/* 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([-23, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([121, 11, 11]) primes_array = [ [2, 2, -w - 5],\ [7, 7, -w + 4],\ [7, 7, w + 4],\ [9, 3, 3],\ [11, 11, -2*w + 9],\ [11, 11, -2*w - 9],\ [13, 13, w + 6],\ [13, 13, -w + 6],\ [19, 19, -w - 2],\ [19, 19, w - 2],\ [23, 23, -w],\ [25, 5, -5],\ [29, 29, 7*w + 34],\ [29, 29, 2*w + 11],\ [41, 41, -w - 8],\ [41, 41, w - 8],\ [43, 43, 2*w - 7],\ [43, 43, -2*w - 7],\ [67, 67, 2*w - 5],\ [67, 67, -2*w - 5],\ [73, 73, 9*w + 44],\ [73, 73, 4*w + 21],\ [79, 79, -4*w - 17],\ [79, 79, 11*w + 52],\ [83, 83, 2*w - 3],\ [83, 83, -2*w - 3],\ [101, 101, 10*w + 49],\ [101, 101, 5*w + 26],\ [103, 103, -7*w - 32],\ [103, 103, 8*w + 37],\ [107, 107, -3*w - 10],\ [107, 107, 3*w - 10],\ [173, 173, -w - 14],\ [173, 173, w - 14],\ [191, 191, -3*w - 4],\ [191, 191, 3*w - 4],\ [193, 193, -3*w - 20],\ [193, 193, 3*w - 20],\ [197, 197, 2*w - 17],\ [197, 197, -2*w - 17],\ [199, 199, -4*w - 13],\ [199, 199, 4*w - 13],\ [227, 227, 18*w + 85],\ [227, 227, -7*w - 30],\ [233, 233, -w - 16],\ [233, 233, w - 16],\ [251, 251, -5*w - 18],\ [251, 251, 5*w - 18],\ [257, 257, 4*w - 25],\ [257, 257, -4*w - 25],\ [263, 263, 16*w + 75],\ [263, 263, -9*w - 40],\ [269, 269, 2*w - 19],\ [269, 269, -2*w - 19],\ [277, 277, 3*w - 22],\ [277, 277, -3*w - 22],\ [283, 283, -11*w - 50],\ [283, 283, 14*w + 65],\ [289, 17, -17],\ [317, 317, 7*w + 38],\ [317, 317, 22*w + 107],\ [349, 349, 2*w - 21],\ [349, 349, -2*w - 21],\ [353, 353, 16*w + 79],\ [353, 353, 11*w + 56],\ [359, 359, 4*w - 3],\ [359, 359, -4*w - 3],\ [367, 367, -4*w - 1],\ [367, 367, 4*w - 1],\ [379, 379, 5*w - 14],\ [379, 379, -5*w - 14],\ [383, 383, 8*w + 33],\ [383, 383, -8*w + 33],\ [397, 397, -6*w - 35],\ [397, 397, 6*w - 35],\ [409, 409, 17*w + 84],\ [409, 409, 12*w + 61],\ [419, 419, 26*w + 123],\ [419, 419, -9*w - 38],\ [431, 431, 5*w - 12],\ [431, 431, -5*w - 12],\ [449, 449, -5*w - 32],\ [449, 449, 5*w - 32],\ [461, 461, -w - 22],\ [461, 461, w - 22],\ [467, 467, -6*w - 19],\ [467, 467, 6*w - 19],\ [479, 479, -11*w - 48],\ [479, 479, 24*w + 113],\ [503, 503, -12*w - 53],\ [503, 503, 23*w + 108],\ [509, 509, 10*w + 53],\ [509, 509, 25*w + 122],\ [523, 523, 22*w + 103],\ [523, 523, -13*w - 58],\ [541, 541, 41*w + 198],\ [541, 541, 6*w + 37],\ [563, 563, 18*w + 83],\ [563, 563, -17*w - 78],\ [571, 571, 5*w - 2],\ [571, 571, -5*w - 2],\ [577, 577, 3*w - 28],\ [577, 577, -3*w - 28],\ [593, 593, -4*w - 31],\ [593, 593, 4*w - 31],\ [601, 601, 20*w + 99],\ [601, 601, 15*w + 76],\ [619, 619, 10*w + 41],\ [619, 619, -10*w + 41],\ [631, 631, 8*w - 29],\ [631, 631, -8*w - 29],\ [643, 643, -7*w - 22],\ [643, 643, 7*w - 22],\ [653, 653, -w - 26],\ [653, 653, w - 26],\ [659, 659, -6*w - 13],\ [659, 659, 6*w - 13],\ [673, 673, 21*w + 104],\ [673, 673, 16*w + 81],\ [727, 727, 7*w - 20],\ [727, 727, -7*w - 20],\ [743, 743, -8*w - 27],\ [743, 743, 8*w - 27],\ [751, 751, 32*w + 151],\ [751, 751, -13*w - 56],\ [761, 761, -w - 28],\ [761, 761, w - 28],\ [787, 787, -14*w - 61],\ [787, 787, 31*w + 146],\ [809, 809, -7*w - 44],\ [809, 809, 7*w - 44],\ [821, 821, 29*w + 142],\ [821, 821, 14*w + 73],\ [827, 827, -6*w - 1],\ [827, 827, 6*w - 1],\ [829, 829, 23*w + 114],\ [829, 829, 18*w + 91],\ [839, 839, -9*w - 32],\ [839, 839, 9*w - 32],\ [853, 853, -6*w - 41],\ [853, 853, 6*w - 41],\ [857, 857, -4*w - 35],\ [857, 857, 4*w - 35],\ [877, 877, -w - 30],\ [877, 877, w - 30],\ [907, 907, -19*w - 86],\ [907, 907, 26*w + 121],\ [911, 911, 12*w + 49],\ [911, 911, -12*w + 49],\ [919, 919, 25*w + 116],\ [919, 919, -20*w - 91],\ [929, 929, 53*w + 256],\ [929, 929, 8*w + 49],\ [961, 31, -31],\ [971, 971, 42*w + 199],\ [971, 971, -13*w - 54],\ [983, 983, -7*w - 12],\ [983, 983, 7*w - 12],\ [997, 997, 2*w - 33],\ [997, 997, -2*w - 33],\ [1013, 1013, 13*w + 70],\ [1013, 1013, 38*w + 185],\ [1019, 1019, 11*w + 42],\ [1019, 1019, -11*w + 42],\ [1021, 1021, 6*w - 43],\ [1021, 1021, -6*w - 43],\ [1031, 1031, 8*w - 21],\ [1031, 1031, -8*w - 21],\ [1061, 1061, -11*w - 62],\ [1061, 1061, 11*w - 62],\ [1063, 1063, -7*w - 8],\ [1063, 1063, 7*w - 8],\ [1091, 1091, 7*w - 6],\ [1091, 1091, -7*w - 6],\ [1093, 1093, 26*w + 129],\ [1093, 1093, 21*w + 106],\ [1097, 1097, 32*w + 157],\ [1097, 1097, 17*w + 88],\ [1103, 1103, -53*w - 252],\ [1103, 1103, 12*w + 47],\ [1117, 1117, 39*w + 190],\ [1117, 1117, 14*w + 75],\ [1123, 1123, 7*w - 2],\ [1123, 1123, -7*w - 2],\ [1129, 1129, 8*w - 51],\ [1129, 1129, -8*w - 51],\ [1153, 1153, -4*w - 39],\ [1153, 1153, 4*w - 39],\ [1171, 1171, -17*w - 74],\ [1171, 1171, 38*w + 179],\ [1181, 1181, 10*w + 59],\ [1181, 1181, 55*w + 266],\ [1187, 1187, 9*w - 26],\ [1187, 1187, -9*w - 26],\ [1237, 1237, -3*w - 38],\ [1237, 1237, 3*w - 38],\ [1259, 1259, 14*w + 57],\ [1259, 1259, -14*w + 57],\ [1277, 1277, 2*w - 37],\ [1277, 1277, -2*w - 37],\ [1279, 1279, -20*w - 89],\ [1279, 1279, 35*w + 164],\ [1289, 1289, 28*w + 139],\ [1289, 1289, 23*w + 116],\ [1297, 1297, 48*w + 233],\ [1297, 1297, 13*w + 72],\ [1301, 1301, 19*w + 98],\ [1301, 1301, 34*w + 167],\ [1303, 1303, 8*w - 13],\ [1303, 1303, -8*w - 13],\ [1307, 1307, 34*w + 159],\ [1307, 1307, -21*w - 94],\ [1361, 1361, -5*w - 44],\ [1361, 1361, 5*w - 44],\ [1367, 1367, 31*w + 144],\ [1367, 1367, -24*w - 109],\ [1369, 37, -37],\ [1373, 1373, 7*w - 50],\ [1373, 1373, -7*w - 50],\ [1381, 1381, -6*w - 47],\ [1381, 1381, 6*w - 47],\ [1399, 1399, 49*w + 232],\ [1399, 1399, -16*w - 67],\ [1409, 1409, 35*w + 172],\ [1409, 1409, 20*w + 103],\ [1423, 1423, 8*w - 7],\ [1423, 1423, -8*w - 7],\ [1429, 1429, 2*w - 39],\ [1429, 1429, -2*w - 39],\ [1447, 1447, 8*w - 5],\ [1447, 1447, -8*w - 5],\ [1453, 1453, 42*w + 205],\ [1453, 1453, 17*w + 90],\ [1459, 1459, 10*w - 29],\ [1459, 1459, -10*w - 29],\ [1471, 1471, -8*w - 1],\ [1471, 1471, 8*w - 1],\ [1481, 1481, -4*w - 43],\ [1481, 1481, 4*w - 43],\ [1483, 1483, -14*w + 55],\ [1483, 1483, 14*w + 55],\ [1487, 1487, -11*w - 36],\ [1487, 1487, 11*w - 36],\ [1523, 1523, 47*w + 222],\ [1523, 1523, -18*w - 77],\ [1549, 1549, 15*w + 82],\ [1549, 1549, 50*w + 243],\ [1553, 1553, -8*w - 55],\ [1553, 1553, 8*w - 55],\ [1571, 1571, -10*w - 27],\ [1571, 1571, 10*w - 27],\ [1579, 1579, 46*w + 217],\ [1579, 1579, -19*w - 82],\ [1583, 1583, 13*w + 48],\ [1583, 1583, -13*w + 48],\ [1607, 1607, -9*w - 16],\ [1607, 1607, 9*w - 16],\ [1613, 1613, 31*w + 154],\ [1613, 1613, 26*w + 131],\ [1627, 1627, -11*w - 34],\ [1627, 1627, 11*w - 34],\ [1637, 1637, 22*w + 113],\ [1637, 1637, 37*w + 182],\ [1657, 1657, 4*w - 45],\ [1657, 1657, -4*w - 45],\ [1663, 1663, 16*w + 65],\ [1663, 1663, -16*w + 65],\ [1667, 1667, -9*w - 14],\ [1667, 1667, 9*w - 14],\ [1669, 1669, -10*w - 63],\ [1669, 1669, 10*w - 63],\ [1697, 1697, 44*w + 215],\ [1697, 1697, 19*w + 100],\ [1699, 1699, -14*w + 53],\ [1699, 1699, 14*w + 53],\ [1723, 1723, -22*w - 97],\ [1723, 1723, 43*w + 202],\ [1733, 1733, -14*w - 79],\ [1733, 1733, 14*w - 79],\ [1741, 1741, -w - 42],\ [1741, 1741, w - 42],\ [1747, 1747, -17*w + 70],\ [1747, 1747, 17*w + 70],\ [1759, 1759, 11*w - 32],\ [1759, 1759, -11*w - 32],\ [1777, 1777, 8*w - 57],\ [1777, 1777, -8*w - 57],\ [1789, 1789, 7*w - 54],\ [1789, 1789, -7*w - 54],\ [1811, 1811, 15*w + 58],\ [1811, 1811, -70*w - 333],\ [1831, 1831, 40*w + 187],\ [1831, 1831, -25*w - 112],\ [1847, 1847, 9*w - 4],\ [1847, 1847, -9*w - 4],\ [1889, 1889, 13*w - 76],\ [1889, 1889, -13*w - 76],\ [1907, 1907, 14*w - 51],\ [1907, 1907, -14*w - 51],\ [1913, 1913, -w - 44],\ [1913, 1913, w - 44],\ [1931, 1931, 35*w + 162],\ [1931, 1931, -30*w - 137],\ [1933, 1933, 2*w - 45],\ [1933, 1933, -2*w - 45],\ [1951, 1951, 13*w - 44],\ [1951, 1951, -13*w - 44],\ [1973, 1973, 34*w + 169],\ [1973, 1973, 29*w + 146],\ [1999, 1999, -11*w - 28],\ [1999, 1999, 11*w - 28],\ [2011, 2011, -10*w - 17],\ [2011, 2011, 10*w - 17],\ [2017, 2017, 77*w + 372],\ [2017, 2017, 12*w + 73],\ [2039, 2039, -15*w + 56],\ [2039, 2039, 15*w + 56],\ [2053, 2053, -14*w - 81],\ [2053, 2053, 14*w - 81],\ [2087, 2087, 12*w - 35],\ [2087, 2087, -12*w - 35],\ [2129, 2129, -5*w - 52],\ [2129, 2129, 5*w - 52],\ [2131, 2131, 10*w - 13],\ [2131, 2131, -10*w - 13],\ [2141, 2141, 41*w + 202],\ [2141, 2141, 26*w + 133],\ [2179, 2179, -10*w - 11],\ [2179, 2179, 10*w - 11],\ [2207, 2207, 11*w - 24],\ [2207, 2207, -11*w - 24],\ [2209, 47, -47],\ [2221, 2221, -15*w - 86],\ [2221, 2221, 15*w - 86],\ [2237, 2237, -7*w - 58],\ [2237, 2237, 7*w - 58],\ [2251, 2251, -10*w - 7],\ [2251, 2251, 10*w - 7],\ [2281, 2281, -w - 48],\ [2281, 2281, w - 48],\ [2287, 2287, -13*w - 40],\ [2287, 2287, 13*w - 40],\ [2293, 2293, -3*w - 50],\ [2293, 2293, 3*w - 50],\ [2309, 2309, 2*w - 49],\ [2309, 2309, -2*w - 49],\ [2311, 2311, -20*w - 83],\ [2311, 2311, 65*w + 308],\ [2341, 2341, -5*w - 54],\ [2341, 2341, 5*w - 54],\ [2351, 2351, 12*w - 31],\ [2351, 2351, -12*w - 31],\ [2377, 2377, 49*w + 240],\ [2377, 2377, 24*w + 125],\ [2381, 2381, 14*w + 83],\ [2381, 2381, 79*w + 382],\ [2383, 2383, -11*w - 20],\ [2383, 2383, 11*w - 20],\ [2393, 2393, 16*w - 91],\ [2393, 2393, -16*w - 91],\ [2399, 2399, 64*w + 303],\ [2399, 2399, -21*w - 88],\ [2411, 2411, -18*w + 71],\ [2411, 2411, 18*w + 71],\ [2417, 2417, 28*w + 143],\ [2417, 2417, 43*w + 212],\ [2441, 2441, 4*w - 53],\ [2441, 2441, -4*w - 53],\ [2459, 2459, 11*w - 18],\ [2459, 2459, -11*w - 18],\ [2473, 2473, 7*w - 60],\ [2473, 2473, -7*w - 60],\ [2477, 2477, -w - 50],\ [2477, 2477, w - 50],\ [2503, 2503, -31*w - 140],\ [2503, 2503, 44*w + 205],\ [2551, 2551, 17*w + 64],\ [2551, 2551, -17*w + 64],\ [2557, 2557, 22*w + 117],\ [2557, 2557, 57*w + 278],\ [2591, 2591, -13*w - 36],\ [2591, 2591, 13*w - 36],\ [2617, 2617, 12*w - 77],\ [2617, 2617, -12*w - 77],\ [2657, 2657, -4*w - 55],\ [2657, 2657, 4*w - 55],\ [2659, 2659, -14*w - 43],\ [2659, 2659, 14*w - 43],\ [2677, 2677, 26*w + 135],\ [2677, 2677, 51*w + 250],\ [2683, 2683, 11*w - 10],\ [2683, 2683, -11*w - 10],\ [2687, 2687, -12*w - 25],\ [2687, 2687, 12*w - 25],\ [2693, 2693, -11*w - 74],\ [2693, 2693, 11*w - 74],\ [2711, 2711, 60*w + 283],\ [2711, 2711, -25*w - 108],\ [2719, 2719, 11*w - 8],\ [2719, 2719, -11*w - 8],\ [2731, 2731, -13*w - 34],\ [2731, 2731, 13*w - 34],\ [2741, 2741, 10*w - 71],\ [2741, 2741, -10*w - 71],\ [2749, 2749, 18*w - 101],\ [2749, 2749, -18*w - 101],\ [2753, 2753, 8*w - 65],\ [2753, 2753, -8*w - 65],\ [2767, 2767, -11*w - 4],\ [2767, 2767, 11*w - 4],\ [2789, 2789, 5*w - 58],\ [2789, 2789, -5*w - 58],\ [2801, 2801, 40*w + 199],\ [2801, 2801, 35*w + 176],\ [2803, 2803, 17*w - 62],\ [2803, 2803, -17*w - 62],\ [2809, 53, -53],\ [2833, 2833, 52*w + 255],\ [2833, 2833, 27*w + 140],\ [2837, 2837, -13*w - 82],\ [2837, 2837, 13*w - 82],\ [2843, 2843, 58*w + 273],\ [2843, 2843, -27*w - 118],\ [2851, 2851, 73*w + 346],\ [2851, 2851, -22*w - 91],\ [2861, 2861, 31*w + 158],\ [2861, 2861, 46*w + 227],\ [2903, 2903, 57*w + 268],\ [2903, 2903, -28*w - 123],\ [2953, 2953, 41*w + 204],\ [2953, 2953, 36*w + 181],\ [2957, 2957, 17*w - 98],\ [2957, 2957, -17*w - 98],\ [2963, 2963, 18*w + 67],\ [2963, 2963, -18*w + 67],\ [2969, 2969, 7*w - 64],\ [2969, 2969, -7*w - 64],\ [3011, 3011, -30*w - 133],\ [3011, 3011, 55*w + 258],\ [3023, 3023, -12*w - 17],\ [3023, 3023, 12*w - 17],\ [3037, 3037, 9*w - 70],\ [3037, 3037, -9*w - 70],\ [3049, 3049, 25*w + 132],\ [3049, 3049, 60*w + 293],\ [3061, 3061, 14*w - 87],\ [3061, 3061, -14*w - 87],\ [3079, 3079, 16*w - 53],\ [3079, 3079, -16*w - 53],\ [3109, 3109, 42*w + 209],\ [3109, 3109, 37*w + 186],\ [3119, 3119, -19*w + 72],\ [3119, 3119, 19*w + 72],\ [3121, 3121, 20*w + 111],\ [3121, 3121, 75*w + 364],\ [3137, 3137, 16*w + 95],\ [3137, 3137, 91*w + 440],\ [3169, 3169, -13*w - 84],\ [3169, 3169, 13*w - 84],\ [3191, 3191, 12*w - 11],\ [3191, 3191, -12*w - 11],\ [3209, 3209, 23*w + 124],\ [3209, 3209, 68*w + 331],\ [3221, 3221, 26*w + 137],\ [3221, 3221, 61*w + 298],\ [3229, 3229, -7*w - 66],\ [3229, 3229, 7*w - 66],\ [3271, 3271, -95*w - 452],\ [3271, 3271, 20*w + 77],\ [3299, 3299, -39*w - 178],\ [3299, 3299, 46*w + 213],\ [3301, 3301, 11*w - 78],\ [3301, 3301, -11*w - 78],\ [3313, 3313, 76*w + 369],\ [3313, 3313, 21*w + 116],\ [3319, 3319, -41*w - 188],\ [3319, 3319, 44*w + 203],\ [3323, 3323, 43*w + 198],\ [3323, 3323, -42*w - 193],\ [3331, 3331, -23*w + 94],\ [3331, 3331, 23*w + 94],\ [3361, 3361, 19*w - 108],\ [3361, 3361, -19*w - 108],\ [3389, 3389, 2*w - 59],\ [3389, 3389, -2*w - 59],\ [3391, 3391, 67*w + 316],\ [3391, 3391, -28*w - 121],\ [3413, 3413, 14*w - 89],\ [3413, 3413, -14*w - 89],\ [3433, 3433, 44*w + 219],\ [3433, 3433, 39*w + 196],\ [3467, 3467, -29*w - 126],\ [3467, 3467, 66*w + 311],\ [3481, 59, -59],\ [3511, 3511, -17*w - 56],\ [3511, 3511, 17*w - 56],\ [3539, 3539, -30*w - 131],\ [3539, 3539, 65*w + 306],\ [3547, 3547, -14*w - 31],\ [3547, 3547, 14*w - 31],\ [3559, 3559, 80*w + 379],\ [3559, 3559, -25*w - 104],\ [3581, 3581, 25*w + 134],\ [3581, 3581, 70*w + 341],\ [3607, 3607, -31*w - 136],\ [3607, 3607, 64*w + 301],\ [3613, 3613, -9*w - 74],\ [3613, 3613, 9*w - 74],\ [3617, 3617, 11*w - 80],\ [3617, 3617, -11*w - 80],\ [3631, 3631, 13*w - 16],\ [3631, 3631, -13*w - 16],\ [3637, 3637, -3*w - 62],\ [3637, 3637, 3*w - 62],\ [3671, 3671, -32*w - 141],\ [3671, 3671, 63*w + 296],\ [3673, 3673, 57*w + 280],\ [3673, 3673, 32*w + 165],\ [3691, 3691, -13*w - 14],\ [3691, 3691, 13*w - 14],\ [3709, 3709, 23*w + 126],\ [3709, 3709, 78*w + 379],\ [3721, 61, -61],\ [3761, 3761, 29*w + 152],\ [3761, 3761, 64*w + 313],\ [3779, 3779, 14*w - 27],\ [3779, 3779, -14*w - 27],\ [3797, 3797, -19*w - 110],\ [3797, 3797, 19*w - 110],\ [3821, 3821, -w - 62],\ [3821, 3821, w - 62],\ [3823, 3823, -13*w - 8],\ [3823, 3823, 13*w - 8],\ [3851, 3851, 13*w - 6],\ [3851, 3851, -13*w - 6],\ [3853, 3853, 33*w + 170],\ [3853, 3853, 58*w + 285],\ [3863, 3863, -16*w - 45],\ [3863, 3863, 16*w - 45],\ [3877, 3877, 2*w - 63],\ [3877, 3877, -2*w - 63],\ [3889, 3889, 3*w - 64],\ [3889, 3889, -3*w - 64],\ [3907, 3907, 22*w + 85],\ [3907, 3907, -103*w - 490],\ [3931, 3931, 58*w + 271],\ [3931, 3931, -37*w - 166],\ [3943, 3943, -17*w - 52],\ [3943, 3943, 17*w - 52],\ [3947, 3947, 19*w - 66],\ [3947, 3947, -19*w - 66],\ [3967, 3967, -29*w - 124],\ [3967, 3967, 76*w + 359],\ [4007, 4007, -39*w - 176],\ [4007, 4007, 56*w + 261],\ [4019, 4019, -15*w - 34],\ [4019, 4019, 15*w - 34],\ [4049, 4049, 5*w - 68],\ [4049, 4049, -5*w - 68],\ [4057, 4057, -7*w - 72],\ [4057, 4057, 7*w - 72],\ [4073, 4073, -w - 64],\ [4073, 4073, w - 64],\ [4091, 4091, -42*w - 191],\ [4091, 4091, 53*w + 246],\ [4099, 4099, -26*w - 107],\ [4099, 4099, 89*w + 422],\ [4111, 4111, -43*w - 196],\ [4111, 4111, 52*w + 241],\ [4127, 4127, 51*w + 236],\ [4127, 4127, -44*w - 201],\ [4129, 4129, 48*w + 239],\ [4129, 4129, 43*w + 216],\ [4133, 4133, 2*w - 65],\ [4133, 4133, -2*w - 65],\ [4139, 4139, 50*w + 231],\ [4139, 4139, -45*w - 206],\ [4153, 4153, 8*w - 75],\ [4153, 4153, -8*w - 75],\ [4159, 4159, 20*w - 71],\ [4159, 4159, -20*w - 71],\ [4217, 4217, 23*w + 128],\ [4217, 4217, 88*w + 427],\ [4219, 4219, -14*w - 17],\ [4219, 4219, 14*w - 17],\ [4231, 4231, -32*w - 139],\ [4231, 4231, 73*w + 344],\ [4241, 4241, 104*w + 503],\ [4241, 4241, 19*w + 112],\ [4243, 4243, -22*w + 83],\ [4243, 4243, 22*w + 83],\ [4261, 4261, 10*w - 81],\ [4261, 4261, -10*w - 81],\ [4273, 4273, -11*w - 84],\ [4273, 4273, 11*w - 84],\ [4283, 4283, -14*w - 15],\ [4283, 4283, 14*w - 15],\ [4337, 4337, 32*w + 167],\ [4337, 4337, 67*w + 328],\ [4339, 4339, 14*w - 13],\ [4339, 4339, -14*w - 13],\ [4349, 4349, 7*w - 74],\ [4349, 4349, -7*w - 74],\ [4373, 4373, 74*w + 361],\ [4373, 4373, 29*w + 154],\ [4391, 4391, -15*w - 28],\ [4391, 4391, 15*w - 28],\ [4397, 4397, 2*w - 67],\ [4397, 4397, -2*w - 67],\ [4409, 4409, 40*w + 203],\ [4409, 4409, 55*w + 272],\ [4423, 4423, -23*w + 88],\ [4423, 4423, 23*w + 88],\ [4441, 4441, 24*w + 133],\ [4441, 4441, 89*w + 432],\ [4457, 4457, -8*w - 77],\ [4457, 4457, 8*w - 77],\ [4483, 4483, -14*w - 5],\ [4483, 4483, 14*w - 5],\ 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97],\ [8581, 8581, -6*w - 97],\ [8597, 8597, 19*w - 130],\ [8597, 8597, -19*w - 130],\ [8599, 8599, -25*w - 76],\ [8599, 8599, 25*w - 76],\ [8623, 8623, -28*w - 97],\ [8623, 8623, 28*w - 97],\ [8629, 8629, 3*w - 94],\ [8629, 8629, -3*w - 94],\ [8641, 8641, 5*w - 96],\ [8641, 8641, -5*w - 96],\ [8647, 8647, -31*w + 116],\ [8647, 8647, 31*w + 116],\ [8663, 8663, 33*w + 128],\ [8663, 8663, -152*w - 723],\ [8677, 8677, 18*w - 127],\ [8677, 8677, -18*w - 127],\ [8689, 8689, 35*w + 192],\ [8689, 8689, 120*w + 583],\ [8699, 8699, -21*w - 38],\ [8699, 8699, 21*w - 38],\ [8731, 8731, -22*w - 49],\ [8731, 8731, 22*w - 49],\ [8741, 8741, 74*w + 367],\ [8741, 8741, 59*w + 298],\ [8747, 8747, -51*w - 226],\ [8747, 8747, 94*w + 441],\ [8753, 8753, -16*w - 121],\ [8753, 8753, 16*w - 121],\ [8783, 8783, 36*w + 145],\ [8783, 8783, -36*w + 145],\ [8803, 8803, -23*w - 58],\ [8803, 8803, 23*w - 58],\ [8807, 8807, -44*w - 189],\ [8807, 8807, 111*w + 524],\ [8819, 8819, 30*w - 109],\ [8819, 8819, -30*w - 109],\ [8821, 8821, 86*w + 423],\ [8821, 8821, 51*w + 262],\ [8831, 8831, 93*w + 436],\ [8831, 8831, -52*w - 231],\ [8839, 8839, 20*w - 19],\ [8839, 8839, -20*w - 19],\ [8861, 8861, 106*w + 517],\ [8861, 8861, 41*w + 218],\ [8923, 8923, 22*w - 47],\ [8923, 8923, -22*w - 47],\ [8933, 8933, 2*w - 95],\ [8933, 8933, -2*w - 95],\ [9001, 9001, 121*w + 588],\ [9001, 9001, 36*w + 197],\ [9007, 9007, 28*w - 95],\ [9007, 9007, -28*w - 95],\ [9029, 9029, 5*w - 98],\ [9029, 9029, -5*w - 98],\ [9041, 9041, 4*w - 97],\ [9041, 9041, -4*w - 97],\ [9059, 9059, 90*w + 421],\ [9059, 9059, -55*w - 246],\ [9067, 9067, 109*w + 514],\ [9067, 9067, -46*w - 199],\ [9109, 9109, 13*w - 114],\ [9109, 9109, -13*w - 114],\ [9127, 9127, -56*w - 251],\ [9127, 9127, 89*w + 416],\ [9133, 9133, 129*w + 626],\ [9133, 9133, 34*w + 189],\ [9137, 9137, -8*w - 103],\ [9137, 9137, 8*w - 103],\ [9151, 9151, -20*w - 7],\ [9151, 9151, 20*w - 7],\ [9157, 9157, 107*w + 522],\ [9157, 9157, 42*w + 223],\ [9181, 9181, 14*w - 117],\ [9181, 9181, -14*w - 117],\ [9187, 9187, 38*w + 155],\ [9187, 9187, -38*w + 155],\ [9199, 9199, -20*w - 1],\ [9199, 9199, 20*w - 1],\ [9209, 9209, -32*w - 181],\ [9209, 9209, 32*w - 181],\ [9241, 9241, 16*w - 123],\ [9241, 9241, -16*w - 123],\ [9277, 9277, 7*w - 102],\ [9277, 9277, -7*w - 102],\ [9281, 9281, 61*w + 308],\ [9281, 9281, 76*w + 377],\ [9283, 9283, 22*w - 43],\ [9283, 9283, -22*w - 43],\ [9293, 9293, 94*w + 461],\ [9293, 9293, 49*w + 254],\ [9311, 9311, -48*w - 209],\ [9311, 9311, 107*w + 504],\ [9341, 9341, 25*w + 154],\ [9341, 9341, 170*w + 821],\ [9343, 9343, -29*w - 100],\ [9343, 9343, 29*w - 100],\ [9371, 9371, -27*w - 86],\ [9371, 9371, 27*w - 86],\ [9377, 9377, 53*w + 272],\ [9377, 9377, 88*w + 433],\ [9391, 9391, 32*w + 119],\ [9391, 9391, -32*w + 119],\ [9397, 9397, -3*w - 98],\ [9397, 9397, 3*w - 98],\ [9403, 9403, -43*w - 182],\ [9403, 9403, 122*w + 577],\ [9409, 97, -97],\ [9413, 9413, 101*w + 494],\ [9413, 9413, 46*w + 241],\ [9433, 9433, -4*w - 99],\ [9433, 9433, 4*w - 99],\ [9461, 9461, 35*w + 194],\ [9461, 9461, 130*w + 631],\ [9463, 9463, -23*w - 52],\ [9463, 9463, 23*w - 52],\ [9467, 9467, 21*w - 26],\ [9467, 9467, -21*w - 26],\ [9491, 9491, -63*w - 286],\ [9491, 9491, 82*w + 381],\ [9539, 9539, 105*w + 494],\ [9539, 9539, -50*w - 219],\ [9587, 9587, -66*w - 301],\ [9587, 9587, 79*w + 366],\ [9619, 9619, 26*w - 77],\ [9619, 9619, -26*w - 77],\ [9631, 9631, -68*w - 311],\ [9631, 9631, 77*w + 356],\ [9649, 9649, 72*w + 359],\ [9649, 9649, 67*w + 336],\ [9661, 9661, 54*w + 277],\ [9661, 9661, 89*w + 438],\ [9679, 9679, -160*w - 761],\ [9679, 9679, 35*w + 136],\ [9689, 9689, -7*w - 104],\ [9689, 9689, 7*w - 104],\ [9733, 9733, 171*w + 826],\ [9733, 9733, 26*w + 159],\ [9739, 9739, -29*w - 98],\ [9739, 9739, 29*w - 98],\ [9743, 9743, 21*w - 20],\ [9743, 9743, -21*w - 20],\ [9767, 9767, -24*w - 59],\ [9767, 9767, 24*w - 59],\ [9781, 9781, 6*w - 103],\ [9781, 9781, -6*w - 103],\ [9803, 9803, 38*w + 153],\ [9803, 9803, -38*w + 153],\ [9829, 9829, -5*w - 102],\ [9829, 9829, 5*w - 102],\ [9833, 9833, 4*w - 101],\ [9833, 9833, -4*w - 101],\ [9851, 9851, 102*w + 479],\ [9851, 9851, -53*w - 234],\ [9857, 9857, 28*w + 167],\ [9857, 9857, 163*w + 788],\ [9859, 9859, 119*w + 562],\ [9859, 9859, -46*w - 197],\ [9887, 9887, -21*w - 16],\ [9887, 9887, 21*w - 16],\ [9907, 9907, 22*w - 35],\ [9907, 9907, -22*w - 35],\ [9923, 9923, 26*w - 75],\ [9923, 9923, -26*w - 75],\ [9929, 9929, 73*w + 364],\ [9929, 9929, 68*w + 341],\ [9949, 9949, 90*w + 443],\ [9949, 9949, 55*w + 282]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, -2, -5, 1, 1, 4, 4, 0, 0, -1, -9, 0, 0, -8, -8, -6, -6, -7, -7, 4, 4, -10, -10, -6, -6, 2, 2, -16, -16, 18, 18, -6, -6, 17, 17, 4, 4, -2, -2, 0, 0, 18, 18, 24, 24, -23, -23, -2, -2, 14, 14, 10, 10, -2, -2, 4, 4, -30, 13, 13, 30, 30, -21, -21, -20, -20, -17, -17, -5, -5, -1, -1, -2, -2, -30, -30, 20, 20, -18, -18, 35, 35, 12, 12, -27, -27, 20, 20, -26, -26, 15, 15, -16, -16, -8, -8, 4, 4, -28, -28, 33, 33, 44, 44, 2, 2, -25, -25, 7, 7, 29, 29, -41, -41, 10, 10, 14, 14, 3, 3, 4, 4, -23, -23, 12, 12, -32, -32, 0, 0, 22, 22, -52, -52, 25, 25, -5, -5, 14, 14, 8, 8, -12, -12, -12, -12, 12, 12, 10, 10, -30, -30, -13, 47, 47, 39, 39, 38, 38, 39, 39, -10, -10, 22, 22, 32, 32, -13, -13, 44, 44, -58, -58, -51, -51, -42, -42, -51, -51, 48, 48, 24, 24, 50, 50, -31, -31, -3, -3, -18, -18, -12, -12, 18, 18, -25, -25, -47, -47, -15, -15, 0, 0, 48, 48, 27, 27, 39, 39, 28, 28, 12, 12, -72, -72, -65, 39, 39, -68, -68, 60, 60, -15, -15, 29, 29, -70, -70, 28, 28, -71, -71, -20, -20, 22, 22, 32, 32, 49, 49, 58, 58, -41, -41, -15, -15, -56, -56, -28, -28, -30, -30, 34, 34, 33, 33, -6, -6, 78, 78, 33, 33, -2, -2, 4, 4, 48, 48, 50, 50, -42, -42, 40, 40, -46, -46, -6, -6, 17, 17, -57, -57, -40, -40, 8, 8, 10, 10, 12, 12, -43, -43, -52, -52, 70, 70, -52, -52, -36, -36, -18, -18, 54, 54, -23, -23, 79, 79, -20, -20, -13, -13, -17, -17, 60, 60, 84, 84, 48, 48, 20, 20, -68, -68, -58, -58, -45, -45, 48, 48, -30, 22, 22, 78, 78, -48, -48, 7, 7, 38, 38, 29, 29, 60, 60, -13, -13, 67, 67, -48, -48, 3, 3, -18, -18, -36, -36, 54, 54, -75, -75, 62, 62, -22, -22, 42, 42, -50, -50, -11, -11, 48, 48, 14, 14, -98, -98, 13, 13, -58, -58, 18, 18, 38, 38, 40, 40, -7, -7, -16, -16, 23, 23, -41, -41, 87, 87, -70, -70, -68, -68, -58, -58, 50, 50, 49, 49, 48, 48, -20, -20, 52, 52, 44, 44, -70, -6, -6, -62, -62, 4, 4, 2, 2, -63, -63, 54, 54, -86, -86, 3, 3, -81, -81, 70, 70, 62, 62, 39, 39, 13, 13, -40, -40, 37, 37, -20, -20, 80, 80, -90, -90, 22, 22, 8, 8, 45, 45, -8, -8, -10, -10, -103, -103, 70, 70, -3, -3, 100, 100, -73, -73, 4, 4, 0, 0, -76, -76, -43, -43, -88, -88, 15, 15, 92, 92, 9, 9, -66, -66, 38, 38, -93, 12, 12, 20, 20, 53, 53, 0, 0, 32, 32, 58, 58, -26, -26, 63, 63, 32, 32, -72, -72, -78, -78, -76, -76, 92, 92, 20, 20, 22, -88, -88, -30, -30, -82, -82, -3, -3, 84, 84, -73, -73, 74, 74, 54, 54, 58, 58, -70, -70, -22, -22, 107, 107, -96, -96, -107, -107, -92, -92, -32, -32, 15, 15, 25, 25, 103, 103, -31, -31, 92, 92, 20, 20, 62, 62, 48, 48, -25, -25, 4, 4, 20, 20, -36, -36, 85, 85, 33, 33, 10, 10, -68, -68, 92, 92, 64, 64, -113, -113, -41, -41, 39, 39, -2, -2, 55, 55, -30, -30, 84, 84, 42, 42, 108, 108, -30, -30, 49, 49, 42, 42, 78, 78, -106, -106, 29, 29, -82, -82, 8, 8, 5, 5, -36, -36, -10, -10, -8, -8, -81, -81, -80, -80, -73, -73, 64, 64, 114, 114, 25, 25, 17, 17, -36, -36, 22, 22, 129, 129, 30, 30, -101, -101, -36, -36, 105, 105, -76, -76, -88, -88, 93, 93, 5, 5, 30, 30, -76, -76, 98, 98, -52, -52, 100, 100, 28, 28, 44, 44, -45, -45, -38, -38, -133, -48, -48, 10, 10, 2, 2, -111, -111, 28, 28, 97, 97, -18, -18, -96, -96, 63, 63, -21, -21, -76, -76, 23, 23, 77, 77, -2, -2, -15, -15, 14, 14, -2, -2, -110, -110, -2, -2, -108, -108, 109, 109, -3, -3, 128, 128, -95, -95, 27, 27, 48, 48, 0, 0, 22, 22, 8, 8, -93, -93, 134, 134, -25, -25, 64, 64, 17, 17, 4, 4, 50, 50, -146, -146, -138, -138, -72, -72, 104, 104, -92, -92, -78, -78, 100, 100, 10, 10, -55, -55, -68, -68, -27, -27, -66, -66, 40, 40, -18, -18, 73, 73, 105, 105, -101, -101, -42, -42, -26, -26, -26, -26, 100, 100, -8, -8, -48, -48, -16, -16, 97, 97, 52, 52, 59, 59, -86, -86, -102, -102, -47, -47, 19, 19, -30, -30, -53, -53, -30, -30, 89, 89, 50, 50, 38, 38, 60, 60, -138, -138, -12, -12, -146, -146, -75, -75, -22, -22, -28, -28, -37, -37, 105, 105, 52, 52, -55, -55, -18, -18, 117, 117, -3, -3, 68, 68, -98, -98, -93, -93, -50, -50, -122, -122, 69, 69, 4, 4, -83, -83, 102, 102, -91, -91, 60, 60, 60, 60, 104, 104, -56, -56, -132, -132, 24, 24, -127, -127, 122, 122, -90, -90, 108, 108, -88, -88, 130, 130, 8, 8, -37, -37, -101, -101, 142, 142, -98, -98, 164, 164, -60, -60, 24, 24, 15, 15, -72, -72, -73, -73, -142, -142, 153, 153, 25, 25, -21, -21, 59, 59, -141, -141, 138, 138, -25, -25, -68, -68, -150, -150, -48, -48, -80, -80, -88, -88, 54, 54, -148, -148, 135, 135, 138, 138, -43, -43, 145, 145, -92, -92, -30, -30, 109, 109, 38, 38, 22, 22, 159, 159, -130, -130, -17, -17, 50, 50, -51, -51, 48, 48, 33, 33, 92, 92, 19, 19, 28, 28, 60, 60, -36, -36, 127, 127, 20, 20, 47, -132, -132, 18, 18, -136, -136, -26, -26, 137, 137, -62, -62, -46, -46, -18, -18, -42, -42, 135, 135, 112, 112, -112, -112, -130, -130, 107, 107, -17, -17, -100, -100, -26, -26, -72, -72, -108, -108, -6, -6, -110, -110, 59, 59, 84, 84, 168, 168, -156, -156, -36, -36, 148, 148, 13, 13, -126, -126, -76, -76, -93, -93, 78, 78, 80, 80, 74, 74, 145, 145, -108, -108, -127, -127, 124, 124, 98, 98, 90, 90, 135, 135, 82, 82, -108, -108, -32, -32, 24, 24, 69, 69, 124, 124, 48, 48, 50, 50, -78, -78, 157, 157, -70, -70, 12, 12, -36, -36, 109, 109, -23, -23, 153, 153, 115, 115, 42, 42, 100, 100, -147, -147, 85, 85, -12, -12, 79, 79, 78, 78, 102, 102, 63, 63, 82, 82, 58, 58, 80, 80, 120, 120, -133, -133, 43, 43, 132, 132, -166, -166, -66, -66, -13, -13, 42, 42, -151, -151, -78, -78, -142, -142, 142, 142, 83, 83, 119, 119, -145, -166, -166, 94, 94, 62, 62, 184, 184, 8, 8, -108, -108, 0, 0, 18, 18, -140, -140, -118, -118, -90, -90, -13, -13, 30, 30, -175, -175, 49, 49, -115, -115, 164, 164, 18, 18, -18, -18, 144, 144, -80, -80, 134, 134, -48, -48, -117, -117, -85, -85, -117, -117, 148, 148, 49, 49, 0, 0, -10, -10] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, -2*w + 9])] = -1 AL_eigenvalues[ZF.ideal([11, 11, -2*w - 9])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]