/* 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. = PolynomialRing(QQ) g = P([1, 7, 11, -2, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([55, 55, w^5 - 8*w^3 - 2*w^2 + 15*w + 5]) primes_array = [ [5, 5, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 5],\ [9, 3, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 23*w + 6],\ [11, 11, w - 1],\ [25, 5, w^3 + w^2 - 4*w - 3],\ [29, 29, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w],\ [41, 41, w^4 - w^3 - 5*w^2 + 3*w + 3],\ [49, 7, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w + 1],\ [59, 59, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 24*w + 7],\ [59, 59, -w^5 + 8*w^3 + 2*w^2 - 15*w - 8],\ [61, 61, w^5 - 7*w^3 - 2*w^2 + 12*w + 4],\ [61, 61, -w^5 + 7*w^3 - 11*w - 1],\ [64, 2, 2],\ [71, 71, w^3 + w^2 - 5*w - 3],\ [71, 71, -3*w^5 + w^4 + 21*w^3 - w^2 - 33*w - 9],\ [79, 79, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w - 5],\ [81, 3, 2*w^5 - w^4 - 13*w^3 + w^2 + 19*w + 8],\ [89, 89, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 7],\ [89, 89, -w^5 + 8*w^3 + w^2 - 16*w - 5],\ [89, 89, -3*w^5 + w^4 + 20*w^3 - 30*w - 11],\ [89, 89, -w^5 + 7*w^3 + 2*w^2 - 11*w - 4],\ [89, 89, -2*w^5 + 14*w^3 + 3*w^2 - 22*w - 8],\ [89, 89, 2*w^5 - w^4 - 14*w^3 + 3*w^2 + 22*w + 6],\ [101, 101, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 22*w + 6],\ [101, 101, w^2 - w - 4],\ [101, 101, -3*w^5 + w^4 + 20*w^3 - 2*w^2 - 29*w - 7],\ [109, 109, w^4 - w^3 - 5*w^2 + 4*w + 5],\ [121, 11, w^5 - 7*w^3 - 2*w^2 + 10*w + 6],\ [131, 131, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 4*w - 3],\ [131, 131, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 20*w - 6],\ [131, 131, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 11],\ [131, 131, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 2],\ [139, 139, -w^5 + 6*w^3 + w^2 - 8*w - 1],\ [151, 151, -w^3 + w^2 + 4*w - 2],\ [179, 179, w^4 - 6*w^2 + 6],\ [181, 181, w^3 + w^2 - 3*w],\ [191, 191, 3*w^5 - w^4 - 20*w^3 + 2*w^2 + 28*w + 5],\ [199, 199, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 15*w - 2],\ [199, 199, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 15],\ [211, 211, 3*w^5 - w^4 - 19*w^3 + w^2 + 26*w + 9],\ [229, 229, -w^5 + w^4 + 7*w^3 - 3*w^2 - 11*w],\ [229, 229, -w^4 + 2*w^3 + 6*w^2 - 7*w - 6],\ [239, 239, -w^5 + w^4 + 7*w^3 - 3*w^2 - 13*w - 6],\ [239, 239, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 10],\ [239, 239, w^3 - w^2 - 4*w + 1],\ [239, 239, 5*w^5 - 2*w^4 - 34*w^3 + 2*w^2 + 53*w + 17],\ [241, 241, -w^5 + 7*w^3 + w^2 - 13*w - 4],\ [241, 241, -3*w^5 + w^4 + 21*w^3 - 35*w - 10],\ [241, 241, -w^5 + 7*w^3 - 11*w],\ [251, 251, 3*w^5 - w^4 - 21*w^3 + 35*w + 11],\ [251, 251, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 3],\ [269, 269, -w^5 + 8*w^3 + 3*w^2 - 16*w - 8],\ [269, 269, -2*w^5 + w^4 + 13*w^3 - w^2 - 21*w - 9],\ [269, 269, 3*w^5 - 21*w^3 - 3*w^2 + 32*w + 12],\ [271, 271, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 14],\ [281, 281, -w^5 + 8*w^3 + 3*w^2 - 16*w - 11],\ [281, 281, 4*w^5 - w^4 - 29*w^3 + 49*w + 13],\ [281, 281, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 5],\ [281, 281, -5*w^5 + 3*w^4 + 33*w^3 - 8*w^2 - 50*w - 12],\ [311, 311, 2*w^5 - w^4 - 14*w^3 + w^2 + 21*w + 9],\ [311, 311, -3*w^5 + 20*w^3 + 3*w^2 - 30*w - 10],\ [311, 311, 5*w^5 - 2*w^4 - 35*w^3 + 2*w^2 + 57*w + 19],\ [331, 331, -w^5 - w^4 + 7*w^3 + 6*w^2 - 11*w - 7],\ [349, 349, -6*w^5 + 3*w^4 + 41*w^3 - 7*w^2 - 64*w - 17],\ [349, 349, 4*w^5 - w^4 - 29*w^3 - w^2 + 50*w + 17],\ [349, 349, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 17],\ [359, 359, w^5 - 6*w^3 - w^2 + 5*w + 3],\ [379, 379, -w^5 + w^4 + 8*w^3 - 3*w^2 - 17*w - 3],\ [379, 379, 2*w^5 - 14*w^3 - 4*w^2 + 22*w + 11],\ [379, 379, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 13],\ [379, 379, 4*w^5 - 2*w^4 - 27*w^3 + 3*w^2 + 43*w + 14],\ [389, 389, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 44*w + 13],\ [401, 401, -2*w^5 + 2*w^4 + 13*w^3 - 6*w^2 - 20*w - 6],\ [409, 409, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w],\ [419, 419, -5*w^5 + w^4 + 34*w^3 + 2*w^2 - 53*w - 19],\ [419, 419, 2*w^5 - w^4 - 14*w^3 + 4*w^2 + 23*w + 3],\ [421, 421, -w^5 - w^4 + 8*w^3 + 6*w^2 - 13*w - 7],\ [421, 421, 2*w^5 - 2*w^4 - 13*w^3 + 8*w^2 + 18*w + 2],\ [421, 421, 4*w^5 - w^4 - 26*w^3 + 37*w + 11],\ [431, 431, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 9],\ [431, 431, w^5 - 8*w^3 - w^2 + 14*w + 2],\ [449, 449, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 38*w + 9],\ [449, 449, -3*w^5 + w^4 + 20*w^3 - 31*w - 14],\ [461, 461, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 23*w + 4],\ [461, 461, -4*w^5 + 2*w^4 + 26*w^3 - 5*w^2 - 36*w - 9],\ [461, 461, -4*w^5 + 2*w^4 + 27*w^3 - 3*w^2 - 42*w - 15],\ [491, 491, -3*w^5 + w^4 + 20*w^3 - 29*w - 10],\ [491, 491, -5*w^5 + w^4 + 35*w^3 + 2*w^2 - 56*w - 18],\ [491, 491, 2*w^5 - 14*w^3 - 4*w^2 + 24*w + 13],\ [491, 491, -3*w^5 + w^4 + 21*w^3 - 2*w^2 - 33*w - 10],\ [499, 499, 6*w^5 - 3*w^4 - 40*w^3 + 6*w^2 + 61*w + 18],\ [499, 499, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 17],\ [499, 499, -w^5 - w^4 + 8*w^3 + 5*w^2 - 14*w - 4],\ [499, 499, -3*w^5 + w^4 + 19*w^3 - 2*w^2 - 26*w - 8],\ [509, 509, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 11],\ [509, 509, -2*w^5 + 16*w^3 + 2*w^2 - 30*w - 9],\ [521, 521, 3*w^5 - 21*w^3 - 3*w^2 + 34*w + 10],\ [521, 521, -3*w^5 + w^4 + 19*w^3 - 26*w - 9],\ [521, 521, 4*w^5 - w^4 - 27*w^3 + 40*w + 15],\ [521, 521, -3*w^5 + 22*w^3 + 3*w^2 - 37*w - 11],\ [541, 541, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 18],\ [569, 569, -6*w^5 + 2*w^4 + 40*w^3 - 2*w^2 - 60*w - 19],\ [569, 569, -w^5 + w^4 + 7*w^3 - 2*w^2 - 12*w - 6],\ [571, 571, 4*w^5 - w^4 - 28*w^3 + 43*w + 14],\ [571, 571, -4*w^5 + 2*w^4 + 28*w^3 - 4*w^2 - 45*w - 14],\ [599, 599, -w^5 + w^4 + 7*w^3 - 2*w^2 - 13*w - 7],\ [601, 601, 4*w^5 - w^4 - 26*w^3 + 38*w + 13],\ [601, 601, 4*w^5 - 2*w^4 - 28*w^3 + 5*w^2 + 44*w + 11],\ [601, 601, 3*w^5 - w^4 - 21*w^3 + 2*w^2 + 35*w + 9],\ [619, 619, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 13],\ [619, 619, -4*w^5 + w^4 + 26*w^3 - 36*w - 12],\ [619, 619, w^4 - w^3 - 6*w^2 + 4*w + 4],\ [631, 631, -3*w^5 + w^4 + 20*w^3 - 30*w - 9],\ [631, 631, -5*w^5 + 2*w^4 + 35*w^3 - 3*w^2 - 57*w - 15],\ [641, 641, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 16],\ [641, 641, -5*w^5 + 2*w^4 + 34*w^3 - 2*w^2 - 52*w - 18],\ [659, 659, 3*w^5 - w^4 - 20*w^3 + w^2 + 32*w + 9],\ [659, 659, -4*w^5 + w^4 + 27*w^3 - w^2 - 40*w - 11],\ [661, 661, 4*w^5 - w^4 - 26*w^3 + 38*w + 12],\ [661, 661, -w^5 + 6*w^3 - 8*w + 1],\ [691, 691, 3*w^5 - 20*w^3 - 3*w^2 + 29*w + 9],\ [691, 691, w^5 + w^4 - 8*w^3 - 7*w^2 + 14*w + 9],\ [691, 691, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w + 2],\ [701, 701, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 9],\ [701, 701, 5*w^5 - 2*w^4 - 33*w^3 + 3*w^2 + 48*w + 14],\ [701, 701, w^4 + 3*w^3 - 3*w^2 - 10*w - 1],\ [701, 701, -2*w^5 + w^4 + 14*w^3 - 3*w^2 - 24*w - 3],\ [709, 709, -2*w^5 + 2*w^4 + 14*w^3 - 7*w^2 - 22*w - 5],\ [709, 709, -3*w^5 + 21*w^3 + 4*w^2 - 34*w - 11],\ [719, 719, 5*w^5 - 2*w^4 - 35*w^3 + 3*w^2 + 58*w + 17],\ [719, 719, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 37*w + 11],\ [719, 719, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 12],\ [719, 719, 2*w^5 - 16*w^3 - 3*w^2 + 30*w + 10],\ [739, 739, -5*w^5 + w^4 + 34*w^3 + w^2 - 51*w - 17],\ [751, 751, -w^5 - w^4 + 9*w^3 + 7*w^2 - 18*w - 10],\ [761, 761, 4*w^5 - 2*w^4 - 28*w^3 + 3*w^2 + 46*w + 16],\ [761, 761, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 12],\ [769, 769, -4*w^5 + w^4 + 28*w^3 - 44*w - 12],\ [769, 769, -w^4 + w^3 + 3*w^2 - 3*w + 1],\ [809, 809, 2*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 20*w + 1],\ [811, 811, -2*w^5 + 15*w^3 + 2*w^2 - 24*w - 8],\ [811, 811, -w^5 + 9*w^3 + w^2 - 18*w - 6],\ [821, 821, -w^5 + 8*w^3 + 3*w^2 - 17*w - 9],\ [821, 821, w^5 + w^4 - 7*w^3 - 6*w^2 + 11*w + 8],\ [821, 821, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 46*w + 11],\ [821, 821, 5*w^5 - 2*w^4 - 34*w^3 + 4*w^2 + 51*w + 13],\ [829, 829, -2*w^5 + w^4 + 15*w^3 - w^2 - 28*w - 10],\ [829, 829, -6*w^5 + 3*w^4 + 42*w^3 - 7*w^2 - 68*w - 21],\ [829, 829, 4*w^5 - 2*w^4 - 26*w^3 + 5*w^2 + 38*w + 12],\ [829, 829, w^5 - 7*w^3 - 3*w^2 + 11*w + 6],\ [839, 839, 3*w^5 - 2*w^4 - 20*w^3 + 5*w^2 + 32*w + 11],\ [839, 839, -w^4 + w^3 + 6*w^2 - 3*w - 4],\ [841, 29, -3*w^5 + w^4 + 22*w^3 - 38*w - 11],\ [911, 911, 3*w^5 - w^4 - 21*w^3 + 36*w + 12],\ [919, 919, -w^5 - w^4 + 7*w^3 + 6*w^2 - 12*w - 5],\ [941, 941, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w],\ [941, 941, 4*w^5 - w^4 - 29*w^3 + 48*w + 15],\ [971, 971, -4*w^5 + w^4 + 27*w^3 + w^2 - 41*w - 13],\ [991, 991, w^5 - w^4 - 8*w^3 + 3*w^2 + 16*w + 2],\ [991, 991, -4*w^5 + 3*w^4 + 27*w^3 - 9*w^2 - 42*w - 10]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - 27*x^3 - 6*x^2 + 40*x - 16 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, 1, -e, 5/2*e^4 + 3/2*e^3 - 133/2*e^2 - 109/2*e + 59, 3/4*e^4 + 1/2*e^3 - 81/4*e^2 - 17*e + 21, -1/2*e^4 + 27/2*e^2 + 2*e - 16, -5/2*e^4 - 2*e^3 + 133/2*e^2 + 66*e - 66, -9/4*e^4 - 3/2*e^3 + 239/4*e^2 + 53*e - 57, e^4 + e^3 - 27*e^2 - 31*e + 24, -3/2*e^4 - e^3 + 81/2*e^2 + 36*e - 48, 9/4*e^4 + e^3 - 239/4*e^2 - 87/2*e + 59, e^4 + 1/2*e^3 - 27*e^2 - 39/2*e + 25, -7/2*e^4 - 2*e^3 + 185/2*e^2 + 74*e - 86, -5/4*e^4 - 1/2*e^3 + 135/4*e^2 + 21*e - 41, 3/2*e^4 + 1/2*e^3 - 79/2*e^2 - 47/2*e + 41, 7/2*e^4 + 5/2*e^3 - 187/2*e^2 - 175/2*e + 89, 9/4*e^4 + 3/2*e^3 - 239/4*e^2 - 54*e + 53, -4*e^4 - 5/2*e^3 + 106*e^2 + 181/2*e - 101, -e^4 - e^3 + 27*e^2 + 31*e - 32, e^4 + e^3 - 27*e^2 - 31*e + 32, -1/2*e^4 + 27/2*e^2 + e - 18, 3*e^4 + 2*e^3 - 80*e^2 - 71*e + 80, -5/4*e^4 - 1/2*e^3 + 131/4*e^2 + 22*e - 25, -1/4*e^4 - 1/2*e^3 + 27/4*e^2 + 13*e - 3, -5*e^4 - 3*e^3 + 132*e^2 + 111*e - 120, -3/4*e^4 - 1/2*e^3 + 77/4*e^2 + 19*e - 13, 3/2*e^4 + e^3 - 79/2*e^2 - 36*e + 42, e^4 + 1/2*e^3 - 27*e^2 - 39/2*e + 25, -15/4*e^4 - 5/2*e^3 + 401/4*e^2 + 90*e - 105, -3*e^4 - 2*e^3 + 80*e^2 + 71*e - 86, 3*e - 2, -5/2*e^4 - 3/2*e^3 + 133/2*e^2 + 117/2*e - 69, -3*e^4 - 2*e^3 + 80*e^2 + 73*e - 90, 7/2*e^4 + 2*e^3 - 185/2*e^2 - 77*e + 78, 3/2*e^4 + e^3 - 79/2*e^2 - 35*e + 40, 1/2*e^3 - 19/2*e - 7, e^4 + 1/2*e^3 - 26*e^2 - 41/2*e + 15, -5/2*e^4 - 2*e^3 + 133/2*e^2 + 63*e - 64, -7/2*e^4 - 2*e^3 + 187/2*e^2 + 76*e - 96, 3*e^4 + 2*e^3 - 80*e^2 - 69*e + 84, -7/2*e^4 - 2*e^3 + 187/2*e^2 + 72*e - 86, -8*e^4 - 5*e^3 + 213*e^2 + 180*e - 204, 3*e^4 + 2*e^3 - 80*e^2 - 66*e + 76, 31/4*e^4 + 11/2*e^3 - 829/4*e^2 - 193*e + 207, 13/2*e^4 + 4*e^3 - 347/2*e^2 - 147*e + 166, -1/2*e^4 - e^3 + 27/2*e^2 + 33*e - 10, -3*e^4 - 2*e^3 + 79*e^2 + 72*e - 70, -e^4 - e^3 + 28*e^2 + 30*e - 40, 1/2*e^4 + 1/2*e^3 - 27/2*e^2 - 43/2*e + 19, 1/4*e^4 + 1/2*e^3 - 23/4*e^2 - 13*e - 1, e^4 - 27*e^2 - 6*e + 26, 2*e^4 + e^3 - 52*e^2 - 41*e + 40, -23/4*e^4 - 7/2*e^3 + 613/4*e^2 + 130*e - 137, e^4 + e^3 - 26*e^2 - 32*e + 6, 2*e^4 + e^3 - 52*e^2 - 41*e + 40, e^4 - 26*e^2 - 7*e + 24, -3*e^4 - 2*e^3 + 80*e^2 + 69*e - 88, -7*e^4 - 5*e^3 + 187*e^2 + 171*e - 182, 11/2*e^4 + 4*e^3 - 293/2*e^2 - 134*e + 134, 2*e^4 + e^3 - 53*e^2 - 43*e + 42, 3/2*e^4 + e^3 - 77/2*e^2 - 35*e + 20, 31/4*e^4 + 11/2*e^3 - 825/4*e^2 - 188*e + 191, -3/2*e^4 - 1/2*e^3 + 79/2*e^2 + 47/2*e - 41, -5*e^4 - 5/2*e^3 + 132*e^2 + 193/2*e - 121, 3/2*e^4 + e^3 - 81/2*e^2 - 32*e + 50, 1/2*e^4 + e^3 - 25/2*e^2 - 27*e, 9/2*e^4 + 5/2*e^3 - 239/2*e^2 - 195/2*e + 123, 5/2*e^4 + 2*e^3 - 133/2*e^2 - 69*e + 52, 19/4*e^4 + 5/2*e^3 - 501/4*e^2 - 98*e + 117, -27/4*e^4 - 9/2*e^3 + 721/4*e^2 + 158*e - 179, -7/4*e^4 - 3/2*e^3 + 189/4*e^2 + 48*e - 59, 3/2*e^4 + 3/2*e^3 - 81/2*e^2 - 101/2*e + 31, 7*e^4 + 5*e^3 - 186*e^2 - 171*e + 178, 2*e^4 + 1/2*e^3 - 53*e^2 - 59/2*e + 49, -1/2*e^4 - e^3 + 29/2*e^2 + 29*e - 6, 2*e^4 + e^3 - 53*e^2 - 40*e + 38, e^4 + e^3 - 28*e^2 - 32*e + 30, 3*e^4 + 3/2*e^3 - 80*e^2 - 115/2*e + 69, 31/4*e^4 + 9/2*e^3 - 821/4*e^2 - 169*e + 195, -1/2*e^4 + 1/2*e^3 + 23/2*e^2 - 13/2*e + 7, 9/4*e^4 + 3/2*e^3 - 231/4*e^2 - 51*e + 27, -3*e^4 - 2*e^3 + 78*e^2 + 72*e - 62, 3*e^4 + 5/2*e^3 - 80*e^2 - 171/2*e + 63, 7/2*e^4 + 3*e^3 - 185/2*e^2 - 100*e + 88, 11*e^4 + 7*e^3 - 292*e^2 - 256*e + 284, 5/2*e^4 + 2*e^3 - 131/2*e^2 - 66*e + 38, -10*e^4 - 6*e^3 + 265*e^2 + 218*e - 244, e^4 - 27*e^2 - 7*e + 46, 6*e^4 + 7/2*e^3 - 160*e^2 - 257/2*e + 163, -1/2*e^4 + 29/2*e^2 - 18, 7*e^4 + 4*e^3 - 186*e^2 - 152*e + 180, -9/2*e^4 - 3*e^3 + 237/2*e^2 + 107*e - 96, -6*e^4 - 5*e^3 + 160*e^2 + 165*e - 144, 2*e^4 + e^3 - 54*e^2 - 36*e + 62, e^4 + 3/2*e^3 - 26*e^2 - 91/2*e + 23, 2*e^2 - 2*e - 34, -7*e^4 - 4*e^3 + 185*e^2 + 154*e - 166, 2*e^4 + e^3 - 53*e^2 - 42*e + 34, -3*e^4 - 2*e^3 + 80*e^2 + 76*e - 86, 7/4*e^4 - 1/2*e^3 - 185/4*e^2 - 7*e + 49, -21/4*e^4 - 5/2*e^3 + 551/4*e^2 + 101*e - 127, 15/2*e^4 + 5*e^3 - 401/2*e^2 - 176*e + 198, -13*e^4 - 8*e^3 + 344*e^2 + 295*e - 318, 15/2*e^4 + 5*e^3 - 401/2*e^2 - 178*e + 206, -6*e^4 - 9/2*e^3 + 160*e^2 + 301/2*e - 153, 19/2*e^4 + 6*e^3 - 507/2*e^2 - 216*e + 228, 3/2*e^4 + e^3 - 81/2*e^2 - 32*e + 64, -27/4*e^4 - 9/2*e^3 + 717/4*e^2 + 165*e - 167, -23/4*e^4 - 5/2*e^3 + 613/4*e^2 + 106*e - 157, 6*e^4 + 4*e^3 - 160*e^2 - 147*e + 154, 19/2*e^4 + 11/2*e^3 - 503/2*e^2 - 405/2*e + 245, 5/2*e^4 + e^3 - 131/2*e^2 - 40*e + 58, -4*e^4 - 3/2*e^3 + 107*e^2 + 123/2*e - 103, 11/4*e^4 + 3/2*e^3 - 289/4*e^2 - 61*e + 73, -e^4 + 27*e^2 + 7*e + 2, -2*e^4 + 54*e^2 + 7*e - 66, 2*e^2 - 2*e - 18, -10*e^4 - 6*e^3 + 265*e^2 + 224*e - 234, e^4 + e^3 - 28*e^2 - 36*e + 32, e^4 + 3/2*e^3 - 28*e^2 - 95/2*e + 33, 19/2*e^4 + 7*e^3 - 509/2*e^2 - 240*e + 254, -6*e^4 - 7/2*e^3 + 157*e^2 + 263/2*e - 119, -6*e^4 - 4*e^3 + 160*e^2 + 147*e - 164, 17/2*e^4 + 5*e^3 - 453/2*e^2 - 188*e + 224, -15/2*e^4 - 9/2*e^3 + 397/2*e^2 + 327/2*e - 197, -9/2*e^4 - 7/2*e^3 + 239/2*e^2 + 239/2*e - 93, -9/2*e^4 - 3*e^3 + 241/2*e^2 + 108*e - 144, 4*e^4 + 2*e^3 - 105*e^2 - 79*e + 78, -3/2*e^4 - e^3 + 83/2*e^2 + 33*e - 68, e^4 - 1/2*e^3 - 26*e^2 + 1/2*e + 13, 9*e^4 + 5*e^3 - 238*e^2 - 192*e + 216, 1/2*e^4 - 27/2*e^2 - 3*e + 8, -39/4*e^4 - 11/2*e^3 + 1037/4*e^2 + 202*e - 249, 2*e^4 + e^3 - 56*e^2 - 38*e + 86, -23/2*e^4 - 7*e^3 + 613/2*e^2 + 256*e - 304, 5*e^4 + 2*e^3 - 133*e^2 - 88*e + 118, 8*e^4 + 5*e^3 - 212*e^2 - 181*e + 192, 2*e^4 + e^3 - 53*e^2 - 39*e + 40, -1/2*e^4 + 25/2*e^2 + 8*e + 6, -4*e^4 - 2*e^3 + 106*e^2 + 78*e - 108, -9/2*e^4 - 2*e^3 + 241/2*e^2 + 82*e - 132, 15/2*e^4 + 5*e^3 - 399/2*e^2 - 173*e + 174, -13/2*e^4 - 9/2*e^3 + 345/2*e^2 + 315/2*e - 169, -8*e^4 - 11/2*e^3 + 213*e^2 + 401/2*e - 205, -13/2*e^4 - 4*e^3 + 347/2*e^2 + 147*e - 166, 7*e^4 + 5*e^3 - 186*e^2 - 167*e + 180, -5*e^4 - 4*e^3 + 132*e^2 + 139*e - 120, -3*e^4 - 5/2*e^3 + 82*e^2 + 159/2*e - 115, -5/2*e^4 - 2*e^3 + 135/2*e^2 + 71*e - 80, 13/2*e^4 + 4*e^3 - 347/2*e^2 - 147*e + 168, -2*e^2 - e + 24, -1/2*e^4 + e^3 + 23/2*e^2 - 14*e + 6, 37/4*e^4 + 13/2*e^3 - 983/4*e^2 - 229*e + 229, -8*e^4 - 6*e^3 + 212*e^2 + 206*e - 202, e^4 + e^3 - 25*e^2 - 34*e + 6, -9/2*e^4 - 3*e^3 + 241/2*e^2 + 100*e - 130, -15/2*e^4 - 5*e^3 + 399/2*e^2 + 172*e - 206, 15/4*e^4 + 5/2*e^3 - 393/4*e^2 - 93*e + 83] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 5])] = 1 AL_eigenvalues[ZF.ideal([11, 11, w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]