/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([100, 10, -10]) primes_array = [ [3, 3, -w + 5],\ [4, 2, 2],\ [7, 7, w - 6],\ [7, 7, -w - 5],\ [11, 11, -w - 3],\ [11, 11, w - 4],\ [17, 17, w + 2],\ [17, 17, w - 3],\ [19, 19, w + 6],\ [19, 19, -w + 7],\ [23, 23, w],\ [23, 23, w - 1],\ [25, 5, -5],\ [29, 29, -2*w + 9],\ [29, 29, 2*w + 7],\ [31, 31, 3*w - 17],\ [53, 53, 3*w - 14],\ [53, 53, -3*w - 11],\ [67, 67, -w - 9],\ [67, 67, w - 10],\ [83, 83, 4*w - 19],\ [83, 83, 7*w - 36],\ [89, 89, 2*w - 3],\ [89, 89, -2*w - 1],\ [97, 97, 3*w - 19],\ [97, 97, -3*w - 16],\ [103, 103, 2*w - 15],\ [103, 103, -2*w - 13],\ [109, 109, -w - 11],\ [109, 109, w - 12],\ [137, 137, -3*w - 7],\ [137, 137, 3*w - 10],\ [157, 157, -4*w + 25],\ [157, 157, 4*w + 21],\ [163, 163, 2*w - 17],\ [163, 163, -2*w - 15],\ [167, 167, 3*w - 8],\ [167, 167, -3*w - 5],\ [169, 13, -13],\ [179, 179, -3*w - 4],\ [179, 179, 3*w - 7],\ [193, 193, 7*w - 40],\ [193, 193, 8*w - 45],\ [197, 197, 3*w - 5],\ [197, 197, -3*w - 2],\ [211, 211, 3*w - 22],\ [211, 211, -3*w - 19],\ [239, 239, 17*w - 89],\ [239, 239, 5*w - 21],\ [251, 251, -4*w - 9],\ [251, 251, 4*w - 13],\ [263, 263, 8*w - 39],\ [263, 263, 11*w - 56],\ [269, 269, 13*w - 67],\ [269, 269, 7*w - 33],\ [283, 283, -w - 17],\ [283, 283, w - 18],\ [307, 307, 2*w - 21],\ [307, 307, -2*w - 19],\ [347, 347, 4*w - 7],\ [347, 347, -4*w - 3],\ [349, 349, 5*w - 33],\ [349, 349, -19*w + 103],\ [353, 353, 21*w - 110],\ [353, 353, 6*w - 25],\ [373, 373, -9*w + 52],\ [373, 373, 12*w - 67],\ [379, 379, 10*w - 57],\ [379, 379, 11*w - 62],\ [383, 383, -7*w + 31],\ [383, 383, -19*w + 99],\ [389, 389, 10*w - 49],\ [389, 389, 13*w - 66],\ [397, 397, -w - 20],\ [397, 397, w - 21],\ [401, 401, 15*w - 77],\ [401, 401, 9*w - 43],\ [421, 421, -7*w + 43],\ [421, 421, 7*w + 36],\ [439, 439, -w - 21],\ [439, 439, w - 22],\ [449, 449, 5*w - 14],\ [449, 449, -5*w - 9],\ [461, 461, 11*w - 54],\ [461, 461, 14*w - 71],\ [491, 491, 5*w - 12],\ [491, 491, -5*w - 7],\ [509, 509, -5*w - 6],\ [509, 509, 5*w - 11],\ [541, 541, 5*w - 36],\ [541, 541, -5*w - 31],\ [547, 547, -3*w - 26],\ [547, 547, 3*w - 29],\ [557, 557, 17*w - 87],\ [557, 557, 11*w - 53],\ [569, 569, -5*w - 1],\ [569, 569, 5*w - 6],\ [577, 577, -w - 24],\ [577, 577, w - 25],\ [587, 587, 7*w - 27],\ [587, 587, -7*w - 20],\ [607, 607, -6*w - 35],\ [607, 607, 6*w - 41],\ [641, 641, 6*w - 17],\ [641, 641, -6*w - 11],\ [647, 647, -8*w - 25],\ [647, 647, 8*w - 33],\ [661, 661, 3*w - 31],\ [661, 661, -3*w - 28],\ [677, 677, -7*w - 18],\ [677, 677, 7*w - 25],\ [691, 691, 2*w - 29],\ [691, 691, -2*w - 27],\ [719, 719, 7*w - 24],\ [719, 719, -7*w - 17],\ [727, 727, 19*w - 105],\ [727, 727, -11*w + 65],\ [733, 733, -w - 27],\ [733, 733, w - 28],\ [743, 743, 11*w - 51],\ [743, 743, -11*w - 40],\ [751, 751, -5*w - 34],\ [751, 751, 5*w - 39],\ [761, 761, 9*w - 38],\ [761, 761, 30*w - 157],\ [769, 769, 9*w + 47],\ [769, 769, -9*w + 56],\ [773, 773, 6*w - 11],\ [773, 773, -6*w - 5],\ [797, 797, -7*w - 15],\ [797, 797, 7*w - 22],\ [809, 809, 15*w - 74],\ [809, 809, 18*w - 91],\ [811, 811, -10*w + 61],\ [811, 811, 10*w + 51],\ [821, 821, -6*w - 1],\ [821, 821, 6*w - 7],\ [827, 827, -9*w - 28],\ [827, 827, 9*w - 37],\ [853, 853, 4*w - 37],\ [853, 853, -4*w - 33],\ [863, 863, 8*w - 29],\ [863, 863, -8*w - 21],\ [877, 877, 21*w - 116],\ [877, 877, -12*w + 71],\ [881, 881, 10*w - 43],\ [881, 881, -31*w + 162],\ [907, 907, -w - 30],\ [907, 907, w - 31],\ [911, 911, 16*w - 79],\ [911, 911, 19*w - 96],\ [919, 919, 19*w - 106],\ [919, 919, -14*w + 81],\ [929, 929, -7*w - 11],\ [929, 929, 7*w - 18],\ [937, 937, 16*w - 91],\ [937, 937, 17*w - 96],\ [941, 941, 21*w - 107],\ [941, 941, 15*w - 73],\ [947, 947, 12*w - 55],\ [947, 947, -12*w - 43],\ [953, 953, 9*w - 35],\ [953, 953, -9*w - 26],\ [983, 983, 7*w - 16],\ [983, 983, -7*w - 9],\ [997, 997, -4*w - 35],\ [997, 997, 4*w - 39],\ [1013, 1013, -9*w - 25],\ [1013, 1013, 9*w - 34],\ [1019, 1019, 17*w - 84],\ [1019, 1019, 20*w - 101],\ [1033, 1033, -w - 32],\ [1033, 1033, w - 33],\ [1039, 1039, 10*w + 53],\ [1039, 1039, -10*w + 63],\ [1049, 1049, 7*w - 13],\ [1049, 1049, -7*w - 6],\ [1051, 1051, 3*w - 37],\ [1051, 1051, -3*w - 34],\ [1063, 1063, 2*w - 35],\ [1063, 1063, -2*w - 33],\ [1087, 1087, 9*w - 59],\ [1087, 1087, -33*w + 179],\ [1091, 1091, 35*w - 183],\ [1091, 1091, 11*w - 47],\ [1093, 1093, 11*w + 57],\ [1093, 1093, -11*w + 68],\ [1097, 1097, 7*w - 10],\ [1097, 1097, -7*w - 3],\ [1109, 1109, 7*w - 9],\ [1109, 1109, -7*w - 2],\ [1117, 1117, -7*w - 44],\ [1117, 1117, 7*w - 51],\ [1123, 1123, -3*w - 35],\ [1123, 1123, 3*w - 38],\ [1181, 1181, 9*w - 31],\ [1181, 1181, -9*w - 22],\ [1193, 1193, 14*w - 65],\ [1193, 1193, -14*w - 51],\ [1213, 1213, -7*w - 45],\ [1213, 1213, 7*w - 52],\ [1237, 1237, -w - 35],\ [1237, 1237, w - 36],\ [1249, 1249, -15*w + 88],\ [1249, 1249, 24*w - 133],\ [1277, 1277, 13*w - 58],\ [1277, 1277, -13*w - 45],\ [1279, 1279, 6*w - 49],\ [1279, 1279, -6*w - 43],\ [1283, 1283, 9*w - 29],\ [1283, 1283, -9*w - 20],\ [1291, 1291, -17*w + 98],\ [1291, 1291, 22*w - 123],\ [1301, 1301, -10*w - 27],\ [1301, 1301, 10*w - 37],\ [1303, 1303, 18*w - 103],\ [1303, 1303, 21*w - 118],\ [1319, 1319, -8*w - 9],\ [1319, 1319, 8*w - 17],\ [1321, 1321, 8*w - 57],\ [1321, 1321, -8*w - 49],\ [1327, 1327, -13*w + 79],\ [1327, 1327, 29*w - 159],\ [1367, 1367, 8*w - 15],\ [1367, 1367, -8*w - 7],\ [1369, 37, -37],\ [1399, 1399, -5*w - 42],\ [1399, 1399, 5*w - 47],\ [1423, 1423, -9*w - 53],\ [1423, 1423, 9*w - 62],\ [1439, 1439, -8*w - 3],\ [1439, 1439, 8*w - 11],\ [1459, 1459, -w - 38],\ [1459, 1459, w - 39],\ [1471, 1471, 25*w - 139],\ [1471, 1471, -17*w + 99],\ [1481, 1481, -11*w - 31],\ [1481, 1481, 11*w - 42],\ [1487, 1487, 8*w - 5],\ [1487, 1487, 8*w - 3],\ [1489, 1489, 5*w - 48],\ [1489, 1489, -5*w - 43],\ [1499, 1499, -12*w - 37],\ [1499, 1499, 12*w - 49],\ [1511, 1511, 21*w - 104],\ [1511, 1511, 24*w - 121],\ [1553, 1553, 11*w - 41],\ [1553, 1553, -11*w - 30],\ [1571, 1571, -15*w - 53],\ [1571, 1571, 15*w - 68],\ [1597, 1597, -3*w - 41],\ [1597, 1597, 3*w - 44],\ [1607, 1607, 17*w - 80],\ [1607, 1607, 32*w - 165],\ [1609, 1609, 11*w - 72],\ [1609, 1609, -40*w + 217],\ [1621, 1621, 13*w + 68],\ [1621, 1621, -13*w + 81],\ [1657, 1657, 9*w - 64],\ [1657, 1657, -9*w - 55],\ [1663, 1663, -6*w - 47],\ [1663, 1663, 6*w - 53],\ [1667, 1667, 12*w - 47],\ [1667, 1667, -12*w - 35],\ [1681, 41, -41],\ [1693, 1693, -12*w + 77],\ [1693, 1693, 12*w + 65],\ [1697, 1697, 27*w - 137],\ [1697, 1697, 21*w - 103],\ [1699, 1699, -w - 41],\ [1699, 1699, w - 42],\ [1723, 1723, 7*w - 57],\ [1723, 1723, -7*w - 50],\ [1741, 1741, -15*w + 91],\ [1741, 1741, 33*w - 181],\ [1777, 1777, -9*w - 56],\ [1777, 1777, 9*w - 65],\ [1783, 1783, -w - 42],\ [1783, 1783, w - 43],\ [1811, 1811, 9*w - 13],\ [1811, 1811, -9*w - 4],\ [1831, 1831, -7*w - 51],\ [1831, 1831, 7*w - 58],\ [1849, 43, -43],\ [1861, 1861, -3*w - 44],\ [1861, 1861, 3*w - 47],\ [1867, 1867, 6*w - 55],\ [1867, 1867, -6*w - 49],\ [1871, 1871, 9*w - 8],\ [1871, 1871, 9*w - 1],\ [1877, 1877, 9*w - 2],\ [1877, 1877, 9*w - 7],\ [1879, 1879, -46*w + 249],\ [1879, 1879, 11*w - 74],\ [1889, 1889, 17*w - 78],\ [1889, 1889, -17*w - 61],\ [1913, 1913, 19*w - 90],\ [1913, 1913, 34*w - 175],\ [1949, 1949, 13*w - 51],\ [1949, 1949, -13*w - 38],\ [1979, 1979, 12*w - 43],\ [1979, 1979, -12*w - 31],\ [1993, 1993, -8*w - 55],\ [1993, 1993, 8*w - 63],\ [1997, 1997, 29*w - 147],\ [1997, 1997, 23*w - 113],\ [2017, 2017, 11*w - 75],\ [2017, 2017, -11*w - 64],\ [2027, 2027, -17*w - 60],\ [2027, 2027, 17*w - 77],\ [2029, 2029, -4*w - 47],\ [2029, 2029, 4*w - 51],\ [2039, 2039, 48*w - 251],\ [2039, 2039, 15*w - 64],\ [2053, 2053, 7*w - 60],\ [2053, 2053, -7*w - 53],\ [2063, 2063, 33*w - 169],\ [2063, 2063, 21*w - 101],\ [2069, 2069, -10*w - 11],\ [2069, 2069, 10*w - 21],\ [2099, 2099, 25*w - 124],\ [2099, 2099, 28*w - 141],\ [2111, 2111, 11*w - 32],\ [2111, 2111, -11*w - 21],\ [2113, 2113, -19*w + 112],\ [2113, 2113, 32*w - 177],\ [2129, 2129, 10*w - 19],\ [2129, 2129, -10*w - 9],\ [2143, 2143, -3*w - 47],\ [2143, 2143, 3*w - 50],\ [2179, 2179, -21*w + 122],\ [2179, 2179, 30*w - 167],\ [2203, 2203, 29*w - 162],\ [2203, 2203, -22*w + 127],\ [2207, 2207, -13*w - 35],\ [2207, 2207, 13*w - 48],\ [2209, 47, -47],\ [2213, 2213, 11*w - 30],\ [2213, 2213, -11*w - 19],\ [2221, 2221, 28*w - 157],\ [2221, 2221, 23*w - 132],\ [2239, 2239, 25*w - 142],\ [2239, 2239, 26*w - 147],\ [2243, 2243, 36*w - 185],\ [2243, 2243, 21*w - 100],\ [2251, 2251, -15*w + 94],\ [2251, 2251, 15*w + 79],\ [2281, 2281, 5*w - 56],\ [2281, 2281, -5*w - 51],\ [2297, 2297, -47*w + 245],\ [2297, 2297, 17*w - 75],\ [2309, 2309, 10*w - 9],\ [2309, 2309, 10*w - 1],\ [2341, 2341, 3*w - 52],\ [2341, 2341, -3*w - 49],\ [2351, 2351, 11*w - 27],\ [2351, 2351, -11*w - 16],\ [2389, 2389, -5*w - 52],\ [2389, 2389, 5*w - 57],\ [2393, 2393, -11*w - 15],\ [2393, 2393, 11*w - 26],\ [2399, 2399, 23*w - 111],\ [2399, 2399, 35*w - 179],\ [2411, 2411, 20*w - 93],\ [2411, 2411, 41*w - 212],\ [2417, 2417, 22*w - 105],\ [2417, 2417, 37*w - 190],\ [2437, 2437, -4*w - 51],\ [2437, 2437, 4*w - 55],\ [2441, 2441, 14*w - 53],\ [2441, 2441, -14*w - 39],\ [2447, 2447, 13*w - 45],\ [2447, 2447, -13*w - 32],\ [2467, 2467, -18*w + 109],\ [2467, 2467, 39*w - 214],\ [2521, 2521, 7*w - 64],\ [2521, 2521, -7*w - 57],\ [2539, 2539, -9*w - 62],\ [2539, 2539, 9*w - 71],\ [2551, 2551, 13*w - 87],\ [2551, 2551, -53*w + 287],\ [2579, 2579, 15*w - 59],\ [2579, 2579, -15*w - 44],\ [2593, 2593, -17*w + 105],\ [2593, 2593, 17*w + 88],\ [2621, 2621, 14*w - 51],\ [2621, 2621, -14*w - 37],\ [2633, 2633, 18*w - 79],\ [2633, 2633, 18*w + 61],\ [2657, 2657, 11*w - 18],\ [2657, 2657, -11*w - 7],\ [2671, 2671, -22*w + 129],\ [2671, 2671, 35*w - 194],\ [2687, 2687, 17*w - 72],\ [2687, 2687, 56*w - 293],\ [2693, 2693, 19*w - 85],\ [2693, 2693, -19*w - 66],\ [2707, 2707, 34*w - 189],\ [2707, 2707, -23*w + 134],\ [2713, 2713, 13*w - 88],\ [2713, 2713, -13*w - 75],\ [2741, 2741, -11*w - 3],\ [2741, 2741, 11*w - 14],\ [2767, 2767, -7*w - 59],\ [2767, 2767, 7*w - 66],\ [2789, 2789, 43*w - 222],\ [2789, 2789, 22*w - 103],\ [2791, 2791, 27*w - 154],\ [2791, 2791, 30*w - 169],\ [2797, 2797, 28*w - 159],\ [2797, 2797, 29*w - 164],\ [2801, 2801, 11*w - 2],\ [2801, 2801, 11*w - 9],\ [2819, 2819, -12*w - 17],\ [2819, 2819, 12*w - 29],\ [2843, 2843, 19*w - 84],\ [2843, 2843, 19*w + 65],\ [2857, 2857, 39*w - 215],\ [2857, 2857, -21*w + 125],\ [2879, 2879, 15*w - 56],\ [2879, 2879, -15*w - 41],\ [2887, 2887, 11*w - 81],\ [2887, 2887, -11*w - 70],\ [2909, 2909, 18*w - 77],\ [2909, 2909, 57*w - 298],\ [2927, 2927, 16*w - 63],\ [2927, 2927, -16*w - 47],\ [2953, 2953, 37*w - 205],\ [2953, 2953, -23*w + 135],\ [2957, 2957, -14*w - 33],\ [2957, 2957, 14*w - 47],\ [2969, 2969, 30*w - 149],\ [2969, 2969, 33*w - 166],\ [2999, 2999, -13*w - 24],\ [2999, 2999, 13*w - 37],\ [3001, 3001, -8*w - 63],\ [3001, 3001, 8*w - 71],\ [3041, 3041, 35*w - 177],\ [3041, 3041, 29*w - 143],\ [3079, 3079, 5*w - 63],\ [3079, 3079, -5*w - 58],\ [3109, 3109, 4*w - 61],\ [3109, 3109, -4*w - 57],\ [3137, 3137, 19*w - 82],\ [3137, 3137, -58*w + 303],\ [3163, 3163, 19*w + 98],\ [3163, 3163, -19*w + 117],\ [3169, 3169, -w - 56],\ [3169, 3169, w - 57],\ [3181, 3181, -17*w + 108],\ [3181, 3181, 17*w + 91],\ [3187, 3187, -14*w - 81],\ [3187, 3187, 14*w - 95],\ [3191, 3191, 24*w - 113],\ [3191, 3191, 45*w - 232],\ [3229, 3229, -9*w - 67],\ [3229, 3229, 9*w - 76],\ [3251, 3251, 15*w - 52],\ [3251, 3251, -15*w - 37],\ [3259, 3259, 6*w - 67],\ [3259, 3259, -6*w - 61],\ [3271, 3271, 2*w - 59],\ [3271, 3271, -2*w - 57],\ [3299, 3299, -12*w - 1],\ [3299, 3299, 12*w - 13],\ [3319, 3319, -21*w + 127],\ [3319, 3319, 45*w - 247],\ [3323, 3323, 12*w - 11],\ [3323, 3323, 12*w - 1],\ [3329, 3329, 13*w - 31],\ [3329, 3329, -13*w - 18],\ [3331, 3331, 3*w - 61],\ [3331, 3331, -3*w - 58],\ [3347, 3347, 12*w - 7],\ [3347, 3347, 12*w - 5],\ [3359, 3359, 32*w - 159],\ [3359, 3359, 35*w - 176],\ [3371, 3371, -59*w + 308],\ [3371, 3371, 20*w - 87],\ [3373, 3373, 9*w - 77],\ [3373, 3373, -9*w - 68],\ [3413, 3413, -17*w - 49],\ [3413, 3413, 17*w - 66],\ [3457, 3457, -59*w + 320],\ [3457, 3457, 16*w - 105],\ [3467, 3467, 13*w - 28],\ [3467, 3467, -13*w - 15],\ [3469, 3469, -20*w + 123],\ [3469, 3469, 20*w + 103],\ [3481, 59, -59],\ [3511, 3511, -63*w + 341],\ [3511, 3511, 15*w - 101],\ [3517, 3517, -w - 59],\ [3517, 3517, w - 60],\ [3527, 3527, 17*w - 65],\ [3527, 3527, -17*w - 48],\ [3533, 3533, 14*w - 39],\ [3533, 3533, -14*w - 25],\ [3541, 3541, 12*w - 89],\ [3541, 3541, -12*w - 77],\ [3557, 3557, 23*w - 105],\ [3557, 3557, -23*w - 82],\ [3559, 3559, -25*w + 147],\ [3559, 3559, 41*w - 227],\ [3583, 3583, -58*w + 315],\ [3583, 3583, 17*w - 110],\ [3617, 3617, 47*w - 242],\ [3617, 3617, 26*w - 123],\ [3623, 3623, -13*w - 11],\ [3623, 3623, 13*w - 24],\ [3631, 3631, -22*w + 133],\ [3631, 3631, 47*w - 258],\ [3637, 3637, -w - 60],\ [3637, 3637, w - 61],\ [3643, 3643, 39*w - 217],\ [3643, 3643, -27*w + 157],\ [3671, 3671, 15*w - 47],\ [3671, 3671, -15*w - 32],\ [3691, 3691, -7*w - 66],\ [3691, 3691, 7*w - 73],\ [3697, 3697, 3*w - 64],\ [3697, 3697, -3*w - 61],\ [3701, 3701, 19*w - 78],\ [3701, 3701, -19*w - 59],\ [3709, 3709, 5*w - 68],\ [3709, 3709, -5*w - 63],\ [3719, 3719, -13*w - 8],\ [3719, 3719, 13*w - 21],\ [3721, 61, -61],\ [3727, 3727, -13*w - 81],\ [3727, 3727, 13*w - 94],\ [3739, 3739, 35*w - 197],\ [3739, 3739, 31*w - 177],\ [3769, 3769, 45*w - 248],\ [3769, 3769, -24*w + 143],\ [3797, 3797, 13*w - 18],\ [3797, 3797, -13*w - 5],\ [3803, 3803, 29*w - 140],\ [3803, 3803, 44*w - 225],\ [3823, 3823, -3*w - 62],\ [3823, 3823, 3*w - 65],\ [3853, 3853, -4*w - 63],\ [3853, 3853, 4*w - 67],\ [3877, 3877, -12*w - 79],\ [3877, 3877, 12*w - 91],\ [3881, 3881, -14*w - 19],\ [3881, 3881, 14*w - 33],\ [3889, 3889, 15*w - 103],\ [3889, 3889, -15*w 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102],\ [9323, 9323, 21*w - 41],\ [9323, 9323, -21*w - 20],\ [9349, 9349, 76*w - 417],\ [9349, 9349, -35*w + 212],\ [9377, 9377, 59*w - 297],\ [9377, 9377, 53*w - 263],\ [9397, 9397, 11*w - 116],\ [9397, 9397, -11*w - 105],\ [9403, 9403, 58*w - 325],\ [9403, 9403, 47*w - 270],\ [9419, 9419, 25*w - 84],\ [9419, 9419, -25*w - 59],\ [9421, 9421, -12*w - 107],\ [9421, 9421, 12*w - 119],\ [9433, 9433, 48*w - 275],\ [9433, 9433, 57*w - 320],\ [9437, 9437, 23*w - 65],\ [9437, 9437, -23*w - 42],\ [9461, 9461, 31*w - 129],\ [9461, 9461, -31*w - 98],\ [9463, 9463, 33*w + 170],\ [9463, 9463, -33*w + 203],\ [9467, 9467, -27*w - 73],\ [9467, 9467, 27*w - 100],\ [9479, 9479, -37*w - 131],\ [9479, 9479, 37*w - 168],\ [9497, 9497, -21*w - 17],\ [9497, 9497, 21*w - 38],\ [9511, 9511, 2*w - 99],\ [9511, 9511, -2*w - 97],\ [9539, 9539, 68*w - 347],\ [9539, 9539, 47*w - 228],\ [9551, 9551, -21*w - 16],\ [9551, 9551, 21*w - 37],\ [9619, 9619, -11*w - 106],\ [9619, 9619, 11*w - 117],\ [9623, 9623, 51*w - 251],\ [9623, 9623, 63*w - 319],\ [9643, 9643, -13*w - 110],\ [9643, 9643, 13*w - 123],\ [9649, 9649, 25*w - 168],\ [9649, 9649, -104*w + 563],\ [9661, 9661, -28*w + 181],\ [9661, 9661, -95*w + 516],\ [9679, 9679, -w - 98],\ [9679, 9679, w - 99],\ [9689, 9689, -30*w - 91],\ [9689, 9689, 30*w - 121],\ [9697, 9697, 19*w - 144],\ [9697, 9697, -19*w - 125],\ [9721, 9721, -5*w - 99],\ [9721, 9721, 5*w - 104],\ [9739, 9739, -35*w + 213],\ [9739, 9739, 79*w - 433],\ [9749, 9749, 23*w - 62],\ [9749, 9749, -23*w - 39],\ [9769, 9769, -21*w - 131],\ [9769, 9769, 21*w - 152],\ [9781, 9781, -7*w - 101],\ [9781, 9781, 7*w - 108],\ [9791, 9791, -21*w - 11],\ [9791, 9791, 21*w - 32],\ [9829, 9829, -4*w - 99],\ [9829, 9829, 4*w - 103],\ [9833, 9833, 21*w - 31],\ [9833, 9833, -21*w - 10],\ [9839, 9839, 25*w - 81],\ [9839, 9839, -25*w - 56],\ [9851, 9851, 29*w - 113],\ [9851, 9851, -29*w - 84],\ [9857, 9857, 38*w - 173],\ [9857, 9857, -38*w - 135],\ [9859, 9859, 29*w + 157],\ [9859, 9859, -29*w + 186],\ [9883, 9883, -103*w + 558],\ [9883, 9883, -26*w + 173],\ [9887, 9887, 48*w - 233],\ [9887, 9887, 69*w - 352],\ [9907, 9907, 2*w - 101],\ [9907, 9907, -2*w - 99],\ [9923, 9923, -39*w - 140],\ [9923, 9923, 39*w - 179],\ [9941, 9941, 26*w - 89],\ [9941, 9941, -26*w - 63],\ [9967, 9967, 19*w - 145],\ [9967, 9967, -19*w - 126]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, 2, 2, 6, -6, 6, -6, 4, 4, 0, 0, -1, 6, -6, 4, 6, -6, 4, 4, -12, 12, -12, 12, 2, 2, -2, -2, 2, 2, -6, 6, 4, 4, 20, 20, 24, -24, -10, -6, 6, 10, 10, 18, -18, -4, -4, -12, 12, 18, -18, -24, 24, -18, 18, -4, -4, 16, 16, 0, 0, 22, 22, 30, -30, -28, -28, 20, 20, 0, 0, 18, -18, -16, -16, 36, -36, -14, -14, -8, -8, -12, 12, 18, -18, 6, -6, -18, 18, 22, 22, 40, 40, -42, 42, 36, -36, 22, 22, -36, 36, -38, -38, -24, 24, -48, 48, 2, 2, 6, -6, 44, 44, -24, 24, -10, -10, -32, -32, 0, 0, -20, -20, -36, 36, -14, -14, -6, 6, 18, -18, 24, -24, 52, 52, 30, -30, -24, 24, -8, -8, 24, -24, 28, 28, 36, -36, 40, 40, 0, 0, 52, 52, -36, 36, 22, 22, 42, -42, 24, -24, -30, 30, 48, -48, 44, 44, 6, -6, -6, 6, -34, -34, -4, -4, 36, -36, 44, 44, -34, -34, 10, 10, -18, 18, -40, -40, -6, 6, 54, -54, 20, 20, 28, 28, 30, -30, -66, 66, 4, 4, 20, 20, 14, 14, 42, -42, -4, -4, -24, 24, -4, -4, 54, -54, 26, 26, -36, 36, -50, -50, 22, 22, 0, 0, -10, -40, -40, 34, 34, 72, -72, -52, -52, 40, 40, -60, 60, -24, 24, -2, -2, -6, 6, 12, -12, 18, -18, 30, -30, -32, -32, -48, 48, 46, 46, 50, 50, 38, 38, -2, -2, -48, 48, 82, -32, -32, -54, 54, -28, -28, -4, -4, -10, -10, -14, -14, 22, 22, -78, 78, 40, 40, -22, -62, -62, 32, 32, -36, 36, -54, 54, 32, 32, -48, 48, -78, 78, -42, 42, 30, -30, 34, 34, 18, -18, -2, -2, 36, -36, -10, -10, -36, 36, -28, -28, 24, -24, 6, -6, 66, -66, 60, -60, -62, -62, -24, 24, 34, 34, -20, -20, 64, 64, -24, 24, 94, 54, -54, -62, -62, -44, -44, -36, 36, -52, -52, -22, -22, -6, 6, 66, -66, -34, -34, -60, 60, -50, -50, -66, 66, -48, 48, -54, 54, 78, -78, -92, -92, -48, 48, 72, -72, 44, 44, -38, -38, 76, 76, -88, -88, 66, -66, -74, -74, 66, -66, -66, 66, -42, 42, -28, -28, -72, 72, -66, 66, 44, 44, 46, 46, -30, 30, -22, -22, 18, -18, 20, 20, -88, -88, -84, 84, -54, 54, 36, -36, -62, -62, -24, 24, -2, -2, -102, 102, -72, 72, 34, 34, 90, -90, 48, -48, 0, 0, 86, 86, -48, 48, -92, -92, 34, 34, -18, 18, -40, -40, -22, -22, 58, 58, 44, 44, -84, 84, -46, -46, 66, -66, 92, 92, -4, -4, -30, 30, -4, -4, 72, -72, 24, -24, 20, 20, 0, 0, -24, 24, -6, 6, -80, -80, -42, 42, -70, -70, -24, 24, -62, -62, 82, -68, -68, -16, -16, 72, -72, 42, -42, 22, 22, 6, -6, 80, 80, 26, 26, -30, 30, 24, -24, -32, -32, 16, 16, -16, -16, 24, -24, 100, 100, -58, -58, -78, 78, -106, -106, 48, -48, -118, -38, -38, 20, 20, -74, -74, 54, -54, 84, -84, -98, -98, -56, -56, 8, 8, 36, -36, -34, -34, 40, 40, 18, -18, -108, 108, 0, 0, -68, -68, -66, 66, 56, 56, 68, 68, -6, 6, -6, 6, -68, -68, 100, 100, -16, -16, -42, 42, 80, 80, -46, -46, -54, 54, 6, -6, -18, 18, 42, -42, -122, -122, -108, 108, -84, 84, 74, 74, 10, 10, -18, 18, 10, 10, -70, -70, -6, 6, 48, -48, -12, 12, 44, 44, 30, -30, 50, 50, -126, 126, -12, 12, -62, -62, -86, -86, 96, -96, -100, -100, 82, 82, 40, 40, -108, 108, 48, -48, -44, -44, 86, 86, -6, 6, 120, -120, 24, -24, 30, -30, -44, -44, 50, 50, -48, 48, 4, 4, -6, 6, -74, -74, 60, -60, -130, -130, -72, 72, -76, -76, 32, 32, -10, -10, 54, -54, 14, 14, -68, -68, -24, 24, -76, -76, 78, -78, 118, 118, 84, -84, -2, 30, -30, -48, 48, -54, 54, 112, 112, 68, 68, -66, 66, -40, -40, -10, -10, 64, 64, -24, 24, 94, 94, 138, -138, -18, 18, -6, 6, -54, 54, -46, -72, 72, -54, 54, 4, 4, -54, 54, 92, 92, 68, 68, -12, 12, -54, 54, 12, -12, -122, -122, -22, -22, -78, 78, 52, 52, -32, -32, 62, 62, 90, -90, -2, -2, -132, 132, -106, -106, -42, 42, -30, 30, -40, -40, -118, -118, 58, 58, 42, -42, -58, -58, 66, -66, -142, -142, -74, -74, -72, 72, -52, -52, 48, -48, 120, -120, 110, 110, -48, 48, -104, -104, 144, -144, 22, 22, -150, 150, 102, -102, -10, -10, 0, 0, -78, 78, -122, -122, -54, 54, -100, -100, 84, -84, -90, 90, -142, -14, -14, 102, -102, -100, -100, 54, -54, -38, -38, -114, 114, -24, 24, 26, 26, 138, -138, 116, 116, 138, -138, -94, -94, 124, 124, 118, 118, -114, 114, -48, 48, -34, -34, -84, 84, 22, 22, 0, 0, 98, 98, -44, -44, 122, 122, -88, -88, -24, 24, 34, 34, 60, -60, -72, 72, 20, 20, 30, -30, -46, -46, 110, 110, -54, 54, -114, 114, -24, 24, -76, -76, -8, -8, -18, 18, 92, 92, -36, 36, -108, 108, 14, 14, -96, 96, 66, -66, -52, -52, -24, 24, 90, -90, 8, 8, -36, 36, -38, -38, 130, 130, 24, -24, -60, 60, 24, -24, -58, -58, -168, 168, -102, 102, -28, -28, -28, -28, -96, 96, 78, -78, -108, 108, -72, 72, 86, 86, 42, -42, 40, 40, -76, -76, -10, -10, -78, 78, 42, -42, 6, -6, 20, 20, 14, 14, -16, -16, 30, -30, 24, -24, -120, 120, -86, -86, -50, -50, 60, -60, -130, -130, -56, -56, 78, -78, 76, 76, 24, -24, 84, -84, 120, -120, -6, 6, -48, 48, -92, -92, 92, 92, -110, -110, 6, -6, -168, 168, -102, 102, -24, 24, 78, -78, 40, 40, 150, -150, -68, -68, 30, -30, -120, 120, 106, 106, -72, 72, -24, 24, 106, 106, -150, 150, -26, -26, 22, 22, -16, -16, -14, -14, -98, -98, 6, -6, -102, 102, -10, -10, 32, 32, -92, -92, -2, -2, -132, 132, -84, 84, -98, -98, -12, 12, -34, -34, -4, -4, 120, -120, 0, 0, -128, -128, 74, 74, 102, -102, 68, 68, -4, -4, -54, 54, 142, 142, 48, -48, -14, -14, -8, -8, -58, -58, 126, -126, 34, 34, 64, 64, 52, 52, -18, 18, -174, 174, -86, -86, -144, 144, -18, 18, -60, 60, 76, 76, -18, 18, -98, -98, -110, -110, -84, 84, -54, 54, -166, -166, -100, -100, -122, -122, 116, 116, -66, 66, 82, 82, -36, 36, -44, -44, -36, 36, -92, -92, -66, 66, 108, -108, 172, 172, -60, 60, -22, -22, 66, -66, -88, -88, -116, -116, -126, 126, -38, -38, 46, 46, 30, -30, -90, 90, -122, -122, -36, 36, -12, 12, -138, 138, 28, 28, 6, -6, -60, 60, 4, 4, 24, -24, -100, -100, 110, 110, 118, 118, -88, -88, -24, 24, -58, -58, 74, 74, 196, 196, 102, -102, -122, -122, -82, -82, 72, -72, 178, 178, -126, 126, -120, 120, -162, 162, -90, 90, 52, 52, -40, -40, 24, -24, -196, -196, 12, -12, 6, -6, 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([4, 2, 2])] = 1 AL_eigenvalues[ZF.ideal([25, 5, -5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]