/* 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([-19, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([28, 14, -2*w - 6]) primes_array = [ [4, 2, 2],\ [7, 7, -w - 3],\ [9, 3, 3],\ [11, 11, w + 5],\ [13, 13, w + 2],\ [13, 13, w - 3],\ [17, 17, w + 1],\ [17, 17, -w + 2],\ [19, 19, w],\ [19, 19, w - 1],\ [23, 23, w + 6],\ [23, 23, -w + 7],\ [25, 5, -5],\ [37, 37, -w - 7],\ [37, 37, w - 8],\ [41, 41, 2*w - 7],\ [41, 41, -2*w - 5],\ [53, 53, -w - 8],\ [53, 53, w - 9],\ [61, 61, 2*w - 5],\ [61, 61, -2*w - 3],\ [67, 67, 2*w - 13],\ [67, 67, -2*w - 11],\ [71, 71, -w - 9],\ [71, 71, w - 10],\ [73, 73, 2*w - 3],\ [73, 73, -2*w - 1],\ [83, 83, 3*w - 11],\ [83, 83, -3*w - 8],\ [101, 101, -3*w - 7],\ [101, 101, 3*w - 10],\ [113, 113, -w - 11],\ [113, 113, w - 12],\ [131, 131, 3*w - 8],\ [131, 131, -3*w - 5],\ [137, 137, -w - 12],\ [137, 137, w - 13],\ [139, 139, 4*w - 15],\ [139, 139, -4*w - 11],\ [163, 163, -w - 13],\ [163, 163, w - 14],\ [167, 167, -3*w - 1],\ [167, 167, 3*w - 4],\ [173, 173, 3*w - 2],\ [173, 173, 3*w - 1],\ [179, 179, 2*w - 17],\ [179, 179, -2*w - 15],\ [191, 191, -w - 14],\ [191, 191, w - 15],\ [227, 227, 4*w - 11],\ [227, 227, -4*w - 7],\ [241, 241, -5*w - 13],\ [241, 241, 5*w - 18],\ [271, 271, 5*w - 17],\ [271, 271, -5*w - 12],\ [283, 283, 4*w - 7],\ [283, 283, -4*w - 3],\ [293, 293, 6*w - 23],\ [293, 293, -6*w - 17],\ [307, 307, 4*w - 3],\ [307, 307, 4*w - 1],\ [317, 317, -4*w - 23],\ [317, 317, 4*w - 27],\ [331, 331, 5*w - 31],\ [331, 331, -5*w - 26],\ [349, 349, 5*w - 14],\ [349, 349, -5*w - 9],\ [379, 379, 3*w - 25],\ [379, 379, -3*w - 22],\ [389, 389, -5*w - 27],\ [389, 389, 5*w - 32],\ [401, 401, -w - 20],\ [401, 401, w - 21],\ [409, 409, -5*w - 6],\ [409, 409, 5*w - 11],\ [421, 421, 4*w - 29],\ [421, 421, -4*w - 25],\ [439, 439, 5*w - 9],\ [439, 439, -5*w - 4],\ [443, 443, -w - 21],\ [443, 443, w - 22],\ [449, 449, 5*w - 33],\ [449, 449, -5*w - 28],\ [461, 461, 5*w - 7],\ [461, 461, -5*w - 2],\ [463, 463, -7*w - 34],\ [463, 463, 7*w - 41],\ [479, 479, 5*w - 4],\ [479, 479, 5*w - 1],\ [487, 487, -w - 22],\ [487, 487, w - 23],\ [499, 499, 2*w - 25],\ [499, 499, -2*w - 23],\ [503, 503, 9*w + 28],\ [503, 503, 8*w + 23],\ [523, 523, 7*w - 24],\ [523, 523, -7*w - 17],\ [563, 563, 7*w - 23],\ [563, 563, -7*w - 16],\ [593, 593, -6*w - 7],\ [593, 593, 6*w - 13],\ [599, 599, 2*w - 27],\ [599, 599, -2*w - 25],\ [601, 601, -7*w - 15],\ [601, 601, 7*w - 22],\ [607, 607, 8*w - 29],\ [607, 607, -8*w - 21],\ [617, 617, -8*w - 39],\ [617, 617, 8*w - 47],\ [631, 631, -w - 25],\ [631, 631, w - 26],\ [641, 641, 5*w - 36],\ [641, 641, -5*w - 31],\ [653, 653, 4*w - 33],\ [653, 653, -4*w - 29],\ [677, 677, -6*w - 1],\ [677, 677, 6*w - 7],\ [683, 683, -w - 26],\ [683, 683, w - 27],\ [709, 709, -5*w - 32],\ [709, 709, 5*w - 37],\ [733, 733, -7*w - 11],\ [733, 733, 7*w - 18],\ [751, 751, -6*w - 35],\ [751, 751, 6*w - 41],\ [757, 757, -3*w - 29],\ [757, 757, 3*w - 32],\ [761, 761, 7*w - 17],\ [761, 761, -7*w - 10],\ [769, 769, 11*w + 34],\ [769, 769, 10*w + 29],\ [787, 787, 7*w - 16],\ [787, 787, -7*w - 9],\ [811, 811, -7*w - 8],\ [811, 811, 7*w - 15],\ [823, 823, 2*w - 31],\ [823, 823, -2*w - 29],\ [841, 29, -29],\ [853, 853, 7*w - 13],\ [853, 853, -7*w - 6],\ [857, 857, 9*w - 31],\ [857, 857, -9*w - 22],\ [863, 863, 7*w - 46],\ [863, 863, -7*w - 39],\ [883, 883, 3*w - 34],\ [883, 883, -3*w - 31],\ [887, 887, -7*w - 4],\ [887, 887, 7*w - 11],\ [907, 907, 6*w - 43],\ [907, 907, -6*w - 37],\ [911, 911, -w - 30],\ [911, 911, w - 31],\ [937, 937, 7*w - 6],\ [937, 937, 7*w - 1],\ [941, 941, 7*w - 2],\ [941, 941, 7*w - 5],\ [947, 947, 2*w - 33],\ [947, 947, -2*w - 31],\ [961, 31, -31],\ [977, 977, 8*w - 51],\ [977, 977, -8*w - 43],\ [991, 991, -10*w - 49],\ [991, 991, 10*w - 59],\ [997, 997, -11*w - 31],\ [997, 997, 11*w - 42],\ [1061, 1061, -4*w - 35],\ [1061, 1061, 4*w - 39],\ [1063, 1063, -8*w - 9],\ [1063, 1063, 8*w - 17],\ [1069, 1069, 11*w - 41],\ [1069, 1069, -11*w - 30],\ [1087, 1087, 3*w - 37],\ [1087, 1087, -3*w - 34],\ [1091, 1091, 13*w + 40],\ [1091, 1091, 12*w + 35],\ [1093, 1093, -9*w - 47],\ [1093, 1093, 9*w - 56],\ [1097, 1097, 9*w - 26],\ [1097, 1097, -9*w - 17],\ [1103, 1103, -w - 33],\ [1103, 1103, w - 34],\ [1151, 1151, 8*w - 13],\ [1151, 1151, -8*w - 5],\ [1171, 1171, -w - 34],\ [1171, 1171, w - 35],\ [1213, 1213, 4*w - 41],\ [1213, 1213, -4*w - 37],\ [1217, 1217, -9*w - 14],\ [1217, 1217, 9*w - 23],\ [1223, 1223, 8*w - 7],\ [1223, 1223, 8*w - 1],\ [1231, 1231, 8*w - 5],\ [1231, 1231, 8*w - 3],\ [1249, 1249, -10*w - 21],\ [1249, 1249, 10*w - 31],\ [1303, 1303, -9*w - 49],\ [1303, 1303, 9*w - 58],\ [1319, 1319, 9*w - 20],\ [1319, 1319, -9*w - 11],\ [1361, 1361, -13*w - 37],\ [1361, 1361, 13*w - 50],\ [1367, 1367, 2*w - 39],\ [1367, 1367, -2*w - 37],\ [1373, 1373, -4*w - 39],\ [1373, 1373, 4*w - 43],\ [1399, 1399, -11*w - 25],\ [1399, 1399, 11*w - 36],\ [1409, 1409, -7*w - 45],\ [1409, 1409, 7*w - 52],\ [1423, 1423, 6*w - 49],\ [1423, 1423, -6*w - 43],\ [1427, 1427, -9*w - 7],\ [1427, 1427, 9*w - 16],\ [1439, 1439, -10*w - 53],\ [1439, 1439, 10*w - 63],\ [1447, 1447, -13*w - 36],\ [1447, 1447, 13*w - 49],\ [1453, 1453, -12*w - 59],\ [1453, 1453, 12*w - 71],\ [1459, 1459, 11*w - 35],\ [1459, 1459, -11*w - 24],\ [1487, 1487, 9*w - 13],\ [1487, 1487, -9*w - 4],\ [1499, 1499, -5*w - 42],\ [1499, 1499, 5*w - 47],\ [1523, 1523, 2*w - 41],\ [1523, 1523, -2*w - 39],\ [1531, 1531, -13*w - 35],\ [1531, 1531, 13*w - 48],\ [1549, 1549, 3*w - 43],\ [1549, 1549, -3*w - 40],\ [1553, 1553, 9*w - 2],\ [1553, 1553, 9*w - 7],\ [1559, 1559, 9*w - 4],\ [1559, 1559, 9*w - 5],\ [1601, 1601, 10*w - 23],\ [1601, 1601, -10*w - 13],\ [1607, 1607, 7*w - 54],\ [1607, 1607, -7*w - 47],\ [1613, 1613, -13*w - 34],\ [1613, 1613, 13*w - 47],\ [1621, 1621, -w - 40],\ [1621, 1621, w - 41],\ [1627, 1627, 11*w - 32],\ [1627, 1627, -11*w - 21],\ [1657, 1657, 14*w - 53],\ [1657, 1657, -14*w - 39],\ [1669, 1669, -10*w - 11],\ [1669, 1669, 10*w - 21],\ [1693, 1693, -13*w - 33],\ [1693, 1693, 13*w - 46],\ [1709, 1709, -7*w - 48],\ [1709, 1709, 7*w - 55],\ [1747, 1747, -9*w - 53],\ [1747, 1747, 9*w - 62],\ [1777, 1777, 11*w - 29],\ [1777, 1777, -11*w - 18],\ [1787, 1787, -w - 42],\ [1787, 1787, w - 43],\ [1811, 1811, -12*w - 25],\ [1811, 1811, 12*w - 37],\ [1823, 1823, -11*w - 17],\ [1823, 1823, 11*w - 28],\ [1831, 1831, 11*w - 70],\ [1831, 1831, -11*w - 59],\ [1847, 1847, 13*w - 44],\ [1847, 1847, -13*w - 31],\ [1849, 43, -43],\ [1861, 1861, 10*w - 13],\ [1861, 1861, -10*w - 3],\ [1867, 1867, 11*w - 27],\ [1867, 1867, -11*w - 16],\ [1871, 1871, 5*w - 51],\ [1871, 1871, -5*w - 46],\ [1873, 1873, -w - 43],\ [1873, 1873, w - 44],\ [1889, 1889, -10*w - 1],\ [1889, 1889, 10*w - 11],\ [1901, 1901, 4*w - 49],\ [1901, 1901, -4*w - 45],\ [1931, 1931, 12*w - 35],\ [1931, 1931, -12*w - 23],\ [1949, 1949, -11*w - 14],\ [1949, 1949, 11*w - 25],\ [1979, 1979, 15*w - 56],\ [1979, 1979, -15*w - 41],\ [1987, 1987, 11*w - 24],\ [1987, 1987, -11*w - 13],\ [1993, 1993, 13*w - 42],\ [1993, 1993, -13*w - 29],\ [2003, 2003, -14*w - 69],\ [2003, 2003, 14*w - 83],\ [2011, 2011, 6*w - 55],\ [2011, 2011, -6*w - 49],\ [2017, 2017, -8*w - 53],\ [2017, 2017, 8*w - 61],\ [2027, 2027, -7*w - 51],\ [2027, 2027, 7*w - 58],\ [2039, 2039, 2*w - 47],\ [2039, 2039, -2*w - 45],\ [2063, 2063, 13*w - 41],\ [2063, 2063, -13*w - 28],\ [2069, 2069, 5*w - 53],\ [2069, 2069, -5*w - 48],\ [2083, 2083, 3*w - 49],\ [2083, 2083, -3*w - 46],\ [2089, 2089, 11*w - 21],\ [2089, 2089, -11*w - 10],\ [2131, 2131, -13*w - 27],\ [2131, 2131, 13*w - 40],\ [2137, 2137, -7*w - 52],\ [2137, 2137, 7*w - 59],\ [2141, 2141, 18*w + 55],\ [2141, 2141, 17*w + 50],\ [2143, 2143, -w - 46],\ [2143, 2143, w - 47],\ [2179, 2179, -3*w - 47],\ [2179, 2179, 3*w - 50],\ [2209, 47, -47],\ [2237, 2237, -w - 47],\ [2237, 2237, w - 48],\ [2239, 2239, -11*w - 4],\ [2239, 2239, 11*w - 15],\ [2243, 2243, -12*w - 17],\ [2243, 2243, 12*w - 29],\ [2269, 2269, 12*w - 77],\ [2269, 2269, -12*w - 65],\ [2273, 2273, 11*w - 13],\ [2273, 2273, -11*w - 2],\ [2287, 2287, -11*w - 1],\ [2287, 2287, 11*w - 12],\ [2293, 2293, 4*w - 53],\ [2293, 2293, -4*w - 49],\ [2297, 2297, -13*w - 68],\ [2297, 2297, 13*w - 81],\ [2309, 2309, 11*w - 10],\ [2309, 2309, 11*w - 1],\ [2311, 2311, -15*w - 74],\ [2311, 2311, 15*w - 89],\ [2333, 2333, -w - 48],\ [2333, 2333, w - 49],\ [2347, 2347, -9*w - 58],\ [2347, 2347, 9*w - 67],\ [2351, 2351, 15*w - 52],\ [2351, 2351, -15*w - 37],\ [2371, 2371, 17*w - 65],\ [2371, 2371, -17*w - 48],\ [2377, 2377, 3*w - 52],\ [2377, 2377, -3*w - 49],\ [2381, 2381, 5*w - 56],\ [2381, 2381, -5*w - 51],\ [2383, 2383, -13*w - 23],\ [2383, 2383, 13*w - 36],\ [2393, 2393, 19*w + 58],\ [2393, 2393, 18*w + 53],\ [2411, 2411, -12*w - 13],\ [2411, 2411, 12*w - 25],\ [2423, 2423, 2*w - 51],\ [2423, 2423, -2*w - 49],\ [2441, 2441, -13*w - 22],\ [2441, 2441, 13*w - 35],\ [2447, 2447, -13*w - 69],\ [2447, 2447, 13*w - 82],\ [2473, 2473, 9*w - 68],\ [2473, 2473, -9*w - 59],\ [2477, 2477, -14*w - 29],\ [2477, 2477, 14*w - 43],\ [2531, 2531, -w - 50],\ [2531, 2531, w - 51],\ [2551, 2551, -13*w - 20],\ [2551, 2551, 13*w - 33],\ [2557, 2557, -12*w - 67],\ [2557, 2557, 12*w - 79],\ [2593, 2593, 17*w - 63],\ [2593, 2593, -17*w - 46],\ [2609, 2609, -15*w - 34],\ [2609, 2609, 15*w - 49],\ [2617, 2617, 14*w - 41],\ [2617, 2617, -14*w - 27],\ [2633, 2633, -w - 51],\ [2633, 2633, w - 52],\ [2659, 2659, 20*w + 61],\ [2659, 2659, 19*w + 56],\ [2671, 2671, 6*w - 61],\ [2671, 2671, -6*w - 55],\ [2689, 2689, 3*w - 55],\ [2689, 2689, -3*w - 52],\ [2699, 2699, -10*w - 63],\ [2699, 2699, 10*w - 73],\ [2711, 2711, -5*w - 54],\ [2711, 2711, 5*w - 59],\ [2719, 2719, -16*w - 39],\ [2719, 2719, 16*w - 55],\ [2731, 2731, 9*w - 70],\ [2731, 2731, -9*w - 61],\ [2749, 2749, 14*w - 39],\ [2749, 2749, -14*w - 25],\ [2753, 2753, -13*w - 71],\ [2753, 2753, 13*w - 84],\ [2789, 2789, 19*w + 55],\ [2789, 2789, 21*w + 65],\ [2791, 2791, 13*w - 28],\ [2791, 2791, -13*w - 15],\ [2797, 2797, -3*w - 53],\ [2797, 2797, 3*w - 56],\ [2833, 2833, -13*w - 14],\ [2833, 2833, 13*w - 27],\ [2843, 2843, -w - 53],\ [2843, 2843, w - 54],\ [2903, 2903, 16*w - 53],\ [2903, 2903, -16*w - 37],\ [2909, 2909, 13*w - 85],\ [2909, 2909, -13*w - 72],\ [2917, 2917, -19*w - 54],\ [2917, 2917, 19*w - 73],\ [2927, 2927, 11*w - 78],\ [2927, 2927, -11*w - 67],\ [2939, 2939, 21*w + 64],\ [2939, 2939, 20*w + 59],\ [2963, 2963, -7*w - 59],\ [2963, 2963, 7*w - 66],\ [2999, 2999, 15*w - 44],\ [2999, 2999, -15*w - 29],\ [3019, 3019, 3*w - 58],\ [3019, 3019, -3*w - 55],\ [3061, 3061, -w - 55],\ [3061, 3061, w - 56],\ [3067, 3067, 13*w - 86],\ [3067, 3067, -13*w - 73],\ [3079, 3079, 16*w - 51],\ [3079, 3079, -16*w - 35],\ [3089, 3089, 7*w - 67],\ [3089, 3089, -7*w - 60],\ [3121, 3121, 13*w - 18],\ [3121, 3121, -13*w - 5],\ [3163, 3163, 13*w - 16],\ [3163, 3163, -13*w - 3],\ [3167, 3167, 19*w - 71],\ [3167, 3167, -19*w - 52],\ [3181, 3181, 13*w - 15],\ [3181, 3181, -13*w - 2],\ [3209, 3209, 15*w - 41],\ [3209, 3209, -15*w - 26],\ [3217, 3217, 7*w - 68],\ [3217, 3217, -7*w - 61],\ [3221, 3221, 11*w - 80],\ [3221, 3221, -11*w - 69],\ [3251, 3251, 13*w - 5],\ [3251, 3251, 13*w - 8],\ [3253, 3253, 13*w - 6],\ [3253, 3253, 13*w - 7],\ [3257, 3257, -8*w - 63],\ [3257, 3257, 8*w - 71],\ [3259, 3259, 10*w - 77],\ [3259, 3259, -10*w - 67],\ [3271, 3271, -9*w - 65],\ [3271, 3271, 9*w - 74],\ [3301, 3301, -5*w - 59],\ [3301, 3301, 5*w - 64],\ [3307, 3307, -17*w - 39],\ [3307, 3307, 17*w - 56],\ [3347, 3347, -7*w - 62],\ [3347, 3347, 7*w - 69],\ [3371, 3371, 11*w - 81],\ [3371, 3371, -11*w - 70],\ [3373, 3373, 14*w - 27],\ [3373, 3373, -14*w - 13],\ [3389, 3389, 13*w - 88],\ [3389, 3389, -13*w - 75],\ [3407, 3407, 16*w - 47],\ [3407, 3407, -16*w - 31],\ [3413, 3413, -4*w - 59],\ [3413, 3413, 4*w - 63],\ [3449, 3449, 14*w - 25],\ [3449, 3449, -14*w - 11],\ [3461, 3461, 15*w - 37],\ [3461, 3461, -15*w - 22],\ [3469, 3469, 12*w - 85],\ [3469, 3469, -12*w - 73],\ [3481, 59, -59],\ [3517, 3517, 14*w - 23],\ [3517, 3517, -14*w - 9],\ [3527, 3527, -19*w - 49],\ [3527, 3527, 19*w - 68],\ [3529, 3529, 8*w - 73],\ [3529, 3529, -8*w - 65],\ [3533, 3533, 18*w - 61],\ [3533, 3533, -18*w - 43],\ [3541, 3541, 23*w + 70],\ [3541, 3541, 22*w + 65],\ [3557, 3557, 19*w - 112],\ [3557, 3557, -19*w - 93],\ [3559, 3559, -16*w - 29],\ [3559, 3559, 16*w - 45],\ [3583, 3583, 17*w - 53],\ [3583, 3583, -17*w - 36],\ [3613, 3613, 7*w - 71],\ [3613, 3613, -7*w - 64],\ [3623, 3623, -14*w - 79],\ [3623, 3623, 14*w - 93],\ [3643, 3643, -19*w - 48],\ [3643, 3643, 19*w - 67],\ [3659, 3659, -21*w - 59],\ [3659, 3659, 21*w - 80],\ [3671, 3671, -17*w - 35],\ [3671, 3671, 17*w - 52],\ [3673, 3673, -14*w - 3],\ [3673, 3673, 14*w - 17],\ [3677, 3677, 11*w - 83],\ [3677, 3677, -11*w - 72],\ [3697, 3697, 9*w - 77],\ [3697, 3697, -9*w - 68],\ [3709, 3709, -14*w - 1],\ [3709, 3709, 14*w - 15],\ [3719, 3719, -13*w - 77],\ [3719, 3719, 13*w - 90],\ [3733, 3733, 3*w - 64],\ 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8329, 35*w + 106],\ [8329, 8329, 34*w + 101],\ [8353, 8353, -w - 91],\ [8353, 8353, w - 92],\ [8369, 8369, -7*w - 93],\ [8369, 8369, 7*w - 100],\ [8377, 8377, -23*w - 31],\ [8377, 8377, 23*w - 54],\ [8387, 8387, 2*w - 93],\ [8387, 8387, -2*w - 91],\ [8389, 8389, -26*w - 55],\ [8389, 8389, 26*w - 81],\ [8429, 8429, -20*w - 117],\ [8429, 8429, 20*w - 137],\ [8447, 8447, 21*w - 4],\ [8447, 8447, 21*w - 17],\ [8461, 8461, -23*w - 30],\ [8461, 8461, 23*w - 53],\ [8537, 8537, -w - 92],\ [8537, 8537, w - 93],\ [8543, 8543, -23*w - 29],\ [8543, 8543, 23*w - 52],\ [8563, 8563, -7*w - 94],\ [8563, 8563, 7*w - 101],\ [8599, 8599, 31*w - 115],\ [8599, 8599, -31*w - 84],\ [8609, 8609, -25*w - 46],\ [8609, 8609, 25*w - 71],\ [8623, 8623, 23*w - 51],\ [8623, 8623, -23*w - 28],\ [8641, 8641, -22*w - 15],\ [8641, 8641, 22*w - 37],\ [8647, 8647, -18*w - 113],\ [8647, 8647, 18*w - 131],\ [8677, 8677, 12*w - 113],\ [8677, 8677, -12*w - 101],\ [8707, 8707, 29*w - 101],\ [8707, 8707, -29*w - 72],\ [8737, 8737, -13*w - 103],\ [8737, 8737, 13*w - 116],\ [8741, 8741, 22*w - 35],\ [8741, 8741, -22*w - 13],\ [8753, 8753, -33*w - 94],\ [8753, 8753, 33*w - 127],\ [8761, 8761, 16*w - 125],\ [8761, 8761, -16*w - 109],\ [8779, 8779, -15*w - 107],\ [8779, 8779, 15*w - 122],\ [8803, 8803, 21*w - 142],\ [8803, 8803, -21*w - 121],\ [8819, 8819, 36*w + 109],\ [8819, 8819, 35*w + 104],\ [8831, 8831, -5*w - 94],\ [8831, 8831, 5*w - 99],\ [8839, 8839, -25*w - 44],\ [8839, 8839, 25*w - 69],\ [8849, 8849, -25*w - 132],\ [8849, 8849, 25*w - 157],\ [8861, 8861, 30*w - 107],\ [8861, 8861, -30*w - 77],\ [8923, 8923, -23*w - 24],\ [8923, 8923, 23*w - 47],\ [8933, 8933, -29*w - 144],\ [8933, 8933, 29*w - 173],\ [8941, 8941, -20*w - 119],\ [8941, 8941, 20*w - 139],\ [8951, 8951, -25*w - 43],\ [8951, 8951, 25*w - 68],\ [8969, 8969, 8*w - 105],\ [8969, 8969, -8*w - 97],\ [8999, 8999, 23*w - 150],\ [8999, 8999, -23*w - 127],\ [9013, 9013, -11*w - 101],\ [9013, 9013, 11*w - 112],\ [9049, 9049, 29*w - 99],\ [9049, 9049, -29*w - 70],\ [9067, 9067, 21*w - 143],\ [9067, 9067, -21*w - 122],\ [9103, 9103, -32*w - 87],\ [9103, 9103, 32*w - 119],\ [9109, 9109, -12*w - 103],\ [9109, 9109, 12*w - 115],\ [9127, 9127, -23*w - 21],\ [9127, 9127, 23*w - 44],\ [9157, 9157, -7*w - 97],\ [9157, 9157, 7*w - 104],\ [9173, 9173, -22*w - 1],\ [9173, 9173, 22*w - 23],\ [9187, 9187, 31*w - 112],\ [9187, 9187, -31*w - 81],\ [9199, 9199, -17*w - 113],\ [9199, 9199, 17*w - 130],\ [9203, 9203, 27*w - 83],\ [9203, 9203, -27*w - 56],\ [9221, 9221, 5*w - 101],\ [9221, 9221, -5*w - 96],\ [9227, 9227, 11*w - 113],\ [9227, 9227, -11*w - 102],\ [9239, 9239, -24*w - 31],\ [9239, 9239, 24*w - 55],\ [9241, 9241, 15*w - 124],\ [9241, 9241, -15*w - 109],\ [9257, 9257, 34*w - 131],\ [9257, 9257, -34*w - 97],\ [9277, 9277, -23*w - 128],\ [9277, 9277, 23*w - 151],\ [9281, 9281, 22*w - 17],\ [9281, 9281, 22*w - 5],\ [9293, 9293, -w - 96],\ [9293, 9293, w - 97],\ [9311, 9311, 10*w - 111],\ [9311, 9311, -10*w - 101],\ [9323, 9323, 37*w + 112],\ [9323, 9323, 36*w + 107],\ [9341, 9341, -27*w - 55],\ [9341, 9341, 27*w - 82],\ [9371, 9371, 23*w - 40],\ [9371, 9371, -23*w - 17],\ [9377, 9377, 8*w - 107],\ [9377, 9377, -8*w - 99],\ [9403, 9403, -13*w - 106],\ [9403, 9403, 13*w - 119],\ [9409, 97, -97],\ [9413, 9413, -26*w - 47],\ [9413, 9413, 26*w - 73],\ [9419, 9419, -5*w - 97],\ [9419, 9419, 5*w - 102],\ [9431, 9431, -25*w - 134],\ [9431, 9431, 25*w - 159],\ [9461, 9461, 20*w - 141],\ [9461, 9461, -20*w - 121],\ [9467, 9467, 28*w - 89],\ [9467, 9467, -28*w - 61],\ [9511, 9511, 32*w - 117],\ [9511, 9511, -32*w - 85],\ [9533, 9533, -23*w - 14],\ [9533, 9533, 23*w - 37],\ [9539, 9539, 35*w - 136],\ [9539, 9539, -35*w - 101],\ [9547, 9547, -29*w - 67],\ [9547, 9547, 29*w - 96],\ [9601, 9601, 21*w - 145],\ [9601, 9601, -21*w - 124],\ [9619, 9619, 5*w - 103],\ [9619, 9619, -5*w - 98],\ [9629, 9629, -13*w - 107],\ [9629, 9629, 13*w - 120],\ [9631, 9631, -23*w - 12],\ [9631, 9631, 23*w - 35],\ [9649, 9649, -26*w - 45],\ [9649, 9649, 26*w - 71],\ [9661, 9661, -11*w - 104],\ [9661, 9661, 11*w - 115],\ [9677, 9677, 23*w - 34],\ [9677, 9677, -23*w - 11],\ [9679, 9679, 25*w - 61],\ [9679, 9679, -25*w - 36],\ [9689, 9689, 17*w - 132],\ [9689, 9689, -17*w - 115],\ [9719, 9719, -24*w - 25],\ [9719, 9719, 24*w - 49],\ [9721, 9721, -23*w - 10],\ [9721, 9721, 23*w - 33],\ [9739, 9739, -10*w - 103],\ [9739, 9739, 10*w - 113],\ [9743, 9743, -27*w - 52],\ [9743, 9743, 27*w - 79],\ [9769, 9769, -7*w - 100],\ [9769, 9769, 7*w - 107],\ [9803, 9803, -23*w - 8],\ [9803, 9803, 23*w - 31],\ [9833, 9833, 33*w - 122],\ [9833, 9833, -33*w - 89],\ [9839, 9839, -23*w - 130],\ [9839, 9839, 23*w - 153],\ [9857, 9857, -13*w - 108],\ [9857, 9857, 13*w - 121],\ [9871, 9871, -21*w - 125],\ [9871, 9871, 21*w - 146],\ [9923, 9923, 2*w - 101],\ [9923, 9923, -2*w - 99],\ [9929, 9929, -30*w - 71],\ [9929, 9929, 30*w - 101],\ [9949, 9949, -15*w - 112],\ [9949, 9949, 15*w - 127],\ [9973, 9973, -23*w - 3],\ [9973, 9973, 23*w - 26]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 1, -2, 0, -4, -4, 6, 6, 2, 2, 0, 0, -10, 2, 2, 6, 6, 6, 6, 8, 8, -4, -4, 0, 0, 2, 2, -6, -6, 0, 0, 6, 6, 18, 18, 18, 18, 14, 14, -16, -16, -12, -12, -12, -12, -12, -12, 24, 24, 18, 18, -10, -10, -16, -16, -22, -22, 24, 24, 2, 2, 6, 6, 8, 8, -28, -28, -16, -16, 18, 18, -18, -18, 14, 14, -10, -10, 8, 8, -12, -12, 18, 18, 12, 12, 32, 32, -36, -36, -16, -16, -4, -4, 0, 0, 2, 2, 30, 30, -6, -6, -24, -24, 26, 26, 32, 32, 6, 6, -16, -16, -18, -18, 18, 18, -12, -12, -12, -12, -46, -46, -40, -40, -40, -40, 2, 2, -18, -18, 14, 14, -22, -22, 2, 2, -40, -40, -22, 44, 44, -18, -18, -24, -24, 20, 20, -36, -36, 44, 44, 48, 48, 2, 2, -24, -24, 24, 24, -46, -6, -6, -16, -16, 8, 8, -30, -30, -16, -16, 8, 8, 8, 8, 30, 30, -22, -22, -6, -6, 48, 48, -12, -12, 20, 20, 26, 26, -6, -6, -24, -24, -28, -28, 26, 26, 8, 8, -24, -24, -18, -18, -24, -24, -30, -30, -40, -40, 18, 18, 56, 56, -30, -30, 24, 24, -64, -64, 50, 50, 38, 38, 0, 0, -12, -12, -72, -72, 2, 2, -34, -34, 42, 42, -12, -12, 66, 66, 48, 48, -72, -72, 74, 74, -10, -10, -34, -34, 32, 32, 56, 56, 54, 54, 56, 56, 50, 50, 72, 72, 42, 42, -24, -24, -40, -40, 12, 12, -22, 8, 8, 50, 50, 48, 48, 2, 2, 18, 18, -18, -18, -30, -30, 84, 84, 30, 30, -82, -82, 14, 14, -48, -48, -40, -40, -70, -70, -72, -72, 0, 0, 24, 24, -30, -30, 32, 32, -70, -70, -10, -10, 50, 50, -72, -72, 56, 56, -88, -88, 50, -78, -78, -28, -28, 54, 54, 2, 2, 18, 18, 20, 20, -82, -82, -42, -42, -12, -12, -64, -64, -30, -30, 80, 80, -24, -24, 14, 14, -70, -70, -66, -66, -28, -28, 18, 18, 42, 42, 48, 48, -30, -30, -48, -48, -10, -10, 84, 84, 36, 36, -40, -40, 38, 38, -70, -70, -42, -42, -82, -82, 6, 6, 14, 14, 8, 8, 62, 62, 60, 60, 24, 24, -52, -52, -4, -4, -40, -40, -78, -78, 60, 60, 92, 92, 62, 62, 26, 26, 0, 0, 0, 0, 18, 18, 56, 56, -96, -96, 6, 6, 24, 24, 36, 36, -40, -40, -70, -70, -64, -64, -52, -52, -66, -66, 98, 98, -22, -22, 60, 60, -40, -40, 30, 30, 86, 86, -18, -18, -90, -90, 32, 32, 30, 30, 56, 56, -40, -40, -82, -82, 14, 14, 36, 36, -24, -24, -28, -28, 42, 42, 72, 72, -18, -18, -102, -102, 48, 48, 50, 50, -82, 80, 80, 72, 72, 74, 74, 108, 108, -4, -4, -42, -42, -76, -76, -88, -88, -58, -58, -96, -96, -10, -10, 90, 90, -120, -120, 74, 74, -18, -18, -46, -46, -16, -16, 24, 24, -46, -46, 96, 96, -10, -10, 54, 54, -12, -12, 42, 42, 72, 72, -24, -24, 72, 72, -18, -18, -66, -66, 8, 8, 56, 56, -100, -100, 12, 12, -46, -46, -78, -78, 60, 60, 44, 44, -112, -112, -10, -10, -42, -42, 108, 108, -60, -60, 72, 72, 56, 56, 74, 74, -84, -84, 62, 62, -126, -126, -52, -52, 30, 30, -18, -18, -48, -48, 90, 90, -22, -22, -64, -64, 78, 78, 114, 114, -24, -24, -58, -58, -16, -16, 114, 114, -102, -102, 126, 126, 38, 38, -82, -82, -16, -16, -36, -36, 32, 32, -112, -112, -12, -12, -28, -28, -4, -4, -22, -22, -108, -108, 104, 104, -24, -24, 50, 50, 18, 18, -132, -132, -84, -84, 66, 66, 18, 18, -60, -60, 116, 116, 104, 104, -54, -54, -34, -34, -90, -90, -72, -72, 20, 20, 116, 116, 86, 86, 36, 36, 54, 54, -24, -24, 56, 56, 110, 110, -40, -40, -114, -114, -118, -118, 102, 102, -34, -34, 114, 114, -78, -78, 80, 80, 68, 68, -64, -64, 78, 78, 98, 98, -18, -18, 102, 102, 102, 102, 18, 18, 72, 72, 24, 24, 86, 86, -24, -24, -24, -24, -28, -28, 86, 86, 68, 68, -100, -100, -48, -48, 12, 12, 24, 24, -40, -40, -6, -6, 0, 0, -130, -130, 56, 56, 60, 60, 104, 104, 38, 38, -10, -10, 110, 110, 114, 114, 50, 50, 2, 2, 132, 132, -120, -120, 128, 128, 32, 32, -58, -58, 8, 8, 6, 6, 110, 110, -66, -66, -72, -72, 20, 20, -124, -124, 6, 6, -130, -130, -24, -24, -48, -48, 32, 32, 30, 30, 104, 104, 108, 108, 38, 38, -10, -10, -112, -112, -30, -30, -96, -96, 32, 32, -108, -108, 18, 18, 96, 96, -94, 56, 56, 32, 32, 126, 126, 2, 2, 36, 36, -6, -6, 110, 110, 32, 32, -28, -28, 20, 20, 54, 54, -100, -100, 134, 134, -70, -70, -156, -156, 138, 138, 50, 50, -72, -72, 42, 42, 102, 102, 24, 24, -52, -52, 50, 50, -60, -60, 18, 18, 8, 8, -4, -4, 138, 138, -112, -112, -120, -120, -46, -46, -10, -10, 42, 42, 12, 12, 42, 42, -58, -58, 48, 48, -30, -30, -30, -30, -160, -160, 56, 56, 42, 42, -120, -120, -28, -28, 50, 50, 90, 90, 84, 84, -48, -48, 32, 32, 96, 96, 150, 150, -30, -30, -24, -24, -58, -58, -4, -4, 128, 128, 168, 168, -16, -16, 96, 96, 90, 90, -106, -106, 158, 158, -36, -36, -64, -64, -10, -10, 50, 50, -22, -22, 38, 38, 54, 54, 80, 80, -78, -78, 30, 30, 14, 14, -48, -48, -144, -144, 146, 146, -72, -72, 60, 60, -64, -64, -130, -130, 128, 128, -162, -162, 86, 86, -4, -4, -124, -124, -124, -124, -58, -58, 66, 66, 18, 18, 60, 60, 30, 30, -120, -120, 110, 110, 62, 62, 6, 6, 104, 104, -168, -168, -142, -28, -28, 126, 126, 2, 2, -90, -90, -46, -46, -108, -108, 42, 42, -46, -46, -70, -70, -6, -6, 170, 170, -24, -24, -118, -118, 26, 26, 96, 96, -88, -88, -126, -126, 104, 104, -150, -150, -106, -106, 14, 14, 146, 146, -30, -30, -82, -82, -36, -36, 56, 56, 78, 78, -36, -36, -88, -88, 30, 30, -108, -108, -76, -76, 104, 104, -102, -102, -124, -124, 38, 38, 8, 8, -142, -142, -22, -22, -82, -82, -120, -120, -42, -42, -22, -22, -4, -4, -124, -124, 54, 54, 144, 144, 56, 56, -150, -150, 132, 132, 122, 122, -30, -30, 122, 122, -108, -108, -54, -54, 168, 168, -166, -166, 158, 158, -40, -40, 68, 68, -70, -70, -124, -124, 122, 122, 108, 108, -10, -10, 128, 128, 90, 90, -90, -90, 120, 120, -48, -48, 170, 170, -186, -186, 62, 62, 138, 138, 102, 102, -192, -192, 18, 18, -48, -48, -30, -30, 114, 114, -136, -136, -94, -132, -132, -60, -60, 48, 48, -54, -54, 78, 78, -28, -28, 48, 48, -78, -78, -10, -10, 62, 62, 116, 116, 78, 78, -88, -88, 146, 146, 86, 86, 108, 108, -184, -184, 42, 42, 24, 24, 2, 2, 20, 20, -84, -84, -58, -58, 126, 126, 126, 126, -72, -72, 138, 138, -136, -136, -24, -24, 54, 54, -22, -22, -196, -196] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, 2])] = -1 AL_eigenvalues[ZF.ideal([7, 7, -w - 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]