/* 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, 3, 4, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([27, 3, -w^3 + w^2 + 3*w - 2]) primes_array = [ [3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3],\ [9, 3, -w^4 + 5*w^2 - 3],\ [9, 3, -w^4 + w^3 + 5*w^2 - 3*w - 2],\ [13, 13, -w^4 + w^3 + 4*w^2 - 3*w - 1],\ [17, 17, w^4 - w^3 - 5*w^2 + 3*w + 1],\ [19, 19, -w^3 + w^2 + 4*w - 2],\ [23, 23, -w^2 + 3],\ [31, 31, w^3 - 4*w + 2],\ [32, 2, 2],\ [37, 37, w^3 - 3*w - 1],\ [53, 53, -2*w^4 + w^3 + 9*w^2 - 3*w - 2],\ [59, 59, -w^4 + 5*w^2 + w - 4],\ [61, 61, -w^4 + w^3 + 5*w^2 - 4*w],\ [67, 67, -w^4 + 6*w^2 + 2*w - 4],\ [71, 71, 2*w^4 - w^3 - 9*w^2 + 4*w + 5],\ [79, 79, 2*w^4 - w^3 - 10*w^2 + 2*w + 7],\ [83, 83, -w^4 + 2*w^3 + 5*w^2 - 7*w - 2],\ [83, 83, -w^4 + w^3 + 4*w^2 - 3*w + 3],\ [83, 83, w^4 - w^3 - 5*w^2 + 4*w - 1],\ [83, 83, -w^4 + w^3 + 4*w^2 - 4*w - 2],\ [83, 83, -2*w^4 + w^3 + 9*w^2 - 3*w - 5],\ [97, 97, -w^4 - w^3 + 6*w^2 + 4*w - 4],\ [101, 101, -w^4 + 4*w^2 + 2*w - 2],\ [107, 107, -2*w^4 + w^3 + 11*w^2 - 3*w - 7],\ [127, 127, w^3 - w^2 - 4*w],\ [131, 131, w^4 - w^3 - 4*w^2 + 2*w - 1],\ [137, 137, w^4 - w^3 - 6*w^2 + 3*w + 3],\ [139, 139, -2*w^4 + w^3 + 9*w^2 - 3*w + 1],\ [157, 157, 2*w^4 - w^3 - 9*w^2 + 4*w + 2],\ [163, 163, -w^2 - 2*w + 3],\ [167, 167, w^4 - 5*w^2 + 2*w + 1],\ [169, 13, -2*w^4 + 2*w^3 + 9*w^2 - 7*w - 5],\ [169, 13, w^4 - 2*w^3 - 5*w^2 + 8*w + 2],\ [191, 191, 2*w^4 - w^3 - 9*w^2 + 3*w + 4],\ [193, 193, 2*w^4 - 2*w^3 - 8*w^2 + 7*w],\ [199, 199, -w^4 + 2*w^3 + 5*w^2 - 9*w - 3],\ [211, 211, -3*w^4 + w^3 + 13*w^2 - 2*w - 1],\ [227, 227, 2*w^3 - w^2 - 9*w + 1],\ [233, 233, -w^3 + w^2 + 4*w + 1],\ [251, 251, -3*w^4 + 14*w^2 + w - 2],\ [257, 257, -2*w^4 + 2*w^3 + 10*w^2 - 6*w - 5],\ [257, 257, -w^4 + w^3 + 5*w^2 - 6*w - 1],\ [257, 257, 2*w^4 - 2*w^3 - 11*w^2 + 9*w + 9],\ [257, 257, -2*w^4 + 2*w^3 + 9*w^2 - 6*w - 3],\ [257, 257, 2*w^4 - w^3 - 10*w^2 + 5*w + 5],\ [269, 269, -w^4 + 2*w^3 + 4*w^2 - 6*w - 2],\ [271, 271, -w^4 + 4*w^2 + w - 3],\ [277, 277, -2*w^4 + 9*w^2 + w - 4],\ [281, 281, w^4 - w^3 - 3*w^2 + 3*w - 4],\ [283, 283, 2*w^4 - 3*w^3 - 8*w^2 + 13*w],\ [289, 17, -w^4 + w^3 + 7*w^2 - 5*w - 5],\ [289, 17, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 6],\ [293, 293, -2*w^4 + 11*w^2 - 7],\ [317, 317, w^3 - 6*w],\ [337, 337, -w^4 + 2*w^3 + 5*w^2 - 9*w - 1],\ [337, 337, w^4 - 2*w^3 - 5*w^2 + 6*w + 3],\ [337, 337, -w^4 + w^3 + 5*w^2 - 4*w - 6],\ [337, 337, -2*w^3 + 8*w + 1],\ [337, 337, w^2 + w - 5],\ [347, 347, -2*w^4 + w^3 + 9*w^2 - 5*w - 3],\ [349, 349, 3*w^4 - 2*w^3 - 13*w^2 + 8*w + 2],\ [353, 353, w^4 - 3*w^3 - 4*w^2 + 12*w + 2],\ [359, 359, 2*w^3 - w^2 - 7*w + 3],\ [361, 19, w^4 - 2*w^3 - 4*w^2 + 7*w + 3],\ [361, 19, w^4 - w^3 - 3*w^2 + 3*w - 3],\ [367, 367, -2*w^4 + w^3 + 9*w^2 - w - 2],\ [379, 379, -2*w^3 + w^2 + 7*w + 2],\ [379, 379, -2*w^4 + w^3 + 10*w^2 - 4*w],\ [379, 379, 2*w^3 - w^2 - 6*w - 2],\ [379, 379, -2*w^3 + 2*w^2 + 6*w - 3],\ [379, 379, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 6],\ [383, 383, 2*w^4 + w^3 - 10*w^2 - 7*w + 4],\ [383, 383, -2*w^3 + w^2 + 10*w],\ [383, 383, w^3 + w^2 - 5*w - 1],\ [383, 383, 3*w^4 + 3*w^3 - 15*w^2 - 15*w + 4],\ [383, 383, -2*w^4 + 3*w^3 + 10*w^2 - 10*w - 2],\ [389, 389, 3*w^4 - w^3 - 14*w^2 + 3*w + 3],\ [397, 397, w^4 - 6*w^2 - 2*w + 5],\ [397, 397, w^4 - 2*w^3 - 2*w^2 + 6*w - 5],\ [397, 397, 2*w^4 - 2*w^3 - 11*w^2 + 10*w + 6],\ [397, 397, w^4 - w^3 - 3*w^2 + 4*w - 6],\ [397, 397, w^3 + w^2 - 3*w - 4],\ [401, 401, w^3 - w^2 - 6*w + 3],\ [401, 401, -w^4 + 4*w^2 + 2*w - 3],\ [401, 401, -w^4 + 6*w^2 - w - 7],\ [421, 421, -w^4 - w^3 + 5*w^2 + 5*w - 4],\ [421, 421, -w^4 + w^3 + 6*w^2 - 3*w - 2],\ [421, 421, -w^4 - w^3 + 6*w^2 + 6*w - 5],\ [421, 421, 3*w^4 - w^3 - 15*w^2 + w + 10],\ [421, 421, 2*w^4 - 9*w^2 + 2*w + 4],\ [431, 431, 2*w^4 - 11*w^2 - 2*w + 11],\ [439, 439, 2*w^4 - 3*w^3 - 9*w^2 + 10*w + 6],\ [443, 443, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 2],\ [449, 449, -w^4 + 2*w^3 + 5*w^2 - 6*w - 4],\ [461, 461, 3*w^4 - 4*w^3 - 14*w^2 + 14*w + 5],\ [463, 463, w^3 - 6*w - 1],\ [467, 467, 3*w^4 - 3*w^3 - 13*w^2 + 10*w],\ [487, 487, 3*w^4 - w^3 - 14*w^2 + w + 3],\ [487, 487, 2*w^2 - w - 4],\ [487, 487, -2*w^4 + 2*w^3 + 9*w^2 - 8*w - 5],\ [487, 487, 2*w^4 - 10*w^2 - 3*w + 4],\ [487, 487, -2*w^4 + w^3 + 8*w^2 - 3*w - 1],\ [499, 499, -w^4 + 2*w^3 + 4*w^2 - 8*w - 2],\ [499, 499, -2*w^4 + w^3 + 10*w^2 - w - 9],\ [499, 499, -w^3 - 2*w^2 + 2*w + 5],\ [499, 499, -w^4 + 4*w^2 + 4*w],\ [499, 499, -2*w^4 + w^3 + 12*w^2 - 4*w - 9],\ [509, 509, 3*w^4 - 2*w^3 - 16*w^2 + 6*w + 9],\ [521, 521, -2*w^4 + w^3 + 10*w^2 - 5*w - 4],\ [523, 523, w - 4],\ [529, 23, -w^3 + 2*w^2 + 4*w - 4],\ [529, 23, w^4 + 2*w^3 - 6*w^2 - 11*w + 4],\ [569, 569, -2*w^4 + 11*w^2 - 10],\ [571, 571, -2*w^4 + w^3 + 10*w^2 - 3*w - 2],\ [593, 593, -2*w^4 + 3*w^3 + 10*w^2 - 11*w - 8],\ [613, 613, -2*w^3 + 2*w^2 + 9*w - 5],\ [617, 617, -2*w^4 + 10*w^2 - w - 7],\ [631, 631, -2*w^4 + 2*w^3 + 7*w^2 - 8*w + 3],\ [641, 641, -2*w^4 + 2*w^3 + 8*w^2 - 9*w + 3],\ [643, 643, -3*w^4 + w^3 + 13*w^2 - w + 1],\ [643, 643, w^4 + w^3 - 3*w^2 - 6*w - 2],\ [643, 643, -w^4 - w^3 + 6*w^2 + 3*w - 4],\ [643, 643, 2*w^4 - w^3 - 10*w^2 + 4*w + 1],\ [643, 643, 2*w^4 - 2*w^3 - 8*w^2 + 6*w + 5],\ [647, 647, -2*w^3 + w^2 + 6*w - 4],\ [659, 659, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 10],\ [661, 661, 2*w^4 + 3*w^3 - 11*w^2 - 14*w + 6],\ [673, 673, w^4 - 3*w^3 - 3*w^2 + 10*w - 1],\ [683, 683, w^4 - 2*w^3 - 4*w^2 + 6*w - 4],\ [701, 701, w^3 - w^2 - 2*w + 4],\ [727, 727, -w^4 + 6*w^2 + 2*w - 7],\ [743, 743, w^4 - w^3 - 7*w^2 + 5*w + 9],\ [769, 769, w^4 + 2*w^3 - 5*w^2 - 9*w + 4],\ [787, 787, w^4 + w^3 - 7*w^2 - 3*w + 5],\ [797, 797, -2*w^4 - w^3 + 10*w^2 + 4*w - 4],\ [797, 797, w^4 - 3*w^3 - 5*w^2 + 12*w + 5],\ [797, 797, -3*w^4 + 2*w^3 + 13*w^2 - 8*w],\ [797, 797, -w^4 + w^3 + 3*w^2 - 5*w - 1],\ [797, 797, 2*w^4 - 11*w^2 + 2*w + 7],\ [809, 809, -4*w^4 + 2*w^3 + 18*w^2 - 6*w + 1],\ [809, 809, 3*w^4 - 3*w^3 - 14*w^2 + 11*w + 8],\ [809, 809, w^4 - 2*w^3 - 2*w^2 + 8*w - 4],\ [809, 809, 2*w^4 - 8*w^2 - 2*w + 3],\ [809, 809, 2*w^4 - 3*w^3 - 9*w^2 + 13*w + 4],\ [821, 821, -2*w^4 + 2*w^3 + 8*w^2 - 6*w + 3],\ [823, 823, -2*w^4 + 3*w^3 + 8*w^2 - 12*w - 1],\ [829, 829, 2*w^4 - 3*w^3 - 10*w^2 + 13*w + 4],\ [839, 839, -2*w^4 + 12*w^2 - w - 10],\ [863, 863, 2*w^4 - w^3 - 9*w^2 + 5],\ [877, 877, -w^4 + w^3 + 5*w^2 - 5*w - 7],\ [881, 881, 2*w^4 - w^3 - 9*w^2 + w - 1],\ [887, 887, 3*w^4 - 3*w^3 - 15*w^2 + 11*w + 6],\ [907, 907, -3*w^4 + w^3 + 13*w^2 - w - 5],\ [919, 919, w^4 + w^3 - 3*w^2 - 5*w - 3],\ [929, 929, 2*w^4 - 3*w^3 - 10*w^2 + 9*w + 4],\ [937, 937, -2*w^4 + 10*w^2 + 3*w - 7],\ [941, 941, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\ [961, 31, 2*w^4 + 2*w^3 - 10*w^2 - 12*w + 5],\ [961, 31, -w^4 + 5*w^2 - w - 7],\ [967, 967, -2*w^4 + w^3 + 9*w^2 - 3*w + 2],\ [991, 991, -3*w^4 + w^3 + 15*w^2 - 4*w - 5],\ [997, 997, -3*w^4 + 15*w^2 - 5],\ [997, 997, 2*w^4 - w^3 - 9*w^2 + 6*w + 2],\ [997, 997, 2*w^4 - w^3 - 11*w^2 + w + 7],\ [997, 997, 2*w^3 - 5*w - 1],\ [997, 997, 2*w^4 - 3*w^3 - 6*w^2 + 5*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - 7*x^4 + 6*x^3 + 35*x^2 - 40*x - 20 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, e, -1, 2/5*e^4 - 7/5*e^3 - 2*e^2 + 5*e + 2, 3/10*e^4 - 13/10*e^3 - 2*e^2 + 15/2*e + 4, 1/5*e^4 - 6/5*e^3 + 7*e - 1, -2/5*e^4 + 7/5*e^3 + 3*e^2 - 8*e - 4, 1/10*e^4 - 1/10*e^3 - e^2 - 3/2*e + 4, 1/10*e^4 - 1/10*e^3 - e^2 - 1/2*e, e^2 - 3*e - 2, 1/2*e^4 - 3/2*e^3 - 5*e^2 + 17/2*e + 14, -1/5*e^4 + 6/5*e^3 - 2*e^2 - 2*e + 11, -1/5*e^4 + 1/5*e^3 + 2*e^2 + 2*e - 2, 3/5*e^4 - 18/5*e^3 + e^2 + 16*e - 5, -e^3 + 4*e^2 + e - 8, 3/5*e^4 - 13/5*e^3 - e^2 + 7*e + 2, 3/5*e^4 - 13/5*e^3 - e^2 + 8*e - 4, -2/5*e^4 + 2/5*e^3 + 5*e^2 - 4, -e^4 + 4*e^3 + 3*e^2 - 16*e + 9, -1/5*e^4 + 6/5*e^3 - 2*e^2 - 2*e + 10, -1/2*e^4 + 5/2*e^3 + e^2 - 21/2*e + 4, 2*e^3 - 6*e^2 - 11*e + 8, 3/5*e^4 - 13/5*e^3 - e^2 + 11*e - 1, -1/5*e^4 + 1/5*e^3 + 2*e^2 - e - 1, -4/5*e^4 + 24/5*e^3 - 22*e + 7, -3*e^2 + 4*e + 22, 3/5*e^4 - 13/5*e^3 + 6*e, 1/5*e^4 - 6/5*e^3 + e^2 + 8*e - 16, 17/10*e^4 - 67/10*e^3 - 8*e^2 + 63/2*e + 2, -2/5*e^4 + 2/5*e^3 + 6*e^2 - 5*e - 4, 1/5*e^4 - 16/5*e^3 + 7*e^2 + 17*e - 18, -1/5*e^4 + 6/5*e^3 - 8*e - 4, -2/5*e^4 + 12/5*e^3 - 15*e + 12, -7/5*e^4 + 32/5*e^3 + 5*e^2 - 31*e - 1, 3/2*e^4 - 11/2*e^3 - 9*e^2 + 41/2*e + 24, -7/5*e^4 + 37/5*e^3 + 2*e^2 - 34*e + 2, 1/5*e^4 + 4/5*e^3 - 8*e^2 + 26, -1/5*e^4 + 6/5*e^3 - 2*e^2 - 7*e + 24, -1/5*e^4 + 1/5*e^3 + 5*e + 15, -3*e^3 + 8*e^2 + 18*e - 18, -2/5*e^4 + 12/5*e^3 - 20*e + 10, -2/5*e^4 + 22/5*e^3 - 7*e^2 - 16*e + 20, -1/5*e^4 + 1/5*e^3 + 3*e^2 - 4*e + 14, -e^4 + 2*e^3 + 10*e^2 - 4*e - 22, 9/10*e^4 - 59/10*e^3 + 4*e^2 + 47/2*e - 14, -2/5*e^4 + 17/5*e^3 - 4*e^2 - 9*e + 12, -6/5*e^4 + 31/5*e^3 + 2*e^2 - 22*e - 12, 1/5*e^4 - 1/5*e^3 - 3*e^2 + 7, -3/10*e^4 + 23/10*e^3 + e^2 - 27/2*e - 14, -1/5*e^4 + 6/5*e^3 + e^2 - 5*e - 20, 6/5*e^4 - 26/5*e^3 - 6*e^2 + 28*e + 14, -7/10*e^4 + 27/10*e^3 + 9*e^2 - 39/2*e - 34, -7/5*e^4 + 17/5*e^3 + 14*e^2 - 16*e - 24, 2/5*e^4 - 7/5*e^3 - 3*e^2 + 7*e + 6, -12/5*e^4 + 57/5*e^3 + 4*e^2 - 48*e, -1/5*e^4 + 1/5*e^3 - 2*e^2 + 14*e + 14, -e^3 + 5*e^2 + 6*e - 22, -2/5*e^4 + 2/5*e^3 + e^2 + 10*e + 10, 4/5*e^4 - 4/5*e^3 - 12*e^2 + 2*e + 24, -1/5*e^4 + 16/5*e^3 - 7*e^2 - 18*e + 24, -7/5*e^4 + 32/5*e^3 - 2*e^2 - 13*e + 27, 6/5*e^4 - 26/5*e^3 - 6*e^2 + 26*e + 3, -9/5*e^4 + 44/5*e^3 + 2*e^2 - 35*e + 14, -1/2*e^4 + 5/2*e^3 - 2*e^2 - 5/2*e + 22, -7/5*e^4 + 27/5*e^3 + 7*e^2 - 30*e + 4, 9/10*e^4 - 39/10*e^3 + 9/2*e - 14, 9/5*e^4 - 39/5*e^3 - 6*e^2 + 30*e + 6, -2*e^4 + 12*e^3 - 4*e^2 - 51*e + 20, 13/5*e^4 - 63/5*e^3 - 4*e^2 + 51*e + 2, -e^4 + 4*e^3 + 6*e^2 - 28*e, 4/5*e^4 - 19/5*e^3 - 2*e^2 + 21*e - 4, -8/5*e^4 + 28/5*e^3 + 11*e^2 - 26*e - 18, 1/5*e^4 + 4/5*e^3 - 7*e^2 - e + 18, -1/5*e^4 + 6/5*e^3 - e^2 - 2*e - 15, -1/2*e^4 + 7/2*e^3 - 3*e^2 - 41/2*e + 4, -7/5*e^4 + 27/5*e^3 + 6*e^2 - 20*e - 4, 8/5*e^4 - 33/5*e^3 - 4*e^2 + 20*e + 2, 6/5*e^4 - 31/5*e^3 + 3*e^2 + 19*e - 28, 1/5*e^4 - 1/5*e^3 - 2*e^2 + 2*e + 12, -4/5*e^4 + 19/5*e^3 + 5*e^2 - 25*e - 3, 2/5*e^4 + 8/5*e^3 - 11*e^2 - 14*e + 26, e^4 - 4*e^3 - 6*e^2 + 24*e - 7, 4/5*e^4 - 19/5*e^3 - 2*e^2 + 14*e + 8, -14/5*e^4 + 59/5*e^3 + 10*e^2 - 50*e - 4, 8/5*e^4 - 23/5*e^3 - 12*e^2 + 21*e + 14, 1/5*e^4 - 16/5*e^3 + 5*e^2 + 21*e - 14, -12/5*e^4 + 57/5*e^3 + 8*e^2 - 54*e - 6, 3/10*e^4 - 13/10*e^3 + 2*e^2 + 5/2*e - 12, -7/5*e^4 + 22/5*e^3 + 14*e^2 - 22*e - 36, -14/5*e^4 + 69/5*e^3 + 2*e^2 - 53*e + 16, 6/5*e^4 - 16/5*e^3 - 9*e^2 + 14*e + 6, 6/5*e^4 - 16/5*e^3 - 11*e^2 + 15*e + 4, e^4 - 4*e^3 - 2*e^2 + 4*e + 4, -9/5*e^4 + 24/5*e^3 + 16*e^2 - 16*e - 36, 3/5*e^4 - 13/5*e^3 - 7*e^2 + 22*e + 14, -8/5*e^4 + 18/5*e^3 + 17*e^2 - 14*e - 48, 4/5*e^4 - 24/5*e^3 - e^2 + 29*e + 4, -2/5*e^4 + 22/5*e^3 - 9*e^2 - 9*e + 30, -e^4 + 3*e^3 + 8*e^2 - 13*e - 12, -7/5*e^4 + 22/5*e^3 + 10*e^2 - 24*e, -6/5*e^4 + 16/5*e^3 + 16*e^2 - 26*e - 46, e^4 - 7*e^3 + 7*e^2 + 28*e - 22, -9/5*e^4 + 39/5*e^3 + 9*e^2 - 46*e - 6, -2/5*e^4 + 7/5*e^3 - e^2 + 3*e + 2, -e^4 + 5*e^3 - e^2 - 20*e + 30, 2/5*e^4 - 17/5*e^3 + 3*e^2 + 22*e - 12, 9/10*e^4 - 9/10*e^3 - 10*e^2 - 21/2*e + 28, 1/10*e^4 - 31/10*e^3 + 8*e^2 + 27/2*e - 18, -7/5*e^4 + 22/5*e^3 + 11*e^2 - 14*e - 36, 1/5*e^4 + 4/5*e^3 - 8*e^2 - 4*e + 28, 4/5*e^4 - 14/5*e^3 - 2*e^2 + 3*e + 6, -4/5*e^4 + 4/5*e^3 + 13*e^2 - 8*e - 36, -8/5*e^4 + 38/5*e^3 + 5*e^2 - 31*e + 8, 2/5*e^4 - 7/5*e^3 - 4*e^2 + 17*e - 10, -e^4 + 6*e^3 - 5*e^2 - 19*e + 24, -3/10*e^4 + 33/10*e^3 - 9*e^2 + 5/2*e + 28, -9/5*e^4 + 19/5*e^3 + 19*e^2 - 12*e - 38, -19/5*e^4 + 79/5*e^3 + 15*e^2 - 69*e - 4, e^3 - 3*e^2 - 4*e + 12, -4/5*e^4 + 14/5*e^3 + 7*e^2 - 19*e - 12, 2*e^4 - 8*e^3 - 12*e^2 + 45*e - 6, e^4 - e^3 - 12*e^2 - 7*e + 24, 3*e^4 - 14*e^3 - 10*e^2 + 66*e + 4, -19/10*e^4 + 69/10*e^3 + 15*e^2 - 69/2*e - 44, 11/10*e^4 - 51/10*e^3 - 2*e^2 + 43/2*e - 20, -2/5*e^4 - 3/5*e^3 + 13*e^2 - 4*e - 48, -8/5*e^4 + 38/5*e^3 + 6*e^2 - 39*e - 10, 4/5*e^4 - 4/5*e^3 - 9*e^2 - 2*e + 10, -1/10*e^4 + 1/10*e^3 - 5/2*e + 12, 12/5*e^4 - 57/5*e^3 - 6*e^2 + 63*e - 10, 17/5*e^4 - 67/5*e^3 - 14*e^2 + 51*e + 16, -21/10*e^4 + 61/10*e^3 + 12*e^2 - 31/2*e + 2, -13/10*e^4 + 23/10*e^3 + 12*e^2 - 19/2*e + 4, -13/10*e^4 + 73/10*e^3 + e^2 - 79/2*e + 22, 31/10*e^4 - 131/10*e^3 - 9*e^2 + 99/2*e - 20, -e^4 + 2*e^3 + 10*e^2 - e - 2, 6/5*e^4 - 6/5*e^3 - 14*e^2 - 10*e + 37, 8/5*e^4 - 38/5*e^3 - 6*e^2 + 38*e + 10, -11/10*e^4 + 61/10*e^3 + e^2 - 59/2*e + 16, 5/2*e^4 - 15/2*e^3 - 18*e^2 + 65/2*e + 20, -6/5*e^4 + 21/5*e^3 + 14*e^2 - 26*e - 44, -9/5*e^4 + 39/5*e^3 + 3*e^2 - 28*e + 34, -e^4 + 3*e^3 + 5*e^2 - 7*e + 25, -7/5*e^4 + 47/5*e^3 - 7*e^2 - 42*e + 12, -7/10*e^4 + 17/10*e^3 + 9*e^2 - 9/2*e - 32, 13/10*e^4 - 83/10*e^3 + 3*e^2 + 73/2*e - 10, -7/5*e^4 + 12/5*e^3 + 20*e^2 - 8*e - 58, -7/5*e^4 + 17/5*e^3 + 13*e^2 - 20*e - 3, -33/10*e^4 + 143/10*e^3 + 12*e^2 - 131/2*e - 2, -2*e^4 + 9*e^3 - e^2 - 22*e + 23, 3/5*e^4 - 23/5*e^3 + 28*e + 4, -3/5*e^4 - 12/5*e^3 + 17*e^2 + 15*e - 44, 6/5*e^4 - 26/5*e^3 - 4*e^2 + 17*e + 22, 1/5*e^4 - 16/5*e^3 + 10*e^2 + 11*e - 36, -11/5*e^4 + 46/5*e^3 + 9*e^2 - 26*e - 24, -6/5*e^4 + 46/5*e^3 - 4*e^2 - 52*e + 14, -13/5*e^4 + 53/5*e^3 + 15*e^2 - 49*e - 45, e^4 - 7*e^3 + 4*e^2 + 30*e - 38, 17/10*e^4 - 67/10*e^3 - 5*e^2 + 59/2*e - 4, -8/5*e^4 - 2/5*e^3 + 30*e^2 + e - 59, -11/5*e^4 + 61/5*e^3 - 2*e^2 - 51*e + 8, 6/5*e^4 - 16/5*e^3 - 7*e^2 - 4*e + 32, -4/5*e^4 + 14/5*e^3 + 9*e^2 - 15*e - 18, 6/5*e^4 - 46/5*e^3 + 5*e^2 + 62*e - 28, -e^4 + e^3 + 15*e^2 - 7*e - 22, 4/5*e^4 - 9/5*e^3 - 14*e^2 + 12*e + 39] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3])] = -1 AL_eigenvalues[ZF.ideal([9, 3, -w^4 + w^3 + 5*w^2 - 3*w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]