/* 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([41, 41, 2*w^5 + w^4 - 13*w^3 - 5*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^4 + x^3 - 12*x^2 - 8*x - 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e, 4/5*e^3 + 1/5*e^2 - 9*e - 12/5, 7/5*e^3 + 3/5*e^2 - 17*e - 36/5, -6/5*e^3 - 4/5*e^2 + 15*e + 13/5, -8/5*e^3 - 7/5*e^2 + 18*e + 39/5, -4/5*e^3 - 1/5*e^2 + 11*e + 7/5, 1, -3/5*e^3 - 2/5*e^2 + 7*e + 34/5, -13/5*e^3 - 12/5*e^2 + 29*e + 59/5, -5*e^3 - 4*e^2 + 59*e + 21, 11/5*e^3 + 9/5*e^2 - 26*e - 93/5, -7/5*e^3 - 3/5*e^2 + 19*e + 31/5, -1/5*e^3 - 4/5*e^2 + e + 3/5, 4/5*e^3 + 1/5*e^2 - 11*e - 7/5, -11/5*e^3 - 9/5*e^2 + 27*e + 3/5, 19/5*e^3 + 11/5*e^2 - 45*e - 37/5, -18/5*e^3 - 22/5*e^2 + 44*e + 129/5, -e^3 + 14*e - 6, -8/5*e^3 - 2/5*e^2 + 19*e + 29/5, 26/5*e^3 + 19/5*e^2 - 67*e - 118/5, 14/5*e^3 + 16/5*e^2 - 35*e - 77/5, 14/5*e^3 + 11/5*e^2 - 36*e - 72/5, 3/5*e^3 + 2/5*e^2 - 8*e - 14/5, 5*e^3 + 4*e^2 - 61*e - 30, -11/5*e^3 - 4/5*e^2 + 27*e + 3/5, 19/5*e^3 + 16/5*e^2 - 42*e - 112/5, -14/5*e^3 - 6/5*e^2 + 32*e + 17/5, 21/5*e^3 + 19/5*e^2 - 54*e - 143/5, -26/5*e^3 - 14/5*e^2 + 66*e + 93/5, 13/5*e^3 + 7/5*e^2 - 32*e - 124/5, 17/5*e^3 + 13/5*e^2 - 40*e - 101/5, -6*e^3 - 5*e^2 + 73*e + 28, 27/5*e^3 + 18/5*e^2 - 71*e - 106/5, 9/5*e^3 + 16/5*e^2 - 23*e - 62/5, 7*e^3 + 4*e^2 - 82*e - 23, 39/5*e^3 + 26/5*e^2 - 98*e - 182/5, 33/5*e^3 + 27/5*e^2 - 82*e - 169/5, -43/5*e^3 - 22/5*e^2 + 106*e + 164/5, -10*e^3 - 7*e^2 + 120*e + 39, 49/5*e^3 + 26/5*e^2 - 123*e - 182/5, -26/5*e^3 - 19/5*e^2 + 65*e + 183/5, 47/5*e^3 + 23/5*e^2 - 114*e - 156/5, 3/5*e^3 + 7/5*e^2 - 11*e - 4/5, -21/5*e^3 - 14/5*e^2 + 50*e - 7/5, -22/5*e^3 - 18/5*e^2 + 51*e + 126/5, 1/5*e^3 - 6/5*e^2 - 2*e + 27/5, -4*e^3 - 2*e^2 + 55*e + 8, -3/5*e^3 + 3/5*e^2 + 7*e - 21/5, 7*e^3 + 4*e^2 - 86*e - 20, 18/5*e^3 + 12/5*e^2 - 39*e - 99/5, -48/5*e^3 - 27/5*e^2 + 113*e + 124/5, -42/5*e^3 - 33/5*e^2 + 99*e + 151/5, -3*e^3 + 37*e - 2, -8*e^3 - 6*e^2 + 98*e + 42, -27/5*e^3 - 23/5*e^2 + 66*e + 46/5, 24/5*e^3 + 6/5*e^2 - 57*e + 13/5, 52/5*e^3 + 33/5*e^2 - 121*e - 221/5, -29/5*e^3 - 26/5*e^2 + 77*e + 202/5, 36/5*e^3 + 29/5*e^2 - 87*e - 183/5, -59/5*e^3 - 31/5*e^2 + 148*e + 232/5, 23/5*e^3 + 12/5*e^2 - 58*e - 94/5, -38/5*e^3 - 17/5*e^2 + 94*e + 144/5, 33/5*e^3 + 12/5*e^2 - 83*e - 79/5, 9*e^3 + 3*e^2 - 113*e - 25, -8/5*e^3 - 2/5*e^2 + 22*e - 36/5, -2/5*e^3 - 18/5*e^2 + 7*e + 151/5, -46/5*e^3 - 29/5*e^2 + 109*e + 208/5, 43/5*e^3 + 37/5*e^2 - 105*e - 199/5, -29/5*e^3 - 6/5*e^2 + 72*e + 57/5, -e^3 - e^2 + 9*e - 3, 47/5*e^3 + 23/5*e^2 - 107*e - 86/5, 58/5*e^3 + 37/5*e^2 - 140*e - 174/5, -1/5*e^3 - 4/5*e^2 + 58/5, -9/5*e^3 + 9/5*e^2 + 20*e - 83/5, -39/5*e^3 - 16/5*e^2 + 94*e + 187/5, -37/5*e^3 - 18/5*e^2 + 87*e + 16/5, 46/5*e^3 + 44/5*e^2 - 110*e - 223/5, -3/5*e^3 - 2/5*e^2 - 61/5, -31/5*e^3 - 24/5*e^2 + 68*e + 133/5, 1/5*e^3 - 6/5*e^2 - 4*e + 27/5, -51/5*e^3 - 44/5*e^2 + 124*e + 243/5, 79/5*e^3 + 51/5*e^2 - 195*e - 287/5, -57/5*e^3 - 43/5*e^2 + 140*e + 251/5, 57/5*e^3 + 38/5*e^2 - 134*e - 226/5, -62/5*e^3 - 28/5*e^2 + 149*e + 216/5, -53/5*e^3 - 32/5*e^2 + 132*e + 194/5, -2*e^3 - e^2 + 21*e - 10, 24/5*e^3 + 1/5*e^2 - 57*e - 37/5, 22/5*e^3 - 2/5*e^2 - 53*e + 44/5, -6*e^3 - 3*e^2 + 72*e + 10, -67/5*e^3 - 38/5*e^2 + 165*e + 306/5, 5*e^3 + 4*e^2 - 60*e - 27, 8/5*e^3 + 22/5*e^2 - 13*e - 149/5, -21/5*e^3 - 4/5*e^2 + 44*e - 7/5, -84/5*e^3 - 56/5*e^2 + 204*e + 312/5, -1/5*e^3 - 14/5*e^2 + 3*e + 68/5, 13/5*e^3 + 22/5*e^2 - 29*e - 149/5, -61/5*e^3 - 24/5*e^2 + 149*e + 213/5, 82/5*e^3 + 63/5*e^2 - 199*e - 356/5, 19/5*e^3 + 26/5*e^2 - 51*e - 137/5, -49/5*e^3 - 36/5*e^2 + 128*e + 297/5, 42/5*e^3 + 23/5*e^2 - 104*e - 96/5, 54/5*e^3 + 31/5*e^2 - 132*e - 202/5, -4*e^3 - 4*e^2 + 50*e + 39, 18/5*e^3 + 2/5*e^2 - 48*e + 26/5, 21/5*e^3 + 14/5*e^2 - 53*e - 118/5, -39/5*e^3 - 16/5*e^2 + 93*e + 22/5, 76/5*e^3 + 59/5*e^2 - 189*e - 318/5, 3*e^3 + 6*e^2 - 40*e - 39, e^3 + 3*e^2 - 7*e - 41, 13/5*e^3 + 2/5*e^2 - 40*e + 21/5, 49/5*e^3 + 26/5*e^2 - 116*e - 132/5, -6*e^3 - 3*e^2 + 71*e - 9, -7*e^3 - 8*e^2 + 82*e + 63, 38/5*e^3 + 32/5*e^2 - 93*e - 204/5, 2*e^3 - e^2 - 21*e + 3, 97/5*e^3 + 68/5*e^2 - 240*e - 366/5, -24/5*e^3 - 16/5*e^2 + 58*e + 182/5, 39/5*e^3 + 36/5*e^2 - 92*e - 117/5, -36/5*e^3 - 24/5*e^2 + 90*e + 193/5, e^3 + 2*e^2 - 17*e - 14, 14/5*e^3 - 4/5*e^2 - 33*e + 43/5, 37/5*e^3 + 18/5*e^2 - 95*e - 106/5, 58/5*e^3 + 57/5*e^2 - 140*e - 329/5, 63/5*e^3 + 42/5*e^2 - 162*e - 259/5, -42/5*e^3 - 28/5*e^2 + 107*e + 161/5, 7/5*e^3 + 3/5*e^2 - 19*e + 74/5, -68/5*e^3 - 57/5*e^2 + 158*e + 304/5, 5*e^3 + 3*e^2 - 64*e - 26, -82/5*e^3 - 43/5*e^2 + 204*e + 351/5, 37/5*e^3 + 23/5*e^2 - 86*e - 201/5, -46/5*e^3 - 19/5*e^2 + 111*e + 48/5, e^3 + 5*e^2 - 7*e - 22, 2/5*e^3 + 18/5*e^2 - 6*e - 36/5, 15*e^3 + 11*e^2 - 169*e - 66, -49/5*e^3 - 61/5*e^2 + 117*e + 332/5, -38/5*e^3 - 7/5*e^2 + 87*e - 11/5, -78/5*e^3 - 62/5*e^2 + 197*e + 409/5, 13/5*e^3 - 3/5*e^2 - 28*e - 24/5, -5*e^3 - 2*e^2 + 62*e, 87/5*e^3 + 53/5*e^2 - 209*e - 346/5, 21*e^3 + 13*e^2 - 254*e - 79, 6/5*e^3 + 4/5*e^2 - 15*e + 122/5, -67/5*e^3 - 68/5*e^2 + 162*e + 331/5, -18/5*e^3 - 22/5*e^2 + 34*e + 204/5, 15*e^3 + 12*e^2 - 175*e - 54, 19/5*e^3 + 31/5*e^2 - 47*e - 167/5, 13/5*e^3 + 2/5*e^2 - 30*e + 71/5, 12/5*e^3 - 7/5*e^2 - 31*e - 61/5, 51/5*e^3 + 14/5*e^2 - 129*e - 53/5, 42/5*e^3 + 23/5*e^2 - 95*e - 111/5, -7/5*e^3 - 3/5*e^2 + 14*e - 144/5, -61/5*e^3 - 39/5*e^2 + 150*e + 183/5, -12/5*e^3 + 17/5*e^2 + 35*e - 184/5, -14*e^3 - 7*e^2 + 174*e + 31, 33/5*e^3 + 37/5*e^2 - 85*e - 254/5, 9*e^3 + 12*e^2 - 113*e - 69, 57/5*e^3 + 23/5*e^2 - 143*e - 166/5, -4*e^3 - 8*e^2 + 43*e + 60, 13*e^3 + 8*e^2 - 167*e - 42, 99/5*e^3 + 76/5*e^2 - 236*e - 407/5, -8*e^3 - 7*e^2 + 96*e + 20, 117/5*e^3 + 93/5*e^2 - 291*e - 491/5, -10*e^3 - 10*e^2 + 114*e + 59, -74/5*e^3 - 41/5*e^2 + 182*e + 242/5, 68/5*e^3 + 27/5*e^2 - 156*e - 129/5, 38/5*e^3 + 22/5*e^2 - 89*e - 324/5, -10*e^3 - 6*e^2 + 123*e + 46, 33/5*e^3 + 32/5*e^2 - 84*e - 309/5, -12/5*e^3 - 3/5*e^2 + 23*e - 204/5, -49/5*e^3 - 41/5*e^2 + 117*e + 377/5, -63/5*e^3 - 42/5*e^2 + 141*e + 289/5, 56/5*e^3 + 49/5*e^2 - 128*e - 343/5, 44/5*e^3 + 41/5*e^2 - 119*e - 267/5, -49/5*e^3 - 11/5*e^2 + 118*e + 112/5, -8/5*e^3 - 12/5*e^2 + 17*e + 144/5, -81/5*e^3 - 74/5*e^2 + 191*e + 448/5, -21/5*e^3 - 34/5*e^2 + 42*e + 193/5, -41/5*e^3 - 19/5*e^2 + 108*e + 23/5, 42/5*e^3 + 38/5*e^2 - 97*e - 411/5, -12/5*e^3 - 28/5*e^2 + 24*e + 251/5, -7/5*e^3 - 8/5*e^2 + 8*e + 6/5, -73/5*e^3 - 42/5*e^2 + 179*e + 219/5, -5*e^3 - 2*e^2 + 62*e - 19, 29/5*e^3 + 41/5*e^2 - 69*e - 152/5, -24/5*e^3 - 11/5*e^2 + 54*e - 58/5, 47/5*e^3 + 48/5*e^2 - 125*e - 281/5, -6*e^3 - 5*e^2 + 83*e + 36, -77/5*e^3 - 33/5*e^2 + 186*e + 246/5, 79/5*e^3 + 51/5*e^2 - 184*e - 362/5, 67/5*e^3 + 38/5*e^2 - 151*e - 206/5, 18/5*e^3 + 17/5*e^2 - 41*e - 9/5, -49/5*e^3 - 31/5*e^2 + 133*e + 202/5, -e^2 - 2*e - 29, -56/5*e^3 - 64/5*e^2 + 132*e + 293/5, 97/5*e^3 + 78/5*e^2 - 228*e - 381/5, 99/5*e^3 + 66/5*e^2 - 242*e - 347/5, -12/5*e^3 - 43/5*e^2 + 21*e + 261/5, -10*e^3 - 2*e^2 + 123*e - 8, -20*e^3 - 17*e^2 + 247*e + 84, 23/5*e^3 + 32/5*e^2 - 60*e - 99/5, -47/5*e^3 - 28/5*e^2 + 122*e + 56/5, 3*e^3 + e^2 - 35*e - 30, -102/5*e^3 - 68/5*e^2 + 266*e + 441/5, 7/5*e^3 - 2/5*e^2 - 15*e - 21/5, -9*e^3 - 7*e^2 + 115*e + 41, 27*e^3 + 20*e^2 - 338*e - 100, 87/5*e^3 + 63/5*e^2 - 200*e - 461/5, 31/5*e^3 + 39/5*e^2 - 78*e - 303/5, -16*e^3 - 11*e^2 + 203*e + 65, 66/5*e^3 + 39/5*e^2 - 146*e - 258/5, -44/5*e^3 - 6/5*e^2 + 107*e + 42/5, 11*e^3 + 9*e^2 - 139*e - 73, 4/5*e^3 - 14/5*e^2 + 4*e + 93/5, -33/5*e^3 - 17/5*e^2 + 89*e + 84/5, -15*e^3 - 10*e^2 + 190*e + 77, 44/5*e^3 + 21/5*e^2 - 98*e - 157/5, 8*e^3 + 5*e^2 - 101*e - 12, -8/5*e^3 + 13/5*e^2 + 35*e - 121/5, 36/5*e^3 - 11/5*e^2 - 87*e + 167/5, 32/5*e^3 + 13/5*e^2 - 84*e - 86/5, -3*e^3 + 2*e^2 + 36*e - 41, 6*e^3 + 4*e^2 - 66*e - 36, 51/5*e^3 + 29/5*e^2 - 128*e - 138/5, 4/5*e^3 - 4/5*e^2 - 10*e - 197/5, -32/5*e^3 - 28/5*e^2 + 80*e - 19/5, 41/5*e^3 + 4/5*e^2 - 111*e - 43/5, 82/5*e^3 + 48/5*e^2 - 206*e - 301/5, 17*e^3 + 12*e^2 - 203*e - 74, -9/5*e^3 + 4/5*e^2 + 4*e - 53/5, -98/5*e^3 - 62/5*e^2 + 246*e + 329/5, -129/5*e^3 - 86/5*e^2 + 312*e + 457/5, 99/5*e^3 + 56/5*e^2 - 235*e - 477/5, 13/5*e^3 + 17/5*e^2 - 32*e - 104/5, -127/5*e^3 - 88/5*e^2 + 298*e + 436/5, 31/5*e^3 + 24/5*e^2 - 72*e - 293/5, -49/5*e^3 - 46/5*e^2 + 124*e + 102/5, -11/5*e^3 - 9/5*e^2 + 14*e - 27/5, -76/5*e^3 - 49/5*e^2 + 201*e + 203/5, -66/5*e^3 - 64/5*e^2 + 164*e + 303/5, 28/5*e^3 - 8/5*e^2 - 69*e - 94/5, 33/5*e^3 + 37/5*e^2 - 78*e - 79/5, -174/5*e^3 - 116/5*e^2 + 424*e + 677/5, 11/5*e^3 - 21/5*e^2 - 27*e + 12/5, 56/5*e^3 + 39/5*e^2 - 128*e - 243/5, 11*e^3 + 8*e^2 - 132*e - 30, -72/5*e^3 - 48/5*e^2 + 194*e + 306/5, -1/5*e^3 + 11/5*e^2 - 9*e - 27/5, 68/5*e^3 + 22/5*e^2 - 173*e - 144/5, -11/5*e^3 - 29/5*e^2 + 35*e + 293/5, -17*e^3 - 14*e^2 + 218*e + 80, 16*e^3 + 12*e^2 - 183*e - 58, -74/5*e^3 - 36/5*e^2 + 175*e + 82/5, 6*e^3 + 3*e^2 - 63*e - 28, -7/5*e^3 - 8/5*e^2 + 29*e - 19/5, 98/5*e^3 + 72/5*e^2 - 233*e - 529/5, -54/5*e^3 - 56/5*e^2 + 141*e + 337/5, 5*e^3 + 6*e^2 - 59*e - 29, -48/5*e^3 - 27/5*e^2 + 127*e + 194/5, -157/5*e^3 - 118/5*e^2 + 376*e + 696/5, -47/5*e^3 - 43/5*e^2 + 107*e + 136/5, -19*e^3 - 8*e^2 + 241*e + 48, -169/5*e^3 - 116/5*e^2 + 425*e + 647/5, 23/5*e^3 + 7/5*e^2 - 74*e + 71/5, -129/5*e^3 - 96/5*e^2 + 307*e + 402/5, -8*e^3 - 2*e^2 + 83*e - 3, 61/5*e^3 + 74/5*e^2 - 145*e - 328/5, -23/5*e^3 - 42/5*e^2 + 56*e + 204/5, -141/5*e^3 - 84/5*e^2 + 339*e + 468/5, -14*e^3 - 4*e^2 + 169*e + 36, -32*e^3 - 24*e^2 + 384*e + 146, -148/5*e^3 - 127/5*e^2 + 357*e + 634/5, -26/5*e^3 - 24/5*e^2 + 68*e + 148/5, 8/5*e^3 - 13/5*e^2 - 29*e + 21/5, -98/5*e^3 - 42/5*e^2 + 238*e + 259/5, -16*e^3 - 13*e^2 + 197*e + 83, -24/5*e^3 - 26/5*e^2 + 53*e - 48/5, 18/5*e^3 + 2/5*e^2 - 39*e + 81/5, 122/5*e^3 + 88/5*e^2 - 287*e - 556/5, 2*e^3 - 5*e^2 - 40*e + 64, 16*e^3 + 4*e^2 - 208*e - 22, 58/5*e^3 + 47/5*e^2 - 152*e - 359/5, 9/5*e^3 - 9/5*e^2 - 17*e - 67/5, 10*e^3 + 5*e^2 - 116*e - 10, 116/5*e^3 + 79/5*e^2 - 294*e - 548/5] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([41, 41, 2*w^5 + w^4 - 13*w^3 - 5*w^2 + 19*w + 4])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]