/* 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([-7, -14, 7, 13, -4, -3, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([13,13,w^2 - 2*w - 2]) primes_array = [ [7, 7, w],\ [7, 7, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 + 5],\ [13, 13, w^2 - 3],\ [13, 13, -w^2 + 2*w + 2],\ [29, 29, w^4 - 2*w^3 - 4*w^2 + 4*w + 6],\ [29, 29, -w^4 + 2*w^3 + 4*w^2 - 6*w - 5],\ [41, 41, -w^2 + 4],\ [41, 41, -w^2 + 2*w + 3],\ [43, 43, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 - w + 3],\ [43, 43, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 4*w + 2],\ [64, 2, -2],\ [71, 71, w^5 - 3*w^4 - w^3 + 6*w^2 - 2*w + 2],\ [71, 71, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 - w + 5],\ [71, 71, w^4 - 3*w^3 - 2*w^2 + 6*w + 2],\ [71, 71, 2*w^5 - 6*w^4 - 4*w^3 + 19*w^2 - w - 12],\ [83, 83, -w^4 + w^3 + 5*w^2 - w - 6],\ [83, 83, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 4*w - 1],\ [97, 97, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 5*w + 4],\ [97, 97, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + 2*w - 2],\ [113, 113, -2*w^4 + 3*w^3 + 8*w^2 - 6*w - 6],\ [113, 113, -w^5 + 4*w^4 - w^3 - 12*w^2 + 9*w + 10],\ [113, 113, -w^5 + w^4 + 5*w^3 + w^2 - 7*w - 9],\ [113, 113, 2*w^5 - 5*w^4 - 6*w^3 + 13*w^2 + 6*w - 1],\ [125, 5, -w^5 + 4*w^4 - 12*w^2 + 4*w + 4],\ [125, 5, w^5 - w^4 - 6*w^3 + 2*w^2 + 9*w - 1],\ [139, 139, -w^4 + w^3 + 5*w^2 - 2*w - 8],\ [139, 139, w^5 - 4*w^4 + 13*w^2 - 4*w - 10],\ [167, 167, -w^5 + 3*w^4 + 2*w^3 - 11*w^2 + 2*w + 9],\ [167, 167, -w^5 + 7*w^3 + 2*w^2 - 9*w - 3],\ [167, 167, 2*w^5 - 6*w^4 - 3*w^3 + 15*w^2 - w - 5],\ [167, 167, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - 8],\ [167, 167, -w^5 + 5*w^4 - 3*w^3 - 13*w^2 + 11*w + 4],\ [167, 167, 2*w^4 - 5*w^3 - 4*w^2 + 11*w + 2],\ [169, 13, -w^4 + 2*w^3 + 2*w^2 - 3*w + 1],\ [169, 13, 2*w^4 - 4*w^3 - 7*w^2 + 9*w + 8],\ [181, 181, -w^5 + 4*w^4 - 14*w^2 + 5*w + 12],\ [181, 181, -w^3 + 2*w^2 + 3*w - 2],\ [181, 181, -w^3 + w^2 + 4*w - 2],\ [181, 181, 3*w^4 - 7*w^3 - 9*w^2 + 15*w + 9],\ [197, 197, w^5 - 2*w^4 - 5*w^3 + 5*w^2 + 8*w + 3],\ [197, 197, -w^5 + 8*w^3 + w^2 - 14*w - 4],\ [197, 197, w^4 - w^3 - 6*w^2 + 5*w + 6],\ [197, 197, w^5 - 3*w^4 - 3*w^3 + 12*w^2 - 10],\ [211, 211, -w^5 + 4*w^4 + w^3 - 13*w^2 + 2*w + 8],\ [211, 211, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 3*w - 3],\ [211, 211, -w^5 + 3*w^4 + w^3 - 8*w^2 + 3*w + 5],\ [211, 211, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 3],\ [223, 223, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 6*w + 2],\ [223, 223, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 - w + 4],\ [293, 293, w^5 - 8*w^3 - w^2 + 13*w + 4],\ [293, 293, -w^5 + 5*w^4 - 2*w^3 - 15*w^2 + 8*w + 9],\ [307, 307, -w^5 + 4*w^4 + w^3 - 13*w^2 + w + 10],\ [307, 307, 2*w^5 - 6*w^4 - 4*w^3 + 17*w^2 + w - 6],\ [307, 307, -w^5 + 3*w^4 + w^3 - 8*w^2 + 4*w + 6],\ [307, 307, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 2*w - 5],\ [307, 307, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 9*w + 4],\ [307, 307, 2*w^4 - 4*w^3 - 9*w^2 + 10*w + 11],\ [337, 337, w^5 - 4*w^4 - w^3 + 13*w^2 - 2*w - 5],\ [337, 337, -w^5 + w^4 + 5*w^3 + w^2 - 9*w - 5],\ [337, 337, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 6*w + 2],\ [337, 337, -2*w^4 + 4*w^3 + 9*w^2 - 12*w - 11],\ [337, 337, w^5 - w^4 - 7*w^3 + 5*w^2 + 9*w - 2],\ [337, 337, -w^5 + 5*w^4 - 2*w^3 - 14*w^2 + 7*w + 8],\ [349, 349, 2*w^4 - 4*w^3 - 9*w^2 + 10*w + 13],\ [349, 349, w^5 - 5*w^4 + 3*w^3 + 15*w^2 - 12*w - 11],\ [379, 379, -w^5 + 5*w^4 - 2*w^3 - 15*w^2 + 7*w + 11],\ [379, 379, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 1],\ [379, 379, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 8*w - 1],\ [379, 379, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 4*w + 8],\ [379, 379, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 7*w + 2],\ [379, 379, 2*w^4 - 3*w^3 - 8*w^2 + 5*w + 10],\ [419, 419, -w^5 + w^4 + 6*w^3 - 10*w - 9],\ [419, 419, w^4 - 2*w^3 - w^2 + w - 3],\ [419, 419, -2*w^5 + 5*w^4 + 6*w^3 - 14*w^2 - 5*w + 6],\ [419, 419, w^5 - 4*w^4 + 14*w^2 - 7*w - 13],\ [421, 421, 2*w^5 - 4*w^4 - 7*w^3 + 8*w^2 + 8*w + 2],\ [421, 421, 3*w^4 - 6*w^3 - 11*w^2 + 15*w + 12],\ [421, 421, -3*w^4 + 6*w^3 + 11*w^2 - 13*w - 13],\ [421, 421, w^5 - 4*w^4 - w^3 + 15*w^2 - 4*w - 13],\ [433, 433, -2*w^3 + 3*w^2 + 6*w - 3],\ [433, 433, w^5 - 3*w^4 - w^3 + 5*w^2 + 3],\ [433, 433, -w^5 + 2*w^4 + 3*w^3 - 6*w^2 + 5],\ [433, 433, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 6*w - 3],\ [449, 449, w^5 - 5*w^4 + w^3 + 17*w^2 - 7*w - 11],\ [449, 449, 2*w^4 - 4*w^3 - 7*w^2 + 10*w + 9],\ [463, 463, w^5 - w^4 - 6*w^3 + 3*w^2 + 9*w - 3],\ [463, 463, w^5 - 9*w^3 + 16*w + 3],\ [463, 463, -w^5 + 5*w^4 - w^3 - 17*w^2 + 6*w + 11],\ [463, 463, -2*w^4 + 5*w^3 + 4*w^2 - 11*w - 1],\ [491, 491, 3*w^4 - 7*w^3 - 9*w^2 + 16*w + 10],\ [491, 491, -w^5 + w^4 + 7*w^3 - 5*w^2 - 10*w + 4],\ [491, 491, w^3 - w^2 - 3*w - 3],\ [491, 491, -w^3 + 2*w^2 + 2*w - 6],\ [491, 491, -w^5 + 4*w^4 + w^3 - 12*w^2 + 4],\ [491, 491, 3*w^4 - 5*w^3 - 12*w^2 + 11*w + 13],\ [503, 503, -w^3 + 4*w^2 + w - 8],\ [503, 503, -w^5 + 4*w^4 - w^3 - 10*w^2 + 7*w + 6],\ [547, 547, w^5 - 3*w^4 - w^3 + 7*w^2 - 3*w - 4],\ [547, 547, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 - w - 3],\ [587, 587, w^5 - 5*w^4 + 3*w^3 + 14*w^2 - 11*w - 11],\ [587, 587, w^5 - 7*w^3 - 3*w^2 + 11*w + 9],\ [601, 601, w^5 - 5*w^4 + 2*w^3 + 15*w^2 - 7*w - 9],\ [601, 601, w^5 - 8*w^3 - w^2 + 14*w + 3],\ [631, 631, w^5 - 2*w^4 - 4*w^3 + 4*w^2 + 6*w - 1],\ [631, 631, -w^5 + 3*w^4 + 2*w^3 - 6*w^2 - 3*w - 3],\ [631, 631, -w^5 + 2*w^4 + 4*w^3 - 8*w^2 - 2*w + 8],\ [631, 631, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + w + 4],\ [643, 643, w^5 - 4*w^4 + 12*w^2 - 4*w - 10],\ [643, 643, -3*w^4 + 6*w^3 + 10*w^2 - 14*w - 10],\ [643, 643, -3*w^4 + 6*w^3 + 10*w^2 - 12*w - 11],\ [643, 643, -w^5 + 3*w^4 + w^3 - 9*w^2 + 5*w + 6],\ [659, 659, -w^5 + w^4 + 6*w^3 - 2*w^2 - 10*w + 1],\ [659, 659, 2*w^4 - 5*w^3 - 4*w^2 + 9*w + 1],\ [659, 659, -2*w^4 + 4*w^3 + 5*w^2 - 6*w - 2],\ [659, 659, 2*w^4 - 4*w^3 - 5*w^2 + 8*w + 1],\ [659, 659, -2*w^4 + 3*w^3 + 7*w^2 - 6*w - 3],\ [659, 659, -w^5 + 4*w^4 - 12*w^2 + 3*w + 5],\ [673, 673, 2*w^4 - 3*w^3 - 10*w^2 + 9*w + 10],\ [673, 673, -2*w^4 + 5*w^3 + 7*w^2 - 12*w - 8],\ [701, 701, -4*w^4 + 8*w^3 + 12*w^2 - 17*w - 8],\ [701, 701, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + 2*w - 6],\ [701, 701, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 5*w - 5],\ [701, 701, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - 3*w + 1],\ [701, 701, w^5 - w^4 - 7*w^3 + 6*w^2 + 7*w - 4],\ [727, 727, w^3 - w^2 - 2*w - 3],\ [727, 727, w^5 - 3*w^4 - 2*w^3 + 11*w^2 - 3*w - 10],\ [727, 727, -w^5 + 2*w^4 + 4*w^3 - 3*w^2 - 6*w - 6],\ [727, 727, -w^3 + 2*w^2 + w - 5],\ [729, 3, -3],\ [743, 743, -2*w^5 + 3*w^4 + 9*w^3 - 5*w^2 - 12*w - 5],\ [743, 743, 2*w^5 - 7*w^4 - w^3 + 20*w^2 - 7*w - 12],\ [757, 757, -2*w^4 + 5*w^3 + 7*w^2 - 12*w - 11],\ [757, 757, -w^5 + 4*w^4 + 2*w^3 - 15*w^2 - w + 10],\ [757, 757, -w^5 + w^4 + 8*w^3 - 5*w^2 - 14*w + 1],\ [757, 757, -2*w^4 + 3*w^3 + 10*w^2 - 9*w - 13],\ [769, 769, w^5 - 3*w^4 + 5*w^2 - 4*w - 1],\ [769, 769, -w^5 + 2*w^4 + 2*w^3 - 3*w^2 + w - 2],\ [797, 797, -w^5 + 5*w^4 - w^3 - 17*w^2 + 5*w + 12],\ [797, 797, w^5 - 9*w^3 + 17*w + 3],\ [811, 811, -w^4 + w^3 + 4*w^2 - 6],\ [811, 811, w^4 - 3*w^3 - w^2 + 7*w + 2],\ [827, 827, w^5 + w^4 - 9*w^3 - 5*w^2 + 16*w + 6],\ [827, 827, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 10*w + 2],\ [827, 827, 2*w^5 - 6*w^4 - 4*w^3 + 17*w^2 + 2*w - 9],\ [827, 827, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 7*w + 6],\ [839, 839, -2*w^5 + 6*w^4 + 4*w^3 - 18*w^2 - w + 10],\ [839, 839, -w^5 + 4*w^4 - w^3 - 12*w^2 + 7*w + 12],\ [839, 839, -w^5 + w^4 + 5*w^3 + w^2 - 9*w - 9],\ [839, 839, -2*w^5 + 4*w^4 + 8*w^3 - 10*w^2 - 11*w + 1],\ [841, 29, -3*w^4 + 6*w^3 + 11*w^2 - 14*w - 12],\ [841, 29, -2*w^4 + 4*w^3 + 9*w^2 - 11*w - 11],\ [853, 853, -w^4 + 6*w^2 + w - 4],\ [853, 853, -w^5 + 5*w^4 - 2*w^3 - 17*w^2 + 9*w + 15],\ [853, 853, -w^5 + 8*w^3 + 3*w^2 - 16*w - 9],\ [853, 853, w^4 - 4*w^3 + 9*w - 2],\ [881, 881, -w - 3],\ [881, 881, w - 4],\ [883, 883, w^2 + w - 5],\ [883, 883, w^5 - 7*w^3 - 5*w^2 + 13*w + 11],\ [883, 883, w^5 - 5*w^4 + 3*w^3 + 16*w^2 - 13*w - 13],\ [883, 883, w^2 - 3*w - 3],\ [911, 911, -w^5 + 2*w^4 + 4*w^3 - 4*w^2 - 4*w - 3],\ [911, 911, -w^4 + 3*w^3 + 2*w^2 - 5*w - 5],\ [937, 937, -2*w^5 + 4*w^4 + 6*w^3 - 10*w^2 - 2*w + 3],\ [937, 937, -w^5 + 4*w^4 - 10*w^2 + 2*w + 1],\ [937, 937, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 4],\ [937, 937, -2*w^4 + 5*w^3 + 4*w^2 - 7*w - 2],\ [953, 953, w^5 - 4*w^4 + 2*w^3 + 9*w^2 - 9*w - 4],\ [953, 953, w^5 - w^4 - 4*w^3 - w^2 + 4*w + 5],\ [967, 967, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 7*w + 2],\ [967, 967, w^4 - 3*w^3 - 3*w^2 + 10*w + 3],\ [967, 967, -w^4 + w^3 + 6*w^2 - w - 8],\ [967, 967, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 5*w + 9],\ [1021, 1021, w^5 - 3*w^4 - 2*w^3 + 11*w^2 - 3*w - 8],\ [1021, 1021, -w^5 + 2*w^4 + 4*w^3 - 3*w^2 - 6*w - 4],\ [1049, 1049, -w^5 + w^4 + 5*w^3 - 2*w^2 - 4*w - 2],\ [1049, 1049, 2*w^5 - 6*w^4 - 4*w^3 + 17*w^2 + 2*w - 8],\ [1049, 1049, 2*w^5 - 4*w^4 - 8*w^3 + 11*w^2 + 10*w - 3],\ [1049, 1049, w^5 - 4*w^4 + w^3 + 9*w^2 - 6*w - 3],\ [1051, 1051, -w^5 + 7*w^3 + 3*w^2 - 10*w - 9],\ [1051, 1051, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w + 3],\ [1051, 1051, -w^5 + 4*w^4 + w^3 - 12*w^2 - w + 6],\ [1051, 1051, w^5 - 5*w^4 + 3*w^3 + 14*w^2 - 12*w - 10],\ [1063, 1063, 2*w^5 - 5*w^4 - 6*w^3 + 16*w^2 + 3*w - 9],\ [1063, 1063, -2*w^5 + 5*w^4 + 6*w^3 - 12*w^2 - 7*w + 1],\ [1091, 1091, -w^4 + 2*w^3 + 4*w^2 - 3*w - 8],\ [1091, 1091, -w^4 + 2*w^3 + 4*w^2 - 7*w - 6],\ [1093, 1093, 3*w^5 - 10*w^4 - 4*w^3 + 30*w^2 - 5*w - 16],\ [1093, 1093, 3*w^4 - 5*w^3 - 11*w^2 + 10*w + 9],\ [1093, 1093, 3*w^4 - 7*w^3 - 8*w^2 + 15*w + 6],\ [1093, 1093, 2*w^5 - 2*w^4 - 11*w^3 + 4*w^2 + 14*w + 4],\ [1217, 1217, -w^5 + 4*w^4 + w^3 - 12*w^2 - w + 5],\ [1217, 1217, -w^5 + 6*w^4 - 4*w^3 - 19*w^2 + 13*w + 15],\ [1217, 1217, -w^5 - w^4 + 10*w^3 + 5*w^2 - 18*w - 10],\ [1217, 1217, w^5 - w^4 - 7*w^3 + 5*w^2 + 11*w - 4],\ [1231, 1231, -w^4 + w^3 + 7*w^2 - 3*w - 8],\ [1231, 1231, w^4 - 3*w^3 - 4*w^2 + 10*w + 4],\ [1259, 1259, -w^5 - w^4 + 9*w^3 + 9*w^2 - 17*w - 19],\ [1259, 1259, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 4*w - 10],\ [1259, 1259, -w^5 + 7*w^4 - 6*w^3 - 22*w^2 + 17*w + 16],\ [1259, 1259, 2*w^5 - 6*w^4 - 3*w^3 + 17*w^2 - w - 13],\ [1289, 1289, -w^5 + 3*w^4 + 2*w^3 - 11*w^2 + 3*w + 9],\ [1289, 1289, w^5 - 8*w^3 - w^2 + 14*w + 2],\ [1289, 1289, w^5 - 5*w^4 + 2*w^3 + 15*w^2 - 7*w - 8],\ [1289, 1289, w^5 - 2*w^4 - 4*w^3 + 3*w^2 + 6*w + 5],\ [1301, 1301, w^5 - w^4 - 7*w^3 + 2*w^2 + 14*w + 2],\ [1301, 1301, w^5 - 4*w^4 - 2*w^3 + 13*w^2 + w - 4],\ [1301, 1301, -2*w^5 + 6*w^4 + 4*w^3 - 17*w^2 - w + 9],\ [1301, 1301, 2*w^5 - 4*w^4 - 8*w^3 + 11*w^2 + 9*w - 1],\ [1301, 1301, 2*w^5 - w^4 - 15*w^3 + 26*w + 10],\ [1301, 1301, w^5 - 8*w^3 + 13*w + 2],\ [1303, 1303, -w^5 + 3*w^4 + w^3 - 5*w^2 + w - 2],\ [1303, 1303, w^5 + w^4 - 8*w^3 - 7*w^2 + 13*w + 9],\ [1303, 1303, -2*w^5 + 2*w^4 + 13*w^3 - 5*w^2 - 21*w - 6],\ [1303, 1303, w^5 - 2*w^4 - 3*w^3 + 6*w^2 - w - 3],\ [1373, 1373, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + 3*w - 4],\ [1373, 1373, -2*w^5 + 7*w^4 + 3*w^3 - 21*w^2 - 2*w + 12],\ [1373, 1373, -w^5 + w^4 + 6*w^3 - 2*w^2 - 11*w - 1],\ [1373, 1373, w^5 - 4*w^4 + 12*w^2 - 2*w - 8],\ [1373, 1373, -2*w^5 + 3*w^4 + 11*w^3 - 10*w^2 - 17*w + 3],\ [1373, 1373, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 5],\ [1399, 1399, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 5*w + 8],\ [1399, 1399, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 8*w + 1],\ [1399, 1399, -2*w^5 + 6*w^4 + 4*w^3 - 17*w^2 + 8],\ [1399, 1399, w^5 - 3*w^4 + 6*w^2 - 6*w - 2],\ [1427, 1427, -2*w^4 + 3*w^3 + 10*w^2 - 9*w - 11],\ [1427, 1427, -2*w^4 + 5*w^3 + 7*w^2 - 12*w - 9],\ [1429, 1429, 3*w^5 - 7*w^4 - 10*w^3 + 19*w^2 + 10*w - 2],\ [1429, 1429, -w^4 + 7*w^2 - 2*w - 3],\ [1429, 1429, -w^5 + 2*w^4 + 4*w^3 - 2*w^2 - 7*w - 4],\ [1429, 1429, -3*w^5 + 8*w^4 + 8*w^3 - 23*w^2 - 5*w + 13],\ [1471, 1471, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 8*w + 3],\ [1471, 1471, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 2*w - 5],\ [1483, 1483, w^4 - 3*w^3 + 4*w - 4],\ [1483, 1483, w^4 - w^3 - 3*w^2 + w - 2],\ [1499, 1499, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 - 2*w + 4],\ [1499, 1499, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 7*w + 3],\ [1511, 1511, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 4*w + 5],\ [1511, 1511, -2*w^5 + 5*w^4 + 5*w^3 - 15*w^2 + 8],\ [1511, 1511, 3*w^5 - 10*w^4 - 4*w^3 + 31*w^2 - 5*w - 20],\ [1511, 1511, 2*w^5 - 5*w^4 - 6*w^3 + 13*w^2 + 6*w - 5],\ [1553, 1553, w^5 - 3*w^4 - 2*w^3 + 7*w^2 + 3*w + 2],\ [1553, 1553, -w^5 + 2*w^4 + 4*w^3 - 7*w^2 - 4*w + 8],\ [1567, 1567, -3*w^4 + 7*w^3 + 7*w^2 - 15*w - 1],\ [1567, 1567, -2*w^5 + 6*w^4 + 4*w^3 - 19*w^2 - w + 13],\ [1583, 1583, -3*w^5 + 6*w^4 + 13*w^3 - 18*w^2 - 15*w + 6],\ [1583, 1583, 2*w^5 - 3*w^4 - 10*w^3 + 9*w^2 + 10*w - 3],\ [1583, 1583, 2*w^5 - 4*w^4 - 7*w^3 + 12*w^2 + 5*w - 9],\ [1583, 1583, -w^5 + w^4 + 5*w^3 + 2*w^2 - 10*w - 9],\ [1597, 1597, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 7*w - 4],\ [1597, 1597, w^5 - 4*w^4 + 12*w^2 - 5*w - 9],\ [1597, 1597, -w^5 + w^4 + 6*w^3 - 2*w^2 - 8*w - 5],\ [1597, 1597, 2*w^5 - 5*w^4 - 7*w^3 + 16*w^2 + 6*w - 8],\ [1609, 1609, w^5 - 7*w^3 - 4*w^2 + 13*w + 10],\ [1609, 1609, w^4 - 4*w^3 + 8*w - 1],\ [1609, 1609, -w^4 + 6*w^2 - 4],\ [1609, 1609, w^5 - 5*w^4 + 3*w^3 + 15*w^2 - 11*w - 13],\ [1667, 1667, -w^5 + 9*w^3 - 17*w - 4],\ [1667, 1667, w^5 - 3*w^4 - 4*w^3 + 12*w^2 + 4*w - 8],\ [1667, 1667, 2*w^5 - 5*w^4 - 5*w^3 + 12*w^2 + 4*w - 3],\ [1667, 1667, w^5 - 5*w^4 + w^3 + 17*w^2 - 5*w - 13],\ [1681, 41, 3*w^2 - 3*w - 5],\ [1681, 41, -3*w^4 + 6*w^3 + 12*w^2 - 15*w - 16],\ [1693, 1693, w^5 - w^4 - 6*w^3 + w^2 + 8*w + 6],\ [1693, 1693, -w^5 + 4*w^4 - 12*w^2 + 7*w + 3],\ [1693, 1693, w^5 - 6*w^4 + 4*w^3 + 22*w^2 - 17*w - 20],\ [1693, 1693, w^5 - 4*w^4 + w^3 + 13*w^2 - 9*w - 13],\ [1709, 1709, -w^5 - w^4 + 10*w^3 + 6*w^2 - 20*w - 13],\ [1709, 1709, -w^5 + 4*w^4 - w^3 - 11*w^2 + 7*w + 10],\ [1709, 1709, 2*w^4 - 4*w^3 - 6*w^2 + 5*w + 8],\ [1709, 1709, 3*w^5 - 7*w^4 - 10*w^3 + 19*w^2 + 10*w - 3],\ [1709, 1709, -w^5 + w^4 + 5*w^3 - 7*w - 8],\ [1709, 1709, w^4 - 3*w^3 - w^2 + 3*w - 1],\ [1723, 1723, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w + 2],\ [1723, 1723, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + w - 4],\ [1847, 1847, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 3],\ [1847, 1847, -2*w^5 + 6*w^4 + 5*w^3 - 19*w^2 - 2*w + 13],\ [1849, 43, w^4 - 2*w^3 - 6*w^2 + 7*w + 8],\ [1849, 43, -3*w^4 + 6*w^3 + 11*w^2 - 14*w - 13],\ [1861, 1861, -w^5 + 9*w^3 - 2*w^2 - 14*w + 2],\ [1861, 1861, -w^5 + 4*w^4 - w^3 - 10*w^2 + 3*w + 4],\ [1861, 1861, -w^5 + w^4 + 5*w^3 - w^2 - 9*w + 1],\ [1861, 1861, -w^5 + 5*w^4 - w^3 - 15*w^2 + 4*w + 6],\ [1877, 1877, -2*w^5 + 7*w^4 + 2*w^3 - 21*w^2 + 4*w + 15],\ [1877, 1877, 2*w^5 - 6*w^4 - 3*w^3 + 17*w^2 - 3*w - 10],\ [1877, 1877, w^5 - w^4 - 6*w^3 + w^2 + 12*w + 3],\ [1877, 1877, -w^5 + 4*w^4 - 13*w^2 + 3*w + 10],\ [1877, 1877, -2*w^5 + 4*w^4 + 7*w^3 - 8*w^2 - 8*w - 3],\ [1877, 1877, 2*w^5 - 3*w^4 - 10*w^3 + 7*w^2 + 14*w + 5],\ [1889, 1889, -w^5 + 5*w^4 - w^3 - 15*w^2 + 4*w + 4],\ [1889, 1889, -2*w^5 + 3*w^4 + 9*w^3 - 7*w^2 - 10*w - 3],\ [1931, 1931, -2*w^5 + 5*w^4 + 7*w^3 - 17*w^2 - 4*w + 10],\ [1931, 1931, -2*w^5 + 6*w^4 + 3*w^3 - 19*w^2 + 5*w + 12],\ [1933, 1933, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 4*w - 4],\ [1933, 1933, w^5 - 6*w^4 + 3*w^3 + 22*w^2 - 13*w - 16],\ [1933, 1933, -2*w^5 + 8*w^4 - 23*w^2 + 7*w + 13],\ [1933, 1933, -w^5 + 3*w^4 - 3*w^2 + 3*w - 6],\ [1987, 1987, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 5*w - 1],\ [1987, 1987, 2*w^5 - 5*w^4 - 4*w^3 + 10*w^2 + 2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^9 - 4*x^8 - 37*x^7 + 111*x^6 + 584*x^5 - 939*x^4 - 4600*x^3 + 1184*x^2 + 14528*x + 10992 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 105/3184*e^8 - 28/199*e^7 - 2545/3184*e^6 + 8619/3184*e^5 + 1470/199*e^4 - 41983/3184*e^3 - 22723/796*e^2 + 3137/796*e + 3299/199, -49/398*e^8 + 1221/1592*e^7 + 1055/398*e^6 - 30377/1592*e^5 - 37337/1592*e^4 + 63717/398*e^3 + 231501/1592*e^2 - 184571/398*e - 203905/398, -1, -167/1592*e^8 + 271/398*e^7 + 3555/1592*e^6 - 27445/1592*e^5 - 7959/398*e^4 + 235669/1592*e^3 + 53171/398*e^2 - 175701/398*e - 99790/199, 16/199*e^8 - 419/796*e^7 - 312/199*e^6 + 10183/796*e^5 + 9759/796*e^4 - 20968/199*e^3 - 62779/796*e^2 + 60727/199*e + 63515/199, -47/1592*e^8 + 143/398*e^7 + 419/1592*e^6 - 16685/1592*e^5 - 45/398*e^4 + 173133/1592*e^3 + 18389/398*e^2 - 158527/398*e - 81276/199, -169/1592*e^8 + 867/1592*e^7 + 3793/1592*e^6 - 9401/796*e^5 - 32483/1592*e^4 + 122671/1592*e^3 + 140139/1592*e^2 - 55705/398*e - 57607/398, -39/398*e^8 + 1183/1592*e^7 + 661/398*e^6 - 30107/1592*e^5 - 16835/1592*e^4 + 66333/398*e^3 + 141743/1592*e^2 - 207635/398*e - 198461/398, -42/199*e^8 + 1553/1592*e^7 + 2235/398*e^6 - 36297/1592*e^5 - 94169/1592*e^4 + 66501/398*e^3 + 479785/1592*e^2 - 74709/199*e - 234501/398, -281/3184*e^8 + 825/1592*e^7 + 5977/3184*e^6 - 38861/3184*e^5 - 24905/1592*e^4 + 298103/3184*e^3 + 135175/1592*e^2 - 190285/796*e - 105299/398, -107/796*e^8 + 207/199*e^7 + 1987/796*e^6 - 22065/796*e^5 - 4002/199*e^4 + 204401/796*e^3 + 35780/199*e^2 - 167114/199*e - 181066/199, -247/1592*e^8 + 779/796*e^7 + 5115/1592*e^6 - 37935/1592*e^5 - 21495/796*e^4 + 308669/1592*e^3 + 129435/796*e^2 - 214347/398*e - 112199/199, 15/199*e^8 - 57/796*e^7 - 591/199*e^6 + 405/796*e^5 + 30753/796*e^4 + 3725/199*e^3 - 132249/796*e^2 - 33004/199*e + 5579/199, 81/398*e^8 - 2059/1592*e^7 - 1679/398*e^6 + 50743/1592*e^5 + 56855/1592*e^4 - 105653/398*e^3 - 358651/1592*e^2 + 306423/398*e + 334517/398, -55/796*e^8 + 5/1592*e^7 + 2167/796*e^6 + 3337/1592*e^5 - 53097/1592*e^4 - 41651/796*e^3 + 172309/1592*e^2 + 121733/398*e + 82539/398, -21/199*e^8 + 219/398*e^7 + 509/199*e^6 - 5159/398*e^5 - 10005/398*e^4 + 19660/199*e^3 + 54227/398*e^2 - 49593/199*e - 67630/199, -19/796*e^8 + 213/398*e^7 - 525/796*e^6 - 11919/796*e^5 + 6031/398*e^4 + 121713/796*e^3 - 4249/398*e^2 - 112146/199*e - 95300/199, 101/1592*e^8 - 160/199*e^7 - 477/1592*e^6 + 35855/1592*e^5 - 953/199*e^4 - 358723/1592*e^3 - 26459/398*e^2 + 319147/398*e + 153546/199, -67/398*e^8 + 591/398*e^7 + 504/199*e^6 - 15825/398*e^5 - 6053/398*e^4 + 74299/199*e^3 + 39815/199*e^2 - 247424/199*e - 252540/199, 97/1592*e^8 - 65/199*e^7 - 2389/1592*e^6 + 12943/1592*e^5 + 2915/199*e^4 - 106323/1592*e^3 - 15794/199*e^2 + 72783/398*e + 42988/199, -149/3184*e^8 + 411/796*e^7 + 1413/3184*e^6 - 45731/3184*e^5 + 213/796*e^4 + 450283/3184*e^3 + 9486/199*e^2 - 392005/796*e - 91580/199, -29/398*e^8 + 747/1592*e^7 + 665/398*e^6 - 19887/1592*e^5 - 26183/1592*e^4 + 45467/398*e^3 + 183723/1592*e^2 - 145129/398*e - 174311/398, -31/199*e^8 + 675/796*e^7 + 704/199*e^6 - 15563/796*e^5 - 25587/796*e^4 + 28785/199*e^3 + 131547/796*e^2 - 68916/199*e - 80039/199, -63/796*e^8 + 1055/1592*e^7 + 1129/796*e^6 - 29009/1592*e^5 - 18871/1592*e^4 + 140371/796*e^3 + 196511/1592*e^2 - 120327/199*e - 265023/398, 177/1592*e^8 - 1591/1592*e^7 - 3153/1592*e^6 + 22761/796*e^5 + 26315/1592*e^4 - 453943/1592*e^3 - 302883/1592*e^2 + 197502/199*e + 430189/398, -57/1592*e^8 - 89/199*e^7 + 4793/1592*e^6 + 21157/1592*e^5 - 9357/199*e^4 - 237433/1592*e^3 + 68351/398*e^2 + 239667/398*e + 60030/199, -13/199*e^8 + 363/398*e^7 - 45/199*e^6 - 9827/398*e^5 + 6713/398*e^4 + 47583/199*e^3 - 3407/398*e^2 - 166390/199*e - 135074/199, 205/1592*e^8 - 1167/796*e^7 - 1709/1592*e^6 + 65213/1592*e^5 - 2313/796*e^4 - 648643/1592*e^3 - 109585/796*e^2 + 574715/398*e + 280859/199, 839/3184*e^8 - 237/199*e^7 - 22231/3184*e^6 + 86109/3184*e^5 + 14532/199*e^4 - 599721/3184*e^3 - 285203/796*e^2 + 300611/796*e + 123067/199, -611/3184*e^8 + 631/398*e^7 + 9427/3184*e^6 - 130937/3184*e^5 - 6561/398*e^4 + 1176925/3184*e^3 + 145925/796*e^2 - 934511/796*e - 231585/199, -331/796*e^8 + 1797/796*e^7 + 7947/796*e^6 - 21639/398*e^5 - 77925/796*e^4 + 341141/796*e^3 + 430009/796*e^2 - 222349/199*e - 279093/199, 221/1592*e^8 - 1593/1592*e^7 - 3613/1592*e^6 + 4807/199*e^5 + 19853/1592*e^4 - 316187/1592*e^3 - 147653/1592*e^2 + 115326/199*e + 212183/398, 1/1592*e^8 + 251/398*e^7 - 2905/1592*e^6 - 30689/1592*e^5 + 12593/398*e^4 + 340273/1592*e^3 - 13264/199*e^2 - 333623/398*e - 130068/199, 317/1592*e^8 - 2719/1592*e^7 - 4689/1592*e^6 + 35671/796*e^5 + 25039/1592*e^4 - 654527/1592*e^3 - 322715/1592*e^2 + 534971/398*e + 534415/398, -251/1592*e^8 + 240/199*e^7 + 4795/1592*e^6 - 50897/1592*e^5 - 5237/199*e^4 + 468733/1592*e^3 + 92125/398*e^2 - 379519/398*e - 214996/199, -291/796*e^8 + 5309/1592*e^7 + 3983/796*e^6 - 141935/1592*e^5 - 36241/1592*e^4 + 667617/796*e^3 + 605877/1592*e^2 - 1118671/398*e - 1102707/398, -87/1592*e^8 + 13/1592*e^7 + 2791/1592*e^6 + 2567/796*e^5 - 28841/1592*e^4 - 111951/1592*e^3 + 37745/1592*e^2 + 73061/199*e + 142643/398, 59/1592*e^8 - 315/398*e^7 + 541/1592*e^6 + 39253/1592*e^5 - 3661/398*e^4 - 432037/1592*e^3 - 17620/199*e^2 + 410865/398*e + 207980/199, 3/199*e^8 + 307/796*e^7 - 357/199*e^6 - 9471/796*e^5 + 23185/796*e^4 + 26615/199*e^3 - 69593/796*e^2 - 105663/199*e - 71559/199, 965/1592*e^8 - 2921/796*e^7 - 21305/1592*e^6 + 143973/1592*e^5 + 97533/796*e^4 - 1189311/1592*e^3 - 593141/796*e^2 + 840561/398*e + 485409/199, 81/1592*e^8 - 83/199*e^7 - 1281/1592*e^6 + 17611/1592*e^5 + 676/199*e^4 - 159383/1592*e^3 - 12503/398*e^2 + 126903/398*e + 50894/199, -371/1592*e^8 + 2233/1592*e^7 + 7931/1592*e^6 - 26749/796*e^5 - 69373/1592*e^4 + 426197/1592*e^3 + 400765/1592*e^2 - 144318/199*e - 311601/398, 619/1592*e^8 - 1045/398*e^7 - 12767/1592*e^6 + 106713/1592*e^5 + 28097/398*e^4 - 931097/1592*e^3 - 198153/398*e^2 + 706461/398*e + 395338/199, -11/796*e^8 + 399/1592*e^7 + 115/796*e^6 - 13581/1592*e^5 - 3535/1592*e^4 + 79389/796*e^3 + 111435/1592*e^2 - 78113/199*e - 182731/398, -59/398*e^8 + 1657/1592*e^7 + 1051/398*e^6 - 40597/1592*e^5 - 27989/1592*e^4 + 84583/398*e^3 + 189521/1592*e^2 - 246679/398*e - 225269/398, 39/1592*e^8 + 19/199*e^7 - 1855/1592*e^6 - 6851/1592*e^5 + 3281/199*e^4 + 96847/1592*e^3 - 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3448391/3184*e^3 - 683793/796*e^2 + 2392481/796*e + 621949/199, 683/1592*e^8 - 2001/796*e^7 - 14811/1592*e^6 + 95603/1592*e^5 + 64357/796*e^4 - 757861/1592*e^3 - 362523/796*e^2 + 510677/398*e + 290283/199, 123/398*e^8 - 4129/1592*e^7 - 2299/398*e^6 + 115557/1592*e^5 + 77373/1592*e^4 - 279497/398*e^3 - 766201/1592*e^2 + 936541/398*e + 1007873/398, 89/398*e^8 - 179/1592*e^7 - 3029/398*e^6 - 13517/1592*e^5 + 139643/1592*e^4 + 86047/398*e^3 - 392727/1592*e^2 - 236721/199*e - 352613/398, -291/1592*e^8 + 581/796*e^7 + 7963/1592*e^6 - 24899/1592*e^5 - 40353/796*e^4 + 146237/1592*e^3 + 166643/796*e^2 - 37657/398*e - 41603/199, -423/796*e^8 + 690/199*e^7 + 7751/796*e^6 - 64993/796*e^5 - 12942/199*e^4 + 511457/796*e^3 + 74956/199*e^2 - 349357/199*e - 323494/199, -1131/3184*e^8 + 1883/796*e^7 + 20363/3184*e^6 - 177829/3184*e^5 - 32491/796*e^4 + 1389541/3184*e^3 + 91509/398*e^2 - 926811/796*e - 197936/199, -871/796*e^8 + 6091/796*e^7 + 16487/796*e^6 - 38148/199*e^5 - 128439/796*e^4 + 1308705/796*e^3 + 939471/796*e^2 - 986580/199*e - 1047893/199, 77/796*e^8 - 2093/796*e^7 + 3175/796*e^6 + 14943/199*e^5 - 69715/796*e^4 - 617015/796*e^3 + 111159/796*e^2 + 570273/199*e + 451205/199, 431/796*e^8 - 4779/1592*e^7 - 9499/796*e^6 + 109597/1592*e^5 + 163039/1592*e^4 - 400153/796*e^3 - 798771/1592*e^2 + 469275/398*e + 485309/398, -923/796*e^8 + 11445/1592*e^7 + 19889/796*e^6 - 283399/1592*e^5 - 353605/1592*e^4 + 1181831/796*e^3 + 2199037/1592*e^2 - 851087/199*e - 1923557/398, -809/796*e^8 + 5455/796*e^7 + 16671/796*e^6 - 34735/199*e^5 - 145595/796*e^4 + 1205365/796*e^3 + 1011505/796*e^2 - 907745/199*e - 996033/199, -73/398*e^8 + 2467/796*e^7 - 69/398*e^6 - 75113/796*e^5 + 22021/796*e^4 + 404017/398*e^3 + 248355/796*e^2 - 755676/199*e - 744549/199, 869/1592*e^8 - 2955/796*e^7 - 17045/1592*e^6 + 148101/1592*e^5 + 68871/796*e^4 - 1264891/1592*e^3 - 478745/796*e^2 + 939615/398*e + 501801/199, 1183/3184*e^8 - 1281/398*e^7 - 15407/3184*e^6 + 263949/3184*e^5 + 4667/398*e^4 - 2369505/3184*e^3 - 179225/796*e^2 + 1898355/796*e + 417869/199, -553/1592*e^8 + 497/398*e^7 + 16057/1592*e^6 - 41095/1592*e^5 - 44699/398*e^4 + 226311/1592*e^3 + 103133/199*e^2 - 39579/398*e - 112784/199, 1/8*e^8 - 5/8*e^7 - 25/8*e^6 + 14*e^5 + 281/8*e^4 - 815/8*e^3 - 1721/8*e^2 + 237*e + 985/2, 1011/3184*e^8 - 977/398*e^7 - 17227/3184*e^6 + 201297/3184*e^5 + 13781/398*e^4 - 1780725/3184*e^3 - 237587/796*e^2 + 1383655/796*e + 331561/199, -641/796*e^8 + 4579/796*e^7 + 12201/796*e^6 - 58555/398*e^5 - 96819/796*e^4 + 1032563/796*e^3 + 740071/796*e^2 - 803982/199*e - 852813/199, -137/199*e^8 + 5459/1592*e^7 + 3368/199*e^6 - 125803/1592*e^5 - 260031/1592*e^4 + 113769/199*e^3 + 1263419/1592*e^2 - 508197/398*e - 630865/398, 741/796*e^8 - 4077/796*e^7 - 18131/796*e^6 + 50435/398*e^5 + 184093/796*e^4 - 830885/796*e^3 - 1079687/796*e^2 + 581749/199*e + 762545/199, 3/398*e^8 - 1285/1592*e^7 + 837/398*e^6 + 38289/1592*e^5 - 61191/1592*e^4 - 104327/398*e^3 + 141347/1592*e^2 + 401389/398*e + 302561/398, -225/398*e^8 + 281/199*e^7 + 6875/398*e^6 - 7837/398*e^5 - 37140/199*e^4 - 20453/398*e^3 + 126751/199*e^2 + 205342/199*e + 121636/199, 201/1592*e^8 - 579/1592*e^7 - 7601/1592*e^6 + 8315/796*e^5 + 102535/1592*e^4 - 145503/1592*e^3 - 573807/1592*e^2 + 46268/199*e + 260007/398, 967/1592*e^8 - 6023/1592*e^7 - 21543/1592*e^6 + 38111/398*e^5 + 203275/1592*e^4 - 1308745/1592*e^3 - 1320299/1592*e^2 + 488140/199*e + 1149633/398, 1463/1592*e^8 - 5257/796*e^7 - 26439/1592*e^6 + 264247/1592*e^5 + 95201/796*e^4 - 2288297/1592*e^3 - 734691/796*e^2 + 1755215/398*e + 902353/199, 247/796*e^8 - 3315/1592*e^7 - 5911/796*e^6 + 91193/1592*e^5 + 125979/1592*e^4 - 427273/796*e^3 - 919919/1592*e^2 + 341508/199*e + 846199/398, -131/398*e^8 + 811/398*e^7 + 1526/199*e^6 - 21033/398*e^5 - 29543/398*e^4 + 90962/199*e^3 + 92995/199*e^2 - 264602/199*e - 312308/199, 949/1592*e^8 - 2595/796*e^7 - 21789/1592*e^6 + 120781/1592*e^5 + 101711/796*e^4 - 909643/1592*e^3 - 541041/796*e^2 + 559167/398*e + 335707/199, -2907/3184*e^8 + 5051/796*e^7 + 56587/3184*e^6 - 512197/3184*e^5 - 114435/796*e^4 + 4447717/3184*e^3 + 417511/398*e^2 - 3387339/796*e - 912756/199, 1597/1592*e^8 - 5649/796*e^7 - 31241/1592*e^6 + 290325/1592*e^5 + 128517/796*e^4 - 2559623/1592*e^3 - 962377/796*e^2 + 1975575/398*e + 1064841/199, 401/796*e^8 - 3157/796*e^7 - 6725/796*e^6 + 20415/199*e^5 + 44253/796*e^4 - 731575/796*e^3 - 413657/796*e^2 + 579589/199*e + 582941/199, -1777/1592*e^8 + 9877/1592*e^7 + 41517/1592*e^6 - 29776/199*e^5 - 390685/1592*e^4 + 1881307/1592*e^3 + 2137625/1592*e^2 - 1240161/398*e - 1470217/398, 171/398*e^8 - 3091/796*e^7 - 1319/199*e^6 + 84595/796*e^5 + 36211/796*e^4 - 204334/199*e^3 - 485229/796*e^2 + 701845/199*e + 748857/199, -415/796*e^8 + 5067/1592*e^7 + 9187/796*e^6 - 125301/1592*e^5 - 171791/1592*e^4 + 521669/796*e^3 + 1074339/1592*e^2 - 746267/398*e - 887073/398, -2597/1592*e^8 + 6721/796*e^7 + 61885/1592*e^6 - 310209/1592*e^5 - 293849/796*e^4 + 2278123/1592*e^3 + 1491531/796*e^2 - 1329723/398*e - 843943/199, 129/199*e^8 - 3515/796*e^7 - 5031/398*e^6 + 88257/796*e^5 + 79167/796*e^4 - 377511/398*e^3 - 549177/796*e^2 + 565020/199*e + 590931/199, 103/1592*e^8 - 1461/1592*e^7 + 81/1592*e^6 + 19775/796*e^5 - 12947/1592*e^4 - 388209/1592*e^3 - 142741/1592*e^2 + 342829/398*e + 371681/398, -463/398*e^8 + 10595/1592*e^7 + 10521/398*e^6 - 255679/1592*e^5 - 389575/1592*e^4 + 510147/398*e^3 + 2199307/1592*e^2 - 1376613/398*e - 1609277/398, -831/1592*e^8 + 2073/1592*e^7 + 27647/1592*e^6 - 19247/796*e^5 - 328429/1592*e^4 + 106065/1592*e^3 + 1415669/1592*e^2 + 83422/199*e - 164063/398, 425/796*e^8 - 1769/398*e^7 - 7193/796*e^6 + 95553/796*e^5 + 25511/398*e^4 - 902327/796*e^3 - 267765/398*e^2 + 751338/199*e + 772750/199, 43/199*e^8 + 188/199*e^7 - 2132/199*e^6 - 7620/199*e^5 + 28537/199*e^4 + 104540/199*e^3 - 79147/199*e^2 - 465176/199*e - 335746/199, 41/796*e^8 - 1849/1592*e^7 + 1091/796*e^6 + 51995/1592*e^5 - 48695/1592*e^4 - 268551/796*e^3 + 1683/1592*e^2 + 253049/199*e + 445617/398, 1239/1592*e^8 - 5565/1592*e^7 - 33215/1592*e^6 + 64205/796*e^5 + 348977/1592*e^4 - 918553/1592*e^3 - 1722977/1592*e^2 + 245826/199*e + 771379/398, -375/398*e^8 + 1799/398*e^7 + 9999/398*e^6 - 21688/199*e^5 - 106885/398*e^4 + 335521/398*e^3 + 574075/398*e^2 - 415887/199*e - 634002/199, 55/1592*e^8 + 347/796*e^7 - 3759/1592*e^6 - 25449/1592*e^5 + 27453/796*e^4 + 321047/1592*e^3 - 57455/796*e^2 - 334989/398*e - 135209/199, 112/199*e^8 - 385/199*e^7 - 6557/398*e^6 + 15243/398*e^5 + 36232/199*e^4 - 71269/398*e^3 - 314749/398*e^2 - 15696/199*e + 107698/199, -375/1592*e^8 + 1795/796*e^7 + 3631/1592*e^6 - 92131/1592*e^5 + 4765/796*e^4 + 825857/1592*e^3 + 81769/796*e^2 - 661763/398*e - 286557/199, -99/199*e^8 + 3799/796*e^7 + 1234/199*e^6 - 102571/796*e^5 - 16467/796*e^4 + 244662/199*e^3 + 404079/796*e^2 - 833610/199*e - 811409/199, 2469/3184*e^8 - 3947/796*e^7 - 49837/3184*e^6 + 383771/3184*e^5 + 101847/796*e^4 - 3134035/3184*e^3 - 321567/398*e^2 + 2217597/796*e + 607124/199, -479/796*e^8 + 1725/398*e^7 + 8445/796*e^6 - 85669/796*e^5 - 28773/398*e^4 + 726931/796*e^3 + 111207/199*e^2 - 543808/199*e - 555508/199, 15/796*e^8 + 1329/796*e^7 - 4173/796*e^6 - 20919/398*e^5 + 68035/796*e^4 + 474161/796*e^3 - 108533/796*e^2 - 471125/199*e - 399043/199, -305/1592*e^8 + 229/199*e^7 + 7241/1592*e^6 - 46187/1592*e^5 - 9535/199*e^4 + 394031/1592*e^3 + 124871/398*e^2 - 287409/398*e - 190950/199, -1613/1592*e^8 + 3587/796*e^7 + 41901/1592*e^6 - 157501/1592*e^5 - 213491/796*e^4 + 1037147/1592*e^3 + 1008109/796*e^2 - 467163/398*e - 398643/199, 1019/1592*e^8 - 570/199*e^7 - 26139/1592*e^6 + 100657/1592*e^5 + 31915/199*e^4 - 664869/1592*e^3 - 280661/398*e^2 + 301497/398*e + 207240/199, 3407/3184*e^8 - 6115/796*e^7 - 61959/3184*e^6 + 614873/3184*e^5 + 112983/796*e^4 - 5312713/3184*e^3 - 216679/199*e^2 + 4050259/796*e + 1046880/199, 1585/1592*e^8 - 1177/199*e^7 - 33793/1592*e^6 + 223579/1592*e^5 + 36221/199*e^4 - 1754663/1592*e^3 - 406727/398*e^2 + 1165639/398*e + 634264/199, 1083/796*e^8 - 6571/796*e^7 - 24203/796*e^6 + 40844/199*e^5 + 225279/796*e^4 - 1361661/796*e^3 - 1386811/796*e^2 + 971164/199*e + 1140665/199, 1211/1592*e^8 - 1349/199*e^7 - 17147/1592*e^6 + 286625/1592*e^5 + 10625/199*e^4 - 2672461/1592*e^3 - 317049/398*e^2 + 2214381/398*e + 1109358/199, -1281/1592*e^8 + 7575/1592*e^7 + 29457/1592*e^6 - 94545/796*e^5 - 281571/1592*e^4 + 1583927/1592*e^3 + 1708947/1592*e^2 - 568913/199*e - 1357021/398, -1711/1592*e^8 + 1682/199*e^7 + 28887/1592*e^6 - 349501/1592*e^5 - 24227/199*e^4 + 3158561/1592*e^3 + 452621/398*e^2 - 2531439/398*e - 1271340/199, -1817/3184*e^8 + 3623/796*e^7 + 26377/3184*e^6 - 360863/3184*e^5 - 26331/796*e^4 + 3091111/3184*e^3 + 68952/199*e^2 - 2345029/796*e - 511250/199, 883/1592*e^8 - 2295/796*e^7 - 21099/1592*e^6 + 106903/1592*e^5 + 100687/796*e^4 - 801061/1592*e^3 - 517865/796*e^2 + 488887/398*e + 311057/199, 1415/1592*e^8 - 7961/1592*e^7 - 33463/1592*e^6 + 97833/796*e^5 + 324721/1592*e^4 - 1594961/1592*e^3 - 1877361/1592*e^2 + 1099685/398*e + 1361209/398, 239/199*e^8 - 4729/796*e^7 - 5755/199*e^6 + 105953/796*e^5 + 217129/796*e^4 - 183163/199*e^3 - 1028269/796*e^2 + 378180/199*e + 484849/199, -251/1592*e^8 + 240/199*e^7 + 3203/1592*e^6 - 44529/1592*e^5 - 660/199*e^4 + 354109/1592*e^3 + 19689/398*e^2 - 260915/398*e - 112312/199, -867/796*e^8 + 9269/1592*e^7 + 20787/796*e^6 - 221351/1592*e^5 - 404137/1592*e^4 + 865265/796*e^3 + 2193997/1592*e^2 - 1127207/398*e - 1407789/398, -929/1592*e^8 + 3181/1592*e^7 + 25777/1592*e^6 - 14341/398*e^5 - 262821/1592*e^4 + 180167/1592*e^3 + 958797/1592*e^2 + 175153/398*e + 54275/398, -1319/796*e^8 + 16655/1592*e^7 + 28009/796*e^6 - 412921/1592*e^5 - 492407/1592*e^4 + 1725067/796*e^3 + 3084407/1592*e^2 - 1240927/199*e - 2722515/398, 667/1592*e^8 + 29/199*e^7 - 27235/1592*e^6 - 27487/1592*e^5 + 43153/199*e^4 + 563771/1592*e^3 - 299785/398*e^2 - 770891/398*e - 218216/199, 509/796*e^8 - 2981/796*e^7 - 11617/796*e^6 + 18259/199*e^5 + 111429/796*e^4 - 597295/796*e^3 - 672441/796*e^2 + 413677/199*e + 509045/199, 67/398*e^8 + 3/199*e^7 - 2799/398*e^6 - 1687/398*e^5 + 18051/199*e^4 + 41845/398*e^3 - 69068/199*e^2 - 126895/199*e - 40786/199, -535/1592*e^8 + 1075/796*e^7 + 15507/1592*e^6 - 49431/1592*e^5 - 87183/796*e^4 + 345405/1592*e^3 + 429639/796*e^2 - 169517/398*e - 168891/199, 557/1592*e^8 - 1573/796*e^7 - 13349/1592*e^6 + 77937/1592*e^5 + 66165/796*e^4 - 640299/1592*e^3 - 381379/796*e^2 + 439969/398*e + 270505/199, 191/796*e^8 + 525/796*e^7 - 8799/796*e^6 - 5685/199*e^5 + 111439/796*e^4 + 338635/796*e^3 - 292767/796*e^2 - 403576/199*e - 313877/199] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([13,13,w^2 - 2*w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]