/* 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, -11, 10, 10, -6, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([29, 29, -w^4 + w^3 + 4*w^2 - 3*w - 2]) primes_array = [ [7, 7, w^4 - 2*w^3 - 3*w^2 + 6*w - 1],\ [7, 7, -w^4 + w^3 + 4*w^2 - w - 1],\ [13, 13, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + 3*w - 3],\ [29, 29, -w^4 + w^3 + 4*w^2 - 3*w - 2],\ [29, 29, w^4 - 5*w^2 - 2*w + 4],\ [29, 29, -w^4 + w^3 + 3*w^2 - w + 2],\ [29, 29, -w^2 + w + 1],\ [41, 41, -w^5 + w^4 + 4*w^3 - w^2 - 3*w - 1],\ [43, 43, 2*w^3 - 2*w^2 - 7*w + 3],\ [43, 43, w^3 - w^2 - 2*w + 1],\ [64, 2, -2],\ [71, 71, w^5 - w^4 - 6*w^3 + 4*w^2 + 8*w - 3],\ [71, 71, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 3*w - 1],\ [83, 83, -2*w^4 + 3*w^3 + 6*w^2 - 7*w + 2],\ [83, 83, w^4 - w^3 - 5*w^2 + 2*w + 3],\ [83, 83, -w^5 + 3*w^4 + w^3 - 9*w^2 + 5*w + 3],\ [83, 83, w^5 - 7*w^3 + 10*w - 1],\ [97, 97, w^5 - 2*w^4 - 3*w^3 + 5*w^2 - w - 1],\ [97, 97, w^5 - 5*w^3 - w^2 + 3*w - 3],\ [113, 113, w^4 - w^3 - 4*w^2 + w + 4],\ [113, 113, w^4 - 2*w^3 - 3*w^2 + 6*w + 2],\ [127, 127, -w^4 + 2*w^3 + 4*w^2 - 5*w - 3],\ [127, 127, w^5 - 9*w^3 + w^2 + 18*w - 1],\ [127, 127, 2*w^4 - 4*w^3 - 5*w^2 + 10*w - 2],\ [127, 127, w^5 - w^4 - 6*w^3 + 3*w^2 + 9*w - 2],\ [127, 127, -3*w^4 + 5*w^3 + 9*w^2 - 11*w],\ [127, 127, -w^5 + 3*w^4 + w^3 - 8*w^2 + 4*w - 1],\ [139, 139, w^4 - 3*w^3 - 2*w^2 + 10*w - 3],\ [139, 139, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 4*w - 3],\ [167, 167, -w^4 + w^3 + 5*w^2 - 4*w - 3],\ [167, 167, -w^5 + w^4 + 6*w^3 - 3*w^2 - 8*w + 3],\ [169, 13, w^4 - 3*w^3 - 2*w^2 + 8*w - 2],\ [169, 13, 2*w^4 - 3*w^3 - 7*w^2 + 7*w + 3],\ [181, 181, -w^5 + 4*w^3 + 3*w^2 - 2],\ [181, 181, w^5 - 3*w^4 - 3*w^3 + 11*w^2 - 4],\ [181, 181, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 2*w - 4],\ [181, 181, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 3*w - 2],\ [197, 197, -3*w^4 + 5*w^3 + 10*w^2 - 11*w - 3],\ [197, 197, -3*w^4 + 6*w^3 + 9*w^2 - 16*w - 1],\ [197, 197, 2*w^3 - 3*w^2 - 5*w + 4],\ [197, 197, -w^5 + 6*w^3 - 6*w + 1],\ [223, 223, 2*w^4 - 2*w^3 - 9*w^2 + 3*w + 6],\ [223, 223, -3*w^4 + 5*w^3 + 9*w^2 - 13*w + 1],\ [223, 223, w^5 - w^4 - 6*w^3 + 4*w^2 + 10*w - 4],\ [223, 223, w^4 - 4*w^3 - 2*w^2 + 12*w],\ [239, 239, 2*w^4 - w^3 - 8*w^2 + 3],\ [239, 239, -w^5 + 3*w^4 - 8*w^2 + 9*w + 3],\ [239, 239, -w^5 + 2*w^4 + 2*w^3 - 6*w^2 + 3*w + 4],\ [239, 239, w^4 - 6*w^2 + 6],\ [239, 239, 3*w^4 - 4*w^3 - 11*w^2 + 10*w + 3],\ [239, 239, -w^5 + 7*w^3 - 9*w - 1],\ [251, 251, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 3*w - 2],\ [251, 251, -w^5 + w^4 + 6*w^3 - 4*w^2 - 8*w + 2],\ [281, 281, -3*w^4 + 4*w^3 + 11*w^2 - 10*w - 4],\ [281, 281, 3*w^4 - 3*w^3 - 12*w^2 + 5*w + 6],\ [293, 293, -w^5 + 8*w^3 - 15*w + 1],\ [293, 293, w^5 - 4*w^4 + w^3 + 11*w^2 - 9*w + 1],\ [293, 293, -2*w^4 + 5*w^3 + 5*w^2 - 14*w + 3],\ [293, 293, -w^5 + 8*w^3 - 14*w + 2],\ [293, 293, -2*w^4 + 4*w^3 + 6*w^2 - 9*w + 1],\ [293, 293, w^5 - 4*w^4 + 12*w^2 - 5*w - 2],\ [307, 307, 2*w^4 - 3*w^3 - 7*w^2 + 9*w + 2],\ [307, 307, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 8*w + 6],\ [307, 307, -w^3 + 6*w],\ [307, 307, w^5 - w^4 - 7*w^3 + 5*w^2 + 12*w - 3],\ [337, 337, -2*w^4 + 2*w^3 + 9*w^2 - 4*w - 8],\ [337, 337, 3*w^4 - 4*w^3 - 10*w^2 + 9*w + 3],\ [349, 349, 2*w^5 - 4*w^4 - 7*w^3 + 13*w^2 + 3*w - 6],\ [349, 349, 2*w^5 - 2*w^4 - 9*w^3 + 5*w^2 + 7*w - 2],\ [349, 349, w^5 - 3*w^4 + 8*w^2 - 7*w - 2],\ [349, 349, w^5 - 9*w^3 + 2*w^2 + 17*w - 4],\ [379, 379, w^5 - 3*w^4 + 6*w^2 - 8*w + 5],\ [379, 379, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 3*w + 1],\ [379, 379, w^5 - 4*w^4 + 12*w^2 - 8*w - 2],\ [379, 379, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w + 5],\ [419, 419, w^5 - 4*w^4 + w^3 + 10*w^2 - 10*w + 3],\ [419, 419, 3*w^4 - 3*w^3 - 11*w^2 + 5*w + 4],\ [421, 421, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 8*w - 4],\ [421, 421, -w^5 + w^4 + 5*w^3 - 3*w^2 - 7*w + 4],\ [433, 433, -2*w^2 + w + 5],\ [433, 433, -2*w^4 + 3*w^3 + 5*w^2 - 6*w + 3],\ [461, 461, 2*w^3 - 2*w^2 - 5*w + 3],\ [461, 461, -w^5 + 5*w^3 + 2*w^2 - 4*w + 1],\ [461, 461, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + 3*w + 5],\ [461, 461, -w^5 + 3*w^4 + 3*w^3 - 11*w^2 - w + 3],\ [463, 463, -2*w^4 + 3*w^3 + 7*w^2 - 8*w - 4],\ [463, 463, -w^5 + 4*w^4 + w^3 - 12*w^2 + 3*w - 1],\ [491, 491, w^5 - 7*w^3 - w^2 + 10*w + 3],\ [491, 491, -w^5 + 4*w^4 - w^3 - 11*w^2 + 10*w + 2],\ [503, 503, -2*w^5 + 5*w^4 + 5*w^3 - 15*w^2 + w + 3],\ [503, 503, 2*w^4 - w^3 - 8*w^2 + w + 1],\ [503, 503, -2*w^5 + 3*w^4 + 7*w^3 - 7*w^2 - 3*w + 1],\ [503, 503, -2*w^5 + 2*w^4 + 10*w^3 - 5*w^2 - 11*w + 2],\ [547, 547, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 10*w - 5],\ [547, 547, -w^4 + 2*w^3 + 2*w^2 - 4*w + 5],\ [547, 547, -2*w^5 + 4*w^4 + 7*w^3 - 12*w^2 - 3*w + 4],\ [547, 547, -w^5 + w^4 + 3*w^3 - 2*w^2 + 3*w + 2],\ [587, 587, -w^5 - w^4 + 8*w^3 + 4*w^2 - 13*w + 1],\ [587, 587, w^5 - w^4 - 5*w^3 + 2*w^2 + 7*w - 2],\ [617, 617, w^5 - w^4 - 4*w^3 + 3*w^2 - 1],\ [617, 617, w^4 - 2*w^3 - 5*w^2 + 5*w + 6],\ [617, 617, -w^5 + w^4 + 4*w^3 - 3*w^2 + 4],\ [617, 617, -w^5 + 3*w^4 + 6*w^3 - 13*w^2 - 11*w + 8],\ [631, 631, -2*w^5 + 2*w^4 + 10*w^3 - 5*w^2 - 11*w + 1],\ [631, 631, -w^5 + w^4 + 4*w^3 - 2*w - 4],\ [631, 631, -2*w^4 + 5*w^3 + 4*w^2 - 12*w + 4],\ [631, 631, -2*w^5 + 5*w^4 + 5*w^3 - 15*w^2 + w + 4],\ [643, 643, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 6*w - 2],\ [643, 643, -w^5 + 2*w^4 + w^3 - 3*w^2 + 6*w - 3],\ [659, 659, -2*w^4 + 4*w^3 + 7*w^2 - 10*w - 2],\ [659, 659, w^4 - 3*w^3 - 3*w^2 + 10*w - 1],\ [659, 659, w^5 - 4*w^4 + 13*w^2 - 6*w - 6],\ [659, 659, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 7*w - 5],\ [673, 673, 2*w^5 - 3*w^4 - 7*w^3 + 8*w^2 + 2*w - 3],\ [673, 673, w^5 - 4*w^4 - w^3 + 12*w^2 - 3*w - 2],\ [673, 673, -2*w^5 + 3*w^4 + 9*w^3 - 10*w^2 - 8*w + 5],\ [673, 673, w^5 - w^4 - 4*w^3 + 3*w + 6],\ [701, 701, -2*w^4 + 4*w^3 + 6*w^2 - 11*w - 3],\ [701, 701, 2*w^4 - 3*w^3 - 7*w^2 + 6*w + 5],\ [727, 727, -w^5 + 2*w^4 + w^3 - 3*w^2 + 7*w - 2],\ [727, 727, 2*w^5 - 3*w^4 - 7*w^3 + 8*w^2 + 3*w - 4],\ [727, 727, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 2*w + 1],\ [727, 727, w^5 + 2*w^4 - 9*w^3 - 8*w^2 + 16*w + 2],\ [729, 3, -3],\ [743, 743, w^5 - 4*w^4 + 13*w^2 - 8*w - 5],\ [743, 743, -w^3 + w^2 + w - 2],\ [743, 743, w^4 - 4*w^3 - w^2 + 10*w - 2],\ [743, 743, 3*w^3 - 3*w^2 - 11*w + 6],\ [757, 757, -w^5 + 4*w^4 - 11*w^2 + 5*w - 2],\ [757, 757, -3*w^4 + 3*w^3 + 11*w^2 - 5*w - 2],\ [757, 757, w^5 - 3*w^4 - 2*w^3 + 10*w^2 - 4],\ [757, 757, w^5 - 8*w^3 + w^2 + 15*w - 4],\ [769, 769, w^5 - 5*w^3 - 3*w^2 + 4*w + 6],\ [769, 769, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 4*w + 3],\ [769, 769, w^4 - 3*w^3 - w^2 + 9*w - 3],\ [769, 769, w^5 - 4*w^4 - w^3 + 13*w^2 - 4*w - 5],\ [797, 797, w^5 + w^4 - 8*w^3 - 4*w^2 + 11*w + 2],\ [797, 797, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 9*w - 6],\ [811, 811, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 4*w - 4],\ [811, 811, 2*w^4 - 2*w^3 - 6*w^2 + 3*w - 4],\ [811, 811, -2*w^5 + 3*w^4 + 9*w^3 - 8*w^2 - 9*w + 1],\ [811, 811, -w^5 + w^4 + 2*w^3 + w^2 + 4*w - 5],\ [827, 827, w^5 + w^4 - 9*w^3 - 2*w^2 + 14*w - 3],\ [827, 827, w^5 - 3*w^4 + w^3 + 6*w^2 - 11*w + 4],\ [827, 827, w^5 - 3*w^4 + 9*w^2 - 9*w - 4],\ [827, 827, w^5 - w^4 - 4*w^3 + 4*w + 5],\ [827, 827, -w^5 + 4*w^4 + 2*w^3 - 13*w^2 - w + 3],\ [827, 827, -w^5 + w^4 + 7*w^3 - 4*w^2 - 11*w + 3],\ [839, 839, -w^5 + w^4 + 7*w^3 - 4*w^2 - 13*w + 4],\ [839, 839, -w^5 + 3*w^4 + w^3 - 8*w^2 + 3*w - 1],\ [841, 29, -2*w^4 + 5*w^3 + 5*w^2 - 13*w + 1],\ [853, 853, -2*w^4 + 10*w^2 + 3*w - 6],\ [853, 853, 2*w^5 - 4*w^4 - 8*w^3 + 13*w^2 + 8*w - 6],\ [853, 853, -2*w^4 + w^3 + 9*w^2 - 2*w - 4],\ [853, 853, -2*w^5 + 3*w^4 + 8*w^3 - 8*w^2 - 7*w + 1],\ [881, 881, w^5 - 5*w^3 - 2*w^2 + 5*w - 1],\ [881, 881, -w^5 + 3*w^4 + 4*w^3 - 12*w^2 - 5*w + 5],\ [883, 883, 3*w^4 - 4*w^3 - 11*w^2 + 10*w + 5],\ [883, 883, -3*w^4 + 3*w^3 + 12*w^2 - 5*w - 7],\ [883, 883, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + 5*w - 2],\ [883, 883, w^5 - w^4 - 6*w^3 + 4*w^2 + 10*w - 6],\ [911, 911, -w^5 + w^4 + 6*w^3 - 5*w^2 - 7*w + 4],\ [911, 911, 2*w^5 - 4*w^4 - 6*w^3 + 10*w^2 + 2*w + 1],\ [911, 911, w^5 - w^4 - 3*w^3 + 2*w^2 - 2*w - 3],\ [911, 911, -w^5 + 3*w^4 + 4*w^3 - 10*w^2 - 5*w + 2],\ [911, 911, w^5 - 2*w^4 - w^3 + 2*w^2 - 5*w + 6],\ [911, 911, -2*w^5 + 4*w^4 + 8*w^3 - 12*w^2 - 8*w + 3],\ [937, 937, w^4 - 2*w^3 - 5*w^2 + 7*w + 5],\ [937, 937, w^5 + w^4 - 7*w^3 - 5*w^2 + 9*w + 4],\ [937, 937, 3*w^4 - 4*w^3 - 9*w^2 + 7*w - 1],\ [937, 937, -w^5 + 4*w^4 + w^3 - 14*w^2 + 4*w + 8],\ [953, 953, w^5 - 3*w^4 - w^3 + 7*w^2 - 5*w + 4],\ [953, 953, w^5 - 2*w^4 - 3*w^3 + 4*w^2 + 2],\ [967, 967, w^5 - 6*w^4 + 2*w^3 + 20*w^2 - 12*w - 6],\ [967, 967, w^5 - 4*w^4 - 2*w^3 + 14*w^2 + w - 5],\ [967, 967, -w^5 + 8*w^3 - 2*w^2 - 14*w + 10],\ [967, 967, w^5 - 3*w^4 + 7*w^2 - 9*w],\ [967, 967, -w^5 + 6*w^3 + 2*w^2 - 9*w - 2],\ [967, 967, -w^5 + w^4 + 5*w^3 - 2*w^2 - 4*w - 3],\ [1009, 1009, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - 2*w - 4],\ [1009, 1009, -2*w^5 + 4*w^4 + 6*w^3 - 11*w^2 - w + 2],\ [1009, 1009, 2*w^5 - 3*w^4 - 9*w^3 + 9*w^2 + 9*w - 3],\ [1009, 1009, -w^5 + w^4 + 4*w^3 - w^2 - 2*w - 5],\ [1021, 1021, w^5 - w^4 - 5*w^3 + 5*w^2 + 6*w - 10],\ [1021, 1021, w^5 - 8*w^3 + 3*w^2 + 14*w - 6],\ [1021, 1021, 2*w^5 - 4*w^4 - 7*w^3 + 12*w^2 + 4*w - 4],\ [1021, 1021, -2*w^5 + 3*w^4 + 8*w^3 - 8*w^2 - 6*w + 1],\ [1051, 1051, w^5 - w^4 - 3*w^3 + w^2 - w - 2],\ [1051, 1051, 3*w^4 - 6*w^3 - 8*w^2 + 16*w - 3],\ [1091, 1091, -w^5 + 4*w^4 - 13*w^2 + 6*w + 5],\ [1091, 1091, -w^5 - w^4 + 9*w^3 + 3*w^2 - 16*w + 1],\ [1093, 1093, w^2 + w - 5],\ [1093, 1093, w^4 - 3*w^3 - w^2 + 9*w - 2],\ [1093, 1093, 2*w^5 - 5*w^4 - 5*w^3 + 14*w^2 - w - 2],\ [1093, 1093, 2*w^5 - 3*w^4 - 8*w^3 + 7*w^2 + 6*w + 2],\ [1163, 1163, -w^3 + 3*w^2 + 2*w - 5],\ [1163, 1163, 2*w^4 - 2*w^3 - 6*w^2 + 3*w - 3],\ [1217, 1217, w^5 + w^4 - 6*w^3 - 6*w^2 + 3*w + 5],\ [1217, 1217, w^5 - w^4 - 5*w^3 + w^2 + 9*w],\ [1231, 1231, -w^5 + 4*w^4 - w^3 - 10*w^2 + 10*w - 1],\ [1231, 1231, -w^5 + w^4 + 5*w^3 - w^2 - 5*w - 5],\ [1259, 1259, w^5 - w^4 - 5*w^3 + 4*w^2 + 6*w - 7],\ [1259, 1259, w^5 - w^4 - 6*w^3 + 5*w^2 + 9*w - 4],\ [1289, 1289, w^5 + w^4 - 11*w^3 + 23*w - 7],\ [1289, 1289, -w^5 + w^4 + 5*w^3 - 2*w^2 - 8*w - 2],\ [1289, 1289, 2*w^5 - 13*w^3 - w^2 + 19*w - 1],\ [1289, 1289, -2*w^5 + 4*w^4 + 10*w^3 - 15*w^2 - 14*w + 9],\ [1301, 1301, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 6*w + 4],\ [1301, 1301, -w^5 - w^4 + 11*w^3 + 2*w^2 - 23*w + 3],\ [1301, 1301, -2*w^5 + w^4 + 11*w^3 - 2*w^2 - 12*w + 1],\ [1301, 1301, -2*w^5 + 3*w^4 + 9*w^3 - 10*w^2 - 9*w + 6],\ [1303, 1303, w^5 - 4*w^4 - w^3 + 13*w^2 - 2*w - 2],\ [1303, 1303, w^5 - 4*w^4 - w^3 + 14*w^2 - 3*w - 4],\ [1331, 11, -w^4 + 4*w^3 - 2*w^2 - 10*w + 8],\ [1331, 11, w^5 - 5*w^4 + w^3 + 16*w^2 - 10*w - 4],\ [1399, 1399, -w^5 + 6*w^4 - w^3 - 21*w^2 + 8*w + 8],\ [1399, 1399, 2*w^4 - 4*w^3 - 6*w^2 + 13*w - 4],\ [1399, 1399, 2*w^5 - 4*w^4 - 9*w^3 + 15*w^2 + 9*w - 7],\ [1399, 1399, w^5 - 7*w^3 + w^2 + 10*w],\ [1427, 1427, 2*w^5 - 5*w^4 - 7*w^3 + 17*w^2 + 6*w - 6],\ [1427, 1427, -w^5 + 3*w^4 + 2*w^3 - 12*w^2 + 3*w + 9],\ [1471, 1471, w^5 - 5*w^3 - w^2 + 4*w - 3],\ [1471, 1471, w^5 - w^4 - 6*w^3 + 3*w^2 + 7*w - 1],\ [1471, 1471, -w^5 + 3*w^4 - w^3 - 6*w^2 + 12*w - 4],\ [1471, 1471, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 6*w - 6],\ [1483, 1483, -2*w^4 + 2*w^3 + 9*w^2 - 6*w - 6],\ [1483, 1483, -w^5 + 4*w^4 - 2*w^3 - 8*w^2 + 12*w - 7],\ [1483, 1483, -w^5 + 5*w^4 + w^3 - 18*w^2 + w + 3],\ [1483, 1483, w^5 - 4*w^4 - 4*w^3 + 17*w^2 + 7*w - 8],\ [1499, 1499, -2*w^5 + 6*w^4 + 6*w^3 - 21*w^2 - 2*w + 8],\ [1499, 1499, 2*w^5 - 5*w^4 - 7*w^3 + 17*w^2 + 5*w - 7],\ [1567, 1567, 2*w^5 - 7*w^4 - w^3 + 19*w^2 - 11*w],\ [1567, 1567, -w^5 + w^4 + 4*w^3 - 2*w^2 - w - 3],\ [1567, 1567, w^5 - 2*w^4 - 3*w^3 + 6*w^2 - w - 5],\ [1567, 1567, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w - 2],\ [1583, 1583, 2*w^4 - 6*w^3 - 4*w^2 + 17*w - 3],\ [1583, 1583, -2*w^4 + 5*w^3 + 5*w^2 - 12*w + 1],\ [1609, 1609, -4*w^4 + 5*w^3 + 13*w^2 - 11*w + 2],\ [1609, 1609, 2*w^5 - 2*w^4 - 10*w^3 + 3*w^2 + 12*w + 5],\ [1637, 1637, -w^5 - 2*w^4 + 10*w^3 + 6*w^2 - 18*w],\ [1637, 1637, -w^4 + 6*w^2 - 10],\ [1637, 1637, -2*w^4 + w^3 + 8*w^2 - 7],\ [1637, 1637, -w^5 + 4*w^4 - 3*w^3 - 11*w^2 + 17*w + 2],\ [1667, 1667, 2*w^4 - w^3 - 10*w^2 + 2*w + 7],\ [1667, 1667, 3*w^4 - 2*w^3 - 12*w^2 + 2*w + 4],\ [1667, 1667, w^5 - 7*w^3 + w^2 + 9*w - 2],\ [1667, 1667, w^5 - 2*w^4 - 2*w^3 + 6*w^2 - 4*w - 5],\ [1681, 41, -w^4 + 4*w^3 + w^2 - 11*w + 4],\ [1681, 41, -3*w^4 + 6*w^3 + 9*w^2 - 15*w + 1],\ [1693, 1693, w^5 - 3*w^4 - 2*w^3 + 11*w^2 - w - 7],\ [1693, 1693, -w^4 - 3*w^3 + 7*w^2 + 12*w - 7],\ [1693, 1693, -w^4 + 5*w^2 - w + 1],\ [1693, 1693, -w^5 - w^4 + 9*w^3 + 2*w^2 - 16*w + 4],\ [1709, 1709, -w^5 + 7*w^3 - 12*w + 3],\ [1709, 1709, -w^5 + 3*w^4 + 3*w^3 - 11*w^2 - 3*w + 5],\ [1723, 1723, 2*w^5 - w^4 - 10*w^3 + 11*w + 2],\ [1723, 1723, 2*w^5 - 6*w^4 - 6*w^3 + 21*w^2 + 4*w - 9],\ [1723, 1723, -w^5 + 2*w^4 + 6*w^3 - 11*w^2 - 8*w + 10],\ [1723, 1723, -w^5 - w^4 + 5*w^3 + 5*w^2 - 2*w + 2],\ [1777, 1777, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 8*w - 2],\ [1777, 1777, w^5 - 5*w^4 + 17*w^2 - 5*w - 4],\ [1777, 1777, -2*w^5 + 6*w^4 + 5*w^3 - 20*w^2 + 9],\ [1777, 1777, -w^5 + 6*w^4 - 3*w^3 - 17*w^2 + 11*w],\ [1847, 1847, 3*w^5 - 4*w^4 - 14*w^3 + 11*w^2 + 14*w - 3],\ [1847, 1847, 2*w^3 - 3*w^2 - 8*w + 3],\ [1849, 43, 2*w^4 - 5*w^3 - 5*w^2 + 13*w - 2],\ [1849, 43, -w^4 - w^3 + 6*w^2 + 4*w - 3],\ [1861, 1861, 3*w^4 - 5*w^3 - 8*w^2 + 13*w - 6],\ [1861, 1861, 3*w^4 - w^3 - 12*w^2 - w + 2],\ [1861, 1861, -w^5 + w^4 + 6*w^3 - 4*w^2 - 11*w + 6],\ [1861, 1861, -w^5 + 4*w^4 + 3*w^3 - 13*w^2 - 4*w + 2],\ [1933, 1933, -2*w^5 + 4*w^4 + 7*w^3 - 11*w^2 - 4*w + 2],\ [1933, 1933, -2*w^5 + 4*w^4 + 6*w^3 - 10*w^2 - w - 2],\ [1933, 1933, 2*w^4 - 3*w^3 - 7*w^2 + 8*w + 6],\ [1933, 1933, -2*w^4 + 2*w^3 + 8*w^2 - 3*w - 8],\ [1973, 1973, w^4 - 4*w^3 + 12*w - 4],\ [1973, 1973, w^3 - 2*w - 3],\ [1987, 1987, -3*w^5 + 6*w^4 + 10*w^3 - 19*w^2 - 3*w + 9],\ [1987, 1987, -w^4 + 4*w^3 + w^2 - 14*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^9 + 10*x^8 + 15*x^7 - 115*x^6 - 281*x^5 + 515*x^4 + 1326*x^3 - 1268*x^2 - 2069*x + 1697 K. = NumberField(heckePol) hecke_eigenvalues_array = [-2089/29705*e^8 - 17168/29705*e^7 - 682/2285*e^6 + 184023/29705*e^5 + 36182/5941*e^4 - 143937/5941*e^3 - 393164/29705*e^2 + 1055944/29705*e - 313211/29705, e, 5223/29705*e^8 + 45441/29705*e^7 + 2974/2285*e^6 - 472686/29705*e^5 - 124682/5941*e^4 + 371102/5941*e^3 + 1421583/29705*e^2 - 3062083/29705*e + 924802/29705, 1, 2064/5941*e^8 + 15879/5941*e^7 - 159/457*e^6 - 200167/5941*e^5 - 78203/5941*e^4 + 952543/5941*e^3 + 13462/5941*e^2 - 1730441/5941*e + 965609/5941, -4772/29705*e^8 - 29079/29705*e^7 + 6019/2285*e^6 + 577614/29705*e^5 - 92512/5941*e^4 - 724662/5941*e^3 + 2096053/29705*e^2 + 7609607/29705*e - 5825553/29705, -4388/29705*e^8 - 53481/29705*e^7 - 13364/2285*e^6 + 206296/29705*e^5 + 355652/5941*e^4 + 175570/5941*e^3 - 5135508/29705*e^2 - 3299612/29705*e + 4644598/29705, 12084/29705*e^8 + 91688/29705*e^7 - 2363/2285*e^6 - 1234323/29705*e^5 - 68352/5941*e^4 + 1239701/5941*e^3 - 281306/29705*e^2 - 11757339/29705*e + 6974451/29705, 589/5941*e^8 + 5179/5941*e^7 + 492/457*e^6 - 41696/5941*e^5 - 72369/5941*e^4 + 117892/5941*e^3 + 151198/5941*e^2 - 146699/5941*e - 14913/5941, -10887/29705*e^8 - 86529/29705*e^7 - 986/2285*e^6 + 1033449/29705*e^5 + 126596/5941*e^4 - 941725/5941*e^3 - 795482/29705*e^2 + 8400552/29705*e - 4361588/29705, -7187/29705*e^8 - 56164/29705*e^7 + 549/2285*e^6 + 737429/29705*e^5 + 58157/5941*e^4 - 753838/5941*e^3 - 64762/29705*e^2 + 7460807/29705*e - 4292068/29705, -277/5941*e^8 - 499/5941*e^7 + 1211/457*e^6 + 51160/5941*e^5 - 116508/5941*e^4 - 414435/5941*e^3 + 366046/5941*e^2 + 923345/5941*e - 650622/5941, 24/5941*e^8 + 2188/5941*e^7 + 1502/457*e^6 + 29519/5941*e^5 - 170366/5941*e^4 - 375158/5941*e^3 + 547972/5941*e^2 + 918902/5941*e - 864655/5941, -11003/29705*e^8 - 107006/29705*e^7 - 14339/2285*e^6 + 844236/29705*e^5 + 439016/5941*e^4 - 428963/5941*e^3 - 5759023/29705*e^2 + 2388788/29705*e + 2076148/29705, -4152/29705*e^8 - 51769/29705*e^7 - 13066/2285*e^6 + 216349/29705*e^5 + 354087/5941*e^4 + 143154/5941*e^3 - 5125702/29705*e^2 - 2822743/29705*e + 4280337/29705, 928/5941*e^8 + 9350/5941*e^7 + 1257/457*e^6 - 84425/5941*e^5 - 216753/5941*e^4 + 259256/5941*e^3 + 604666/5941*e^2 - 378507/5941*e - 141943/5941, -4902/29705*e^8 - 60734/29705*e^7 - 15446/2285*e^6 + 237014/29705*e^5 + 417816/5941*e^4 + 209518/5941*e^3 - 6090307/29705*e^2 - 3897928/29705*e + 5494587/29705, -718/2285*e^8 - 7571/2285*e^7 - 17092/2285*e^6 + 51036/2285*e^5 + 38010/457*e^4 - 14606/457*e^3 - 510613/2285*e^2 - 1097/2285*e + 256668/2285, -14043/29705*e^8 - 77201/29705*e^7 + 23146/2285*e^6 + 1758946/29705*e^5 - 405794/5941*e^4 - 2317818/5941*e^3 + 8015092/29705*e^2 + 24261408/29705*e - 18221637/29705, 380/5941*e^8 + 2958/5941*e^7 + 170/457*e^6 - 20768/5941*e^5 - 20051/5941*e^4 + 34664/5941*e^3 + 18206/5941*e^2 + 25517/5941*e - 56766/5941, -1578/29705*e^8 + 4664/29705*e^7 + 12066/2285*e^6 + 347896/29705*e^5 - 289959/5941*e^4 - 708840/5941*e^3 + 5207322/29705*e^2 + 8643348/29705*e - 8489537/29705, 6232/29705*e^8 + 53264/29705*e^7 + 2331/2285*e^6 - 618634/29705*e^5 - 118761/5941*e^4 + 588265/5941*e^3 + 1157647/29705*e^2 - 5901557/29705*e + 2392433/29705, 13794/29705*e^8 + 128763/29705*e^7 + 14397/2285*e^6 - 1113903/29705*e^5 - 485039/5941*e^4 + 613824/5941*e^3 + 6205019/29705*e^2 - 3215204/29705*e - 1497399/29705, 11744/29705*e^8 + 100298/29705*e^7 + 5302/2285*e^6 - 1083163/29705*e^5 - 237178/5941*e^4 + 908494/5941*e^3 + 2213884/29705*e^2 - 8090809/29705*e + 3603851/29705, -3709/29705*e^8 - 16333/29705*e^7 + 9898/2285*e^6 + 582743/29705*e^5 - 200684/5941*e^4 - 919307/5941*e^3 + 3819561/29705*e^2 + 10767634/29705*e - 8295116/29705, 8939/29705*e^8 + 67363/29705*e^7 - 2868/2285*e^6 - 994588/29705*e^5 - 46716/5941*e^4 + 1055936/5941*e^3 - 118206/29705*e^2 - 10383764/29705*e + 5679631/29705, -9013/29705*e^8 - 113716/29705*e^7 - 29564/2285*e^6 + 427796/29705*e^5 + 787264/5941*e^4 + 378860/5941*e^3 - 11603743/29705*e^2 - 6885157/29705*e + 10884863/29705, -3893/5941*e^8 - 35088/5941*e^7 - 3293/457*e^6 + 316824/5941*e^5 + 562143/5941*e^4 - 997502/5941*e^3 - 1292511/5941*e^2 + 1312653/5941*e - 149159/5941, 8002/29705*e^8 + 66104/29705*e^7 + 2281/2285*e^6 - 736319/29705*e^5 - 115646/5941*e^4 + 660018/5941*e^3 + 696502/29705*e^2 - 6201542/29705*e + 3121108/29705, 696/29705*e^8 - 25663/29705*e^7 - 22707/2285*e^6 - 498497/29705*e^5 + 531585/5941*e^4 + 1195007/5941*e^3 - 9013484/29705*e^2 - 15170541/29705*e + 14694059/29705, 9273/29705*e^8 + 87911/29705*e^7 + 10799/2285*e^6 - 697156/29705*e^5 - 316729/5941*e^4 + 378702/5941*e^3 + 3648068/29705*e^2 - 2359403/29705*e - 522888/29705, -23371/29705*e^8 - 175077/29705*e^7 + 5287/2285*e^6 + 2330282/29705*e^5 + 93482/5941*e^4 - 2307231/5941*e^3 + 1442824/29705*e^2 + 21408346/29705*e - 13718349/29705, -489/2285*e^8 - 23/2285*e^7 + 34594/2285*e^6 + 91648/2285*e^5 - 56998/457*e^4 - 158955/457*e^3 + 955396/2285*e^2 + 1780334/2285*e - 1557746/2285, 14882/29705*e^8 + 148739/29705*e^7 + 22316/2285*e^6 - 1086689/29705*e^5 - 664845/5941*e^4 + 423700/5941*e^3 + 8920152/29705*e^2 - 1206567/29705*e - 4839177/29705, -1591/5941*e^8 - 1472/5941*e^7 + 7863/457*e^6 + 296013/5941*e^5 - 838171/5941*e^4 - 2548361/5941*e^3 + 2903436/5941*e^2 + 5838026/5941*e - 5105884/5941, 30898/29705*e^8 + 282041/29705*e^7 + 27629/2285*e^6 - 2565361/29705*e^5 - 939314/5941*e^4 + 1705032/5941*e^3 + 11276298/29705*e^2 - 12722448/29705*e + 1033092/29705, 1358/5941*e^8 + 8945/5941*e^7 - 1461/457*e^6 - 173902/5941*e^5 + 98413/5941*e^4 + 1129283/5941*e^3 - 483198/5941*e^2 - 2485422/5941*e + 1615520/5941, 16569/29705*e^8 + 129258/29705*e^7 - 1018/2285*e^6 - 1662673/29705*e^5 - 130895/5941*e^4 + 1656286/5941*e^3 - 79091/29705*e^2 - 16047079/29705*e + 9456476/29705, -933/29705*e^8 - 10796/29705*e^7 - 2979/2285*e^6 - 20989/29705*e^5 + 31537/5941*e^4 + 74382/5941*e^3 + 224802/29705*e^2 - 502582/29705*e - 711407/29705, -8587/29705*e^8 - 104584/29705*e^7 - 26896/2285*e^6 + 332409/29705*e^5 + 701114/5941*e^4 + 484177/5941*e^3 - 10265932/29705*e^2 - 8406558/29705*e + 11074437/29705, -4294/29705*e^8 - 84518/29705*e^7 - 35282/2285*e^6 - 147922/29705*e^5 + 866005/5941*e^4 + 1098215/5941*e^3 - 12997889/29705*e^2 - 14266921/29705*e + 14633699/29705, -12874/29705*e^8 - 124103/29705*e^7 - 16992/2285*e^6 + 898838/29705*e^5 + 481959/5941*e^4 - 369030/5941*e^3 - 5685974/29705*e^2 + 1358039/29705*e + 1671399/29705, -19423/29705*e^8 - 141906/29705*e^7 + 7871/2285*e^6 + 2097691/29705*e^5 + 57534/5941*e^4 - 2184523/5941*e^3 + 710682/29705*e^2 + 20674178/29705*e - 11798702/29705, 4566/29705*e^8 + 59807/29705*e^7 + 17268/2285*e^6 - 127472/29705*e^5 - 438647/5941*e^4 - 367475/5941*e^3 + 6391521/29705*e^2 + 5553104/29705*e - 6810136/29705, -1804/29705*e^8 - 35743/29705*e^7 - 15407/2285*e^6 - 92957/29705*e^5 + 381614/5941*e^4 + 529031/5941*e^3 - 6139309/29705*e^2 - 7110131/29705*e + 8136874/29705, -1198/5941*e^8 - 10201/5941*e^7 - 560/457*e^6 + 107311/5941*e^5 + 116401/5941*e^4 - 455862/5941*e^3 - 222369/5941*e^2 + 826745/5941*e - 359605/5941, -11722/29705*e^8 - 108194/29705*e^7 - 11161/2285*e^6 + 973084/29705*e^5 + 376847/5941*e^4 - 626952/5941*e^3 - 4686037/29705*e^2 + 4454612/29705*e + 346942/29705, -10012/29705*e^8 - 71119/29705*e^7 + 5599/2285*e^6 + 1123209/29705*e^5 + 7688/5941*e^4 - 1199360/5941*e^3 + 493268/29705*e^2 + 11303562/29705*e - 6104968/29705, 12637/29705*e^8 + 117349/29705*e^7 + 11871/2285*e^6 - 1091569/29705*e^5 - 400058/5941*e^4 + 782915/5941*e^3 + 4739412/29705*e^2 - 6634412/29705*e + 1231288/29705, -26107/29705*e^8 - 216574/29705*e^7 - 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8809832/29705, -26418/29705*e^8 - 239976/29705*e^7 - 22979/2285*e^6 + 2174181/29705*e^5 + 767525/5941*e^4 - 1442629/5941*e^3 - 8747483/29705*e^2 + 10902343/29705*e - 1335242/29705, -1497/29705*e^8 - 62214/29705*e^7 - 33706/2285*e^6 - 301786/29705*e^5 + 825128/5941*e^4 + 1121140/5941*e^3 - 13109997/29705*e^2 - 13209043/29705*e + 15755247/29705, -31524/29705*e^8 - 259898/29705*e^7 - 12347/2285*e^6 + 2602888/29705*e^5 + 511333/5941*e^4 - 1953455/5941*e^3 - 4031129/29705*e^2 + 14616584/29705*e - 7047801/29705, 91373/29705*e^8 + 691036/29705*e^7 - 18256/2285*e^6 - 9264666/29705*e^5 - 489297/5941*e^4 + 9296548/5941*e^3 - 2593222/29705*e^2 - 88397198/29705*e + 52005527/29705, -10597/29705*e^8 - 139304/29705*e^7 - 41866/2285*e^6 + 125199/29705*e^5 + 997144/5941*e^4 + 1162740/5941*e^3 - 13502207/29705*e^2 - 16879723/29705*e + 15338597/29705, -26833/29705*e^8 - 104531/29705*e^7 + 75391/2285*e^6 + 3952271/29705*e^5 - 1491507/5941*e^4 - 5922335/5941*e^3 + 26834702/29705*e^2 + 64921238/29705*e - 52320352/29705, -66434/29705*e^8 - 571043/29705*e^7 - 35902/2285*e^6 + 5829088/29705*e^5 + 1477252/5941*e^4 - 4456022/5941*e^3 - 15503834/29705*e^2 + 35629419/29705*e - 13413996/29705, 5921/5941*e^8 + 41744/5941*e^7 - 3689/457*e^6 - 671178/5941*e^5 + 78601/5941*e^4 + 3748510/5941*e^3 - 769536/5941*e^2 - 7362242/5941*e + 4464366/5941, -21233/29705*e^8 - 297016/29705*e^7 - 89029/2285*e^6 + 730436/29705*e^5 + 2275712/5941*e^4 + 1560118/5941*e^3 - 33030863/29705*e^2 - 23075097/29705*e + 30906683/29705, -30683/29705*e^8 - 89161/29705*e^7 + 109026/2285*e^6 + 5006931/29705*e^5 - 2217110/5941*e^4 - 7961235/5941*e^3 + 38808972/29705*e^2 + 89095073/29705*e - 72851407/29705, -3234/5941*e^8 - 45311/5941*e^7 - 13882/457*e^6 + 93385/5941*e^5 + 1797947/5941*e^4 + 1441264/5941*e^3 - 5446435/5941*e^2 - 4303977/5941*e + 5675480/5941, 43076/29705*e^8 + 402102/29705*e^7 + 42193/2285*e^6 - 3678622/29705*e^5 - 1412227/5941*e^4 + 2542535/5941*e^3 + 17183076/29705*e^2 - 20594596/29705*e + 1688599/29705, -16139/5941*e^8 - 141545/5941*e^7 - 10383/457*e^6 + 1406848/5941*e^5 + 1991493/5941*e^4 - 5254820/5941*e^3 - 4448612/5941*e^2 + 8391270/5941*e - 2274880/5941, 26989/29705*e^8 + 148458/29705*e^7 - 42778/2285*e^6 - 3228678/29705*e^5 + 775740/5941*e^4 + 4195337/5941*e^3 - 15145596/29705*e^2 - 43228489/29705*e + 31856506/29705, -6739/29705*e^8 - 114338/29705*e^7 - 41487/2285*e^6 + 56683/29705*e^5 + 1020649/5941*e^4 + 940041/5941*e^3 - 14803994/29705*e^2 - 11806666/29705*e + 13453189/29705, 1134/29705*e^8 - 15437/29705*e^7 - 19288/2285*e^6 - 540508/29705*e^5 + 491373/5941*e^4 + 1344794/5941*e^3 - 8880996/29705*e^2 - 18715829/29705*e + 15969231/29705, -47114/29705*e^8 - 384068/29705*e^7 - 10422/2285*e^6 + 4372338/29705*e^5 + 646183/5941*e^4 - 3907741/5941*e^3 - 4158314/29705*e^2 + 35512799/29705*e - 18166511/29705, 7119/29705*e^8 + 40063/29705*e^7 - 10898/2285*e^6 - 891368/29705*e^5 + 152847/5941*e^4 + 1129607/5941*e^3 - 1967066/29705*e^2 - 10963434/29705*e + 4972496/29705, 1379/29705*e^8 - 57462/29705*e^7 - 46418/2285*e^6 - 787473/29705*e^5 + 1115391/5941*e^4 + 1966565/5941*e^3 - 18085156/29705*e^2 - 23284344/29705*e + 23147351/29705, -14608/5941*e^8 - 127720/5941*e^7 - 9205/457*e^6 + 1271707/5941*e^5 + 1776270/5941*e^4 - 4774710/5941*e^3 - 4022647/5941*e^2 + 7557478/5941*e - 1854361/5941, 15377/29705*e^8 - 28921/29705*e^7 - 103799/2285*e^6 - 3162449/29705*e^5 + 2296507/5941*e^4 + 5867245/5941*e^3 - 37925463/29705*e^2 - 66608987/29705*e + 57839003/29705, 1678/29705*e^8 + 53961/29705*e^7 + 24659/2285*e^6 - 51621/29705*e^5 - 685733/5941*e^4 - 485040/5941*e^3 + 10581768/29705*e^2 + 5918817/29705*e - 7445718/29705, -46744/29705*e^8 - 211713/29705*e^7 + 108323/2285*e^6 + 6344853/29705*e^5 - 2082233/5941*e^4 - 8966725/5941*e^3 + 39034536/29705*e^2 + 95865529/29705*e - 78829051/29705, 11867/29705*e^8 + 126364/29705*e^7 + 22711/2285*e^6 - 833109/29705*e^5 - 690139/5941*e^4 + 66203/5941*e^3 + 9843362/29705*e^2 + 4040358/29705*e - 6938567/29705, -4936/5941*e^8 - 24227/5941*e^7 + 10684/457*e^6 + 697705/5941*e^5 - 959892/5941*e^4 - 4913459/5941*e^3 + 3623225/5941*e^2 + 10691479/5941*e - 8209723/5941, 3118/5941*e^8 + 36716/5941*e^7 + 8755/457*e^6 - 145955/5941*e^5 - 1156702/5941*e^4 - 576580/5941*e^3 + 3239518/5941*e^2 + 2189509/5941*e - 2933046/5941, 21774/29705*e^8 + 291878/29705*e^7 + 84232/2285*e^6 - 759878/29705*e^5 - 2166194/5941*e^4 - 1502920/5941*e^3 + 31652424/29705*e^2 + 23003596/29705*e - 30784474/29705, 8518/5941*e^8 + 83441/5941*e^7 + 11267/457*e^6 - 674967/5941*e^5 - 1799348/5941*e^4 + 1656414/5941*e^3 + 4849656/5941*e^2 - 1636286/5941*e - 2074990/5941, -43022/29705*e^8 - 308064/29705*e^7 + 24024/2285*e^6 + 4869374/29705*e^5 - 56414/5941*e^4 - 5455504/5941*e^3 + 5241408/29705*e^2 + 54722732/29705*e - 33697018/29705, -40229/29705*e^8 - 276223/29705*e^7 + 26873/2285*e^6 + 4341258/29705*e^5 - 215581/5941*e^4 - 4732502/5941*e^3 + 7798556/29705*e^2 + 45375274/29705*e - 29640081/29705, -44678/29705*e^8 - 399626/29705*e^7 - 33914/2285*e^6 + 3830651/29705*e^5 + 1220504/5941*e^4 - 2758097/5941*e^3 - 13961448/29705*e^2 + 22027523/29705*e - 4804262/29705, -62657/29705*e^8 - 508904/29705*e^7 - 10316/2285*e^6 + 6083499/29705*e^5 + 884714/5941*e^4 - 5593787/5941*e^3 - 7310687/29705*e^2 + 51148147/29705*e - 24038178/29705, 4345/5941*e^8 + 8964/5941*e^7 - 17623/457*e^6 - 712433/5941*e^5 + 1889090/5941*e^4 + 5871456/5941*e^3 - 6545026/5941*e^2 - 13062116/5941*e + 11085495/5941, -20141/29705*e^8 - 197462/29705*e^7 - 25258/2285*e^6 + 1666592/29705*e^5 + 740828/5941*e^4 - 1171793/5941*e^3 - 8567476/29705*e^2 + 11112641/29705*e - 2104984/29705, 27704/29705*e^8 + 278003/29705*e^7 + 42147/2285*e^6 - 2038593/29705*e^5 - 1252793/5941*e^4 + 887175/5941*e^3 + 17195349/29705*e^2 - 4399114/29705*e - 8779024/29705, -9563/5941*e^8 - 58900/5941*e^7 + 11344/457*e^6 + 1130126/5941*e^5 - 832329/5941*e^4 - 6920410/5941*e^3 + 3693934/5941*e^2 + 14112021/5941*e - 10313325/5941, 12245/5941*e^8 + 101415/5941*e^7 + 3638/457*e^6 - 1136059/5941*e^5 - 974201/5941*e^4 + 4970522/5941*e^3 + 1458897/5941*e^2 - 8895739/5941*e + 4818613/5941, -109/29705*e^8 - 74298/29705*e^7 - 50427/2285*e^6 - 722472/29705*e^5 + 1235318/5941*e^4 + 2042766/5941*e^3 - 20239424/29705*e^2 - 24636626/29705*e + 25651479/29705, 131/2285*e^8 + 4707/2285*e^7 + 30984/2285*e^6 + 13723/2285*e^5 - 60087/457*e^4 - 72609/457*e^3 + 910826/2285*e^2 + 917564/2285*e - 914041/2285, 12042/5941*e^8 + 99741/5941*e^7 + 3920/457*e^6 - 1088443/5941*e^5 - 961504/5941*e^4 + 4701419/5941*e^3 + 1451016/5941*e^2 - 8568060/5941*e + 4458114/5941, -12122/5941*e^8 - 87231/5941*e^7 + 6002/457*e^6 + 1314821/5941*e^5 - 120227/5941*e^4 - 7334326/5941*e^3 + 1893061/5941*e^2 + 14961145/5941*e - 9627966/5941, 67196/29705*e^8 + 432577/29705*e^7 - 68362/2285*e^6 - 7875727/29705*e^5 + 881357/5941*e^4 + 9466155/5941*e^3 - 21541379/29705*e^2 - 97057501/29705*e + 68180184/29705, -14384/29705*e^8 - 14223/29705*e^7 + 69403/2285*e^6 + 2588873/29705*e^5 - 1486431/5941*e^4 - 4489490/5941*e^3 + 25049831/29705*e^2 + 51407594/29705*e - 43174271/29705, -8510/5941*e^8 - 78751/5941*e^7 - 8329/457*e^6 + 692728/5941*e^5 + 1360355/5941*e^4 - 2181494/5941*e^3 - 3278785/5941*e^2 + 3079298/5941*e + 125272/5941, -508/2285*e^8 - 6706/2285*e^7 - 21042/2285*e^6 + 41411/2285*e^5 + 44917/457*e^4 - 15109/457*e^3 - 651458/2285*e^2 + 166328/2285*e + 295988/2285, -1016/2285*e^8 + 2583/2285*e^7 + 97301/2285*e^6 + 229062/2285*e^5 - 165629/457*e^4 - 433749/457*e^3 + 2766669/2285*e^2 + 5012336/2285*e - 4407604/2285, 55709/29705*e^8 + 439873/29705*e^7 + 497/2285*e^6 - 5560313/29705*e^5 - 617614/5941*e^4 + 5255314/5941*e^3 + 3798244/29705*e^2 - 48239029/29705*e + 25609101/29705, -40762/29705*e^8 - 468389/29705*e^7 - 103406/2285*e^6 + 2326934/29705*e^5 + 2840394/5941*e^4 + 612591/5941*e^3 - 40837837/29705*e^2 - 18164163/29705*e + 33906337/29705, 49037/29705*e^8 + 425709/29705*e^7 + 28516/2285*e^6 - 4314464/29705*e^5 - 1117827/5941*e^4 + 3373139/5941*e^3 + 11625447/29705*e^2 - 28875007/29705*e + 11334108/29705, -12384/29705*e^8 - 178448/29705*e^7 - 59827/2285*e^6 - 40667/29705*e^5 + 1397299/5941*e^4 + 1741898/5941*e^3 - 19935594/29705*e^2 - 23760281/29705*e + 24463859/29705, 59672/29705*e^8 + 400149/29705*e^7 - 47964/2285*e^6 - 6706449/29705*e^5 + 452447/5941*e^4 + 7599104/5941*e^3 - 12973723/29705*e^2 - 74977432/29705*e + 49278228/29705, 21277/29705*e^8 + 73289/29705*e^7 - 62074/2285*e^6 - 2851714/29705*e^5 + 1324645/5941*e^4 + 4314220/5941*e^3 - 23392208/29705*e^2 - 46429272/29705*e + 38424843/29705, -123408/29705*e^8 - 1061881/29705*e^7 - 63964/2285*e^6 + 11139286/29705*e^5 + 2758552/5941*e^4 - 8867154/5941*e^3 - 30475638/29705*e^2 + 74009073/29705*e - 24201912/29705, 40244/29705*e^8 + 322148/29705*e^7 + 8912/2285*e^6 - 3442798/29705*e^5 - 490415/5941*e^4 + 2812707/5941*e^3 + 2539659/29705*e^2 - 22425669/29705*e + 12624536/29705, -24491/29705*e^8 - 356397/29705*e^7 - 113553/2285*e^6 + 616072/29705*e^5 + 2921273/5941*e^4 + 2455716/5941*e^3 - 44081061/29705*e^2 - 35623229/29705*e + 45811746/29705, -5895/5941*e^8 - 47295/5941*e^7 - 244/457*e^6 + 602655/5941*e^5 + 325985/5941*e^4 - 3001387/5941*e^3 - 314170/5941*e^2 + 5861509/5941*e - 3264791/5941, -7463/5941*e^8 - 81326/5941*e^7 - 15810/457*e^6 + 478164/5941*e^5 + 2238112/5941*e^4 - 78678/5941*e^3 - 6217915/5941*e^2 - 1716372/5941*e + 4258300/5941, -1572/29705*e^8 - 54199/29705*e^7 - 29831/2285*e^6 - 368041/29705*e^5 + 731098/5941*e^4 + 1279866/5941*e^3 - 11569712/29705*e^2 - 16385088/29705*e + 15460802/29705, -27098/29705*e^8 - 252461/29705*e^7 - 28214/2285*e^6 + 2149746/29705*e^5 + 911094/5941*e^4 - 1255480/5941*e^3 - 11747748/29705*e^2 + 7482193/29705*e + 3270868/29705, -1949/29705*e^8 - 113323/29705*e^7 - 70372/2285*e^6 - 1124082/29705*e^5 + 1603879/5941*e^4 + 3085956/5941*e^3 - 24515359/29705*e^2 - 37616506/29705*e + 34185274/29705, -1991/2285*e^8 - 12042/2285*e^7 + 34686/2285*e^6 + 249757/2285*e^5 - 42154/457*e^4 - 325814/457*e^3 + 900074/2285*e^2 + 3494176/2285*e - 2456624/2285, -7121/29705*e^8 - 20442/29705*e^7 + 28672/2285*e^6 + 1446867/29705*e^5 - 526865/5941*e^4 - 2315317/5941*e^3 + 9212989/29705*e^2 + 25989871/29705*e - 21075309/29705, -17041/29705*e^8 - 162387/29705*e^7 - 20143/2285*e^6 + 1286107/29705*e^5 + 567718/5941*e^4 - 789419/5941*e^3 - 6119161/29705*e^2 + 7191811/29705*e - 1420524/29705, 2461/29705*e^8 + 80787/29705*e^7 + 44528/2285*e^6 + 579483/29705*e^5 - 1089501/5941*e^4 - 1988624/5941*e^3 + 17328891/29705*e^2 + 26625579/29705*e - 24136231/29705] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([29, 29, -w^4 + w^3 + 4*w^2 - 3*w - 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]