/*
  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, 2, 8, -4, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([61, 61, -w^5 + w^4 + 5*w^3 - 3*w^2 - 7*w + 1])

primes_array = [
[9, 3, -w^2 + 2],\
[19, 19, -w^3 + 4*w],\
[19, 19, w^3 - 3*w - 1],\
[29, 29, w^5 - w^4 - 6*w^3 + 4*w^2 + 8*w - 3],\
[29, 29, w^4 - w^3 - 4*w^2 + 2*w + 2],\
[31, 31, -w^4 + 4*w^2 + w - 3],\
[41, 41, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 11*w - 4],\
[49, 7, -2*w^5 + 3*w^4 + 10*w^3 - 12*w^2 - 11*w + 6],\
[59, 59, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 7*w - 5],\
[59, 59, w^5 - w^4 - 4*w^3 + 3*w^2 + 3*w - 3],\
[59, 59, 2*w^5 - 3*w^4 - 9*w^3 + 11*w^2 + 9*w - 4],\
[61, 61, -w^5 + w^4 + 5*w^3 - 3*w^2 - 7*w + 1],\
[64, 2, -2],\
[71, 71, -2*w^5 + 2*w^4 + 10*w^3 - 8*w^2 - 11*w + 6],\
[79, 79, -3*w^5 + 4*w^4 + 13*w^3 - 14*w^2 - 9*w + 5],\
[79, 79, -w^4 - w^3 + 5*w^2 + 4*w - 3],\
[79, 79, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 8*w + 4],\
[81, 3, 3*w^5 - 5*w^4 - 14*w^3 + 19*w^2 + 13*w - 8],\
[89, 89, 2*w^5 - 2*w^4 - 9*w^3 + 6*w^2 + 8*w - 1],\
[101, 101, -w^4 - w^3 + 5*w^2 + 3*w - 3],\
[101, 101, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w + 4],\
[109, 109, -2*w^5 + 4*w^4 + 8*w^3 - 14*w^2 - 6*w + 5],\
[109, 109, -3*w^5 + 4*w^4 + 13*w^3 - 14*w^2 - 10*w + 7],\
[125, 5, w^5 - w^4 - 5*w^3 + 4*w^2 + 5*w],\
[131, 131, -w^2 - w + 3],\
[131, 131, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 3*w - 4],\
[131, 131, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 6*w - 5],\
[131, 131, -2*w^5 + 4*w^4 + 8*w^3 - 15*w^2 - 6*w + 7],\
[139, 139, w^4 - 3*w^3 - 3*w^2 + 9*w],\
[149, 149, 2*w^5 - 3*w^4 - 9*w^3 + 12*w^2 + 7*w - 5],\
[149, 149, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 2*w - 2],\
[151, 151, 3*w^5 - 4*w^4 - 13*w^3 + 14*w^2 + 10*w - 5],\
[151, 151, -3*w^5 + 4*w^4 + 14*w^3 - 15*w^2 - 12*w + 6],\
[151, 151, 4*w^5 - 5*w^4 - 18*w^3 + 18*w^2 + 15*w - 9],\
[151, 151, 2*w^5 - 2*w^4 - 9*w^3 + 7*w^2 + 8*w - 5],\
[169, 13, -2*w^5 + w^4 + 11*w^3 - 3*w^2 - 13*w + 1],\
[179, 179, w^3 - w^2 - 2*w + 3],\
[181, 181, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 10*w - 3],\
[181, 181, -2*w^4 + w^3 + 8*w^2 - 3*w - 2],\
[191, 191, w^5 - w^4 - 6*w^3 + 5*w^2 + 9*w - 4],\
[191, 191, -w^3 + 2*w^2 + 3*w - 4],\
[191, 191, -2*w^5 + w^4 + 11*w^3 - 3*w^2 - 12*w],\
[191, 191, w^4 - 2*w^3 - 4*w^2 + 7*w],\
[199, 199, -3*w^5 + 4*w^4 + 15*w^3 - 14*w^2 - 16*w + 6],\
[199, 199, -2*w^5 + 3*w^4 + 10*w^3 - 12*w^2 - 12*w + 7],\
[211, 211, -2*w^5 + 4*w^4 + 9*w^3 - 15*w^2 - 8*w + 5],\
[211, 211, -3*w^5 + 5*w^4 + 13*w^3 - 18*w^2 - 10*w + 8],\
[229, 229, -3*w^5 + 4*w^4 + 13*w^3 - 14*w^2 - 10*w + 6],\
[229, 229, w^4 - 4*w^2 - 1],\
[229, 229, w^5 - w^4 - 3*w^3 + 3*w^2 - 3*w - 2],\
[239, 239, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 8*w + 8],\
[241, 241, w^5 - 3*w^4 - 4*w^3 + 10*w^2 + 3*w - 2],\
[241, 241, w^5 - w^4 - 5*w^3 + 3*w^2 + 4*w + 1],\
[251, 251, -3*w^5 + 3*w^4 + 15*w^3 - 10*w^2 - 17*w + 3],\
[271, 271, -2*w^5 + 4*w^4 + 9*w^3 - 14*w^2 - 8*w + 2],\
[271, 271, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 4*w],\
[271, 271, w^5 - 2*w^4 - 3*w^3 + 7*w^2 - 2*w - 4],\
[289, 17, 4*w^5 - 6*w^4 - 17*w^3 + 22*w^2 + 12*w - 9],\
[311, 311, -2*w^5 + 3*w^4 + 7*w^3 - 9*w^2 - 3*w + 2],\
[331, 331, 3*w^5 - 5*w^4 - 14*w^3 + 19*w^2 + 14*w - 12],\
[349, 349, -4*w^5 + 6*w^4 + 18*w^3 - 21*w^2 - 17*w + 7],\
[349, 349, -w^4 + w^3 + 5*w^2 - 3*w - 3],\
[359, 359, -2*w^5 + 4*w^4 + 9*w^3 - 15*w^2 - 10*w + 9],\
[361, 19, 2*w^5 - 3*w^4 - 9*w^3 + 11*w^2 + 6*w - 4],\
[361, 19, -3*w^5 + 5*w^4 + 13*w^3 - 18*w^2 - 10*w + 9],\
[379, 379, -4*w^5 + 5*w^4 + 18*w^3 - 17*w^2 - 14*w + 7],\
[379, 379, 2*w^5 - 4*w^4 - 10*w^3 + 15*w^2 + 11*w - 5],\
[389, 389, -5*w^5 + 7*w^4 + 22*w^3 - 25*w^2 - 17*w + 11],\
[389, 389, w^5 - 3*w^4 - 3*w^3 + 12*w^2 - 2*w - 5],\
[401, 401, -4*w^5 + 6*w^4 + 18*w^3 - 23*w^2 - 15*w + 10],\
[401, 401, -w^5 + 3*w^4 + 4*w^3 - 12*w^2 - w + 4],\
[401, 401, 4*w^5 - 5*w^4 - 20*w^3 + 19*w^2 + 21*w - 11],\
[401, 401, -3*w^5 + 3*w^4 + 16*w^3 - 12*w^2 - 18*w + 6],\
[409, 409, -2*w^4 + 2*w^3 + 7*w^2 - 6*w - 2],\
[409, 409, -w^5 + 3*w^4 + 5*w^3 - 13*w^2 - 5*w + 9],\
[419, 419, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 10*w - 6],\
[419, 419, -w^5 + 7*w^3 - w^2 - 10*w + 4],\
[419, 419, w^5 - 2*w^4 - 5*w^3 + 10*w^2 + 5*w - 9],\
[421, 421, 3*w^5 - 3*w^4 - 16*w^3 + 12*w^2 + 18*w - 7],\
[431, 431, 4*w^5 - 7*w^4 - 17*w^3 + 25*w^2 + 13*w - 10],\
[431, 431, -2*w^5 + 3*w^4 + 7*w^3 - 10*w^2 - w + 5],\
[431, 431, 4*w^5 - 6*w^4 - 19*w^3 + 23*w^2 + 17*w - 10],\
[439, 439, -2*w^5 + 4*w^4 + 10*w^3 - 15*w^2 - 11*w + 4],\
[461, 461, w^5 - 2*w^4 - 3*w^3 + 6*w^2 + 2],\
[461, 461, w^5 - w^4 - 5*w^3 + 5*w^2 + 6*w - 7],\
[479, 479, -2*w^5 + w^4 + 9*w^3 - 2*w^2 - 8*w],\
[479, 479, 2*w^5 - 2*w^4 - 10*w^3 + 8*w^2 + 12*w - 7],\
[491, 491, -3*w^5 + 3*w^4 + 14*w^3 - 12*w^2 - 12*w + 7],\
[491, 491, -3*w^5 + 3*w^4 + 15*w^3 - 12*w^2 - 14*w + 8],\
[491, 491, -2*w^2 + w + 6],\
[499, 499, -3*w^5 + 3*w^4 + 14*w^3 - 10*w^2 - 13*w + 6],\
[509, 509, -2*w^5 + 2*w^4 + 8*w^3 - 6*w^2 - 5*w],\
[521, 521, 3*w^5 - 4*w^4 - 14*w^3 + 15*w^2 + 15*w - 9],\
[521, 521, -3*w^5 + 5*w^4 + 14*w^3 - 19*w^2 - 15*w + 9],\
[521, 521, -4*w^5 + 5*w^4 + 18*w^3 - 17*w^2 - 16*w + 6],\
[529, 23, w^5 - 3*w^4 - 5*w^3 + 11*w^2 + 7*w - 5],\
[541, 541, -3*w^5 + 4*w^4 + 14*w^3 - 15*w^2 - 14*w + 10],\
[569, 569, -w^5 - w^4 + 6*w^3 + 4*w^2 - 6*w - 1],\
[571, 571, -2*w^4 + w^3 + 9*w^2 - 3*w - 4],\
[599, 599, -3*w^5 + 3*w^4 + 14*w^3 - 11*w^2 - 11*w + 4],\
[601, 601, w^4 - 2*w^2 - w - 2],\
[619, 619, 2*w^5 - 3*w^4 - 9*w^3 + 11*w^2 + 10*w - 5],\
[619, 619, w^5 - 3*w^4 - 4*w^3 + 12*w^2 + 3*w - 3],\
[619, 619, -3*w^5 + 5*w^4 + 13*w^3 - 20*w^2 - 10*w + 10],\
[619, 619, w^5 - 2*w^4 - 5*w^3 + 10*w^2 + 5*w - 8],\
[619, 619, -4*w^5 + 6*w^4 + 19*w^3 - 23*w^2 - 17*w + 11],\
[619, 619, -4*w^5 + 6*w^4 + 17*w^3 - 22*w^2 - 13*w + 10],\
[631, 631, w^5 - 3*w^4 - 5*w^3 + 13*w^2 + 5*w - 6],\
[641, 641, -w^3 + w^2 + 3*w - 5],\
[641, 641, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + 3*w + 4],\
[659, 659, -w^5 + 3*w^4 + 5*w^3 - 12*w^2 - 5*w + 5],\
[661, 661, -2*w^5 + 3*w^4 + 8*w^3 - 12*w^2 - 3*w + 8],\
[661, 661, 2*w^5 - 3*w^4 - 8*w^3 + 10*w^2 + 6*w - 1],\
[691, 691, -w^3 - w^2 + 5*w + 1],\
[691, 691, -3*w^5 + 4*w^4 + 13*w^3 - 13*w^2 - 10*w + 6],\
[691, 691, 3*w^5 - 4*w^4 - 15*w^3 + 15*w^2 + 14*w - 6],\
[701, 701, 3*w^5 - 6*w^4 - 13*w^3 + 23*w^2 + 10*w - 10],\
[701, 701, -3*w^5 + 6*w^4 + 13*w^3 - 23*w^2 - 11*w + 9],\
[709, 709, 3*w^5 - 6*w^4 - 13*w^3 + 22*w^2 + 11*w - 10],\
[709, 709, -w^5 + 5*w^3 - 4*w - 2],\
[709, 709, -w^5 + w^4 + 7*w^3 - 6*w^2 - 11*w + 5],\
[719, 719, -2*w^5 + 3*w^4 + 9*w^3 - 12*w^2 - 7*w + 4],\
[751, 751, w^4 + w^3 - 5*w^2 - 6*w + 4],\
[769, 769, 4*w^5 - 5*w^4 - 19*w^3 + 18*w^2 + 18*w - 10],\
[769, 769, 4*w^5 - 6*w^4 - 17*w^3 + 22*w^2 + 13*w - 11],\
[809, 809, w^5 - w^4 - 4*w^3 + 5*w^2 + w - 7],\
[809, 809, 2*w^5 - 5*w^4 - 9*w^3 + 19*w^2 + 10*w - 7],\
[809, 809, -w^5 + 5*w^3 + w^2 - 7*w],\
[809, 809, -3*w^5 + 4*w^4 + 15*w^3 - 16*w^2 - 15*w + 11],\
[811, 811, -2*w^5 + 4*w^4 + 8*w^3 - 13*w^2 - 6*w + 5],\
[811, 811, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - w],\
[811, 811, 2*w^5 - 4*w^4 - 9*w^3 + 16*w^2 + 10*w - 9],\
[811, 811, 2*w^5 - 4*w^4 - 10*w^3 + 16*w^2 + 10*w - 7],\
[821, 821, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 5*w - 2],\
[829, 829, 3*w^5 - 5*w^4 - 13*w^3 + 19*w^2 + 12*w - 9],\
[839, 839, 2*w^5 - 4*w^4 - 7*w^3 + 14*w^2 + w - 6],\
[839, 839, 4*w^5 - 5*w^4 - 18*w^3 + 19*w^2 + 14*w - 10],\
[841, 29, -2*w^5 + 4*w^4 + 10*w^3 - 15*w^2 - 10*w + 5],\
[841, 29, -w^5 + 3*w^4 + 6*w^3 - 12*w^2 - 10*w + 6],\
[859, 859, 3*w^5 - 3*w^4 - 15*w^3 + 10*w^2 + 14*w - 2],\
[881, 881, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 10*w - 4],\
[911, 911, -4*w^5 + 5*w^4 + 19*w^3 - 20*w^2 - 17*w + 11],\
[919, 919, 2*w^5 - 3*w^4 - 10*w^3 + 13*w^2 + 9*w - 10],\
[929, 929, -w^5 + w^4 + 5*w^3 - 2*w^2 - 8*w - 1],\
[941, 941, -5*w^5 + 7*w^4 + 23*w^3 - 26*w^2 - 20*w + 11],\
[961, 31, -3*w^5 + 4*w^4 + 16*w^3 - 16*w^2 - 20*w + 8],\
[971, 971, w^5 - 5*w^3 + 5*w - 4],\
[991, 991, 3*w^5 - 5*w^4 - 12*w^3 + 18*w^2 + 8*w - 6],\
[991, 991, 3*w^5 - 5*w^4 - 14*w^3 + 18*w^2 + 12*w - 7]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - 6*x^7 - 32*x^6 + 246*x^5 - 117*x^4 - 1204*x^3 + 1284*x^2 - 368*x + 16
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -5/15438*e^7 - 793/30876*e^6 + 730/7719*e^5 + 7621/7719*e^4 - 53185/15438*e^3 - 122719/30876*e^2 + 99404/7719*e - 40151/7719, -2093/30876*e^7 + 6167/15438*e^6 + 35413/15438*e^5 - 255611/15438*e^4 + 90983/30876*e^3 + 674998/7719*e^2 - 459044/7719*e + 54104/7719, -33/20584*e^7 + 91/2573*e^6 - 82/2573*e^5 - 14541/10292*e^4 + 76097/20584*e^3 + 70123/10292*e^2 - 47484/2573*e + 14929/2573, 1823/15438*e^7 - 5294/7719*e^6 - 61457/15438*e^5 + 219443/7719*e^4 - 41893/7719*e^3 - 1150283/7719*e^2 + 805414/7719*e - 68728/7719, 4/93*e^7 - 89/372*e^6 - 145/93*e^5 + 938/93*e^4 + 233/93*e^3 - 21623/372*e^2 + 1174/93*e + 890/93, -1685/15438*e^7 + 9181/15438*e^6 + 29878/7719*e^5 - 382531/15438*e^4 - 46141/15438*e^3 + 1025222/7719*e^2 - 394981/7719*e - 30356/7719, 470/2573*e^7 - 5221/5146*e^6 - 16309/2573*e^5 + 108479/2573*e^4 - 2522/2573*e^3 - 1146731/5146*e^2 + 321372/2573*e - 11086/2573, -19927/61752*e^7 + 54739/30876*e^6 + 173317/15438*e^5 - 2275549/30876*e^4 + 15679/61752*e^3 + 2998978/7719*e^2 - 3338779/15438*e + 104633/7719, 97/1992*e^7 - 125/498*e^6 - 428/249*e^5 + 10417/996*e^4 + 2423/1992*e^3 - 54541/996*e^2 + 6080/249*e + 973/249, 16/249*e^7 - 353/996*e^6 - 1127/498*e^5 + 3665/249*e^4 + 499/498*e^3 - 77483/996*e^2 + 8824/249*e - 151/249, -1, -2567/7719*e^7 + 54907/30876*e^6 + 179179/15438*e^5 - 1141427/15438*e^4 - 10795/7719*e^3 + 11913679/30876*e^2 - 3478801/15438*e + 140618/7719, -3043/10292*e^7 + 8381/5146*e^6 + 26591/2573*e^5 - 174424/2573*e^4 - 15489/10292*e^3 + 1859429/5146*e^2 - 486877/2573*e + 4058/2573, 3547/30876*e^7 - 4748/7719*e^6 - 62441/15438*e^5 + 395263/15438*e^4 + 60719/30876*e^3 - 2090197/15438*e^2 + 512791/7719*e + 20846/7719, 20321/61752*e^7 - 53783/30876*e^6 - 89461/7719*e^5 + 2240045/30876*e^4 + 346675/61752*e^3 - 2949776/7719*e^2 + 3115031/15438*e - 49279/7719, 3547/30876*e^7 - 4748/7719*e^6 - 62441/15438*e^5 + 395263/15438*e^4 + 60719/30876*e^3 - 2090197/15438*e^2 + 512791/7719*e + 20846/7719, -344/7719*e^7 + 2053/7719*e^6 + 23359/15438*e^5 - 170543/15438*e^4 + 22513/15438*e^3 + 910817/15438*e^2 - 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17303/5146*e^6 - 55794/2573*e^5 + 718509/5146*e^4 - 37639/10292*e^3 - 1863462/2573*e^2 + 1204391/2573*e - 106540/2573, -12429/20584*e^7 + 8310/2573*e^6 + 109687/5146*e^5 - 1386535/10292*e^4 - 258687/20584*e^3 + 7408565/10292*e^2 - 889770/2573*e - 49959/2573, -15045/20584*e^7 + 42213/10292*e^6 + 130837/5146*e^5 - 1758919/10292*e^4 + 22373/20584*e^3 + 2367324/2573*e^2 - 2446657/5146*e - 38381/2573, 8183/30876*e^7 - 23285/15438*e^6 - 137215/15438*e^5 + 961619/15438*e^4 - 429137/30876*e^3 - 2448310/7719*e^2 + 1890140/7719*e - 434168/7719, -12893/30876*e^7 + 16684/7719*e^6 + 115256/7719*e^5 - 1393571/15438*e^4 - 501103/30876*e^3 + 7462799/15438*e^2 - 1639583/7719*e - 283270/7719, 241/996*e^7 - 308/249*e^6 - 2155/249*e^5 + 25789/498*e^4 + 9275/996*e^3 - 137881/498*e^2 + 35251/249*e + 2540/249, -2489/7719*e^7 + 13351/7719*e^6 + 179941/15438*e^5 - 559165/7719*e^4 - 268811/15438*e^3 + 3086152/7719*e^2 - 898712/7719*e - 264712/7719, 6212/7719*e^7 - 35368/7719*e^6 - 424423/15438*e^5 + 1466200/7719*e^4 - 342547/15438*e^3 - 7674031/7719*e^2 + 4947557/7719*e - 558182/7719, 3145/7719*e^7 - 16907/7719*e^6 - 223409/15438*e^5 + 1412137/15438*e^4 + 175975/15438*e^3 - 7641559/15438*e^2 + 1734343/7719*e + 228392/7719, -4357/15438*e^7 + 12115/7719*e^6 + 72635/7719*e^5 - 999815/15438*e^4 + 261913/15438*e^3 + 5000441/15438*e^2 - 2282165/7719*e + 215690/7719, 12131/10292*e^7 - 16224/2573*e^6 - 214461/5146*e^5 + 675681/2573*e^4 + 274235/10292*e^3 - 3584579/2573*e^2 + 1678880/2573*e + 47374/2573, 93203/61752*e^7 - 257015/30876*e^6 - 403078/7719*e^5 + 10671209/30876*e^4 - 846263/61752*e^3 - 13966901/7719*e^2 + 16661651/15438*e - 634537/7719, 3549/20584*e^7 - 4837/5146*e^6 - 15040/2573*e^5 + 399419/10292*e^4 - 139285/20584*e^3 - 2001507/10292*e^2 + 437629/2573*e - 69699/2573, 3557/5146*e^7 - 10386/2573*e^6 - 120083/5146*e^5 + 860389/5146*e^4 - 79841/2573*e^3 - 4510523/5146*e^2 + 1539495/2573*e - 166182/2573, 9449/10292*e^7 - 12660/2573*e^6 - 82549/2573*e^5 + 526408/2573*e^4 + 53947/10292*e^3 - 2752969/2573*e^2 + 1575716/2573*e - 132200/2573, 8795/20584*e^7 - 26293/10292*e^6 - 36701/2573*e^5 + 1085797/10292*e^4 - 531903/20584*e^3 - 2816681/5146*e^2 + 2014235/5146*e - 144255/2573, 767/2573*e^7 - 8033/5146*e^6 - 54259/5146*e^5 + 166950/2573*e^4 + 37787/5146*e^3 - 1736263/5146*e^2 + 423623/2573*e - 67066/2573, -14827/30876*e^7 + 20411/7719*e^6 + 258149/15438*e^5 - 1697011/15438*e^4 - 191/30876*e^3 + 8939707/15438*e^2 - 2464180/7719*e + 277240/7719, 15649/15438*e^7 - 170317/30876*e^6 - 547909/15438*e^5 + 3545117/15438*e^4 + 60841/7719*e^3 - 37624657/30876*e^2 + 4984586/7719*e - 210677/7719, 3509/15438*e^7 - 42467/30876*e^6 - 56893/7719*e^5 + 877033/15438*e^4 - 343487/15438*e^3 - 8995499/30876*e^2 + 1946239/7719*e - 329839/7719, 6511/10292*e^7 - 18565/5146*e^6 - 55904/2573*e^5 + 770351/5146*e^4 - 136303/10292*e^3 - 2029547/2573*e^2 + 1233823/2573*e - 122096/2573, 20179/30876*e^7 - 27005/7719*e^6 - 176275/7719*e^5 + 2243437/15438*e^4 + 133013/30876*e^3 - 11666167/15438*e^2 + 3259108/7719*e - 222544/7719, 275/498*e^7 - 737/249*e^6 - 9833/498*e^5 + 30788/249*e^4 + 5564/249*e^3 - 166481/249*e^2 + 55102/249*e + 7394/249, 4777/15438*e^7 - 29519/15438*e^6 - 79922/7719*e^5 + 612346/7719*e^4 - 286831/15438*e^3 - 6608087/15438*e^2 + 2160683/7719*e - 84986/7719, 9113/15438*e^7 - 50011/15438*e^6 - 157210/7719*e^5 + 2075479/15438*e^4 - 123725/15438*e^3 - 5415560/7719*e^2 + 3554290/7719*e - 192970/7719, 4531/30876*e^7 - 12163/15438*e^6 - 82601/15438*e^5 + 510265/15438*e^4 + 307571/30876*e^3 - 1415624/7719*e^2 + 290647/7719*e + 161606/7719, 3547/10292*e^7 - 4748/2573*e^6 - 32507/2573*e^5 + 198918/2573*e^4 + 271705/10292*e^3 - 1108137/2573*e^2 + 147425/2573*e + 134058/2573]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([61, 61, -w^5 + w^4 + 5*w^3 - 3*w^2 - 7*w + 1])] = 1

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