/* 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, -6, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, w^3 - w^2 - 5*w - 1]) primes_array = [ [4, 2, w^3 - w^2 - 5*w - 2],\ [9, 3, w^3 - w^2 - 5*w - 1],\ [11, 11, -w^3 + w^2 + 6*w + 2],\ [11, 11, w - 1],\ [13, 13, w^3 - 2*w^2 - 4*w + 2],\ [13, 13, -w^2 + w + 4],\ [23, 23, w^2 - 2*w - 2],\ [23, 23, w^3 - w^2 - 6*w - 3],\ [23, 23, -w^2 + 2*w + 5],\ [23, 23, -w + 2],\ [37, 37, 2*w^3 - 2*w^2 - 12*w - 1],\ [37, 37, w^3 - 2*w^2 - 5*w + 2],\ [37, 37, w^3 - 2*w^2 - 5*w + 3],\ [37, 37, -w^3 + w^2 + 6*w - 2],\ [47, 47, w^2 - 2*w - 1],\ [47, 47, w^2 - 2*w - 6],\ [59, 59, 2*w - 1],\ [59, 59, -2*w^3 + 2*w^2 + 12*w + 3],\ [73, 73, -w^3 + w^2 + 7*w + 1],\ [83, 83, -w^3 + w^2 + 4*w + 3],\ [83, 83, 2*w^3 - 2*w^2 - 11*w - 4],\ [107, 107, w^3 - w^2 - 4*w - 5],\ [107, 107, -2*w^3 + 2*w^2 + 11*w + 6],\ [121, 11, 2*w^3 - 2*w^2 - 10*w - 3],\ [131, 131, 2*w^3 - 3*w^2 - 7*w + 2],\ [131, 131, 3*w^3 - 2*w^2 - 18*w - 6],\ [157, 157, -2*w^3 + 2*w^2 + 9*w],\ [157, 157, -2*w^3 + 4*w^2 + 8*w - 3],\ [167, 167, -2*w^3 + w^2 + 11*w + 10],\ [167, 167, -3*w^3 + 4*w^2 + 14*w + 4],\ [169, 13, -2*w^3 + 2*w^2 + 10*w + 7],\ [179, 179, -w^3 + 6*w + 2],\ [179, 179, 2*w^3 - 3*w^2 - 9*w + 4],\ [181, 181, 2*w^2 - w - 8],\ [181, 181, 3*w^3 - 5*w^2 - 14*w + 3],\ [181, 181, -3*w^3 + 3*w^2 + 18*w + 2],\ [181, 181, w^3 - 7*w - 9],\ [191, 191, -2*w^3 + 3*w^2 + 10*w + 1],\ [191, 191, w^2 - 6],\ [193, 193, w^3 - 3*w^2 - 4*w + 3],\ [193, 193, 2*w^3 - 4*w^2 - 9*w + 8],\ [229, 229, -2*w^3 + 2*w^2 + 13*w + 3],\ [229, 229, w^2 - w - 8],\ [239, 239, w^3 - 7*w - 2],\ [239, 239, -w^3 + 2*w^2 + 3*w - 5],\ [241, 241, -3*w^3 + 3*w^2 + 16*w + 2],\ [241, 241, 2*w^3 - 2*w^2 - 9*w - 1],\ [251, 251, -2*w^3 + 3*w^2 + 8*w - 3],\ [251, 251, -2*w^3 + w^2 + 12*w + 4],\ [251, 251, w^3 + w^2 - 7*w - 7],\ [251, 251, 2*w^3 - 3*w^2 - 10*w - 2],\ [263, 263, 3*w^3 - 4*w^2 - 16*w],\ [263, 263, w^2 + w - 4],\ [277, 277, 2*w^2 - w - 7],\ [277, 277, 3*w^3 - 5*w^2 - 14*w + 4],\ [313, 313, 2*w^3 - 4*w^2 - 9*w + 3],\ [313, 313, -w^3 + 3*w^2 + 4*w - 8],\ [337, 337, 2*w^3 - 2*w^2 - 13*w - 1],\ [337, 337, w^3 - w^2 - 8*w - 2],\ [347, 347, 4*w^3 - 4*w^2 - 22*w + 1],\ [347, 347, -2*w^3 + 5*w^2 + 6*w - 10],\ [347, 347, -4*w^3 + 5*w^2 + 20*w + 3],\ [347, 347, -3*w^2 + 4*w + 9],\ [349, 349, -4*w^3 + 5*w^2 + 19*w + 4],\ [349, 349, -w^3 + 4*w^2 + w - 11],\ [349, 349, 2*w^3 - 3*w^2 - 9*w - 4],\ [349, 349, w^3 - 6*w - 10],\ [361, 19, -w^3 + 3*w^2 + 4*w - 4],\ [361, 19, -2*w^3 + 4*w^2 + 9*w - 7],\ [397, 397, 3*w^3 - 3*w^2 - 14*w - 6],\ [397, 397, -2*w^3 + 5*w^2 + 6*w - 6],\ [397, 397, 3*w^2 - 4*w - 13],\ [397, 397, -4*w^3 + 4*w^2 + 21*w + 7],\ [409, 409, 2*w^3 - 4*w^2 - 10*w + 7],\ [409, 409, -2*w^3 + 4*w^2 + 10*w - 3],\ [421, 421, w^3 - w^2 - 6*w - 6],\ [421, 421, w - 5],\ [431, 431, -3*w^3 + 4*w^2 + 18*w - 4],\ [431, 431, 2*w^3 - 3*w^2 - 6*w + 3],\ [433, 433, 2*w^3 - 15*w - 12],\ [433, 433, w^3 - w^2 - 9*w - 5],\ [443, 443, -3*w^3 + 5*w^2 + 14*w - 9],\ [443, 443, 2*w^3 - 12*w - 13],\ [457, 457, -w^3 + 2*w^2 + 5*w - 8],\ [457, 457, -2*w^3 + 4*w^2 + 9*w - 4],\ [457, 457, 2*w^3 - 2*w^2 - 14*w - 5],\ [457, 457, -w^3 + 3*w^2 + 4*w - 7],\ [467, 467, -2*w^3 + 3*w^2 + 8*w - 4],\ [467, 467, -2*w^3 + w^2 + 12*w + 3],\ [479, 479, w^3 + w^2 - 8*w - 7],\ [479, 479, 2*w^3 - 14*w - 9],\ [479, 479, -2*w^3 + 4*w^2 + 6*w - 5],\ [479, 479, -2*w^3 + 4*w^2 + 7*w - 6],\ [491, 491, -2*w^3 + 3*w^2 + 11*w + 2],\ [491, 491, -w^3 + 2*w^2 + 6*w - 6],\ [541, 541, -4*w^2 + 6*w + 15],\ [541, 541, -2*w^3 + 6*w^2 + 4*w - 11],\ [563, 563, -2*w^3 + w^2 + 14*w],\ [563, 563, -w^2 + 4*w + 9],\ [577, 577, w^2 - 4*w - 4],\ [577, 577, -2*w^3 + w^2 + 14*w + 5],\ [587, 587, w^3 - 4*w^2 + 6],\ [587, 587, -w^3 + 3*w^2 + 6*w - 7],\ [587, 587, 4*w^3 - 6*w^2 - 21*w + 2],\ [587, 587, 3*w^3 - 5*w^2 - 14*w],\ [599, 599, 2*w^3 - 2*w^2 - 7*w - 3],\ [599, 599, 5*w^3 - 5*w^2 - 28*w - 6],\ [601, 601, w^3 + w^2 - 10*w - 10],\ [601, 601, 2*w^3 - 3*w^2 - 10*w - 5],\ [613, 613, w^2 - 4*w - 3],\ [613, 613, 2*w^3 - w^2 - 14*w - 6],\ [625, 5, -5],\ [647, 647, -3*w^3 + 4*w^2 + 17*w + 1],\ [647, 647, -w^3 + 2*w^2 + 7*w - 4],\ [659, 659, -5*w^3 + 7*w^2 + 23*w + 3],\ [659, 659, w^3 - 2*w^2 - w - 2],\ [659, 659, -w^3 + 2*w^2 + 2*w - 6],\ [659, 659, -2*w^3 + w^2 + 13*w + 2],\ [683, 683, -2*w^3 + 3*w^2 + 8*w - 5],\ [683, 683, -2*w^3 + w^2 + 12*w + 2],\ [709, 709, w^3 + w^2 - 10*w - 8],\ [709, 709, 2*w^2 - 5*w - 7],\ [719, 719, w^3 - 5*w - 10],\ [719, 719, -3*w^3 + 4*w^2 + 15*w + 5],\ [733, 733, -w^3 + w^2 + 4*w - 5],\ [733, 733, 2*w^2 - 5*w - 6],\ [733, 733, -2*w^3 + 2*w^2 + 11*w - 4],\ [733, 733, w^3 + w^2 - 10*w - 9],\ [743, 743, -w^3 + 3*w^2 + 2*w - 10],\ [743, 743, 2*w^2 - 3*w - 3],\ [757, 757, 2*w^3 - 3*w^2 - 8*w - 5],\ [757, 757, w^3 - 9*w - 5],\ [757, 757, -2*w^3 + w^2 + 12*w + 12],\ [757, 757, w^3 - 9*w - 4],\ [769, 769, -4*w^3 + 4*w^2 + 21*w + 6],\ [769, 769, 3*w^3 - 3*w^2 - 14*w - 5],\ [827, 827, -2*w^3 + w^2 + 12*w + 1],\ [827, 827, -4*w^3 + 4*w^2 + 22*w + 7],\ [827, 827, 2*w^3 - 2*w^2 - 8*w - 5],\ [827, 827, -2*w^3 + 3*w^2 + 8*w - 6],\ [829, 829, -3*w^3 + w^2 + 17*w + 11],\ [829, 829, -4*w^3 + 2*w^2 + 23*w + 16],\ [839, 839, w^2 + 2*w - 4],\ [839, 839, 2*w^3 + w^2 - 14*w - 13],\ [839, 839, -4*w^3 + 7*w^2 + 16*w - 6],\ [839, 839, -4*w^3 + 5*w^2 + 22*w + 1],\ [863, 863, 2*w^3 - 13*w - 8],\ [863, 863, 3*w^3 - 5*w^2 - 12*w + 5],\ [887, 887, 2*w^2 + w - 7],\ [887, 887, -5*w^3 + 7*w^2 + 26*w - 2],\ [911, 911, -3*w^3 + 3*w^2 + 17*w + 7],\ [911, 911, 2*w^2 - 9],\ [911, 911, w^3 - w^2 - 3*w - 5],\ [911, 911, 4*w^3 - 6*w^2 - 20*w + 1],\ [937, 937, -4*w^3 + 5*w^2 + 22*w - 7],\ [937, 937, 4*w^3 - 4*w^2 - 21*w - 2],\ [937, 937, -4*w^2 + 8*w + 13],\ [937, 937, 3*w^3 - 3*w^2 - 14*w - 1],\ [947, 947, 3*w^3 - 4*w^2 - 12*w - 6],\ [947, 947, 3*w^3 - 5*w^2 - 10*w + 4],\ [947, 947, -3*w^3 + 4*w^2 + 19*w + 3],\ [947, 947, -3*w^3 + 4*w^2 + 19*w - 4],\ [971, 971, -3*w^3 + 5*w^2 + 13*w - 7],\ [971, 971, w^3 + w^2 - 7*w - 5],\ [983, 983, -5*w^3 + 8*w^2 + 23*w - 2],\ [983, 983, -w^3 + w^2 + 3*w + 7],\ [1009, 1009, w^3 - w^2 - 6*w - 7],\ [1009, 1009, w - 6],\ [1033, 1033, 4*w^3 - 4*w^2 - 21*w - 5],\ [1033, 1033, -3*w^3 + 3*w^2 + 14*w + 4],\ [1069, 1069, -w^2 - 3],\ [1069, 1069, 2*w^3 - 3*w^2 - 10*w + 8],\ [1103, 1103, -w^3 + 2*w^2 + 7*w - 5],\ [1103, 1103, 3*w^3 - 3*w^2 - 19*w - 7],\ [1103, 1103, 2*w^3 - 11*w - 12],\ [1103, 1103, 3*w^3 - 4*w^2 - 17*w - 2],\ [1117, 1117, -3*w^3 + 3*w^2 + 14*w + 2],\ [1117, 1117, 4*w^3 - 4*w^2 - 21*w - 3],\ [1129, 1129, -w^3 + 2*w^2 + 5*w - 9],\ [1129, 1129, -2*w^3 + w^2 + 15*w + 2],\ [1151, 1151, -3*w^2 + 5*w + 8],\ [1151, 1151, 3*w^3 - 3*w^2 - 18*w - 11],\ [1153, 1153, 3*w^3 - 3*w^2 - 14*w - 3],\ [1153, 1153, -4*w^3 + 4*w^2 + 21*w + 4],\ [1163, 1163, -w^3 + 3*w^2 + w - 9],\ [1163, 1163, -w^3 - w^2 + 9*w + 5],\ [1187, 1187, -3*w^3 + 4*w^2 + 18*w - 6],\ [1187, 1187, -2*w^3 + 11*w + 5],\ [1187, 1187, 2*w^3 - 3*w^2 - 13*w - 4],\ [1187, 1187, 5*w^3 - 7*w^2 - 24*w + 6],\ [1201, 1201, -5*w^3 + 5*w^2 + 30*w + 4],\ [1201, 1201, -5*w - 1],\ [1213, 1213, -6*w^3 + 7*w^2 + 31*w - 2],\ [1213, 1213, 2*w^3 - 6*w^2 - 5*w + 14],\ [1249, 1249, 3*w^3 - 3*w^2 - 13*w - 1],\ [1249, 1249, 3*w^3 - 2*w^2 - 15*w - 4],\ [1249, 1249, -5*w^3 + 6*w^2 + 25*w - 1],\ [1249, 1249, -5*w^3 + 5*w^2 + 27*w + 3],\ [1283, 1283, -w^3 - 3*w^2 + 12*w + 15],\ [1283, 1283, -2*w^3 + 6*w^2 + 3*w - 12],\ [1297, 1297, 5*w^3 - 7*w^2 - 22*w - 2],\ [1297, 1297, 6*w^3 - 8*w^2 - 29*w + 2],\ [1307, 1307, -5*w^3 + 6*w^2 + 27*w + 2],\ [1307, 1307, -3*w^3 + 2*w^2 + 19*w + 2],\ [1319, 1319, 3*w - 4],\ [1319, 1319, -3*w^3 + 3*w^2 + 18*w + 7],\ [1321, 1321, -5*w^3 + 5*w^2 + 27*w + 5],\ [1321, 1321, 4*w^3 - 7*w^2 - 18*w + 7],\ [1367, 1367, -3*w^3 + 4*w^2 + 12*w - 4],\ [1367, 1367, 4*w^3 - 3*w^2 - 23*w - 4],\ [1381, 1381, -2*w^3 + 2*w^2 + 12*w - 5],\ [1381, 1381, 2*w^3 - 16*w - 13],\ [1381, 1381, -2*w - 7],\ [1381, 1381, 2*w^2 - 6*w - 3],\ [1427, 1427, 3*w^3 - 5*w^2 - 15*w - 1],\ [1427, 1427, -w^3 + 3*w^2 + 5*w - 11],\ [1429, 1429, -w^3 + 4*w^2 + 2*w - 10],\ [1429, 1429, 2*w^3 - 5*w^2 - 7*w + 8],\ [1439, 1439, 4*w^3 - 5*w^2 - 22*w - 2],\ [1439, 1439, w^2 + 2*w - 5],\ [1451, 1451, 3*w^3 - 5*w^2 - 12*w + 6],\ [1451, 1451, 3*w^3 - w^2 - 19*w - 9],\ [1451, 1451, 3*w^3 - 5*w^2 - 11*w + 5],\ [1451, 1451, 2*w^3 - 13*w - 7],\ [1453, 1453, 5*w^3 - 6*w^2 - 25*w - 2],\ [1453, 1453, 3*w^3 - 6*w^2 - 13*w + 10],\ [1487, 1487, 4*w^3 - 5*w^2 - 20*w - 6],\ [1487, 1487, 2*w^3 - w^2 - 10*w - 11],\ [1487, 1487, -3*w^3 + 4*w^2 + 16*w + 4],\ [1487, 1487, w^2 + w - 8],\ [1489, 1489, -4*w^3 + 3*w^2 + 22*w + 7],\ [1489, 1489, -4*w^3 + 5*w^2 + 18*w],\ [1499, 1499, 3*w^3 - 4*w^2 - 16*w - 6],\ [1499, 1499, w^2 + w - 10],\ [1511, 1511, -2*w^3 + w^2 + 9*w + 8],\ [1511, 1511, -5*w^3 + 6*w^2 + 26*w + 4],\ [1523, 1523, 2*w^3 - 5*w^2 - 4*w + 9],\ [1523, 1523, 6*w^3 - 6*w^2 - 33*w + 1],\ [1559, 1559, 2*w^3 - 14*w - 7],\ [1559, 1559, -2*w^3 + 4*w^2 + 6*w - 7],\ [1571, 1571, -4*w^3 + 6*w^2 + 23*w - 7],\ [1571, 1571, -4*w^3 + 8*w^2 + 15*w - 11],\ [1571, 1571, 5*w^3 - 7*w^2 - 23*w - 5],\ [1571, 1571, 4*w^3 - w^2 - 28*w - 13],\ [1597, 1597, w^2 - 5*w - 4],\ [1597, 1597, 5*w^3 - 6*w^2 - 25*w - 1],\ [1597, 1597, -3*w^3 + 2*w^2 + 20*w + 6],\ [1597, 1597, 3*w^3 - 2*w^2 - 15*w - 6],\ [1607, 1607, 3*w^3 - 4*w^2 - 13*w + 6],\ [1607, 1607, 4*w^3 - 3*w^2 - 24*w - 4],\ [1607, 1607, -3*w^3 + 2*w^2 + 17*w + 1],\ [1607, 1607, -2*w^3 + 3*w^2 + 6*w - 5],\ [1609, 1609, -2*w^3 + 2*w^2 + 11*w - 5],\ [1609, 1609, -w^3 + w^2 + 4*w - 6],\ [1609, 1609, w^3 - 6*w^2 + 5*w + 13],\ [1609, 1609, -4*w^3 + 3*w^2 + 21*w + 18],\ [1619, 1619, -3*w^3 + 4*w^2 + 17*w + 3],\ [1619, 1619, -w^3 + 2*w^2 + 7*w - 6],\ [1621, 1621, -w^3 + 2*w^2 + 3*w - 10],\ [1621, 1621, -w^3 + 7*w - 3],\ [1657, 1657, -4*w^3 + 3*w^2 + 22*w + 9],\ [1657, 1657, -4*w^3 + 5*w^2 + 18*w + 2],\ [1667, 1667, 2*w^3 + w^2 - 14*w - 12],\ [1667, 1667, 3*w^3 - 5*w^2 - 15*w - 3],\ [1667, 1667, -4*w^3 + 6*w^2 + 17*w - 5],\ [1667, 1667, 3*w^3 - w^2 - 18*w - 8],\ [1669, 1669, 2*w^3 - 3*w^2 - 15*w - 2],\ [1669, 1669, 2*w^3 - 5*w^2 - 8*w + 18],\ [1681, 41, 4*w^3 - 3*w^2 - 22*w - 8],\ [1681, 41, -4*w^3 + 5*w^2 + 18*w + 1],\ [1693, 1693, -4*w^3 + 4*w^2 + 21*w - 5],\ [1693, 1693, -3*w^3 + 3*w^2 + 14*w - 6],\ [1741, 1741, 2*w^3 - 5*w^2 - 11*w + 4],\ [1741, 1741, -5*w^2 + 7*w + 22],\ [1787, 1787, 4*w^3 - 6*w^2 - 19*w - 2],\ [1787, 1787, 4*w^3 - 4*w^2 - 22*w - 9],\ [1787, 1787, 2*w^3 - 2*w^2 - 8*w - 7],\ [1787, 1787, w^3 + w^2 - 6*w - 13],\ [1801, 1801, 4*w^2 - 4*w - 19],\ [1801, 1801, 3*w^3 - 2*w^2 - 19*w - 16],\ [1801, 1801, -w^3 + 4*w^2 - 2*w - 8],\ [1801, 1801, 4*w^3 - 8*w^2 - 16*w + 5],\ [1811, 1811, 2*w^3 + 2*w^2 - 16*w - 17],\ [1811, 1811, -4*w^3 + 8*w^2 + 14*w - 9],\ [1823, 1823, -3*w^3 + 8*w^2 + 7*w - 14],\ [1823, 1823, -4*w^3 + 4*w^2 + 24*w + 7],\ [1823, 1823, 4*w - 3],\ [1823, 1823, -w^3 - 4*w^2 + 13*w + 19],\ [1847, 1847, 3*w^2 - 2*w - 19],\ [1847, 1847, -7*w^3 + 8*w^2 + 39*w + 2],\ [1861, 1861, -w^3 - 3*w^2 + 8*w + 17],\ [1861, 1861, -6*w^3 + 10*w^2 + 27*w - 6],\ [1861, 1861, -w^3 + 4*w^2 + 3*w - 8],\ [1861, 1861, -3*w^3 + 6*w^2 + 13*w - 9],\ [1871, 1871, 2*w^3 + 2*w^2 - 17*w - 17],\ [1871, 1871, w^3 - 5*w^2 + w + 9],\ [1871, 1871, -5*w^3 + 4*w^2 + 30*w + 12],\ [1871, 1871, -w^3 + 5*w^2 - w - 17],\ [1873, 1873, -4*w^3 + 7*w^2 + 22*w - 5],\ [1873, 1873, 4*w^3 - 2*w^2 - 24*w - 21],\ [1873, 1873, 4*w^2 - 5*w - 17],\ [1873, 1873, -4*w^3 + 6*w^2 + 16*w + 7],\ [1907, 1907, -4*w^3 + 6*w^2 + 15*w + 6],\ [1907, 1907, 3*w^3 - 2*w^2 - 14*w - 10],\ [1907, 1907, -6*w^3 + 9*w^2 + 28*w - 1],\ [1907, 1907, 6*w^3 - 7*w^2 - 31*w - 6],\ [1931, 1931, 6*w^3 - 7*w^2 - 34*w - 2],\ [1931, 1931, 3*w^3 - 20*w - 14],\ [1933, 1933, -3*w^3 + 6*w^2 + 13*w - 6],\ [1933, 1933, w^3 - 10*w - 6],\ [1933, 1933, -2*w^3 + w^2 + 15*w + 4],\ [1933, 1933, -w^3 + 4*w^2 + 3*w - 11],\ [1993, 1993, 6*w^3 - 7*w^2 - 31*w],\ [1993, 1993, 5*w^3 - 8*w^2 - 25*w + 9]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^4 - 28*x^2 + 71 K. = NumberField(heckePol) hecke_eigenvalues_array = [1/10*e^2 + 11/10, -1, e, e, -1/10*e^2 + 29/10, -1/10*e^2 + 29/10, -1/10*e^3 + 9/10*e, -1/5*e^3 + 24/5*e, -1/10*e^3 + 9/10*e, -1/5*e^3 + 24/5*e, -1/5*e^2 + 4/5, -1/10*e^2 + 69/10, -1/10*e^2 + 69/10, -1/5*e^2 + 4/5, 3/10*e^3 - 77/10*e, 3/10*e^3 - 77/10*e, 3/10*e^3 - 67/10*e, 3/10*e^3 - 67/10*e, -7/5*e^2 + 93/5, 1/5*e^3 - 29/5*e, 1/5*e^3 - 29/5*e, -3/10*e^3 + 57/10*e, -3/10*e^3 + 57/10*e, 17, -1/2*e^3 + 21/2*e, -1/2*e^3 + 21/2*e, -1/5*e^2 - 21/5, -1/5*e^2 - 21/5, 1/2*e^3 - 31/2*e, 1/2*e^3 - 31/2*e, 11/5*e^2 - 154/5, 1/5*e^3 - 14/5*e, 1/5*e^3 - 14/5*e, 3/2*e^2 - 43/2, 3/2*e^2 - 43/2, 2/5*e^2 - 43/5, 2/5*e^2 - 43/5, 3/5*e^3 - 62/5*e, 3/5*e^3 - 62/5*e, 1/10*e^2 + 101/10, 1/10*e^2 + 101/10, -9/10*e^2 - 49/10, -9/10*e^2 - 49/10, 3/10*e^3 - 117/10*e, 3/10*e^3 - 117/10*e, -9/5*e^2 + 136/5, -9/5*e^2 + 136/5, 2/5*e^3 - 23/5*e, 2/5*e^3 - 23/5*e, 1/10*e^3 - 29/10*e, 1/10*e^3 - 29/10*e, 3/10*e^3 - 47/10*e, 3/10*e^3 - 47/10*e, -9/10*e^2 + 131/10, -9/10*e^2 + 131/10, 17/10*e^2 - 223/10, 17/10*e^2 - 223/10, 9/10*e^2 - 321/10, 9/10*e^2 - 321/10, 1/5*e^3 - 44/5*e, 4*e, 1/5*e^3 - 44/5*e, 4*e, -9/10*e^2 + 251/10, -9/10*e^2 + 251/10, 19/10*e^2 - 391/10, 19/10*e^2 - 391/10, -4/5*e^2 + 116/5, -4/5*e^2 + 116/5, 12/5*e^2 - 203/5, 3/5*e^2 - 2/5, 3/5*e^2 - 2/5, 12/5*e^2 - 203/5, -1/5*e^2 + 14/5, -1/5*e^2 + 14/5, -1/2*e^2 + 13/2, -1/2*e^2 + 13/2, e, e, 1/2*e^2 + 29/2, 1/2*e^2 + 29/2, -9/10*e^3 + 171/10*e, -9/10*e^3 + 171/10*e, -27/10*e^2 + 433/10, -1/5*e^2 + 54/5, -27/10*e^2 + 433/10, -1/5*e^2 + 54/5, -1/10*e^3 + 79/10*e, -1/10*e^3 + 79/10*e, -1/5*e^3 + 14/5*e, -1/5*e^3 + 39/5*e, -1/5*e^3 + 39/5*e, -1/5*e^3 + 14/5*e, 3/5*e^3 - 87/5*e, 3/5*e^3 - 87/5*e, -29/10*e^2 + 351/10, -29/10*e^2 + 351/10, 1/5*e^3 - 29/5*e, 1/5*e^3 - 29/5*e, e^2 - 21, e^2 - 21, -13/10*e^3 + 247/10*e, -6/5*e^3 + 129/5*e, -6/5*e^3 + 129/5*e, -13/10*e^3 + 247/10*e, -1/5*e^3 + 14/5*e, -1/5*e^3 + 14/5*e, 8/5*e^2 - 127/5, 8/5*e^2 - 127/5, 11/5*e^2 - 209/5, 11/5*e^2 - 209/5, -e^2 + 50, 3/5*e^3 - 47/5*e, 3/5*e^3 - 47/5*e, 10*e, 10*e, 4/5*e^3 - 81/5*e, 4/5*e^3 - 81/5*e, -2/5*e^3 + 63/5*e, -2/5*e^3 + 63/5*e, -3*e^2 + 42, -3*e^2 + 42, 11/10*e^3 - 279/10*e, 11/10*e^3 - 279/10*e, -9/5*e^2 + 46/5, 8/5*e^2 - 92/5, -9/5*e^2 + 46/5, 8/5*e^2 - 92/5, 9/10*e^3 - 231/10*e, 9/10*e^3 - 231/10*e, -6/5*e^2 + 99/5, -13/5*e^2 + 197/5, -6/5*e^2 + 99/5, -13/5*e^2 + 197/5, 23/10*e^2 - 447/10, 23/10*e^2 - 447/10, e^3 - 25*e, -e^3 + 28*e, -e^3 + 28*e, e^3 - 25*e, -21/5*e^2 + 294/5, -21/5*e^2 + 294/5, -e^3 + 24*e, -2/5*e^3 + 53/5*e, -2/5*e^3 + 53/5*e, -e^3 + 24*e, -9/10*e^3 + 321/10*e, -9/10*e^3 + 321/10*e, -1/5*e^3 - 16/5*e, -1/5*e^3 - 16/5*e, -3/2*e^3 + 59/2*e, 3/5*e^3 - 87/5*e, -3/2*e^3 + 59/2*e, 3/5*e^3 - 87/5*e, -3/5*e^2 - 168/5, -2/5*e^2 - 107/5, -3/5*e^2 - 168/5, -2/5*e^2 - 107/5, -9/5*e^3 + 171/5*e, -9/5*e^3 + 171/5*e, -6/5*e^3 + 154/5*e, -6/5*e^3 + 154/5*e, 1/10*e^3 + 71/10*e, 1/10*e^3 + 71/10*e, -7/10*e^3 + 243/10*e, -7/10*e^3 + 243/10*e, 13/10*e^2 + 193/10, 13/10*e^2 + 193/10, -21/10*e^2 + 159/10, -21/10*e^2 + 159/10, -3/10*e^2 + 467/10, -3/10*e^2 + 467/10, -7/5*e^3 + 208/5*e, 3/5*e^3 - 82/5*e, 3/5*e^3 - 82/5*e, -7/5*e^3 + 208/5*e, -2*e^2 + 71, -2*e^2 + 71, -27/10*e^2 + 453/10, -27/10*e^2 + 453/10, 7/5*e^3 - 218/5*e, 7/5*e^3 - 218/5*e, 19, 19, 7*e, 7*e, 3/5*e^3 - 47/5*e, 6/5*e^3 - 114/5*e, 3/5*e^3 - 47/5*e, 6/5*e^3 - 114/5*e, -9/10*e^2 - 79/10, -9/10*e^2 - 79/10, -6, -6, 17/5*e^2 - 288/5, 13/10*e^2 - 107/10, 13/10*e^2 - 107/10, 17/5*e^2 - 288/5, e^3 - 22*e, e^3 - 22*e, -27/10*e^2 + 183/10, -27/10*e^2 + 183/10, 23/10*e^3 - 457/10*e, 23/10*e^3 - 457/10*e, -e^3 + 29*e, -e^3 + 29*e, e^2 + 23, e^2 + 23, 3/10*e^3 - 77/10*e, 3/10*e^3 - 77/10*e, 1/5*e^2 - 229/5, e^2 - 12, 1/5*e^2 - 229/5, e^2 - 12, -3/10*e^3 + 107/10*e, -3/10*e^3 + 107/10*e, 7/2*e^2 - 153/2, 7/2*e^2 - 153/2, 6/5*e^3 - 184/5*e, 6/5*e^3 - 184/5*e, -1/5*e^3 - 31/5*e, 3/5*e^3 - 12/5*e, 3/5*e^3 - 12/5*e, -1/5*e^3 - 31/5*e, 12/5*e^2 - 173/5, 12/5*e^2 - 173/5, -11/10*e^3 + 419/10*e, -11/10*e^3 + 419/10*e, -e^3 + 28*e, -e^3 + 28*e, -12/5*e^2 - 7/5, -12/5*e^2 - 7/5, e^3 - 24*e, e^3 - 24*e, -9/10*e^3 + 211/10*e, -9/10*e^3 + 211/10*e, -8/5*e^3 + 222/5*e, -8/5*e^3 + 222/5*e, 13/10*e^3 - 457/10*e, 13/10*e^3 - 457/10*e, -7/5*e^3 + 203/5*e, -7/5*e^3 + 203/5*e, 1/2*e^3 - 27/2*e, 1/2*e^3 - 27/2*e, -21/5*e^2 + 259/5, -1/2*e^2 + 95/2, -21/5*e^2 + 259/5, -1/2*e^2 + 95/2, -6/5*e^3 + 154/5*e, 1/5*e^3 - 69/5*e, -6/5*e^3 + 154/5*e, 1/5*e^3 - 69/5*e, 11/5*e^2 - 104/5, 11/5*e^2 - 104/5, 3/10*e^2 + 433/10, 3/10*e^2 + 433/10, -4/5*e^3 + 31/5*e, -4/5*e^3 + 31/5*e, -3/2*e^2 - 49/2, -3/2*e^2 - 49/2, 16/5*e^2 - 109/5, 16/5*e^2 - 109/5, 8/5*e^3 - 167/5*e, 8/5*e^3 - 167/5*e, 11/5*e^3 - 234/5*e, 11/5*e^3 - 234/5*e, -7/10*e^2 + 323/10, -7/10*e^2 + 323/10, 5*e^2 - 58, 5*e^2 - 58, 11/10*e^2 + 211/10, 11/10*e^2 + 211/10, -13/10*e^2 - 373/10, -13/10*e^2 - 373/10, 1/2*e^3 - 21/2*e, -9/10*e^3 + 91/10*e, -9/10*e^3 + 91/10*e, 1/2*e^3 - 21/2*e, 2*e^2 + 9, 19/10*e^2 - 271/10, 19/10*e^2 - 271/10, 2*e^2 + 9, 1/2*e^3 - 17/2*e, 1/2*e^3 - 17/2*e, 7*e, 1/2*e^3 + 5/2*e, 1/2*e^3 + 5/2*e, 7*e, -2/5*e^3 + 98/5*e, -2/5*e^3 + 98/5*e, -12/5*e^2 + 253/5, -12/5*e^2 + 253/5, 33/5*e^2 - 477/5, 33/5*e^2 - 477/5, -27/10*e^3 + 563/10*e, -11/5*e^3 + 209/5*e, -27/10*e^3 + 563/10*e, -11/5*e^3 + 209/5*e, -27/10*e^2 + 143/10, -31, -27/10*e^2 + 143/10, -31, 4/5*e^3 - 61/5*e, -2/5*e^3 - 27/5*e, 4/5*e^3 - 61/5*e, -2/5*e^3 - 27/5*e, -9/5*e^3 + 206/5*e, -9/5*e^3 + 206/5*e, 27/10*e^2 - 463/10, -16/5*e^2 + 269/5, -16/5*e^2 + 269/5, 27/10*e^2 - 463/10, 9/5*e^2 - 106/5, 9/5*e^2 - 106/5] 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 - w^2 - 5*w - 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]