/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([576, 72, 8*w + 24]) primes_array = [ [3, 3, -w],\ [3, 3, -w + 1],\ [4, 2, 2],\ [13, 13, -2*w + 1],\ [17, 17, w + 4],\ [17, 17, -w + 5],\ [23, 23, 3*w + 1],\ [23, 23, -3*w + 4],\ [25, 5, 5],\ [29, 29, 3*w - 2],\ [29, 29, -3*w + 1],\ [43, 43, -4*w - 1],\ [43, 43, 4*w - 5],\ [49, 7, -7],\ [53, 53, -w - 7],\ [53, 53, w - 8],\ [61, 61, -3*w - 8],\ [61, 61, 3*w - 11],\ [79, 79, 5*w - 4],\ [79, 79, 5*w - 1],\ [101, 101, -6*w - 1],\ [101, 101, 6*w - 7],\ [103, 103, 3*w - 13],\ [103, 103, -3*w - 10],\ [107, 107, -w - 10],\ [107, 107, w - 11],\ [113, 113, 6*w - 5],\ [113, 113, 6*w - 1],\ [121, 11, -11],\ [127, 127, -3*w - 11],\ [127, 127, 3*w - 14],\ [131, 131, 2*w - 13],\ [131, 131, -2*w - 11],\ [139, 139, -7*w - 1],\ [139, 139, 7*w - 8],\ [157, 157, 7*w - 2],\ [157, 157, 7*w - 5],\ [173, 173, 4*w - 17],\ [173, 173, -4*w - 13],\ [179, 179, -w - 13],\ [179, 179, w - 14],\ [181, 181, 3*w - 16],\ [181, 181, -3*w - 13],\ [191, 191, 9*w - 13],\ [191, 191, -9*w - 4],\ [199, 199, 8*w - 7],\ [199, 199, 8*w - 1],\ [211, 211, -3*w - 14],\ [211, 211, 3*w - 17],\ [233, 233, -9*w - 1],\ [233, 233, 9*w - 10],\ [251, 251, 9*w - 8],\ [251, 251, 9*w - 1],\ [257, 257, 9*w - 2],\ [257, 257, 9*w - 7],\ [263, 263, 9*w - 4],\ [263, 263, 9*w - 5],\ [269, 269, -w - 16],\ [269, 269, w - 17],\ [277, 277, 3*w - 19],\ [277, 277, -3*w - 16],\ [283, 283, 11*w - 16],\ [283, 283, -11*w - 5],\ [311, 311, 2*w - 19],\ [311, 311, -2*w - 17],\ [313, 313, -3*w - 17],\ [313, 313, 3*w - 20],\ [337, 337, 11*w - 13],\ [337, 337, -11*w - 2],\ [347, 347, -12*w - 5],\ [347, 347, 12*w - 17],\ [361, 19, -19],\ [367, 367, 6*w - 25],\ [367, 367, -6*w - 19],\ [373, 373, 11*w - 10],\ [373, 373, 11*w - 1],\ [389, 389, -4*w - 19],\ [389, 389, 4*w - 23],\ [419, 419, -12*w - 1],\ [419, 419, 12*w - 13],\ [433, 433, -3*w - 20],\ [433, 433, 3*w - 23],\ [439, 439, 13*w - 17],\ [439, 439, -13*w - 4],\ [443, 443, 12*w - 11],\ [443, 443, 12*w - 1],\ [467, 467, 12*w - 7],\ [467, 467, 12*w - 5],\ [491, 491, 7*w - 29],\ [491, 491, -7*w - 22],\ [503, 503, -w - 22],\ [503, 503, w - 23],\ [521, 521, -15*w + 22],\ [521, 521, 8*w - 31],\ [523, 523, 3*w - 25],\ [523, 523, -3*w - 22],\ [547, 547, 13*w - 5],\ [547, 547, 13*w - 8],\ [563, 563, 2*w - 25],\ [563, 563, -2*w - 23],\ [569, 569, 5*w - 28],\ [569, 569, -5*w - 23],\ [571, 571, -3*w - 23],\ [571, 571, 3*w - 26],\ [599, 599, -15*w - 4],\ [599, 599, 15*w - 19],\ [601, 601, 14*w - 13],\ [601, 601, 14*w - 1],\ [607, 607, 9*w - 34],\ [607, 607, -9*w - 25],\ [641, 641, 15*w - 17],\ [641, 641, -15*w - 2],\ [647, 647, -w - 25],\ [647, 647, w - 26],\ [653, 653, 7*w - 32],\ [653, 653, -7*w - 25],\ [659, 659, -15*w - 1],\ [659, 659, 15*w - 16],\ [673, 673, 3*w - 28],\ [673, 673, -3*w - 25],\ [677, 677, 4*w - 29],\ [677, 677, -4*w - 25],\ [701, 701, 15*w - 2],\ [701, 701, 15*w - 13],\ [719, 719, 15*w - 11],\ [719, 719, 15*w - 4],\ [727, 727, -3*w - 26],\ [727, 727, 3*w - 29],\ [751, 751, -16*w - 1],\ [751, 751, 16*w - 17],\ [757, 757, -17*w - 5],\ [757, 757, 17*w - 22],\ [797, 797, 18*w - 25],\ [797, 797, -18*w - 7],\ [809, 809, -w - 28],\ [809, 809, w - 29],\ [823, 823, 16*w - 5],\ [823, 823, 16*w - 11],\ [829, 829, 17*w - 19],\ [829, 829, -17*w - 2],\ [857, 857, 18*w - 23],\ [857, 857, -18*w - 5],\ [859, 859, -9*w - 29],\ [859, 859, 9*w - 38],\ [881, 881, -8*w - 29],\ [881, 881, 8*w - 37],\ [883, 883, 17*w - 16],\ [883, 883, 17*w - 1],\ [887, 887, 2*w - 31],\ [887, 887, -2*w - 29],\ [907, 907, -6*w - 29],\ [907, 907, 6*w - 35],\ [911, 911, -5*w - 29],\ [911, 911, 5*w - 34],\ [919, 919, 17*w - 4],\ [919, 919, 17*w - 13],\ [937, 937, 17*w - 10],\ [937, 937, 17*w - 7],\ [953, 953, -18*w - 1],\ [953, 953, 18*w - 19],\ [961, 31, -31],\ [971, 971, 10*w - 41],\ [971, 971, 21*w - 32],\ [991, 991, -19*w - 4],\ [991, 991, 19*w - 23],\ [997, 997, -9*w - 31],\ [997, 997, 9*w - 40],\ [1013, 1013, -21*w + 31],\ [1013, 1013, 11*w - 43],\ [1031, 1031, -7*w - 31],\ [1031, 1031, 7*w - 38],\ [1039, 1039, 6*w - 37],\ [1039, 1039, -6*w - 31],\ [1049, 1049, 18*w - 7],\ [1049, 1049, 18*w - 11],\ [1063, 1063, -19*w - 1],\ [1063, 1063, 19*w - 20],\ [1069, 1069, 9*w - 41],\ [1069, 1069, -9*w - 32],\ [1091, 1091, -21*w - 8],\ [1091, 1091, 21*w - 29],\ [1093, 1093, -3*w - 32],\ [1093, 1093, 3*w - 35],\ [1109, 1109, -5*w - 32],\ [1109, 1109, 5*w - 37],\ [1117, 1117, 19*w - 2],\ [1117, 1117, 19*w - 17],\ [1153, 1153, 19*w - 14],\ [1153, 1153, 19*w - 5],\ [1171, 1171, 19*w - 8],\ [1171, 1171, 19*w - 11],\ [1187, 1187, -w - 34],\ [1187, 1187, w - 35],\ [1193, 1193, 21*w - 26],\ [1193, 1193, -21*w - 5],\ [1213, 1213, -23*w + 34],\ [1213, 1213, 12*w - 47],\ [1223, 1223, 21*w - 25],\ [1223, 1223, -21*w - 4],\ [1231, 1231, 3*w - 37],\ [1231, 1231, -3*w - 34],\ [1249, 1249, 22*w - 29],\ [1249, 1249, -22*w - 7],\ [1277, 1277, 21*w - 23],\ [1277, 1277, -21*w - 2],\ [1283, 1283, 2*w - 37],\ [1283, 1283, -2*w - 35],\ [1291, 1291, 20*w - 13],\ [1291, 1291, 20*w - 7],\ [1297, 1297, -9*w - 35],\ [1297, 1297, 9*w - 44],\ [1301, 1301, -21*w - 1],\ [1301, 1301, 21*w - 22],\ [1303, 1303, -3*w - 35],\ [1303, 1303, 3*w - 38],\ [1327, 1327, -6*w - 35],\ [1327, 1327, 6*w - 41],\ [1361, 1361, 21*w - 2],\ [1361, 1361, 21*w - 19],\ [1369, 37, -37],\ [1381, 1381, 12*w - 49],\ [1381, 1381, 25*w - 38],\ [1427, 1427, 21*w - 13],\ [1427, 1427, 21*w - 8],\ [1429, 1429, -22*w - 1],\ [1429, 1429, 22*w - 23],\ [1433, 1433, 21*w - 10],\ [1433, 1433, 21*w - 11],\ [1439, 1439, 10*w - 47],\ [1439, 1439, -10*w - 37],\ [1447, 1447, 23*w - 28],\ [1447, 1447, -23*w - 5],\ [1453, 1453, 3*w - 40],\ [1453, 1453, -3*w - 37],\ [1459, 1459, 9*w - 46],\ [1459, 1459, -9*w - 37],\ [1481, 1481, -7*w - 37],\ [1481, 1481, 7*w - 44],\ [1483, 1483, 6*w - 43],\ [1483, 1483, -6*w - 37],\ [1499, 1499, -11*w - 38],\ [1499, 1499, 11*w - 49],\ [1511, 1511, -24*w - 7],\ [1511, 1511, 24*w - 31],\ [1531, 1531, -3*w - 38],\ [1531, 1531, 3*w - 41],\ [1543, 1543, -9*w - 38],\ [1543, 1543, 9*w - 47],\ [1559, 1559, 5*w - 43],\ [1559, 1559, -5*w - 38],\ [1583, 1583, -24*w - 5],\ [1583, 1583, 24*w - 29],\ [1609, 1609, 23*w - 22],\ [1609, 1609, 23*w - 1],\ [1613, 1613, 13*w - 53],\ [1613, 1613, 27*w - 41],\ [1621, 1621, -15*w - 41],\ [1621, 1621, 15*w - 56],\ [1637, 1637, -w - 40],\ [1637, 1637, w - 41],\ [1663, 1663, 23*w - 19],\ [1663, 1663, 23*w - 4],\ [1667, 1667, -27*w + 40],\ [1667, 1667, 14*w - 55],\ [1681, 41, -41],\ [1693, 1693, 3*w - 43],\ [1693, 1693, -3*w - 40],\ [1699, 1699, 23*w - 16],\ [1699, 1699, 23*w - 7],\ [1733, 1733, 7*w - 47],\ [1733, 1733, -7*w - 40],\ [1741, 1741, 12*w - 53],\ [1741, 1741, -12*w - 41],\ [1759, 1759, 25*w - 29],\ [1759, 1759, -25*w - 4],\ [1777, 1777, -3*w - 41],\ [1777, 1777, 3*w - 44],\ [1811, 1811, 5*w - 46],\ [1811, 1811, -5*w - 41],\ [1823, 1823, 24*w - 19],\ [1823, 1823, 24*w - 5],\ [1847, 1847, 24*w - 17],\ [1847, 1847, 24*w - 7],\ [1871, 1871, 24*w - 13],\ [1871, 1871, 24*w - 11],\ [1873, 1873, 26*w - 31],\ [1873, 1873, -26*w - 5],\ [1889, 1889, -w - 43],\ [1889, 1889, w - 44],\ [1901, 1901, -13*w - 43],\ [1901, 1901, 13*w - 56],\ [1907, 1907, 27*w - 35],\ [1907, 1907, -27*w - 8],\ [1933, 1933, -12*w - 43],\ [1933, 1933, 12*w - 55],\ [1949, 1949, -27*w - 7],\ [1949, 1949, 27*w - 34],\ [1951, 1951, 3*w - 46],\ [1951, 1951, -3*w - 43],\ [1973, 1973, -4*w - 43],\ [1973, 1973, 4*w - 47],\ [1979, 1979, -10*w - 43],\ [1979, 1979, 10*w - 53],\ [1993, 1993, 9*w - 52],\ [1993, 1993, -9*w - 43],\ [1999, 1999, 6*w - 49],\ [1999, 1999, -6*w - 43],\ [2003, 2003, 7*w - 50],\ [2003, 2003, -7*w - 43],\ [2011, 2011, 25*w - 8],\ [2011, 2011, 25*w - 17],\ [2027, 2027, -27*w - 5],\ [2027, 2027, 27*w - 32],\ [2029, 2029, 25*w - 11],\ [2029, 2029, 25*w - 14],\ [2053, 2053, 26*w - 25],\ [2053, 2053, 26*w - 1],\ [2063, 2063, -27*w - 4],\ [2063, 2063, 27*w - 31],\ [2081, 2081, -5*w - 44],\ [2081, 2081, 5*w - 49],\ [2083, 2083, -29*w - 11],\ [2083, 2083, 29*w - 40],\ [2089, 2089, -9*w - 44],\ [2089, 2089, 9*w - 53],\ [2129, 2129, 27*w - 29],\ [2129, 2129, -27*w - 2],\ [2131, 2131, 15*w - 61],\ [2131, 2131, 31*w - 47],\ [2141, 2141, 17*w - 64],\ [2141, 2141, -17*w - 47],\ [2161, 2161, 26*w - 7],\ [2161, 2161, 26*w - 19],\ [2207, 2207, 13*w - 59],\ [2207, 2207, -13*w - 46],\ [2209, 47, -47],\ [2213, 2213, 27*w - 26],\ [2213, 2213, 27*w - 1],\ [2237, 2237, 27*w - 2],\ [2237, 2237, 27*w - 25],\ [2239, 2239, 32*w - 49],\ [2239, 2239, 15*w - 62],\ [2287, 2287, 9*w - 55],\ [2287, 2287, -9*w - 46],\ [2297, 2297, 27*w - 22],\ [2297, 2297, 27*w - 5],\ [2311, 2311, 18*w - 67],\ [2311, 2311, -18*w - 49],\ [2339, 2339, 27*w - 8],\ [2339, 2339, 27*w - 19],\ [2341, 2341, -12*w - 47],\ [2341, 2341, 12*w - 59],\ [2357, 2357, 27*w - 10],\ [2357, 2357, 27*w - 17],\ [2383, 2383, -6*w - 47],\ [2383, 2383, 6*w - 53],\ [2389, 2389, -9*w - 47],\ [2389, 2389, 9*w - 56],\ [2393, 2393, -8*w - 47],\ [2393, 2393, 8*w - 55],\ [2417, 2417, 16*w - 65],\ [2417, 2417, 33*w - 50],\ [2441, 2441, -30*w - 7],\ [2441, 2441, 30*w - 37],\ [2447, 2447, -w - 49],\ [2447, 2447, w - 50],\ [2467, 2467, 28*w - 5],\ [2467, 2467, 28*w - 23],\ [2473, 2473, 31*w - 41],\ [2473, 2473, -31*w - 10],\ [2521, 2521, 3*w - 52],\ [2521, 2521, -3*w - 49],\ [2531, 2531, 13*w - 62],\ [2531, 2531, -13*w - 49],\ [2539, 2539, 28*w - 11],\ [2539, 2539, 28*w - 17],\ [2549, 2549, 4*w - 53],\ [2549, 2549, -4*w - 49],\ [2551, 2551, 29*w - 28],\ [2551, 2551, 29*w - 1],\ [2557, 2557, 12*w - 61],\ [2557, 2557, -12*w - 49],\ [2591, 2591, -10*w - 49],\ [2591, 2591, 10*w - 59],\ [2609, 2609, -19*w - 52],\ [2609, 2609, 19*w - 71],\ [2617, 2617, -31*w - 7],\ [2617, 2617, 31*w - 38],\ [2677, 2677, 29*w - 7],\ [2677, 2677, 29*w - 22],\ [2687, 2687, 11*w - 61],\ [2687, 2687, -11*w - 50],\ [2707, 2707, 9*w - 59],\ [2707, 2707, -9*w - 50],\ [2713, 2713, 29*w - 19],\ [2713, 2713, 29*w - 10],\ [2729, 2729, 30*w - 29],\ [2729, 2729, 30*w - 1],\ [2731, 2731, 29*w - 16],\ [2731, 2731, 29*w - 13],\ [2753, 2753, -w - 52],\ [2753, 2753, w - 53],\ [2791, 2791, -35*w + 52],\ [2791, 2791, 18*w - 71],\ [2833, 2833, 3*w - 55],\ [2833, 2833, -3*w - 52],\ [2837, 2837, -33*w - 10],\ [2837, 2837, 33*w - 43],\ [2843, 2843, 36*w - 55],\ [2843, 2843, 17*w - 70],\ [2851, 2851, -31*w - 1],\ [2851, 2851, 31*w - 32],\ [2857, 2857, 34*w - 47],\ [2857, 2857, -34*w - 13],\ [2861, 2861, 30*w - 23],\ [2861, 2861, 30*w - 7],\ [2887, 2887, -32*w - 5],\ [2887, 2887, 32*w - 37],\ [2903, 2903, 2*w - 55],\ [2903, 2903, -2*w - 53],\ [2909, 2909, 30*w - 19],\ [2909, 2909, 30*w - 11],\ [2939, 2939, 33*w - 41],\ [2939, 2939, -33*w - 8],\ [2963, 2963, -14*w - 53],\ [2963, 2963, 14*w - 67],\ [2999, 2999, 5*w - 58],\ [2999, 2999, -5*w - 53],\ [3019, 3019, -6*w - 53],\ [3019, 3019, 6*w - 59],\ [3041, 3041, -8*w - 53],\ [3041, 3041, 8*w - 61],\ [3067, 3067, 31*w - 23],\ [3067, 3067, 31*w - 8],\ [3119, 3119, 33*w - 37],\ [3119, 3119, -33*w - 4],\ [3121, 3121, 31*w - 14],\ [3121, 3121, 31*w - 17],\ [3137, 3137, 16*w - 71],\ [3137, 3137, -16*w - 55],\ [3163, 3163, 3*w - 58],\ [3163, 3163, -3*w - 55],\ [3169, 3169, -35*w - 11],\ [3169, 3169, 35*w - 46],\ [3181, 3181, -34*w - 7],\ [3181, 3181, 34*w - 41],\ [3221, 3221, 17*w - 73],\ [3221, 3221, -17*w - 56],\ [3251, 3251, 36*w - 49],\ [3251, 3251, -36*w - 13],\ [3253, 3253, -12*w - 55],\ [3253, 3253, 12*w - 67],\ [3259, 3259, 21*w - 79],\ [3259, 3259, -21*w - 58],\ [3299, 3299, 33*w - 32],\ [3299, 3299, 33*w - 1],\ [3301, 3301, -15*w - 56],\ [3301, 3301, 15*w - 71],\ [3319, 3319, 32*w - 19],\ [3319, 3319, 32*w - 13],\ [3329, 3329, 33*w - 2],\ [3329, 3329, 33*w - 31],\ [3331, 3331, 35*w - 43],\ [3331, 3331, -35*w - 8],\ [3371, 3371, 36*w - 47],\ [3371, 3371, -36*w - 11],\ [3389, 3389, 11*w - 67],\ [3389, 3389, -11*w - 56],\ [3407, 3407, 33*w - 5],\ [3407, 3407, 33*w - 28],\ [3433, 3433, -34*w - 1],\ [3433, 3433, 34*w - 35],\ [3449, 3449, 33*w - 7],\ [3449, 3449, 33*w - 26],\ [3457, 3457, 37*w - 50],\ [3457, 3457, -37*w - 13],\ [3461, 3461, -39*w + 58],\ [3461, 3461, 20*w - 79],\ [3467, 3467, 33*w - 8],\ [3467, 3467, 33*w - 25],\ [3481, 59, -59],\ [3511, 3511, 3*w - 61],\ [3511, 3511, -3*w - 58],\ [3527, 3527, 33*w - 13],\ [3527, 3527, 33*w - 20],\ [3533, 3533, 33*w - 14],\ [3533, 3533, 33*w - 19],\ [3539, 3539, 33*w - 16],\ [3539, 3539, 33*w - 17],\ [3559, 3559, 15*w - 73],\ [3559, 3559, -15*w - 58],\ [3571, 3571, -18*w - 59],\ [3571, 3571, 18*w - 77],\ [3613, 3613, 34*w - 29],\ [3613, 3613, 34*w - 5],\ [3617, 3617, -17*w - 59],\ [3617, 3617, 17*w - 76],\ [3623, 3623, -7*w - 58],\ [3623, 3623, 7*w - 65],\ [3631, 3631, -3*w - 59],\ [3631, 3631, 3*w - 62],\ [3637, 3637, 37*w - 47],\ [3637, 3637, -37*w - 10],\ [3643, 3643, -9*w - 58],\ [3643, 3643, 9*w - 67],\ [3691, 3691, -15*w - 59],\ [3691, 3691, 15*w - 74],\ [3701, 3701, -5*w - 59],\ [3701, 3701, 5*w - 64],\ [3709, 3709, 35*w - 34],\ [3709, 3709, 35*w - 1],\ [3719, 3719, 14*w - 73],\ [3719, 3719, -14*w - 59],\ [3727, 3727, -6*w - 59],\ [3727, 3727, 6*w - 65],\ [3761, 3761, 8*w - 67],\ [3761, 3761, -8*w - 59],\ [3767, 3767, 11*w - 70],\ [3767, 3767, -11*w - 59],\ [3769, 3769, 9*w - 68],\ [3769, 3769, -9*w - 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125],\ [8867, 8867, 63*w - 95],\ [8893, 8893, 33*w - 128],\ [8893, 8893, -62*w + 91],\ [8941, 8941, -12*w - 91],\ [8941, 8941, 12*w - 103],\ [8969, 8969, 16*w - 107],\ [8969, 8969, -16*w - 91],\ [8971, 8971, 15*w - 106],\ [8971, 8971, -15*w - 91],\ [8999, 8999, -57*w - 11],\ [8999, 8999, 57*w - 68],\ [9013, 9013, 36*w - 133],\ [9013, 9013, -36*w - 97],\ [9049, 9049, -9*w - 92],\ [9049, 9049, 9*w - 101],\ [9091, 9091, 3*w - 97],\ [9091, 9091, -3*w - 94],\ [9103, 9103, 56*w - 61],\ [9103, 9103, -56*w - 5],\ [9109, 9109, 53*w - 22],\ [9109, 9109, 53*w - 31],\ [9127, 9127, 53*w - 28],\ [9127, 9127, 53*w - 25],\ [9151, 9151, -59*w - 17],\ [9151, 9151, 59*w - 76],\ [9161, 9161, 17*w - 109],\ [9161, 9161, -17*w - 92],\ [9181, 9181, 55*w - 2],\ [9181, 9181, 55*w - 53],\ [9187, 9187, -27*w - 94],\ [9187, 9187, 27*w - 121],\ [9203, 9203, 2*w - 97],\ [9203, 9203, -2*w - 95],\ [9221, 9221, 54*w - 43],\ [9221, 9221, 54*w - 11],\ [9227, 9227, 57*w - 65],\ [9227, 9227, -57*w - 8],\ [9239, 9239, -34*w - 97],\ [9239, 9239, 34*w - 131],\ [9257, 9257, 29*w - 124],\ [9257, 9257, -29*w - 95],\ [9281, 9281, 54*w - 41],\ [9281, 9281, 54*w - 13],\ [9283, 9283, -3*w - 95],\ [9283, 9283, 3*w - 98],\ [9311, 9311, 25*w - 119],\ [9311, 9311, -25*w - 94],\ [9337, 9337, -61*w - 22],\ [9337, 9337, 61*w - 83],\ [9343, 9343, 33*w - 130],\ [9343, 9343, -64*w + 95],\ [9377, 9377, 54*w - 17],\ [9377, 9377, 54*w - 37],\ [9403, 9403, 27*w - 122],\ [9403, 9403, -27*w - 95],\ [9409, 97, -97],\ [9413, 9413, 54*w - 19],\ [9413, 9413, 54*w - 35],\ [9421, 9421, 59*w - 73],\ [9421, 9421, -59*w - 14],\ [9437, 9437, -57*w - 5],\ [9437, 9437, 57*w - 62],\ [9439, 9439, -9*w - 94],\ [9439, 9439, 9*w - 103],\ [9461, 9461, 54*w - 23],\ [9461, 9461, 54*w - 31],\ [9463, 9463, 56*w - 55],\ [9463, 9463, 56*w - 1],\ [9467, 9467, -26*w - 95],\ [9467, 9467, 26*w - 121],\ [9473, 9473, 54*w - 29],\ [9473, 9473, 54*w - 25],\ [9491, 9491, 60*w - 77],\ [9491, 9491, -60*w - 17],\ [9533, 9533, 31*w - 128],\ [9533, 9533, 66*w - 101],\ [9539, 9539, -19*w - 94],\ [9539, 9539, 19*w - 113],\ [9551, 9551, -13*w - 94],\ [9551, 9551, 13*w - 107],\ [9619, 9619, 30*w - 127],\ [9619, 9619, -30*w - 97],\ [9623, 9623, 23*w - 118],\ [9623, 9623, -23*w - 95],\ [9629, 9629, 57*w - 59],\ [9629, 9629, -57*w - 2],\ [9643, 9643, 61*w - 80],\ [9643, 9643, -61*w - 19],\ [9649, 9649, 55*w - 41],\ [9649, 9649, 55*w - 14],\ [9689, 9689, -57*w - 1],\ [9689, 9689, 57*w - 58],\ [9697, 9697, 21*w - 116],\ [9697, 9697, -21*w - 95],\ [9721, 9721, 55*w - 38],\ [9721, 9721, 55*w - 17],\ [9733, 9733, -12*w - 95],\ [9733, 9733, 12*w - 107],\ [9749, 9749, 4*w - 101],\ [9749, 9749, -4*w - 97],\ [9767, 9767, -14*w - 95],\ [9767, 9767, 14*w - 109],\ [9803, 9803, 57*w - 56],\ [9803, 9803, 57*w - 1],\ [9811, 9811, 55*w - 32],\ [9811, 9811, 55*w - 23],\ [9829, 9829, 55*w - 26],\ [9829, 9829, 55*w - 29],\ [9851, 9851, 60*w - 73],\ [9851, 9851, -60*w - 13],\ [9857, 9857, 57*w - 2],\ [9857, 9857, 57*w - 55],\ [9871, 9871, -3*w - 98],\ [9871, 9871, 3*w - 101],\ [9883, 9883, 6*w - 103],\ [9883, 9883, -6*w - 97],\ [9907, 9907, 59*w - 67],\ [9907, 9907, -59*w - 8],\ [9923, 9923, 29*w - 127],\ [9923, 9923, -29*w - 98],\ [9929, 9929, -63*w - 23],\ [9929, 9929, 63*w - 86],\ [9931, 9931, 61*w - 77],\ [9931, 9931, -61*w - 16],\ [9941, 9941, -7*w - 97],\ [9941, 9941, 7*w - 104],\ [9949, 9949, 36*w - 137],\ [9949, 9949, -36*w - 101],\ [9967, 9967, 56*w - 43],\ [9967, 9967, 56*w - 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^2 - x - 4 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, e, 0, 2*e + 2, e - 2, -e + 2, 2*e, -2*e, e - 6, 2*e - 2, -2*e + 2, -e + 8, -e + 8, -5*e + 6, -4*e + 6, 4*e - 6, -2*e - 6, -2*e - 6, -2*e + 8, -2*e + 8, 6*e - 2, -6*e + 2, -2*e, -2*e, -4, 4, 10, -10, -4*e - 2, 2*e + 8, 2*e + 8, -3*e - 8, 3*e + 8, 5*e, 5*e, -4*e + 6, -4*e + 6, 4*e + 2, -4*e - 2, -e + 16, e - 16, 4*e - 2, 4*e - 2, -4*e + 16, 4*e - 16, -4*e + 8, -4*e + 8, -9*e + 8, -9*e + 8, e - 2, -e + 2, -8*e + 12, 8*e - 12, -7*e - 10, 7*e + 10, -8*e - 8, 8*e + 8, 2*e + 14, -2*e - 14, -6*e - 2, -6*e - 2, -12, -12, -2*e + 16, 2*e - 16, -e - 6, -e - 6, -3*e - 6, -3*e - 6, -e, e, 34, -8*e + 16, -8*e + 16, -6*e + 26, -6*e + 26, -4*e - 18, 4*e + 18, -e - 32, e + 32, -3*e - 14, -3*e - 14, 14*e - 16, 14*e - 16, 11*e + 8, -11*e - 8, 8*e - 4, -8*e + 4, 5*e - 24, -5*e + 24, -6*e, 6*e, 7*e + 10, -7*e - 10, -4*e - 20, -4*e - 20, -5*e + 16, -5*e + 16, 7*e - 16, -7*e + 16, -5*e - 10, 5*e + 10, -9*e, -9*e, -6*e + 32, 6*e - 32, 5*e - 14, 5*e - 14, 10*e + 8, 10*e + 8, 4*e + 10, -4*e - 10, -2*e, 2*e, 10*e + 2, -10*e - 2, -12*e - 12, 12*e + 12, 13*e - 2, 13*e - 2, -12*e + 10, 12*e - 10, -20*e + 6, 20*e - 6, -16, 16, 20*e - 8, 20*e - 8, -8*e - 16, -8*e - 16, -22, -22, 4*e - 6, -4*e + 6, -3*e + 38, 3*e - 38, 22*e - 16, 22*e - 16, 2*e + 10, 2*e + 10, 8*e - 38, -8*e + 38, -4*e + 4, -4*e + 4, -21*e + 10, 21*e - 10, -5*e + 24, -5*e + 24, -12*e - 24, 12*e + 24, e + 24, e + 24, -4*e - 32, 4*e + 32, -4*e - 8, -4*e - 8, -4*e - 26, -4*e - 26, -9*e + 6, 9*e - 6, 4*e + 42, -11*e + 40, 11*e - 40, 10*e + 8, 10*e + 8, 10*e + 14, 10*e + 14, -6*e - 14, 6*e + 14, -20*e + 24, 20*e - 24, 8*e + 16, 8*e + 16, 7*e - 14, -7*e + 14, -8*e + 8, -8*e + 8, -12*e + 42, -12*e + 42, -20, 20, 10*e - 30, 10*e - 30, 8*e - 14, -8*e + 14, -8*e + 22, -8*e + 22, -13*e - 10, -13*e - 10, -e - 16, -e - 16, 5*e - 8, -5*e + 8, -4*e - 38, 4*e + 38, -22, -22, 2*e, -2*e, 6*e - 24, 6*e - 24, -e + 6, -e + 6, 16*e - 34, -16*e + 34, -12, 12, 7*e - 16, 7*e - 16, 20*e - 2, 20*e - 2, -18*e + 14, 18*e - 14, 26*e - 16, 26*e - 16, -8*e + 16, -8*e + 16, -e + 62, e - 62, 15*e + 6, -6*e + 14, -6*e + 14, -21*e - 8, 21*e + 8, -24*e + 22, -24*e + 22, -13*e - 30, 13*e + 30, 2*e + 8, -2*e - 8, 22*e - 16, 22*e - 16, 24*e + 6, 24*e + 6, -24*e + 4, -24*e + 4, -13*e - 34, 13*e + 34, -e + 8, -e + 8, -16*e + 20, 16*e - 20, 12*e - 40, -12*e + 40, 9*e + 40, 9*e + 40, 12*e - 24, 12*e - 24, -14*e - 32, 14*e + 32, 6*e + 8, -6*e - 8, 13*e - 30, 13*e - 30, 24*e - 6, -24*e + 6, 4*e + 34, 4*e + 34, 8*e - 66, -8*e + 66, 64, 64, -e - 40, e + 40, -18, 2*e - 26, 2*e - 26, -13*e + 40, -13*e + 40, 18*e + 2, -18*e - 2, -16*e + 18, -16*e + 18, -6*e + 8, -6*e + 8, 32*e - 10, 32*e - 10, e - 8, -e + 8, -18*e + 24, 18*e - 24, -8*e + 56, 8*e - 56, 22*e + 8, -22*e - 8, -19*e + 18, -19*e + 18, 12*e - 14, -12*e + 14, -14*e - 10, 14*e + 10, 17*e - 8, -17*e + 8, 22*e - 2, 22*e - 2, -26*e + 14, 26*e - 14, -20*e + 16, -20*e + 16, 14*e - 26, -14*e + 26, -e + 24, e - 24, 15*e + 22, 15*e + 22, 4*e, 4*e, -32*e - 4, 32*e + 4, 3*e - 24, 3*e - 24, -3*e - 56, 3*e + 56, 10*e - 42, 10*e - 42, -18*e + 58, -18*e + 58, 10*e + 56, -10*e - 56, -25*e + 18, 25*e - 18, 24*e + 12, 24*e + 12, e + 18, e + 18, -8*e + 10, 8*e - 10, 8*e + 36, 8*e + 36, 4*e + 14, -4*e - 14, -8*e - 18, -8*e - 18, 22*e - 8, -22*e + 8, -11*e - 54, -4*e + 46, 4*e - 46, 10*e - 34, -10*e + 34, -26*e - 8, -26*e - 8, 4*e + 64, 4*e + 64, -5*e + 42, 5*e - 42, -34*e, -34*e, 11*e + 16, -11*e - 16, 12*e - 14, 12*e - 14, -6*e - 70, 6*e + 70, -32*e + 16, -32*e + 16, -2*e + 34, -2*e + 34, -24*e + 14, 24*e - 14, e + 2, -e - 2, -24*e + 34, 24*e - 34, 4*e - 64, -4*e + 64, -44, -44, 15*e - 18, 15*e - 18, -3*e - 42, -3*e - 42, 5*e + 16, -5*e - 16, e - 48, e - 48, -24*e + 10, 24*e - 10, 36*e - 8, 36*e - 8, 14*e - 10, 14*e - 10, 6*e + 56, -6*e - 56, 24*e + 18, -24*e - 18, 12*e + 2, 12*e + 2, 4*e - 6, 4*e - 6, -22*e - 24, 22*e + 24, 7*e - 56, 7*e - 56, -15*e + 26, -15*e + 26, 29*e - 26, -29*e + 26, 8*e - 60, 8*e - 60, 12*e - 22, -12*e + 22, 6*e - 16, 6*e - 16, -11*e + 54, -11*e + 54, -16*e - 10, 16*e + 10, 17*e - 24, -17*e + 24, 7*e, 7*e, 13*e + 14, 13*e + 14, -4*e - 2, 4*e + 2, -20*e + 8, -20*e + 8, 6*e - 16, -6*e + 16, -4*e - 14, 4*e + 14, -29*e - 24, 29*e + 24, 9*e - 16, -9*e + 16, 12*e + 40, -12*e - 40, -33*e + 16, -33*e + 16, -8*e + 30, 8*e - 30, 36*e - 36, 36*e - 36, 6*e + 72, -6*e - 72, 7*e - 74, 7*e - 74, 21*e + 42, -21*e - 42, 11*e + 8, 11*e + 8, -13*e + 2, -13*e + 2, 2*e + 46, 2*e + 46, -18*e + 38, 18*e - 38, 4*e + 76, -4*e - 76, -34*e + 6, -34*e + 6, 16*e - 20, 16*e - 20, 16*e + 52, -16*e - 52, -24*e + 26, -24*e + 26, 14*e, 14*e, -48*e + 34, 48*e - 34, 8*e + 44, 8*e + 44, 16*e + 28, -16*e - 28, -8*e - 2, 8*e + 2, -28*e + 64, 28*e - 64, -e + 86, -e + 86, -21*e + 2, 21*e - 2, 23*e - 18, 23*e - 18, 2*e - 22, -2*e + 22, e + 48, -e - 48, -18, 26*e - 32, 26*e - 32, 38*e - 48, -38*e + 48, -6*e - 10, 6*e + 10, -19*e + 32, 19*e - 32, -8*e + 40, -8*e + 40, -5*e + 88, -5*e + 88, 86, 86, 5*e + 66, -5*e - 66, 4*e + 56, -4*e - 56, -28*e + 32, -28*e + 32, 30*e - 18, 30*e - 18, 5*e + 16, 5*e + 16, 35*e - 32, 35*e - 32, -6*e + 50, 6*e - 50, -32*e + 10, -32*e + 10, 12*e - 72, -12*e + 72, -12*e + 96, -12*e + 96, -9*e - 10, 9*e + 10, 30*e - 48, -30*e + 48, -32*e - 26, -32*e - 26, -15*e - 24, 15*e + 24, -20*e - 26, -20*e - 26, 24*e - 46, -24*e + 46, -14*e + 34, 14*e - 34, 2*e - 8, 2*e - 8, 10*e - 16, 10*e - 16, -5*e + 24, 5*e - 24, -12*e - 18, -12*e - 18, 6*e + 74, -6*e - 74, -13*e + 96, 13*e - 96, 17*e - 38, -17*e + 38, -32*e + 8, -32*e + 8, 25*e - 38, -25*e + 38, -13*e + 72, -13*e + 72, -18*e - 48, 18*e + 48, 6, -6, 14*e + 46, 14*e + 46, -35*e - 16, -35*e - 16, 11*e + 34, 11*e + 34, -12*e + 18, 12*e - 18, -6*e + 88, 6*e - 88, -5*e + 16, 5*e - 16, 21*e - 48, 21*e - 48, -18*e + 72, -18*e + 72, -26*e + 58, 26*e - 58, 4*e + 70, -4*e - 70, -6*e - 88, -6*e - 88, -7*e - 58, -7*e - 58, -5*e - 8, 5*e + 8, -2*e - 66, 2*e + 66, -13*e + 82, 13*e - 82, -12*e + 22, -12*e + 22, 28*e - 34, 28*e - 34, 15*e + 10, -15*e - 10, 17*e + 24, 17*e + 24, 20*e - 40, -20*e + 40, -2*e + 10, 2*e - 10, -8*e - 98, 8*e + 98, -12*e - 24, -12*e - 24, -2*e - 40, -2*e - 40, -16*e - 48, 16*e + 48, -17*e - 26, 17*e + 26, 20*e + 82, 24*e - 44, 24*e - 44, -16*e - 68, 16*e + 68, -15*e + 32, 15*e - 32, 16*e + 26, 16*e + 26, 72, 72, -37*e + 40, -37*e + 40, 36*e - 26, -36*e + 26, -27*e - 56, -27*e - 56, 16*e - 74, 16*e - 74, -8*e + 24, -8*e + 24, 14*e - 16, -14*e + 16, 16*e - 96, -16*e + 96, 68, 68, 55*e - 38, 55*e - 38, 28*e - 38, -28*e + 38, -12*e + 40, -12*e + 40, -4*e + 32, -4*e + 32, 20*e - 52, -20*e + 52, 25*e - 90, -25*e + 90, 7*e - 22, 7*e - 22, 56*e - 14, 56*e - 14, 22*e - 82, 22*e - 82, -22*e + 16, 22*e - 16, 21*e - 10, -21*e + 10, -25*e + 56, 25*e - 56, 15*e + 78, -15*e - 78, 2*e + 24, -2*e - 24, -8*e + 34, -8*e + 34, -12*e + 56, 12*e - 56, 40*e - 74, 40*e - 74, -19*e + 74, -19*e + 74, -27*e + 82, 27*e - 82, 4*e + 18, -4*e - 18, -3*e - 102, 20*e + 80, -20*e - 80, -39*e + 56, 39*e - 56, -28*e + 66, -28*e + 66, -36*e + 16, -36*e + 16, 11*e - 48, -11*e + 48, -36*e + 52, 36*e - 52, 6*e - 34, 6*e - 34, 19*e - 94, 19*e - 94, -21*e, -21*e, 56*e - 38, -56*e + 38, 28*e - 48, -28*e + 48, -3*e + 2, -3*e + 2, -20*e - 24, 20*e + 24, -36*e + 2, -18*e - 26, 18*e + 26, 21*e - 16, 21*e - 16, 40*e - 58, -40*e + 58, -22*e, 22*e, -44*e + 16, -44*e + 16, -5*e - 6, 5*e + 6, -6*e - 16, -6*e - 16, 16*e - 94, 16*e - 94, 45*e + 16, 45*e + 16, -14*e - 86, 14*e + 86, -28*e + 76, 28*e - 76, 4*e - 112, 4*e - 112, 33*e - 66, 33*e - 66, -36*e + 36, -36*e + 36, 28*e + 10, -28*e - 10, -36*e + 30, -36*e + 30, 12*e - 40, -12*e + 40, -2*e + 112, 2*e - 112, -17*e + 86, -17*e + 86, 60*e - 52, -60*e + 52, -13*e - 24, -13*e - 24, 8*e - 130, -8*e + 130, 36*e + 6, -36*e - 6, 6*e + 8, -6*e - 8, -8*e + 18, 8*e - 18, 51*e - 2, 51*e - 2, -18*e + 8, -18*e + 8, 16*e - 50, 16*e - 50, -41*e - 22, 41*e + 22, -10*e + 72, 10*e - 72, -12*e + 58, -12*e + 58, 24*e - 76, 24*e - 76, -20*e + 34, 20*e - 34, -16*e + 20, -16*e + 20, -e + 72, e - 72, -24, 24, -52*e + 32, 52*e - 32, 34*e - 64, -34*e + 64, -12*e - 54, -12*e - 54, -20*e + 110, 20*e - 110, 88, 88, 52*e - 2, -52*e + 2, 43*e - 72, 43*e - 72, 18*e - 6, -18*e + 6, -15*e + 14, 15*e - 14, 28*e + 34, 28*e + 34, 32*e + 68, 32*e + 68, 6*e - 122, -6*e + 122, 8*e - 52, 8*e - 52, -23*e - 74, -23*e - 74, 27*e - 46, -27*e + 46, 6*e - 48, -6*e + 48, 10*e + 42, -10*e - 42, -20*e - 82, -20*e - 82, 2*e - 74, -2*e + 74, 24*e + 24, 24*e + 24, -53*e + 42, 53*e - 42, 47*e - 46, 47*e - 46, -2*e - 72, -2*e - 72, -24*e - 38, -24*e - 38, 68, 68, 28*e - 50, 28*e - 50, -2*e - 94, -2*e - 94, -27*e + 22, 27*e - 22, -41*e - 16, -41*e - 16, 19*e - 6, -19*e + 6, -33*e - 72, 33*e + 72, -27*e - 22, -27*e - 22, -64*e + 40, 64*e - 40, -24*e - 14, -24*e - 14, -28*e + 26, 28*e - 26, -e + 30, -e + 30, -50*e + 2, 50*e - 2, -4*e - 128, -4*e - 128, 48*e - 30, -48*e + 30, 33*e - 56, -33*e + 56, 11*e + 50, 11*e + 50, -42*e + 96, -42*e + 96, -32*e - 44, -32*e - 44, 26*e + 94, 26*e + 94, 10*e - 74, 10*e - 74, 12*e - 70, -12*e + 70, -25*e + 66, 25*e - 66, -21*e - 40, -21*e - 40, 11*e + 64, -11*e - 64, -4*e - 54, -4*e - 54, -5*e - 82, -5*e - 82, 6*e + 40, -6*e - 40, -98, 40*e + 36, -40*e - 36, -7*e - 88, -7*e - 88, 12*e - 106, -12*e + 106, -22*e + 88, 22*e - 88, -14*e - 112, -14*e - 112, -47*e - 32, 47*e + 32, -8*e + 26, 8*e - 26, 4*e + 32, 4*e + 32, 32*e + 50, 32*e + 50, -39*e + 24, 39*e - 24, 37*e - 8, -37*e + 8, 24*e + 10, 24*e + 10, -64*e + 22, 64*e - 22, 26*e, -26*e, 10*e + 88, -10*e - 88, 30*e - 96, 30*e - 96, -4*e - 50, -4*e - 50, 35*e - 22, -35*e + 22, 40*e + 28, -40*e - 28, 8*e - 124, 8*e - 124, -6*e + 102, 6*e - 102, -18*e - 78, -18*e - 78, -6*e - 110, 6*e + 110, -17*e + 112, 17*e - 112, 19*e - 2, 19*e - 2, 39*e - 24, -39*e + 24, 24*e - 78, 24*e - 78, 69*e - 8, -69*e + 8, 30*e - 10, 30*e - 10, -24*e - 18, 24*e + 18, 35*e - 6, 35*e - 6, 17*e + 16, 17*e + 16, 67*e - 26, -67*e + 26, 24*e - 20, 24*e - 20, 64, -64, -21*e - 70, -21*e - 70, 10*e + 10, -10*e - 10, 40*e - 44, -40*e + 44, -5*e - 114, -5*e - 114, 30*e - 18, -30*e + 18, -8*e - 22, -8*e - 22, 96, -96, 48*e - 70, -48*e + 70, 34*e + 32, 34*e + 32, -8*e - 122, -8*e - 122, 36*e - 28, -36*e + 28, -24*e + 110, -24*e + 110, -8*e + 78, 8*e - 78, 36*e + 56, 36*e + 56, 44*e + 20, 44*e + 20, -25*e + 48, -25*e + 48, -48*e + 38, 48*e - 38, -35*e + 46, 35*e - 46, 60*e - 32, -60*e + 32, 26*e + 22, -26*e - 22, -6*e + 14, 6*e - 14, -12*e - 74, 12*e + 74, -6*e + 128, -6*e + 128, 26*e - 2, -26*e + 2, 4*e - 68, -4*e + 68, 4*e - 162, 12*e - 136, 12*e - 136, -6*e + 102, -6*e + 102, -25*e - 10, 25*e + 10, 9*e - 40, 9*e - 40, 31*e - 66, 31*e - 66, 24*e + 44, 24*e + 44, 24*e - 30, -24*e + 30, -40*e - 8, 40*e + 8, -47*e + 58, -47*e + 58, -8*e - 48, 8*e + 48, -37*e - 32, 37*e + 32, -40*e + 38, -40*e + 38, 42*e + 32, 42*e + 32, -6*e - 56, -6*e - 56, -20*e + 4, 20*e - 4, 24*e + 62, 24*e + 62, 16*e - 68, -16*e + 68, 10*e - 50, 10*e - 50, 29*e - 48, -29*e + 48, -6*e - 122, -6*e - 122, 41*e - 106, -41*e + 106, -2*e + 48, -2*e + 48, 50*e + 10, 50*e + 10, e + 10, e + 10, 24*e + 28, -24*e - 28, -39*e + 6, 39*e - 6, 68*e - 74, 68*e - 74, -6*e + 96, 6*e - 96, -12*e - 48, 12*e + 48, 27*e - 40, 27*e - 40, -14*e + 126, 14*e - 126, -2*e - 120, -2*e - 120, 51*e + 46, -51*e - 46, -5*e - 32, -5*e - 32, 34*e + 10, 34*e + 10, -18*e + 102, 18*e - 102, -57*e + 38, 57*e - 38, 4*e, 4*e, -16*e - 50, -16*e - 50, 9*e - 50, 9*e - 50, 22, -22, 4*e - 26, -4*e + 26, 45*e - 104, 45*e - 104, -36*e + 38, -36*e + 38, 12*e + 128, 12*e + 128, -7*e - 18, -7*e - 18, 40*e - 78, -40*e + 78, 23*e - 110, 23*e - 110, 5*e + 32, 5*e + 32, -38*e + 8, 38*e - 8, -52*e - 42, 52*e + 42, -30*e + 80, -30*e + 80, 35*e + 82, -35*e - 82, -40*e, -40*e, -13*e + 8, 13*e - 8, 46*e - 70, 46*e - 70, 38*e + 62, 38*e + 62, 33*e - 78, -33*e + 78, -47*e + 112, -47*e + 112, 48*e + 56, -48*e - 56, -54*e - 34, -54*e - 34, 4*e + 30, 4*e + 30, 31*e, 31*e, -12*e - 128, -12*e - 128, -38*e + 18, -38*e + 18, 30*e + 16, 30*e + 16, 20*e + 48, 20*e + 48, 76*e - 46, -76*e + 46, 4*e + 70, 4*e + 70, 47*e + 64, 47*e + 64, 19*e - 64, -19*e + 64, 2*e - 126, -2*e + 126, -7*e - 112, 7*e + 112, -10*e + 48, 10*e - 48, -118, 118, -25*e + 6, 25*e - 6, -23*e - 32, -23*e - 32, -14*e + 40, 14*e - 40, 25*e - 50, 25*e - 50, -60*e + 16, -60*e + 16, 27*e - 10, -27*e + 10, 13*e + 120, 13*e + 120, -16*e + 130, 2*e + 66, -2*e - 66, -44*e + 74, -44*e + 74, -66*e + 26, 66*e - 26, -22*e - 24, -22*e - 24, 18*e - 66, -18*e + 66, -34*e, -34*e, 72*e - 44, -72*e + 44, 31*e + 38, -31*e - 38, 31*e + 16, -31*e - 16, 4*e + 26, -4*e - 26, 24*e + 84, -24*e - 84, 42*e - 8, -42*e + 8, -61*e + 32, -61*e + 32, 6*e - 112, -6*e + 112, 6*e + 54, -6*e - 54, 32*e - 68, 32*e - 68, -28*e + 90, -28*e + 90, -e + 102, e - 102, 55*e + 10, 55*e + 10, -37*e + 110, -37*e + 110, 56*e - 30, 56*e - 30, 4*e - 38, -4*e + 38, 16*e + 120, -16*e - 120, -7*e + 48, 7*e - 48, -21*e + 160, -21*e + 160, 52*e - 18, 52*e - 18, 59*e - 16, -59*e + 16, -30, 30, 68*e, 68*e, 77*e - 48, 77*e - 48, 49*e - 48, 49*e - 48, 40*e - 44, -40*e + 44, 39*e + 74, -39*e - 74, 13*e + 64, 13*e + 64, 24*e - 82, -24*e + 82, -6*e - 54, -6*e - 54, 40*e - 112, 40*e - 112] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, -w])] = -1 AL_eigenvalues[ZF.ideal([4, 2, 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]