/* 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, -12, 12, 7, -7, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([44, 22, -2*w^5 + 13*w^3 - w^2 - 19*w + 4]) primes_array = [ [4, 2, -w^5 + 6*w^3 + w^2 - 8*w - 2],\ [11, 11, w + 1],\ [16, 2, -w^5 + 6*w^3 + w^2 - 7*w - 2],\ [19, 19, -w^3 + w^2 + 4*w - 3],\ [29, 29, 2*w^5 - 13*w^3 + 19*w - 2],\ [31, 31, -2*w^5 + 12*w^3 + w^2 - 16*w - 2],\ [41, 41, -w^5 + 7*w^3 + w^2 - 12*w - 2],\ [41, 41, 2*w^5 + w^4 - 13*w^3 - 5*w^2 + 19*w + 4],\ [59, 59, -w^5 + 7*w^3 + w^2 - 11*w],\ [61, 61, w^5 - 7*w^3 + 10*w],\ [61, 61, -2*w^5 + 12*w^3 + w^2 - 16*w - 3],\ [71, 71, -2*w^5 - w^4 + 12*w^3 + 5*w^2 - 16*w - 4],\ [71, 71, -3*w^5 - w^4 + 20*w^3 + 6*w^2 - 31*w - 5],\ [71, 71, -w^5 + 7*w^3 - w^2 - 12*w + 2],\ [79, 79, w^5 + w^4 - 7*w^3 - 5*w^2 + 10*w + 4],\ [79, 79, -w^5 - w^4 + 8*w^3 + 4*w^2 - 15*w + 1],\ [79, 79, 2*w^5 + w^4 - 13*w^3 - 5*w^2 + 20*w + 3],\ [89, 89, 2*w^5 + w^4 - 14*w^3 - 5*w^2 + 23*w + 1],\ [89, 89, -2*w^5 - w^4 + 12*w^3 + 5*w^2 - 15*w - 4],\ [89, 89, 2*w^5 + w^4 - 11*w^3 - 5*w^2 + 13*w + 3],\ [101, 101, w^5 + w^4 - 7*w^3 - 3*w^2 + 11*w - 2],\ [109, 109, w^5 + w^4 - 8*w^3 - 4*w^2 + 14*w],\ [121, 11, -w^5 - w^4 + 8*w^3 + 4*w^2 - 13*w - 2],\ [125, 5, -w^5 + 6*w^3 - 8*w - 2],\ [131, 131, -w^4 + 5*w^2 - w - 3],\ [131, 131, -w^5 - w^4 + 6*w^3 + 5*w^2 - 9*w - 3],\ [139, 139, 2*w^5 - w^4 - 11*w^3 + 4*w^2 + 12*w - 2],\ [149, 149, w^5 + w^4 - 7*w^3 - 5*w^2 + 9*w + 4],\ [151, 151, w^5 - 8*w^3 + 2*w^2 + 15*w - 6],\ [151, 151, -w^5 + 7*w^3 - 12*w + 3],\ [151, 151, w^5 - 5*w^3 + 4*w - 3],\ [151, 151, -w^4 + w^3 + 5*w^2 - 4*w - 5],\ [179, 179, -3*w^5 - w^4 + 20*w^3 + 4*w^2 - 29*w - 1],\ [179, 179, -3*w^5 - 2*w^4 + 20*w^3 + 10*w^2 - 31*w - 6],\ [179, 179, -w^4 + 3*w^2 - 2*w + 2],\ [179, 179, 3*w^5 + w^4 - 18*w^3 - 4*w^2 + 23*w + 1],\ [181, 181, -2*w^5 - w^4 + 13*w^3 + 4*w^2 - 20*w + 1],\ [181, 181, w^5 - 8*w^3 + 14*w - 3],\ [191, 191, w^5 + w^4 - 7*w^3 - 6*w^2 + 11*w + 5],\ [199, 199, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 23*w - 5],\ [199, 199, w^5 + w^4 - 8*w^3 - 6*w^2 + 14*w + 4],\ [199, 199, -w^5 + 6*w^3 + 2*w^2 - 8*w - 2],\ [199, 199, w^5 - w^4 - 6*w^3 + 4*w^2 + 8*w - 2],\ [211, 211, -3*w^5 - 2*w^4 + 20*w^3 + 9*w^2 - 30*w - 5],\ [229, 229, 2*w^5 + w^4 - 14*w^3 - 4*w^2 + 22*w - 1],\ [229, 229, 4*w^5 + w^4 - 25*w^3 - 5*w^2 + 35*w + 1],\ [239, 239, 2*w^4 - w^3 - 8*w^2 + 5*w + 2],\ [241, 241, w^4 - 3*w^2 + w - 2],\ [251, 251, -3*w^5 - 2*w^4 + 21*w^3 + 9*w^2 - 33*w - 3],\ [251, 251, -3*w^5 - w^4 + 21*w^3 + 4*w^2 - 34*w + 1],\ [251, 251, -2*w^5 - 2*w^4 + 15*w^3 + 9*w^2 - 26*w - 4],\ [251, 251, 2*w^5 - 11*w^3 + w^2 + 12*w - 3],\ [269, 269, -2*w^5 + 11*w^3 - w^2 - 12*w + 1],\ [271, 271, -w^5 + 5*w^3 - w^2 - 5*w + 3],\ [281, 281, w^4 - w^3 - 5*w^2 + 5*w + 5],\ [289, 17, -2*w^5 - w^4 + 11*w^3 + 4*w^2 - 12*w - 2],\ [311, 311, -3*w^5 + 19*w^3 - w^2 - 26*w + 4],\ [311, 311, -w^4 + 3*w^2 - w + 3],\ [311, 311, 3*w^5 - 19*w^3 + w^2 + 27*w - 4],\ [311, 311, w^5 + 2*w^4 - 7*w^3 - 10*w^2 + 12*w + 8],\ [331, 331, -3*w^5 - w^4 + 19*w^3 + 4*w^2 - 27*w - 1],\ [349, 349, -2*w^5 - 2*w^4 + 14*w^3 + 8*w^2 - 22*w - 3],\ [349, 349, -2*w^5 - w^4 + 14*w^3 + 4*w^2 - 22*w + 2],\ [349, 349, 3*w^5 + w^4 - 19*w^3 - 6*w^2 + 25*w + 4],\ [359, 359, -4*w^5 - w^4 + 25*w^3 + 4*w^2 - 35*w + 2],\ [359, 359, 4*w^5 + w^4 - 25*w^3 - 6*w^2 + 34*w + 4],\ [361, 19, 2*w^5 - w^4 - 12*w^3 + 5*w^2 + 15*w - 6],\ [379, 379, 2*w^5 + 2*w^4 - 14*w^3 - 8*w^2 + 23*w + 1],\ [379, 379, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 23*w - 7],\ [389, 389, w^5 - w^4 - 4*w^3 + 5*w^2 + w - 3],\ [401, 401, -w^5 + w^4 + 7*w^3 - 4*w^2 - 12*w + 1],\ [401, 401, -3*w^5 - 2*w^4 + 20*w^3 + 8*w^2 - 31*w - 2],\ [401, 401, 2*w^5 + w^4 - 11*w^3 - 6*w^2 + 12*w + 5],\ [401, 401, -4*w^5 - w^4 + 26*w^3 + 4*w^2 - 38*w + 1],\ [409, 409, -w^5 + w^4 + 7*w^3 - 4*w^2 - 11*w + 3],\ [409, 409, 3*w^5 - 17*w^3 - w^2 + 20*w + 2],\ [419, 419, -3*w^5 - w^4 + 21*w^3 + 4*w^2 - 33*w + 1],\ [419, 419, -2*w^5 + w^4 + 12*w^3 - 5*w^2 - 16*w + 4],\ [419, 419, -2*w^5 - 2*w^4 + 15*w^3 + 9*w^2 - 26*w - 3],\ [419, 419, w^2 + 2*w - 2],\ [421, 421, 3*w^5 + w^4 - 21*w^3 - 5*w^2 + 34*w],\ [421, 421, w^4 - 4*w^2 - 2*w + 2],\ [421, 421, -3*w^5 + 18*w^3 + w^2 - 24*w - 3],\ [421, 421, -2*w^5 + 14*w^3 + w^2 - 22*w + 1],\ [431, 431, 2*w^5 + w^4 - 13*w^3 - 3*w^2 + 18*w - 1],\ [431, 431, 3*w^5 + 2*w^4 - 20*w^3 - 8*w^2 + 30*w + 1],\ [431, 431, 2*w^5 + w^4 - 11*w^3 - 6*w^2 + 12*w + 7],\ [439, 439, -3*w^5 + 19*w^3 + 2*w^2 - 27*w - 3],\ [461, 461, -3*w^5 + 20*w^3 - w^2 - 30*w + 5],\ [461, 461, w^5 - 5*w^3 + 5*w - 3],\ [491, 491, -w^5 - w^4 + 9*w^3 + 4*w^2 - 18*w + 1],\ [491, 491, 2*w^5 - w^4 - 12*w^3 + 3*w^2 + 15*w],\ [499, 499, -3*w^5 - w^4 + 20*w^3 + 5*w^2 - 29*w - 3],\ [499, 499, -2*w^5 - w^4 + 12*w^3 + 4*w^2 - 16*w - 3],\ [509, 509, -w^5 + w^4 + 6*w^3 - 4*w^2 - 9*w],\ [509, 509, 2*w^5 - 14*w^3 + 24*w - 3],\ [509, 509, -2*w^5 - w^4 + 14*w^3 + 5*w^2 - 24*w],\ [509, 509, -2*w^5 - 2*w^4 + 14*w^3 + 9*w^2 - 22*w - 5],\ [569, 569, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 17*w + 3],\ [571, 571, -w^5 + w^4 + 5*w^3 - 4*w^2 - 5*w - 1],\ [571, 571, -w^5 - w^4 + 8*w^3 + 3*w^2 - 16*w + 2],\ [571, 571, -2*w^5 + 13*w^3 - 21*w + 2],\ [571, 571, 2*w^5 + w^4 - 12*w^3 - 7*w^2 + 15*w + 8],\ [571, 571, 2*w^5 + 2*w^4 - 13*w^3 - 10*w^2 + 19*w + 8],\ [571, 571, 2*w^5 - 12*w^3 + 15*w - 4],\ [601, 601, 3*w^5 + 2*w^4 - 21*w^3 - 9*w^2 + 33*w + 2],\ [601, 601, 3*w^5 + w^4 - 19*w^3 - 3*w^2 + 25*w - 4],\ [601, 601, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 22*w - 5],\ [601, 601, -3*w^5 - w^4 + 18*w^3 + 6*w^2 - 23*w - 6],\ [619, 619, w^5 + w^4 - 7*w^3 - 5*w^2 + 13*w + 4],\ [631, 631, 2*w^5 + w^4 - 15*w^3 - 4*w^2 + 26*w - 1],\ [631, 631, -2*w^5 + 12*w^3 + w^2 - 14*w - 4],\ [641, 641, -w^5 + w^4 + 6*w^3 - 6*w^2 - 9*w + 7],\ [641, 641, -2*w^5 - w^4 + 13*w^3 + 7*w^2 - 19*w - 8],\ [659, 659, 2*w^5 - w^4 - 12*w^3 + 4*w^2 + 16*w - 4],\ [659, 659, 2*w^5 - 13*w^3 + 20*w - 4],\ [661, 661, -2*w^5 - w^4 + 13*w^3 + 3*w^2 - 19*w],\ [661, 661, -w^5 - w^4 + 6*w^3 + 7*w^2 - 8*w - 8],\ [661, 661, -3*w^5 - 2*w^4 + 21*w^3 + 10*w^2 - 34*w - 5],\ [691, 691, 3*w^5 + w^4 - 20*w^3 - 3*w^2 + 31*w - 3],\ [691, 691, 5*w^5 + 2*w^4 - 34*w^3 - 9*w^2 + 54*w + 3],\ [691, 691, -2*w^5 - w^4 + 13*w^3 + 5*w^2 - 22*w - 1],\ [691, 691, 3*w^5 + w^4 - 19*w^3 - 5*w^2 + 28*w],\ [691, 691, w^5 + w^4 - 8*w^3 - 3*w^2 + 14*w - 4],\ [691, 691, -w^5 - 2*w^4 + 8*w^3 + 9*w^2 - 15*w - 5],\ [701, 701, -3*w^5 - w^4 + 19*w^3 + 7*w^2 - 26*w - 11],\ [709, 709, -w^5 + 7*w^3 - w^2 - 13*w + 4],\ [709, 709, -w^5 + 4*w^3 - 2*w - 4],\ [709, 709, 2*w^5 + 2*w^4 - 15*w^3 - 8*w^2 + 27*w + 1],\ [709, 709, -w^5 - w^4 + 6*w^3 + 6*w^2 - 7*w - 4],\ [719, 719, -w^4 + w^3 + 4*w^2 - 3*w + 2],\ [719, 719, -3*w^5 - w^4 + 20*w^3 + 6*w^2 - 32*w - 2],\ [729, 3, -3],\ [739, 739, w^5 + 2*w^4 - 7*w^3 - 9*w^2 + 11*w + 7],\ [739, 739, -3*w^5 - 2*w^4 + 21*w^3 + 10*w^2 - 34*w - 6],\ [739, 739, w^5 + w^4 - 6*w^3 - 3*w^2 + 9*w - 3],\ [739, 739, w^4 + w^3 - 4*w^2 - 2*w + 1],\ [739, 739, -3*w^5 + 18*w^3 + w^2 - 23*w + 1],\ [739, 739, 3*w^5 - 18*w^3 - 2*w^2 + 24*w + 5],\ [751, 751, -w^5 + w^4 + 5*w^3 - 5*w^2 - 5*w + 2],\ [761, 761, -w^5 - 2*w^4 + 8*w^3 + 8*w^2 - 15*w - 4],\ [761, 761, -w^5 + 6*w^3 - 6*w + 2],\ [769, 769, w^3 - 2*w^2 - 3*w + 3],\ [811, 811, -3*w^5 + 19*w^3 + w^2 - 25*w - 1],\ [829, 829, -2*w^5 + w^4 + 13*w^3 - 4*w^2 - 19*w + 2],\ [829, 829, 3*w^5 + w^4 - 20*w^3 - 4*w^2 + 29*w - 1],\ [839, 839, -2*w^5 - w^4 + 15*w^3 + 5*w^2 - 25*w - 1],\ [839, 839, -w^5 + 6*w^3 + 2*w^2 - 6*w - 6],\ [841, 29, 4*w^5 + 2*w^4 - 27*w^3 - 10*w^2 + 41*w + 5],\ [859, 859, -2*w^5 + 13*w^3 - 17*w + 2],\ [881, 881, -2*w^5 - 2*w^4 + 14*w^3 + 8*w^2 - 23*w - 3],\ [881, 881, w^5 - 7*w^3 + w^2 + 11*w],\ [911, 911, 4*w^5 - 25*w^3 + 35*w - 3],\ [911, 911, 6*w^5 + 2*w^4 - 39*w^3 - 11*w^2 + 58*w + 5],\ [919, 919, w^4 + w^3 - 6*w^2 - 3*w + 6],\ [919, 919, -3*w^5 + 17*w^3 - 20*w + 1],\ [929, 929, -w^3 + 2*w^2 + 3*w - 8],\ [941, 941, 2*w^5 + 2*w^4 - 15*w^3 - 8*w^2 + 27*w],\ [941, 941, 2*w^5 + w^4 - 15*w^3 - 3*w^2 + 25*w - 3],\ [961, 31, -3*w^5 - w^4 + 18*w^3 + 6*w^2 - 21*w - 6],\ [971, 971, -w^5 + 4*w^3 + 2*w^2 - 5],\ [991, 991, -2*w^5 - 3*w^4 + 14*w^3 + 13*w^2 - 22*w - 6],\ [1009, 1009, -3*w^5 + 17*w^3 - 20*w],\ [1009, 1009, 4*w^5 - 25*w^3 + 35*w - 1],\ [1019, 1019, -3*w^5 + 17*w^3 + 2*w^2 - 20*w - 4],\ [1019, 1019, -w^5 + 5*w^3 - w^2 - 3*w + 1],\ [1019, 1019, -w^3 + 2*w^2 + 5*w - 5],\ [1021, 1021, 2*w^5 + w^4 - 13*w^3 - 4*w^2 + 18*w + 3],\ [1031, 1031, 2*w^5 - 11*w^3 - 2*w^2 + 12*w + 6],\ [1031, 1031, 2*w^5 - 14*w^3 + w^2 + 23*w - 2],\ [1039, 1039, w^4 - 2*w^3 - 5*w^2 + 7*w + 5],\ [1039, 1039, 2*w^5 - w^4 - 11*w^3 + 5*w^2 + 13*w - 5],\ [1039, 1039, -w^5 - w^4 + 7*w^3 + 6*w^2 - 13*w - 6],\ [1039, 1039, 4*w^5 + w^4 - 23*w^3 - 5*w^2 + 28*w + 3],\ [1049, 1049, -w^5 + w^4 + 6*w^3 - 6*w^2 - 9*w + 6],\ [1049, 1049, -3*w^5 + 19*w^3 + w^2 - 25*w + 2],\ [1051, 1051, w^5 + w^4 - 7*w^3 - 2*w^2 + 12*w - 5],\ [1069, 1069, w^5 + 2*w^4 - 7*w^3 - 9*w^2 + 12*w + 6],\ [1091, 1091, -4*w^5 + w^4 + 24*w^3 - 4*w^2 - 30*w + 2],\ [1109, 1109, w^5 + w^4 - 5*w^3 - 5*w^2 + 6*w + 3],\ [1129, 1129, -3*w^5 + 19*w^3 + 2*w^2 - 26*w - 3],\ [1129, 1129, -2*w^5 - w^4 + 14*w^3 + 2*w^2 - 22*w + 2],\ [1129, 1129, 2*w^5 - 11*w^3 - 2*w^2 + 11*w + 3],\ [1129, 1129, -4*w^5 - 2*w^4 + 25*w^3 + 11*w^2 - 35*w - 11],\ [1151, 1151, 2*w^5 + w^4 - 14*w^3 - 5*w^2 + 21*w + 4],\ [1181, 1181, w^5 - 7*w^3 + w^2 + 12*w],\ [1201, 1201, w^5 + 2*w^4 - 6*w^3 - 9*w^2 + 8*w + 5],\ [1229, 1229, w^5 + 2*w^4 - 8*w^3 - 10*w^2 + 14*w + 6],\ [1229, 1229, 2*w^5 + w^4 - 13*w^3 - 5*w^2 + 17*w + 4],\ [1231, 1231, -2*w^5 - 2*w^4 + 15*w^3 + 9*w^2 - 25*w - 3],\ [1249, 1249, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 21*w - 7],\ [1249, 1249, -w^5 - w^4 + 7*w^3 + 7*w^2 - 11*w - 8],\ [1259, 1259, w^3 + w^2 - 3*w - 5],\ [1259, 1259, -w^5 - w^4 + 9*w^3 + 3*w^2 - 19*w + 2],\ [1259, 1259, -w^4 + w^3 + 3*w^2 - 3*w + 4],\ [1279, 1279, -5*w^5 - 2*w^4 + 35*w^3 + 9*w^2 - 57*w - 2],\ [1279, 1279, 3*w^5 + 2*w^4 - 20*w^3 - 9*w^2 + 31*w + 5],\ [1289, 1289, -w^5 + w^4 + 5*w^3 - 5*w^2 - 6*w + 4],\ [1291, 1291, w^5 + w^4 - 7*w^3 - 3*w^2 + 10*w - 4],\ [1291, 1291, -w^5 - w^4 + 9*w^3 + 3*w^2 - 18*w + 4],\ [1291, 1291, 2*w^5 - 13*w^3 + 17*w],\ [1291, 1291, -5*w^5 - 3*w^4 + 32*w^3 + 15*w^2 - 46*w - 8],\ [1321, 1321, w^4 - w^3 - 4*w^2 + 2*w - 1],\ [1321, 1321, 2*w^5 - 2*w^4 - 12*w^3 + 8*w^2 + 14*w - 3],\ [1321, 1321, 3*w^5 - 19*w^3 - 2*w^2 + 26*w + 4],\ [1321, 1321, -2*w^5 - w^4 + 12*w^3 + 3*w^2 - 15*w + 1],\ [1331, 11, -3*w^5 + 18*w^3 - 24*w + 1],\ [1361, 1361, -4*w^5 - w^4 + 25*w^3 + 6*w^2 - 35*w - 6],\ [1381, 1381, -2*w^5 - 3*w^4 + 14*w^3 + 14*w^2 - 24*w - 6],\ [1381, 1381, -3*w^5 - w^4 + 19*w^3 + 4*w^2 - 28*w + 3],\ [1381, 1381, 2*w^5 + w^4 - 12*w^3 - 3*w^2 + 15*w - 3],\ [1399, 1399, 4*w^5 + 2*w^4 - 27*w^3 - 10*w^2 + 44*w + 4],\ [1409, 1409, 2*w^5 - 14*w^3 + 21*w - 1],\ [1429, 1429, -3*w^5 - w^4 + 20*w^3 + 6*w^2 - 29*w - 5],\ [1429, 1429, -3*w^5 + 18*w^3 - w^2 - 23*w + 3],\ [1429, 1429, w^4 - 2*w^2 - 2*w - 5],\ [1439, 1439, 3*w^5 + 3*w^4 - 19*w^3 - 14*w^2 + 27*w + 5],\ [1451, 1451, w^5 + 2*w^4 - 10*w^3 - 6*w^2 + 22*w - 4],\ [1459, 1459, -w^5 + w^4 + 7*w^3 - 5*w^2 - 10*w + 4],\ [1471, 1471, -w^5 - 2*w^4 + 9*w^3 + 9*w^2 - 17*w - 6],\ [1481, 1481, 2*w^5 + w^4 - 14*w^3 - 5*w^2 + 21*w + 5],\ [1489, 1489, 3*w^5 - w^4 - 17*w^3 + 3*w^2 + 22*w - 2],\ [1499, 1499, -2*w^4 + w^3 + 8*w^2 - 3*w - 4],\ [1511, 1511, 3*w^5 - 18*w^3 - 2*w^2 + 23*w + 4],\ [1511, 1511, w^5 + 2*w^4 - 8*w^3 - 10*w^2 + 14*w + 8],\ [1511, 1511, w^5 + 2*w^4 - 10*w^3 - 7*w^2 + 22*w - 3],\ [1511, 1511, 5*w^5 + w^4 - 29*w^3 - 5*w^2 + 34*w + 4],\ [1531, 1531, 2*w^4 - 3*w^3 - 8*w^2 + 8*w + 2],\ [1549, 1549, -4*w^5 + 27*w^3 - 41*w + 6],\ [1549, 1549, w^5 + w^4 - 7*w^3 - 4*w^2 + 13*w + 5],\ [1559, 1559, 2*w^5 - 11*w^3 + w^2 + 12*w - 4],\ [1559, 1559, -w^5 + 6*w^3 + w^2 - 10*w - 3],\ [1571, 1571, w^3 + 2*w^2 - 4*w - 6],\ [1579, 1579, 2*w^5 + 2*w^4 - 15*w^3 - 11*w^2 + 26*w + 8],\ [1601, 1601, -w^5 + 8*w^3 - 2*w^2 - 16*w + 3],\ [1601, 1601, 3*w^5 + 2*w^4 - 19*w^3 - 7*w^2 + 27*w - 2],\ [1609, 1609, -5*w^5 - 2*w^4 + 32*w^3 + 10*w^2 - 47*w - 2],\ [1619, 1619, 4*w^5 + 3*w^4 - 25*w^3 - 14*w^2 + 35*w + 8],\ [1619, 1619, -2*w^5 + 13*w^3 - 17*w + 1],\ [1621, 1621, -5*w^5 - 3*w^4 + 34*w^3 + 15*w^2 - 53*w - 7],\ [1621, 1621, 4*w^5 + 2*w^4 - 26*w^3 - 7*w^2 + 38*w - 5],\ [1669, 1669, w^5 + w^4 - 9*w^3 - 4*w^2 + 17*w - 1],\ [1681, 41, 4*w^5 - 24*w^3 - 2*w^2 + 33*w + 5],\ [1681, 41, 2*w^4 - 2*w^3 - 9*w^2 + 6*w + 4],\ [1699, 1699, -3*w^5 - 2*w^4 + 18*w^3 + 10*w^2 - 24*w - 3],\ [1699, 1699, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w + 4],\ [1699, 1699, 4*w^5 - w^4 - 23*w^3 + 3*w^2 + 28*w - 1],\ [1699, 1699, 2*w^4 - w^3 - 8*w^2 + 3*w + 2],\ [1709, 1709, -4*w^5 - 2*w^4 + 26*w^3 + 11*w^2 - 38*w - 7],\ [1709, 1709, 3*w^5 - 17*w^3 + w^2 + 20*w - 4],\ [1721, 1721, 2*w^5 + 2*w^4 - 14*w^3 - 9*w^2 + 22*w - 1],\ [1721, 1721, -2*w^5 + w^4 + 12*w^3 - 5*w^2 - 17*w + 5],\ [1721, 1721, w^5 - w^4 - 7*w^3 + 7*w^2 + 10*w - 12],\ [1721, 1721, -2*w^5 - w^4 + 16*w^3 + 4*w^2 - 30*w + 4],\ [1741, 1741, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 15*w + 1],\ [1741, 1741, 3*w^5 + 2*w^4 - 19*w^3 - 10*w^2 + 26*w + 8],\ [1759, 1759, 3*w^5 + w^4 - 19*w^3 - 6*w^2 + 25*w + 5],\ [1789, 1789, w^4 + w^3 - 4*w^2 - 5*w + 2],\ [1789, 1789, w^5 - 3*w^3 - 3*w + 3],\ [1789, 1789, -3*w^5 - w^4 + 19*w^3 + 7*w^2 - 26*w - 8],\ [1789, 1789, 2*w^5 - 13*w^3 + w^2 + 20*w - 1],\ [1801, 1801, 6*w^5 + 2*w^4 - 39*w^3 - 9*w^2 + 56*w + 3],\ [1811, 1811, 2*w^5 + w^4 - 15*w^3 - 4*w^2 + 26*w - 3],\ [1811, 1811, -4*w^5 - w^4 + 26*w^3 + 5*w^2 - 37*w - 5],\ [1811, 1811, -4*w^5 + w^4 + 23*w^3 - 3*w^2 - 27*w],\ [1831, 1831, 5*w^5 + w^4 - 30*w^3 - 4*w^2 + 39*w],\ [1831, 1831, 2*w^5 - 12*w^3 - w^2 + 16*w + 6],\ [1831, 1831, 2*w^5 + 2*w^4 - 14*w^3 - 12*w^2 + 22*w + 13],\ [1831, 1831, w^5 - 7*w^3 + 11*w + 3],\ [1871, 1871, 3*w^5 + w^4 - 21*w^3 - 3*w^2 + 32*w - 1],\ [1871, 1871, 3*w^5 + w^4 - 17*w^3 - 7*w^2 + 22*w + 8],\ [1871, 1871, w - 4],\ [1879, 1879, -3*w^5 - 2*w^4 + 21*w^3 + 9*w^2 - 32*w - 6],\ [1901, 1901, 3*w^5 + 2*w^4 - 20*w^3 - 7*w^2 + 31*w - 5],\ [1931, 1931, -4*w^5 - 3*w^4 + 27*w^3 + 15*w^2 - 41*w - 10],\ [1931, 1931, -3*w^5 - w^4 + 19*w^3 + 7*w^2 - 26*w - 7],\ [1949, 1949, -2*w^5 - 3*w^4 + 13*w^3 + 13*w^2 - 19*w - 8],\ [1949, 1949, -5*w^5 - 2*w^4 + 33*w^3 + 8*w^2 - 50*w - 2],\ [1949, 1949, -4*w^5 - 2*w^4 + 28*w^3 + 11*w^2 - 45*w - 6],\ [1951, 1951, 5*w^5 + w^4 - 31*w^3 - 3*w^2 + 42*w - 5],\ [1951, 1951, 3*w^5 + 2*w^4 - 21*w^3 - 11*w^2 + 35*w + 8],\ [1979, 1979, 5*w^5 + w^4 - 31*w^3 - 3*w^2 + 43*w - 6],\ [1979, 1979, -5*w^5 - w^4 + 31*w^3 + 7*w^2 - 42*w - 9],\ [1999, 1999, -3*w^5 - w^4 + 21*w^3 + 4*w^2 - 33*w + 2],\ [1999, 1999, 3*w^5 + 2*w^4 - 17*w^3 - 10*w^2 + 20*w + 7],\ [1999, 1999, w^5 + w^4 - 9*w^3 - 5*w^2 + 19*w + 6]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -1, 1, -8, -6, 4, 2, -2, 8, -2, -6, 12, 8, -8, -8, -16, -12, -14, 18, -10, 10, -6, -10, 14, 0, -20, 0, -6, 0, -12, 16, -8, 0, 12, 12, -24, -10, 2, -8, -24, -16, 16, 0, 16, 14, 26, -8, -18, 12, -12, -4, 4, 18, 0, 2, -2, 8, 24, -4, -20, 20, -26, 18, -6, -24, 8, -34, -28, 4, 2, 14, -10, 10, -6, -14, 10, -8, 12, -12, 4, 18, -6, 6, -26, 32, -12, -24, 0, 14, -18, -28, -36, 4, 4, 26, -2, 30, -30, 2, -12, -4, 28, -44, 20, 40, 10, -26, -22, -2, 36, 16, 20, 30, 14, -36, 28, -38, 18, -22, -4, 16, -24, 52, 0, -4, -18, -10, 14, -22, -22, 8, -24, -26, 20, 20, 8, 4, -4, -12, -48, -34, 50, -2, -20, 54, -2, 0, -24, -2, -52, -14, 34, -20, 24, 24, -24, 30, 38, 18, -10, 20, 40, -22, -22, -4, -8, 4, -18, -8, 32, 4, -32, 56, -44, 22, 54, 28, 10, -28, -46, -26, -22, -22, -10, -16, 18, -34, -6, -26, -24, 50, -54, 0, -12, -12, 40, 0, -6, -20, 20, 36, -4, 46, 26, -58, 42, 40, -62, 6, -30, -34, -12, -62, 66, 10, -46, 24, -36, -24, -44, -2, -26, 12, 0, 8, 0, 0, 20, -62, 14, 20, 0, -48, -12, -18, -18, -10, 0, -12, 30, 10, 42, 38, 54, 4, -36, -56, 16, -30, -30, 2, -42, -22, -54, -14, 10, 4, 2, -46, -62, -22, 26, -36, -44, -40, 72, -68, 12, 12, -56, -68, 32, 80, 14, 12, -36, 46, 18, -34, -80, 48, -80, 4, -32, -76, -52] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, -w^5 + 6*w^3 + w^2 - 8*w - 2])] = -1 AL_eigenvalues[ZF.ideal([11, 11, w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]