/* 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([1369, 37, -37]) 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 - 59],\ [3779, 3779, -w - 61],\ [3779, 3779, w - 62],\ [3793, 3793, -38*w - 11],\ [3793, 3793, 38*w - 49],\ [3797, 3797, 19*w - 80],\ [3797, 3797, -19*w - 61],\ [3821, 3821, -39*w - 14],\ [3821, 3821, 39*w - 53],\ [3823, 3823, -41*w + 61],\ [3823, 3823, 21*w - 83],\ [3847, 3847, -18*w - 61],\ [3847, 3847, 18*w - 79],\ [3851, 3851, -36*w - 1],\ [3851, 3851, 36*w - 37],\ [3877, 3877, 3*w - 64],\ [3877, 3877, -3*w - 61],\ [3917, 3917, 4*w - 65],\ [3917, 3917, -4*w - 61],\ [3923, 3923, 36*w - 35],\ [3923, 3923, 36*w - 1],\ [3929, 3929, 16*w - 77],\ [3929, 3929, -16*w - 61],\ [3943, 3943, 37*w - 41],\ [3943, 3943, -37*w - 4],\ [4001, 4001, 7*w - 68],\ [4001, 4001, -7*w - 61],\ [4003, 4003, -3*w - 62],\ [4003, 4003, 3*w - 65],\ [4007, 4007, 13*w - 74],\ [4007, 4007, -13*w - 61],\ [4013, 4013, 39*w - 50],\ [4013, 4013, -39*w - 11],\ [4021, 4021, 12*w - 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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 K = QQ e = 1 hecke_eigenvalues_array = [1, 1, -4, -4, 6, 6, 6, 6, -10, -6, -6, 8, 8, -13, -3, -3, 8, 8, -10, -10, 3, 3, -4, -4, 12, 12, -6, -6, -13, -7, -7, -6, -6, -4, -4, -13, -13, 9, 9, 18, 18, -7, -7, -24, -24, 2, 2, -13, -13, -18, -18, 0, 0, -24, -24, 15, 15, -18, -18, 8, 8, -4, -4, -6, -6, -28, -28, 23, 23, 6, 6, -34, 8, 8, 5, 5, -12, -12, 3, 3, 29, 29, -28, -28, -15, -15, 18, 18, -12, -12, 42, 42, 3, 3, -16, -16, -28, -28, -12, -12, 12, 12, 23, 23, -27, -27, -10, -10, 14, 14, -9, -9, -6, -6, 36, 36, -3, -3, -1, -1, 21, 21, -48, -48, 15, 15, -10, -10, 41, 41, 2, 2, 12, 12, 30, 30, 32, 32, 20, 20, -6, -6, 14, 14, -6, -6, -52, -52, -3, -3, 8, 8, -24, -24, 20, 20, -7, -7, -3, -3, -46, -12, -12, 20, 20, -10, -10, -30, -30, 0, 0, 5, 5, 0, 0, 11, 11, -10, -10, 42, 42, -40, -40, -51, -51, -7, -7, 20, 20, 38, 38, -33, -33, 57, 57, 26, 26, 42, 42, -19, -19, -37, -37, -24, -24, -24, -24, -49, -49, 56, 56, -48, -48, 26, 26, 68, 68, -24, -24, 1, 59, 59, 57, 57, 26, 26, 66, 66, -33, -33, -37, -37, -13, -13, -25, -25, -3, -3, 53, 53, 0, 0, 0, 0, -70, -70, 23, 23, 6, 6, 36, 36, -46, -46, 36, 36, 29, 29, 33, 33, 80, 80, 18, 18, -1, -34, -34, 17, 17, -48, -48, -22, -22, -76, -76, 14, 14, -54, -54, 51, 51, -12, -12, -21, -21, 2, 2, -48, -48, 48, 48, 60, 60, 53, 53, -33, -33, -55, -55, -54, -54, 30, 30, 32, 32, -25, -25, -54, -54, -58, -58, -60, -60, -76, -76, -52, -52, -63, -63, 9, 9, -49, -49, 74, 74, 48, 48, 8, 8, 66, 66, 38, 38, 42, 42, -85, -78, -78, -6, -6, 44, 44, 56, 56, 87, 87, -28, -28, 36, 36, -7, -7, 27, 27, -10, -10, -22, -22, -30, -30, 3, 3, -15, -15, -60, -60, 11, 11, 62, 62, 20, 20, -72, -72, 20, 20, 6, 6, 68, 68, -7, -7, 27, 27, -96, -96, 17, 17, -4, -4, -84, -84, -46, -46, 86, 86, -99, -99, -13, -13, -30, -30, -97, -97, -37, -37, -81, -81, 36, 36, 80, 80, -4, -4, 6, 6, 17, 17, -96, -96, -78, -78, -51, -51, -84, -84, 0, 0, -40, -40, 21, 21, 89, 89, -48, -48, 62, 62, 24, 24, 68, 68, 74, 74, 14, 14, 42, 42, -30, -30, -31, -31, 20, 20, 60, 60, 80, 80, -55, -55, 9, 9, -25, -25, 0, 0, 102, 102, 99, 99, 50, 50, 66, 66, 83, 83, 30, 30, 57, 57, 26, -16, -16, -57, -57, 90, 90, -84, -84, -49, -49, -100, -100, 14, 14, 69, 69, -36, -36, -58, -58, -70, -70, 44, 44, 20, 20, -78, -78, 74, 74, -30, -30, -88, -88, 48, 48, -45, -45, -100, -100, 84, 84, 86, 86, 54, 54, -30, -30, -55, -55, 32, 32, -69, -69, 62, 62, -12, -12, -45, -45, -99, -99, -25, -25, 0, 0, -28, -28, -51, -51, 6, 6, -73, -73, -112, -112, 26, 26, 9, 9, 63, 63, -33, -33, -58, -58, -73, -73, 21, 21, 12, 12, 56, 56, 101, 101, 57, 57, 90, 90, -42, -42, 14, 14, -28, -28, 9, 9, -115, -115, 51, 51, -30, -30, -30, -30, 104, 104, -7, -7, 18, 18, -42, -42, -118, 107, 107, -69, -69, -21, -21, 122, 122, 32, 32, -40, -40, 99, 99, 80, 80, -22, -22, 119, 119, 24, 24, -72, -72, 26, 26, -121, -121, 57, 57, -82, -82, 113, 113, -36, -36, -42, -42, 95, 95, 53, 53, -34, -34, -102, -102, 96, 96, -81, -81, 57, 57, -36, -36, -46, -46, -12, -12, -7, -7, 8, 8, -84, -84, 45, 45, 83, -120, -120, 72, 72, 65, 65, 62, 62, 84, 84, -15, -15, -76, -76, -28, -28, -100, -100, 45, 45, 84, 84, 62, 62, 36, 36, -25, 90, 90, -52, -52, -129, -129, -87, -87, 26, 26, -12, -12, 140, 140, 38, 38, 8, 8, -30, -30, -39, -39, 104, 104, -76, -76, 2, 2, -60, -60, -88, -88, 51, 51, 84, 84, -64, -64, -63, -63, 80, 80, 72, 72, 18, 18, 72, 72, 132, 132, 86, 86, 74, 74, -64, -64, 42, 42, 54, 54, -109, -109, 32, 32, 93, 93, -88, -88, -75, -75, -39, -39, 6, 6, 144, 144, -85, -85, 126, 126, -58, -58, 96, 96, 92, 92, 66, 66, 30, 30, 131, 131, 44, 44, -108, -108, 2, 2, 26, 26, -93, -93, -99, -99, 93, 93, 110, 110, -18, -18, 71, 71, -135, -135, -127, -127, 59, 59, -133, -133, -10, -10, 17, 17, 122, 122, 15, 15, -28, -28, -144, -144, 27, 27, 122, 122, -30, -30, 2, 2, -84, -84, -154, -154, 60, 60, 56, 56, 51, 51, -36, -36, -58, -58, -70, -70, -40, -40, 59, 59, 83, 83, -81, -81, 75, 75, -130, -130, 84, 84, 71, 71, 65, 65, 72, 72, -85, 66, 66, 41, 41, -60, -60, 105, 105, -7, -7, 66, 66, 54, 54, 62, 62, 95, 95, -36, -36, 54, 54, 68, 68, 0, 0, 36, 36, -48, -48, -94, -94, -31, -31, 54, 54, 51, 51, 65, 65, -24, -24, 164, 164, -9, -9, 102, 102, -28, -28, -42, -42, -34, -34, -18, -18, -46, -46, 150, 150, 59, 59, -76, -76, 102, 102, -64, -64, 48, 48, 74, 74, -42, -42, 159, 159, 23, 23, -42, -42, 89, 89, 66, 66, 51, 51, -112, -112, -1, -1, -9, -9, -25, -25, -120, -120, -7, -7, -121, -121, 101, 101, -60, -60, -57, -57, 9, 9, -84, -84, -114, -114, 42, 42, -58, -58, -48, -48, -147, -147, -142, 107, 107, -94, -94, -48, -48, 74, 74, 143, 143, -112, -112, -18, -18, 48, 48, 116, 116, 84, 84, 168, 168, -91, -91, -67, -67, -70, -70, 78, 78, 44, 44, -54, -54, 80, 80, -48, -48, -58, -58, 51, 51, -4, -4, -34, -34, 131, 131, -141, -141, -51, -51, 146, 146, -42, -42, -147, -147, 170, 170, 102, 102, -4, -4, 123, 123, -103, -103, 5, 5, -102, -102, 66, 66, 146, 146, -46, -46, 92, 92, 24, 24, -156, -156, -103, -103, -34, -34, -28, -28, -100, -100, -42, -42, 32, 32, -139, -139, 81, 81, -18, -18, -151, -151, -6, -6, -10, -10, -48, -48, 38, 38, 14, 14, -96, -96, -82, -82, 162, 162, -112, -112, -139, -139, 65, 65, 32, 32, 65, 65, -52, -52, -37, -37, -48, -48, -52, -52, 143, 143, 33, 33, -102, -102, 84, 84, -3, -3, -117, -117, -6, -6, -148, -148, -162, -162, -94, -94, 2, 2, 141, 141, 80, 80, -130, 42, 42, -10, -10, 30, 30, 35, 35, -105, -105, 140, 140, -168, -168, 51, 51, 54, 54, 186, 186, -69, -69, -102, -102, -1, -1, 96, 96, -21, -21, 104, 104, -70, -70, 180, 180, -31, -31, -61, -61, -76, -76, -48, -48, 129, 129, 54, 54, 164, 164, 56, 56, -60, -60, 72, 72, 8, 8, -124, -124, 89, 89, -180, -180, -174, -174, 68, 68, 21, 21, 23, 23, 50, 50] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([1369, 37, -37])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]