/* 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 + 2]) 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 - 73],\ [4021, 4021, -12*w - 61],\ [4027, 4027, 9*w - 70],\ [4027, 4027, -9*w - 61],\ [4057, 4057, -24*w - 65],\ [4057, 4057, 24*w - 89],\ [4073, 4073, -39*w - 10],\ [4073, 4073, 39*w - 49],\ [4079, 4079, -5*w - 62],\ [4079, 4079, 5*w - 67],\ [4091, 4091, 36*w - 7],\ [4091, 4091, 36*w - 29],\ [4099, 4099, -15*w - 62],\ [4099, 4099, 15*w - 77],\ [4111, 4111, 40*w - 53],\ [4111, 4111, -40*w - 13],\ [4133, 4133, -23*w - 65],\ [4133, 4133, 23*w - 88],\ [4157, 4157, -w - 64],\ [4157, 4157, w - 65],\ [4159, 4159, -9*w - 62],\ [4159, 4159, 9*w - 71],\ [4177, 4177, 37*w - 2],\ [4177, 4177, 37*w - 35],\ [4211, 4211, 36*w - 19],\ [4211, 4211, 36*w - 17],\ [4229, 4229, -19*w - 64],\ [4229, 4229, 19*w - 83],\ [4241, 4241, 39*w - 46],\ [4241, 4241, -39*w - 7],\ [4261, 4261, 3*w - 67],\ [4261, 4261, -3*w - 64],\ [4273, 4273, -41*w - 14],\ [4273, 4273, 41*w - 55],\ [4289, 4289, 25*w - 92],\ [4289, 4289, -25*w - 67],\ [4339, 4339, 37*w - 29],\ [4339, 4339, 37*w - 8],\ [4391, 4391, -39*w - 4],\ [4391, 4391, 39*w - 43],\ [4397, 4397, 7*w - 71],\ [4397, 4397, -7*w - 64],\ [4421, 4421, -13*w - 64],\ [4421, 4421, 13*w - 77],\ [4423, 4423, 18*w - 83],\ [4423, 4423, -18*w - 65],\ [4447, 4447, 37*w - 17],\ [4447, 4447, 37*w - 20],\ [4463, 4463, -17*w - 65],\ [4463, 4463, 17*w - 82],\ [4481, 4481, 39*w - 41],\ [4481, 4481, -39*w - 2],\ [4489, 67, -67],\ [4507, 4507, -6*w - 65],\ [4507, 4507, 6*w - 71],\ [4523, 4523, -39*w - 1],\ [4523, 4523, 39*w - 40],\ [4547, 4547, -14*w - 65],\ [4547, 4547, 14*w - 79],\ [4549, 4549, 38*w - 31],\ [4549, 4549, 38*w - 7],\ [4567, 4567, -9*w - 65],\ [4567, 4567, 9*w - 74],\ [4603, 4603, 43*w - 59],\ [4603, 4603, -43*w - 16],\ [4637, 4637, 39*w - 2],\ [4637, 4637, 39*w - 37],\ [4651, 4651, 41*w - 49],\ [4651, 4651, -41*w - 8],\ [4657, 4657, 38*w - 25],\ [4657, 4657, 38*w - 13],\ [4663, 4663, 3*w - 70],\ [4663, 4663, -3*w - 67],\ [4679, 4679, 19*w - 86],\ [4679, 4679, -19*w - 67],\ [4703, 4703, 39*w - 35],\ [4703, 4703, 39*w - 4],\ [4723, 4723, 18*w - 85],\ [4723, 4723, -18*w - 67],\ [4729, 4729, -21*w - 68],\ [4729, 4729, 21*w - 89],\ [4733, 4733, 39*w - 34],\ [4733, 4733, 39*w - 5],\ [4759, 4759, -40*w - 1],\ [4759, 4759, 40*w - 41],\ [4783, 4783, 6*w - 73],\ [4783, 4783, -6*w - 67],\ [4787, 4787, 39*w - 7],\ [4787, 4787, 39*w - 32],\ [4793, 4793, -16*w - 67],\ [4793, 4793, 16*w - 83],\ [4801, 4801, -3*w - 68],\ [4801, 4801, 3*w - 71],\ [4813, 4813, 41*w - 46],\ [4813, 4813, -41*w - 5],\ [4861, 4861, -12*w - 67],\ [4861, 4861, 12*w - 79],\ [4871, 4871, 39*w - 11],\ [4871, 4871, 39*w - 28],\ [4889, 4889, 5*w - 73],\ [4889, 4889, -5*w - 68],\ [4931, 4931, 39*w - 16],\ [4931, 4931, 39*w - 23],\ [4937, 4937, 39*w - 17],\ [4937, 4937, 39*w - 22],\ [4943, 4943, 39*w - 19],\ [4943, 4943, 39*w - 20],\ [4957, 4957, 41*w - 43],\ [4957, 4957, -41*w - 2],\ [4967, 4967, -w - 70],\ [4967, 4967, w - 71],\ [4969, 4969, 15*w - 83],\ [4969, 4969, -15*w - 68],\ [4993, 4993, 9*w - 77],\ [4993, 4993, -9*w - 68],\ [5009, 5009, -11*w - 68],\ [5009, 5009, 11*w - 79],\ [5021, 5021, -45*w - 17],\ [5021, 5021, 45*w - 62],\ [5041, 71, -71],\ [5087, 5087, 48*w - 73],\ [5087, 5087, 23*w - 94],\ [5099, 5099, 45*w - 61],\ [5099, 5099, -45*w - 16],\ [5113, 5113, 27*w - 100],\ [5113, 5113, -27*w - 73],\ [5119, 5119, 40*w - 29],\ [5119, 5119, 40*w - 11],\ [5147, 5147, 19*w - 89],\ [5147, 5147, -19*w - 70],\ [5171, 5171, 2*w - 73],\ [5171, 5171, -2*w - 71],\ [5197, 5197, 43*w - 50],\ [5197, 5197, -43*w - 7],\ [5209, 5209, 21*w - 92],\ [5209, 5209, -21*w - 71],\ [5227, 5227, -3*w - 71],\ [5227, 5227, 3*w - 74],\ [5261, 5261, -20*w - 71],\ [5261, 5261, 20*w - 91],\ [5279, 5279, 25*w - 98],\ [5279, 5279, -48*w + 71],\ [5281, 5281, 41*w - 34],\ [5281, 5281, 41*w - 7],\ [5303, 5303, -13*w - 70],\ [5303, 5303, 13*w - 83],\ [5329, 73, -73],\ [5333, 5333, 42*w - 41],\ [5333, 5333, 42*w - 1],\ [5347, 5347, -18*w - 71],\ [5347, 5347, 18*w - 89],\ [5381, 5381, 17*w - 88],\ [5381, 5381, -17*w - 71],\ [5399, 5399, -w - 73],\ [5399, 5399, w - 74],\ [5407, 5407, 41*w - 28],\ [5407, 5407, 41*w - 13],\ [5417, 5417, -8*w - 71],\ [5417, 5417, 8*w - 79],\ [5431, 5431, -15*w - 71],\ [5431, 5431, 15*w - 86],\ [5437, 5437, -9*w - 71],\ [5437, 5437, 9*w - 80],\ [5443, 5443, 41*w - 25],\ [5443, 5443, 41*w - 16],\ [5477, 5477, 42*w - 37],\ [5477, 5477, 42*w - 5],\ [5483, 5483, -22*w - 73],\ [5483, 5483, 22*w - 95],\ [5503, 5503, -43*w - 1],\ [5503, 5503, 43*w - 44],\ [5521, 5521, 3*w - 76],\ [5521, 5521, -3*w - 73],\ [5563, 5563, -44*w - 5],\ [5563, 5563, 44*w - 49],\ [5573, 5573, 4*w - 77],\ [5573, 5573, -4*w - 73],\ [5581, 5581, 46*w - 59],\ [5581, 5581, -46*w - 13],\ [5591, 5591, -23*w - 74],\ [5591, 5591, 23*w - 97],\ [5639, 5639, -29*w - 77],\ [5639, 5639, 29*w - 106],\ [5641, 5641, -27*w - 76],\ [5641, 5641, 27*w - 103],\ [5651, 5651, -45*w - 8],\ [5651, 5651, 45*w - 53],\ [5659, 5659, 6*w - 79],\ [5659, 5659, -6*w - 73],\ [5669, 5669, 42*w - 29],\ [5669, 5669, 42*w - 13],\ [5693, 5693, -7*w - 73],\ [5693, 5693, 7*w - 80],\ [5711, 5711, -45*w - 7],\ [5711, 5711, 45*w - 52],\ [5717, 5717, 42*w - 25],\ [5717, 5717, 42*w - 17],\ [5737, 5737, 43*w - 5],\ [5737, 5737, 43*w - 38],\ [5743, 5743, 9*w - 82],\ [5743, 5743, -9*w - 73],\ [5749, 5749, 15*w - 88],\ [5749, 5749, -15*w - 73],\ [5801, 5801, 25*w - 101],\ [5801, 5801, 51*w - 77],\ [5807, 5807, -48*w - 17],\ [5807, 5807, 48*w - 65],\ [5821, 5821, -27*w - 77],\ [5821, 5821, 27*w - 104],\ [5827, 5827, 43*w - 8],\ [5827, 5827, 43*w - 35],\ [5849, 5849, -w - 76],\ [5849, 5849, w - 77],\ [5851, 5851, 44*w - 43],\ [5851, 5851, 44*w - 1],\ [5867, 5867, 17*w - 91],\ [5867, 5867, -17*w - 74],\ [5879, 5879, 45*w - 49],\ [5879, 5879, -45*w - 4],\ [5903, 5903, -51*w + 76],\ [5903, 5903, 26*w - 103],\ [5927, 5927, -11*w - 74],\ [5927, 5927, 11*w - 85],\ [5953, 5953, 43*w - 14],\ [5953, 5953, 43*w - 29],\ [5981, 5981, 45*w - 47],\ [5981, 5981, -45*w - 2],\ [6007, 6007, 43*w - 20],\ [6007, 6007, 43*w - 23],\ [6029, 6029, -45*w - 1],\ [6029, 6029, 45*w - 46],\ [6067, 6067, 44*w - 37],\ [6067, 6067, 44*w - 7],\ [6101, 6101, 28*w - 107],\ [6101, 6101, -28*w - 79],\ [6113, 6113, 23*w - 100],\ [6113, 6113, -23*w - 77],\ [6133, 6133, -3*w - 77],\ [6133, 6133, 3*w - 80],\ [6163, 6163, 49*w - 65],\ [6163, 6163, -49*w - 16],\ [6197, 6197, 29*w - 109],\ [6197, 6197, -29*w - 80],\ [6211, 6211, 44*w - 31],\ [6211, 6211, 44*w - 13],\ [6217, 6217, -9*w - 76],\ [6217, 6217, 9*w - 85],\ [6257, 6257, 13*w - 89],\ [6257, 6257, -13*w - 76],\ [6263, 6263, 48*w - 59],\ [6263, 6263, -48*w - 11],\ [6269, 6269, -20*w - 77],\ [6269, 6269, 20*w - 97],\ [6301, 6301, -46*w - 1],\ [6301, 6301, 46*w - 47],\ [6317, 6317, -w - 79],\ [6317, 6317, w - 80],\ [6343, 6343, -18*w - 77],\ [6343, 6343, 18*w - 95],\ [6353, 6353, -8*w - 77],\ [6353, 6353, 8*w - 85],\ [6361, 6361, -50*w - 17],\ [6361, 6361, 50*w - 67],\ [6367, 6367, -47*w - 5],\ [6367, 6367, 47*w - 52],\ [6373, 6373, -53*w + 79],\ [6373, 6373, 27*w - 107],\ [6379, 6379, 9*w - 86],\ [6379, 6379, -9*w - 77],\ [6397, 6397, 49*w - 62],\ [6397, 6397, -49*w - 13],\ [6421, 6421, 12*w - 89],\ [6421, 6421, -12*w - 77],\ [6449, 6449, 45*w - 11],\ [6449, 6449, 45*w - 34],\ [6451, 6451, 3*w - 82],\ [6451, 6451, -3*w - 79],\ [6473, 6473, 51*w - 70],\ [6473, 6473, -51*w - 19],\ [6491, 6491, 45*w - 32],\ [6491, 6491, 45*w - 13],\ [6529, 6529, 47*w - 49],\ [6529, 6529, -47*w - 2],\ [6551, 6551, 45*w - 28],\ [6551, 6551, 45*w - 17],\ [6553, 6553, 46*w - 5],\ [6553, 6553, 46*w - 41],\ [6569, 6569, 45*w - 26],\ [6569, 6569, 45*w - 19],\ [6577, 6577, 21*w - 100],\ [6577, 6577, -21*w - 79],\ [6581, 6581, 45*w - 22],\ [6581, 6581, 45*w - 23],\ [6607, 6607, 6*w - 85],\ [6607, 6607, -6*w - 79],\ [6653, 6653, -23*w - 80],\ [6653, 6653, 23*w - 103],\ [6659, 6659, -19*w - 79],\ [6659, 6659, 19*w - 98],\ [6673, 6673, 47*w - 46],\ [6673, 6673, 47*w - 1],\ [6679, 6679, -30*w - 83],\ [6679, 6679, 30*w - 113],\ [6691, 6691, -18*w - 79],\ [6691, 6691, 18*w - 97],\ [6709, 6709, 9*w - 88],\ [6709, 6709, -9*w - 79],\ [6733, 6733, 46*w - 35],\ [6733, 6733, 46*w - 11],\ [6737, 6737, -16*w - 79],\ [6737, 6737, 16*w - 95],\ [6761, 6761, 13*w - 92],\ [6761, 6761, -13*w - 79],\ [6763, 6763, -52*w - 19],\ [6763, 6763, 52*w - 71],\ [6803, 6803, -w - 82],\ [6803, 6803, w - 83],\ [6829, 6829, 50*w - 61],\ [6829, 6829, -50*w - 11],\ [6841, 6841, 46*w - 29],\ [6841, 6841, 46*w - 17],\ [6863, 6863, -48*w - 1],\ [6863, 6863, 48*w - 49],\ [6889, 83, -83],\ [6899, 6899, -25*w - 82],\ [6899, 6899, 25*w - 107],\ [6907, 6907, 47*w - 7],\ [6907, 6907, 47*w - 40],\ [6917, 6917, 11*w - 91],\ [6917, 6917, -11*w - 80],\ [6959, 6959, 48*w - 47],\ [6959, 6959, 48*w - 1],\ [6967, 6967, -53*w - 20],\ [6967, 6967, 53*w - 73],\ [6971, 6971, -51*w - 13],\ [6971, 6971, 51*w - 64],\ [6977, 6977, -31*w - 85],\ [6977, 6977, 31*w - 116],\ [6991, 6991, 49*w - 53],\ [6991, 6991, -49*w - 4],\ [6997, 6997, 47*w - 10],\ [6997, 6997, 47*w - 37],\ [7019, 7019, -26*w - 83],\ [7019, 7019, 26*w - 109],\ [7043, 7043, 2*w - 85],\ [7043, 7043, -2*w - 83],\ [7069, 7069, 47*w - 13],\ [7069, 7069, 47*w - 34],\ [7121, 7121, -51*w - 11],\ [7121, 7121, 51*w - 62],\ [7127, 7127, 48*w - 5],\ [7127, 7127, 48*w - 43],\ [7151, 7151, 7*w - 89],\ [7151, 7151, -7*w - 82],\ [7159, 7159, 47*w - 28],\ [7159, 7159, 47*w - 19],\ [7177, 7177, 47*w - 25],\ [7177, 7177, 47*w - 22],\ [7193, 7193, 51*w - 61],\ [7193, 7193, -51*w - 10],\ [7211, 7211, 23*w - 106],\ [7211, 7211, -23*w - 83],\ [7219, 7219, 9*w - 91],\ [7219, 7219, -9*w - 82],\ [7229, 7229, 5*w - 88],\ [7229, 7229, -5*w - 83],\ [7237, 7237, -53*w - 17],\ [7237, 7237, 53*w - 70],\ [7253, 7253, 28*w - 113],\ [7253, 7253, 57*w - 86],\ [7283, 7283, -13*w - 82],\ [7283, 7283, 13*w - 95],\ [7297, 7297, 49*w - 2],\ [7297, 7297, 49*w - 47],\ [7307, 7307, -w - 85],\ [7307, 7307, w - 86],\ [7309, 7309, -21*w - 83],\ [7309, 7309, 21*w - 104],\ [7331, 7331, 51*w - 59],\ [7331, 7331, -51*w - 8],\ [7333, 7333, 27*w - 112],\ [7333, 7333, -27*w - 85],\ [7349, 7349, 20*w - 103],\ [7349, 7349, -20*w - 83],\ [7393, 7393, -9*w - 83],\ [7393, 7393, 9*w - 92],\ [7411, 7411, 18*w - 101],\ [7411, 7411, -18*w - 83],\ [7433, 7433, 17*w - 100],\ [7433, 7433, -17*w - 83],\ [7459, 7459, 15*w - 98],\ [7459, 7459, -15*w - 83],\ [7487, 7487, 48*w - 25],\ [7487, 7487, 48*w - 23],\ [7489, 7489, -53*w - 14],\ [7489, 7489, 53*w - 67],\ [7517, 7517, 4*w - 89],\ [7517, 7517, -4*w - 85],\ [7523, 7523, 51*w - 56],\ [7523, 7523, -51*w - 5],\ [7537, 7537, -24*w - 85],\ [7537, 7537, 24*w - 109],\ [7541, 7541, 54*w - 71],\ [7541, 7541, -54*w - 17],\ [7549, 7549, 50*w - 49],\ [7549, 7549, 50*w - 1],\ [7583, 7583, -51*w - 4],\ [7583, 7583, 51*w - 55],\ [7589, 7589, 31*w - 119],\ [7589, 7589, -31*w - 88],\ [7591, 7591, -33*w - 89],\ [7591, 7591, 33*w - 122],\ [7621, 7621, 49*w - 38],\ [7621, 7621, 49*w - 11],\ [7643, 7643, 22*w - 107],\ [7643, 7643, -22*w - 85],\ [7669, 7669, 55*w - 74],\ [7669, 7669, -55*w - 19],\ [7673, 7673, 7*w - 92],\ [7673, 7673, -7*w - 85],\ [7687, 7687, 21*w - 106],\ [7687, 7687, -21*w - 85],\ [7699, 7699, -52*w - 7],\ [7699, 7699, 52*w - 59],\ [7723, 7723, 53*w - 64],\ [7723, 7723, -53*w - 11],\ [7757, 7757, -19*w - 85],\ [7757, 7757, 19*w - 104],\ [7817, 7817, -16*w - 85],\ [7817, 7817, 16*w - 101],\ [7823, 7823, 13*w - 98],\ [7823, 7823, -13*w - 85],\ [7829, 7829, -w - 88],\ [7829, 7829, w - 89],\ [7853, 7853, 51*w - 50],\ [7853, 7853, 51*w - 1],\ [7877, 7877, -54*w - 13],\ [7877, 7877, 54*w - 67],\ [7879, 7879, -21*w - 86],\ [7879, 7879, 21*w - 107],\ [7901, 7901, 51*w - 2],\ [7901, 7901, 51*w - 49],\ [7907, 7907, 34*w - 125],\ [7907, 7907, -34*w - 91],\ [7921, 89, -89],\ [7927, 7927, 9*w - 95],\ [7927, 7927, -9*w - 86],\ [7933, 7933, 27*w - 115],\ [7933, 7933, -27*w - 88],\ [8009, 8009, -57*w - 22],\ [8009, 8009, 57*w - 79],\ [8011, 8011, -15*w - 86],\ [8011, 8011, 15*w - 101],\ [8017, 8017, 33*w - 124],\ [8017, 8017, -33*w - 91],\ [8059, 8059, -52*w - 1],\ [8059, 8059, 52*w - 53],\ [8069, 8069, 25*w - 113],\ [8069, 8069, -25*w - 88],\ [8087, 8087, 2*w - 91],\ [8087, 8087, -2*w - 89],\ [8089, 8089, 50*w - 19],\ [8089, 8089, 50*w - 31],\ [8111, 8111, 51*w - 44],\ [8111, 8111, 51*w - 7],\ [8147, 8147, 51*w - 8],\ [8147, 8147, 51*w - 43],\ [8161, 8161, -3*w - 89],\ [8161, 8161, 3*w - 92],\ [8167, 8167, 56*w - 73],\ [8167, 8167, -56*w - 17],\ [8191, 8191, -55*w - 13],\ [8191, 8191, 55*w - 68],\ [8219, 8219, 31*w - 122],\ [8219, 8219, -60*w + 89],\ [8233, 8233, 33*w - 125],\ [8233, 8233, -33*w - 92],\ [8243, 8243, 51*w - 40],\ [8243, 8243, 51*w - 11],\ [8269, 8269, -21*w - 88],\ [8269, 8269, 21*w - 109],\ [8291, 8291, -5*w - 89],\ [8291, 8291, 5*w - 94],\ [8293, 8293, 9*w - 97],\ [8293, 8293, -9*w - 88],\ [8297, 8297, 51*w - 38],\ [8297, 8297, 51*w - 13],\ [8311, 8311, 30*w - 121],\ [8311, 8311, 61*w - 92],\ [8317, 8317, 53*w - 55],\ [8317, 8317, -53*w - 2],\ [8329, 8329, -24*w - 89],\ [8329, 8329, 24*w - 113],\ [8363, 8363, 51*w - 35],\ [8363, 8363, 51*w - 16],\ [8369, 8369, -w - 91],\ [8369, 8369, w - 92],\ [8389, 8389, 15*w - 103],\ [8389, 8389, -15*w - 88],\ [8423, 8423, 51*w - 31],\ [8423, 8423, 51*w - 20],\ [8447, 8447, 51*w - 28],\ [8447, 8447, 51*w - 23],\ [8467, 8467, -21*w - 89],\ [8467, 8467, 21*w - 110],\ [8501, 8501, 20*w - 109],\ [8501, 8501, -20*w - 89],\ [8527, 8527, 3*w - 94],\ [8527, 8527, -3*w - 91],\ [8537, 8537, 11*w - 100],\ [8537, 8537, -11*w - 89],\ [8563, 8563, 52*w - 41],\ [8563, 8563, 52*w - 11],\ [8581, 8581, -15*w - 89],\ [8581, 8581, 15*w - 104],\ [8597, 8597, -4*w - 91],\ [8597, 8597, 4*w - 95],\ [8609, 8609, 29*w - 121],\ [8609, 8609, -29*w - 92],\ [8623, 8623, 53*w - 4],\ [8623, 8623, 53*w - 49],\ [8629, 8629, 58*w - 77],\ [8629, 8629, -58*w - 19],\ [8641, 8641, -55*w - 7],\ [8641, 8641, 55*w - 62],\ [8681, 8681, 25*w - 116],\ [8681, 8681, -25*w - 91],\ [8693, 8693, -54*w - 1],\ [8693, 8693, 54*w - 55],\ [8707, 8707, 52*w - 17],\ [8707, 8707, 52*w - 35],\ [8713, 8713, -3*w - 92],\ [8713, 8713, 3*w - 95],\ [8719, 8719, 6*w - 97],\ [8719, 8719, -6*w - 91],\ [8737, 8737, -24*w - 91],\ [8737, 8737, 24*w - 115],\ [8753, 8753, 57*w - 71],\ [8753, 8753, -57*w - 14],\ [8761, 8761, 27*w - 119],\ [8761, 8761, -27*w - 92],\ [8779, 8779, 52*w - 23],\ [8779, 8779, 52*w - 29],\ [8831, 8831, -22*w - 91],\ [8831, 8831, 22*w - 113],\ [8837, 8837, -57*w - 13],\ [8837, 8837, 57*w - 70],\ [8839, 8839, -55*w - 4],\ [8839, 8839, 55*w - 59],\ [8849, 8849, -5*w - 92],\ [8849, 8849, 5*w - 97],\ [8863, 8863, -59*w - 20],\ [8863, 8863, 59*w - 79],\ [8867, 8867, 31*w - 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 K = QQ e = 1 hecke_eigenvalues_array = [-1, 0, -2, -5, 3, -3, 0, -3, 1, -9, -3, -4, -7, 5, 9, 3, -2, -11, -8, 1, 9, 18, -1, -19, 9, 3, 6, -3, -5, 4, -8, 3, 12, 11, -4, 5, -10, 18, -15, -15, -9, 5, -19, 0, 15, 13, -11, 1, -20, 21, -9, -15, 3, -30, -21, 9, -12, -30, 6, -1, 23, 19, 4, 15, 3, 7, -17, 22, -29, -36, 21, 2, -28, 17, -14, -17, 6, -3, -9, -24, -11, -11, 35, -28, -24, 9, 21, 27, 39, -9, -33, -39, -30, -6, -28, -28, 17, -1, 12, -21, 33, -21, 43, -23, -9, 36, -5, -26, 32, 41, 3, 33, 15, 21, 9, -33, -15, 21, 2, -19, 27, -3, -33, 21, -36, 48, -8, 37, 23, 5, 25, -11, 33, -33, 39, -3, 23, -16, 46, 34, -39, -21, -5, 4, -45, 21, 52, 52, -27, 48, 28, -5, -24, -9, -23, 49, -47, 1, 42, -42, -55, 36, 12, -31, -31, 2, 11, 27, 9, -48, 9, -19, -16, -21, 21, 32, -16, 10, -17, -12, 57, 1, 46, -54, 39, 38, 2, -7, -19, -1, -25, -12, -60, 45, -21, 31, -2, -24, 48, 29, -37, 5, -31, 33, -45, -3, 45, -11, -8, -47, -11, -42, 63, 49, -41, 49, -32, -15, -21, -34, 26, 23, 3, 15, 26, -1, -18, 21, 45, 63, 43, 13, -31, 50, -37, -25, -45, -54, 20, -49, -9, 36, 21, -45, -65, 43, -32, 49, -24, -57, -21, 69, 10, -17, 9, -30, -29, -65, -33, -15, -41, 52, -9, 0, 37, 2, 74, 37, 52, -9, -63, -59, 22, -13, -67, -17, -5, -27, -27, -51, 0, 51, 60, -3, 39, 34, -62, 21, -57, -18, 3, -45, -51, 62, 17, 39, -18, 8, -55, -21, 45, 3, 45, -34, -1, 11, 35, -9, -81, -28, 77, -60, 45, 59, -13, -29, 7, -15, 60, -27, -9, -59, -29, -89, -5, 15, 66, 59, 32, 33, 15, 1, 13, 63, 15, 55, -9, -39, -30, -63, -53, -80, -7, 65, 45, -66, -37, 41, -57, 9, -89, -17, -27, -57, 76, -23, 13, -86, 33, -57, -78, 57, -42, 57, 21, 27, 20, -52, 29, 53, -43, -67, -9, -81, -13, 47, 42, -15, 16, 91, -1, 23, 24, 0, 42, -66, 26, 53, 73, 61, 9, -39, 88, 13, 49, -86, 102, -63, -11, -32, 78, 78, -20, -56, -25, 35, -54, -69, 36, 84, 17, 44, -22, 83, 45, 87, -35, -32, -33, -9, 63, -18, 45, 81, -72, -33, 36, -105, 31, -68, -69, -75, 11, -79, 24, 105, -70, -103, 45, 87, -67, -4, 7, -101, 38, 29, -6, -18, 27, -33, 5, 86, 92, -16, 93, -12, 1, 1, -44, -53, 21, -9, -47, 1, 45, 105, -42, 111, 9, -75, 35, 11, 63, -90, 23, 47, -15, -6, 12, -57, -53, -40, 8, -27, 27, -63, -54, -9, -105, -4, -49, -35, -53, 14, -31, 15, -39, 39, 51, 31, 85, 35, -13, 71, 8, -59, -83, 75, 81, -86, -98, 96, 21, -53, -65, -18, 78, 27, 12, -83, 58, -33, -27, -50, -65, 33, 87, -3, -78, 16, -5, -97, 65, -36, -24, 14, 17, 75, 21, -24, -24, -69, -90, 11, 119, -75, -105, -44, 1, -15, -48, 90, 66, -25, 50, 68, 17, -14, 49, 15, 117, 33, -3, -45, -45, -41, 85, 80, 83, -42, -33, -45, -63, 55, -101, -82, 62, 24, 84, 9, -69, 30, 75, 83, 59, 46, 1, -57, 66, -67, -31, 72, 24, 75, 126, 51, 93, 103, -47, -52, 20, 57, -9, 15, -75, 89, -92, -89, -60, 57, -51, -87, 61, 46, 31, 112, -76, 5, 27, -87, -53, 37, -74, -113, 23, 47, -15, -57, 72, -75, 53, 23, -5, -50, -75, 3, -64, 53, -7, -88, -12, 120, 87, 42, -95, -50, 49, -71, -43, 41, 15, -84, 63, -54, -129, -87, -6, 21, -33, 15, 82, 37, 12, -96, -62, 82, -14, -41, -105, 93, 63, -87, -98, -75, -36, 93, -12, 113, -67, -1, 5, -60, -36, 57, 57, 137, -79, 1, 121, -143, 55, -75, -117, 24, -141, 37, -14, -99, 96, -34, -90, -39, 52, -68, 90, 102, -132, -96, 97, 91, 57, 3, 64, -5, 85, -107, 28, -125, 117, 6, -12, -99, -49, -100, -55, -82, 124, 76, -45, -66, 74, -94, 9, 144, 24, 117, -145, 62, 63, -27, 44, 71, -57, -27, -9, 78, 3, 48, -42, -105, 50, -67, -49, -1, -139, -43, 105, 123, 123, -36, -62, -137, 104, 23, -21, -63, -71, 109, 84, 36, -60, -105, -144, 36, -69, -48, -91, 65, -3, -66, -67, 8, 45, -69, 13, 121, 45, -57, 15, 105, -65, 19, 44, 113, 27, 90, 52, 52, -139, -142, 33, 30, 117, 3, -9, 30, 71, 71, -75, 147, -17, 49, -18, 66, 10, 97, -80, 67, 37, -59, 103, 52, 71, -121, 85, -86, 9, 30, -16, 53, 129, 123, 111, 24, 22, 7, -57, 9, 50, -58, -111, 159, -82, 71, -33, 6, -133, 143, -105, -3, 57, -129, -74, -53, -23, -83, -163, 155, -46, 107, -61, 47, 30, 141, -93, 66, 65, 95, 9, -9, -125, -5, 101, 137, -21, 0, -125, 60, -117, 103, 121, -39, 18, -72, -39, 88, 124, -129, 99, -69, 33, -13, -40, -158, -53, 21, -81, -9, 144, -86, 31, -87, 66, -21, 33, -75, 120, -56, -35, -77, -149, 117, 54, -51, -72, 29, -115, 45, 66, -2, -38, -78, 78, 3, 3, 35, -82, 81, -81, -2, -74, 15, 99, -91, 62, 159, 150, 13, -50, -59, 91, -75, -81, -92, -5, -69, -39, 61, 61, 30, 69, 33, 27, -94, -97, -162, 54, 163, -98, -69, -48, -54, -99, 160, -119, -13, 2, 108, -75, 122, -58, 69, 78, 137, -79, -52, 125, -5, -29, 63, -171, 21, 30, -33, -57, 18, -138, 75, -30, -3, -141, -125, -104, 27, 105, 147, -69, 130, -32, 97, 11, -46, -174, -90, -20, -20, -37, 35, -85, 149, 54, -117, 3, -153, -26, 1, -72, -99, 12, -87, -89, 19, 67, -119, 149, -139, 84, -81, -17, 127, 60, 144, 29, 17, 39, -84, -103, 86, -165, 57, -136, 23, -26, 142, -23, 82, -147, 129, 90, 30, 119, -85, -21, -87, 75, 39, 127, -71, -3, -69, 41, 140, -42, -159, -157, 116, -158, 139, 114, -27, -30, -99, -83, -119, -163, 170, 101, 65, 90, -123, -90, 42, -175, -85, 109, -167, -160, -91, 17, -118, -126, 27, -23, -158, -31, 140, 96, -21, -147, -129, -79, -115, 69, 78, -35, 40, -57, 108, -107, 37, -43, -130, -99, -117, 53, -109, 48, 36, -73, -61, 58, -5, 8, 164, 40, 103, -119, 133, -173, 91, -101, -32, -138, -126, -34, 2, 53, 116, -132, -9, -177, -27, 9, -48, 144, -33, 69, -162, 147, 93, 19, -11, 33, -159, 23, 23, -160, -88, -18, -54, -71, 172, -157, 66, -6, 55, 82, 39, -135, 23, -40, -51, 3, 13, 175, -108, 108, -9, -87, 108, -111, 57, 30, -123, -105, 120, 9, -151, 92, 63, 111, 189, -93, 68, -7, 89, -151, 114, -93, 73, -59, 2, 122, 34, 139, -105, -15, 57, -168, 9, 129, -187, -127, -79, 41, -105, -156, -3, 123, 136, 133, -43, -115, -143, 187, 81, -84, -90, 123, -112, -85, 159, -87, -155, -119, 136, 169] 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])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]