/* 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([18, 0, -12, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, w - 3]) primes_array = [ [2, 2, -1/3*w^3 - 1/3*w^2 + 3*w + 4],\ [7, 7, 1/3*w^3 + 1/3*w^2 - 3*w - 3],\ [7, 7, -1/3*w^2 + w + 1],\ [7, 7, 1/3*w^2 + w - 1],\ [7, 7, 1/3*w^3 - 1/3*w^2 - 3*w + 3],\ [9, 3, w - 3],\ [41, 41, 1/3*w^3 - 1/3*w^2 - 3*w + 1],\ [41, 41, -1/3*w^2 + w + 3],\ [41, 41, 1/3*w^2 + w - 3],\ [41, 41, -1/3*w^3 - 1/3*w^2 + 3*w + 1],\ [47, 47, 1/3*w^3 + 1/3*w^2 - 4*w - 1],\ [47, 47, -1/3*w^3 + 1/3*w^2 + 2*w - 3],\ [47, 47, 1/3*w^3 + 1/3*w^2 - 2*w - 3],\ [47, 47, 1/3*w^3 - 1/3*w^2 - 4*w + 1],\ [89, 89, -1/3*w^3 + 2/3*w^2 + 3*w - 3],\ [89, 89, 2/3*w^2 + w - 5],\ [89, 89, 2/3*w^2 - w - 5],\ [89, 89, 1/3*w^3 + 2/3*w^2 - 3*w - 3],\ [97, 97, 2/3*w^3 - 1/3*w^2 - 6*w + 5],\ [97, 97, -w^3 - 5/3*w^2 + 10*w + 15],\ [97, 97, -5/3*w^3 - 5/3*w^2 + 16*w + 21],\ [97, 97, -2/3*w^3 - 1/3*w^2 + 6*w + 5],\ [103, 103, -4/3*w^3 - 4/3*w^2 + 13*w + 17],\ [103, 103, 1/3*w^3 + w^2 - 5*w - 7],\ [103, 103, -w^3 - w^2 + 9*w + 11],\ [103, 103, -2/3*w^3 - 4/3*w^2 + 7*w + 11],\ [137, 137, -1/3*w^3 - 1/3*w^2 + 3*w - 1],\ [137, 137, 1/3*w^2 + w - 5],\ [137, 137, 1/3*w^2 - w - 5],\ [137, 137, 1/3*w^3 - 1/3*w^2 - 3*w - 1],\ [151, 151, w^2 - w - 5],\ [151, 151, 1/3*w^3 + w^2 - 3*w - 7],\ [151, 151, -1/3*w^3 + w^2 + 3*w - 7],\ [151, 151, w^2 + w - 5],\ [191, 191, 1/3*w^3 + 2/3*w^2 - 4*w - 3],\ [191, 191, 1/3*w^3 + 2/3*w^2 - 2*w - 5],\ [191, 191, -1/3*w^3 + 2/3*w^2 + 2*w - 5],\ [191, 191, -1/3*w^3 + 2/3*w^2 + 4*w - 3],\ [193, 193, 2/3*w^3 + w^2 - 8*w - 7],\ [193, 193, -1/3*w^3 - 1/3*w^2 + 4*w + 7],\ [193, 193, -7/3*w^3 - 13/3*w^2 + 26*w + 37],\ [193, 193, -2/3*w^3 + w^2 + 8*w - 7],\ [199, 199, 5/3*w^3 + 2*w^2 - 17*w - 23],\ [199, 199, -2/3*w^3 - 5/3*w^2 + 9*w + 13],\ [199, 199, -2/3*w^3 - 1/3*w^2 + 5*w + 5],\ [199, 199, -w^3 - 2*w^2 + 11*w + 17],\ [233, 233, 1/3*w^3 - 4/3*w^2 - 3*w + 5],\ [233, 233, 1/3*w^3 - 4/3*w^2 - 5*w + 7],\ [233, 233, 4/3*w^2 + w - 11],\ [233, 233, 1/3*w^3 + 4/3*w^2 - 3*w - 5],\ [239, 239, 1/3*w^3 + w^2 - 4*w - 5],\ [239, 239, 4/3*w^3 + 4/3*w^2 - 14*w - 17],\ [239, 239, 4/3*w^3 + 2/3*w^2 - 12*w - 13],\ [239, 239, -1/3*w^3 + w^2 + 4*w - 5],\ [241, 241, -2/3*w^3 + 6*w + 1],\ [241, 241, 2/3*w^3 - 1/3*w^2 - 6*w + 3],\ [241, 241, -2/3*w^3 - 1/3*w^2 + 6*w + 3],\ [241, 241, 2/3*w^3 - 6*w + 1],\ [281, 281, -w^3 - w^2 + 9*w + 13],\ [281, 281, -2/3*w^3 - 2/3*w^2 + 5*w + 7],\ [281, 281, -2/3*w^3 + 2/3*w^2 + 5*w - 7],\ [281, 281, -7/3*w^3 - 3*w^2 + 23*w + 31],\ [289, 17, w^2 - 5],\ [289, 17, w^2 - 7],\ [337, 337, -w^3 + 4/3*w^2 + 8*w - 7],\ [337, 337, -2*w + 7],\ [337, 337, 2/3*w^3 - 2*w^2 - 4*w + 11],\ [337, 337, 1/3*w^3 + 2/3*w^2 - 6*w + 1],\ [383, 383, 2/3*w^3 + 5/3*w^2 - 8*w - 11],\ [383, 383, -w^3 - 2/3*w^2 + 10*w + 11],\ [383, 383, -5/3*w^3 - 4/3*w^2 + 16*w + 19],\ [383, 383, -4/3*w^3 - 7/3*w^2 + 14*w + 19],\ [431, 431, -2/3*w^3 + 1/3*w^2 + 4*w - 5],\ [431, 431, -2/3*w^3 - 1/3*w^2 + 8*w - 1],\ [431, 431, 2/3*w^3 - 1/3*w^2 - 8*w - 1],\ [431, 431, 2/3*w^3 + 1/3*w^2 - 4*w - 5],\ [433, 433, 2/3*w^3 + 7/3*w^2 - 10*w - 15],\ [433, 433, -3*w^3 - 10/3*w^2 + 30*w + 39],\ [433, 433, -1/3*w^3 - 4/3*w^2 + 4*w + 9],\ [433, 433, -4/3*w^3 - 5/3*w^2 + 12*w + 15],\ [439, 439, -4/3*w^3 - 1/3*w^2 + 11*w + 13],\ [439, 439, 1/3*w^3 + 2/3*w^2 - 5*w - 5],\ [439, 439, -3*w^3 - 10/3*w^2 + 29*w + 37],\ [439, 439, -4/3*w^3 - 7/3*w^2 + 13*w + 19],\ [479, 479, 1/3*w^2 - 2*w - 5],\ [479, 479, 2/3*w^3 + 1/3*w^2 - 6*w + 1],\ [479, 479, 2/3*w^3 - 1/3*w^2 - 6*w - 1],\ [479, 479, -1/3*w^2 - 2*w + 5],\ [487, 487, 1/3*w^3 + 4/3*w^2 - 3*w - 7],\ [487, 487, 4/3*w^2 - w - 9],\ [487, 487, -4/3*w^2 - w + 9],\ [487, 487, 1/3*w^3 - 4/3*w^2 - 3*w + 7],\ [521, 521, 2/3*w^3 - 2/3*w^2 - 5*w - 3],\ [521, 521, 5/3*w^3 + 7/3*w^2 - 17*w - 21],\ [521, 521, -7/3*w^3 - 11/3*w^2 + 25*w + 33],\ [521, 521, -4/3*w^3 - 2/3*w^2 + 13*w + 15],\ [529, 23, -1/3*w^2 - 3],\ [529, 23, 1/3*w^2 - 7],\ [569, 569, 2/3*w^3 + 2/3*w^2 - 5*w + 1],\ [569, 569, 1/3*w^3 - 2/3*w^2 - 5*w + 9],\ [569, 569, -1/3*w^3 - 2/3*w^2 + 5*w + 9],\ [569, 569, -2/3*w^3 + 2/3*w^2 + 5*w + 1],\ [577, 577, -w^3 + 1/3*w^2 + 8*w + 3],\ [577, 577, -1/3*w^3 - 1/3*w^2 + 6*w + 7],\ [577, 577, 1/3*w^3 - 1/3*w^2 - 6*w + 7],\ [577, 577, w^3 + 1/3*w^2 - 8*w + 3],\ [617, 617, -2/3*w^3 - 5/3*w^2 + 5*w + 7],\ [617, 617, -5/3*w^2 + 3*w + 5],\ [617, 617, -8/3*w^3 - 13/3*w^2 + 27*w + 37],\ [617, 617, -w^3 - 5/3*w^2 + 9*w + 15],\ [625, 5, -5],\ [631, 631, -1/3*w^3 - 5/3*w^2 + 3*w + 7],\ [631, 631, -5/3*w^2 - w + 13],\ [631, 631, 5/3*w^2 - w - 13],\ [631, 631, 1/3*w^3 - 5/3*w^2 - 3*w + 7],\ [673, 673, 2/3*w^3 + 1/3*w^2 - 8*w - 1],\ [673, 673, -2/3*w^3 - 1/3*w^2 + 4*w + 3],\ [673, 673, -2/3*w^3 + 1/3*w^2 + 4*w - 3],\ [673, 673, 2/3*w^3 - 1/3*w^2 - 8*w + 1],\ [719, 719, 1/3*w^3 - 1/3*w^2 - 6*w + 9],\ [719, 719, w^3 - 1/3*w^2 - 8*w - 5],\ [719, 719, w^3 + 1/3*w^2 - 8*w + 5],\ [719, 719, -1/3*w^3 - 1/3*w^2 + 6*w + 9],\ [727, 727, 2/3*w^3 + 1/3*w^2 - 5*w - 1],\ [727, 727, -1/3*w^3 - 1/3*w^2 + 5*w + 3],\ [727, 727, 1/3*w^3 - 1/3*w^2 - 5*w + 3],\ [727, 727, -2/3*w^3 + 1/3*w^2 + 5*w - 1],\ [761, 761, -2/3*w^3 + 1/3*w^2 + 3*w + 3],\ [761, 761, 7/3*w^3 + 10/3*w^2 - 23*w - 33],\ [761, 761, 3*w^3 + 10/3*w^2 - 29*w - 39],\ [761, 761, -2*w^3 - 5/3*w^2 + 17*w + 21],\ [769, 769, -4/3*w^3 - w^2 + 12*w + 13],\ [769, 769, -w^3 - 2/3*w^2 + 10*w + 13],\ [769, 769, -w^3 - 8/3*w^2 + 12*w + 19],\ [769, 769, -2*w^3 - 3*w^2 + 22*w + 29],\ [809, 809, -2/3*w^3 - 2/3*w^2 + 7*w + 3],\ [809, 809, w^2 + w - 11],\ [809, 809, w^2 - w - 11],\ [809, 809, 2/3*w^3 - 2/3*w^2 - 7*w + 3],\ [823, 823, 1/3*w^3 - 5*w - 1],\ [823, 823, 2/3*w^3 - 5*w - 1],\ [823, 823, 2/3*w^3 - 5*w + 1],\ [823, 823, -1/3*w^3 + 5*w - 1],\ [857, 857, -5/3*w^2 + w + 15],\ [857, 857, -1/3*w^3 - 5/3*w^2 + 3*w + 5],\ [857, 857, 1/3*w^3 - 5/3*w^2 - 3*w + 5],\ [857, 857, 5/3*w^2 + w - 15],\ [863, 863, -2/3*w^3 - 5/3*w^2 + 10*w + 15],\ [863, 863, -5/3*w^3 - 8/3*w^2 + 18*w + 27],\ [863, 863, -3*w^3 - 14/3*w^2 + 32*w + 45],\ [863, 863, -5/3*w^2 + 4*w + 9],\ [911, 911, 1/3*w^3 - 2/3*w^2 - 4*w - 1],\ [911, 911, -1/3*w^3 + 2/3*w^2 + 2*w - 9],\ [911, 911, 1/3*w^3 + 2/3*w^2 - 2*w - 9],\ [911, 911, -1/3*w^3 - 2/3*w^2 + 4*w - 1],\ [919, 919, w^3 + 1/3*w^2 - 9*w - 1],\ [919, 919, -w^3 - 2/3*w^2 + 9*w + 7],\ [919, 919, w^3 - 2/3*w^2 - 9*w + 7],\ [919, 919, -w^3 + 1/3*w^2 + 9*w - 1],\ [953, 953, -w^3 - w^2 + 9*w + 5],\ [953, 953, -w^2 - 3*w + 7],\ [953, 953, w^2 - 3*w - 7],\ [953, 953, w^3 - w^2 - 9*w + 5],\ [961, 31, 4/3*w^2 - 7],\ [961, 31, 4/3*w^2 - 9],\ [967, 967, -w^3 - 1/3*w^2 + 9*w + 5],\ [967, 967, w^3 + 2/3*w^2 - 9*w - 5],\ [967, 967, -w^3 + 2/3*w^2 + 9*w - 5],\ [967, 967, w^3 - 1/3*w^2 - 9*w + 5],\ [1009, 1009, 1/3*w^3 + 5/3*w^2 - 4*w - 9],\ [1009, 1009, -8/3*w^3 - 10/3*w^2 + 26*w + 33],\ [1009, 1009, 4/3*w^3 + 8/3*w^2 - 16*w - 21],\ [1009, 1009, 7/3*w^3 + 5/3*w^2 - 22*w - 27],\ [1049, 1049, -2/3*w^3 + 2/3*w^2 + 5*w - 9],\ [1049, 1049, -1/3*w^3 - 2/3*w^2 + 5*w - 1],\ [1049, 1049, 1/3*w^3 - 2/3*w^2 - 5*w - 1],\ [1049, 1049, 2/3*w^3 + 2/3*w^2 - 5*w - 9],\ [1063, 1063, w^3 + 2/3*w^2 - 9*w - 13],\ [1063, 1063, 2*w^3 + w^2 - 17*w - 19],\ [1063, 1063, -2/3*w^3 - w^2 + 9*w + 11],\ [1063, 1063, -3*w^3 - 14/3*w^2 + 31*w + 43],\ [1097, 1097, -2/3*w^3 + 1/3*w^2 + 7*w + 1],\ [1097, 1097, 1/3*w^3 + 1/3*w^2 - w - 5],\ [1097, 1097, -1/3*w^3 + 1/3*w^2 + w - 5],\ [1097, 1097, 2/3*w^3 + 1/3*w^2 - 7*w + 1],\ [1103, 1103, 2/3*w^2 + 2*w - 7],\ [1103, 1103, 2/3*w^3 + 2/3*w^2 - 6*w - 1],\ [1103, 1103, -2/3*w^3 + 2/3*w^2 + 6*w - 1],\ [1103, 1103, 2/3*w^2 - 2*w - 7],\ [1151, 1151, -2/3*w^3 + 4*w - 7],\ [1151, 1151, 2/3*w^3 - 8*w - 7],\ [1151, 1151, -2/3*w^3 + 8*w - 7],\ [1151, 1151, 2/3*w^3 - 4*w - 7],\ [1153, 1153, -1/3*w^3 + 6*w - 5],\ [1153, 1153, -w^3 + 8*w + 5],\ [1153, 1153, -w^3 + 8*w - 5],\ [1153, 1153, 1/3*w^3 - 6*w - 5],\ [1193, 1193, -1/3*w^3 - 2/3*w^2 + 5*w - 3],\ [1193, 1193, 2/3*w^3 + 2/3*w^2 - 5*w - 11],\ [1193, 1193, -2/3*w^3 + 2/3*w^2 + 5*w - 11],\ [1193, 1193, 1/3*w^3 - 2/3*w^2 - 5*w - 3],\ [1201, 1201, -7/3*w^3 - 4/3*w^2 + 20*w + 23],\ [1201, 1201, -w^3 + 2/3*w^2 + 8*w - 1],\ [1201, 1201, w^3 + 2/3*w^2 - 8*w - 1],\ [1201, 1201, 1/3*w^3 + 2/3*w^2 - 6*w - 7],\ [1249, 1249, -2/3*w^3 + 2*w^2 + 6*w - 11],\ [1249, 1249, 2*w^2 + 2*w - 13],\ [1249, 1249, 2*w^2 - 2*w - 13],\ [1249, 1249, 2/3*w^3 + 2*w^2 - 6*w - 11],\ [1289, 1289, w^3 - 2/3*w^2 - 11*w + 3],\ [1289, 1289, 1/3*w^3 + w^2 - 5*w - 11],\ [1289, 1289, -1/3*w^3 + w^2 + 5*w - 11],\ [1289, 1289, -w^3 - 2/3*w^2 + 11*w + 3],\ [1297, 1297, -1/3*w^3 + 4*w - 7],\ [1297, 1297, -1/3*w^3 + 2*w - 7],\ [1297, 1297, 1/3*w^3 - 2*w - 7],\ [1297, 1297, 1/3*w^3 - 4*w - 7],\ [1303, 1303, 1/3*w^3 - 2/3*w^2 - 5*w + 13],\ [1303, 1303, -11/3*w^3 - 13/3*w^2 + 37*w + 49],\ [1303, 1303, -w^3 - 7/3*w^2 + 11*w + 19],\ [1303, 1303, -1/3*w^3 - 2/3*w^2 + 5*w + 13],\ [1399, 1399, 4/3*w^3 + 2/3*w^2 - 11*w + 1],\ [1399, 1399, -1/3*w^3 - 2/3*w^2 + 7*w + 9],\ [1399, 1399, 1/3*w^3 - 2/3*w^2 - 7*w + 9],\ [1399, 1399, -4/3*w^3 + 2/3*w^2 + 11*w + 1],\ [1433, 1433, w^3 - 9*w - 7],\ [1433, 1433, 4/3*w^3 + 11/3*w^2 - 17*w - 25],\ [1433, 1433, -4/3*w^3 - 7/3*w^2 + 13*w + 17],\ [1433, 1433, -w^3 + 9*w - 7],\ [1439, 1439, -1/3*w^3 - 4/3*w^2 + 6*w + 11],\ [1439, 1439, -2*w^3 - 3*w^2 + 22*w + 31],\ [1439, 1439, 4/3*w^3 + 3*w^2 - 16*w - 25],\ [1439, 1439, -5/3*w^3 - 10/3*w^2 + 20*w + 29],\ [1447, 1447, 1/3*w^2 + w - 9],\ [1447, 1447, 1/3*w^3 - 1/3*w^2 - 3*w - 5],\ [1447, 1447, -1/3*w^3 - 1/3*w^2 + 3*w - 5],\ [1447, 1447, 1/3*w^2 - w - 9],\ [1481, 1481, -2/3*w^3 + 5/3*w^2 + 7*w - 9],\ [1481, 1481, 1/3*w^3 + 5/3*w^2 - w - 11],\ [1481, 1481, -1/3*w^3 + 5/3*w^2 + w - 11],\ [1481, 1481, -2/3*w^3 - 5/3*w^2 + 7*w + 9],\ [1487, 1487, 2/3*w^3 + 8/3*w^2 - 10*w - 15],\ [1487, 1487, -w^3 - 1/3*w^2 + 10*w + 9],\ [1487, 1487, -w^3 + 1/3*w^2 + 10*w - 9],\ [1487, 1487, -2*w^3 - 10/3*w^2 + 20*w + 27],\ [1489, 1489, -1/3*w^3 + 5/3*w^2 + 2*w - 9],\ [1489, 1489, -1/3*w^3 + 5/3*w^2 + 4*w - 11],\ [1489, 1489, 1/3*w^3 + 5/3*w^2 - 4*w - 11],\ [1489, 1489, 1/3*w^3 + 5/3*w^2 - 2*w - 9],\ [1543, 1543, -4*w^3 - 13/3*w^2 + 39*w + 49],\ [1543, 1543, 4*w^3 + 5*w^2 - 41*w - 55],\ [1543, 1543, 2/3*w^3 - 2/3*w^2 - 9*w + 1],\ [1543, 1543, 4/3*w^3 + 5/3*w^2 - 15*w - 17],\ [1583, 1583, -1/3*w^3 + w^2 + 4*w + 1],\ [1583, 1583, 1/3*w^3 + w^2 - 2*w - 13],\ [1583, 1583, -1/3*w^3 + w^2 + 2*w - 13],\ [1583, 1583, -1/3*w^3 - w^2 + 4*w - 1],\ [1721, 1721, w^3 - 1/3*w^2 - 7*w + 9],\ [1721, 1721, 2/3*w^3 + 1/3*w^2 - 9*w + 5],\ [1721, 1721, -2/3*w^3 + 1/3*w^2 + 9*w + 5],\ [1721, 1721, w^3 + 1/3*w^2 - 7*w - 9],\ [1777, 1777, -8/3*w^3 - 3*w^2 + 28*w + 37],\ [1777, 1777, -w^3 - 2/3*w^2 + 8*w + 7],\ [1777, 1777, -w^3 + 2/3*w^2 + 8*w - 7],\ [1777, 1777, -2/3*w^3 - 3*w^2 + 10*w + 19],\ [1783, 1783, -1/3*w^2 - w - 5],\ [1783, 1783, -1/3*w^3 + 1/3*w^2 + 3*w - 9],\ [1783, 1783, 1/3*w^3 + 1/3*w^2 - 3*w - 9],\ [1783, 1783, -1/3*w^2 + w - 5],\ [1823, 1823, 2/3*w^3 - 4/3*w^2 - 4*w + 9],\ [1823, 1823, 2/3*w^3 - 4/3*w^2 - 8*w + 7],\ [1823, 1823, 2/3*w^3 + 4/3*w^2 - 8*w - 7],\ [1823, 1823, 2/3*w^3 + 4/3*w^2 - 4*w - 9],\ [1831, 1831, -w - 7],\ [1831, 1831, -1/3*w^3 + 3*w - 7],\ [1831, 1831, 1/3*w^3 - 3*w - 7],\ [1831, 1831, w - 7],\ [1871, 1871, -4*w^3 - 13/3*w^2 + 38*w + 49],\ [1871, 1871, -7/3*w^3 - 10/3*w^2 + 22*w + 31],\ [1871, 1871, -7/3*w^3 - 4/3*w^2 + 20*w + 25],\ [1871, 1871, 2/3*w^3 + 1/3*w^2 - 4*w - 7],\ [1873, 1873, -1/3*w^2 + 4*w - 3],\ [1873, 1873, 4/3*w^3 + 1/3*w^2 - 12*w - 7],\ [1873, 1873, 4/3*w^3 - 1/3*w^2 - 12*w + 7],\ [1873, 1873, 1/3*w^2 + 4*w + 3],\ [1879, 1879, -1/3*w^3 + 7/3*w^2 + 5*w - 11],\ [1879, 1879, 2/3*w^3 + 7/3*w^2 - 5*w - 17],\ [1879, 1879, -2/3*w^3 + 7/3*w^2 + 5*w - 17],\ [1879, 1879, 1/3*w^3 + 7/3*w^2 - 5*w - 11],\ [1913, 1913, 1/3*w^3 + 1/3*w^2 - w - 7],\ [1913, 1913, -2/3*w^3 - 1/3*w^2 + 7*w - 3],\ [1913, 1913, 2/3*w^3 - 1/3*w^2 - 7*w - 3],\ [1913, 1913, -1/3*w^3 + 1/3*w^2 + w - 7]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 + x^7 - 33*x^6 + 8*x^5 + 305*x^4 - 353*x^3 - 373*x^2 + 354*x + 211 K. = NumberField(heckePol) hecke_eigenvalues_array = [47/4705*e^7 + 42/941*e^6 - 1103/4705*e^5 - 822/941*e^4 + 1678/941*e^3 + 19814/4705*e^2 - 3998/941*e - 16911/4705, e, 103/10351*e^7 + 359/51755*e^6 - 13908/51755*e^5 + 4187/10351*e^4 + 17826/10351*e^3 - 75304/10351*e^2 + 225453/51755*e + 294969/51755, -8/10351*e^7 + 2384/51755*e^6 + 5904/51755*e^5 - 14897/10351*e^4 - 12640/10351*e^3 + 127046/10351*e^2 - 222722/51755*e - 544882/51755, 42/51755*e^7 - 433/51755*e^6 - 4129/51755*e^5 + 1668/10351*e^4 + 13272/10351*e^3 - 40756/51755*e^2 - 274376/51755*e + 12137/51755, -1, -3183/51755*e^7 - 4892/51755*e^6 + 19849/10351*e^5 + 5195/10351*e^4 - 167397/10351*e^3 + 700599/51755*e^2 + 459981/51755*e - 64630/10351, 7321/51755*e^7 + 14972/51755*e^6 - 215236/51755*e^5 - 28654/10351*e^4 + 357097/10351*e^3 - 950243/51755*e^2 - 1391271/51755*e + 175768/51755, 953/51755*e^7 + 3237/51755*e^6 - 28872/51755*e^5 - 15386/10351*e^4 + 52724/10351*e^3 + 477541/51755*e^2 - 698781/51755*e - 476039/51755, -1472/51755*e^7 + 2853/51755*e^6 + 59932/51755*e^5 - 24449/10351*e^4 - 113218/10351*e^3 + 1297781/51755*e^2 + 90841/51755*e - 575216/51755, 2072/51755*e^7 + 2791/51755*e^6 - 65684/51755*e^5 - 520/10351*e^4 + 116500/10351*e^3 - 526986/51755*e^2 - 548828/51755*e + 63957/51755, -4338/51755*e^7 - 8511/51755*e^6 + 124809/51755*e^5 + 11080/10351*e^4 - 201145/10351*e^3 + 941554/51755*e^2 + 469793/51755*e - 599987/51755, 4338/51755*e^7 + 8511/51755*e^6 - 124809/51755*e^5 - 11080/10351*e^4 + 201145/10351*e^3 - 941554/51755*e^2 - 469793/51755*e + 651742/51755, -2072/51755*e^7 - 2791/51755*e^6 + 65684/51755*e^5 + 520/10351*e^4 - 116500/10351*e^3 + 526986/51755*e^2 + 548828/51755*e - 12202/51755, -6416/51755*e^7 - 3431/10351*e^6 + 185168/51755*e^5 + 51287/10351*e^4 - 319541/10351*e^3 - 263127/51755*e^2 + 481281/10351*e + 675516/51755, -1050/10351*e^7 - 18332/51755*e^6 + 133138/51755*e^5 + 60626/10351*e^4 - 199509/10351*e^3 - 171465/10351*e^2 + 1028886/51755*e + 1546771/51755, 4068/51755*e^7 + 3901/51755*e^6 - 136712/51755*e^5 + 4814/10351*e^4 + 250388/10351*e^3 - 1234069/51755*e^2 - 1005348/51755*e + 570761/51755, 589/10351*e^7 + 10796/51755*e^6 - 72397/51755*e^5 - 35349/10351*e^4 + 102540/10351*e^3 + 78587/10351*e^2 - 450933/51755*e + 19751/51755, 502/4705*e^7 + 1322/4705*e^6 - 13683/4705*e^5 - 3454/941*e^4 + 21246/941*e^3 - 6101/4705*e^2 - 77806/4705*e - 55591/4705, 1636/51755*e^7 + 2443/10351*e^6 - 28243/51755*e^5 - 56282/10351*e^4 + 40830/10351*e^3 + 1801177/51755*e^2 - 247920/10351*e - 1571311/51755, -716/10351*e^7 - 4003/51755*e^6 + 114368/51755*e^5 - 3178/10351*e^4 - 189339/10351*e^3 + 232941/10351*e^2 + 23109/51755*e - 531279/51755, 6762/51755*e^7 + 23446/51755*e^6 - 178272/51755*e^5 - 83386/10351*e^4 + 283963/10351*e^3 + 1460309/51755*e^2 - 2325443/51755*e - 1679144/51755, -2547/51755*e^7 - 5534/51755*e^6 + 73688/51755*e^5 + 11230/10351*e^4 - 121686/10351*e^3 + 268276/51755*e^2 + 494342/51755*e + 237711/51755, 3781/51755*e^7 + 1717/10351*e^6 - 106772/51755*e^5 - 16935/10351*e^4 + 170047/10351*e^3 - 524278/51755*e^2 - 94525/10351*e + 344636/51755, -868/10351*e^7 - 10462/51755*e^6 + 123034/51755*e^5 + 24309/10351*e^4 - 201777/10351*e^3 + 69416/10351*e^2 + 915136/51755*e - 67242/51755, 311/10351*e^7 + 481/51755*e^6 - 53551/51755*e^5 + 8522/10351*e^4 + 98042/10351*e^3 - 148988/10351*e^2 - 277183/51755*e + 301733/51755, -2548/10351*e^7 - 27372/51755*e^6 + 379529/51755*e^5 + 63345/10351*e^4 - 641063/10351*e^3 + 198761/10351*e^2 + 3000236/51755*e + 662413/51755, 683/10351*e^7 + 3486/51755*e^6 - 110716/51755*e^5 + 2540/10351*e^4 + 188954/10351*e^3 - 177259/10351*e^2 - 302663/51755*e - 114542/51755, 9313/51755*e^7 + 22531/51755*e^6 - 269112/51755*e^5 - 58968/10351*e^4 + 448317/10351*e^3 - 310279/51755*e^2 - 2592563/51755*e + 29796/51755, 3631/51755*e^7 + 3505/10351*e^6 - 84632/51755*e^5 - 70211/10351*e^4 + 132998/10351*e^3 + 1728447/51755*e^2 - 328848/10351*e - 1569284/51755, -4781/51755*e^7 - 11091/51755*e^6 + 140511/51755*e^5 + 27497/10351*e^4 - 237623/10351*e^3 + 257468/51755*e^2 + 1146228/51755*e + 89972/51755, -1236/51755*e^7 - 5002/51755*e^6 + 31309/51755*e^5 + 18934/10351*e^4 - 48993/10351*e^3 - 338472/51755*e^2 + 527136/51755*e - 153112/51755, 2312/51755*e^7 + 9189/51755*e^6 - 59704/51755*e^5 - 35350/10351*e^4 + 99181/10351*e^3 + 733624/51755*e^2 - 1189537/51755*e - 620833/51755, 1258/10351*e^7 + 18454/51755*e^6 - 172781/51755*e^5 - 56291/10351*e^4 + 279725/10351*e^3 + 87430/10351*e^2 - 1583277/51755*e - 1125967/51755, 1800/10351*e^7 + 22554/51755*e^6 - 262247/51755*e^5 - 64005/10351*e^4 + 452919/10351*e^3 + 35165/10351*e^2 - 3319412/51755*e - 723364/51755, 2141/51755*e^7 + 2634/10351*e^6 - 30324/51755*e^5 - 48056/10351*e^4 + 14092/10351*e^3 + 1040037/51755*e^2 - 32823/10351*e - 330883/51755, -1277/51755*e^7 + 11933/51755*e^6 + 72554/51755*e^5 - 77332/10351*e^4 - 144757/10351*e^3 + 3518861/51755*e^2 - 813369/51755*e - 2610507/51755, 3061/51755*e^7 + 10093/51755*e^6 - 83308/51755*e^5 - 36657/10351*e^4 + 139196/10351*e^3 + 714127/51755*e^2 - 1200354/51755*e - 571731/51755, -6813/51755*e^7 - 26617/51755*e^6 + 169238/51755*e^5 + 94669/10351*e^4 - 269026/10351*e^3 - 1713956/51755*e^2 + 2673401/51755*e + 1647401/51755, -11578/51755*e^7 - 32451/51755*e^6 + 323949/51755*e^5 + 99142/10351*e^4 - 532646/10351*e^3 - 841096/51755*e^2 + 3289728/51755*e + 2340383/51755, -4526/51755*e^7 - 15938/51755*e^6 + 113224/51755*e^5 + 53890/10351*e^4 - 167394/10351*e^3 - 803272/51755*e^2 + 1176459/51755*e + 776588/51755, 8958/51755*e^7 + 12636/51755*e^6 - 55764/10351*e^5 - 3567/10351*e^4 + 470700/10351*e^3 - 2526434/51755*e^2 - 1202558/51755*e + 331116/10351, -2591/51755*e^7 - 17403/51755*e^6 + 44989/51755*e^5 + 74546/10351*e^4 - 52782/10351*e^3 - 2096867/51755*e^2 + 1141604/51755*e + 1679558/51755, -7797/51755*e^7 - 2703/10351*e^6 + 237879/51755*e^5 + 20101/10351*e^4 - 404003/10351*e^3 + 1274131/51755*e^2 + 298435/10351*e + 138673/51755, -5532/51755*e^7 - 13946/51755*e^6 + 32468/10351*e^5 + 42033/10351*e^4 - 278270/10351*e^3 - 213999/51755*e^2 + 2068183/51755*e + 83670/10351, 10233/51755*e^7 + 19454/51755*e^6 - 62349/10351*e^5 - 37218/10351*e^4 + 532017/10351*e^3 - 1360759/51755*e^2 - 2283172/51755*e + 44738/10351, 986/51755*e^7 - 160/10351*e^6 - 25462/51755*e^5 + 19935/10351*e^4 + 21748/10351*e^3 - 1358513/51755*e^2 + 203072/10351*e + 2042136/51755, -8837/51755*e^7 - 23988/51755*e^6 + 246469/51755*e^5 + 67521/10351*e^4 - 401411/10351*e^3 - 117119/51755*e^2 + 2336394/51755*e + 1260168/51755, 942/10351*e^7 + 9112/51755*e^6 - 146593/51755*e^5 - 18487/10351*e^4 + 266942/10351*e^3 - 111157/10351*e^2 - 1944731/51755*e + 692699/51755, 1073/51755*e^7 + 6436/51755*e^6 - 25882/51755*e^5 - 32801/10351*e^4 + 38889/10351*e^3 + 1159601/51755*e^2 - 527463/51755*e - 1025454/51755, -768/4705*e^7 - 406/941*e^6 + 21327/4705*e^5 + 5123/941*e^4 - 34727/941*e^3 + 36814/4705*e^2 + 33315/941*e + 13854/4705, -474/4705*e^7 - 356/4705*e^6 + 15949/4705*e^5 - 1080/941*e^4 - 28395/941*e^3 + 156152/4705*e^2 + 76188/4705*e + 14123/4705, -1668/51755*e^7 - 2027/51755*e^6 + 51598/51755*e^5 - 1180/10351*e^4 - 81995/10351*e^3 + 642644/51755*e^2 + 115341/51755*e - 928584/51755, 18949/51755*e^7 + 44443/51755*e^6 - 109313/10351*e^5 - 106587/10351*e^4 + 905543/10351*e^3 - 1239592/51755*e^2 - 4324964/51755*e - 43103/10351, -2428/10351*e^7 - 21728/51755*e^6 + 373777/51755*e^5 + 38376/10351*e^4 - 637781/10351*e^3 + 342569/10351*e^2 + 2542249/51755*e + 306419/51755, 18902/51755*e^7 + 45174/51755*e^6 - 541698/51755*e^5 - 111411/10351*e^4 + 890691/10351*e^3 - 1028861/51755*e^2 - 4401897/51755*e - 412211/51755, 71/4705*e^7 + 97/4705*e^6 - 2387/4705*e^5 - 541/941*e^4 + 3616/941*e^3 + 25427/4705*e^2 + 4299/4705*e - 93859/4705, 212/51755*e^7 + 10137/51755*e^6 + 12183/51755*e^5 - 56644/10351*e^4 - 15816/10351*e^3 + 2305629/51755*e^2 - 1485991/51755*e - 2273134/51755, -4821/51755*e^7 - 19058/51755*e^6 + 125713/51755*e^5 + 74706/10351*e^4 - 208859/10351*e^3 - 1746807/51755*e^2 + 2455454/51755*e + 2453721/51755, 4652/51755*e^7 + 4288/51755*e^6 - 135962/51755*e^5 + 23571/10351*e^4 + 207210/10351*e^3 - 2683071/51755*e^2 + 567461/51755*e + 2654951/51755, -8123/51755*e^7 - 10647/51755*e^6 + 248733/51755*e^5 - 7633/10351*e^4 - 424211/10351*e^3 + 2812879/51755*e^2 + 1388011/51755*e - 1752664/51755, 3639/51755*e^7 + 4627/51755*e^6 - 129287/51755*e^5 - 9266/10351*e^4 + 259738/10351*e^3 - 344587/51755*e^2 - 2431916/51755*e - 129169/51755, -806/4705*e^7 - 1459/4705*e^6 + 24301/4705*e^5 + 2404/941*e^4 - 40148/941*e^3 + 127908/4705*e^2 + 126157/4705*e - 71018/4705, 853/4705*e^7 + 1669/4705*e^6 - 25404/4705*e^5 - 3226/941*e^4 + 41826/941*e^3 - 108094/4705*e^2 - 146147/4705*e - 54108/4705, 18322/51755*e^7 + 38338/51755*e^6 - 549249/51755*e^5 - 84169/10351*e^4 + 935133/10351*e^3 - 1806741/51755*e^2 - 4453609/51755*e - 115008/51755, -626/4705*e^7 - 1836/4705*e^6 + 17494/4705*e^5 + 5923/941*e^4 - 29377/941*e^3 - 58187/4705*e^2 + 255158/4705*e + 16218/4705, -8553/51755*e^7 - 16072/51755*e^6 + 260446/51755*e^5 + 31481/10351*e^4 - 446230/10351*e^3 + 869129/51755*e^2 + 1855801/51755*e + 1058817/51755, -13223/51755*e^7 - 9654/10351*e^6 + 339029/51755*e^5 + 168375/10351*e^4 - 534916/10351*e^3 - 2781411/51755*e^2 + 837774/10351*e + 2960498/51755, 1645/10351*e^7 + 6638/51755*e^6 - 56484/10351*e^5 + 16120/10351*e^4 + 528900/10351*e^3 - 554276/10351*e^2 - 2518669/51755*e + 270071/10351, -11236/51755*e^7 - 30062/51755*e^6 + 316944/51755*e^5 + 83150/10351*e^4 - 538435/10351*e^3 - 4782/51755*e^2 + 3950846/51755*e + 207833/51755, 6/55*e^7 + 12/55*e^6 - 164/55*e^5 - 10/11*e^4 + 235/11*e^3 - 1878/55*e^2 + 504/55*e + 2342/55, -3629/10351*e^7 - 57168/51755*e^6 + 96758/10351*e^5 + 181400/10351*e^4 - 765340/10351*e^3 - 399052/10351*e^2 + 4690259/51755*e + 736360/10351, 771/51755*e^7 + 12014/51755*e^6 - 4079/51755*e^5 - 64018/10351*e^4 + 15914/10351*e^3 + 2327562/51755*e^2 - 2135522/51755*e - 1411918/51755, -3721/51755*e^7 - 362/10351*e^6 + 128969/51755*e^5 - 17650/10351*e^4 - 244246/10351*e^3 + 1796898/51755*e^2 + 165482/10351*e - 1380142/51755, 19531/51755*e^7 + 10646/10351*e^6 - 537239/51755*e^5 - 147058/10351*e^4 + 851382/10351*e^3 + 132762/51755*e^2 - 747050/10351*e - 2132318/51755, -6241/51755*e^7 - 17234/51755*e^6 + 169689/51755*e^5 + 47886/10351*e^4 - 253890/10351*e^3 + 101858/51755*e^2 + 645562/51755*e - 452202/51755, 5664/51755*e^7 + 28851/51755*e^6 - 138349/51755*e^5 - 128471/10351*e^4 + 237174/10351*e^3 + 3790088/51755*e^2 - 3740843/51755*e - 3211943/51755, 8553/51755*e^7 + 36774/51755*e^6 - 208691/51755*e^5 - 145342/10351*e^4 + 322018/10351*e^3 + 3426536/51755*e^2 - 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11730/941*e^5 - 16340/941*e^4 + 91865/941*e^3 - 817/4705*e^2 - 349558/4705*e - 25334/941, -3094/10351*e^7 - 50982/51755*e^6 + 420192/51755*e^5 + 172296/10351*e^4 - 706716/10351*e^3 - 472127/10351*e^2 + 5825726/51755*e + 1850549/51755, -23538/51755*e^7 - 54556/51755*e^6 + 660807/51755*e^5 + 116571/10351*e^4 - 1041090/10351*e^3 + 2308879/51755*e^2 + 2611018/51755*e + 782404/51755, -17137/51755*e^7 - 26156/51755*e^6 + 519257/51755*e^5 + 14412/10351*e^4 - 850501/10351*e^3 + 4427561/51755*e^2 + 1759138/51755*e - 2382426/51755, 21898/51755*e^7 + 9758/10351*e^6 - 615412/51755*e^5 - 95937/10351*e^4 + 957592/10351*e^3 - 2866519/51755*e^2 - 392185/10351*e + 187886/51755, 1875/10351*e^7 + 31257/51755*e^6 - 255491/51755*e^5 - 117133/10351*e^4 + 405803/10351*e^3 + 476979/10351*e^2 - 3097161/51755*e - 4146907/51755, -5347/51755*e^7 - 14621/51755*e^6 + 29077/10351*e^5 + 44944/10351*e^4 - 199108/10351*e^3 - 240719/51755*e^2 - 439182/51755*e + 14758/10351, 1472/51755*e^7 - 2853/51755*e^6 - 59932/51755*e^5 + 24449/10351*e^4 + 123569/10351*e^3 - 1246026/51755*e^2 - 815411/51755*e + 2904191/51755, -2283/51755*e^7 + 3574/51755*e^6 + 100968/51755*e^5 - 27083/10351*e^4 - 214229/10351*e^3 + 1520384/51755*e^2 + 1455038/51755*e + 819721/51755, 794/51755*e^7 + 18924/51755*e^6 + 21509/51755*e^5 - 97115/10351*e^4 - 69977/10351*e^3 + 3522718/51755*e^2 - 1362072/51755*e - 463577/51755, 11391/51755*e^7 + 6235/10351*e^6 - 329471/51755*e^5 - 99175/10351*e^4 + 566713/10351*e^3 + 997912/51755*e^2 - 823027/10351*e - 3587/51755, 16636/51755*e^7 + 8401/51755*e^6 - 575732/51755*e^5 + 54414/10351*e^4 + 1033768/10351*e^3 - 6152078/51755*e^2 - 2731613/51755*e + 1711966/51755, -790/10351*e^7 - 2653/51755*e^6 + 137927/51755*e^5 + 1351/10351*e^4 - 244153/10351*e^3 + 88364/10351*e^2 + 1104459/51755*e + 1068729/51755, -50707/51755*e^7 - 116286/51755*e^6 + 1478703/51755*e^5 + 282651/10351*e^4 - 2473953/10351*e^3 + 2941066/51755*e^2 + 12683538/51755*e + 2192151/51755, 14756/51755*e^7 + 6588/51755*e^6 - 494913/51755*e^5 + 68474/10351*e^4 + 853728/10351*e^3 - 7038738/51755*e^2 - 1161334/51755*e + 5623564/51755, 16153/51755*e^7 + 28907/51755*e^6 - 512722/51755*e^5 - 68278/10351*e^4 + 912193/10351*e^3 - 870169/51755*e^2 - 4927756/51755*e - 2976874/51755, 4432/51755*e^7 + 58804/51755*e^6 - 10331/51755*e^5 - 291260/10351*e^4 - 58979/10351*e^3 + 10178349/51755*e^2 - 4508082/51755*e - 8902177/51755, -31558/51755*e^7 - 10542/10351*e^6 + 1006128/51755*e^5 + 95284/10351*e^4 - 1795038/10351*e^3 + 4270129/51755*e^2 + 1958613/10351*e - 112169/51755, 32687/51755*e^7 + 62019/51755*e^6 - 992661/51755*e^5 - 115510/10351*e^4 + 1717060/10351*e^3 - 4424241/51755*e^2 - 9592607/51755*e + 1331813/51755, 101/941*e^7 + 1896/4705*e^6 - 11491/4705*e^5 - 4948/941*e^4 + 18430/941*e^3 - 1668/941*e^2 - 221213/4705*e + 186508/4705, 43218/51755*e^7 + 113397/51755*e^6 - 1226249/51755*e^5 - 322775/10351*e^4 + 2022364/10351*e^3 + 915216/51755*e^2 - 11726711/51755*e - 5066323/51755, 2491/51755*e^7 + 13012/51755*e^6 - 30229/51755*e^5 - 44507/10351*e^4 - 40924/10351*e^3 + 786662/51755*e^2 + 2162514/51755*e + 11782/51755, -5393/10351*e^7 - 7739/10351*e^6 + 812628/51755*e^5 - 3264/10351*e^4 - 1316644/10351*e^3 + 1726740/10351*e^2 + 332542/10351*e - 5791789/51755, -252/51755*e^7 + 2598/51755*e^6 - 3326/10351*e^5 - 41061/10351*e^4 + 96335/10351*e^3 + 2470001/51755*e^2 - 3684509/51755*e - 300252/10351, -15174/51755*e^7 - 21009/51755*e^6 + 465521/51755*e^5 - 5224/10351*e^4 - 799498/10351*e^3 + 4780207/51755*e^2 + 3107817/51755*e - 1557623/51755, 11186/51755*e^7 + 2468/10351*e^6 - 340617/51755*e^5 + 30204/10351*e^4 + 564039/10351*e^3 - 4868353/51755*e^2 - 186491/10351*e + 5078416/51755, -1447/51755*e^7 - 19339/51755*e^6 + 25189/51755*e^5 + 115543/10351*e^4 - 63914/10351*e^3 - 4779349/51755*e^2 + 3927937/51755*e + 6444318/51755] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([9, 3, w - 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]