^3 - 160/19*e^2 + 486/19*e + 71/2, 1/38*e^4 - 13/19*e^3 - 42/19*e^2 + 300/19*e + 43/2, -22/19*e^4 + 97/19*e^3 + 404/19*e^2 - 1059/19*e - 98, 37/38*e^4 - 82/19*e^3 - 281/19*e^2 + 650/19*e + 139/2, -24/19*e^4 + 92/19*e^3 + 458/19*e^2 - 1024/19*e - 104, 1/19*e^4 - 7/19*e^3 + 30/19*e^2 - 27/19*e - 5, -22/19*e^4 + 78/19*e^3 + 518/19*e^2 - 888/19*e - 168, 33/19*e^4 - 98/19*e^3 - 720/19*e^2 + 1104/19*e + 183, -1/2*e^4 + 3*e^3 + 7*e^2 - 32*e - 115/2, 85/38*e^4 - 155/19*e^3 - 834/19*e^2 + 1598/19*e + 475/2, 5/2*e^4 - 9*e^3 - 49*e^2 + 94*e + 541/2, 5/38*e^4 + 11/19*e^3 - 39/19*e^2 - 286/19*e - 13/2, 5/38*e^4 + 11/19*e^3 - 77/19*e^2 - 324/19*e + 67/2, -41/38*e^4 + 96/19*e^3 + 221/19*e^2 - 805/19*e - 63/2, 67/38*e^4 - 111/19*e^3 - 743/19*e^2 + 1176/19*e + 441/2, 69/38*e^4 - 118/19*e^3 - 675/19*e^2 + 1111/19*e + 375/2, 27/19*e^4 - 75/19*e^3 - 672/19*e^2 + 905/19*e + 191, 23/19*e^4 - 66/19*e^3 - 564/19*e^2 + 842/19*e + 159, -18/19*e^4 + 50/19*e^3 + 524/19*e^2 - 692/19*e - 190, 28/19*e^4 - 120/19*e^3 - 414/19*e^2 + 1030/19*e + 86, 36/19*e^4 - 138/19*e^3 - 668/19*e^2 + 1460/19*e + 196, 17/19*e^4 - 62/19*e^3 - 326/19*e^2 + 586/19*e + 95, 5/38*e^4 - 27/19*e^3 + 18/19*e^2 + 170/19*e + 11/2, -1/2*e^4 + 3*e^3 - e^2 - 17*e + 99/2, -47/38*e^4 + 117/19*e^3 + 340/19*e^2 - 1218/19*e - 181/2, -17/19*e^4 + 62/19*e^3 + 326/19*e^2 - 624/19*e - 109, 29/19*e^4 - 108/19*e^3 - 460/19*e^2 + 946/19*e + 95, -9/38*e^4 + 3/19*e^3 + 245/19*e^2 - 173/19*e - 199/2, -55/38*e^4 + 107/19*e^3 + 486/19*e^2 - 1110/19*e - 273/2, 12/19*e^4 - 46/19*e^3 - 324/19*e^2 + 702/19*e + 106, -10/19*e^4 + 70/19*e^3 + 42/19*e^2 - 604/19*e + 16, -e^4 + 4*e^3 + 16*e^2 - 42*e - 73, 23/38*e^4 - 14/19*e^3 - 339/19*e^2 + 98/19*e + 193/2, 55/38*e^4 - 145/19*e^3 - 372/19*e^2 + 1376/19*e + 201/2, 34/19*e^4 - 124/19*e^3 - 671/19*e^2 + 1248/19*e + 186, -53/38*e^4 + 100/19*e^3 + 497/19*e^2 - 1061/19*e - 283/2, 49/38*e^4 - 86/19*e^3 - 519/19*e^2 + 963/19*e + 275/2, 65/38*e^4 - 123/19*e^3 - 621/19*e^2 + 1488/19*e + 315/2, 25/38*e^4 - 59/19*e^3 - 233/19*e^2 + 546/19*e + 147/2, -63/38*e^4 + 97/19*e^3 + 727/19*e^2 - 1078/19*e - 453/2, 21/38*e^4 - 64/19*e^3 - 103/19*e^2 + 562/19*e + 27/2, -54/19*e^4 + 226/19*e^3 + 926/19*e^2 - 2190/19*e - 250, 13/38*e^4 - 36/19*e^3 - 33/19*e^2 + 328/19*e - 29/2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([79,79,-w^3 + w^2 + 4*w - 1])] = 1

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