/* 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([-16, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([1, 1, 1]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [5, 5, w + 2],\ [7, 7, w + 1],\ [7, 7, w + 5],\ [9, 3, 3],\ [13, 13, w + 6],\ [29, 29, -2*w + 7],\ [29, 29, 2*w + 5],\ [37, 37, w + 9],\ [37, 37, w + 27],\ [47, 47, w + 10],\ [47, 47, w + 36],\ [61, 61, 2*w - 3],\ [61, 61, -2*w - 1],\ [67, 67, w + 23],\ [67, 67, w + 43],\ [73, 73, w + 24],\ [73, 73, w + 48],\ [79, 79, 2*w - 13],\ [79, 79, -2*w - 11],\ [83, 83, w + 13],\ [83, 83, w + 69],\ [97, 97, w + 14],\ [97, 97, w + 82],\ [101, 101, 4*w - 21],\ [101, 101, 6*w - 25],\ [121, 11, -11],\ [131, 131, 2*w - 15],\ [131, 131, -2*w - 13],\ [137, 137, w + 52],\ [137, 137, w + 84],\ [139, 139, -4*w - 9],\ [139, 139, 4*w - 13],\ [163, 163, w + 18],\ [163, 163, w + 144],\ [167, 167, w + 68],\ [167, 167, w + 98],\ [179, 179, 4*w - 11],\ [179, 179, -4*w - 7],\ [181, 181, 4*w + 19],\ [181, 181, 10*w + 33],\ [191, 191, 2*w - 17],\ [191, 191, -2*w - 15],\ [193, 193, w + 39],\ [193, 193, w + 153],\ [197, 197, w + 79],\ [197, 197, w + 117],\ [199, 199, 6*w - 31],\ [199, 199, 8*w - 33],\ [211, 211, -4*w - 5],\ [211, 211, 4*w - 9],\ [223, 223, w + 21],\ [223, 223, w + 201],\ [227, 227, w + 67],\ [227, 227, w + 159],\ [251, 251, -4*w - 1],\ [251, 251, 4*w - 5],\ [269, 269, 4*w - 25],\ [269, 269, -4*w - 21],\ [289, 17, -17],\ [293, 293, w + 123],\ [293, 293, w + 169],\ [307, 307, w + 133],\ [307, 307, w + 173],\ [311, 311, 8*w - 31],\ [311, 311, 8*w + 23],\ [317, 317, w + 25],\ [317, 317, w + 291],\ [353, 353, w + 99],\ [353, 353, w + 253],\ [361, 19, -19],\ [383, 383, w + 55],\ [383, 383, w + 327],\ [389, 389, 6*w - 17],\ [389, 389, -6*w - 11],\ [397, 397, w + 56],\ [397, 397, w + 340],\ [419, 419, 2*w - 23],\ [419, 419, -2*w - 21],\ [439, 439, 6*w + 29],\ [439, 439, 16*w + 53],\ [457, 457, w + 30],\ [457, 457, w + 426],\ [463, 463, w + 192],\ [463, 463, w + 270],\ [487, 487, w + 218],\ [487, 487, w + 268],\ [491, 491, 10*w - 51],\ [491, 491, 12*w - 49],\ [521, 521, 6*w - 11],\ [521, 521, -6*w - 5],\ [529, 23, -23],\ [557, 557, w + 197],\ [557, 557, w + 359],\ [569, 569, -6*w - 1],\ [569, 569, 6*w - 7],\ [571, 571, 6*w - 37],\ [571, 571, -6*w - 31],\ [577, 577, w + 107],\ [577, 577, w + 469],\ [587, 587, w + 34],\ [587, 587, w + 552],\ [593, 593, w + 185],\ [593, 593, w + 407],\ [599, 599, -8*w - 17],\ [599, 599, 8*w - 25],\ [601, 601, -16*w + 77],\ [601, 601, 10*w - 37],\ [613, 613, w + 273],\ [613, 613, w + 339],\ [617, 617, w + 131],\ [617, 617, w + 485],\ [641, 641, 18*w - 77],\ [641, 641, 18*w + 59],\ [643, 643, w + 143],\ [643, 643, w + 499],\ [659, 659, 12*w - 47],\ [659, 659, 12*w + 35],\ [683, 683, w + 188],\ [683, 683, w + 494],\ [701, 701, 4*w - 33],\ [701, 701, -4*w - 29],\ [719, 719, 2*w - 29],\ [719, 719, -2*w - 27],\ [733, 733, w + 38],\ [733, 733, w + 694],\ [743, 743, w + 288],\ [743, 743, w + 454],\ [751, 751, 8*w - 21],\ [751, 751, -8*w - 13],\ [773, 773, w + 349],\ [773, 773, w + 423],\ [787, 787, w + 148],\ [787, 787, w + 638],\ [809, 809, -8*w - 39],\ [809, 809, 8*w - 47],\ [827, 827, w + 361],\ [827, 827, w + 465],\ [829, 829, -4*w - 31],\ [829, 829, 4*w - 35],\ [853, 853, w + 41],\ [853, 853, w + 811],\ [859, 859, -6*w - 35],\ [859, 859, 6*w - 41],\ [863, 863, w + 155],\ [863, 863, w + 707],\ [877, 877, w + 132],\ [877, 877, w + 744],\ [881, 881, 14*w - 55],\ [881, 881, 14*w + 41],\ [911, 911, 16*w + 49],\ [911, 911, 16*w - 65],\ [919, 919, 8*w - 15],\ [919, 919, -8*w - 7],\ [947, 947, w + 257],\ [947, 947, w + 689],\ [961, 31, -31],\ [967, 967, w + 448],\ [967, 967, w + 518],\ [971, 971, 12*w - 43],\ [971, 971, -12*w - 31],\ [977, 977, w + 88],\ [977, 977, w + 888],\ [983, 983, w + 357],\ [983, 983, w + 625],\ [991, 991, -8*w - 3],\ [991, 991, 8*w - 11],\ [1031, 1031, 8*w - 7],\ [1031, 1031, 8*w - 1],\ [1033, 1033, w + 287],\ [1033, 1033, w + 745],\ [1039, 1039, 8*w - 5],\ [1039, 1039, 8*w - 3],\ [1049, 1049, 10*w - 29],\ [1049, 1049, -10*w - 19],\ [1069, 1069, 14*w - 53],\ [1069, 1069, 14*w + 39],\ [1087, 1087, w + 147],\ [1087, 1087, w + 939],\ [1091, 1091, 2*w - 35],\ [1091, 1091, -2*w - 33],\ [1097, 1097, w + 504],\ [1097, 1097, w + 592],\ [1103, 1103, w + 351],\ [1103, 1103, w + 751],\ [1109, 1109, -4*w - 35],\ [1109, 1109, 4*w - 39],\ [1123, 1123, w + 459],\ [1123, 1123, w + 663],\ [1163, 1163, w + 180],\ [1163, 1163, w + 982],\ [1171, 1171, 14*w - 73],\ [1171, 1171, 20*w - 83],\ [1217, 1217, w + 49],\ [1217, 1217, w + 1167],\ [1231, 1231, 2*w - 37],\ [1231, 1231, -2*w - 35],\ [1237, 1237, w + 474],\ [1237, 1237, w + 762],\ [1249, 1249, 14*w - 51],\ [1249, 1249, 14*w + 37],\ [1291, 1291, -10*w - 49],\ [1291, 1291, 10*w - 59],\ [1301, 1301, 10*w - 23],\ [1301, 1301, -10*w - 13],\ [1307, 1307, w + 302],\ [1307, 1307, w + 1004],\ [1361, 1361, -8*w - 45],\ [1361, 1361, 8*w - 53],\ [1367, 1367, w + 525],\ [1367, 1367, w + 841],\ [1373, 1373, w + 422],\ [1373, 1373, w + 950],\ [1381, 1381, 26*w - 111],\ [1381, 1381, 26*w + 85],\ [1423, 1423, w + 53],\ [1423, 1423, w + 1369],\ [1429, 1429, 10*w - 19],\ [1429, 1429, -10*w - 9],\ [1439, 1439, 24*w + 77],\ [1439, 1439, 24*w - 101],\ [1459, 1459, 20*w + 61],\ [1459, 1459, 20*w - 81],\ [1481, 1481, -10*w - 7],\ [1481, 1481, 10*w - 17],\ [1487, 1487, w + 172],\ [1487, 1487, w + 1314],\ [1493, 1493, w + 204],\ [1493, 1493, w + 1288],\ [1499, 1499, 12*w - 35],\ [1499, 1499, -12*w - 23],\ [1511, 1511, 10*w - 61],\ [1511, 1511, -10*w - 51],\ [1523, 1523, w + 526],\ [1523, 1523, w + 996],\ [1531, 1531, 6*w - 49],\ [1531, 1531, -6*w - 43],\ [1553, 1553, w + 352],\ [1553, 1553, w + 1200],\ [1559, 1559, -26*w + 125],\ [1559, 1559, 16*w - 59],\ [1567, 1567, w + 301],\ [1567, 1567, w + 1265],\ [1597, 1597, w + 211],\ [1597, 1597, w + 1385],\ [1607, 1607, w + 758],\ [1607, 1607, w + 848],\ [1609, 1609, 10*w - 9],\ [1609, 1609, 10*w - 1],\ [1621, 1621, 10*w - 3],\ [1621, 1621, 10*w - 7],\ [1627, 1627, w + 337],\ [1627, 1627, w + 1289],\ [1657, 1657, w + 774],\ [1657, 1657, w + 882],\ [1681, 41, -41],\ [1697, 1697, w + 585],\ [1697, 1697, w + 1111],\ [1699, 1699, 2*w - 43],\ [1699, 1699, -2*w - 41],\ [1723, 1723, w + 458],\ [1723, 1723, w + 1264],\ [1741, 1741, -14*w - 31],\ [1741, 1741, 14*w - 45],\ [1747, 1747, w + 508],\ [1747, 1747, w + 1238],\ [1753, 1753, w + 414],\ [1753, 1753, w + 1338],\ [1759, 1759, 16*w - 57],\ [1759, 1759, -16*w - 41],\ [1783, 1783, w + 119],\ [1783, 1783, w + 1663],\ [1787, 1787, w + 418],\ [1787, 1787, w + 1368],\ [1811, 1811, -12*w - 17],\ [1811, 1811, 12*w - 29],\ [1849, 43, -43],\ [1867, 1867, w + 855],\ [1867, 1867, w + 1011],\ [1871, 1871, 2*w - 45],\ [1871, 1871, -2*w - 43],\ [1877, 1877, w + 362],\ [1877, 1877, w + 1514],\ [1889, 1889, -14*w - 29],\ [1889, 1889, 14*w - 43],\ [1901, 1901, -28*w + 135],\ [1901, 1901, 18*w - 67],\ [1913, 1913, w + 898],\ [1913, 1913, w + 1014],\ [1949, 1949, 4*w - 49],\ [1949, 1949, -4*w - 45],\ [1951, 1951, -16*w - 39],\ [1951, 1951, 16*w - 55],\ [1979, 1979, -12*w - 13],\ [1979, 1979, 12*w - 25],\ [1987, 1987, w + 943],\ [1987, 1987, w + 1043],\ [1997, 1997, w + 236],\ [1997, 1997, w + 1760],\ [1999, 1999, 32*w - 137],\ [1999, 1999, 32*w + 105],\ [2011, 2011, 20*w - 77],\ [2011, 2011, 20*w + 57],\ [2017, 2017, w + 854],\ [2017, 2017, w + 1162],\ [2029, 2029, 14*w - 41],\ [2029, 2029, -14*w - 27],\ [2081, 2081, 30*w + 97],\ [2081, 2081, 30*w - 127],\ [2087, 2087, w + 904],\ [2087, 2087, w + 1182],\ [2089, 2089, 22*w - 87],\ [2089, 2089, 22*w + 65],\ [2113, 2113, w + 331],\ [2113, 2113, w + 1781],\ [2129, 2129, -18*w - 47],\ [2129, 2129, 18*w - 65],\ [2131, 2131, 28*w - 117],\ [2131, 2131, 18*w - 95],\ [2137, 2137, w + 65],\ [2137, 2137, w + 2071],\ [2141, 2141, -4*w - 47],\ [2141, 2141, 4*w - 51],\ [2143, 2143, w + 843],\ [2143, 2143, w + 1299],\ [2153, 2153, w + 564],\ [2153, 2153, w + 1588],\ [2161, 2161, 14*w - 39],\ [2161, 2161, -14*w - 25],\ [2203, 2203, w + 66],\ [2203, 2203, w + 2136],\ [2239, 2239, 2*w - 49],\ [2239, 2239, -2*w - 47],\ [2243, 2243, w + 792],\ [2243, 2243, w + 1450],\ [2267, 2267, w + 598],\ [2267, 2267, w + 1668],\ [2273, 2273, w + 780],\ [2273, 2273, w + 1492],\ [2293, 2293, w + 135],\ [2293, 2293, w + 2157],\ [2311, 2311, 16*w - 51],\ [2311, 2311, -16*w - 35],\ [2333, 2333, w + 686],\ [2333, 2333, w + 1646],\ [2339, 2339, 12*w - 7],\ [2339, 2339, 12*w - 5],\ [2341, 2341, 4*w - 53],\ [2341, 2341, -4*w - 49],\ [2347, 2347, w + 966],\ [2347, 2347, w + 1380],\ [2377, 2377, w + 668],\ [2377, 2377, w + 1708],\ [2389, 2389, 22*w + 63],\ [2389, 2389, 22*w - 85],\ [2423, 2423, w + 260],\ [2423, 2423, w + 2162],\ [2437, 2437, w + 899],\ [2437, 2437, w + 1537],\ [2441, 2441, -8*w - 55],\ [2441, 2441, 8*w - 63],\ [2477, 2477, w + 70],\ [2477, 2477, w + 2406],\ [2503, 2503, w + 447],\ [2503, 2503, w + 2055],\ [2521, 2521, 26*w + 79],\ [2521, 2521, 26*w - 105],\ [2531, 2531, 20*w - 73],\ [2531, 2531, 20*w + 53],\ [2539, 2539, 28*w - 115],\ [2539, 2539, 22*w - 113],\ [2543, 2543, w + 1180],\ [2543, 2543, w + 1362],\ [2549, 2549, -4*w - 51],\ [2549, 2549, 4*w - 55],\ [2551, 2551, -6*w - 53],\ [2551, 2551, 6*w - 59],\ [2591, 2591, -14*w - 69],\ [2591, 2591, 14*w - 83],\ [2593, 2593, w + 619],\ [2593, 2593, w + 1973],\ [2609, 2609, -14*w - 17],\ [2609, 2609, 14*w - 31],\ [2633, 2633, w + 1248],\ [2633, 2633, w + 1384],\ [2647, 2647, w + 544],\ [2647, 2647, w + 2102],\ [2657, 2657, w + 1117],\ [2657, 2657, w + 1539],\ [2663, 2663, w + 1174],\ [2663, 2663, w + 1488],\ [2683, 2683, w + 394],\ [2683, 2683, w + 2288],\ [2693, 2693, w + 73],\ [2693, 2693, w + 2619],\ [2729, 2729, 38*w + 125],\ [2729, 2729, 38*w - 163],\ [2731, 2731, 10*w - 71],\ [2731, 2731, -10*w - 61],\ [2767, 2767, w + 74],\ [2767, 2767, w + 2692],\ [2777, 2777, w + 900],\ [2777, 2777, w + 1876],\ [2791, 2791, -16*w - 29],\ [2791, 2791, 16*w - 45],\ [2797, 2797, w + 442],\ [2797, 2797, w + 2354],\ [2803, 2803, w + 665],\ [2803, 2803, w + 2137],\ [2809, 53, -53],\ [2851, 2851, 2*w - 55],\ [2851, 2851, -2*w - 53],\ [2861, 2861, 14*w - 25],\ [2861, 2861, -14*w - 11],\ [2897, 2897, w + 304],\ [2897, 2897, w + 2592],\ [2909, 2909, 34*w + 109],\ [2909, 2909, 34*w - 143],\ [2917, 2917, w + 1109],\ [2917, 2917, w + 1807],\ [2927, 2927, w + 924],\ [2927, 2927, w + 2002],\ [2939, 2939, 28*w + 85],\ [2939, 2939, 28*w - 113],\ [2953, 2953, w + 1404],\ [2953, 2953, w + 1548],\ [2957, 2957, w + 575],\ [2957, 2957, w + 2381],\ [2999, 2999, -10*w - 63],\ [2999, 2999, 10*w - 73],\ [3019, 3019, -20*w - 49],\ [3019, 3019, 20*w - 69],\ [3023, 3023, w + 396],\ [3023, 3023, w + 2626],\ [3037, 3037, w + 623],\ [3037, 3037, w + 2413],\ [3041, 3041, -14*w - 5],\ [3041, 3041, 14*w - 19],\ [3083, 3083, w + 675],\ [3083, 3083, w + 2407],\ [3119, 3119, 24*w - 91],\ [3119, 3119, 24*w + 67],\ [3121, 3121, -14*w - 1],\ [3121, 3121, 14*w - 15],\ [3167, 3167, w + 1082],\ [3167, 3167, w + 2084],\ [3169, 3169, 14*w - 11],\ [3169, 3169, 14*w - 3],\ [3181, 3181, 14*w - 9],\ [3181, 3181, 14*w - 5],\ [3187, 3187, w + 252],\ [3187, 3187, w + 2934],\ [3203, 3203, w + 299],\ [3203, 3203, w + 2903],\ [3217, 3217, w + 561],\ [3217, 3217, w + 2655],\ [3221, 3221, 4*w - 61],\ [3221, 3221, -4*w - 57],\ [3251, 3251, -20*w - 47],\ [3251, 3251, 20*w - 67],\ [3257, 3257, w + 477],\ [3257, 3257, w + 2779],\ [3259, 3259, -6*w - 59],\ [3259, 3259, 6*w - 65],\ [3299, 3299, 2*w - 59],\ [3299, 3299, -2*w - 57],\ [3301, 3301, 38*w + 123],\ [3301, 3301, 38*w - 161],\ [3307, 3307, w + 788],\ [3307, 3307, w + 2518],\ [3313, 3313, w + 81],\ [3313, 3313, w + 3231],\ [3319, 3319, 16*w - 37],\ [3319, 3319, -16*w - 21],\ [3323, 3323, w + 1557],\ [3323, 3323, w + 1765],\ [3329, 3329, 18*w - 53],\ [3329, 3329, -18*w - 35],\ [3331, 3331, 28*w - 111],\ [3331, 3331, 28*w + 83],\ [3343, 3343, w + 967],\ [3343, 3343, w + 2375],\ [3347, 3347, w + 1497],\ [3347, 3347, w + 1849],\ [3371, 3371, 36*w - 151],\ [3371, 3371, 22*w - 117],\ [3373, 3373, w + 641],\ [3373, 3373, w + 2731],\ [3389, 3389, 30*w + 91],\ [3389, 3389, 30*w - 121],\ [3413, 3413, w + 1165],\ [3413, 3413, w + 2247],\ [3449, 3449, -8*w - 63],\ [3449, 3449, 8*w - 71],\ [3461, 3461, -4*w - 59],\ [3461, 3461, 4*w - 63],\ [3463, 3463, w + 1318],\ [3463, 3463, w + 2144],\ [3481, 59, -59],\ [3511, 3511, 6*w - 67],\ [3511, 3511, -6*w - 61],\ [3517, 3517, w + 335],\ [3517, 3517, w + 3181],\ [3539, 3539, 14*w - 89],\ [3539, 3539, -14*w - 75],\ [3547, 3547, w + 168],\ [3547, 3547, w + 3378],\ [3557, 3557, w + 1699],\ [3557, 3557, w + 1857],\ [3559, 3559, 10*w - 77],\ [3559, 3559, -10*w - 67],\ [3571, 3571, 44*w + 145],\ [3571, 3571, 18*w + 85],\ [3583, 3583, w + 682],\ [3583, 3583, w + 2900],\ [3593, 3593, w + 864],\ [3593, 3593, w + 2728],\ [3607, 3607, w + 502],\ [3607, 3607, w + 3104],\ [3631, 3631, 16*w - 31],\ [3631, 3631, -16*w - 15],\ [3673, 3673, w + 1010],\ [3673, 3673, w + 2662],\ [3677, 3677, w + 1406],\ [3677, 3677, w + 2270],\ [3691, 3691, -20*w - 43],\ [3691, 3691, 20*w - 63],\ [3697, 3697, w + 1571],\ [3697, 3697, w + 2125],\ [3701, 3701, 42*w - 179],\ [3701, 3701, 42*w + 137],\ [3709, 3709, 4*w - 65],\ [3709, 3709, -4*w - 61],\ [3719, 3719, -16*w - 13],\ [3719, 3719, 16*w - 29],\ [3733, 3733, w + 86],\ [3733, 3733, w + 3646],\ [3761, 3761, 16*w - 97],\ [3761, 3761, -16*w - 81],\ [3769, 3769, -22*w - 53],\ [3769, 3769, 22*w - 75],\ [3779, 3779, 2*w - 63],\ [3779, 3779, -2*w - 61],\ [3803, 3803, w + 610],\ [3803, 3803, w + 3192],\ [3821, 3821, -18*w - 29],\ [3821, 3821, 18*w - 47],\ [3833, 3833, w + 1834],\ [3833, 3833, w + 1998],\ [3851, 3851, -10*w - 69],\ [3851, 3851, 10*w - 79],\ [3853, 3853, w + 614],\ [3853, 3853, w + 3238],\ [3863, 3863, w + 838],\ [3863, 3863, w + 3024],\ [3907, 3907, w + 1883],\ [3907, 3907, w + 2023],\ [3929, 3929, -40*w + 193],\ [3929, 3929, 26*w - 97],\ [3947, 3947, w + 1028],\ [3947, 3947, w + 2918],\ [3967, 3967, w + 1433],\ [3967, 3967, w + 2533],\ [4001, 4001, 8*w - 75],\ [4001, 4001, -8*w - 67],\ [4021, 4021, 22*w - 73],\ [4021, 4021, -22*w - 51],\ [4079, 4079, -16*w - 1],\ [4079, 4079, 16*w - 17],\ [4091, 4091, 28*w + 79],\ [4091, 4091, 28*w - 107],\ [4093, 4093, w + 1210],\ [4093, 4093, w + 2882],\ [4099, 4099, 20*w - 59],\ [4099, 4099, -20*w - 39],\ [4111, 4111, 16*w - 15],\ [4111, 4111, 16*w - 1],\ [4127, 4127, w + 537],\ [4127, 4127, w + 3589],\ [4153, 4153, w + 1074],\ [4153, 4153, w + 3078],\ [4159, 4159, 16*w - 9],\ [4159, 4159, 16*w - 7],\ [4211, 4211, -14*w - 79],\ [4211, 4211, 14*w - 93],\ [4217, 4217, w + 2022],\ [4217, 4217, w + 2194],\ [4229, 4229, 4*w - 69],\ [4229, 4229, -4*w - 65],\ [4241, 4241, 18*w - 41],\ [4241, 4241, -18*w - 23],\ [4243, 4243, w + 368],\ [4243, 4243, w + 3874],\ [4253, 4253, w + 184],\ [4253, 4253, w + 4068],\ [4261, 4261, 26*w - 95],\ [4261, 4261, 26*w + 69],\ [4283, 4283, w + 1489],\ [4283, 4283, w + 2793],\ [4289, 4289, -8*w - 69],\ [4289, 4289, 8*w - 77],\ [4297, 4297, w + 1681],\ [4297, 4297, w + 2615],\ [4327, 4327, w + 1600],\ [4327, 4327, w + 2726],\ [4337, 4337, w + 348],\ [4337, 4337, w + 3988],\ [4339, 4339, -18*w - 89],\ [4339, 4339, 18*w - 107],\ [4357, 4357, w + 890],\ [4357, 4357, w + 3466],\ [4363, 4363, w + 93],\ [4363, 4363, w + 4269],\ [4373, 4373, w + 804],\ [4373, 4373, w + 3568],\ [4391, 4391, 40*w - 167],\ [4391, 4391, 26*w - 137],\ [4421, 4421, 38*w - 157],\ [4421, 4421, 28*w - 145],\ [4457, 4457, w + 94],\ [4457, 4457, w + 4362],\ [4481, 4481, -18*w - 19],\ [4481, 4481, 18*w - 37],\ [4483, 4483, w + 1612],\ [4483, 4483, w + 2870],\ [4493, 4493, w + 510],\ [4493, 4493, w + 3982],\ [4513, 4513, w + 355],\ [4513, 4513, w + 4157],\ [4517, 4517, w + 2169],\ [4517, 4517, w + 2347],\ [4549, 4549, 12*w - 89],\ [4549, 4549, -12*w - 77],\ [4583, 4583, w + 1495],\ [4583, 4583, w + 3087],\ [4597, 4597, w + 1704],\ [4597, 4597, w + 2892],\ [4643, 4643, w + 1115],\ [4643, 4643, w + 3527],\ [4651, 4651, 20*w - 53],\ [4651, 4651, -20*w - 33],\ [4673, 4673, w + 1106],\ [4673, 4673, w + 3566],\ [4679, 4679, 48*w - 205],\ [4679, 4679, 48*w + 157],\ [4729, 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42*w - 215],\ [8971, 8971, 52*w - 213],\ [8999, 8999, -24*w - 7],\ [8999, 8999, 24*w - 31],\ [9007, 9007, w + 2057],\ [9007, 9007, w + 6949],\ [9043, 9043, w + 1953],\ [9043, 9043, w + 7089],\ [9049, 9049, 26*w - 57],\ [9049, 9049, -26*w - 31],\ [9067, 9067, w + 2103],\ [9067, 9067, w + 6963],\ [9091, 9091, 68*w - 291],\ [9091, 9091, 68*w + 223],\ [9109, 9109, 12*w - 113],\ [9109, 9109, -12*w - 101],\ [9133, 9133, w + 1564],\ [9133, 9133, w + 7568],\ [9137, 9137, w + 427],\ [9137, 9137, w + 8709],\ [9151, 9151, 2*w - 97],\ [9151, 9151, -2*w - 95],\ [9157, 9157, w + 2883],\ [9157, 9157, w + 6273],\ [9161, 9161, 8*w - 105],\ [9161, 9161, -8*w - 97],\ [9173, 9173, w + 4194],\ [9173, 9173, w + 4978],\ [9181, 9181, 34*w - 115],\ [9181, 9181, -34*w - 81],\ [9221, 9221, -26*w - 29],\ [9221, 9221, 26*w - 55],\ [9239, 9239, 24*w - 23],\ [9239, 9239, 24*w - 1],\ [9277, 9277, w + 953],\ [9277, 9277, w + 8323],\ [9281, 9281, 66*w - 281],\ [9281, 9281, 66*w + 215],\ [9293, 9293, w + 1756],\ [9293, 9293, w + 7536],\ [9311, 9311, 24*w - 19],\ [9311, 9311, 24*w - 5],\ [9323, 9323, w + 1066],\ [9323, 9323, w + 8256],\ [9397, 9397, w + 1218],\ [9397, 9397, w + 8178],\ [9421, 9421, 46*w + 135],\ [9421, 9421, 46*w - 181],\ [9433, 9433, w + 2210],\ [9433, 9433, w + 7222],\ [9439, 9439, 64*w - 271],\ [9439, 9439, 64*w + 207],\ [9461, 9461, 28*w - 163],\ [9461, 9461, -28*w - 135],\ [9491, 9491, 28*w - 71],\ [9491, 9491, -28*w - 43],\ [9497, 9497, w + 2522],\ [9497, 9497, w + 6974],\ [9539, 9539, 2*w - 99],\ [9539, 9539, -2*w - 97],\ [9547, 9547, w + 817],\ [9547, 9547, w + 8729],\ [9551, 9551, 48*w - 191],\ [9551, 9551, 48*w + 143],\ [9587, 9587, w + 3938],\ [9587, 9587, w + 5648],\ [9613, 9613, w + 1393],\ [9613, 9613, w + 8219],\ [9619, 9619, -18*w - 113],\ [9619, 9619, 18*w - 131],\ [9629, 9629, -20*w - 117],\ [9629, 9629, 20*w - 137],\ [9649, 9649, 50*w + 151],\ [9649, 9649, 50*w - 201],\ [9677, 9677, w + 3318],\ [9677, 9677, w + 6358],\ [9689, 9689, 26*w - 49],\ [9689, 9689, -26*w - 23],\ [9721, 9721, 40*w - 209],\ [9721, 9721, 58*w - 241],\ [9743, 9743, w + 3061],\ [9743, 9743, w + 6681],\ [9749, 9749, 44*w - 225],\ [9749, 9749, 54*w - 221],\ [9787, 9787, w + 523],\ [9787, 9787, w + 9263],\ [9811, 9811, -14*w - 107],\ [9811, 9811, 14*w - 121],\ [9817, 9817, w + 560],\ [9817, 9817, w + 9256],\ [9829, 9829, -26*w - 21],\ [9829, 9829, 26*w - 47],\ [9833, 9833, w + 280],\ [9833, 9833, w + 9552],\ [9851, 9851, 44*w - 169],\ [9851, 9851, 44*w + 125],\ [9871, 9871, -66*w + 317],\ [9871, 9871, 40*w - 147],\ [9887, 9887, w + 3389],\ [9887, 9887, w + 6497],\ [9929, 9929, 70*w - 299],\ [9929, 9929, 70*w + 229],\ [9931, 9931, 28*w - 67],\ [9931, 9931, -28*w - 39],\ [9941, 9941, -4*w - 99],\ [9941, 9941, 4*w - 103],\ [9949, 9949, 34*w - 111],\ [9949, 9949, -34*w - 77],\ [9973, 9973, w + 2785],\ [9973, 9973, w + 7187]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -1, -2, 0, 0, 2, 6, 6, 6, 6, 6, -8, -8, 6, 6, 12, 12, -6, -6, 0, 0, -4, -4, -6, -6, 6, 6, 18, -12, -12, 2, 2, -4, -4, 12, 12, -16, -16, -12, -12, -2, -2, 0, 0, -6, -6, -2, -2, -24, -24, -12, -12, 24, 24, -4, -4, 12, 12, -18, -18, 34, -26, -26, 12, 12, 24, 24, -2, -2, -14, -14, 2, 8, 8, 6, 6, -18, -18, -12, -12, 8, 8, -30, -30, -24, -24, 0, 0, 12, 12, -30, -30, 10, 14, 14, 18, 18, 12, 12, 18, 18, 20, 20, -22, -22, 24, 24, -6, -6, 30, 30, 34, 34, -30, -30, -36, -36, 36, 36, -44, -44, 30, 30, 0, 0, -42, -42, -16, -16, -32, -32, 38, 38, 12, 12, -30, -30, 4, 4, 6, 6, 54, 54, -36, -36, -8, -8, 6, 6, 42, 42, -48, -48, 24, 24, 28, 28, 26, 48, 48, 12, 12, 34, 34, 16, 16, -16, -16, -24, -24, -6, -6, -32, -32, -6, -6, -18, -18, -24, -24, 36, 36, 2, 2, 40, 40, 30, 30, -36, -36, -44, -44, 20, 20, -46, -46, -64, -64, -18, -18, 26, 26, 12, 12, -66, -66, -28, -28, 18, 18, -32, -32, 22, 22, -50, -50, -24, -24, 62, 62, 48, 48, 52, 52, 42, 42, -56, -56, -10, -10, -36, -36, 24, 24, 44, 44, -36, -36, 10, 10, -24, -24, 72, 72, 30, 30, -64, -64, -54, -54, 30, 30, -12, -12, 42, 42, 18, -14, -14, -60, -60, -12, -12, -18, -18, -36, -36, 18, 18, -32, -32, 0, 0, 52, 52, 36, 36, 50, 36, 36, 0, 0, 14, 14, -6, -6, 54, 54, -46, -46, 30, 30, 64, 64, 60, 60, 12, 12, 70, 70, 16, 16, 76, 76, -78, -78, 14, 14, -6, -6, -16, -16, -30, -30, 18, 18, -78, -78, -28, -28, -54, -54, -90, -90, -72, -72, 26, 26, 42, 42, 36, 36, 0, 0, 92, 92, 68, 68, 58, 58, 78, 78, -8, -8, -74, -74, -12, -12, 6, 6, -60, -60, 66, 66, -42, -42, 64, 64, -90, -90, 66, 66, 70, 70, -48, -48, -38, -38, -60, -60, -52, -52, 8, 8, 30, 30, -24, -24, -48, -48, -6, -6, 42, 42, -70, -70, 0, 0, -14, -14, 32, 32, 36, 36, -26, -26, 66, 66, 60, 60, 24, 24, 10, 10, -72, -72, -18, -18, 60, 60, -38, -44, -44, -18, -18, 98, 98, -90, -90, 30, 30, 8, 8, 60, 60, -30, -30, 46, 46, 24, 24, -36, -36, 56, 56, -42, -42, -6, -6, -44, -44, 0, 0, 10, 10, -40, -40, 90, 90, -50, -50, 108, 108, -68, -68, -30, -30, -42, -42, -12, -12, -22, -22, 92, 92, 36, 36, -90, -90, -12, -12, 66, 66, 72, 72, 4, 4, 66, 66, 84, 84, 24, 24, -100, -100, 60, 60, 6, 6, 30, 30, 86, 86, 18, 18, 78, 78, 48, 48, 114, -56, -56, 54, 54, -108, -108, 36, 36, -26, -26, -40, -40, 36, 36, -24, -24, -94, -94, 48, 48, -48, -48, -78, -78, -106, -106, 60, 60, -54, -54, 30, 30, 30, 30, 24, 24, -18, -18, -78, -78, 114, 114, 84, 84, -76, -76, -42, -42, -22, -22, 60, 60, 6, 6, -32, -32, 108, 108, -6, -6, 68, 68, -24, -24, -102, -102, -10, -10, 48, 48, -36, -36, -66, -66, 36, 36, 80, 80, 8, 8, 42, 42, -96, -96, -60, -60, -46, -46, 6, 6, 114, 114, 108, 108, 62, 62, 14, 14, -76, -76, -30, -30, -6, -6, 0, 0, 74, 74, 52, 52, 6, 6, -12, -12, 22, 22, 72, 72, 6, 6, -62, -62, -30, -30, 60, 60, -50, -50, 90, 90, -98, -98, 6, 6, 64, 64, -42, -42, -68, -68, -36, -36, 26, 26, 24, 24, 18, 18, 8, 8, 90, 90, -22, -22, 38, 38, -120, -120, -82, -82, -6, -6, -96, -96, 132, 132, 102, 102, -30, -30, 70, 70, -12, -12, -76, -76, 18, 18, 30, 30, -72, -72, 138, -18, -18, -132, -132, -84, -84, -64, -64, 50, 50, 72, 72, -60, -60, -6, -6, -126, -126, 46, 46, 54, 54, -14, -14, -48, -48, -30, -30, 130, 130, 132, 132, -18, -18, 4, 4, 34, 34, -120, -120, 126, 126, 120, 120, -20, -20, -14, -14, 48, 48, -42, -42, -106, -106, 120, 120, -48, -48, -24, -24, -62, -62, -24, -24, 132, 132, -18, -18, 50, 50, 44, 44, -18, -18, 108, 108, 96, 96, 118, 118, -16, -16, 42, 42, 14, 14, 30, 30, -4, -4, 18, 18, -132, -132, -78, -78, 120, 120, 2, 2, 12, 12, -66, -66, 140, 140, -42, -42, 54, 54, 132, 132, 56, 56, -34, -34, -78, -78, 150, 150, -56, -56, -106, -106, -92, -92, -60, -60, -48, -48, 6, 6, 126, 126, 8, 8, 38, 38, -116, -116, -102, -102, -6, -6, -132, -132, 54, 54, -60, -60, 42, 42, 116, 116, 108, 108, -6, -6, 60, 60, -72, -72, -20, -20, -126, -126, -138, -138, 6, 6, -60, -60, 24, 24, 4, 4, 72, 72, 22, 22, -150, -150, -6, -6, -144, -144, 52, 52, 78, 78, -86, -86, -110, -110, -158, -158, 60, 60, -12, -12, 124, 124, 0, 0, 60, 60, 160, 160, 64, 64, -34, -34, 60, 60, -132, -132, 138, 138, 6, 6, 56, 56, -78, -78, 96, 96, -24, -24, -116, -116, -144, -144, 108, 108, 78, 78, -124, -124, 126, 126, 84, 84, 56, 56, -18, -18, -108, -108, -66, -66, -60, -60, 18, 18, -142, -142, -60, -60, -42, -42, 90, 90, 108, 108, 150, 150, 148, 148, -90, -90, -18, -18, 10, 10, 102, 102, 24, 24, -36, -36, -112, -112, -82, -82, -106, -106, 4, 4, 64, 64, 102, 102, -152, -152, -6, -6, 2, 2, 54, 54, -60, -60, -174, -174, -120, -120, 52, 52, -162, -162, 114, -110, -110, 132, 132, 18, 18, -54, -54, 108, 108, -114, -114, -148, -148, 78, 78, -78, -78, -106, -106, 0, 0, -82, -82, 100, 100, -6, -6, 16, 16, 12, 12, -82, -82, -144, -144, -82, -82, 74, 74, -72, -72, -60, -60, -104, -104, 42, 42, 114, 114, 114, 114, 42, 42, -148, -148, -146, -146, -12, -12, 30, 30, -46, -46, 8, 8, -34, -34, -90, -90, -126, -126, 28, 28, -10, -10, -38, -38, -48, -48, -16, -16, 126, 126, -150, -150, -80, -80, 68, 68, 18, 18, 76, 76, 152, 152, -132, -132, -32, -32, 144, 144, -56, -56, 138, 138, -48, -48, -108, -108, -2, -2, 86, 86, 44, 44, 66, 66, -100, -100, -120, -120, -120, -120, 156, 156, 90, 90, -60, -60, -92, -92, 54, 54, -18, -18, -62, -62, -96, -96, 6, 6, -54, -54, -10, -10, 70, 70, -18, -18, 120, 120, 30, 30, 66, 66, -26, -26, -144, -144, -76, -76, -42, -42, 78, 78, -54, -54, 64, 64, -162, -162, -156, -156, 82, 82, -60, -60, 180, 180, -48, -48, 28, 28, -114, -114, 116, 116, 126, 126, 146, 146, -50, -50, 90, 90, -38, -38, 40, 40, -42, -42, -12, -12, 20, 20, 138, 138, -146, -146, 154, 154, -132, -132, -96, -96, -40, -40, 162, 162, 140, 140, -162, -162, 102, 102, 150, 150] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]