/* 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([8, 2, -1/3*w^3 + 2/3*w^2 + 2*w - 2]) 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^4 - 12*x^2 - 16*x - 4 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, e, -1/2*e^3 + 6*e + 6, -1/2*e^3 + e^2 + 4*e, e^3 - e^2 - 11*e - 6, 0, e^3 + e^2 - 14*e - 14, e^3 - e^2 - 14*e - 2, -3*e^3 + 3*e^2 + 34*e + 22, e^3 - 3*e^2 - 6*e + 10, e^3 - 2*e^2 - 6*e + 4, -e^3 + 10*e + 16, -3*e^3 + 4*e^2 + 30*e + 16, 3*e^3 - 2*e^2 - 34*e - 20, -2*e^3 + 4*e^2 + 16*e, 4*e, 4*e^3 - 4*e^2 - 44*e - 24, -2*e^3 + 24*e + 24, -2*e^3 + 3*e^2 + 22*e + 2, e^3 + e^2 - 16*e - 22, -e^3 - e^2 + 16*e + 14, 2*e^3 - 3*e^2 - 22*e - 10, -7/2*e^3 + 5*e^2 + 36*e + 16, -2*e^2 + 7*e + 16, 3*e^3 - e^2 - 37*e - 26, 1/2*e^3 - 2*e^2 - 6*e + 10, 5*e^3 - 5*e^2 - 54*e - 34, -3*e^3 + e^2 + 34*e + 26, -3*e^3 + 5*e^2 + 26*e + 2, e^3 - e^2 - 6*e - 10, -2*e^3 + 2*e^2 + 23*e + 24, 1/2*e^3 + e^2 - 8*e, 1/2*e^3 - 2*e^2 - 2*e + 18, e^3 - e^2 - 13*e + 6, -5*e^3 + 6*e^2 + 54*e + 28, 3*e^3 - 38*e - 32, e^3 - 4*e^2 - 2*e + 16, e^3 - 2*e^2 - 14*e + 4, -4*e^3 + 7*e^2 + 36*e, -e^2 + 8*e, 6*e^3 - 5*e^2 - 68*e - 48, -2*e^3 - e^2 + 24*e + 24, 7*e^3 - 8*e^2 - 69*e - 32, -11/2*e^3 + 6*e^2 + 52*e + 34, -15/2*e^3 + 7*e^2 + 78*e + 52, 6*e^3 - 5*e^2 - 61*e - 38, -2*e^3 + 2*e^2 + 20*e + 12, 2*e^3 - 2*e^2 - 20*e - 12, 2*e^3 - 2*e^2 - 20*e - 12, -2*e^3 + 2*e^2 + 20*e + 12, 3*e^3 - 2*e^2 - 34*e - 20, -3*e^3 + 4*e^2 + 30*e + 16, -e^3 + 10*e + 16, e^3 - 2*e^2 - 6*e + 4, -6*e^3 + 9*e^2 + 60*e + 24, -3*e^2 + 12*e + 24, 6*e^3 - 3*e^2 - 72*e - 48, -3*e^2 + 24, 4*e + 16, -2*e^3 + 24*e + 40, -2*e^3 + 4*e^2 + 16*e + 16, 4*e^3 - 4*e^2 - 44*e - 8, -4*e^3 + 4*e^2 + 40*e + 18, 4*e^3 - 4*e^2 - 40*e - 30, 3*e^3 - e^2 - 34*e - 30, -5*e^3 + 5*e^2 + 54*e + 30, -e^3 + e^2 + 6*e + 6, 3*e^3 - 5*e^2 - 26*e - 6, 3*e^3 - 38*e - 24, -5*e^3 + 6*e^2 + 54*e + 36, e^3 - 2*e^2 - 14*e + 12, e^3 - 4*e^2 - 2*e + 24, -e^3 - 2*e^2 + 22*e + 36, -5*e^3 + 8*e^2 + 50*e + 24, e^3 - 4*e^2 - 10*e + 24, 5*e^3 - 2*e^2 - 62*e - 36, 5*e^3 - 3*e^2 - 52*e - 54, -4*e^3 + 5*e^2 + 34*e + 6, -8*e^3 + 7*e^2 + 86*e + 42, 7*e^3 - 9*e^2 - 68*e - 42, 5*e^3 - 4*e^2 - 59*e - 48, -5/2*e^3 + 6*e^2 + 20*e - 18, -1/2*e^3 - 3*e^2 + 10*e + 12, -2*e^3 + e^2 + 29*e + 6, 4*e^2 - 16*e - 40, 8*e^3 - 12*e^2 - 80*e - 40, 4*e^2 - 40, -8*e^3 + 4*e^2 + 96*e + 56, -2*e^3 + 6*e^2 + 19*e - 20, -11/2*e^3 + 2*e^2 + 70*e + 46, 5/2*e^3 + e^2 - 40*e - 44, 5*e^3 - 9*e^2 - 49*e - 14, -e^3 - e^2 + 22*e + 14, -e^3 - 3*e^2 + 14*e + 26, -5*e^3 + 9*e^2 + 46*e + 2, 7*e^3 - 5*e^2 - 82*e - 58, 2*e^3 - 2*e^2 - 20*e - 14, -2*e^3 + 2*e^2 + 20*e + 10, 3*e^3 + e^2 - 34*e - 46, -e^3 + 3*e^2 - 2*e - 10, -9*e^3 + 7*e^2 + 102*e + 62, 7*e^3 - 11*e^2 - 66*e - 22, 5*e^3 - 3*e^2 - 58*e - 50, -e^3 - e^2 + 10*e + 10, -5*e^3 + 7*e^2 + 50*e + 10, e^3 - 3*e^2 - 2*e - 2, -6*e^3 + 4*e^2 + 68*e + 64, 2*e^3 - 20*e - 8, 6*e^3 - 8*e^2 - 60*e - 8, -2*e^3 + 4*e^2 + 12*e + 16, -10, -7/2*e^3 + e^2 + 38*e + 44, 2*e^3 - 3*e^2 - 13*e + 2, 7*e^3 - 6*e^2 - 77*e - 40, -11/2*e^3 + 8*e^2 + 52*e + 26, -10*e^3 + 11*e^2 + 98*e + 50, 11*e^3 - 11*e^2 - 112*e - 70, 9*e^3 - 9*e^2 - 88*e - 58, -10*e^3 + 9*e^2 + 102*e + 62, -4*e^3 + 48*e + 40, 8*e - 8, 8*e^3 - 8*e^2 - 88*e - 56, -4*e^3 + 8*e^2 + 32*e - 8, -3/2*e^3 + 7*e^2 + 14*e - 36, -9*e^3 + 4*e^2 + 111*e + 72, 2*e^3 + 3*e^2 - 41*e - 54, 17/2*e^3 - 14*e^2 - 84*e - 30, -7*e^3 + 7*e^2 + 82*e + 46, e^3 - 7*e^2 + 2*e + 34, e^3 + 5*e^2 - 22*e - 38, 5*e^3 - 5*e^2 - 62*e - 26, -10*e^3 + 13*e^2 + 100*e + 48, 4*e^3 - 7*e^2 - 28*e, 10*e^3 - 7*e^2 - 112*e - 72, -4*e^3 + e^2 + 40*e + 48, -7*e^3 + 5*e^2 + 74*e + 74, 9*e^3 - 9*e^2 - 94*e - 34, 5*e^3 - 5*e^2 - 46*e - 10, -7*e^3 + 9*e^2 + 66*e + 50, -13/2*e^3 + 4*e^2 + 78*e + 62, 5*e^3 - 9*e^2 - 47*e + 2, 4*e^2 - 3*e - 16, 3/2*e^3 + e^2 - 28*e - 16, -15*e^3 + 15*e^2 + 154*e + 86, 13*e^3 - 11*e^2 - 134*e - 94, 13*e^3 - 15*e^2 - 126*e - 70, -11*e^3 + 11*e^2 + 106*e + 62, -9*e^3 + 10*e^2 + 94*e + 68, 7*e^3 - 4*e^2 - 78*e - 40, 5*e^3 - 8*e^2 - 42*e + 8, -3*e^3 + 2*e^2 + 26*e + 44, -7*e^3 + 6*e^2 + 74*e + 36, 5*e^3 - 4*e^2 - 50*e - 48, 7*e^3 - 8*e^2 - 70*e - 48, -5*e^3 + 6*e^2 + 46*e + 12, -3*e^3 + 8*e^2 + 27*e - 20, -11/2*e^3 + 2*e^2 + 72*e + 46, 9/2*e^3 - e^2 - 62*e - 56, 4*e^3 - 9*e^2 - 37*e - 2, -9*e^3 + 5*e^2 + 102*e + 90, 3*e^3 - e^2 - 26*e - 18, 11*e^3 - 13*e^2 - 114*e - 42, -5*e^3 + 9*e^2 + 38*e + 18, -5*e^3 + 5*e^2 + 50*e + 14, 5*e^3 - 5*e^2 - 50*e - 46, 8*e^3 - 10*e^2 - 73*e - 20, -23/2*e^3 + 13*e^2 + 116*e + 76, -15/2*e^3 + 6*e^2 + 74*e + 70, 11*e^3 - 9*e^2 - 117*e - 62, -4*e^3 + 5*e^2 + 34*e + 6, 5*e^3 - 3*e^2 - 52*e - 54, 7*e^3 - 9*e^2 - 68*e - 42, -8*e^3 + 7*e^2 + 86*e + 42, -2*e^3 - 2*e^2 + 20*e + 52, 2*e^3 - 6*e^2 - 4*e + 28, 10*e^3 - 6*e^2 - 116*e - 68, -10*e^3 + 14*e^2 + 100*e + 52, -2*e^3 + 9*e^2 - e - 42, 25/2*e^3 - 16*e^2 - 132*e - 66, -3/2*e^3 + 5*e^2 + 22*e - 24, -9*e^3 + 2*e^2 + 111*e + 84, 6*e^3 - 8*e^2 - 56*e - 24, -4*e^3 + 4*e^2 + 36*e + 24, -8*e^3 + 8*e^2 + 84*e + 48, 6*e^3 - 4*e^2 - 64*e - 48, 11*e^3 - 14*e^2 - 122*e - 52, e^3 + 8*e^2 - 34*e - 64, -5*e^3 - 4*e^2 + 74*e + 80, -7*e^3 + 10*e^2 + 82*e + 20, 10*e^3 - 8*e^2 - 116*e - 72, -6*e^3 + 12*e^2 + 52*e, -2*e^3 - 4*e^2 + 28*e + 48, -2*e^3 + 36*e + 24, 2*e^3 - 10*e^2 + 4*e + 66, -14*e^3 + 18*e^2 + 148*e + 90, 2*e^3 - 6*e^2 - 28*e + 42, 10*e^3 - 2*e^2 - 124*e - 78, -10*e^3 + 6*e^2 + 120*e + 52, 6*e^2 - 4*e - 68, 8*e^3 - 14*e^2 - 76*e - 44, 2*e^3 + 2*e^2 - 40*e - 68, -3*e^3 - e^2 + 42*e + 50, -3*e^3 + 5*e^2 + 34*e + 14, 5*e^3 - 7*e^2 - 54*e - 10, e^3 + 3*e^2 - 22*e - 22, -4*e^3 + e^2 + 52*e + 50, 4*e^3 - 7*e^2 - 40*e + 2, -2*e^3 + 5*e^2 + 20*e + 2, 2*e^3 + e^2 - 32*e - 22, -2*e^3 - 2*e^2 + 32*e + 20, 4*e^3 - 6*e^2 - 44*e - 28, -4*e^3 + 6*e^2 + 44*e - 4, 2*e^3 + 2*e^2 - 32*e - 52, 10*e^3 - 13*e^2 - 116*e - 32, 4*e^3 + 7*e^2 - 68*e - 80, -2*e^3 - 9*e^2 + 48*e + 88, -12*e^3 + 15*e^2 + 136*e + 64, -5*e^3 + 2*e^2 + 61*e + 52, 11/2*e^3 - 8*e^2 - 56*e - 14, -1/2*e^3 + 3*e^2 + 6*e - 8, 3*e^2 - 11*e - 14, 12*e^3 - 5*e^2 - 147*e - 98, -25/2*e^3 + 19*e^2 + 126*e + 52, 3/2*e^3 - 8*e^2 - 16*e + 46, -e^3 - 6*e^2 + 37*e + 64, -6*e^2 + 20*e + 52, -10*e^3 + 14*e^2 + 104*e + 52, 2*e^3 - 6*e^2 - 24*e + 28, 8*e^3 - 2*e^2 - 100*e - 68, 4*e^3 - 16*e^2 - 24*e + 56, 12*e^3 - 8*e^2 - 152*e - 88, -12*e^3 + 8*e^2 + 152*e + 104, -4*e^3 + 16*e^2 + 24*e - 40, 7*e^3 - 14*e^2 - 55*e - 8, -29/2*e^3 + 15*e^2 + 158*e + 76, -1/2*e^3 - 8*e - 2, 8*e^3 - e^2 - 95*e - 98, -8*e^3 + 10*e^2 + 96*e + 36, -4*e^3 - 6*e^2 + 64*e + 84, 10*e^2 - 24*e - 60, 12*e^3 - 14*e^2 - 136*e - 60, 8*e^3 - 8*e^2 - 88*e - 72, -4*e^3 + 8*e^2 + 32*e - 24, -4*e^3 + 48*e + 24, 8*e - 24, -9*e^3 + 11*e^2 + 80*e + 30, 10*e^3 - 7*e^2 - 102*e - 90, 14*e^3 - 17*e^2 - 138*e - 78, -15*e^3 + 13*e^2 + 160*e + 90, 5/2*e^3 - 4*e^2 - 14*e - 26, -8*e^3 + 12*e^2 + 75*e + 4, -5*e^3 + e^2 + 55*e + 34, 21/2*e^3 - 9*e^2 - 116*e - 92, 10*e^3 - 12*e^2 - 108*e - 56, -2*e^3 + 8*e^2 + 4*e - 32, -6*e^3 + 76*e + 64, -2*e^3 + 4*e^2 + 28*e - 8, -14*e^3 + 16*e^2 + 132*e + 88, 18*e^3 - 20*e^2 - 180*e - 80, 14*e^3 - 12*e^2 - 140*e - 80, -18*e^3 + 16*e^2 + 188*e + 136, 6*e^3 - 14*e^2 - 52*e + 22, -10*e^3 + 6*e^2 + 124*e + 94, 6*e^3 - 2*e^2 - 84*e - 50, -2*e^3 + 10*e^2 + 12*e - 26, -14*e^3 + 5*e^2 + 173*e + 114, -5/2*e^3 + 10*e^2 + 28*e - 54, 31/2*e^3 - 23*e^2 - 158*e - 72, e^3 + 8*e^2 - 43*e - 84, -18*e^3 + 16*e^2 + 180*e + 112, 22*e^3 - 20*e^2 - 228*e - 152, 18*e^3 - 20*e^2 - 172*e - 104, -22*e^3 + 24*e^2 + 220*e + 112, -17/2*e^3 + 8*e^2 + 94*e + 74, 4*e^3 - 47*e - 28, 5*e^3 - 9*e^2 - 43*e + 14, -1/2*e^3 + e^2 - 4*e + 20, 8*e^3 - 8*e^2 - 80*e - 8, -8*e^3 + 8*e^2 + 80*e + 88, -8*e^3 + 8*e^2 + 80*e + 88, 8*e^3 - 8*e^2 - 80*e - 8, 2*e^3 - 3*e^2 - 16*e + 32, -4*e^3 + 5*e^2 + 40*e + 56, -2*e^3 + e^2 + 20*e + 56, 4*e^3 - 3*e^2 - 44*e + 8, -17/2*e^3 + 9*e^2 + 106*e + 56, -3*e^3 - 8*e^2 + 53*e + 92, -2*e^3 + 13*e^2 - 3*e - 46, 27/2*e^3 - 14*e^2 - 156*e - 70, -4*e^2 + 8*e + 24, 4*e^3 - 4*e^2 - 48*e - 24, -4*e^3 + 4*e^2 + 48*e + 24, 4*e^2 - 8*e - 24] 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, -1/3*w^3 - 1/3*w^2 + 3*w + 4])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]