/* 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([14, 14, 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^2 + 2*x - 7 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, -1/2*e - 5/2, -1, -1/2*e - 1/2, e, -1/2*e - 1/2, e - 3, 2*e + 6, 3/2*e + 5/2, -5/2*e - 13/2, 1/2*e + 17/2, 3*e - 1, -3/2*e - 1/2, -e - 4, -3*e + 6, 3*e - 3, 3/2*e + 29/2, -3/2*e - 7/2, 1/2*e - 27/2, 3/2*e - 17/2, 7/2*e + 1/2, -3/2*e - 15/2, 11, 7/2*e + 7/2, 6, -7, 3*e - 5, 11/2*e + 13/2, 10, -e + 6, -5/2*e - 23/2, -3/2*e + 19/2, 4*e + 6, -2*e, 2*e + 2, 11, 11/2*e + 17/2, -7/2*e + 15/2, -5*e - 13, -7*e - 7, 11/2*e - 5/2, -3*e - 12, -6*e + 3, -4*e + 4, 5/2*e + 21/2, 5/2*e + 19/2, e + 19, -6*e - 4, 7/2*e + 43/2, -13/2*e - 23/2, -9/2*e + 9/2, -3/2*e - 11/2, 4*e + 14, -7/2*e - 17/2, -9/2*e - 17/2, 1/2*e - 5/2, -2*e - 14, -3/2*e + 29/2, 7*e - 1, -11/2*e + 15/2, 6*e - 4, -8*e - 9, 3/2*e + 15/2, 5/2*e + 3/2, -11/2*e - 13/2, -8*e - 9, 3/2*e + 3/2, 15/2*e + 11/2, -15/2*e - 3/2, -11/2*e + 9/2, -4*e - 14, -e + 25, -3*e + 5, 2*e - 33, -1/2*e + 7/2, -2*e + 18, -4*e + 16, 8*e - 2, 7/2*e + 13/2, -4*e - 21, e - 6, -10*e - 15, -3/2*e + 69/2, -8*e - 8, -3/2*e + 53/2, -13/2*e - 57/2, 7/2*e + 53/2, -e + 8, 11*e + 1, 2*e + 15, -6, -6*e + 6, -1/2*e - 7/2, 11/2*e + 1/2, -2*e - 1, 13/2*e + 49/2, 19/2*e + 3/2, -7/2*e - 1/2, -10*e - 10, -4*e - 14, -13/2*e - 3/2, -13/2*e - 9/2, 15/2*e + 21/2, -e + 8, -3/2*e - 55/2, 1/2*e - 41/2, 6, -3*e - 32, -3*e - 8, 4*e + 34, -5*e + 11, 2*e - 10, -7*e - 5, -13/2*e + 15/2, 7/2*e + 37/2, 7*e - 8, -e + 24, 1/2*e + 53/2, 11/2*e + 67/2, -21/2*e - 7/2, 7/2*e - 49/2, -2*e - 2, -23/2*e - 19/2, -1/2*e + 5/2, 5/2*e - 31/2, 16*e + 20, 21/2*e + 67/2, 14, 2*e - 16, 1/2*e + 39/2, -25/2*e - 9/2, -8*e - 17, 5*e + 33, 3/2*e - 35/2, -13/2*e - 47/2, 3/2*e - 5/2, -4*e - 18, -6*e + 25, 2*e + 15, 3*e + 13, 4*e + 28, -9*e - 30, 1/2*e + 25/2, 7/2*e - 9/2, -3/2*e + 61/2, -9*e + 10, 5*e - 11, -5/2*e - 13/2, 33/2*e + 19/2, -6*e + 18, -27/2*e - 1/2, -11*e + 7, e + 46, e - 31, 11*e + 6, 1/2*e + 7/2, -1/2*e + 83/2, -3/2*e + 85/2, -15/2*e - 39/2, 3/2*e + 15/2, 3/2*e + 51/2, 30, 17/2*e - 35/2, -11/2*e + 73/2, -9/2*e - 81/2, -3*e + 35, 31/2*e + 39/2, 10*e + 31, -6*e - 28, 6*e - 6, 14*e + 34, 25/2*e + 9/2, 13*e - 3, -2*e - 16, -10*e + 18, 3*e + 7, -6*e - 10, -7/2*e + 75/2, -10*e - 40, -3*e + 27, 15/2*e + 55/2, 21/2*e - 1/2, 19/2*e + 67/2, -7*e + 13, e - 51, 16*e + 10, 10*e + 18, 21/2*e + 57/2, 11/2*e - 53/2, -3/2*e - 21/2, 5*e - 1, -4*e + 14, 17/2*e + 21/2, -3/2*e + 35/2, 3*e + 14, 2*e + 1, 15/2*e + 63/2, 7*e + 33, 11/2*e + 91/2, -9*e - 21, 9*e + 23, -7/2*e + 75/2, -7*e - 35, -6*e - 34, -13*e + 15, -19/2*e - 83/2, -1/2*e - 71/2, 13/2*e - 13/2, 29/2*e - 9/2, 8*e + 28, -5/2*e + 71/2, 29/2*e + 29/2, -4*e + 18, -43/2*e - 27/2, -13*e - 4, 1/2*e - 133/2, 4*e - 14, 39/2*e + 11/2, 15/2*e - 65/2, -12*e + 1, 5/2*e - 43/2, 3/2*e - 39/2, 17/2*e - 43/2, -11*e - 4, -2*e + 40, -15/2*e - 47/2, -9*e - 18, e + 41, -27/2*e - 17/2, 5/2*e + 21/2, 11/2*e - 1/2, -5/2*e - 25/2, -10*e + 16, -9*e - 49, 17/2*e + 17/2, -18*e - 2, -19*e - 23, -5/2*e - 13/2, -11/2*e + 27/2, -9*e - 51, -45/2*e - 47/2, 19/2*e + 39/2, 22*e + 25, 3*e + 22, -11/2*e + 17/2, 1/2*e + 57/2, -22*e - 17, -7*e + 41, 27/2*e + 51/2, 3*e - 13, -68, -32, -12*e + 13, -14*e + 4, -3*e + 29, -11*e + 20, 7*e + 25, 30, 49/2*e + 67/2, 3/2*e + 45/2, -9/2*e - 35/2, -3*e - 11, -44, -14*e - 8, 15/2*e + 55/2, 31/2*e + 79/2, e + 19, 23*e + 21, 14*e - 12, 43, -3*e - 55, e - 9, -10*e - 7, 17/2*e - 31/2, 29/2*e + 23/2, -4*e - 4, 10*e - 2, 35/2*e + 7/2, -3/2*e + 85/2, 5/2*e + 35/2, 45/2*e + 69/2, 15*e + 23, 2*e + 16, 19/2*e - 17/2, 5*e - 3, -7*e + 15, 7/2*e + 35/2, 9*e + 59, 17/2*e - 43/2, -11*e - 39, 37/2*e - 19/2, 7/2*e - 25/2, 3*e - 11] 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 AL_eigenvalues[ZF.ideal([7, 7, -1/3*w^2 + w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]