/* 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([-3, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([61,61,w - 8]) primes_array = [ [2, 2, -w + 1],\ [3, 3, w],\ [11, 11, -2*w + 1],\ [11, 11, 2*w + 1],\ [13, 13, w + 4],\ [13, 13, -w + 4],\ [23, 23, -3*w + 2],\ [23, 23, 3*w + 2],\ [25, 5, 5],\ [37, 37, 2*w - 7],\ [37, 37, -2*w - 7],\ [47, 47, -4*w - 1],\ [47, 47, 4*w - 1],\ [49, 7, -7],\ [59, 59, 5*w - 4],\ [59, 59, -5*w - 4],\ [61, 61, -w - 8],\ [61, 61, w - 8],\ [71, 71, 5*w - 2],\ [71, 71, -5*w - 2],\ [73, 73, 3*w - 10],\ [73, 73, -3*w - 10],\ [83, 83, 6*w - 5],\ [83, 83, -6*w - 5],\ [97, 97, -w - 10],\ [97, 97, w - 10],\ [107, 107, -6*w - 1],\ [107, 107, 6*w - 1],\ [109, 109, 2*w - 11],\ [109, 109, -2*w - 11],\ [131, 131, -7*w - 4],\ [131, 131, 7*w - 4],\ [157, 157, 2*w - 13],\ [157, 157, -2*w - 13],\ [167, 167, 8*w - 5],\ [167, 167, -8*w - 5],\ [179, 179, 9*w - 8],\ [179, 179, -9*w - 8],\ [181, 181, 5*w - 16],\ [181, 181, -5*w - 16],\ [191, 191, -8*w - 1],\ [191, 191, 8*w - 1],\ [193, 193, -w - 14],\ [193, 193, w - 14],\ [227, 227, 9*w - 4],\ [227, 227, -9*w - 4],\ [229, 229, 3*w - 16],\ [229, 229, -3*w - 16],\ [239, 239, 9*w - 2],\ [239, 239, -9*w - 2],\ [241, 241, 4*w - 17],\ [241, 241, -4*w - 17],\ [251, 251, -10*w - 7],\ [251, 251, 10*w - 7],\ [263, 263, 11*w - 10],\ [263, 263, -11*w - 10],\ [277, 277, 2*w - 17],\ [277, 277, -2*w - 17],\ [289, 17, -17],\ [311, 311, 12*w - 11],\ [311, 311, -12*w - 11],\ [313, 313, -4*w - 19],\ [313, 313, 4*w - 19],\ [337, 337, 7*w - 22],\ [337, 337, -7*w - 22],\ [347, 347, -11*w - 4],\ [347, 347, 11*w - 4],\ [349, 349, 2*w - 19],\ [349, 349, -2*w - 19],\ [359, 359, 11*w - 2],\ [359, 359, -11*w - 2],\ [361, 19, -19],\ [373, 373, -3*w - 20],\ [373, 373, 3*w - 20],\ [383, 383, 12*w - 7],\ [383, 383, -12*w - 7],\ [397, 397, -w - 20],\ [397, 397, w - 20],\ [409, 409, -5*w - 22],\ [409, 409, 5*w - 22],\ [419, 419, 14*w - 13],\ [419, 419, -14*w - 13],\ [421, 421, -6*w - 23],\ [421, 421, 6*w - 23],\ [431, 431, -12*w - 1],\ [431, 431, 12*w - 1],\ [433, 433, -9*w - 26],\ [433, 433, 9*w - 26],\ [443, 443, -13*w - 8],\ [443, 443, 13*w - 8],\ [457, 457, 3*w - 22],\ [457, 457, -3*w - 22],\ [467, 467, 14*w - 11],\ [467, 467, -14*w - 11],\ [479, 479, 15*w - 14],\ [479, 479, -15*w - 14],\ [491, 491, 13*w - 4],\ [491, 491, -13*w - 4],\ [503, 503, 13*w - 2],\ [503, 503, -13*w - 2],\ [541, 541, 9*w - 28],\ [541, 541, -9*w - 28],\ [563, 563, -14*w - 5],\ [563, 563, 14*w - 5],\ [577, 577, 4*w - 25],\ [577, 577, -4*w - 25],\ [587, 587, -14*w - 1],\ [587, 587, 14*w - 1],\ [599, 599, -16*w - 13],\ [599, 599, 16*w - 13],\ [601, 601, 5*w - 26],\ [601, 601, -5*w - 26],\ [613, 613, 2*w - 25],\ [613, 613, -2*w - 25],\ [647, 647, -16*w - 11],\ [647, 647, 16*w - 11],\ [659, 659, -15*w - 4],\ [659, 659, 15*w - 4],\ [661, 661, -11*w - 32],\ [661, 661, 11*w - 32],\ [673, 673, -w - 26],\ [673, 673, w - 26],\ [683, 683, 18*w - 17],\ [683, 683, -18*w - 17],\ [709, 709, 5*w - 28],\ [709, 709, -5*w - 28],\ [719, 719, -16*w - 7],\ [719, 719, 16*w - 7],\ [733, 733, -6*w - 29],\ [733, 733, 6*w - 29],\ [743, 743, 16*w - 5],\ [743, 743, -16*w - 5],\ [757, 757, 3*w - 28],\ [757, 757, -3*w - 28],\ [769, 769, -8*w - 31],\ [769, 769, 8*w - 31],\ [827, 827, -19*w - 16],\ [827, 827, 19*w - 16],\ [829, 829, 2*w - 29],\ [829, 829, -2*w - 29],\ [839, 839, 20*w - 19],\ [839, 839, -20*w - 19],\ [841, 29, -29],\ [853, 853, 6*w - 31],\ [853, 853, -6*w - 31],\ [863, 863, 17*w - 2],\ [863, 863, -17*w - 2],\ [877, 877, 7*w - 32],\ [877, 877, -7*w - 32],\ [887, 887, 19*w - 14],\ [887, 887, -19*w - 14],\ [911, 911, 20*w - 17],\ [911, 911, -20*w - 17],\ [937, 937, -13*w - 38],\ [937, 937, 13*w - 38],\ [947, 947, 18*w - 5],\ [947, 947, -18*w - 5],\ [961, 31, -31],\ [971, 971, -18*w - 1],\ [971, 971, 18*w - 1],\ [983, 983, -19*w - 10],\ [983, 983, 19*w - 10],\ [997, 997, -3*w - 32],\ [997, 997, 3*w - 32],\ [1009, 1009, -7*w - 34],\ [1009, 1009, 7*w - 34],\ [1019, 1019, 19*w - 8],\ [1019, 1019, -19*w - 8],\ [1021, 1021, -w - 32],\ [1021, 1021, w - 32],\ [1031, 1031, 20*w - 13],\ [1031, 1031, -20*w - 13],\ [1033, 1033, 8*w - 35],\ [1033, 1033, -8*w - 35],\ [1069, 1069, 10*w - 37],\ [1069, 1069, -10*w - 37],\ [1091, 1091, -22*w - 19],\ [1091, 1091, 22*w - 19],\ [1093, 1093, 13*w - 40],\ [1093, 1093, -13*w - 40],\ [1103, 1103, 23*w - 22],\ [1103, 1103, -23*w - 22],\ [1117, 1117, -6*w - 35],\ [1117, 1117, 6*w - 35],\ [1129, 1129, 3*w - 34],\ [1129, 1129, -3*w - 34],\ [1151, 1151, -20*w - 7],\ [1151, 1151, 20*w - 7],\ [1153, 1153, -w - 34],\ [1153, 1153, w - 34],\ [1163, 1163, 22*w - 17],\ [1163, 1163, -22*w - 17],\ [1187, 1187, 23*w - 20],\ [1187, 1187, -23*w - 20],\ [1201, 1201, -9*w - 38],\ [1201, 1201, 9*w - 38],\ [1213, 1213, 2*w - 35],\ [1213, 1213, -2*w - 35],\ [1223, 1223, 21*w - 10],\ [1223, 1223, -21*w - 10],\ [1237, 1237, -11*w - 40],\ [1237, 1237, 11*w - 40],\ [1249, 1249, 12*w - 41],\ [1249, 1249, -12*w - 41],\ [1259, 1259, -21*w - 8],\ [1259, 1259, 21*w - 8],\ [1283, 1283, 22*w - 13],\ [1283, 1283, -22*w - 13],\ [1297, 1297, -7*w - 38],\ [1297, 1297, 7*w - 38],\ [1307, 1307, 21*w - 4],\ [1307, 1307, -21*w - 4],\ [1319, 1319, 21*w - 2],\ [1319, 1319, -21*w - 2],\ [1321, 1321, 4*w - 37],\ [1321, 1321, -4*w - 37],\ [1367, 1367, 24*w - 19],\ [1367, 1367, -24*w - 19],\ [1381, 1381, 10*w - 41],\ [1381, 1381, -10*w - 41],\ [1427, 1427, -22*w - 5],\ [1427, 1427, 22*w - 5],\ [1429, 1429, -13*w - 44],\ [1429, 1429, 13*w - 44],\ [1439, 1439, 24*w - 17],\ [1439, 1439, -24*w - 17],\ [1451, 1451, -22*w - 1],\ [1451, 1451, 22*w - 1],\ [1453, 1453, 7*w - 40],\ [1453, 1453, -7*w - 40],\ [1487, 1487, -23*w - 10],\ [1487, 1487, 23*w - 10],\ [1489, 1489, 8*w - 41],\ [1489, 1489, -8*w - 41],\ [1499, 1499, 26*w - 23],\ [1499, 1499, -26*w - 23],\ [1511, 1511, 27*w - 26],\ [1511, 1511, -27*w - 26],\ [1523, 1523, -23*w - 8],\ [1523, 1523, 23*w - 8],\ [1549, 1549, -10*w - 43],\ [1549, 1549, 10*w - 43],\ [1559, 1559, 24*w - 13],\ [1559, 1559, -24*w - 13],\ [1571, 1571, -23*w - 4],\ [1571, 1571, 23*w - 4],\ [1583, 1583, 23*w - 2],\ [1583, 1583, -23*w - 2],\ [1597, 1597, -w - 40],\ [1597, 1597, w - 40],\ [1607, 1607, -24*w - 11],\ [1607, 1607, 24*w - 11],\ [1609, 1609, 13*w - 46],\ [1609, 1609, -13*w - 46],\ [1619, 1619, -25*w - 16],\ [1619, 1619, 25*w - 16],\ [1621, 1621, 14*w - 47],\ [1621, 1621, -14*w - 47],\ [1657, 1657, 8*w - 43],\ [1657, 1657, -8*w - 43],\ [1667, 1667, -26*w - 19],\ [1667, 1667, 26*w - 19],\ [1669, 1669, 2*w - 41],\ [1669, 1669, -2*w - 41],\ [1681, 41, -41],\ [1693, 1693, -9*w - 44],\ [1693, 1693, 9*w - 44],\ [1741, 1741, 6*w - 43],\ [1741, 1741, -6*w - 43],\ [1753, 1753, -11*w - 46],\ [1753, 1753, 11*w - 46],\ [1777, 1777, -12*w - 47],\ [1777, 1777, 12*w - 47],\ [1787, 1787, 27*w - 20],\ [1787, 1787, -27*w - 20],\ [1789, 1789, -7*w - 44],\ [1789, 1789, 7*w - 44],\ [1801, 1801, -4*w - 43],\ [1801, 1801, 4*w - 43],\ [1811, 1811, 25*w - 8],\ [1811, 1811, -25*w - 8],\ [1823, 1823, -28*w - 23],\ [1823, 1823, 28*w - 23],\ [1847, 1847, 29*w - 26],\ [1847, 1847, -29*w - 26],\ [1849, 43, -43],\ [1861, 1861, -5*w - 44],\ [1861, 1861, 5*w - 44],\ [1871, 1871, 25*w - 2],\ [1871, 1871, -25*w - 2],\ [1873, 1873, 9*w - 46],\ [1873, 1873, -9*w - 46],\ [1907, 1907, 26*w - 11],\ [1907, 1907, -26*w - 11],\ [1931, 1931, 27*w - 16],\ [1931, 1931, -27*w - 16],\ [1933, 1933, -w - 44],\ [1933, 1933, w - 44],\ [1979, 1979, 26*w - 7],\ [1979, 1979, -26*w - 7],\ [1993, 1993, 13*w - 50],\ [1993, 1993, -13*w - 50],\ [2003, 2003, 26*w - 5],\ [2003, 2003, -26*w - 5],\ [2017, 2017, -8*w - 47],\ [2017, 2017, 8*w - 47],\ [2027, 2027, -26*w - 1],\ [2027, 2027, 26*w - 1],\ [2029, 2029, -15*w - 52],\ [2029, 2029, 15*w - 52],\ [2039, 2039, -29*w - 22],\ [2039, 2039, 29*w - 22],\ [2053, 2053, 18*w - 55],\ [2053, 2053, -18*w - 55],\ [2063, 2063, -28*w - 17],\ [2063, 2063, 28*w - 17],\ [2087, 2087, 27*w - 10],\ [2087, 2087, -27*w - 10],\ [2089, 2089, 3*w - 46],\ [2089, 2089, -3*w - 46],\ [2099, 2099, -31*w - 28],\ [2099, 2099, 31*w - 28],\ [2111, 2111, 32*w - 31],\ [2111, 2111, -32*w - 31],\ [2113, 2113, -w - 46],\ [2113, 2113, w - 46],\ [2137, 2137, 11*w - 50],\ [2137, 2137, -11*w - 50],\ [2161, 2161, -4*w - 47],\ [2161, 2161, 4*w - 47],\ [2207, 2207, -31*w - 26],\ [2207, 2207, 31*w - 26],\ [2221, 2221, -14*w - 53],\ [2221, 2221, 14*w - 53],\ [2243, 2243, 33*w - 32],\ [2243, 2243, -33*w - 32],\ [2267, 2267, 29*w - 16],\ [2267, 2267, -29*w - 16],\ [2269, 2269, 17*w - 56],\ [2269, 2269, -17*w - 56],\ [2281, 2281, -20*w - 59],\ [2281, 2281, 20*w - 59],\ [2293, 2293, 6*w - 49],\ [2293, 2293, -6*w - 49],\ [2339, 2339, 30*w - 19],\ [2339, 2339, -30*w - 19],\ [2341, 2341, -11*w - 52],\ [2341, 2341, 11*w - 52],\ [2351, 2351, -28*w - 1],\ [2351, 2351, 28*w - 1],\ [2377, 2377, 12*w - 53],\ [2377, 2377, -12*w - 53],\ [2389, 2389, 2*w - 49],\ [2389, 2389, -2*w - 49],\ [2399, 2399, 31*w - 22],\ [2399, 2399, -31*w - 22],\ [2411, 2411, 30*w - 17],\ [2411, 2411, -30*w - 17],\ [2423, 2423, -29*w - 10],\ [2423, 2423, 29*w - 10],\ [2437, 2437, -14*w - 55],\ [2437, 2437, 14*w - 55],\ [2447, 2447, -32*w - 25],\ [2447, 2447, 32*w - 25],\ [2459, 2459, -29*w - 8],\ [2459, 2459, 29*w - 8],\ [2473, 2473, -3*w - 50],\ [2473, 2473, 3*w - 50],\ [2521, 2521, 20*w - 61],\ [2521, 2521, -20*w - 61],\ [2531, 2531, -30*w - 13],\ [2531, 2531, 30*w - 13],\ [2543, 2543, -32*w - 23],\ [2543, 2543, 32*w - 23],\ [2557, 2557, -7*w - 52],\ [2557, 2557, 7*w - 52],\ [2579, 2579, -30*w - 11],\ [2579, 2579, 30*w - 11],\ [2591, 2591, -33*w - 26],\ [2591, 2591, 33*w - 26],\ [2593, 2593, -12*w - 55],\ [2593, 2593, 12*w - 55],\ [2617, 2617, -8*w - 53],\ [2617, 2617, 8*w - 53],\ [2663, 2663, 36*w - 35],\ [2663, 2663, -36*w - 35],\ [2677, 2677, 3*w - 52],\ [2677, 2677, -3*w - 52],\ [2687, 2687, 31*w - 14],\ [2687, 2687, -31*w - 14],\ [2689, 2689, 15*w - 58],\ [2689, 2689, -15*w - 58],\ [2699, 2699, -30*w - 1],\ [2699, 2699, 30*w - 1],\ [2711, 2711, 32*w - 19],\ [2711, 2711, -32*w - 19],\ [2713, 2713, 16*w - 59],\ [2713, 2713, -16*w - 59],\ [2749, 2749, -18*w - 61],\ [2749, 2749, 18*w - 61],\ [2797, 2797, 2*w - 53],\ [2797, 2797, -2*w - 53],\ [2809, 53, -53],\ [2819, 2819, -31*w - 8],\ [2819, 2819, 31*w - 8],\ [2833, 2833, -8*w - 55],\ [2833, 2833, 8*w - 55],\ [2843, 2843, -34*w - 25],\ [2843, 2843, 34*w - 25],\ [2857, 2857, -13*w - 58],\ [2857, 2857, 13*w - 58],\ [2879, 2879, 31*w - 2],\ [2879, 2879, -31*w - 2],\ [2903, 2903, -32*w - 13],\ [2903, 2903, 32*w - 13],\ [2917, 2917, 6*w - 55],\ [2917, 2917, -6*w - 55],\ [2927, 2927, -36*w - 31],\ [2927, 2927, 36*w - 31],\ [2939, 2939, -34*w - 23],\ [2939, 2939, 34*w - 23],\ [2953, 2953, 16*w - 61],\ [2953, 2953, -16*w - 61],\ [2963, 2963, 38*w - 37],\ [2963, 2963, -38*w - 37],\ [2999, 2999, 35*w - 26],\ [2999, 2999, -35*w - 26],\ [3001, 3001, 11*w - 58],\ [3001, 3001, -11*w - 58],\ [3011, 3011, 33*w - 16],\ [3011, 3011, -33*w - 16],\ [3023, 3023, 32*w - 7],\ [3023, 3023, -32*w - 7],\ [3037, 3037, 22*w - 67],\ [3037, 3037, -22*w - 67],\ [3049, 3049, -12*w - 59],\ [3049, 3049, 12*w - 59],\ [3061, 3061, 5*w - 56],\ [3061, 3061, -5*w - 56],\ [3083, 3083, 37*w - 32],\ [3083, 3083, -37*w - 32],\ [3109, 3109, -3*w - 56],\ [3109, 3109, 3*w - 56],\ [3119, 3119, 39*w - 38],\ [3119, 3119, -39*w - 38],\ [3121, 3121, -9*w - 58],\ [3121, 3121, 9*w - 58],\ [3167, 3167, -33*w - 10],\ [3167, 3167, 33*w - 10],\ [3169, 3169, -15*w - 62],\ [3169, 3169, 15*w - 62],\ [3181, 3181, -10*w - 59],\ [3181, 3181, 10*w - 59],\ [3191, 3191, -35*w - 22],\ [3191, 3191, 35*w - 22],\ [3203, 3203, 33*w - 8],\ [3203, 3203, -33*w - 8],\ [3217, 3217, -7*w - 58],\ [3217, 3217, 7*w - 58],\ [3229, 3229, 17*w - 64],\ [3229, 3229, -17*w - 64],\ [3251, 3251, 33*w - 4],\ [3251, 3251, -33*w - 4],\ [3253, 3253, 18*w - 65],\ [3253, 3253, -18*w - 65],\ [3299, 3299, 34*w - 13],\ [3299, 3299, -34*w - 13],\ [3301, 3301, -21*w - 68],\ [3301, 3301, 21*w - 68],\ [3313, 3313, 23*w - 70],\ [3313, 3313, -23*w - 70],\ [3323, 3323, -37*w - 28],\ [3323, 3323, 37*w - 28],\ [3347, 3347, 34*w - 11],\ [3347, 3347, -34*w - 11],\ [3359, 3359, -36*w - 23],\ [3359, 3359, 36*w - 23],\ [3361, 3361, -w - 58],\ [3361, 3361, w - 58],\ [3371, 3371, 38*w - 31],\ [3371, 3371, -38*w - 31],\ [3373, 3373, -6*w - 59],\ [3373, 3373, 6*w - 59],\ [3407, 3407, 39*w - 34],\ [3407, 3407, -39*w - 34],\ [3433, 3433, -4*w - 59],\ [3433, 3433, 4*w - 59],\ [3457, 3457, 16*w - 65],\ [3457, 3457, -16*w - 65],\ [3467, 3467, -34*w - 1],\ [3467, 3467, 34*w - 1],\ [3469, 3469, 2*w - 59],\ [3469, 3469, -2*w - 59],\ [3491, 3491, 38*w - 29],\ [3491, 3491, -38*w - 29],\ [3517, 3517, 18*w - 67],\ [3517, 3517, -18*w - 67],\ [3527, 3527, 36*w - 19],\ [3527, 3527, -36*w - 19],\ [3529, 3529, -8*w - 61],\ [3529, 3529, 8*w - 61],\ [3539, 3539, -39*w - 32],\ [3539, 3539, 39*w - 32],\ [3541, 3541, 19*w - 68],\ [3541, 3541, -19*w - 68],\ [3613, 3613, 6*w - 61],\ [3613, 3613, -6*w - 61],\ [3623, 3623, 37*w - 22],\ [3623, 3623, -37*w - 22],\ [3637, 3637, -14*w - 65],\ [3637, 3637, 14*w - 65],\ [3659, 3659, -35*w - 4],\ [3659, 3659, 35*w - 4],\ [3671, 3671, 35*w - 2],\ [3671, 3671, -35*w - 2],\ [3673, 3673, 4*w - 61],\ [3673, 3673, -4*w - 61],\ [3697, 3697, -7*w - 62],\ [3697, 3697, 7*w - 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59],\ [8807, 8807, -64*w - 59],\ [8819, 8819, 55*w - 16],\ [8819, 8819, -55*w - 16],\ [8821, 8821, -14*w - 97],\ [8821, 8821, 14*w - 97],\ [8831, 8831, 65*w - 62],\ [8831, 8831, -65*w - 62],\ [8867, 8867, -58*w - 35],\ [8867, 8867, 58*w - 35],\ [8893, 8893, 38*w - 115],\ [8893, 8893, -38*w - 115],\ [8929, 8929, 15*w - 98],\ [8929, 8929, -15*w - 98],\ [8941, 8941, -25*w - 104],\ [8941, 8941, 25*w - 104],\ [8951, 8951, -60*w - 43],\ [8951, 8951, 60*w - 43],\ [8963, 8963, 57*w - 28],\ [8963, 8963, -57*w - 28],\ [8999, 8999, -59*w - 38],\ [8999, 8999, 59*w - 38],\ [9001, 9001, 20*w - 101],\ [9001, 9001, -20*w - 101],\ [9011, 9011, -55*w - 8],\ [9011, 9011, 55*w - 8],\ [9013, 9013, 2*w - 95],\ [9013, 9013, -2*w - 95],\ [9049, 9049, 27*w - 106],\ [9049, 9049, -27*w - 106],\ [9059, 9059, -55*w - 4],\ [9059, 9059, 55*w - 4],\ [9109, 9109, 10*w - 97],\ [9109, 9109, -10*w - 97],\ [9133, 9133, 17*w - 100],\ [9133, 9133, -17*w - 100],\ [9157, 9157, 22*w - 103],\ [9157, 9157, -22*w - 103],\ [9181, 9181, -30*w - 109],\ [9181, 9181, 30*w - 109],\ [9203, 9203, 63*w - 52],\ [9203, 9203, -63*w - 52],\ [9227, 9227, 61*w - 44],\ [9227, 9227, -61*w - 44],\ [9239, 9239, -56*w - 13],\ [9239, 9239, 56*w - 13],\ [9241, 9241, -11*w - 98],\ [9241, 9241, 11*w - 98],\ [9277, 9277, -33*w - 112],\ [9277, 9277, 33*w - 112],\ [9311, 9311, 65*w - 58],\ [9311, 9311, -65*w - 58],\ [9323, 9323, 62*w - 47],\ [9323, 9323, -62*w - 47],\ [9337, 9337, -36*w - 115],\ [9337, 9337, 36*w - 115],\ [9349, 9349, 37*w - 116],\ [9349, 9349, -37*w - 116],\ [9371, 9371, -67*w - 64],\ [9371, 9371, 67*w - 64],\ [9397, 9397, 2*w - 97],\ [9397, 9397, -2*w - 97],\ [9419, 9419, -59*w - 32],\ [9419, 9419, 59*w - 32],\ [9421, 9421, 26*w - 107],\ [9421, 9421, -26*w - 107],\ [9431, 9431, -60*w - 37],\ [9431, 9431, 60*w - 37],\ [9433, 9433, -16*w - 101],\ [9433, 9433, 16*w - 101],\ [9467, 9467, -58*w - 25],\ [9467, 9467, 58*w - 25],\ [9479, 9479, -64*w - 53],\ [9479, 9479, 64*w - 53],\ [9491, 9491, -57*w - 16],\ [9491, 9491, 57*w - 16],\ [9539, 9539, 65*w - 56],\ [9539, 9539, -65*w - 56],\ [9551, 9551, 57*w - 14],\ [9551, 9551, -57*w - 14],\ [9587, 9587, 66*w - 59],\ [9587, 9587, -66*w - 59],\ [9601, 9601, -w - 98],\ [9601, 9601, w - 98],\ [9613, 9613, 14*w - 101],\ [9613, 9613, -14*w - 101],\ [9623, 9623, 67*w - 62],\ [9623, 9623, -67*w - 62],\ [9649, 9649, 23*w - 106],\ [9649, 9649, -23*w - 106],\ [9661, 9661, -31*w - 112],\ [9661, 9661, 31*w - 112],\ [9697, 9697, -32*w - 113],\ [9697, 9697, 32*w - 113],\ [9719, 9719, 61*w - 38],\ [9719, 9719, -61*w - 38],\ [9721, 9721, 24*w - 107],\ [9721, 9721, -24*w - 107],\ [9733, 9733, -19*w - 104],\ [9733, 9733, 19*w - 104],\ [9743, 9743, 57*w - 2],\ [9743, 9743, -57*w - 2],\ [9767, 9767, -59*w - 26],\ [9767, 9767, 59*w - 26],\ [9769, 9769, 12*w - 101],\ [9769, 9769, -12*w - 101],\ [9781, 9781, 35*w - 116],\ [9781, 9781, -35*w - 116],\ [9791, 9791, 63*w - 46],\ [9791, 9791, -63*w - 46],\ [9803, 9803, 58*w - 17],\ [9803, 9803, -58*w - 17],\ [9817, 9817, 37*w - 118],\ [9817, 9817, -37*w - 118],\ [9829, 9829, -38*w - 119],\ [9829, 9829, 38*w - 119],\ [9839, 9839, 60*w - 31],\ [9839, 9839, -60*w - 31],\ [9851, 9851, 62*w - 41],\ [9851, 9851, -62*w - 41],\ [9887, 9887, -64*w - 49],\ [9887, 9887, 64*w - 49],\ [9901, 9901, 10*w - 101],\ [9901, 9901, -10*w - 101],\ [9923, 9923, -58*w - 13],\ [9923, 9923, 58*w - 13],\ [9949, 9949, -17*w - 104],\ [9949, 9949, 17*w - 104],\ [9973, 9973, 3*w - 100],\ [9973, 9973, -3*w - 100]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 - 10*x^4 + 23*x^2 - 2 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/2*e^5 + 9/2*e^3 - 9*e, 1/2*e^5 - 11/2*e^3 + 13*e, e^3 - 5*e, -1/2*e^4 + 5/2*e^2 + 1, 1/2*e^4 - 7/2*e^2 + 5, 1/2*e^5 - 9/2*e^3 + 8*e, e^5 - 11*e^3 + 26*e, -1/2*e^4 + 9/2*e^2 - 5, -e^4 + 7*e^2 - 6, -1/2*e^4 + 3/2*e^2 + 3, -1/2*e^5 + 7/2*e^3 - 6*e, -3/2*e^5 + 33/2*e^3 - 42*e, -2*e^2 + 6, e^5 - 8*e^3 + 11*e, e^5 - 9*e^3 + 20*e, 1/2*e^4 - 1/2*e^2 - 5, -1, e^5 - 7*e^3 + 6*e, 3/2*e^5 - 31/2*e^3 + 42*e, e^4 - 9*e^2 + 12, -2*e^4 + 14*e^2 - 14, -2*e^5 + 17*e^3 - 25*e, 2*e^5 - 21*e^3 + 55*e, 1/2*e^4 + 1/2*e^2 - 9, -3/2*e^4 + 11/2*e^2 + 15, 5/2*e^5 - 47/2*e^3 + 45*e, -7/2*e^5 + 63/2*e^3 - 57*e, e^4 - 3*e^2 - 6, 2*e^4 - 14*e^2 + 12, -e^5 + 10*e^3 - 27*e, -2*e^5 + 23*e^3 - 63*e, 2*e^4 - 16*e^2 + 16, 5/2*e^4 - 33/2*e^2 + 11, -4*e^5 + 35*e^3 - 59*e, -3/2*e^5 + 35/2*e^3 - 42*e, -4*e^5 + 37*e^3 - 73*e, 4*e^5 - 37*e^3 + 69*e, -2*e^4 + 20*e^2 - 22, 7/2*e^4 - 47/2*e^2 + 17, -4*e^5 + 38*e^3 - 78*e, -5/2*e^5 + 51/2*e^3 - 56*e, -e^4 + 3*e^2, -3/2*e^4 + 23/2*e^2 - 5, 3/2*e^5 - 37/2*e^3 + 59*e, e^5 - 8*e^3 + 5*e, -e^4 + 5*e^2 + 18, -4*e^2 + 18, 7/2*e^5 - 69/2*e^3 + 76*e, -2*e^5 + 15*e^3 - 17*e, 1/2*e^4 - 11/2*e^2 + 3, 5/2*e^4 - 39/2*e^2 + 29, e^5 - 6*e^3 - 5*e, 7/2*e^5 - 67/2*e^3 + 71*e, -3*e^5 + 31*e^3 - 72*e, e^5 - 7*e^3 + 8*e, -e^4 + 5*e^2 + 4, -3/2*e^4 + 25/2*e^2 - 23, 3*e^4 - 15*e^2 - 4, 1/2*e^5 - 7/2*e^3 + 2*e, -2*e^5 + 22*e^3 - 56*e, -e^4 + 3*e^2 - 4, 1/2*e^4 - 7/2*e^2 - 5, 2*e^4 - 16*e^2 + 10, -3/2*e^4 + 21/2*e^2 - 7, -7/2*e^5 + 57/2*e^3 - 43*e, -7/2*e^5 + 79/2*e^3 - 111*e, -4*e^4 + 30*e^2 - 30, 7/2*e^4 - 41/2*e^2 + 3, -5/2*e^5 + 51/2*e^3 - 62*e, e^5 - 13*e^3 + 32*e, -3/2*e^4 + 13/2*e^2 - 9, e^4 + e^2 - 26, -7/2*e^4 + 43/2*e^2 - 1, -11/2*e^5 + 105/2*e^3 - 116*e, -3*e^5 + 25*e^3 - 40*e, 6*e^2 - 28, 26, -e^4 + 9*e^2 - 24, 2*e^2 + 20, 3*e^5 - 34*e^3 + 79*e, -1/2*e^5 + 1/2*e^3 + 21*e, -3/2*e^4 + 25/2*e^2 - 3, -e^4 - e^2 + 16, e^5 - 5*e^3 - 16*e, e^5 - 9*e^3 + 20*e, 3/2*e^4 - 19/2*e^2 - 5, e^4 + e^2 - 28, -7/2*e^5 + 55/2*e^3 - 33*e, 1/2*e^5 - 17/2*e^3 + 29*e, 5/2*e^4 - 23/2*e^2 - 13, -4*e^4 + 26*e^2 - 10, 5*e^5 - 46*e^3 + 103*e, -5*e^5 + 45*e^3 - 92*e, 2*e^5 - 15*e^3 + 9*e, -1/2*e^5 + 5/2*e^3 - 8*e, 3*e^5 - 28*e^3 + 49*e, -2*e^5 + 23*e^3 - 67*e, 3/2*e^5 - 33/2*e^3 + 40*e, -3/2*e^5 + 31/2*e^3 - 36*e, 6*e^2 - 8, -5/2*e^4 + 37/2*e^2 - 11, 13/2*e^5 - 121/2*e^3 + 113*e, 1/2*e^5 - 11/2*e^3 + 11*e, 6*e^2 - 34, 3/2*e^4 - 21/2*e^2 - 7, 13/2*e^5 - 107/2*e^3 + 89*e, -e^3 + 19*e, 2*e^5 - 22*e^3 + 50*e, 7/2*e^5 - 83/2*e^3 + 104*e, -e^4 + 7*e^2, e^4 - 11*e^2, -5*e^4 + 35*e^2 - 40, 2*e^2 - 24, -9/2*e^5 + 73/2*e^3 - 58*e, 6*e^3 - 24*e, 5/2*e^5 - 65/2*e^3 + 93*e, -7/2*e^5 + 45/2*e^3 - 9*e, 2*e^4 - 24*e^2 + 34, -5/2*e^4 + 27/2*e^2 - 1, 4*e^4 - 36*e^2 + 54, 3/2*e^4 - 21/2*e^2 + 27, -3*e^5 + 33*e^3 - 74*e, e^5 - 17*e^3 + 52*e, -2*e^4 + 14*e^2 + 2, e^4 + 3*e^2 - 18, 4*e^5 - 44*e^3 + 126*e, -8*e^5 + 74*e^3 - 150*e, e^4 - 11*e^2 + 8, -e^4 - 3*e^2 + 36, 3*e^5 - 29*e^3 + 80*e, -5*e^3 + 45*e, 4*e^4 - 24*e^2 + 30, 5/2*e^4 - 43/2*e^2 + 5, 9/2*e^4 - 43/2*e^2 - 21, 3*e^4 - 19*e^2 + 16, 6*e^5 - 57*e^3 + 117*e, -5*e^5 + 60*e^3 - 169*e, -5*e^4 + 23*e^2 + 36, 5*e^4 - 33*e^2 + 40, -8*e^3 + 42*e, 6*e^3 - 22*e, -4*e^4 + 26*e^2 + 2, 7/2*e^4 - 43/2*e^2 - 11, 8*e^4 - 48*e^2 + 18, -11/2*e^5 + 103/2*e^3 - 102*e, 9/2*e^5 - 105/2*e^3 + 148*e, -5*e^4 + 21*e^2 + 40, -5/2*e^4 + 59/2*e^2 - 53, 2*e^5 - 17*e^3 + 39*e, e^5 + e^3 - 42*e, -11/2*e^5 + 101/2*e^3 - 108*e, 17/2*e^5 - 159/2*e^3 + 176*e, -4*e^4 + 26*e^2 - 26, -2*e^4 + 14*e^2 - 18, -5*e^5 + 52*e^3 - 119*e, -9/2*e^5 + 83/2*e^3 - 65*e, 3*e^4 - 13*e^2 - 32, -3*e^5 + 30*e^3 - 75*e, 2*e^5 - 7*e^3 - 23*e, -11*e^5 + 101*e^3 - 186*e, -7/2*e^5 + 71/2*e^3 - 80*e, 11/2*e^4 - 57/2*e^2 + 3, 4*e^4 - 10*e^2 - 42, -2*e^4 + 26*e^2 - 54, 3*e^4 - 9*e^2 - 20, 2*e^5 - 19*e^3 + 39*e, 9/2*e^5 - 75/2*e^3 + 65*e, 4*e^2 - 6, -2*e^4 + 16*e^2 - 14, -e^5 + 23*e^3 - 92*e, 1/2*e^5 - 19/2*e^3 + 48*e, 6*e^4 - 38*e^2 + 22, -6*e^4 + 44*e^2 - 54, -6*e^4 + 42*e^2 - 62, -3*e^4 + 15*e^2, 5/2*e^5 - 25/2*e^3 - 5*e, 8*e^5 - 75*e^3 + 143*e, 7/2*e^4 - 51/2*e^2 + 17, 5/2*e^4 - 47/2*e^2 + 49, 5*e^5 - 49*e^3 + 94*e, 3*e^5 - 41*e^3 + 122*e, e^4 - 11*e^2 + 20, -3*e^4 + 17*e^2 + 30, 15/2*e^4 - 111/2*e^2 + 61, 2*e^4 - 28*e^2 + 42, 8*e^3 - 60*e, 2*e^5 - 27*e^3 + 93*e, -4*e^4 + 32*e^2 - 50, -13/2*e^4 + 71/2*e^2 - 3, 6*e^5 - 65*e^3 + 177*e, -9*e^5 + 76*e^3 - 125*e, 7*e^5 - 66*e^3 + 113*e, -5*e^5 + 45*e^3 - 100*e, -5*e^4 + 27*e^2, -e^4 + 17*e^2 - 48, -7*e^4 + 39*e^2 + 4, -13/2*e^4 + 101/2*e^2 - 47, -3/2*e^5 + 27/2*e^3 - 26*e, 15/2*e^5 - 147/2*e^3 + 152*e, -e^4 + 5*e^2 + 34, 8*e^4 - 52*e^2 + 66, -e^4 + 7*e^2 + 28, -5/2*e^4 + 43/2*e^2 + 19, 5/2*e^5 - 53/2*e^3 + 53*e, 3/2*e^5 - 31/2*e^3 + 35*e, 1/2*e^5 - 19/2*e^3 + 39*e, e^5 - 14*e^3 + 39*e, 13/2*e^4 - 89/2*e^2 + 25, -1/2*e^4 - 27/2*e^2 + 65, -10*e^5 + 101*e^3 - 221*e, 13/2*e^5 - 107/2*e^3 + 81*e, 7*e^5 - 65*e^3 + 148*e, 2*e^5 - 7*e^3 - 31*e, 1/2*e^4 - 29/2*e^2 + 17, -2*e^4 + 14*e^2 - 6, -13/2*e^5 + 161/2*e^3 - 238*e, -19/2*e^5 + 177/2*e^3 - 160*e, 3*e^4 - 19*e^2 + 8, 12*e^2 - 28, -4*e^5 + 35*e^3 - 73*e, -7*e^5 + 61*e^3 - 126*e, e^4 - 7*e^2 - 14, -5/2*e^4 + 15/2*e^2 + 15, 7/2*e^5 - 63/2*e^3 + 46*e, 5/2*e^5 - 45/2*e^3 + 46*e, 11*e^5 - 104*e^3 + 219*e, 2*e^5 - 13*e^3 + 5*e, -15/2*e^4 + 75/2*e^2 + 19, -2*e^4 - 6*e^2 + 58, 3*e^5 - 43*e^3 + 144*e, -9/2*e^5 + 95/2*e^3 - 94*e, 6*e^4 - 32*e^2 - 10, -8*e^4 + 44*e^2 + 6, 5*e^5 - 34*e^3 + 29*e, 3*e^5 - 41*e^3 + 130*e, 3*e^5 - 33*e^3 + 62*e, 2*e^5 - 28*e^3 + 98*e, 2*e^5 - 7*e^3 - 25*e, -17/2*e^5 + 145/2*e^3 - 107*e, 6*e^4 - 42*e^2 + 16, 4*e^2 + 26, 5*e^5 - 65*e^3 + 204*e, -6*e^3 + 16*e, -5*e^5 + 44*e^3 - 87*e, -e^3 + 37*e, 7*e^3 - 31*e, -4*e^5 + 31*e^3 - 47*e, -11/2*e^4 + 57/2*e^2 - 11, -3*e^4 + 39*e^2 - 60, -7*e^5 + 57*e^3 - 92*e, 1/2*e^5 + 7/2*e^3 - 32*e, -2*e^4 + 20*e^2 - 82, 17/2*e^4 - 137/2*e^2 + 81, -29/2*e^5 + 259/2*e^3 - 257*e, -3*e^5 + 20*e^3 - 17*e, 3*e^4 - 25*e^2 - 8, -2*e^4 + 2*e^2 + 30, -4*e^4 + 32*e^2 - 42, 3/2*e^4 - 15/2*e^2 + 23, -9*e^5 + 76*e^3 - 143*e, 6*e^5 - 55*e^3 + 131*e, -5*e^4 + 25*e^2 + 52, -e^4 + 11*e^2 - 22, 5/2*e^4 - 65/2*e^2 + 67, -4*e^4 + 32*e^2 - 68, -e^4 + 21*e^2 - 26, -3*e^4 + 15*e^2 - 10, -3/2*e^4 - 3/2*e^2 + 17, 6*e^4 - 42*e^2 + 34, e^4 - 21*e^2 + 64, -3*e^4 + 11*e^2, -9/2*e^4 + 77/2*e^2 - 33, -11*e^5 + 110*e^3 - 247*e, -25/2*e^5 + 247/2*e^3 - 247*e, -5/2*e^4 + 19/2*e^2 + 47, 3/2*e^4 - 11/2*e^2 + 13, -13/2*e^4 + 89/2*e^2 - 25, 2*e^4 - 34, e^5 - 8*e^3 + 37*e, -12*e^5 + 109*e^3 - 211*e, 9*e^5 - 73*e^3 + 102*e, 4*e^5 - 25*e^3 + 13*e, 3*e^5 - 25*e^3 + 40*e, -27/2*e^5 + 263/2*e^3 - 280*e, 16*e^2 - 30, -7*e^4 + 45*e^2 - 22, 5/2*e^4 - 49/2*e^2 + 51, 17/2*e^5 - 153/2*e^3 + 128*e, 23/2*e^5 - 213/2*e^3 + 186*e, -3/2*e^4 + 55/2*e^2 - 81, -e^4 + 15*e^2 - 40, 9/2*e^5 - 61/2*e^3 + 19*e, -15/2*e^5 + 145/2*e^3 - 153*e, 9*e^5 - 85*e^3 + 184*e, -5*e^5 + 50*e^3 - 145*e, 5/2*e^4 - 49/2*e^2 - 1, 2*e^4 - 10*e^2 + 2, e^5 - 2*e^3 - 23*e, 15*e^5 - 140*e^3 + 271*e, -1/2*e^4 - 23/2*e^2 + 61, -17/2*e^4 + 79/2*e^2 + 33, -19/2*e^5 + 191/2*e^3 - 197*e, 9*e^5 - 98*e^3 + 263*e, 7*e^4 - 55*e^2 + 24, 3*e^4 - 15*e^2 - 12, e^5 - 25*e, -3*e^5 + 20*e^3 - 5*e, 7*e^4 - 23*e^2 - 66, -6*e^4 + 34*e^2 - 22, -5*e^5 + 65*e^3 - 182*e, 29/2*e^5 - 289/2*e^3 + 310*e, -4*e^4 + 32*e^2 - 18, -6*e^4 + 48*e^2 - 62, 2*e^3 - 12*e, -25/2*e^5 + 237/2*e^3 - 234*e, e^5 - 9*e^3 + 14*e, 12*e^5 - 114*e^3 + 254*e, 6*e^4 - 32*e^2 - 30, e^4 - 15*e^2 + 36, 9/2*e^5 - 61/2*e^3 + 21*e, 9*e^5 - 105*e^3 + 296*e, 3*e^5 - 27*e^3 + 22*e, -19/2*e^5 + 199/2*e^3 - 228*e, -11/2*e^4 + 67/2*e^2 - 5, -9/2*e^4 + 73/2*e^2 - 51, -5/2*e^4 + 43/2*e^2 - 85, -6*e^4 + 34*e^2 - 38, -6*e^4 + 44*e^2 - 42, -3/2*e^4 - 3/2*e^2 + 65, -2*e^5 + 12*e^3 - 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175/2*e^2 + 93, 15/2*e^4 - 55/2*e^2 - 87, 19/2*e^5 - 249/2*e^3 + 373*e, 7/2*e^5 - 75/2*e^3 + 107*e, -e^5 - 5*e^3 + 90*e, -3/2*e^5 - 27/2*e^3 + 114*e, 6*e^4 - 34*e^2 - 26, -18*e^4 + 118*e^2 - 132, 17*e^5 - 189*e^3 + 482*e, 3*e^5 - 67*e^3 + 270*e, -e^4 + 15*e^2, -18*e^4 + 102*e^2 - 26, 20*e^4 - 140*e^2 + 78, -15*e^4 + 107*e^2 - 116, -5*e^4 + 53*e^2 - 94, -3*e^4 - 9*e^2 + 54, 10*e^5 - 75*e^3 + 117*e, -1/2*e^5 + 49/2*e^3 - 114*e, 7/2*e^4 - 59/2*e^2 + 13, 21/2*e^4 - 183/2*e^2 + 97, 21*e^5 - 206*e^3 + 425*e, -21*e^5 + 194*e^3 - 393*e, -25*e^5 + 222*e^3 - 437*e, -11*e^5 + 85*e^3 - 90*e, -10*e^5 + 84*e^3 - 96*e, 5/2*e^5 - 43/2*e^3 + 58*e, 21*e^4 - 149*e^2 + 184, -35/2*e^4 + 175/2*e^2 + 39, 3/2*e^4 - 67/2*e^2 + 85, 11/2*e^4 - 99/2*e^2 + 151, 17*e^4 - 103*e^2 + 104, 10*e^4 - 110*e^2 + 138, -15/2*e^4 + 121/2*e^2 - 41, -4*e^5 + 4*e^3 + 116*e, 6*e^5 - 58*e^3 + 112*e, 2*e^4 - 24*e^2 + 110, 12*e^4 - 68*e^2 + 68, 7/2*e^5 - 59/2*e^3 + 74*e, 3*e^5 - 43*e^3 + 174*e, -11/2*e^4 + 97/2*e^2 - 23, 5*e^4 - 43*e^2 + 136, 19/2*e^4 - 173/2*e^2 + 51, 31/2*e^4 - 229/2*e^2 + 127, -7/2*e^5 - 7/2*e^3 + 136*e, 7*e^5 - 87*e^3 + 254*e, 7*e^5 - 84*e^3 + 231*e, 39/2*e^5 - 365/2*e^3 + 353*e, -15/2*e^5 + 83/2*e^3 + 5*e, -7/2*e^5 + 51/2*e^3 + 11*e, -7/2*e^4 + 23/2*e^2 + 127, -12*e^4 + 98*e^2 - 180, 15*e^5 - 158*e^3 + 389*e, 8*e^5 - 77*e^3 + 103*e, 3/2*e^4 - 3/2*e^2 + 11, 14*e^4 - 72*e^2 - 26, 7*e^5 - 78*e^3 + 147*e, 22*e^5 - 217*e^3 + 493*e, -35/2*e^4 + 203/2*e^2 + 15, 29/2*e^4 - 177/2*e^2 + 63, -11*e^5 + 113*e^3 - 234*e, 11*e^5 - 93*e^3 + 148*e, 23/2*e^4 - 123/2*e^2 + 13, 16*e^4 - 100*e^2 + 26, -55/2*e^5 + 521/2*e^3 - 593*e, -18*e^5 + 173*e^3 - 389*e, 23*e^4 - 133*e^2 + 40, -25*e^4 + 143*e^2 - 44, 6*e^5 - 81*e^3 + 217*e, 7*e^5 - 60*e^3 + 133*e, -9*e^4 + 75*e^2 - 22, -14*e^4 + 92*e^2 - 18, -31/2*e^4 + 241/2*e^2 - 67, 2*e^2 - 70, -8*e^4 + 46*e^2 - 54, 1/2*e^4 + 13/2*e^2 + 47, 17*e^4 - 135*e^2 + 132, -10*e^4 + 48*e^2 - 10, 31*e^5 - 280*e^3 + 565*e, 45/2*e^5 - 391/2*e^3 + 369*e, -5/2*e^4 + 55/2*e^2 - 37, -35/2*e^4 + 199/2*e^2 - 59, -43/2*e^5 + 447/2*e^3 - 543*e, -14*e^5 + 143*e^3 - 395*e, 11*e^4 - 101*e^2 + 162, 37/2*e^4 - 251/2*e^2 + 85, 11/2*e^5 - 173/2*e^3 + 320*e, -17/2*e^5 + 183/2*e^3 - 210*e, 3/2*e^5 - 85/2*e^3 + 194*e, 21*e^5 - 219*e^3 + 482*e, 6*e^4 - 14*e^2 - 82, -11*e^4 + 57*e^2 - 26, -20*e^4 + 152*e^2 - 154, 27/2*e^4 - 179/2*e^2 + 143, 17/2*e^5 - 183/2*e^3 + 286*e, -3/2*e^5 + 103/2*e^3 - 222*e, 14*e^4 - 102*e^2 + 182, 1/2*e^4 + 11/2*e^2 - 33, -37/2*e^5 + 355/2*e^3 - 385*e, -23*e^3 + 107*e, -41/2*e^4 + 223/2*e^2 - 13, 3*e^4 - 51*e^2 + 166, -15*e^4 + 111*e^2 - 132, -45/2*e^4 + 293/2*e^2 - 61, -6*e^5 + 80*e^3 - 198*e, 21*e^5 - 161*e^3 + 218*e, e^4 + 15*e^2 - 32, -4*e^4 + 8*e^2 - 60, 5/2*e^4 - 71/2*e^2 + 65, -23/2*e^4 + 195/2*e^2 - 91, -11*e^5 + 98*e^3 - 129*e, -31/2*e^5 + 361/2*e^3 - 507*e, -17/2*e^4 + 173/2*e^2 - 87, -6*e^4 + 46*e^2 - 18, 17/2*e^4 - 89/2*e^2 - 13, -3/2*e^4 + 51/2*e^2 - 143, 10*e^5 - 51*e^3 - 39*e, 11/2*e^5 - 173/2*e^3 + 273*e, -12*e^4 + 88*e^2 - 110, -29/2*e^4 + 203/2*e^2 - 91, 19*e^5 - 171*e^3 + 324*e, -14*e^5 + 126*e^3 - 234*e, -10*e^5 + 101*e^3 - 263*e, -2*e^5 + 4*e^3 + 86*e, e^5 + 16*e^3 - 137*e, -21*e^5 + 221*e^3 - 572*e, 20*e^4 - 116*e^2 + 62, -3*e^4 + e^2 + 4, -17*e^5 + 173*e^3 - 398*e, 17*e^5 - 149*e^3 + 304*e, -22*e^5 + 215*e^3 - 421*e, 2*e^5 - 45*e^3 + 161*e, -7/2*e^4 + 61/2*e^2 + 37, 8*e^4 - 24*e^2 - 94, -16*e^4 + 86*e^2 - 34, 25/2*e^4 - 193/2*e^2 + 13, -8*e^4 + 72*e^2 - 110, -10*e^4 + 96*e^2 - 102, -25/2*e^5 + 277/2*e^3 - 412*e, -19/2*e^5 + 127/2*e^3 - 42*e, 32*e^5 - 297*e^3 + 589*e, 5*e^5 - 46*e^3 + 83*e, -26*e^5 + 245*e^3 - 447*e, e^5 + 7*e^3 - 58*e, -17*e^4 + 109*e^2 - 88, 5*e^4 - 9*e^2 - 64, -9*e^5 + 73*e^3 - 148*e, -6*e^5 + 45*e^3 - 15*e, 16*e^4 - 120*e^2 + 118, 29/2*e^4 - 165/2*e^2 - 5, 2*e^4 - 12*e^2 + 6, 7/2*e^4 - 97/2*e^2 + 151, 61/2*e^5 - 569/2*e^3 + 599*e, 20*e^5 - 205*e^3 + 517*e, -25/2*e^4 + 155/2*e^2 + 63, 21/2*e^4 - 215/2*e^2 + 113, -27/2*e^4 + 201/2*e^2 - 163, -16*e^4 + 138*e^2 - 112, e^4 - 7*e^2 - 98, -27/2*e^4 + 191/2*e^2 - 1, 35/2*e^4 - 209/2*e^2 + 87, 4*e^4 - 8*e^2 - 60, -24*e^5 + 211*e^3 - 421*e, -9*e^5 + 95*e^3 - 282*e, 11*e^5 - 93*e^3 + 170*e, -11/2*e^5 + 93/2*e^3 - 59*e, -7*e^5 + 87*e^3 - 298*e, -9/2*e^5 + 91/2*e^3 - 158*e, -e^4 + 15*e^2 - 112, -23/2*e^4 + 163/2*e^2 - 77, -4*e^4 + 10*e^2 - 36, 10*e^4 - 76*e^2 + 162, -12*e^5 + 142*e^3 - 364*e, -18*e^5 + 156*e^3 - 252*e, 19/2*e^5 - 213/2*e^3 + 321*e, 3*e^5 - 40*e^3 + 125*e, 4*e^4 - 54*e^2 + 14, 4*e^4 - 46*e^2 + 66, -19/2*e^4 + 47/2*e^2 + 143, -23/2*e^4 + 127/2*e^2 + 7, -21/2*e^5 + 171/2*e^3 - 143*e, -10*e^5 + 87*e^3 - 135*e, -9*e^4 + 57*e^2 + 4, 15*e^4 - 83*e^2 - 60, -9*e^5 + 48*e^3 + 27*e, -e^5 + 20*e^3 - 121*e, 39/2*e^4 - 329/2*e^2 + 147, -9/2*e^4 + 13/2*e^2 + 25, 45/2*e^5 - 393/2*e^3 + 362*e, -16*e^5 + 188*e^3 - 538*e, -8*e^4 + 88*e^2 - 134, 37/2*e^4 - 251/2*e^2 + 199, 3/2*e^5 + 11/2*e^3 - 115*e, 19*e^5 - 199*e^3 + 432*e, -4*e^5 + 22*e^3, 22*e^5 - 183*e^3 + 297*e, -19*e^5 + 164*e^3 - 307*e, 26*e^5 - 241*e^3 + 437*e, 39/2*e^5 - 407/2*e^3 + 487*e, 13*e^3 - 99*e, 11/2*e^5 - 145/2*e^3 + 260*e, 22*e^5 - 200*e^3 + 412*e, 17*e^5 - 167*e^3 + 346*e, 17*e^5 - 146*e^3 + 281*e, 8*e^4 - 34*e^2 + 22, 17/2*e^4 - 93/2*e^2 + 63, -29/2*e^4 + 235/2*e^2 - 65, 15/2*e^4 - 113/2*e^2 - 33, -67/2*e^5 + 623/2*e^3 - 602*e, 7/2*e^5 - 51/2*e^3 - 8*e, -10*e^4 + 66*e^2 - 54, 23*e^4 - 145*e^2 + 40, -4*e^4 + 8*e^2 - 6, 7/2*e^4 - 13/2*e^2 - 49, 17/2*e^4 - 99/2*e^2 - 93, -13*e^4 + 99*e^2 - 60, -4*e^5 + 32*e^3 - 10*e, 27*e^5 - 249*e^3 + 442*e, 3*e^4 - 23*e^2 + 76, 5*e^4 - 53*e^2 + 60, 18*e^4 - 130*e^2 + 146, 29/2*e^4 - 115/2*e^2 - 99, 10*e^5 - 131*e^3 + 393*e, -6*e^5 + 86*e^3 - 264*e, -19*e^5 + 183*e^3 - 448*e, -33/2*e^5 + 335/2*e^3 - 356*e, -29/2*e^4 + 203/2*e^2 - 75, -6*e^4 + 22*e^2 + 14, -13/2*e^4 + 47/2*e^2 - 9, 12*e^4 - 86*e^2 + 36, -31*e^5 + 275*e^3 - 544*e, 14*e^5 - 157*e^3 + 443*e, -25*e^5 + 249*e^3 - 544*e, 10*e^5 - 133*e^3 + 369*e, -26*e^4 + 180*e^2 - 174, 6*e^4 - 62*e^2 + 94, -17*e^4 + 107*e^2 - 48, 9/2*e^4 - 75/2*e^2 - 55, -13*e^5 + 127*e^3 - 282*e, 37/2*e^5 - 335/2*e^3 + 344*e, -12*e^5 + 141*e^3 - 361*e, -7/2*e^5 + 25/2*e^3 + 45*e, -8*e^5 + 106*e^3 - 296*e, -15*e^5 + 131*e^3 - 202*e, -39/2*e^4 + 331/2*e^2 - 145, -23/2*e^4 + 115/2*e^2 + 55, 25*e^5 - 258*e^3 + 567*e, -39*e^5 + 344*e^3 - 659*e, 5/2*e^4 - 29/2*e^2 + 51, -16*e^4 + 96*e^2 + 28, 12*e^4 - 80*e^2 + 50, -10*e^4 + 78*e^2 - 148] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([61,61,w - 8])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]