/* 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([11, 6, -8, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([25, 5, 2/3*w^3 - 10/3*w - 1/3]) primes_array = [ [9, 3, 1/3*w^3 - 8/3*w - 2/3],\ [9, 3, -w + 1],\ [11, 11, w],\ [11, 11, -1/3*w^3 + 2/3*w + 5/3],\ [11, 11, 1/3*w^3 - 8/3*w + 1/3],\ [11, 11, -2/3*w^3 + 13/3*w + 4/3],\ [16, 2, 2],\ [25, 5, 2/3*w^3 - 10/3*w - 1/3],\ [29, 29, -w - 3],\ [29, 29, -1/3*w^3 + 8/3*w - 10/3],\ [31, 31, w^3 - 6*w + 1],\ [31, 31, w^3 - 6*w - 2],\ [41, 41, 2/3*w^3 + w^2 - 13/3*w - 10/3],\ [41, 41, 2/3*w^3 - 13/3*w + 5/3],\ [59, 59, 2/3*w^3 - 13/3*w + 8/3],\ [59, 59, w^3 + w^2 - 6*w - 4],\ [79, 79, 2/3*w^3 + w^2 - 10/3*w - 19/3],\ [79, 79, 1/3*w^3 + w^2 - 2/3*w - 17/3],\ [89, 89, 4/3*w^3 - 23/3*w - 5/3],\ [89, 89, 1/3*w^3 + 2*w^2 - 5/3*w - 32/3],\ [101, 101, 5/3*w^3 + w^2 - 31/3*w - 16/3],\ [101, 101, 2/3*w^3 - w^2 - 4/3*w + 8/3],\ [109, 109, -w^3 - 2*w^2 + 7*w + 7],\ [109, 109, -1/3*w^3 + 2*w^2 + 2/3*w - 16/3],\ [131, 131, w^3 - w^2 - 7*w + 5],\ [131, 131, -2/3*w^3 - w^2 + 4/3*w + 13/3],\ [139, 139, -2/3*w^3 - w^2 + 13/3*w + 4/3],\ [139, 139, w^2 - w - 7],\ [151, 151, -5/3*w^3 + 28/3*w - 5/3],\ [151, 151, -1/3*w^3 + w^2 + 2/3*w - 16/3],\ [151, 151, w^3 + w^2 - 6*w - 3],\ [151, 151, -w^3 + w^2 + 7*w - 6],\ [179, 179, 5/3*w^3 + w^2 - 28/3*w - 19/3],\ [179, 179, -1/3*w^3 + w^2 + 11/3*w - 4/3],\ [181, 181, -4/3*w^3 - 2*w^2 + 20/3*w + 29/3],\ [181, 181, 1/3*w^3 + w^2 - 2/3*w - 20/3],\ [181, 181, w^3 + w^2 - 5*w - 7],\ [181, 181, 5/3*w^3 + w^2 - 28/3*w - 16/3],\ [191, 191, 2*w - 1],\ [191, 191, 2/3*w^3 - 16/3*w - 1/3],\ [199, 199, 1/3*w^3 - 11/3*w + 4/3],\ [199, 199, 1/3*w^3 - 11/3*w - 2/3],\ [211, 211, -2/3*w^3 - w^2 + 19/3*w + 16/3],\ [211, 211, 2/3*w^3 + w^2 - 19/3*w - 7/3],\ [229, 229, 1/3*w^3 - 11/3*w + 1/3],\ [239, 239, -5/3*w^3 - w^2 + 25/3*w + 19/3],\ [239, 239, -4/3*w^3 + w^2 + 20/3*w - 7/3],\ [251, 251, -2/3*w^3 + w^2 + 16/3*w - 14/3],\ [251, 251, -1/3*w^3 - w^2 - 1/3*w + 14/3],\ [269, 269, 2/3*w^3 + w^2 - 7/3*w - 19/3],\ [269, 269, 1/3*w^3 + 2*w^2 - 2/3*w - 32/3],\ [281, 281, w^3 - w^2 - 5*w + 1],\ [281, 281, 4/3*w^3 + w^2 - 20/3*w - 23/3],\ [289, 17, 2/3*w^3 + w^2 - 16/3*w - 4/3],\ [289, 17, 1/3*w^3 + w^2 - 11/3*w - 20/3],\ [331, 331, 1/3*w^3 + 2*w^2 - 8/3*w - 23/3],\ [331, 331, 2/3*w^3 + 2*w^2 - 13/3*w - 28/3],\ [349, 349, 4/3*w^3 - 17/3*w + 1/3],\ [349, 349, -5/3*w^3 + 28/3*w - 2/3],\ [361, 19, -1/3*w^3 + 5/3*w + 14/3],\ [361, 19, 4/3*w^3 - 20/3*w - 5/3],\ [379, 379, 4/3*w^3 + 2*w^2 - 23/3*w - 41/3],\ [379, 379, -5/3*w^3 + 31/3*w - 5/3],\ [389, 389, 5/3*w^3 + w^2 - 25/3*w - 16/3],\ [389, 389, -4/3*w^3 + w^2 + 20/3*w - 10/3],\ [401, 401, -1/3*w^3 - 3*w^2 + 5/3*w + 26/3],\ [401, 401, 1/3*w^3 + w^2 - 11/3*w - 23/3],\ [401, 401, -2/3*w^3 - 3*w^2 + 10/3*w + 52/3],\ [401, 401, 2/3*w^3 + w^2 - 16/3*w - 1/3],\ [409, 409, -2*w^3 - w^2 + 11*w + 2],\ [409, 409, -5/3*w^3 - 2*w^2 + 28/3*w + 37/3],\ [409, 409, 1/3*w^3 - 11/3*w - 17/3],\ [409, 409, 5/3*w^3 + 3*w^2 - 25/3*w - 37/3],\ [419, 419, -1/3*w^3 + 3*w^2 - 1/3*w - 37/3],\ [419, 419, 2*w^3 + 3*w^2 - 12*w - 13],\ [421, 421, -1/3*w^3 + 3*w^2 + 2/3*w - 31/3],\ [421, 421, -5/3*w^3 - w^2 + 25/3*w + 13/3],\ [421, 421, -w^3 + 7*w - 4],\ [421, 421, -4/3*w^3 + w^2 + 20/3*w - 13/3],\ [439, 439, -4/3*w^3 + w^2 + 14/3*w - 7/3],\ [439, 439, 4/3*w^3 - 17/3*w - 5/3],\ [439, 439, -7/3*w^3 - w^2 + 41/3*w + 17/3],\ [439, 439, 5/3*w^3 - 28/3*w - 4/3],\ [449, 449, w^3 + 3*w^2 - 6*w - 17],\ [449, 449, 1/3*w^3 + 3*w^2 - 8/3*w - 26/3],\ [449, 449, -4/3*w^3 + 26/3*w + 17/3],\ [449, 449, 7/3*w^3 + w^2 - 38/3*w - 8/3],\ [461, 461, -5/3*w^3 + w^2 + 28/3*w - 14/3],\ [461, 461, -2/3*w^3 - 2*w^2 + 10/3*w + 43/3],\ [461, 461, -2*w^3 - w^2 + 12*w + 4],\ [461, 461, -w^3 + 8*w - 5],\ [479, 479, w^3 + w^2 - 7*w - 2],\ [479, 479, -4/3*w^3 - w^2 + 23/3*w + 5/3],\ [499, 499, -4/3*w^3 - 2*w^2 + 23/3*w + 17/3],\ [499, 499, -4/3*w^3 - w^2 + 29/3*w + 8/3],\ [521, 521, 2*w^3 - 11*w + 2],\ [521, 521, 4/3*w^3 - w^2 - 14/3*w + 1/3],\ [569, 569, w^3 + 3*w^2 - 6*w - 9],\ [569, 569, 4/3*w^3 + w^2 - 26/3*w - 32/3],\ [569, 569, -w^3 + 6*w - 6],\ [569, 569, -1/3*w^3 - 3*w^2 + 8/3*w + 50/3],\ [571, 571, 2/3*w^3 + 3*w^2 - 10/3*w - 46/3],\ [571, 571, 2*w^2 - 15],\ [599, 599, -w^3 + 2*w^2 + 4*w - 10],\ [599, 599, -w^2 - 3*w + 8],\ [601, 601, 5/3*w^3 + 3*w^2 - 28/3*w - 34/3],\ [601, 601, 1/3*w^3 - 3*w^2 - 2/3*w + 43/3],\ [619, 619, 2/3*w^3 - w^2 - 13/3*w + 2/3],\ [619, 619, 2/3*w^3 + w^2 - 7/3*w - 25/3],\ [619, 619, 2*w^3 + w^2 - 11*w - 6],\ [619, 619, -2/3*w^3 + 13/3*w - 17/3],\ [631, 631, 2/3*w^3 + 2*w^2 - 19/3*w - 31/3],\ [631, 631, w^3 + 2*w^2 - 8*w - 6],\ [631, 631, 2/3*w^3 + 2*w^2 - 4/3*w - 31/3],\ [631, 631, -2/3*w^3 + 2*w^2 + 16/3*w - 23/3],\ [659, 659, -2/3*w^3 + 1/3*w + 16/3],\ [659, 659, 5/3*w^3 - 34/3*w - 13/3],\ [661, 661, w^3 - 8*w + 2],\ [661, 661, 4/3*w^3 + w^2 - 23/3*w + 1/3],\ [661, 661, 5/3*w^3 + w^2 - 31/3*w - 10/3],\ [661, 661, -3*w - 1],\ [691, 691, -4/3*w^3 + 29/3*w + 2/3],\ [691, 691, 1/3*w^3 + 4/3*w - 5/3],\ [691, 691, -5/3*w^3 + w^2 + 25/3*w - 5/3],\ [691, 691, 2*w^3 + w^2 - 10*w - 7],\ [701, 701, -2/3*w^3 - 3*w^2 + 19/3*w + 46/3],\ [701, 701, w^3 - 2*w^2 - 6*w + 8],\ [701, 701, 4/3*w^3 + 2*w^2 - 17/3*w - 29/3],\ [701, 701, 5/3*w^3 + 3*w^2 - 28/3*w - 52/3],\ [709, 709, 1/3*w^3 - 14/3*w + 10/3],\ [709, 709, -2/3*w^3 + 19/3*w + 7/3],\ [719, 719, 3*w^2 - w - 10],\ [719, 719, -4/3*w^3 - 3*w^2 + 23/3*w + 47/3],\ [739, 739, 5/3*w^3 + w^2 - 34/3*w - 10/3],\ [739, 739, 4/3*w^3 + 2*w^2 - 23/3*w - 14/3],\ [761, 761, 7/3*w^3 + 2*w^2 - 41/3*w - 26/3],\ [761, 761, 2*w^3 + 3*w^2 - 12*w - 15],\ [769, 769, -2/3*w^3 + 19/3*w - 8/3],\ [769, 769, -4/3*w^3 + 2*w^2 + 17/3*w - 31/3],\ [769, 769, 1/3*w^3 - 14/3*w - 5/3],\ [769, 769, -1/3*w^3 + 3*w^2 + 2/3*w - 34/3],\ [809, 809, -4/3*w^3 + w^2 + 26/3*w - 7/3],\ [809, 809, w^3 + w^2 - 3*w - 7],\ [811, 811, 4/3*w^3 + w^2 - 17/3*w - 23/3],\ [811, 811, -1/3*w^3 - 2*w^2 + 2/3*w + 38/3],\ [821, 821, 8/3*w^3 + 3*w^2 - 43/3*w - 34/3],\ [821, 821, 2/3*w^3 + 2*w^2 - 7/3*w - 34/3],\ [821, 821, -w^3 - w^2 + 4*w + 8],\ [821, 821, 2/3*w^3 + 4*w^2 - 7/3*w - 58/3],\ [829, 829, 4/3*w^3 + 3*w^2 - 26/3*w - 50/3],\ [829, 829, 7/3*w^3 - 41/3*w - 5/3],\ [839, 839, 2*w^3 + w^2 - 10*w - 3],\ [839, 839, 5/3*w^3 - w^2 - 25/3*w + 17/3],\ [841, 29, 5/3*w^3 - 25/3*w - 7/3],\ [859, 859, -7/3*w^3 - w^2 + 32/3*w + 29/3],\ [859, 859, 2*w^3 + w^2 - 14*w - 6],\ [859, 859, 1/3*w^3 + 2*w^2 - 2/3*w - 47/3],\ [859, 859, -5/3*w^3 - 2*w^2 + 31/3*w + 49/3],\ [881, 881, w^3 + 4*w^2 - 4*w - 20],\ [881, 881, 8/3*w^3 + 2*w^2 - 43/3*w - 34/3],\ [919, 919, -w^3 + 3*w - 7],\ [919, 919, 1/3*w^3 + 3*w^2 - 5/3*w - 35/3],\ [919, 919, -5/3*w^3 + 31/3*w - 23/3],\ [919, 919, 2/3*w^3 + 3*w^2 - 10/3*w - 43/3],\ [929, 929, w^2 - 2*w - 9],\ [929, 929, w^3 + w^2 - 7*w + 1],\ [961, 31, 2/3*w^3 - 10/3*w - 19/3],\ [971, 971, -w^3 - 3*w^2 + 7*w + 16],\ [971, 971, -5/3*w^3 + w^2 + 25/3*w - 8/3],\ [971, 971, 2*w^3 + w^2 - 10*w - 6],\ [971, 971, 1/3*w^3 + 2*w^2 - 8/3*w - 47/3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^7 - 35*x^5 - 2*x^4 + 360*x^3 - 104*x^2 - 1184*x + 896 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, e, -1/2*e^2 + 1/2*e + 5, 1/8*e^5 - 1/4*e^4 - 23/8*e^3 + 4*e^2 + 27/2*e - 17, -1/2*e^2 + 1/2*e + 5, 1/8*e^5 - 1/4*e^4 - 23/8*e^3 + 4*e^2 + 27/2*e - 17, 1/32*e^6 - 1/8*e^5 - 19/32*e^4 + 45/16*e^3 + 1/2*e^2 - 65/4*e + 20, -1, -1/16*e^6 + 27/16*e^4 + 9/8*e^3 - 11*e^2 - 17/2*e + 20, -1/16*e^6 + 27/16*e^4 + 9/8*e^3 - 11*e^2 - 17/2*e + 20, 1/16*e^6 - 1/4*e^5 - 23/16*e^4 + 45/8*e^3 + 25/4*e^2 - 61/2*e + 17, 1/16*e^6 - 1/4*e^5 - 23/16*e^4 + 45/8*e^3 + 25/4*e^2 - 61/2*e + 17, 1/4*e^5 - 1/4*e^4 - 25/4*e^3 + 13/4*e^2 + 31*e - 21, 1/4*e^5 - 1/4*e^4 - 25/4*e^3 + 13/4*e^2 + 31*e - 21, -1/8*e^6 + 27/8*e^4 + 7/4*e^3 - 41/2*e^2 - 9*e + 24, -1/8*e^6 + 27/8*e^4 + 7/4*e^3 - 41/2*e^2 - 9*e + 24, -1/16*e^6 + 1/4*e^5 + 27/16*e^4 - 49/8*e^3 - 11*e^2 + 67/2*e - 4, -1/16*e^6 + 1/4*e^5 + 27/16*e^4 - 49/8*e^3 - 11*e^2 + 67/2*e - 4, 1/16*e^6 - 1/2*e^5 - 19/16*e^4 + 95/8*e^3 + 4*e^2 - 121/2*e + 28, 1/16*e^6 - 1/2*e^5 - 19/16*e^4 + 95/8*e^3 + 4*e^2 - 121/2*e + 28, -1/8*e^6 + 3/8*e^5 + 23/8*e^4 - 63/8*e^3 - 49/4*e^2 + 43*e - 26, -1/8*e^6 + 3/8*e^5 + 23/8*e^4 - 63/8*e^3 - 49/4*e^2 + 43*e - 26, 1/16*e^6 + 1/4*e^5 - 35/16*e^4 - 59/8*e^3 + 41/2*e^2 + 83/2*e - 64, 1/16*e^6 + 1/4*e^5 - 35/16*e^4 - 59/8*e^3 + 41/2*e^2 + 83/2*e - 64, 1/8*e^5 - 1/4*e^4 - 27/8*e^3 + 9/2*e^2 + 37/2*e - 17, 1/8*e^5 - 1/4*e^4 - 27/8*e^3 + 9/2*e^2 + 37/2*e - 17, -1/16*e^6 - 1/4*e^5 + 27/16*e^4 + 59/8*e^3 - 9*e^2 - 75/2*e + 16, -1/16*e^6 - 1/4*e^5 + 27/16*e^4 + 59/8*e^3 - 9*e^2 - 75/2*e + 16, 1/4*e^5 - 1/2*e^4 - 25/4*e^3 + 9*e^2 + 67/2*e - 39, -1/8*e^6 + 1/8*e^5 + 27/8*e^4 - 13/8*e^3 - 87/4*e^2 + 5*e + 24, -1/8*e^6 + 1/8*e^5 + 27/8*e^4 - 13/8*e^3 - 87/4*e^2 + 5*e + 24, 1/4*e^5 - 1/2*e^4 - 25/4*e^3 + 9*e^2 + 67/2*e - 39, -1/16*e^6 + 1/4*e^5 + 19/16*e^4 - 45/8*e^3 + 67/2*e - 40, -1/16*e^6 + 1/4*e^5 + 19/16*e^4 - 45/8*e^3 + 67/2*e - 40, -3/16*e^6 - 1/8*e^5 + 85/16*e^4 + 23/4*e^3 - 71/2*e^2 - 31*e + 61, -1/4*e^4 + 21/4*e^2 + 5*e - 25, -1/4*e^4 + 21/4*e^2 + 5*e - 25, -3/16*e^6 - 1/8*e^5 + 85/16*e^4 + 23/4*e^3 - 71/2*e^2 - 31*e + 61, 1/8*e^5 - 1/2*e^4 - 27/8*e^3 + 45/4*e^2 + 22*e - 52, 1/8*e^5 - 1/2*e^4 - 27/8*e^3 + 45/4*e^2 + 22*e - 52, 1/4*e^5 - 1/2*e^4 - 25/4*e^3 + 19/2*e^2 + 35*e - 56, 1/4*e^5 - 1/2*e^4 - 25/4*e^3 + 19/2*e^2 + 35*e - 56, -3/16*e^6 + 1/2*e^5 + 69/16*e^4 - 77/8*e^3 - 79/4*e^2 + 91/2*e - 23, -3/16*e^6 + 1/2*e^5 + 69/16*e^4 - 77/8*e^3 - 79/4*e^2 + 91/2*e - 23, 1/4*e^6 - 27/4*e^4 - 5/2*e^3 + 38*e^2 + 4*e - 24, -1/16*e^6 + 19/16*e^4 + 9/8*e^3 + 1/2*e^2 - 9/2*e - 16, -1/16*e^6 + 19/16*e^4 + 9/8*e^3 + 1/2*e^2 - 9/2*e - 16, 1/4*e^5 - 27/4*e^3 + 71/2*e - 23, 1/4*e^5 - 27/4*e^3 + 71/2*e - 23, -1/16*e^6 - 1/4*e^5 + 35/16*e^4 + 55/8*e^3 - 18*e^2 - 67/2*e + 42, -1/16*e^6 - 1/4*e^5 + 35/16*e^4 + 55/8*e^3 - 18*e^2 - 67/2*e + 42, -3/8*e^5 + 1/2*e^4 + 65/8*e^3 - 23/4*e^2 - 30*e + 26, -3/8*e^5 + 1/2*e^4 + 65/8*e^3 - 23/4*e^2 - 30*e + 26, 1/16*e^6 - 27/16*e^4 - 17/8*e^3 + 12*e^2 + 45/2*e - 32, 1/16*e^6 - 27/16*e^4 - 17/8*e^3 + 12*e^2 + 45/2*e - 32, -7/8*e^5 + e^4 + 177/8*e^3 - 55/4*e^2 - 116*e + 80, -7/8*e^5 + e^4 + 177/8*e^3 - 55/4*e^2 - 116*e + 80, 1/16*e^6 + 3/4*e^5 - 43/16*e^4 - 151/8*e^3 + 23*e^2 + 181/2*e - 82, 1/16*e^6 + 3/4*e^5 - 43/16*e^4 - 151/8*e^3 + 23*e^2 + 181/2*e - 82, -1/8*e^6 - 1/8*e^5 + 27/8*e^4 + 41/8*e^3 - 81/4*e^2 - 29*e + 58, -1/16*e^6 + 3/8*e^5 + 23/16*e^4 - 19/2*e^3 - 11/2*e^2 + 56*e - 11, 1/4*e^6 + 1/4*e^5 - 29/4*e^4 - 35/4*e^3 + 95/2*e^2 + 39*e - 78, 1/4*e^6 + 1/4*e^5 - 29/4*e^4 - 35/4*e^3 + 95/2*e^2 + 39*e - 78, 1/8*e^6 - 27/8*e^4 - 3/4*e^3 + 33/2*e^2 - 5*e + 18, 1/8*e^6 - 27/8*e^4 - 3/4*e^3 + 33/2*e^2 - 5*e + 18, 3/16*e^6 + 1/8*e^5 - 85/16*e^4 - 19/4*e^3 + 63/2*e^2 + 15*e - 21, -1/16*e^6 - 1/4*e^5 + 27/16*e^4 + 63/8*e^3 - 8*e^2 - 43*e + 19, 3/16*e^6 + 1/8*e^5 - 85/16*e^4 - 19/4*e^3 + 63/2*e^2 + 15*e - 21, -1/16*e^6 - 1/4*e^5 + 27/16*e^4 + 63/8*e^3 - 8*e^2 - 43*e + 19, -1/4*e^6 + 1/2*e^5 + 25/4*e^4 - 9*e^3 - 63/2*e^2 + 43*e - 26, -5/16*e^6 + 1/4*e^5 + 135/16*e^4 - 21/8*e^3 - 53*e^2 + 35/2*e + 48, -5/16*e^6 + 1/4*e^5 + 135/16*e^4 - 21/8*e^3 - 53*e^2 + 35/2*e + 48, -1/4*e^6 + 1/2*e^5 + 25/4*e^4 - 9*e^3 - 63/2*e^2 + 43*e - 26, 1/16*e^6 - 27/16*e^4 - 1/8*e^3 + 7*e^2 - 11/2*e + 22, 1/16*e^6 - 27/16*e^4 - 1/8*e^3 + 7*e^2 - 11/2*e + 22, -1/4*e^6 - 1/8*e^5 + 27/4*e^4 + 51/8*e^3 - 157/4*e^2 - 28*e + 46, 3/16*e^6 - 1/2*e^5 - 73/16*e^4 + 69/8*e^3 + 55/2*e^2 - 32*e - 29, -1/4*e^6 - 1/8*e^5 + 27/4*e^4 + 51/8*e^3 - 157/4*e^2 - 28*e + 46, 3/16*e^6 - 1/2*e^5 - 73/16*e^4 + 69/8*e^3 + 55/2*e^2 - 32*e - 29, 1/16*e^6 - 27/16*e^4 - 13/8*e^3 + 25/2*e^2 + 23/2*e - 36, 1/16*e^6 - 27/16*e^4 - 1/8*e^3 + 7*e^2 - 7/2*e + 22, 1/16*e^6 - 27/16*e^4 - 13/8*e^3 + 25/2*e^2 + 23/2*e - 36, 1/16*e^6 - 27/16*e^4 - 1/8*e^3 + 7*e^2 - 7/2*e + 22, -3/16*e^6 - 1/2*e^5 + 97/16*e^4 + 111/8*e^3 - 47*e^2 - 127/2*e + 110, -3/16*e^6 - 1/2*e^5 + 97/16*e^4 + 111/8*e^3 - 47*e^2 - 127/2*e + 110, -1/16*e^6 + 1/4*e^5 + 27/16*e^4 - 53/8*e^3 - 17/2*e^2 + 81/2*e - 26, -1/16*e^6 + 1/4*e^5 + 27/16*e^4 - 53/8*e^3 - 17/2*e^2 + 81/2*e - 26, 3/16*e^6 + 1/4*e^5 - 89/16*e^4 - 61/8*e^3 + 36*e^2 + 34*e - 43, 1/16*e^6 + 1/4*e^5 - 27/16*e^4 - 55/8*e^3 + 7*e^2 + 33*e - 7, 1/16*e^6 + 1/4*e^5 - 27/16*e^4 - 55/8*e^3 + 7*e^2 + 33*e - 7, 3/16*e^6 + 1/4*e^5 - 89/16*e^4 - 61/8*e^3 + 36*e^2 + 34*e - 43, 1/8*e^6 - 3/4*e^5 - 19/8*e^4 + 35/2*e^3 + 2*e^2 - 95*e + 94, 1/8*e^6 - 3/4*e^5 - 19/8*e^4 + 35/2*e^3 + 2*e^2 - 95*e + 94, 1/16*e^6 + 1/4*e^5 - 35/16*e^4 - 51/8*e^3 + 35/2*e^2 + 65/2*e - 50, 1/16*e^6 + 1/4*e^5 - 35/16*e^4 - 51/8*e^3 + 35/2*e^2 + 65/2*e - 50, 1/8*e^5 - 39/8*e^3 + 9/4*e^2 + 42*e - 26, 1/8*e^5 - 39/8*e^3 + 9/4*e^2 + 42*e - 26, 5/16*e^6 - 1/4*e^5 - 135/16*e^4 + 33/8*e^3 + 93/2*e^2 - 67/2*e + 8, -1/8*e^6 + 1/4*e^5 + 23/8*e^4 - 9/2*e^3 - 10*e^2 + 23*e - 26, -1/8*e^6 + 1/4*e^5 + 23/8*e^4 - 9/2*e^3 - 10*e^2 + 23*e - 26, 5/16*e^6 - 1/4*e^5 - 135/16*e^4 + 33/8*e^3 + 93/2*e^2 - 67/2*e + 8, 3/8*e^6 - 5/8*e^5 - 75/8*e^4 + 85/8*e^3 + 101/2*e^2 - 115/2*e - 19, 3/8*e^6 - 5/8*e^5 - 75/8*e^4 + 85/8*e^3 + 101/2*e^2 - 115/2*e - 19, 3/16*e^6 - 1/4*e^5 - 73/16*e^4 + 31/8*e^3 + 41/2*e^2 - 53/2*e + 18, 3/16*e^6 - 1/4*e^5 - 73/16*e^4 + 31/8*e^3 + 41/2*e^2 - 53/2*e + 18, 1/8*e^6 + 1/4*e^5 - 29/8*e^4 - 7*e^3 + 91/4*e^2 + 30*e - 43, 1/8*e^6 + 1/4*e^5 - 29/8*e^4 - 7*e^3 + 91/4*e^2 + 30*e - 43, 1/8*e^6 - 27/8*e^4 - 5/4*e^3 + 20*e^2 + 4*e - 30, 1/8*e^6 - 27/8*e^4 - 5/4*e^3 + 20*e^2 + 4*e - 30, 7/16*e^6 - 1/4*e^5 - 181/16*e^4 - 1/8*e^3 + 65*e^2 + 11/2*e - 62, 7/16*e^6 - 1/4*e^5 - 181/16*e^4 - 1/8*e^3 + 65*e^2 + 11/2*e - 62, 1/8*e^6 + 3/8*e^5 - 29/8*e^4 - 87/8*e^3 + 45/2*e^2 + 101/2*e - 43, 1/8*e^6 + 3/8*e^5 - 29/8*e^4 - 87/8*e^3 + 45/2*e^2 + 101/2*e - 43, -1/8*e^6 + 7/8*e^5 + 19/8*e^4 - 167/8*e^3 - 5/4*e^2 + 113*e - 120, -1/8*e^6 + 7/8*e^5 + 19/8*e^4 - 167/8*e^3 - 5/4*e^2 + 113*e - 120, 1/4*e^5 - 29/4*e^3 + 3*e^2 + 42*e - 52, 1/4*e^5 - 29/4*e^3 + 3*e^2 + 42*e - 52, -1/8*e^6 + 1/4*e^5 + 25/8*e^4 - 5*e^3 - 59/4*e^2 + 24*e - 13, -5/16*e^6 + 7/8*e^5 + 123/16*e^4 - 39/2*e^3 - 40*e^2 + 113*e - 27, -5/16*e^6 + 7/8*e^5 + 123/16*e^4 - 39/2*e^3 - 40*e^2 + 113*e - 27, -1/8*e^6 + 1/4*e^5 + 25/8*e^4 - 5*e^3 - 59/4*e^2 + 24*e - 13, -1/16*e^6 - 1/4*e^5 + 31/16*e^4 + 75/8*e^3 - 73/4*e^2 - 135/2*e + 75, -1/16*e^6 - 1/4*e^5 + 31/16*e^4 + 75/8*e^3 - 73/4*e^2 - 135/2*e + 75, 1/8*e^6 + 7/8*e^5 - 35/8*e^4 - 179/8*e^3 + 119/4*e^2 + 101*e - 64, 1/8*e^6 + 7/8*e^5 - 35/8*e^4 - 179/8*e^3 + 119/4*e^2 + 101*e - 64, -1/16*e^6 + 1/2*e^5 + 27/16*e^4 - 107/8*e^3 - 19/2*e^2 + 80*e - 41, -1/16*e^6 + 1/8*e^5 + 31/16*e^4 - 9/4*e^3 - 19*e^2 + 4*e + 51, -1/16*e^6 + 1/8*e^5 + 31/16*e^4 - 9/4*e^3 - 19*e^2 + 4*e + 51, -1/16*e^6 + 1/2*e^5 + 27/16*e^4 - 107/8*e^3 - 19/2*e^2 + 80*e - 41, 1/16*e^6 + 3/4*e^5 - 43/16*e^4 - 151/8*e^3 + 27*e^2 + 181/2*e - 122, 1/16*e^6 + 3/4*e^5 - 43/16*e^4 - 151/8*e^3 + 27*e^2 + 181/2*e - 122, 5/16*e^6 - 1/4*e^5 - 135/16*e^4 + 25/8*e^3 + 107/2*e^2 - 41/2*e - 62, 5/16*e^6 - 1/4*e^5 - 135/16*e^4 + 25/8*e^3 + 107/2*e^2 - 41/2*e - 62, 1/16*e^6 + 3/4*e^5 - 43/16*e^4 - 159/8*e^3 + 24*e^2 + 215/2*e - 106, 1/16*e^6 + 3/4*e^5 - 43/16*e^4 - 159/8*e^3 + 24*e^2 + 215/2*e - 106, 3/16*e^6 - 9/8*e^5 - 53/16*e^4 + 49/2*e^3 + 11/2*e^2 - 114*e + 81, 3/16*e^6 - 9/8*e^5 - 53/16*e^4 + 49/2*e^3 + 11/2*e^2 - 114*e + 81, 3/16*e^6 - e^5 - 57/16*e^4 + 185/8*e^3 + 5*e^2 - 265/2*e + 110, 3/16*e^6 + 1/4*e^5 - 81/16*e^4 - 65/8*e^3 + 49/2*e^2 + 65/2*e - 2, 3/16*e^6 - e^5 - 57/16*e^4 + 185/8*e^3 + 5*e^2 - 265/2*e + 110, 3/16*e^6 + 1/4*e^5 - 81/16*e^4 - 65/8*e^3 + 49/2*e^2 + 65/2*e - 2, 1/4*e^6 - 1/4*e^5 - 27/4*e^4 + 19/4*e^3 + 36*e^2 - 38*e + 24, 1/4*e^6 - 1/4*e^5 - 27/4*e^4 + 19/4*e^3 + 36*e^2 - 38*e + 24, -1/4*e^6 - 7/8*e^5 + 17/2*e^4 + 193/8*e^3 - 139/2*e^2 - 235/2*e + 179, -1/4*e^6 - 7/8*e^5 + 17/2*e^4 + 193/8*e^3 - 139/2*e^2 - 235/2*e + 179, 1/16*e^6 + 13/8*e^5 - 63/16*e^4 - 85/2*e^3 + 47*e^2 + 227*e - 241, 1/8*e^6 + 1/4*e^5 - 25/8*e^4 - 17/2*e^3 + 55/4*e^2 + 44*e - 15, 1/8*e^6 + 1/4*e^5 - 25/8*e^4 - 17/2*e^3 + 55/4*e^2 + 44*e - 15, 1/16*e^6 + 13/8*e^5 - 63/16*e^4 - 85/2*e^3 + 47*e^2 + 227*e - 241, -1/2*e^6 + 1/4*e^5 + 27/2*e^4 - 1/4*e^3 - 82*e^2 + 8*e + 72, -1/2*e^6 + 1/4*e^5 + 27/2*e^4 - 1/4*e^3 - 82*e^2 + 8*e + 72, -3/16*e^6 - 5/4*e^5 + 121/16*e^4 + 253/8*e^3 - 143/2*e^2 - 303/2*e + 216, -3/16*e^6 - 5/4*e^5 + 121/16*e^4 + 253/8*e^3 - 143/2*e^2 - 303/2*e + 216, -1/4*e^4 + 1/2*e^3 + 11/4*e^2 - 3*e + 49, 3/4*e^5 - 3/2*e^4 - 73/4*e^3 + 27*e^2 + 97*e - 126, -1/8*e^6 + 23/8*e^4 + 13/4*e^3 - 23/2*e^2 - 26*e + 6, 3/4*e^5 - 3/2*e^4 - 73/4*e^3 + 27*e^2 + 97*e - 126, -1/8*e^6 + 23/8*e^4 + 13/4*e^3 - 23/2*e^2 - 26*e + 6, -1/16*e^6 - 7/8*e^5 + 47/16*e^4 + 95/4*e^3 - 34*e^2 - 126*e + 159, -1/16*e^6 - 7/8*e^5 + 47/16*e^4 + 95/4*e^3 - 34*e^2 - 126*e + 159, -1/8*e^6 + 1/4*e^5 + 19/8*e^4 - 3*e^3 - 5*e^2 + 8*e - 10, -1/16*e^6 + 1/2*e^5 + 19/16*e^4 - 103/8*e^3 + 2*e^2 + 133/2*e - 108, -1/8*e^6 + 1/4*e^5 + 19/8*e^4 - 3*e^3 - 5*e^2 + 8*e - 10, -1/16*e^6 + 1/2*e^5 + 19/16*e^4 - 103/8*e^3 + 2*e^2 + 133/2*e - 108, 1/2*e^5 - e^4 - 11*e^3 + 33/2*e^2 + 51*e - 70, 1/2*e^5 - e^4 - 11*e^3 + 33/2*e^2 + 51*e - 70, 3/8*e^6 - 1/2*e^5 - 77/8*e^4 + 37/4*e^3 + 50*e^2 - 57*e + 46, 1/8*e^6 - 1/8*e^5 - 25/8*e^4 + 17/8*e^3 + 29/2*e^2 - 43/2*e + 17, -1/4*e^6 - 1/8*e^5 + 31/4*e^4 + 35/8*e^3 - 221/4*e^2 - 12*e + 68, -1/4*e^6 - 1/8*e^5 + 31/4*e^4 + 35/8*e^3 - 221/4*e^2 - 12*e + 68, 1/8*e^6 - 1/8*e^5 - 25/8*e^4 + 17/8*e^3 + 29/2*e^2 - 43/2*e + 17] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([25, 5, 2/3*w^3 - 10/3*w - 1/3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]