/*
  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([-28, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([7, 7, 6*w - 35])

primes_array = [
[2, 2, -w + 6],\
[2, 2, w + 5],\
[7, 7, 6*w - 35],\
[7, 7, -6*w - 29],\
[9, 3, 3],\
[11, 11, 4*w + 19],\
[11, 11, 4*w - 23],\
[13, 13, -2*w + 11],\
[13, 13, 2*w + 9],\
[25, 5, -5],\
[31, 31, 2*w - 13],\
[31, 31, -2*w - 11],\
[41, 41, -8*w - 39],\
[41, 41, 8*w - 47],\
[53, 53, -26*w - 125],\
[53, 53, 26*w - 151],\
[61, 61, -14*w + 81],\
[61, 61, -14*w - 67],\
[83, 83, 2*w - 15],\
[83, 83, -2*w - 13],\
[97, 97, 2*w - 5],\
[97, 97, -2*w - 3],\
[109, 109, 2*w - 3],\
[109, 109, -2*w - 1],\
[113, 113, 2*w - 1],\
[127, 127, 8*w - 45],\
[127, 127, 8*w + 37],\
[131, 131, -50*w + 291],\
[131, 131, 50*w + 241],\
[139, 139, 6*w - 37],\
[139, 139, -6*w - 31],\
[149, 149, 20*w + 97],\
[149, 149, 20*w - 117],\
[157, 157, -12*w - 59],\
[157, 157, 12*w - 71],\
[163, 163, 4*w - 19],\
[163, 163, 4*w + 15],\
[173, 173, 4*w + 23],\
[173, 173, 4*w - 27],\
[211, 211, 2*w - 19],\
[211, 211, -2*w - 17],\
[227, 227, -4*w - 13],\
[227, 227, 4*w - 17],\
[233, 233, 6*w + 25],\
[233, 233, -6*w + 31],\
[239, 239, -14*w - 69],\
[239, 239, 14*w - 83],\
[241, 241, 46*w + 221],\
[241, 241, -46*w + 267],\
[251, 251, 22*w - 129],\
[251, 251, 22*w + 107],\
[257, 257, -34*w + 197],\
[257, 257, -34*w - 163],\
[277, 277, 4*w - 29],\
[277, 277, -4*w - 25],\
[283, 283, 4*w - 15],\
[283, 283, -4*w - 11],\
[289, 17, -17],\
[307, 307, 68*w - 395],\
[307, 307, 68*w + 327],\
[311, 311, 10*w - 61],\
[311, 311, -10*w - 51],\
[313, 313, -32*w - 155],\
[313, 313, 32*w - 187],\
[317, 317, -18*w - 85],\
[317, 317, 18*w - 103],\
[331, 331, -4*w - 9],\
[331, 331, 4*w - 13],\
[337, 337, -16*w - 79],\
[337, 337, 16*w - 95],\
[347, 347, -12*w + 67],\
[347, 347, 12*w + 55],\
[353, 353, 14*w - 79],\
[353, 353, 14*w + 65],\
[361, 19, -19],\
[367, 367, -32*w - 153],\
[367, 367, -32*w + 185],\
[383, 383, 56*w + 269],\
[383, 383, 56*w - 325],\
[389, 389, -4*w - 27],\
[389, 389, 4*w - 31],\
[401, 401, 8*w - 51],\
[401, 401, -8*w - 43],\
[421, 421, 12*w - 73],\
[421, 421, -12*w - 61],\
[439, 439, -8*w - 33],\
[439, 439, 8*w - 41],\
[443, 443, -4*w - 1],\
[443, 443, 4*w - 5],\
[461, 461, -30*w + 173],\
[461, 461, 30*w + 143],\
[463, 463, 2*w - 25],\
[463, 463, -2*w - 23],\
[467, 467, 34*w + 165],\
[467, 467, 34*w - 199],\
[503, 503, -26*w - 127],\
[503, 503, 26*w - 153],\
[509, 509, 4*w - 33],\
[509, 509, -4*w - 29],\
[521, 521, -10*w + 53],\
[521, 521, 10*w + 43],\
[529, 23, -23],\
[547, 547, 14*w - 85],\
[547, 547, -14*w - 71],\
[557, 557, 66*w + 317],\
[557, 557, 66*w - 383],\
[563, 563, 2*w - 27],\
[563, 563, -2*w - 25],\
[569, 569, -64*w + 373],\
[569, 569, 64*w + 309],\
[587, 587, 12*w + 53],\
[587, 587, -12*w + 65],\
[593, 593, 8*w + 45],\
[593, 593, 8*w - 53],\
[601, 601, -26*w - 123],\
[601, 601, 26*w - 149],\
[617, 617, 6*w - 23],\
[617, 617, -6*w - 17],\
[647, 647, 24*w - 137],\
[647, 647, -24*w - 113],\
[653, 653, 28*w - 165],\
[653, 653, -28*w - 137],\
[677, 677, -22*w - 103],\
[677, 677, 22*w - 125],\
[691, 691, 20*w - 113],\
[691, 691, 20*w + 93],\
[709, 709, -10*w - 41],\
[709, 709, 10*w - 51],\
[719, 719, -8*w + 37],\
[719, 719, -8*w - 29],\
[727, 727, -22*w - 109],\
[727, 727, 22*w - 131],\
[739, 739, 46*w - 269],\
[739, 739, -46*w - 223],\
[761, 761, -6*w - 13],\
[761, 761, 6*w - 19],\
[769, 769, 110*w - 639],\
[769, 769, 110*w + 529],\
[773, 773, 4*w - 37],\
[773, 773, -4*w - 33],\
[787, 787, 2*w - 31],\
[787, 787, -2*w - 29],\
[809, 809, 56*w + 271],\
[809, 809, -56*w + 327],\
[821, 821, 6*w - 17],\
[821, 821, -6*w - 11],\
[823, 823, 38*w - 223],\
[823, 823, -38*w - 185],\
[827, 827, 132*w - 767],\
[827, 827, 132*w + 635],\
[841, 29, -29],\
[853, 853, -76*w + 443],\
[853, 853, 76*w + 367],\
[863, 863, 14*w - 87],\
[863, 863, -14*w - 73],\
[911, 911, 2*w - 33],\
[911, 911, -2*w - 31],\
[919, 919, -6*w - 41],\
[919, 919, 6*w - 47],\
[929, 929, 50*w + 239],\
[929, 929, 50*w - 289],\
[953, 953, 6*w - 11],\
[953, 953, -6*w - 5],\
[967, 967, -8*w - 25],\
[967, 967, 8*w - 33],\
[991, 991, 16*w + 71],\
[991, 991, -16*w + 87]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - x^5 - 9*x^4 + 9*x^3 + 14*x^2 - 9*x - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/7*e^5 + 2/7*e^4 - 10/7*e^3 - 2*e^2 + 3*e + 12/7, 1, -2/7*e^5 + 3/7*e^4 + 20/7*e^3 - 3*e^2 - 6*e - 3/7, -3/7*e^5 + 1/7*e^4 + 23/7*e^3 - 2*e^2 - 4*e + 13/7, -2/7*e^5 - 4/7*e^4 + 20/7*e^3 + 4*e^2 - 7*e - 24/7, -4/7*e^5 - 1/7*e^4 + 33/7*e^3 - 5*e - 6/7, -2/7*e^5 + 3/7*e^4 + 20/7*e^3 - 4*e^2 - 6*e + 18/7, 4/7*e^5 - 6/7*e^4 - 33/7*e^3 + 7*e^2 + 4*e - 36/7, 8/7*e^5 - 5/7*e^4 - 73/7*e^3 + 6*e^2 + 17*e - 51/7, -4/7*e^5 + 6/7*e^4 + 40/7*e^3 - 8*e^2 - 11*e + 43/7, -e^2 + e + 1, 12/7*e^5 + 3/7*e^4 - 106/7*e^3 + 25*e - 31/7, 5/7*e^5 - 4/7*e^4 - 57/7*e^3 + 7*e^2 + 21*e - 66/7, 1/7*e^5 + 2/7*e^4 - 10/7*e^3 - e^2 + 4*e - 37/7, -3/7*e^5 + 1/7*e^4 + 37/7*e^3 - 14*e - 43/7, e^5 - 10*e^3 + e^2 + 21*e - 4, e^4 - 7*e^2 + 6*e + 4, -19/7*e^5 + 11/7*e^4 + 162/7*e^3 - 15*e^2 - 30*e + 52/7, -5/7*e^5 + 4/7*e^4 + 57/7*e^3 - 3*e^2 - 23*e - 4/7, -e^5 + 2*e^4 + 11*e^3 - 15*e^2 - 23*e + 12, -2*e^5 + 2*e^4 + 17*e^3 - 17*e^2 - 22*e + 7, 1/7*e^5 - 12/7*e^4 - 10/7*e^3 + 14*e^2 - 3*e - 114/7, 20/7*e^5 - 9/7*e^4 - 172/7*e^3 + 11*e^2 + 37*e - 33/7, 11/7*e^5 - 13/7*e^4 - 110/7*e^3 + 14*e^2 + 29*e - 92/7, -10/7*e^5 - 6/7*e^4 + 79/7*e^3 + 4*e^2 - 14*e - 57/7, e^5 + 2*e^4 - 7*e^3 - 13*e^2 + 7*e + 10, 5/7*e^5 + 3/7*e^4 - 36/7*e^3 - e^2 + 2*e - 24/7, -8/7*e^5 + 5/7*e^4 + 59/7*e^3 - 7*e^2 - 5*e + 30/7, -5/7*e^5 - 3/7*e^4 + 29/7*e^3 + e^2 + 5*e - 39/7, 22/7*e^5 - 12/7*e^4 - 192/7*e^3 + 19*e^2 + 40*e - 79/7, -13/7*e^5 + 2/7*e^4 + 116/7*e^3 - 4*e^2 - 29*e - 30/7, 18/7*e^5 - 13/7*e^4 - 138/7*e^3 + 19*e^2 + 17*e - 127/7, -3*e^5 + 2*e^4 + 28*e^3 - 17*e^2 - 50*e + 16, 13/7*e^5 - 2/7*e^4 - 102/7*e^3 + 4*e^2 + 18*e + 2/7, -6/7*e^5 + 9/7*e^4 + 53/7*e^3 - 7*e^2 - 8*e + 5/7, -16/7*e^5 + 17/7*e^4 + 125/7*e^3 - 22*e^2 - 15*e + 137/7, 6/7*e^5 + 5/7*e^4 - 53/7*e^3 - 5*e^2 + 12*e - 26/7, 18/7*e^5 - 20/7*e^4 - 166/7*e^3 + 23*e^2 + 33*e - 8/7, -16/7*e^5 + 3/7*e^4 + 132/7*e^3 - 12*e^2 - 24*e + 151/7, 5/7*e^5 - 25/7*e^4 - 64/7*e^3 + 26*e^2 + 20*e - 136/7, -3/7*e^5 + 1/7*e^4 - 5/7*e^3 - 4*e^2 + 16*e + 62/7, -18/7*e^5 - 1/7*e^4 + 166/7*e^3 - 3*e^2 - 42*e + 22/7, -24/7*e^5 + 29/7*e^4 + 212/7*e^3 - 32*e^2 - 44*e + 153/7, 5*e^5 - 3*e^4 - 43*e^3 + 31*e^2 + 53*e - 25, -9/7*e^5 + 3/7*e^4 + 76/7*e^3 - 4*e^2 - 11*e - 87/7, -5/7*e^5 - 3/7*e^4 + 64/7*e^3 + e^2 - 24*e + 87/7, 9/7*e^5 - 3/7*e^4 - 83/7*e^3 + 2*e^2 + 17*e + 66/7, 9/7*e^5 - 10/7*e^4 - 83/7*e^3 + 12*e^2 + 25*e - 74/7, -40/7*e^5 + 25/7*e^4 + 337/7*e^3 - 31*e^2 - 65*e + 122/7, 6/7*e^5 + 5/7*e^4 - 53/7*e^3 - 7*e^2 + 9*e + 156/7, 4/7*e^5 - 6/7*e^4 - 47/7*e^3 + 4*e^2 + 10*e + 41/7, -29/7*e^5 + 26/7*e^4 + 248/7*e^3 - 35*e^2 - 47*e + 149/7, 18/7*e^5 - 13/7*e^4 - 152/7*e^3 + 17*e^2 + 29*e - 120/7, 9/7*e^5 - 17/7*e^4 - 55/7*e^3 + 23*e^2 - 8*e - 123/7, 8/7*e^5 - 5/7*e^4 - 52/7*e^3 + 9*e^2 - 4*e - 86/7, 9/7*e^5 - 17/7*e^4 - 76/7*e^3 + 14*e^2 + 9*e + 45/7, -20/7*e^5 + 2/7*e^4 + 158/7*e^3 - 5*e^2 - 22*e - 65/7, -32/7*e^5 + 20/7*e^4 + 271/7*e^3 - 23*e^2 - 49*e + 57/7, 26/7*e^5 - 18/7*e^4 - 225/7*e^3 + 23*e^2 + 40*e - 108/7, -2/7*e^5 + 10/7*e^4 + 27/7*e^3 - 11*e^2 - 9*e + 53/7, -16/7*e^5 + 31/7*e^4 + 125/7*e^3 - 38*e^2 - 16*e + 221/7, 23/7*e^5 - 3/7*e^4 - 160/7*e^3 + 9*e^2 + 10*e - 39/7, -11/7*e^5 - 8/7*e^4 + 103/7*e^3 + 10*e^2 - 29*e - 139/7, 24/7*e^5 + 6/7*e^4 - 191/7*e^3 - 2*e^2 + 31*e + 78/7, -2*e^5 - 3*e^4 + 15*e^3 + 16*e^2 - 17*e - 11, 8/7*e^5 - 12/7*e^4 - 66/7*e^3 + 13*e^2 + 13*e - 100/7, -12/7*e^5 + 4/7*e^4 + 106/7*e^3 - 7*e^2 - 32*e + 17/7, -1/7*e^5 + 19/7*e^4 - 18/7*e^3 - 21*e^2 + 23*e + 156/7, 9/7*e^5 - 10/7*e^4 - 76/7*e^3 + 13*e^2 + 12*e - 88/7, 15/7*e^5 + 2/7*e^4 - 115/7*e^3 - 4*e^2 + 20*e + 159/7, 5*e^5 - 2*e^4 - 42*e^3 + 16*e^2 + 55*e - 1, -3*e^5 + 2*e^4 + 30*e^3 - 16*e^2 - 60*e + 10, 1/7*e^5 + 2/7*e^4 - 10/7*e^3 - 7*e^2 + 9*e + 173/7, -32/7*e^5 + 27/7*e^4 + 278/7*e^3 - 28*e^2 - 52*e + 43/7, -25/7*e^5 + 13/7*e^4 + 215/7*e^3 - 21*e^2 - 36*e + 211/7, 2*e^5 + 3*e^4 - 17*e^3 - 15*e^2 + 28*e + 5, -10/7*e^5 - 6/7*e^4 + 86/7*e^3 + e^2 - 21*e - 15/7, 11/7*e^5 - 13/7*e^4 - 131/7*e^3 + 17*e^2 + 47*e - 197/7, e^5 + e^4 - 10*e^3 - 10*e^2 + 22*e + 10, 20/7*e^5 - 2/7*e^4 - 179/7*e^3 + 4*e^2 + 53*e + 30/7, -6/7*e^5 + 16/7*e^4 + 46/7*e^3 - 18*e^2 - 5*e + 131/7, -3*e^5 + e^4 + 24*e^3 - 6*e^2 - 23*e - 16, -5*e^5 + 4*e^4 + 41*e^3 - 34*e^2 - 43*e + 21, 22/7*e^5 - 26/7*e^4 - 206/7*e^3 + 33*e^2 + 50*e - 205/7, e^5 + 2*e^4 - 9*e^3 - 9*e^2 + 18*e - 12, -6/7*e^5 - 12/7*e^4 + 60/7*e^3 + 21*e^2 - 19*e - 212/7, 8/7*e^5 - 12/7*e^4 - 38/7*e^3 + 11*e^2 - 10*e + 19/7, 25/7*e^5 - 27/7*e^4 - 236/7*e^3 + 27*e^2 + 56*e - 71/7, -8/7*e^5 + 5/7*e^4 + 73/7*e^3 - 6*e^2 - 17*e - 5/7, 5/7*e^5 + 17/7*e^4 - 36/7*e^3 - 19*e^2 + 5*e + 186/7, -30/7*e^5 + 10/7*e^4 + 272/7*e^3 - 17*e^2 - 60*e + 200/7, -5/7*e^5 - 3/7*e^4 + 50/7*e^3 + e^2 - 17*e - 53/7, -9/7*e^5 - 4/7*e^4 + 48/7*e^3 + 88/7, 2*e^5 - 3*e^4 - 17*e^3 + 23*e^2 + 25*e - 28, 2*e^5 - e^4 - 17*e^3 + 11*e^2 + 16*e, -e^5 + 13*e^3 - 36*e + 2, -20/7*e^5 + 44/7*e^4 + 200/7*e^3 - 46*e^2 - 46*e + 166/7, -12/7*e^5 + 18/7*e^4 + 71/7*e^3 - 26*e^2 + 12*e + 206/7, 6/7*e^5 + 12/7*e^4 - 39/7*e^3 - 17*e^2 - e + 205/7, -23/7*e^5 + 3/7*e^4 + 223/7*e^3 - 6*e^2 - 58*e + 109/7, -1/7*e^5 - 23/7*e^4 + 17/7*e^3 + 22*e^2 - 17*e - 117/7, -2*e^4 + e^3 + 18*e^2 + 5*e - 27, -27/7*e^5 + 30/7*e^4 + 214/7*e^3 - 37*e^2 - 31*e + 236/7, 18/7*e^5 + 15/7*e^4 - 159/7*e^3 - 15*e^2 + 29*e + 118/7, -15/7*e^5 + 19/7*e^4 + 136/7*e^3 - 18*e^2 - 29*e + 37/7, -4/7*e^5 - 8/7*e^4 + 19/7*e^3 + 7*e^2 - 4*e + 78/7, 46/7*e^5 - 48/7*e^4 - 432/7*e^3 + 55*e^2 + 98*e - 232/7, -6/7*e^5 - 26/7*e^4 + 60/7*e^3 + 32*e^2 - 25*e - 219/7, 38/7*e^5 - 29/7*e^4 - 338/7*e^3 + 31*e^2 + 72*e - 83/7, -23/7*e^5 - 4/7*e^4 + 230/7*e^3 + 2*e^2 - 65*e + 32/7, 45/7*e^5 - 36/7*e^4 - 373/7*e^3 + 46*e^2 + 67*e - 258/7, -6/7*e^5 + 9/7*e^4 + 60/7*e^3 - 9*e^2 - 15*e - 93/7, 12/7*e^5 - 4/7*e^4 - 113/7*e^3 + 3*e^2 + 38*e + 88/7, 38/7*e^5 + 6/7*e^4 - 331/7*e^3 + 3*e^2 + 72*e - 132/7, 25/7*e^5 - 20/7*e^4 - 208/7*e^3 + 24*e^2 + 29*e - 50/7, -16/7*e^5 + 10/7*e^4 + 146/7*e^3 - 16*e^2 - 44*e + 221/7, 4/7*e^5 - 27/7*e^4 - 54/7*e^3 + 29*e^2 + 15*e - 85/7, 3*e^5 - 2*e^4 - 25*e^3 + 24*e^2 + 32*e - 17, 19/7*e^5 - 39/7*e^4 - 169/7*e^3 + 45*e^2 + 28*e - 332/7, 9/7*e^5 - 31/7*e^4 - 111/7*e^3 + 26*e^2 + 34*e + 52/7, 2/7*e^5 - 24/7*e^4 - 13/7*e^3 + 28*e^2 - 12*e - 39/7, 10/7*e^5 - 1/7*e^4 - 86/7*e^3 + 7*e^2 + 27*e - 20/7, -3/7*e^5 + 1/7*e^4 + 16/7*e^3 - 9*e^2 + 9*e + 174/7, -6/7*e^5 + 2/7*e^4 + 46/7*e^3 - 3*e^2 - 6*e - 128/7, -16/7*e^5 + 17/7*e^4 + 111/7*e^3 - 18*e^2 - 15*e - 87/7, 18/7*e^5 - 20/7*e^4 - 173/7*e^3 + 26*e^2 + 44*e - 197/7, -44/7*e^5 + 24/7*e^4 + 433/7*e^3 - 33*e^2 - 113*e + 179/7, -15/7*e^5 + 5/7*e^4 + 150/7*e^3 - 5*e^2 - 38*e - 180/7, -9*e^5 + 4*e^4 + 80*e^3 - 41*e^2 - 136*e + 36, 33/7*e^5 + 10/7*e^4 - 246/7*e^3 - 4*e^2 + 40*e - 45/7, -9/7*e^5 - 25/7*e^4 + 69/7*e^3 + 26*e^2 - 6*e - 283/7, -6/7*e^5 - 12/7*e^4 + 67/7*e^3 + 15*e^2 - 16*e - 16/7, -2*e^5 + e^4 + 19*e^3 - 11*e^2 - 38*e + 9, 16/7*e^5 - 24/7*e^4 - 139/7*e^3 + 24*e^2 + 32*e - 39/7, -15/7*e^5 + 26/7*e^4 + 94/7*e^3 - 35*e^2 + 2*e + 198/7, -32/7*e^5 + 20/7*e^4 + 250/7*e^3 - 30*e^2 - 24*e + 134/7, -12/7*e^5 + 11/7*e^4 + 50/7*e^3 - 17*e^2 + 26*e + 108/7, 10/7*e^5 - 1/7*e^4 - 58/7*e^3 - e^2 - 12*e - 27/7, e^5 - e^4 - 5*e^3 + 12*e^2 - 21, 24/7*e^5 - 22/7*e^4 - 191/7*e^3 + 31*e^2 + 33*e - 125/7, -5*e^5 + 2*e^4 + 40*e^3 - 26*e^2 - 39*e + 28, 20/7*e^5 - 37/7*e^4 - 172/7*e^3 + 46*e^2 + 40*e - 173/7, -12/7*e^5 - 3/7*e^4 + 64/7*e^3 - 5*e^2 + 18*e - 4/7, 52/7*e^5 - 15/7*e^4 - 499/7*e^3 + 22*e^2 + 122*e - 146/7, -27/7*e^5 + 16/7*e^4 + 228/7*e^3 - 25*e^2 - 42*e + 362/7, 9/7*e^5 - 3/7*e^4 - 118/7*e^3 - e^2 + 36*e + 199/7, -23/7*e^5 + 3/7*e^4 + 216/7*e^3 - 5*e^2 - 42*e + 67/7, -23/7*e^5 + 24/7*e^4 + 251/7*e^3 - 22*e^2 - 84*e + 81/7, -33/7*e^5 + 53/7*e^4 + 323/7*e^3 - 62*e^2 - 72*e + 290/7, 6/7*e^5 - 37/7*e^4 - 81/7*e^3 + 45*e^2 + 25*e - 348/7, 12/7*e^5 - 4/7*e^4 - 134/7*e^3 + 9*e^2 + 46*e - 220/7, 52/7*e^5 + 6/7*e^4 - 415/7*e^3 + e^2 + 75*e + 127/7, -4/7*e^5 - 8/7*e^4 + 82/7*e^3 + 10*e^2 - 47*e - 195/7, 23/7*e^5 - 24/7*e^4 - 188/7*e^3 + 30*e^2 + 36*e - 151/7, 60/7*e^5 - 48/7*e^4 - 502/7*e^3 + 59*e^2 + 95*e - 148/7, -44/7*e^5 + 24/7*e^4 + 405/7*e^3 - 32*e^2 - 83*e + 214/7, -4*e^5 - 5*e^4 + 39*e^3 + 38*e^2 - 81*e - 33, 31/7*e^5 - 22/7*e^4 - 240/7*e^3 + 28*e^2 + 26*e - 69/7, -34/7*e^5 - 19/7*e^4 + 291/7*e^3 + 13*e^2 - 75*e + 26/7, -8*e^5 + 5*e^4 + 68*e^3 - 39*e^2 - 90*e + 19, 47/7*e^5 - 32/7*e^4 - 386/7*e^3 + 45*e^2 + 52*e - 185/7, -54/7*e^5 + 18/7*e^4 + 449/7*e^3 - 23*e^2 - 72*e - 53/7, 26/7*e^5 - 18/7*e^4 - 232/7*e^3 + 23*e^2 + 34*e - 17/7, -15/7*e^5 + 61/7*e^4 + 150/7*e^3 - 68*e^2 - 21*e + 261/7, 8/7*e^5 + 2/7*e^4 - 87/7*e^3 - 16*e^2 + 33*e + 334/7, -3*e^5 - 3*e^4 + 21*e^3 + 9*e^2 - 19*e + 21]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([7, 7, 6*w - 35])] = -1

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