/*
  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, -9, 2, 11, -5, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([43,43,w^5 - 7*w^3 - w^2 + 10*w + 3])

primes_array = [
[13, 13, 3*w^5 - 2*w^4 - 17*w^3 + 10*w^2 + 16*w - 3],\
[13, 13, w^5 - w^4 - 5*w^3 + 5*w^2 + 3*w - 3],\
[13, 13, 2*w^5 - w^4 - 12*w^3 + 4*w^2 + 13*w],\
[13, 13, -w^2 + 3],\
[41, 41, -2*w^5 + w^4 + 11*w^3 - 4*w^2 - 10*w - 1],\
[41, 41, -4*w^5 + 3*w^4 + 23*w^3 - 14*w^2 - 22*w + 4],\
[41, 41, w^5 - 6*w^3 + w^2 + 7*w - 2],\
[41, 41, -3*w^5 + w^4 + 18*w^3 - 4*w^2 - 20*w - 1],\
[43, 43, 3*w^5 - 2*w^4 - 17*w^3 + 11*w^2 + 16*w - 6],\
[43, 43, -2*w^5 + w^4 + 12*w^3 - 6*w^2 - 14*w + 5],\
[49, 7, 2*w^5 - w^4 - 12*w^3 + 5*w^2 + 13*w - 4],\
[64, 2, -2],\
[71, 71, -2*w^5 + w^4 + 12*w^3 - 4*w^2 - 12*w - 1],\
[71, 71, -3*w^5 + 2*w^4 + 17*w^3 - 9*w^2 - 15*w],\
[83, 83, 4*w^5 - 2*w^4 - 24*w^3 + 9*w^2 + 26*w - 1],\
[83, 83, -4*w^5 + 2*w^4 + 23*w^3 - 9*w^2 - 23*w],\
[97, 97, -w^5 + 7*w^3 + w^2 - 11*w - 3],\
[97, 97, -2*w^5 + w^4 + 11*w^3 - 6*w^2 - 9*w + 3],\
[113, 113, -4*w^5 + 2*w^4 + 24*w^3 - 9*w^2 - 27*w + 2],\
[113, 113, 3*w^5 - 2*w^4 - 18*w^3 + 10*w^2 + 20*w - 6],\
[113, 113, -2*w^5 + w^4 + 12*w^3 - 5*w^2 - 12*w + 3],\
[113, 113, 3*w^5 - w^4 - 18*w^3 + 4*w^2 + 20*w],\
[127, 127, -w^5 + w^4 + 6*w^3 - 5*w^2 - 7*w],\
[127, 127, -2*w^5 + w^4 + 11*w^3 - 4*w^2 - 10*w - 2],\
[127, 127, -4*w^5 + 3*w^4 + 23*w^3 - 14*w^2 - 22*w + 5],\
[127, 127, -8*w^5 + 5*w^4 + 46*w^3 - 23*w^2 - 45*w + 4],\
[139, 139, w^3 + w^2 - 4*w - 1],\
[139, 139, 5*w^5 - 2*w^4 - 29*w^3 + 9*w^2 + 29*w + 1],\
[139, 139, -w^5 + w^4 + 5*w^3 - 6*w^2 - 2*w + 5],\
[139, 139, w^5 - 6*w^3 + 5*w + 2],\
[167, 167, w^4 - 4*w^2 + 1],\
[167, 167, -3*w^5 + w^4 + 18*w^3 - 4*w^2 - 21*w - 1],\
[169, 13, -3*w^5 + w^4 + 18*w^3 - 5*w^2 - 20*w],\
[181, 181, -w^4 + w^3 + 5*w^2 - 3*w - 3],\
[181, 181, -5*w^5 + 3*w^4 + 29*w^3 - 15*w^2 - 30*w + 6],\
[181, 181, -w^5 + w^4 + 5*w^3 - 6*w^2 - 2*w + 4],\
[181, 181, w^3 + w^2 - 4*w - 2],\
[197, 197, w^5 - w^4 - 6*w^3 + 4*w^2 + 6*w + 2],\
[197, 197, -4*w^5 + 2*w^4 + 24*w^3 - 9*w^2 - 26*w + 4],\
[197, 197, -2*w^5 + 2*w^4 + 12*w^3 - 11*w^2 - 12*w + 5],\
[197, 197, 2*w^5 - w^4 - 12*w^3 + 6*w^2 + 13*w - 7],\
[197, 197, w^5 - 6*w^3 - w^2 + 7*w + 1],\
[197, 197, -4*w^5 + 3*w^4 + 24*w^3 - 14*w^2 - 25*w + 2],\
[211, 211, 2*w^5 - w^4 - 13*w^3 + 5*w^2 + 18*w - 1],\
[211, 211, -2*w^5 + w^4 + 12*w^3 - 4*w^2 - 12*w - 4],\
[223, 223, 4*w^5 - w^4 - 23*w^3 + 5*w^2 + 24*w - 1],\
[223, 223, -3*w^5 + w^4 + 17*w^3 - 4*w^2 - 15*w - 4],\
[223, 223, 3*w^5 - 3*w^4 - 16*w^3 + 15*w^2 + 11*w - 5],\
[223, 223, 3*w^5 - 3*w^4 - 16*w^3 + 14*w^2 + 13*w - 5],\
[239, 239, -w^5 + w^4 + 6*w^3 - 6*w^2 - 7*w + 4],\
[239, 239, 2*w^5 - w^4 - 12*w^3 + 4*w^2 + 12*w + 2],\
[251, 251, 3*w^5 - 3*w^4 - 16*w^3 + 14*w^2 + 13*w - 4],\
[251, 251, 5*w^5 - 3*w^4 - 29*w^3 + 14*w^2 + 28*w - 1],\
[251, 251, 6*w^5 - 4*w^4 - 35*w^3 + 19*w^2 + 37*w - 7],\
[251, 251, -8*w^5 + 5*w^4 + 46*w^3 - 24*w^2 - 46*w + 8],\
[281, 281, -6*w^5 + 4*w^4 + 35*w^3 - 18*w^2 - 35*w + 3],\
[281, 281, 3*w^5 - 3*w^4 - 17*w^3 + 15*w^2 + 16*w - 10],\
[281, 281, -3*w^5 + w^4 + 17*w^3 - 5*w^2 - 18*w + 3],\
[281, 281, 5*w^5 - 3*w^4 - 30*w^3 + 14*w^2 + 33*w - 5],\
[293, 293, -w^5 + w^4 + 6*w^3 - 5*w^2 - 8*w + 3],\
[307, 307, 5*w^5 - 3*w^4 - 30*w^3 + 13*w^2 + 32*w],\
[307, 307, -4*w^5 + 3*w^4 + 22*w^3 - 15*w^2 - 20*w + 5],\
[307, 307, 3*w^5 - 2*w^4 - 17*w^3 + 8*w^2 + 15*w],\
[307, 307, -2*w^5 + w^4 + 12*w^3 - 5*w^2 - 11*w - 1],\
[307, 307, 5*w^5 - 4*w^4 - 28*w^3 + 20*w^2 + 26*w - 10],\
[307, 307, -4*w^5 + 2*w^4 + 23*w^3 - 8*w^2 - 22*w - 3],\
[337, 337, -w^5 + w^4 + 5*w^3 - 4*w^2 - 3*w + 3],\
[337, 337, 5*w^5 - 3*w^4 - 29*w^3 + 14*w^2 + 29*w],\
[337, 337, 5*w^5 - 3*w^4 - 28*w^3 + 15*w^2 + 27*w - 5],\
[337, 337, -4*w^5 + 4*w^4 + 22*w^3 - 20*w^2 - 19*w + 10],\
[349, 349, -8*w^5 + 5*w^4 + 46*w^3 - 25*w^2 - 45*w + 9],\
[349, 349, -w^4 + 2*w^3 + 5*w^2 - 7*w - 3],\
[419, 419, 5*w^5 - 3*w^4 - 29*w^3 + 13*w^2 + 28*w - 1],\
[419, 419, -6*w^5 + 4*w^4 + 35*w^3 - 20*w^2 - 35*w + 10],\
[421, 421, -6*w^5 + 3*w^4 + 34*w^3 - 15*w^2 - 32*w + 3],\
[421, 421, -5*w^5 + 3*w^4 + 29*w^3 - 14*w^2 - 28*w],\
[421, 421, w^5 - 5*w^3 - w^2 + 2*w + 3],\
[421, 421, -6*w^5 + 3*w^4 + 35*w^3 - 14*w^2 - 37*w + 2],\
[433, 433, -4*w^5 + 4*w^4 + 22*w^3 - 19*w^2 - 19*w + 6],\
[433, 433, 7*w^5 - 4*w^4 - 40*w^3 + 19*w^2 + 40*w - 6],\
[449, 449, 2*w^4 - w^3 - 10*w^2 + 4*w + 6],\
[449, 449, -4*w^5 + 4*w^4 + 23*w^3 - 20*w^2 - 21*w + 10],\
[461, 461, -6*w^5 + 3*w^4 + 36*w^3 - 15*w^2 - 40*w + 4],\
[461, 461, -7*w^5 + 5*w^4 + 40*w^3 - 23*w^2 - 39*w + 6],\
[461, 461, 4*w^5 - 2*w^4 - 22*w^3 + 9*w^2 + 19*w + 1],\
[461, 461, 5*w^5 - 2*w^4 - 30*w^3 + 10*w^2 + 32*w - 1],\
[463, 463, 4*w^5 - 2*w^4 - 23*w^3 + 10*w^2 + 23*w],\
[463, 463, -6*w^5 + 4*w^4 + 35*w^3 - 20*w^2 - 34*w + 7],\
[491, 491, 7*w^5 - 5*w^4 - 41*w^3 + 24*w^2 + 41*w - 8],\
[491, 491, -2*w^5 + w^4 + 12*w^3 - 4*w^2 - 15*w - 2],\
[491, 491, -w^5 + 6*w^3 + w^2 - 7*w],\
[491, 491, w^5 - w^4 - 6*w^3 + 4*w^2 + 6*w + 3],\
[491, 491, 5*w^5 - 3*w^4 - 29*w^3 + 16*w^2 + 30*w - 9],\
[491, 491, -3*w^5 + 2*w^4 + 18*w^3 - 8*w^2 - 20*w - 2],\
[503, 503, 3*w^5 - 2*w^4 - 18*w^3 + 10*w^2 + 20*w - 7],\
[503, 503, 6*w^5 - 3*w^4 - 35*w^3 + 14*w^2 + 37*w - 3],\
[547, 547, 2*w^5 - 12*w^3 - w^2 + 15*w + 3],\
[547, 547, -w^5 + 2*w^4 + 6*w^3 - 9*w^2 - 6*w + 3],\
[547, 547, 7*w^5 - 4*w^4 - 41*w^3 + 19*w^2 + 41*w - 3],\
[547, 547, 2*w^5 - w^4 - 13*w^3 + 6*w^2 + 17*w - 3],\
[547, 547, -4*w^5 + 3*w^4 + 23*w^3 - 13*w^2 - 21*w],\
[547, 547, -7*w^5 + 4*w^4 + 41*w^3 - 20*w^2 - 43*w + 7],\
[587, 587, 2*w^4 - w^3 - 10*w^2 + 4*w + 7],\
[587, 587, 5*w^5 - 2*w^4 - 29*w^3 + 10*w^2 + 31*w - 2],\
[601, 601, w^3 + 2*w^2 - 4*w - 4],\
[601, 601, w^5 - 7*w^3 - 2*w^2 + 11*w + 5],\
[617, 617, -7*w^5 + 4*w^4 + 41*w^3 - 20*w^2 - 43*w + 9],\
[617, 617, -2*w^5 + 13*w^3 - 16*w],\
[643, 643, -2*w^5 + 2*w^4 + 12*w^3 - 8*w^2 - 13*w],\
[643, 643, -3*w^5 + w^4 + 18*w^3 - 3*w^2 - 21*w - 3],\
[659, 659, 5*w^5 - 2*w^4 - 30*w^3 + 8*w^2 + 33*w + 2],\
[659, 659, w^5 - 6*w^3 + 2*w^2 + 7*w - 4],\
[673, 673, -2*w^5 + 2*w^4 + 10*w^3 - 11*w^2 - 5*w + 6],\
[673, 673, 6*w^5 - 4*w^4 - 34*w^3 + 20*w^2 + 33*w - 9],\
[673, 673, -3*w^5 + 2*w^4 + 17*w^3 - 9*w^2 - 16*w + 5],\
[673, 673, 7*w^5 - 4*w^4 - 40*w^3 + 20*w^2 + 38*w - 6],\
[673, 673, -3*w^5 + 2*w^4 + 16*w^3 - 11*w^2 - 12*w + 6],\
[673, 673, w^5 + w^4 - 6*w^3 - 6*w^2 + 8*w + 5],\
[701, 701, 5*w^5 - 4*w^4 - 28*w^3 + 20*w^2 + 26*w - 9],\
[701, 701, 4*w^5 - 3*w^4 - 22*w^3 + 15*w^2 + 20*w - 6],\
[727, 727, -2*w^5 + 2*w^4 + 11*w^3 - 8*w^2 - 9*w - 2],\
[727, 727, -3*w^5 + 3*w^4 + 18*w^3 - 15*w^2 - 20*w + 9],\
[729, 3, -3],\
[743, 743, -3*w^5 + w^4 + 18*w^3 - 4*w^2 - 22*w],\
[743, 743, -5*w^5 + 2*w^4 + 29*w^3 - 9*w^2 - 31*w - 1],\
[743, 743, -5*w^5 + 3*w^4 + 29*w^3 - 14*w^2 - 31*w + 6],\
[743, 743, -3*w^5 + 3*w^4 + 17*w^3 - 14*w^2 - 17*w + 3],\
[757, 757, -6*w^5 + 3*w^4 + 35*w^3 - 13*w^2 - 37*w + 2],\
[757, 757, 3*w^5 - 3*w^4 - 17*w^3 + 13*w^2 + 16*w - 1],\
[757, 757, -8*w^5 + 5*w^4 + 47*w^3 - 25*w^2 - 48*w + 10],\
[757, 757, 4*w^5 - 2*w^4 - 25*w^3 + 10*w^2 + 29*w - 4],\
[797, 797, -6*w^5 + 4*w^4 + 35*w^3 - 19*w^2 - 34*w + 3],\
[797, 797, -w^5 + w^4 + 7*w^3 - 6*w^2 - 10*w + 3],\
[811, 811, 5*w^5 - 4*w^4 - 28*w^3 + 18*w^2 + 25*w - 4],\
[811, 811, -4*w^5 + 3*w^4 + 22*w^3 - 15*w^2 - 17*w + 7],\
[827, 827, w^5 - w^4 - 5*w^3 + 5*w^2 + w - 4],\
[827, 827, -6*w^5 + 3*w^4 + 36*w^3 - 14*w^2 - 39*w + 3],\
[827, 827, -6*w^5 + 3*w^4 + 36*w^3 - 14*w^2 - 39*w + 2],\
[827, 827, -w^5 - w^4 + 7*w^3 + 6*w^2 - 11*w - 4],\
[839, 839, -2*w^5 + 2*w^4 + 10*w^3 - 10*w^2 - 6*w + 7],\
[839, 839, -6*w^5 + 4*w^4 + 34*w^3 - 20*w^2 - 32*w + 5],\
[841, 29, -4*w^5 + 3*w^4 + 24*w^3 - 15*w^2 - 25*w + 7],\
[841, 29, 5*w^5 - 3*w^4 - 30*w^3 + 15*w^2 + 32*w - 6],\
[841, 29, 5*w^5 - 2*w^4 - 30*w^3 + 10*w^2 + 33*w - 2],\
[853, 853, -5*w^5 + 3*w^4 + 29*w^3 - 16*w^2 - 29*w + 9],\
[853, 853, -5*w^5 + 3*w^4 + 29*w^3 - 16*w^2 - 30*w + 7],\
[881, 881, -3*w^5 + 3*w^4 + 16*w^3 - 14*w^2 - 13*w + 3],\
[881, 881, 4*w^5 - 2*w^4 - 24*w^3 + 9*w^2 + 25*w + 2],\
[881, 881, -8*w^5 + 5*w^4 + 46*w^3 - 24*w^2 - 46*w + 9],\
[881, 881, 5*w^5 - 2*w^4 - 30*w^3 + 8*w^2 + 34*w + 2],\
[883, 883, 3*w^5 - w^4 - 17*w^3 + 6*w^2 + 16*w - 5],\
[883, 883, 7*w^5 - 5*w^4 - 40*w^3 + 24*w^2 + 37*w - 8],\
[911, 911, w^5 - 8*w^3 + 14*w],\
[911, 911, -3*w^5 + 2*w^4 + 17*w^3 - 9*w^2 - 17*w - 1],\
[911, 911, -8*w^5 + 5*w^4 + 46*w^3 - 25*w^2 - 44*w + 9],\
[911, 911, 2*w^5 - 2*w^4 - 12*w^3 + 9*w^2 + 11*w],\
[937, 937, 5*w^5 - 2*w^4 - 30*w^3 + 9*w^2 + 32*w - 1],\
[937, 937, 3*w^5 - 3*w^4 - 17*w^3 + 15*w^2 + 15*w - 4],\
[967, 967, -w^5 + 7*w^3 - 9*w + 2],\
[967, 967, 6*w^5 - 4*w^4 - 35*w^3 + 20*w^2 + 36*w - 11]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - 2*x^7 - 43*x^6 + 48*x^5 + 451*x^4 - 196*x^3 - 1156*x^2 - 768*x - 144
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1849/18909*e^7 + 18233/75636*e^6 + 77173/18909*e^5 - 15175/2292*e^4 - 69461/1719*e^3 + 2957617/75636*e^2 + 152975/1719*e + 176069/6303, 5273/37818*e^7 - 12799/37818*e^6 - 220901/37818*e^5 + 3511/382*e^4 + 201343/3438*e^3 - 2002487/37818*e^2 - 233627/1719*e - 273224/6303, 527/75636*e^7 - 431/37818*e^6 - 25391/75636*e^5 + 152/573*e^4 + 30835/6876*e^3 - 32473/37818*e^2 - 30820/1719*e - 36874/6303, e, 5273/37818*e^7 - 12799/37818*e^6 - 220901/37818*e^5 + 3511/382*e^4 + 201343/3438*e^3 - 2002487/37818*e^2 - 230189/1719*e - 273224/6303, -31025/151272*e^7 + 9749/18909*e^6 + 1300823/151272*e^5 - 10909/764*e^4 - 1195633/13752*e^3 + 6335203/75636*e^2 + 352667/1719*e + 436805/6303, 12269/75636*e^7 - 16349/37818*e^6 - 506087/75636*e^5 + 14011/1146*e^4 + 447763/6876*e^3 - 2820847/37818*e^2 - 234385/1719*e - 229210/6303, -31895/151272*e^7 + 39863/75636*e^6 + 1333985/151272*e^5 - 16607/1146*e^4 - 1215619/13752*e^3 + 3162167/37818*e^2 + 702883/3438*e + 436265/6303, -69/1528*e^7 + 257/2292*e^6 + 2883/1528*e^5 - 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245057/573*e - 217223/2101, -20381/151272*e^7 + 18869/75636*e^6 + 878411/151272*e^5 - 6787/1146*e^4 - 826825/13752*e^3 + 1116347/37818*e^2 + 514447/3438*e + 318221/6303, -71491/75636*e^7 + 44537/18909*e^6 + 2986549/75636*e^5 - 74105/1146*e^4 - 2714363/6876*e^3 + 14178437/37818*e^2 + 1569839/1719*e + 1846346/6303, -22877/37818*e^7 + 30311/18909*e^6 + 946427/37818*e^5 - 25928/573*e^4 - 845785/3438*e^3 + 5196436/18909*e^2 + 931445/1719*e + 969794/6303, -20765/50424*e^7 + 25801/25212*e^6 + 863663/50424*e^5 - 16021/573*e^4 - 775733/4584*e^3 + 2044445/12606*e^2 + 432887/1146*e + 282483/2101, -8071/12606*e^7 + 19361/12606*e^6 + 169058/6303*e^5 - 7939/191*e^4 - 153403/573*e^3 + 3023125/12606*e^2 + 349192/573*e + 440298/2101, -8209/50424*e^7 + 8101/25212*e^6 + 351331/50424*e^5 - 1518/191*e^4 - 326609/4584*e^3 + 537607/12606*e^2 + 191579/1146*e + 104519/2101, -670/1719*e^7 + 6257/6876*e^6 + 28285/1719*e^5 - 18585/764*e^4 - 574775/3438*e^3 + 941023/6876*e^2 + 672985/1719*e + 70544/573, 16288/18909*e^7 - 159515/75636*e^6 - 683362/18909*e^5 + 43879/764*e^4 + 626732/1719*e^3 - 24821095/75636*e^2 - 1477640/1719*e - 1814441/6303, -10885/18909*e^7 + 106703/75636*e^6 + 455767/18909*e^5 - 88273/2292*e^4 - 415520/1719*e^3 + 16959763/75636*e^2 + 956540/1719*e + 1002536/6303, 170579/151272*e^7 - 108139/37818*e^6 - 7098569/151272*e^5 + 60473/764*e^4 + 6391819/13752*e^3 - 35280265/75636*e^2 - 1789085/1719*e - 2059385/6303, 42415/75636*e^7 - 51361/37818*e^6 - 1797139/75636*e^5 + 21266/573*e^4 + 1687727/6876*e^3 - 7978829/37818*e^2 - 1049048/1719*e - 1333862/6303, 7705/8404*e^7 - 58097/25212*e^6 - 320789/8404*e^5 + 145591/2292*e^4 + 866759/2292*e^3 - 3126047/8404*e^2 - 490100/573*e - 623340/2101, -45647/75636*e^7 + 28240/18909*e^6 + 1897817/75636*e^5 - 7764/191*e^4 - 1702669/6876*e^3 + 4422194/18909*e^2 + 957868/1719*e + 1122358/6303, -1391/18909*e^7 + 7385/37818*e^6 + 116779/37818*e^5 - 6553/1146*e^4 - 53398/1719*e^3 + 721865/18909*e^2 + 118096/1719*e - 16760/6303, -2659/3438*e^7 + 3400/1719*e^6 + 110419/3438*e^5 - 10528/191*e^4 - 1087465/3438*e^3 + 572183/1719*e^2 + 1182785/1719*e + 109882/573, 1477/2292*e^7 - 335/191*e^6 - 60733/2292*e^5 + 28639/573*e^4 + 195967/764*e^3 - 353399/1146*e^2 - 101033/191*e - 24564/191, 42517/37818*e^7 - 53071/18909*e^6 - 1771555/37818*e^5 + 88441/1146*e^4 + 799039/1719*e^3 - 17089519/37818*e^2 - 1810717/1719*e - 2111068/6303, 13405/75636*e^7 - 7748/18909*e^6 - 562255/75636*e^5 + 2032/191*e^4 + 515279/6876*e^3 - 1032385/18909*e^2 - 315575/1719*e - 467024/6303, -2326/6303*e^7 + 11257/12606*e^6 + 98050/6303*e^5 - 9191/382*e^4 - 91211/573*e^3 + 1671947/12606*e^2 + 223457/573*e + 303890/2101, 19589/75636*e^7 - 14104/18909*e^6 - 781193/75636*e^5 + 8315/382*e^4 + 628369/6876*e^3 - 2749946/18909*e^2 - 227989/1719*e + 153710/6303, 31481/25212*e^7 - 39349/12606*e^6 - 1313249/25212*e^5 + 98491/1146*e^4 + 1188107/2292*e^3 - 3172208/6303*e^2 - 672944/573*e - 811318/2101, -58799/50424*e^7 + 34547/12606*e^6 + 2483117/50424*e^5 - 168547/2292*e^4 - 2302259/4584*e^3 + 10435399/25212*e^2 + 697888/573*e + 892943/2101, -593/16808*e^7 + 2635/25212*e^6 + 26139/16808*e^5 - 1787/573*e^4 - 83291/4584*e^3 + 79173/4202*e^2 + 56255/1146*e + 42727/2101, 647/8404*e^7 - 1007/6303*e^6 - 28661/8404*e^5 + 4559/1146*e^4 + 89921/2292*e^3 - 74153/4202*e^2 - 72629/573*e - 106118/2101, -15199/50424*e^7 + 17023/25212*e^6 + 639505/50424*e^5 - 3331/191*e^4 - 583055/4584*e^3 + 578477/6303*e^2 + 339815/1146*e + 246381/2101, 5083/12606*e^7 - 7478/6303*e^6 - 206269/12606*e^5 + 40063/1146*e^4 + 88376/573*e^3 - 2838361/12606*e^2 - 166583/573*e - 94024/2101, -9290/18909*e^7 + 89785/75636*e^6 + 783637/37818*e^5 - 24709/764*e^4 - 363790/1719*e^3 + 14018099/75636*e^2 + 894103/1719*e + 1134415/6303, -64865/75636*e^7 + 79457/37818*e^6 + 2714597/75636*e^5 - 65527/1146*e^4 - 2477299/6876*e^3 + 6186071/18909*e^2 + 1458493/1719*e + 1870510/6303, -19265/25212*e^7 + 23147/12606*e^6 + 816485/25212*e^5 - 19031/382*e^4 - 767527/2292*e^3 + 1767137/6303*e^2 + 477730/573*e + 649564/2101, -1109/2101*e^7 + 2703/2101*e^6 + 46503/2101*e^5 - 13323/382*e^4 - 85263/382*e^3 + 822929/4202*e^2 + 101452/191*e + 396290/2101, 9925/25212*e^7 - 6014/6303*e^6 - 417001/25212*e^5 + 4931/191*e^4 + 384911/2292*e^3 - 1862429/12606*e^2 - 235418/573*e - 240234/2101, -20725/75636*e^7 + 61013/75636*e^6 + 837361/75636*e^5 - 18155/764*e^4 - 707345/6876*e^3 + 11662165/75636*e^2 + 308606/1719*e + 109316/6303, -19303/75636*e^7 + 26503/37818*e^6 + 789157/75636*e^5 - 22849/1146*e^4 - 684929/6876*e^3 + 4565057/37818*e^2 + 356579/1719*e + 427970/6303, -13513/75636*e^7 + 7541/18909*e^6 + 584107/75636*e^5 - 2021/191*e^4 - 575471/6876*e^3 + 1088959/18909*e^2 + 416834/1719*e + 531224/6303, 761/6876*e^7 - 340/1719*e^6 - 32627/6876*e^5 + 5209/1146*e^4 + 330947/6876*e^3 - 73639/3438*e^2 - 182741/1719*e - 33106/573, -2729/6876*e^7 + 5563/6876*e^6 + 117197/6876*e^5 - 45907/2292*e^4 - 1229093/6876*e^3 + 661949/6876*e^2 + 812084/1719*e + 111535/573, -17159/37818*e^7 + 43531/37818*e^6 + 705521/37818*e^5 - 18217/573*e^4 - 305429/1719*e^3 + 3615877/18909*e^2 + 601361/1719*e + 623198/6303, -8471/18909*e^7 + 41693/37818*e^6 + 355319/18909*e^5 - 5731/191*e^4 - 650675/3438*e^3 + 3198743/18909*e^2 + 742588/1719*e + 1105228/6303, -11893/151272*e^7 + 14989/75636*e^6 + 483235/151272*e^5 - 3088/573*e^4 - 409469/13752*e^3 + 602354/18909*e^2 + 212411/3438*e + 67747/6303, 31/4584*e^7 - 295/2292*e^6 + 731/4584*e^5 + 948/191*e^4 - 54875/4584*e^3 - 54025/1146*e^2 + 116735/1146*e + 16847/191, -5515/37818*e^7 + 13745/37818*e^6 + 112172/18909*e^5 - 3851/382*e^4 - 186983/3438*e^3 + 1263533/18909*e^2 + 157456/1719*e - 85706/6303, -25303/75636*e^7 + 19610/18909*e^6 + 1028293/75636*e^5 - 11827/382*e^4 - 900731/6876*e^3 + 7413821/37818*e^2 + 462752/1719*e + 438344/6303, -11233/37818*e^7 + 24533/37818*e^6 + 484159/37818*e^5 - 6445/382*e^4 - 470615/3438*e^3 + 3324559/37818*e^2 + 643396/1719*e + 1017250/6303, 7277/6303*e^7 - 23893/8404*e^6 - 607747/12606*e^5 + 177415/2292*e^4 + 91793/191*e^3 - 11193761/25212*e^2 - 210062/191*e - 786661/2101, 3341/4584*e^7 - 1040/573*e^6 - 139031/4584*e^5 + 38035/764*e^4 + 1372307/4584*e^3 - 664159/2292*e^2 - 379792/573*e - 44471/191, 71453/151272*e^7 - 79415/75636*e^6 - 3026483/151272*e^5 + 10473/382*e^4 + 2799253/13752*e^3 - 5741831/37818*e^2 - 1667497/3438*e - 1040273/6303, 13799/151272*e^7 - 11545/37818*e^6 - 538325/151272*e^5 + 21289/2292*e^4 + 424939/13752*e^3 - 4814563/75636*e^2 - 90260/1719*e + 208015/6303, -799/18909*e^7 + 5257/37818*e^6 + 59303/37818*e^5 - 5029/1146*e^4 - 18488/1719*e^3 + 713314/18909*e^2 - 18355/1719*e - 350560/6303, 10283/16808*e^7 - 13457/8404*e^6 - 423605/16808*e^5 + 17107/382*e^4 + 372299/1528*e^3 - 1135905/4202*e^2 - 192097/382*e - 245361/2101, 4381/6876*e^7 - 2888/1719*e^6 - 182269/6876*e^5 + 27226/573*e^4 + 1817905/6876*e^3 - 989987/3438*e^2 - 1043440/1719*e - 92696/573, 1813/18909*e^7 - 19337/75636*e^6 - 76192/18909*e^5 + 16115/2292*e^4 + 71744/1719*e^3 - 2756737/75636*e^2 - 179549/1719*e - 338387/6303]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([43,43,w^5 - 7*w^3 - w^2 + 10*w + 3])] = 1

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