/* 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([8, 8, -7, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([14,14,-1/2*w^2 + 3/2*w + 2]) primes_array = [ [2, 2, 1/2*w^2 + 1/2*w - 2],\ [2, 2, -1/2*w^3 + 1/2*w^2 + 3*w + 1],\ [7, 7, -1/2*w^3 + 3/2*w^2 + w - 3],\ [23, 23, 1/2*w^3 + 1/2*w^2 - 3*w - 3],\ [25, 5, -1/2*w^3 + 9/2*w + 1],\ [25, 5, -1/2*w^3 + 5/2*w - 1],\ [31, 31, -1/2*w^3 + 1/2*w^2 + 2*w - 1],\ [31, 31, 1/2*w^3 - w^2 - 3/2*w + 1],\ [41, 41, 3/2*w^3 - w^2 - 21/2*w - 5],\ [41, 41, 1/2*w^3 - 2*w^2 - 5/2*w + 7],\ [47, 47, -w^2 - w + 5],\ [47, 47, -w^3 + 1/2*w^2 + 13/2*w + 5],\ [49, 7, 1/2*w^2 - 1/2*w - 5],\ [73, 73, -1/2*w^3 + 1/2*w^2 + 4*w - 3],\ [73, 73, 1/2*w^3 - w^2 - 7/2*w + 1],\ [79, 79, w^2 - 3*w + 1],\ [79, 79, w^2 + w - 1],\ [81, 3, -3],\ [89, 89, -1/2*w^3 + 3*w^2 + 7/2*w - 11],\ [89, 89, 1/2*w^3 - 5/2*w - 3],\ [89, 89, -1/2*w^3 + 3/2*w^2 + w - 5],\ [89, 89, 5/2*w^3 - 2*w^2 - 33/2*w - 7],\ [97, 97, -1/2*w^3 + w^2 + 3/2*w - 5],\ [97, 97, -1/2*w^2 - 3/2*w + 3],\ [97, 97, w^3 - w^2 - 6*w - 1],\ [97, 97, 1/2*w^3 - 1/2*w^2 - 2*w - 3],\ [113, 113, w^3 - 3*w^2 - 6*w + 13],\ [113, 113, 3*w^3 - 3/2*w^2 - 43/2*w - 11],\ [127, 127, -1/2*w^3 + w^2 + 3/2*w - 7],\ [127, 127, 3/2*w^3 - w^2 - 13/2*w + 7],\ [127, 127, 3/2*w^3 + w^2 - 29/2*w - 11],\ [127, 127, 1/2*w^3 - 1/2*w^2 - 2*w - 5],\ [137, 137, 2*w^3 - 3/2*w^2 - 25/2*w - 9],\ [137, 137, -3*w^2 - w + 11],\ [167, 167, 1/2*w^2 + 3/2*w - 5],\ [167, 167, 1/2*w^2 - 5/2*w - 3],\ [191, 191, 2*w^3 - w^2 - 15*w - 5],\ [191, 191, -w^3 + 3/2*w^2 + 11/2*w - 7],\ [199, 199, -1/2*w^3 - w^2 + 11/2*w + 7],\ [199, 199, 5/2*w^3 - 3/2*w^2 - 17*w - 9],\ [199, 199, 1/2*w^3 - 5/2*w^2 - 4*w + 11],\ [199, 199, 1/2*w^3 - 5/2*w + 3],\ [223, 223, -w^3 + 2*w^2 + 5*w - 3],\ [223, 223, w^3 - w^2 - 6*w + 3],\ [233, 233, -2*w^2 + 7],\ [233, 233, w^3 + w^2 - 6*w - 5],\ [233, 233, -5/2*w^3 + w^2 + 35/2*w + 13],\ [233, 233, -w^3 + 1/2*w^2 + 13/2*w + 7],\ [241, 241, w^3 + w^2 - 10*w - 9],\ [241, 241, -1/2*w^3 + 3/2*w^2 + 3*w - 3],\ [241, 241, -1/2*w^3 + 9/2*w - 1],\ [241, 241, w^3 - 1/2*w^2 - 9/2*w + 5],\ [257, 257, w^3 - w^2 - 8*w + 3],\ [257, 257, 5/2*w^3 - w^2 - 39/2*w - 7],\ [263, 263, w^3 - 5*w + 3],\ [263, 263, w^3 + 1/2*w^2 - 19/2*w - 5],\ [271, 271, -1/2*w^3 + 2*w^2 + 5/2*w - 13],\ [271, 271, -2*w^3 + 7/2*w^2 + 17/2*w - 15],\ [281, 281, 1/2*w^3 - 5/2*w - 7],\ [281, 281, -1/2*w^3 + 3/2*w^2 + w - 9],\ [289, 17, 3/2*w^2 - 3/2*w - 5],\ [289, 17, 3/2*w^2 - 3/2*w - 7],\ [311, 311, w^3 - 3*w^2 - 2*w + 3],\ [311, 311, -w^3 + 5*w - 1],\ [313, 313, 7/2*w^3 - w^2 - 53/2*w - 15],\ [313, 313, -1/2*w^3 + 3/2*w^2 + w - 7],\ [313, 313, 1/2*w^3 - 5/2*w - 5],\ [313, 313, 3/2*w^3 - 3*w^2 - 17/2*w + 15],\ [337, 337, w^3 - w^2 - 8*w - 1],\ [337, 337, -w^3 + 2*w^2 + 7*w - 9],\ [353, 353, w^3 - w^2 - 6*w - 5],\ [353, 353, 1/2*w^3 - 13/2*w - 5],\ [359, 359, 3/2*w^3 - 5/2*w^2 - 7*w + 13],\ [359, 359, 5/2*w^3 + 1/2*w^2 - 21*w - 17],\ [361, 19, 3/2*w^3 - 3/2*w^2 - 10*w - 3],\ [361, 19, -1/2*w^3 + 5/2*w^2 + 2*w - 7],\ [401, 401, 1/2*w^3 + 1/2*w^2 - 5*w - 1],\ [401, 401, -1/2*w^3 + 2*w^2 + 5/2*w - 5],\ [409, 409, 5/2*w^3 - 5/2*w^2 - 14*w - 9],\ [409, 409, 1/2*w^3 + 7/2*w^2 - 13],\ [431, 431, -w^3 + 3/2*w^2 + 7/2*w - 7],\ [431, 431, -1/2*w^3 + 13/2*w - 9],\ [439, 439, -w^3 + 2*w^2 + 3*w - 7],\ [439, 439, w^3 - w^2 - 4*w - 3],\ [457, 457, -1/2*w^3 + 9/2*w - 3],\ [457, 457, -1/2*w^3 + 3/2*w^2 + 3*w - 1],\ [487, 487, -1/2*w^3 + 1/2*w^2 + 4*w - 7],\ [487, 487, w^2 - 3*w - 5],\ [487, 487, w^2 + w - 7],\ [487, 487, 1/2*w^3 - w^2 - 7/2*w - 3],\ [529, 23, 1/2*w^2 - 1/2*w - 7],\ [569, 569, -w^3 + 3/2*w^2 + 15/2*w - 5],\ [569, 569, -w^3 + 3/2*w^2 + 15/2*w - 3],\ [577, 577, -w^3 + 2*w^2 + 7*w - 7],\ [577, 577, w^3 - w^2 - 8*w + 1],\ [593, 593, 3/2*w^3 + w^2 - 17/2*w - 5],\ [593, 593, -3/2*w^3 + 11/2*w^2 + 2*w - 11],\ [599, 599, -w^3 + 5/2*w^2 + 9/2*w - 5],\ [599, 599, -3/2*w^3 + 2*w^2 + 15/2*w - 7],\ [599, 599, 3/2*w^3 - 5/2*w^2 - 7*w + 1],\ [599, 599, w^3 - 1/2*w^2 - 13/2*w + 1],\ [601, 601, -1/2*w^3 - w^2 + 15/2*w + 1],\ [601, 601, -2*w^3 + 5/2*w^2 + 23/2*w + 1],\ [607, 607, w^3 - w^2 - 6*w + 7],\ [607, 607, 2*w^3 - 1/2*w^2 - 31/2*w - 7],\ [617, 617, 3/2*w^3 - 1/2*w^2 - 7*w + 5],\ [617, 617, 3/2*w^3 + 1/2*w^2 - 14*w - 7],\ [631, 631, -9/2*w^3 + 7/2*w^2 + 29*w + 15],\ [631, 631, w^3 - 3/2*w^2 - 15/2*w + 9],\ [641, 641, 2*w^3 + 1/2*w^2 - 37/2*w - 11],\ [641, 641, -2*w^3 + 2*w^2 + 8*w - 9],\ [647, 647, w^3 - 2*w^2 - 5*w + 1],\ [647, 647, -w^3 + w^2 + 6*w - 5],\ [719, 719, -1/2*w^3 + 3/2*w^2 + 5*w - 9],\ [719, 719, w^3 - 1/2*w^2 - 13/2*w + 7],\ [727, 727, -3*w^2 - w + 9],\ [727, 727, -1/2*w^3 + w^2 + 7/2*w - 9],\ [727, 727, 1/2*w^3 - 1/2*w^2 - 4*w - 5],\ [727, 727, 2*w^3 - 5/2*w^2 - 23/2*w - 3],\ [743, 743, w^3 - 3*w^2 - 2*w + 9],\ [743, 743, w^3 + 1/2*w^2 - 19/2*w - 11],\ [751, 751, -1/2*w^3 + 3*w^2 - 1/2*w - 11],\ [751, 751, 1/2*w^3 + 3/2*w^2 - 4*w - 9],\ [761, 761, w^3 + w^2 - 8*w - 7],\ [761, 761, -w^3 + 4*w^2 + 3*w - 13],\ [823, 823, 3/2*w^3 - 7/2*w^2 - 6*w + 11],\ [823, 823, -3/2*w^3 + 5/2*w^2 + 7*w - 9],\ [823, 823, 5/2*w^3 - 3/2*w^2 - 19*w - 5],\ [823, 823, 5/2*w^3 - 3/2*w^2 - 19*w - 7],\ [841, 29, 1/2*w^3 + 1/2*w^2 - 3*w - 9],\ [841, 29, -1/2*w^3 + 2*w^2 + 1/2*w - 11],\ [857, 857, -3/2*w^3 + 4*w^2 + 11/2*w - 15],\ [857, 857, -w^3 + w^2 + 6*w - 9],\ [863, 863, -2*w^3 + w^2 + 9*w - 7],\ [863, 863, -1/2*w^3 + 2*w^2 + 9/2*w - 9],\ [863, 863, 5/2*w^3 - 2*w^2 - 33/2*w - 5],\ [863, 863, 2*w^3 + 1/2*w^2 - 37/2*w - 9],\ [887, 887, 1/2*w^3 + 1/2*w^2 - 3*w + 3],\ [887, 887, -1/2*w^3 - 3/2*w^2 + 6*w + 9],\ [911, 911, -1/2*w^3 - 3/2*w^2 + 6*w + 7],\ [911, 911, -1/2*w^3 + 3*w^2 + 3/2*w - 11],\ [919, 919, 4*w^3 - w^2 - 31*w - 17],\ [919, 919, 2*w^3 - 7/2*w^2 - 21/2*w + 17],\ [929, 929, 1/2*w^3 + 1/2*w^2 - 5*w + 3],\ [929, 929, -1/2*w^3 + 2*w^2 + 5/2*w - 1],\ [937, 937, -w^3 + 9/2*w^2 + 5/2*w - 13],\ [937, 937, -2*w^3 + 9/2*w^2 + 19/2*w - 13],\ [937, 937, 2*w^3 - 3/2*w^2 - 25/2*w - 1],\ [937, 937, w^3 + 3/2*w^2 - 17/2*w - 7],\ [953, 953, 3/2*w^3 - 2*w^2 - 11/2*w + 9],\ [953, 953, -3/2*w^3 - w^2 + 29/2*w + 13],\ [961, 31, 2*w^2 - 2*w - 7],\ [977, 977, -1/2*w^3 + 3/2*w^2 + 5*w - 13],\ [977, 977, 1/2*w^3 - 13/2*w - 7],\ [983, 983, 2*w^3 + 1/2*w^2 - 25/2*w - 7],\ [983, 983, -2*w^3 + 7/2*w^2 + 17/2*w - 17],\ [983, 983, -3*w^3 - w^2 + 26*w + 23],\ [983, 983, 2*w^3 - 3/2*w^2 - 25/2*w + 1],\ [991, 991, -w^3 - 1/2*w^2 + 11/2*w - 1],\ [991, 991, -11/2*w^2 - 5/2*w + 19],\ [991, 991, -4*w^3 + 4*w^2 + 24*w + 11],\ [991, 991, -w^3 + 9*w + 1],\ [1009, 1009, 1/2*w^3 + 1/2*w^2 - 7*w + 3],\ [1009, 1009, -1/2*w^3 + 2*w^2 + 9/2*w - 3],\ [1031, 1031, -4*w^2 - 2*w + 13],\ [1031, 1031, -3/2*w^3 + 3/2*w^2 + 8*w - 3],\ [1033, 1033, -1/2*w^3 - 2*w^2 + 9/2*w + 15],\ [1033, 1033, -1/2*w^3 + 7/2*w^2 - w - 17],\ [1039, 1039, -1/2*w^3 + 3*w^2 - 1/2*w - 9],\ [1039, 1039, -1/2*w^3 - 3/2*w^2 + 4*w + 7],\ [1049, 1049, 3/2*w^2 - 11/2*w - 3],\ [1049, 1049, -w^3 + 3/2*w^2 + 15/2*w - 13],\ [1049, 1049, 3/2*w^3 - 7/2*w^2 - 6*w + 15],\ [1049, 1049, 3/2*w^2 + 5/2*w - 7],\ [1063, 1063, 7/2*w^3 - 2*w^2 - 47/2*w - 13],\ [1063, 1063, -w^3 + 1/2*w^2 + 21/2*w + 9],\ [1063, 1063, -w^3 - w^2 + 6*w + 9],\ [1063, 1063, w^3 + 1/2*w^2 - 15/2*w - 3],\ [1097, 1097, -3/2*w^3 + 4*w^2 + 7/2*w - 11],\ [1097, 1097, w^3 - 9/2*w^2 - 9/2*w + 17],\ [1103, 1103, w^2 - 3*w - 7],\ [1103, 1103, w^2 + w - 9],\ [1151, 1151, -w^3 + 7/2*w^2 + 3/2*w - 11],\ [1151, 1151, w^3 + 1/2*w^2 - 11/2*w - 7],\ [1153, 1153, 3/2*w^3 - 2*w^2 - 19/2*w - 1],\ [1153, 1153, -3/2*w^3 + 5/2*w^2 + 9*w - 11],\ [1201, 1201, 3/2*w^3 - 9/2*w^2 - 7*w + 15],\ [1201, 1201, w^3 - 7/2*w^2 - 15/2*w + 17],\ [1217, 1217, 1/2*w^3 + w^2 - 11/2*w - 1],\ [1217, 1217, -1/2*w^3 - 2*w^2 + 1/2*w + 9],\ [1217, 1217, -3/2*w^3 + w^2 + 17/2*w + 9],\ [1217, 1217, -1/2*w^3 + 5/2*w^2 + 2*w - 5],\ [1223, 1223, -1/2*w^3 + w^2 + 11/2*w - 1],\ [1223, 1223, -1/2*w^3 + 1/2*w^2 + 6*w - 5],\ [1231, 1231, -1/2*w^3 - 5/2*w^2 + 9*w + 11],\ [1231, 1231, 3/2*w^3 + 1/2*w^2 - 6*w + 3],\ [1249, 1249, -5*w^3 + 3*w^2 + 34*w + 19],\ [1249, 1249, -1/2*w^3 + 9/2*w^2 + 4*w - 19],\ [1249, 1249, 7/2*w^3 - 3/2*w^2 - 24*w - 19],\ [1249, 1249, -3*w^3 - w^2 + 28*w + 17],\ [1279, 1279, 3/2*w^3 - w^2 - 25/2*w + 1],\ [1279, 1279, -w^3 - w^2 + 10*w + 13],\ [1279, 1279, -w^3 + 5/2*w^2 + 5/2*w - 9],\ [1279, 1279, 3/2*w^3 - 7/2*w^2 - 10*w + 11],\ [1289, 1289, 3/2*w^2 - 11/2*w - 1],\ [1289, 1289, 2*w^3 - 1/2*w^2 - 15/2*w + 3],\ [1289, 1289, w^3 + w^2 - 12*w - 5],\ [1289, 1289, 2*w^3 - 3*w^2 - 11*w + 9],\ [1297, 1297, 1/2*w^3 - 7/2*w^2 - 3*w + 11],\ [1297, 1297, 4*w^3 - 5/2*w^2 - 55/2*w - 13],\ [1297, 1297, w^3 - 4*w^2 - 7*w + 17],\ [1297, 1297, 5/2*w^3 - 5/2*w^2 - 16*w - 5],\ [1303, 1303, -w^3 + 2*w^2 + 3*w - 9],\ [1303, 1303, w^3 - w^2 - 4*w - 5],\ [1319, 1319, w^2 + w - 11],\ [1319, 1319, w^2 - 3*w - 9],\ [1321, 1321, 3*w^2 + 3*w - 13],\ [1321, 1321, -2*w^3 + w^2 + 13*w + 13],\ [1321, 1321, 7/2*w^2 + 1/2*w - 13],\ [1321, 1321, 3*w^3 - 5/2*w^2 - 37/2*w - 9],\ [1327, 1327, -w^3 + 1/2*w^2 + 13/2*w - 3],\ [1327, 1327, 3/2*w^3 - 3/2*w^2 - 6*w + 5],\ [1327, 1327, 3/2*w^3 - 1/2*w^2 - 13*w - 3],\ [1327, 1327, w^3 - 5/2*w^2 - 9/2*w + 3],\ [1361, 1361, 1/2*w^3 + w^2 - 7/2*w - 11],\ [1361, 1361, -1/2*w^3 + 5/2*w^2 - 13],\ [1367, 1367, -3/2*w^3 + 3*w^2 + 13/2*w - 9],\ [1367, 1367, 3/2*w^3 - 3/2*w^2 - 8*w - 1],\ [1399, 1399, 3/2*w^3 - 1/2*w^2 - 7*w + 7],\ [1399, 1399, 3/2*w^3 - 4*w^2 - 7/2*w + 7],\ [1399, 1399, 5*w^3 - w^2 - 40*w - 21],\ [1399, 1399, 3/2*w^3 + 3/2*w^2 - 15*w - 13],\ [1409, 1409, -w^3 + 3*w^2 + 6*w - 19],\ [1409, 1409, w^3 + 2*w^2 - 11*w - 9],\ [1409, 1409, -5/2*w^3 + 37/2*w + 17],\ [1409, 1409, w^3 - 9*w - 11],\ [1423, 1423, 2*w^3 - 5/2*w^2 - 15/2*w + 11],\ [1423, 1423, -2*w^3 - w^2 + 19*w + 15],\ [1433, 1433, 2*w^3 - 9/2*w^2 - 19/2*w + 15],\ [1433, 1433, 3*w^2 - 5*w - 13],\ [1433, 1433, 3*w^2 - w - 15],\ [1433, 1433, 2*w^3 - 3/2*w^2 - 25/2*w - 3],\ [1439, 1439, 1/2*w^3 - 4*w^2 - 5/2*w + 15],\ [1439, 1439, 1/2*w^3 - 1/2*w^2 - 2*w - 7],\ [1439, 1439, -1/2*w^3 + w^2 + 3/2*w - 9],\ [1439, 1439, 5/2*w^3 - w^2 - 35/2*w - 15],\ [1447, 1447, -3/2*w^3 + 1/2*w^2 + 13*w + 5],\ [1447, 1447, -1/2*w^3 + 5/2*w - 5],\ [1447, 1447, 1/2*w^3 - 3/2*w^2 - w - 3],\ [1447, 1447, 2*w^3 - 2*w^2 - 14*w - 7],\ [1471, 1471, -1/2*w^3 + 3/2*w^2 + 5*w - 7],\ [1471, 1471, 1/2*w^3 - 13/2*w - 1],\ [1489, 1489, -2*w^3 + 7*w^2 + 5*w - 21],\ [1489, 1489, 1/2*w^3 - 5*w^2 - 7/2*w + 17],\ [1489, 1489, 7/2*w^3 - 3*w^2 - 45/2*w - 11],\ [1489, 1489, 2*w^3 + w^2 - 13*w - 11],\ [1511, 1511, w^3 - w^2 - 4*w - 7],\ [1511, 1511, -1/2*w^3 - 3*w^2 + 19/2*w + 15],\ [1543, 1543, w^3 + 1/2*w^2 - 19/2*w - 3],\ [1543, 1543, -w^3 + 7/2*w^2 + 11/2*w - 11],\ [1553, 1553, 1/2*w^3 - 1/2*w^2 - 5],\ [1553, 1553, -1/2*w^3 + w^2 - 1/2*w - 5],\ [1559, 1559, 7/2*w^3 - 5/2*w^2 - 23*w - 11],\ [1559, 1559, 1/2*w^3 - 7/2*w^2 - 5*w + 15],\ [1567, 1567, 1/2*w^3 - 7/2*w^2 - w + 11],\ [1567, 1567, -1/2*w^3 - 2*w^2 + 13/2*w + 7],\ [1583, 1583, 3/2*w^3 - 3/2*w^2 - 8*w + 1],\ [1583, 1583, -3/2*w^3 + 3*w^2 + 13/2*w - 7],\ [1607, 1607, -w^3 + 5/2*w^2 + 13/2*w - 5],\ [1607, 1607, -w^3 + 1/2*w^2 + 17/2*w - 3],\ [1657, 1657, 1/2*w^3 + 3/2*w^2 - 8*w - 9],\ [1657, 1657, 3/2*w^3 - 3/2*w^2 - 4*w + 5],\ [1663, 1663, 1/2*w^3 - w^2 - 3/2*w - 5],\ [1663, 1663, -1/2*w^3 + 1/2*w^2 + 2*w - 7],\ [1681, 41, 5/2*w^2 - 5/2*w - 13],\ [1697, 1697, -1/2*w^3 + 4*w^2 - 11/2*w - 9],\ [1697, 1697, 5/2*w^3 + w^2 - 15/2*w - 1],\ [1759, 1759, 3/2*w^2 - 7/2*w - 9],\ [1759, 1759, 3/2*w^2 + 1/2*w - 11],\ [1777, 1777, 3/2*w^3 - 5*w^2 - 9/2*w + 19],\ [1777, 1777, 3/2*w^3 + 1/2*w^2 - 10*w - 11],\ [1783, 1783, -3/2*w^3 + 7/2*w^2 + 8*w - 19],\ [1783, 1783, -7/2*w^3 - 1/2*w^2 + 28*w + 25],\ [1801, 1801, 9/2*w^3 - 9/2*w^2 - 28*w - 9],\ [1801, 1801, 1/2*w^3 - 11/2*w^2 - 5*w + 19],\ [1823, 1823, -1/2*w^3 + 1/2*w^2 + 8*w - 11],\ [1823, 1823, 2*w^3 - 7*w^2 - 11*w + 27],\ [1831, 1831, -1/2*w^3 + w^2 + 11/2*w - 5],\ [1831, 1831, -1/2*w^3 + 1/2*w^2 + 6*w - 1],\ [1847, 1847, 5/2*w^3 - 2*w^2 - 33/2*w - 11],\ [1847, 1847, -1/2*w^3 + 1/2*w^2 + 6*w - 3],\ [1847, 1847, -1/2*w^3 + w^2 + 11/2*w - 3],\ [1847, 1847, 1/2*w^2 - 9/2*w - 5],\ [1873, 1873, -w^2 + 3*w - 5],\ [1873, 1873, -w^2 - w - 3],\ [1879, 1879, 2*w^3 + 1/2*w^2 - 25/2*w - 11],\ [1879, 1879, 4*w + 7],\ [1889, 1889, 4*w^3 - 5*w^2 - 21*w - 9],\ [1889, 1889, w^3 + 11/2*w^2 - 1/2*w - 19],\ [1913, 1913, 2*w^3 - 5/2*w^2 - 23/2*w + 1],\ [1913, 1913, 1/2*w^2 - 9/2*w - 1],\ [1913, 1913, 1/2*w^2 + 7/2*w - 5],\ [1913, 1913, w^2 + 3*w - 5],\ [1999, 1999, 3/2*w^3 - 3*w^2 - 9/2*w + 7],\ [1999, 1999, 3/2*w^3 - w^2 - 25/2*w - 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - x^4 - 9*x^3 + 7*x^2 + 16*x - 10 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, -1, -e^3 + 2*e^2 + 5*e - 6, 2*e^2 - 6, e^4 - 9*e^2 + 12, -2*e, e^4 - e^3 - 7*e^2 + 3*e + 8, -e^4 + e^3 + 7*e^2 - 3*e - 6, -2*e^3 + 2*e^2 + 10*e - 8, -e^4 + 7*e^2 + 2*e - 4, -2*e + 4, -e^3 + 5*e, -e^4 - 2*e^3 + 9*e^2 + 12*e - 16, -e^3 - 2*e^2 + 5*e + 8, e^4 - 7*e^2 - 2*e + 10, 2*e^2 + 4*e - 10, e^4 - 9*e^2 + 2*e + 12, 2*e^4 - 14*e^2 - 4*e + 14, -e^4 + 2*e^3 + 5*e^2 - 8*e + 4, 2*e^4 - 16*e^2 - 4*e + 22, -e^3 + e, e^4 + e^3 - 7*e^2 - 7*e + 10, -e^4 + 9*e^2 + 2*e - 16, -2*e^4 + 18*e^2 - 22, e^4 - 9*e^2 - 2*e + 16, 2*e^3 - 2*e^2 - 10*e + 4, -2*e^2 - 4*e + 6, -2*e^4 - e^3 + 16*e^2 + 5*e - 18, -e^4 + e^3 + 7*e^2 - 7*e, e^4 - 2*e^3 - 5*e^2 + 12*e - 2, -e^4 + e^3 + 5*e^2 + e + 4, 2*e^2 - 2*e, -3*e^4 + 2*e^3 + 23*e^2 - 8*e - 24, -2*e^3 + 14*e + 4, e^4 + 2*e^3 - 13*e^2 - 14*e + 26, e^4 - 9*e^2 - 6*e + 18, -e^4 + 7*e^2 + 6*e - 4, -2*e^4 - 2*e^3 + 18*e^2 + 18*e - 28, -2*e^4 + 4*e^3 + 10*e^2 - 20*e - 4, -2*e^4 + e^3 + 16*e^2 - e - 6, 3*e^4 - 2*e^3 - 25*e^2 + 6*e + 32, 2*e^4 - 12*e^2 - 8*e + 2, -2*e^4 - e^3 + 12*e^2 + 13*e - 6, e^4 + e^3 - 7*e^2 - 7*e - 6, e^4 - 3*e^3 - 3*e^2 + 17*e - 2, e^4 + e^3 - 11*e^2 - 11*e + 18, -3*e^4 + e^3 + 25*e^2 - 3*e - 34, 2*e^4 - 2*e^3 - 12*e^2 + 6*e, -e^4 - 2*e^3 + 5*e^2 + 12*e + 4, -2*e^4 + 2*e^3 + 14*e^2 - 6*e - 18, e^4 - 4*e^3 - 9*e^2 + 24*e + 16, -2*e^4 + 18*e^2 + 4*e - 18, -e^4 - 3*e^3 + 11*e^2 + 13*e - 14, -e^4 + 2*e^3 + 5*e^2 - 16*e + 6, 4*e^2 + 2*e - 28, -e^4 - e^3 + 9*e^2 + 7*e, 2*e^4 + 3*e^3 - 20*e^2 - 11*e + 34, 6*e^3 - 4*e^2 - 30*e + 10, e^4 - 2*e^3 - 9*e^2 + 18*e + 16, -e^4 + 2*e^3 + e^2 - 8*e + 12, 5*e^3 - 29*e - 4, 2*e^4 + 2*e^3 - 22*e^2 - 14*e + 40, -e^4 + 3*e^2 + 2*e + 14, -3*e^4 + e^3 + 21*e^2 - 3*e - 14, -e^4 - 2*e^3 + 13*e^2 + 20*e - 20, -2*e^4 - e^3 + 14*e^2 + 5*e - 4, -2*e^4 + 22*e^2 + 4*e - 34, e^4 + 2*e^3 - 13*e^2 - 12*e + 20, -4*e^3 + 20*e - 6, 4*e^4 - 2*e^3 - 28*e^2 + 6*e + 18, -2*e^4 + 18*e^2 - 26, 2*e^4 - 6*e^3 - 14*e^2 + 26*e + 12, -e^4 + 5*e^3 + 9*e^2 - 31*e - 16, -4*e^4 + 2*e^3 + 32*e^2 - 12*e - 42, 2*e^3 - 8*e^2 - 10*e + 38, 2*e^4 - e^3 - 16*e^2 + e + 12, 2*e^4 - 16*e^2 + 6*e + 16, 2*e^3 - 4*e^2 - 6*e + 26, -2*e^4 - 5*e^3 + 20*e^2 + 29*e - 36, -2*e^4 + 18*e^2 - 24, 2*e^4 - 20*e^2 - 8*e + 46, e^4 - 4*e^3 - 5*e^2 + 26*e - 6, -e^4 + 4*e^3 + e^2 - 22*e + 22, 7*e^4 - 3*e^3 - 49*e^2 + 9*e + 46, -4*e^3 + 4*e^2 + 20*e - 10, 2*e^4 + 4*e^3 - 18*e^2 - 16*e + 16, -e^4 + 2*e^3 + e^2 - 20*e + 22, e^4 + 2*e^3 - 17*e^2 - 12*e + 46, -e^4 + 2*e^3 + 13*e^2 - 10*e - 18, e^4 - 2*e^3 - 9*e^2 + 20*e + 4, 3*e^4 - 19*e^2 - 6*e + 24, -4*e^2 + 4*e + 10, e^4 - 3*e^3 - 3*e^2 + 13*e + 10, e^4 - 13*e^2 - 4*e + 16, e^4 - 3*e^3 - 7*e^2 + 29*e + 2, -e^4 + 2*e^3 + e^2 - 6*e + 8, -5*e^4 + 33*e^2 + 6*e - 18, e^4 - 2*e^3 - 5*e^2 + 10*e - 14, -4*e^3 + 8*e^2 + 24*e - 24, e^4 - 3*e^3 - 11*e^2 + 25*e + 20, -e^4 - 2*e^3 - 3*e^2 + 16*e + 32, 2*e^3 - 6*e^2 - 6*e + 20, 4*e^3 - 12*e - 4, 2*e^3 + 4*e^2 - 10*e - 12, -5*e^4 + 41*e^2 - 2*e - 56, -4*e^4 + 5*e^3 + 30*e^2 - 21*e - 36, 6*e^2 - 4*e - 14, 2*e^4 - 3*e^3 - 16*e^2 + 19*e + 10, -4*e^4 + 4*e^3 + 32*e^2 - 20*e - 26, -e^4 + 6*e^3 + 5*e^2 - 36*e - 20, 2*e^4 - 2*e^3 - 14*e^2 - 2*e + 16, e^4 - 6*e^3 - 11*e^2 + 34*e + 32, -e^4 + 2*e^3 + 3*e^2 - 8*e + 10, 6*e^4 + 4*e^3 - 54*e^2 - 24*e + 76, 4*e^4 - 6*e^3 - 28*e^2 + 22*e + 16, 2*e^4 - 4*e^3 - 12*e^2 + 12*e - 6, 2*e^4 - 18*e^2 + 44, -3*e^4 - 2*e^3 + 23*e^2 + 6*e - 6, -5*e^4 + 47*e^2 + 14*e - 68, e^4 - 9*e^2 - 14*e + 18, -e^4 + 2*e^3 + 11*e^2 - 2*e - 16, -4*e^4 + 22*e^2 + 8*e - 10, 2*e^3 - 12*e^2 - 14*e + 46, -2*e^3 + 2*e^2 - 2*e, -4*e^4 + 2*e^3 + 36*e^2 - 10*e - 40, 6*e^3 - 34*e - 4, -e^4 + 2*e^3 + 7*e^2 + 6*e - 12, e^4 + 2*e^3 - 7*e^2 - 20*e + 26, 5*e^3 - 33*e + 4, -e^4 + 2*e^3 - 3*e^2 - 16*e + 44, 4*e^4 - 5*e^3 - 34*e^2 + 29*e + 32, 2*e^4 + 2*e^3 - 18*e^2 - 14*e + 34, -e^4 + 5*e^3 + 5*e^2 - 31*e + 12, 6*e^4 - 2*e^3 - 42*e^2 + 2*e + 44, -2*e^4 + 3*e^3 + 12*e^2 - 7*e + 10, -e^4 + 2*e^3 + 13*e^2 - 18*e - 26, -5*e^4 - 3*e^3 + 45*e^2 + 25*e - 68, 2*e^4 + 2*e^3 - 18*e^2 - 6*e + 12, e^4 + 5*e^3 - 7*e^2 - 39*e, -e^4 + 2*e^3 + 9*e^2 - 22, 2*e^4 + 2*e^3 - 14*e^2 - 22*e + 20, -5*e^4 - e^3 + 49*e^2 + 15*e - 64, -4*e^2 - 4*e + 6, 2*e^4 - 5*e^3 - 10*e^2 + 33*e - 12, 6*e^4 - 46*e^2 - 16*e + 58, 8*e^3 - 8*e^2 - 56*e + 18, e^4 + 2*e^3 - 9*e^2 - 8*e + 4, 3*e^4 + 4*e^3 - 23*e^2 - 32*e + 40, -2*e^3 + 4*e^2 + 14*e - 6, -2*e^4 + e^3 + 8*e^2 + 3*e + 16, 2*e^3 - 4*e^2 - 14*e + 22, -e^4 + 4*e^3 + 5*e^2 - 26*e - 20, -e^4 - e^3 + 11*e^2 - 9*e - 6, 4*e^4 + 4*e^3 - 28*e^2 - 28*e + 32, -4*e^4 + 4*e^3 + 38*e^2 - 20*e - 50, -4*e^4 + 28*e^2 + 20*e - 24, e^4 - e^3 - 9*e^2 + 7*e + 36, -4*e^4 + 6*e^3 + 24*e^2 - 20*e + 16, -4*e^4 + e^3 + 34*e^2 - 5*e - 50, 4*e^3 - 10*e^2 - 24*e + 46, 7*e^4 - e^3 - 57*e^2 - e + 64, 6*e^3 + 6*e^2 - 38*e - 28, 2*e^4 + 3*e^3 - 26*e^2 - 19*e + 36, e^4 - 15*e^2 + 2*e + 16, -3*e^4 + 5*e^3 + 13*e^2 - 11*e + 32, -3*e^4 - 5*e^3 + 25*e^2 + 31*e - 54, -5*e^4 - e^3 + 51*e^2 + 11*e - 78, -4*e^3 + 8*e^2 + 32*e - 32, 2*e^4 - 4*e^3 - 6*e^2 + 12*e - 52, -2*e^4 - 2*e^3 + 14*e^2 + 8*e - 18, 4*e^4 - 10*e^3 - 32*e^2 + 46*e + 46, -3*e^4 + 4*e^3 + 11*e^2 - 8*e + 24, 4*e^4 - 4*e^3 - 36*e^2 + 24*e + 54, e^4 - e^3 - 7*e^2 - e + 28, 5*e^4 - 41*e^2 - 2*e + 34, 3*e^4 + 4*e^3 - 39*e^2 - 26*e + 62, e^4 - 8*e^3 - 3*e^2 + 34*e - 16, 4*e^4 - 2*e^3 - 34*e^2 - 2*e + 70, -9*e^4 + 2*e^3 + 65*e^2 - 72, -e^4 - 4*e^3 + 9*e^2 + 22*e - 2, -2*e^4 - 6*e^3 + 22*e^2 + 32*e - 24, 2*e^4 - 4*e^3 - 18*e^2 + 44*e + 36, -4*e^4 - 4*e^3 + 36*e^2 + 40*e - 52, 2*e^4 + 4*e^3 - 22*e^2 - 28*e + 46, -6*e^4 - 2*e^3 + 52*e^2 + 26*e - 86, -2*e^4 + 6*e^3 + 6*e^2 - 34*e + 30, 3*e^4 + 5*e^3 - 33*e^2 - 23*e + 58, 2*e^3 - 2*e^2 - 18*e + 16, -2*e^4 + 2*e^3 + 6*e^2 - 8*e + 26, -2*e^4 - 2*e^3 + 14*e^2 + 12*e - 18, e^4 - 8*e^3 + 3*e^2 + 54*e - 12, -2*e^4 + 7*e^3 + 20*e^2 - 39*e - 30, 4*e^3 - 6*e^2 - 16*e + 30, -2*e^4 + 5*e^3 + 8*e^2 - 33*e - 10, -3*e^4 + 2*e^3 + 9*e^2 - 4*e + 30, 2*e^4 - 6*e^3 - 8*e^2 + 14*e - 16, -4*e^3 - 6*e^2 + 26*e + 20, -6*e^4 + 6*e^3 + 46*e^2 - 16*e - 46, 5*e^4 - 4*e^3 - 33*e^2 + 18*e + 32, -2*e^4 + 6*e^3 + 22*e^2 - 30*e - 28, 2*e^4 - 5*e^3 - 16*e^2 + 21*e + 50, 3*e^4 + 4*e^3 - 29*e^2 - 10*e + 46, 2*e^4 - 3*e^3 - 24*e^2 + 19*e + 42, e^4 + 6*e^3 - 9*e^2 - 24*e + 16, 2*e^4 - 3*e^3 - 16*e^2 + 7*e, e^4 + 2*e^3 - 13*e^2 - 24*e + 20, 4*e^3 - 16*e^2 - 16*e + 54, 3*e^4 - 6*e^3 - 27*e^2 + 24*e + 56, -2*e^4 + 3*e^3 + 20*e^2 - 31*e - 36, -2*e^4 + 2*e^3 + 14*e^2 - 24*e - 26, 6*e^4 + 8*e^3 - 58*e^2 - 48*e + 102, -e^4 + 7*e^3 - e^2 - 37*e + 28, -3*e^4 + e^3 + 21*e^2 - 7*e - 4, 6*e^4 + 2*e^3 - 50*e^2 - 22*e + 56, 8*e^4 - 6*e^3 - 64*e^2 + 14*e + 64, -e^4 - 7*e^3 + 7*e^2 + 45*e + 10, 4*e^4 - 2*e^3 - 32*e^2 + 54, -e^4 + 4*e^3 + 13*e^2 - 22*e - 40, -4*e^3 + 12*e^2 + 40*e - 50, e^4 + 3*e^3 - 23*e^2 - 9*e + 68, -2*e^4 + 2*e^3 + 6*e^2 - 6*e + 32, 4*e^4 - 28*e^2 - 4*e + 32, -2*e^4 + 6*e^3 + 6*e^2 - 36*e + 12, -6*e^4 + 2*e^3 + 52*e^2 + 2*e - 80, -4*e^4 + 6*e^3 + 24*e^2 - 10*e + 6, 2*e^4 + 6*e^3 - 34*e^2 - 40*e + 72, e^4 + 2*e^3 - 9*e^2 - 36*e + 22, -2*e^4 - 4*e^3 + 24*e^2 + 24*e - 58, 3*e^4 + 8*e^3 - 43*e^2 - 50*e + 102, 2*e^3 - 8*e^2 - 32*e + 36, 2*e^4 - 8*e^3 - 12*e^2 + 56*e + 6, 4*e^4 - 8*e^3 - 28*e^2 + 44*e + 38, 3*e^4 + 7*e^3 - 33*e^2 - 45*e + 74, -3*e^4 - 2*e^3 + 27*e^2 + 8*e - 64, 3*e^4 + 2*e^3 - 15*e^2 - 14*e - 16, 5*e^4 + 6*e^3 - 39*e^2 - 46*e + 64, -2*e^4 - 4*e^3 + 22*e^2 + 20*e - 28, -4*e^4 + 4*e^3 + 20*e^2 - 8*e + 10, 2*e^3 - 6*e^2 - 14*e + 18, -3*e^4 + 4*e^3 + 15*e^2 - 6*e + 36, -3*e^4 + 4*e^3 + 35*e^2 - 14*e - 72, 2*e^4 + 4*e^3 - 2*e^2 - 28*e - 48, 8*e^4 + e^3 - 70*e^2 + 3*e + 90, e^4 - 2*e^3 + 9*e^2 + 16*e - 58, -4*e^4 + 6*e^3 + 28*e^2 - 38*e - 36, -4*e^4 - 4*e^3 + 28*e^2 + 28*e - 32, -e^4 + 7*e^3 + 7*e^2 - 37*e - 52, 7*e^4 - e^3 - 57*e^2 - 21*e + 88, 6*e^4 + e^3 - 44*e^2 + 3*e + 18, -e^4 - e^3 + 5*e^2 + 11*e + 52, e^4 - 6*e^3 - 7*e^2 + 58*e + 4, 6*e^4 - 6*e^3 - 44*e^2 + 18*e + 38, -6*e^4 + 8*e^3 + 38*e^2 - 44*e - 46, 7*e^4 - 4*e^3 - 59*e^2 - 6*e + 96, -e^4 - 7*e^3 + 19*e^2 + 37*e - 46, 2*e^4 - 6*e^3 - 6*e^2 + 28*e - 4, -4*e^4 + 4*e^3 + 28*e^2 - 10*e - 48, -5*e^4 - 2*e^3 + 35*e^2 + 20*e - 42, 8*e^4 - 6*e^3 - 52*e^2 + 34*e + 40, 8*e^4 - 5*e^3 - 58*e^2 + 21*e + 64, -2*e^4 - 3*e^3 + 28*e^2 + 19*e - 80, 9*e^4 - 3*e^3 - 61*e^2 + e + 44, -4*e^4 + 2*e^3 + 24*e^2 - 18*e - 8, 2*e^3 - 4*e^2 - 10*e + 32, -2*e^4 - 2*e^3 + 18*e^2 + 2*e, 4*e^4 - 6*e^3 - 36*e^2 + 22*e + 68, -2*e^4 + 2*e^2 + 4*e + 16, e^4 + 14*e^3 - 19*e^2 - 72*e + 50, -4*e^4 - 2*e^3 + 32*e^2 + 14*e - 64, 2*e^4 + 6*e^3 - 2*e^2 - 48*e - 26, 5*e^4 - 2*e^3 - 41*e^2 + 24*e + 44, 6*e^4 + 4*e^3 - 62*e^2 - 44*e + 116, 4*e^4 - 36*e^2 - 20*e + 84, -2*e^4 - 6*e^3 + 18*e^2 + 34*e - 50, -2*e^4 + 10*e^3 + 4*e^2 - 58*e + 20, 3*e^4 - 23*e^2 - 4*e + 16, -10*e^4 + 4*e^3 + 78*e^2 - 28*e - 84, -9*e^4 + 2*e^3 + 69*e^2 - 2*e - 98, -2*e^4 + 4*e^3 + 16*e^2 + 2*e - 28, -8*e^4 + 8*e^3 + 58*e^2 - 26*e - 48, 3*e^4 + 2*e^3 - 21*e^2 - 2, -7*e^4 - 4*e^3 + 57*e^2 + 26*e - 54, -2*e^3 + 10*e^2 + 22*e - 56, 7*e^4 + 2*e^3 - 59*e^2 - 12*e + 80, 8*e^4 - 10*e^3 - 60*e^2 + 50*e + 76, -2*e^4 + 18*e^2 - 4*e - 12, 3*e^4 - 8*e^3 - 27*e^2 + 62*e + 38, -e^4 + 9*e^3 + 3*e^2 - 39*e + 20, -2*e^4 + 18*e^2 + 4*e - 40, 8*e^4 - 4*e^3 - 64*e^2 + 40*e + 68, -8*e^4 - 3*e^3 + 78*e^2 + 19*e - 102, 5*e^4 - 5*e^3 - 45*e^2 + 19*e + 60, -2*e^4 + 4*e^3 + 22*e^2 - 36*e - 62, -5*e^4 + 2*e^3 + 37*e^2 - 30*e - 28, -4*e^4 + 2*e^3 + 32*e^2 + 6*e - 64, -7*e^4 + e^3 + 55*e^2 - 7*e - 56, 2*e^3 - 4*e^2 - 6*e + 6, -e^4 + e^3 + 23*e^2 + e - 86, -6*e^4 - e^3 + 56*e^2 + 17*e - 84, -4*e^4 - 2*e^3 + 18*e^2 + 22*e + 8, -3*e^4 - 2*e^3 + 35*e^2 + 8*e - 40, -5*e^4 + 10*e^3 + 37*e^2 - 40*e - 20, -3*e^4 + 17*e^2 - 2*e + 22, 4*e^4 - 4*e^3 - 36*e^2 + 24*e + 16] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2,2,1/2*w^3 - w^2 - 5/2*w + 4])] = 1 AL_eigenvalues[ZF.ideal([7,7,1/2*w^3 - 5/2*w - 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]