/* 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([3072, 96, 32*w]) 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],\ 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100],\ [8677, 8677, -21*w - 100],\ [8689, 8689, -7*w - 94],\ [8689, 8689, 7*w - 94],\ [8699, 8699, 54*w - 7],\ [8699, 8699, -54*w - 7],\ [8713, 8713, -29*w - 106],\ [8713, 8713, 29*w - 106],\ [8737, 8737, 17*w - 98],\ [8737, 8737, -17*w - 98],\ [8747, 8747, -54*w - 1],\ [8747, 8747, 54*w - 1],\ [8761, 8761, -5*w - 94],\ [8761, 8761, 5*w - 94],\ [8783, 8783, -56*w - 25],\ [8783, 8783, 56*w - 25],\ [8807, 8807, 64*w - 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 K = QQ e = 1 hecke_eigenvalues_array = [0, -1, -4, -4, -2, 2, 8, -8, 6, -6, 6, 0, 0, 14, 4, 4, 2, -2, -8, 8, -10, -10, 4, 4, 2, 2, -12, -12, -2, 2, -4, -4, -2, 2, -24, 24, 12, 12, -6, 6, 0, 0, -2, -2, -12, -12, 22, -22, -16, 16, -18, -18, -20, -20, 8, -8, 26, -26, -30, 24, -24, 6, 6, -18, -18, 12, 12, 30, -30, 24, -24, -22, -10, 10, 0, 0, 14, -14, -6, -6, -12, -12, 10, -10, 32, -32, -14, -14, -20, -20, -22, -22, 36, 36, 16, -16, -12, -12, -24, 24, 18, -18, -28, -28, -2, -2, -44, -44, 24, -24, 38, 38, -38, 38, -8, 8, 12, 12, 10, -10, 34, 34, -4, -4, -10, 10, -32, 32, 14, -14, 8, -8, -38, 38, -2, -2, -28, -28, -50, 50, 24, -24, 22, -10, 10, -32, 32, 18, -18, 8, -8, -16, 16, 42, 42, 12, 12, -2, -36, -36, -24, 24, 26, -26, -46, -46, 36, 36, -30, 30, -40, 40, 10, 10, 14, -14, 52, 52, -54, 54, -48, 48, -50, 50, -10, -10, 0, 0, -62, -62, -12, -12, -36, -36, 14, 14, 46, -46, -24, 24, -38, 38, -34, -34, 60, 60, -12, -12, -18, -18, -28, -28, -8, 8, -22, -22, -24, 24, 10, -10, -60, -60, 10, -10, 48, -48, 52, 52, 66, -66, 64, -64, 50, 50, -20, -20, -40, 40, 36, 36, -46, 46, 40, -40, 60, 60, -16, 16, -78, 78, -8, 8, 10, 10, 12, 12, 38, -38, 58, 58, 60, 60, -22, 22, -46, -66, 66, 50, -50, -38, -38, -14, -14, 12, 12, -62, 62, -10, -10, 76, 76, 80, -80, 8, -8, -70, 58, -58, 16, -16, -50, -50, 12, 12, -12, -12, -18, 18, 12, 12, -74, -74, -20, -20, -2, -2, -36, -36, 34, -34, -56, 56, 58, -58, 48, -48, 8, -8, -22, -22, -84, -84, -48, 48, -2, -2, 38, 38, 18, 18, 32, -32, -2, 2, -36, -36, -84, -84, -2, 2, 22, 22, 22, -22, 20, 20, -42, 42, 0, 0, -22, -22, 10, -10, -64, 64, -76, -76, -24, 24, -38, 38, -48, 48, -20, -20, -42, -42, -38, -38, 52, 52, 80, -80, 82, -82, -60, -60, 96, -96, 34, 34, -26, -26, -24, 24, 58, -58, 48, -48, -62, -62, -12, -12, 72, -72, 58, 58, -62, 62, -2, 2, 102, -12, -12, 46, 46, 76, 76, -42, -42, 0, 0, -40, 40, -58, 58, 16, -16, 76, 76, -10, -10, -28, -28, -88, 88, 38, 38, 60, 60, -64, 64, -62, 62, 22, 22, 10, -10, -36, -36, -70, 70, 0, 0, -14, -14, -16, 16, -34, -34, 66, -66, -56, 56, 28, 28, 82, 82, 14, -14, -60, -60, -38, 38, -100, -100, -70, 70, 14, 14, 4, 4, -20, -20, -80, 80, -30, -30, -12, -12, -66, 66, -64, 64, 54, 54, 34, 34, 60, 60, -98, 98, 20, 20, -98, 98, 88, -88, -74, -74, 36, 36, 74, -74, -30, 30, 104, -104, -38, 38, 60, 60, 72, -72, -38, -38, 14, 14, -2, 2, -72, 72, 70, -70, 56, -56, 58, 58, -36, -36, 14, 14, 36, 36, -36, -36, 94, -94, 24, -24, -102, 102, 114, 114, -120, 120, 44, 44, 52, 52, 40, -40, 44, 44, -26, 26, -90, -90, -80, 80, -60, -60, 50, -50, 0, 0, -34, -34, 116, 116, 70, 70, -18, -18, -42, -42, -28, -28, 52, 52, 102, -102, -48, 48, 14, 14, 36, 36, -54, -54, 90, -90, 24, -24, -90, -90, 124, 124, 96, -96, -118, 30, 30, -44, -44, 92, 92, 70, -70, 18, 18, -88, 88, 118, -118, 46, -46, -44, -44, -50, -50, -104, 104, 12, 12, 64, -64, -102, -102, -64, 64, 12, 12, 74, -74, -96, 96, 66, 66, -50, 50, -78, 78, 40, -40, -98, 98, -56, 56, -100, -100, -86, 86, -32, 32, 82, -82, 72, -72, 86, 86, 2, 2, 124, 124, -48, 48, 44, 44, 74, -74, 0, 0, -36, -36, -34, 34, 6, 6, 44, 44, 12, 12, -14, 14, -38, -38, 32, -32, -14, -14, 16, -16, -98, -98, 104, -104, 24, -24, 84, 84, -56, 56, 118, -118, -82, 82, -74, -74, 80, -80, -76, -76, 20, 20, 16, -16, 46, 46, -148, -148, 38, -38, 62, 62, -110, 110, -40, 40, 72, -72, 22, 22, 76, 76, 10, -10, 6, 6, -10, 10, 32, -32, 86, 86, 90, -90, -24, 24, 32, -32, 14, -14, -84, -84, 66, 66, -68, -68, 126, -126, -24, 24, -6, -6, -96, 96, 24, -24, 68, 68, -98, -98, 84, 84, -52, -52, 86, -86, 112, -112, -6, -6, 106, 106, 12, 12, -74, 74, -128, 128, 36, 36, -106, -106, -118, 118, 94, 24, -24, -70, 70, 112, -112, 4, 4, -114, 114, -104, 104, -92, -92, -62, -62, 72, -72, -26, -26, 154, -154, -30, 30, 70, -70, 54, -54, 82, 82, -60, -60, 62, 62, -56, 56, 154, 154, -44, -44, 82, 82, -88, 88, -14, 14, -36, -36, 86, -86, 50, 50, 86, -86, 96, -96, -30, 30, 36, 36, 14, -14, -152, 152, -118, -118, 132, 132, 156, 156, 46, -46, 70, 70, 96, -96, -60, -60, 0, 0, -132, -132, 54, -54, -144, 144, 110, 110, 76, 76, -24, 24, -122, 122, -36, -36, -12, -12, 110, 110, -46, 46, 40, -40, -16, 16, -8, 8, 38, 38, -144, 144, 10, 10, -124, -124, 156, 156, -50, 50, 138, -138, -112, 112, 108, 108, 158, 158, -140, -140, -82, 82, 154, 154, -36, -36, -74, 74, -54, -54, 94, 94, -122, -122, -52, -52, 70, -70, 16, -16, -2, -2, 124, 124, -140, -140, -50, -50, 68, 68, -94, 94, -104, 104, 22, 22, -70, 70, -48, 48, 56, -56, 22, -22, 100, 100, -70, 70, 2, 2, -36, -36, 120, -120, -74, 74, -32, 32, 82, -82, 10, 10, 114, -114, 144, -144, -34, -34, -132, -132, -76, -76, 96, -96, -142, 62, -62, -70, -70, 18, 18, 24, -24, 38, -38, -88, 88, -166, -166, 58, -58, -32, 32, 36, 36, 12, 12, -98, -98, -132, -132, 46, 46, 100, 100, -2, 2, 72, -72, 86, 86, -52, -52, -18, 18, 60, 60, 58, -58, -2, 2, 42, 42, 130, 130, 60, 60, 154, 154, -140, -140, -70, 70, 24, -24, -48, 48, -50, 50, 118, 118, -144, 144, -122, 122, 68, 68, 106, -106, 66, 66, -72, 72, 22, -22, 110, 110, -60, -60, -74, -74, 98, 98, -108, -108, -134, -134, 48, -48, 136, -136, -60, -60, -54, 54, -80, 80, -132, -132, -126, 126, -30, -30, -46, 46, -168, 168, -12, -12, -24, 24, 170, 170, 36, 36, -134, 134, -122, -122, -132, -132, 42, -42, -94, 94, -58, 58, 94, -94, -84, -84, 20, 20, 24, -24, 102, 102, 18, -18, 80, -80, -44, -44, 134, 134, -154, 154, 132, 132, -150, 150, -44, -44, 94, -94, -8, 8, 6, 6, 44, 44, 56, -56, -20, -20, 60, 60, 32, -32, -52, -52, -126, -126, -62, 62, 104, -104, 178, 178, -82, 82, 34, 34, -120, 120, 122, 122, -102, 102, 112, -112, -88, 88, 106, 106, 10, -10, 0, 0, -100, -100, -6, -6, -22, 22, -16, 16, -28, -28, 0, 0, -130, 130, 156, 156, 98, -98, -6, 6] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, -w + 1])] = -1 AL_eigenvalues[ZF.ideal([3, 3, w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]