/* 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([81,81,5*w - 3]) 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 = [0, -1, -2, -5, -3, 3, -3, 0, 1, -3, -9, -7, -4, 5, 3, 9, -11, -2, 1, -8, 18, 9, -19, -1, 3, 9, -3, 6, -5, -8, 4, 12, 3, -4, 11, -10, 5, -15, 18, -9, -15, -19, 5, 15, 0, -11, 13, -20, 1, -9, 21, 3, -15, -21, -30, -12, 9, 6, -30, 23, -1, 4, 19, 3, 15, -17, 7, -29, 22, 21, -36, 2, 17, -28, -17, -14, -3, 6, -24, -9, -11, -11, -28, 35, 9, -24, 27, 21, -9, 39, -39, -33, -6, -30, -28, -28, -1, 17, -21, 12, -21, 33, -23, 43, 36, -9, -26, -5, 41, 32, 33, 3, 21, 15, -33, 9, 21, -15, -19, 2, -3, 27, 21, -33, 48, -36, 37, -8, 5, 23, -11, 25, -33, 33, -3, 39, -16, 23, 34, 46, -21, -39, 4, -5, 21, -45, 52, 52, 48, -27, -5, 28, -9, -24, 49, -23, 1, -47, -42, 42, -55, 12, 36, -31, -31, 11, 2, 9, 27, 9, -48, -16, -19, 21, -21, -16, 32, -17, 10, 57, -12, 46, 1, 39, -54, 2, 38, -19, -7, -25, -1, -60, -12, -21, 45, -2, 31, 48, -24, -37, 29, -31, 5, -45, 33, 45, -3, -8, -11, -11, -47, 63, -42, -41, 49, -32, 49, -21, -15, -34, 23, 26, 15, 3, -1, 26, 21, -18, 63, 45, 13, 43, 50, -31, -25, -37, -54, -45, -49, 20, 36, -9, -45, 21, 43, -65, 49, -32, -57, -24, 69, -21, -17, 10, -30, 9, -65, -29, -15, -33, 52, -41, 0, -9, 37, 74, 2, 52, 37, -63, -9, 22, -59, -67, -13, -5, -17, -27, -27, 0, -51, 60, 51, 39, -3, -62, 34, -57, 21, 3, -18, -51, -45, 17, 62, -18, 39, -55, 8, 45, -21, 45, 3, -1, -34, 35, 11, -81, -9, 77, -28, 45, -60, -13, 59, 7, -29, 60, -15, -9, -27, -29, -59, -5, -89, 66, 15, 32, 59, 15, 33, 13, 1, 15, 63, 55, -39, -9, -63, -30, -80, -53, 65, -7, -66, 45, 41, -37, 9, -57, -17, -89, -57, -27, -23, 76, -86, 13, -57, 33, 57, -78, 57, -42, 27, 21, -52, 20, 53, 29, -67, -43, -81, -9, 47, -13, -15, 42, 91, 16, 23, -1, 0, 24, -66, 42, 53, 26, 61, 73, -39, 9, 13, 88, -86, 49, -63, 102, -32, -11, 78, 78, -56, -20, 35, -25, -69, -54, 84, 36, 44, 17, 83, -22, 87, 45, -32, -35, -9, -33, -18, 63, 81, 45, -33, -72, -105, 36, -68, 31, -75, -69, -79, 11, 105, 24, -103, -70, 87, 45, -4, -67, -101, 7, 29, 38, -18, -6, -33, 27, 86, 5, -16, 92, -12, 93, 1, 1, -53, -44, -9, 21, 1, -47, 105, 45, 111, -42, -75, 9, 11, 35, -90, 63, 47, 23, -6, -15, -57, 12, -53, 8, -40, 27, -27, -54, -63, -105, -9, -49, -4, -53, -35, -31, 14, -39, 15, 51, 39, 85, 31, -13, 35, 8, 71, -83, -59, 81, 75, -98, -86, 21, 96, -65, -53, 78, -18, 12, 27, 58, -83, -27, -33, -65, -50, 87, 33, -78, -3, -5, 16, 65, -97, -24, -36, 17, 14, 21, 75, -24, -24, -90, -69, 119, 11, -105, -75, 1, -44, -48, -15, 66, 90, 50, -25, 17, 68, 49, -14, 117, 15, -3, 33, -45, -45, 85, -41, 83, 80, -33, -42, -63, -45, -101, 55, 62, -82, 84, 24, -69, 9, 75, 30, 59, 83, 1, 46, 66, -57, -31, -67, 24, 72, 126, 75, 93, 51, -47, 103, 20, -52, -9, 57, -75, 15, 89, -89, -92, 57, -60, -87, -51, 46, 61, 112, 31, 5, -76, -87, 27, 37, -53, -113, -74, 47, 23, -57, -15, -75, 72, 23, 53, -50, -5, 3, -75, 53, -64, -88, -7, 120, -12, 42, 87, -50, -95, -71, 49, 41, -43, -84, 15, -54, 63, -87, -129, 21, -6, 15, -33, 37, 82, -96, 12, 82, -62, -41, -14, 93, -105, -87, 63, -98, -36, -75, -12, 93, -67, 113, 5, -1, -36, -60, 57, 57, -79, 137, 121, 1, 55, -143, -117, -75, -141, 24, -14, 37, 96, -99, -34, -39, -90, -68, 52, 102, 90, -96, -132, 91, 97, 3, 57, -5, 64, -107, 85, -125, 28, 6, 117, -99, -12, -100, -49, -82, -55, 76, 124, -66, -45, -94, 74, 144, 9, 117, 24, 62, -145, -27, 63, 71, 44, -27, -57, 78, -9, 48, 3, -105, -42, -67, 50, -1, -49, -43, -139, 123, 105, -36, 123, -137, -62, 23, 104, -63, -21, 109, -71, 36, 84, -105, -60, 36, -144, -48, -69, 65, -91, -66, -3, 8, -67, -69, 45, 121, 13, -57, 45, 105, 15, 19, -65, 113, 44, 90, 27, 52, 52, -142, -139, 30, 33, 3, 117, 30, -9, 71, 71, 147, -75, 49, -17, 66, -18, 97, 10, 67, -80, -59, 37, 52, 103, -121, 71, -86, 85, 30, 9, 53, -16, 123, 129, 24, 111, 7, 22, 9, -57, -58, 50, 159, -111, 71, -82, 6, -33, 143, -133, -3, -105, -129, 57, -53, -74, -83, -23, 155, -163, 107, -46, 47, -61, 141, 30, 66, -93, 95, 65, -9, 9, -5, -125, 137, 101, 0, -21, -125, -117, 60, 121, 103, 18, -39, -39, -72, 124, 88, 99, -129, 33, -69, -40, -13, -53, -158, -81, 21, 144, -9, 31, -86, 66, -87, 33, -21, 120, -75, -35, -56, -149, -77, 54, 117, -72, -51, -115, 29, 66, 45, -38, -2, 78, -78, 3, 3, -82, 35, -81, 81, -74, -2, 99, 15, 62, -91, 150, 159, -50, 13, 91, -59, -81, -75, -5, -92, -39, -69, 61, 61, 69, 30, 27, 33, -97, -94, 54, -162, -98, 163, -48, -69, -99, -54, -119, 160, 2, -13, -75, 108, -58, 122, 78, 69, -79, 137, 125, -52, -29, -5, -171, 63, 30, 21, -57, -33, -138, 18, -30, 75, -141, -3, -104, -125, 105, 27, -69, 147, 130, 97, -32, -46, 11, -90, -174, -20, -20, 35, -37, 149, -85, -117, 54, -153, 3, 1, -26, -99, -72, -87, 12, 19, -89, -119, 67, -139, 149, -81, 84, 127, -17, 144, 60, 17, 29, -84, 39, 86, -103, 57, -165, 23, -136, 142, -26, 82, -23, 129, -147, 30, 90, -85, 119, -87, -21, 39, 75, -71, 127, -69, -3, 140, 41, -159, -42, 116, -157, 139, -158, -27, 114, -99, -30, -119, -83, 170, -163, 65, 101, -123, 90, 42, -90, -85, -175, -167, 109, -91, -160, -118, 17, 27, -126, -158, -23, 140, -31, -21, 96, -129, -147, -115, -79, 78, 69, 40, -35, 108, -57, 37, -107, -130, -43, -117, -99, -109, 53, 36, 48, -61, -73, -5, 58, 164, 8, 103, 40, 133, -119, 91, -173, -32, -101, -126, -138, 2, -34, 116, 53, -9, -132, -27, -177, -48, 9, -33, 144, -162, 69, 93, 147, -11, 19, -159, 33, 23, 23, -88, -160, -54, -18, 172, -71, -157, -6, 66, 82, 55, -135, 39, -40, 23, 3, -51, 175, 13, 108, -108, -87, -9, -111, 108, 30, 57, -105, -123, 9, 120, 92, -151, 111, 63, -93, 189, -7, 68, -151, 89, -93, 114, -59, 73, 122, 2, 139, 34, -15, -105, -168, 57, 129, 9, -127, -187, 41, -79, -156, -105, 123, -3, 133, 136, -115, -43, 187, -143, -84, 81, 123, -90, -85, -112, -87, 159, -119, -155, 169, 136] 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 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]