/* 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([-9, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([441, 21, 21]) primes_array = [ [3, 3, -w + 3],\ [3, 3, -w - 2],\ [4, 2, 2],\ [7, 7, w + 1],\ [7, 7, -w + 2],\ [11, 11, w + 4],\ [11, 11, -w + 5],\ [25, 5, 5],\ [37, 37, 2*w - 1],\ [41, 41, 3*w - 8],\ [41, 41, 3*w + 5],\ [47, 47, -w - 7],\ [47, 47, w - 8],\ [53, 53, -3*w - 4],\ [53, 53, 3*w - 7],\ [67, 67, 4*w - 11],\ [67, 67, 4*w + 7],\ [71, 71, 3*w - 5],\ [71, 71, -3*w - 2],\ [73, 73, -3*w - 11],\ [73, 73, 3*w - 14],\ [83, 83, 3*w - 2],\ [83, 83, 3*w - 1],\ [101, 101, -w - 10],\ [101, 101, w - 11],\ [107, 107, 2*w - 13],\ [107, 107, -2*w - 11],\ [127, 127, 3*w - 16],\ [127, 127, -3*w - 13],\ [137, 137, 6*w - 17],\ [137, 137, 6*w + 11],\ [139, 139, -4*w - 1],\ [139, 139, 4*w - 5],\ [149, 149, 9*w - 29],\ [149, 149, 9*w + 20],\ [151, 151, 8*w + 17],\ [151, 151, 8*w - 25],\ [157, 157, -3*w - 14],\ [157, 157, 3*w - 17],\ [169, 13, -13],\ [173, 173, -w - 13],\ [173, 173, w - 14],\ [181, 181, 7*w - 20],\ [181, 181, 7*w + 13],\ [197, 197, 9*w + 19],\ [197, 197, 9*w - 28],\ [211, 211, 5*w - 7],\ [211, 211, -5*w - 2],\ [223, 223, 3*w - 19],\ [223, 223, -3*w - 16],\ [229, 229, 5*w - 4],\ [229, 229, 5*w - 1],\ [233, 233, -6*w - 7],\ [233, 233, 6*w - 13],\ [263, 263, -w - 16],\ [263, 263, w - 17],\ [269, 269, 6*w - 11],\ [269, 269, -6*w - 5],\ [271, 271, 7*w - 17],\ [271, 271, -7*w - 10],\ [289, 17, -17],\ [293, 293, -4*w - 19],\ [293, 293, 4*w - 23],\ [307, 307, 11*w + 23],\ [307, 307, 11*w - 34],\ [317, 317, -6*w - 1],\ [317, 317, 6*w - 7],\ [337, 337, 3*w - 22],\ [337, 337, -3*w - 19],\ [349, 349, 10*w - 29],\ [349, 349, 10*w + 19],\ [359, 359, 7*w - 32],\ [359, 359, -7*w - 25],\ [361, 19, -19],\ [367, 367, -8*w - 11],\ [367, 367, 8*w - 19],\ [373, 373, 13*w - 41],\ [373, 373, 13*w + 28],\ [379, 379, -3*w - 20],\ [379, 379, 3*w - 23],\ [397, 397, -7*w - 4],\ [397, 397, 7*w - 11],\ [419, 419, 5*w - 28],\ [419, 419, -5*w - 23],\ [433, 433, -7*w - 1],\ [433, 433, 7*w - 8],\ [443, 443, 9*w - 22],\ [443, 443, -9*w - 13],\ [491, 491, 12*w - 35],\ [491, 491, 12*w + 23],\ [509, 509, 9*w - 20],\ [509, 509, -9*w - 11],\ [521, 521, 15*w - 47],\ [521, 521, 15*w + 32],\ [529, 23, -23],\ [571, 571, 13*w - 38],\ [571, 571, 13*w + 25],\ [593, 593, 9*w - 17],\ [593, 593, -9*w - 8],\ [599, 599, 15*w + 31],\ [599, 599, 15*w - 46],\ [601, 601, 10*w - 23],\ [601, 601, -10*w - 13],\ [613, 613, 11*w + 17],\ [613, 613, 11*w - 28],\ [617, 617, -9*w - 7],\ [617, 617, 9*w - 16],\ [619, 619, 3*w - 28],\ [619, 619, -3*w - 25],\ [641, 641, -w - 25],\ [641, 641, w - 26],\ [659, 659, -9*w - 5],\ [659, 659, 9*w - 14],\ [673, 673, -3*w - 26],\ [673, 673, 3*w - 29],\ [677, 677, 9*w - 13],\ [677, 677, -9*w - 4],\ [691, 691, -6*w - 29],\ [691, 691, 6*w - 35],\ [719, 719, -9*w - 1],\ [719, 719, 9*w - 10],\ [733, 733, 9*w - 43],\ [733, 733, -9*w - 34],\ [739, 739, -11*w - 14],\ [739, 739, 11*w - 25],\ [743, 743, 9*w - 2],\ [743, 743, 9*w - 7],\ [751, 751, 13*w + 22],\ [751, 751, 13*w - 35],\ [761, 761, -5*w - 29],\ [761, 761, 5*w - 34],\ [773, 773, 21*w - 68],\ [773, 773, 21*w + 47],\ [787, 787, 3*w - 31],\ [787, 787, -3*w - 28],\ [811, 811, 9*w + 35],\ [811, 811, 9*w - 44],\ [821, 821, 15*w + 28],\ [821, 821, 15*w - 43],\ [823, 823, 6*w - 37],\ [823, 823, -6*w - 31],\ [839, 839, 10*w - 47],\ [839, 839, -10*w - 37],\ [841, 29, -29],\ [863, 863, 2*w - 31],\ [863, 863, -2*w - 29],\ [877, 877, 22*w + 49],\ [877, 877, 22*w - 71],\ [881, 881, 18*w + 37],\ [881, 881, 18*w - 55],\ [887, 887, 21*w - 67],\ [887, 887, 21*w + 46],\ [929, 929, 8*w - 43],\ [929, 929, -8*w - 35],\ [937, 937, 11*w - 19],\ [937, 937, -11*w - 8],\ [941, 941, -4*w - 31],\ [941, 941, 4*w - 35],\ [953, 953, -7*w - 34],\ [953, 953, 7*w - 41],\ [961, 31, -31],\ [971, 971, -12*w - 13],\ [971, 971, 12*w - 25],\ [983, 983, -w - 31],\ [983, 983, w - 32],\ [1009, 1009, 11*w - 16],\ [1009, 1009, -11*w - 5],\ [1033, 1033, 17*w + 32],\ [1033, 1033, 17*w - 49],\ [1039, 1039, -3*w - 32],\ [1039, 1039, 3*w - 35],\ [1061, 1061, 18*w - 53],\ [1061, 1061, 18*w + 35],\ [1063, 1063, 11*w - 13],\ [1063, 1063, -11*w - 2],\ [1069, 1069, -12*w - 43],\ [1069, 1069, 12*w - 55],\ [1103, 1103, 24*w + 53],\ [1103, 1103, 24*w - 77],\ [1109, 1109, 21*w - 65],\ [1109, 1109, 21*w + 44],\ [1117, 1117, 11*w - 7],\ [1117, 1117, 11*w - 4],\ [1151, 1151, -15*w - 23],\ [1151, 1151, 15*w - 38],\ [1163, 1163, 12*w - 19],\ [1163, 1163, -12*w - 7],\ [1181, 1181, -w - 34],\ [1181, 1181, w - 35],\ [1187, 1187, -7*w - 37],\ [1187, 1187, 7*w - 44],\ [1193, 1193, 27*w + 61],\ [1193, 1193, 27*w - 88],\ [1217, 1217, 21*w + 43],\ [1217, 1217, 21*w - 64],\ [1231, 1231, -9*w - 40],\ [1231, 1231, 9*w - 49],\ [1237, 1237, -14*w - 17],\ [1237, 1237, 14*w - 31],\ [1249, 1249, -3*w - 35],\ [1249, 1249, 3*w - 38],\ [1259, 1259, 2*w - 37],\ [1259, 1259, -2*w - 35],\ [1279, 1279, 16*w - 41],\ [1279, 1279, 16*w + 25],\ [1283, 1283, -12*w - 1],\ [1283, 1283, 12*w - 13],\ [1291, 1291, -13*w - 10],\ [1291, 1291, 13*w - 23],\ [1307, 1307, 12*w - 11],\ [1307, 1307, 12*w - 1],\ [1321, 1321, 9*w - 50],\ [1321, 1321, -9*w - 41],\ [1373, 1373, 4*w - 41],\ [1373, 1373, -4*w - 37],\ [1381, 1381, -13*w - 7],\ [1381, 1381, 13*w - 20],\ [1399, 1399, 3*w - 40],\ [1399, 1399, -3*w - 37],\ [1409, 1409, 5*w - 43],\ [1409, 1409, -5*w - 38],\ [1427, 1427, 21*w - 62],\ [1427, 1427, 21*w + 41],\ [1433, 1433, 8*w - 49],\ [1433, 1433, -8*w - 41],\ [1439, 1439, 7*w - 47],\ [1439, 1439, -7*w - 40],\ [1447, 1447, 19*w - 53],\ [1447, 1447, 19*w + 34],\ [1453, 1453, 13*w - 17],\ [1453, 1453, -13*w - 4],\ [1459, 1459, 29*w - 94],\ [1459, 1459, 15*w - 67],\ [1471, 1471, 23*w + 47],\ [1471, 1471, 23*w - 70],\ [1481, 1481, 15*w - 32],\ [1481, 1481, -15*w - 17],\ [1483, 1483, 17*w + 26],\ [1483, 1483, 17*w - 43],\ [1487, 1487, 27*w + 59],\ [1487, 1487, 27*w - 86],\ [1489, 1489, 14*w - 25],\ [1489, 1489, -14*w - 11],\ [1543, 1543, 13*w - 2],\ [1543, 1543, 13*w - 11],\ [1553, 1553, 18*w + 29],\ [1553, 1553, 18*w - 47],\ [1579, 1579, 31*w + 70],\ [1579, 1579, 31*w - 101],\ [1601, 1601, 16*w - 71],\ [1601, 1601, 30*w - 97],\ [1607, 1607, 24*w + 49],\ [1607, 1607, 24*w - 73],\ [1619, 1619, 15*w - 29],\ [1619, 1619, -15*w - 14],\ [1621, 1621, 25*w - 77],\ [1621, 1621, 25*w + 52],\ [1627, 1627, 28*w - 89],\ [1627, 1627, 28*w + 61],\ [1637, 1637, 11*w - 58],\ [1637, 1637, -11*w - 47],\ [1669, 1669, -14*w - 5],\ [1669, 1669, 14*w - 19],\ [1693, 1693, -12*w + 61],\ [1693, 1693, 12*w + 49],\ [1699, 1699, 19*w + 31],\ [1699, 1699, 19*w - 50],\ [1709, 1709, 7*w - 50],\ [1709, 1709, -7*w - 43],\ [1723, 1723, -3*w - 41],\ [1723, 1723, 3*w - 44],\ [1777, 1777, 14*w - 13],\ [1777, 1777, 14*w - 1],\ [1783, 1783, 6*w - 49],\ [1783, 1783, -6*w - 43],\ [1787, 1787, -14*w - 53],\ [1787, 1787, 14*w - 67],\ [1801, 1801, 9*w - 55],\ [1801, 1801, -9*w - 46],\ [1823, 1823, 21*w + 37],\ [1823, 1823, 21*w - 58],\ [1847, 1847, 24*w - 71],\ [1847, 1847, 24*w + 47],\ [1849, 43, -43],\ [1861, 1861, -17*w - 20],\ [1861, 1861, 17*w - 37],\ [1871, 1871, 15*w - 22],\ [1871, 1871, -15*w - 7],\ [1877, 1877, -4*w - 43],\ [1877, 1877, 4*w - 47],\ [1913, 1913, 27*w - 83],\ [1913, 1913, 27*w + 56],\ [1931, 1931, -5*w - 44],\ [1931, 1931, 5*w - 49],\ [1933, 1933, 19*w - 47],\ [1933, 1933, -19*w - 28],\ [1949, 1949, -15*w - 4],\ [1949, 1949, 15*w - 19],\ [1951, 1951, -15*w - 56],\ [1951, 1951, 15*w - 71],\ [1973, 1973, 18*w - 41],\ [1973, 1973, -18*w - 23],\ [1987, 1987, -3*w - 44],\ [1987, 1987, 3*w - 47],\ [1997, 1997, 7*w - 53],\ [1997, 1997, -7*w - 46],\ [1999, 1999, 25*w - 74],\ [1999, 1999, 25*w + 49],\ [2039, 2039, 15*w - 14],\ [2039, 2039, 15*w - 1],\ [2063, 2063, 33*w - 106],\ [2063, 2063, 33*w + 73],\ [2069, 2069, 15*w - 11],\ [2069, 2069, 15*w - 4],\ [2081, 2081, 15*w - 7],\ [2081, 2081, 15*w - 8],\ [2083, 2083, 31*w - 98],\ [2083, 2083, 31*w + 67],\ [2099, 2099, 21*w - 55],\ [2099, 2099, 21*w + 34],\ [2113, 2113, -9*w - 49],\ [2113, 2113, 9*w - 58],\ [2137, 2137, 23*w + 41],\ [2137, 2137, 23*w - 64],\ [2143, 2143, -16*w - 7],\ [2143, 2143, 16*w - 23],\ [2153, 2153, -w - 46],\ [2153, 2153, w - 47],\ [2179, 2179, -20*w - 29],\ [2179, 2179, 20*w - 49],\ [2213, 2213, -18*w - 19],\ [2213, 2213, 18*w - 37],\ [2221, 2221, 9*w - 59],\ [2221, 2221, -9*w - 50],\ [2267, 2267, 2*w - 49],\ [2267, 2267, -2*w - 47],\ [2269, 2269, -3*w - 47],\ [2269, 2269, 3*w - 50],\ [2273, 2273, 21*w + 32],\ [2273, 2273, 21*w - 53],\ [2287, 2287, -16*w - 1],\ [2287, 2287, 16*w - 17],\ [2293, 2293, 17*w - 28],\ [2293, 2293, -17*w - 11],\ [2297, 2297, -17*w - 62],\ [2297, 2297, 17*w - 79],\ [2341, 2341, 15*w + 59],\ [2341, 2341, 15*w - 74],\ [2347, 2347, 19*w - 41],\ [2347, 2347, -19*w - 22],\ [2357, 2357, 21*w - 52],\ [2357, 2357, -21*w - 31],\ [2371, 2371, 6*w - 55],\ [2371, 2371, -6*w - 49],\ [2377, 2377, 29*w + 59],\ [2377, 2377, 29*w - 88],\ [2389, 2389, -12*w - 55],\ [2389, 2389, 12*w - 67],\ [2393, 2393, 16*w - 77],\ [2393, 2393, -16*w - 61],\ [2417, 2417, 33*w - 104],\ [2417, 2417, 33*w + 71],\ [2441, 2441, -w - 49],\ [2441, 2441, w - 50],\ [2467, 2467, 3*w - 52],\ [2467, 2467, -3*w - 49],\ [2543, 2543, 14*w - 73],\ [2543, 2543, -14*w - 59],\ [2549, 2549, 30*w + 61],\ [2549, 2549, 30*w - 91],\ [2557, 2557, -9*w - 53],\ [2557, 2557, 9*w - 62],\ [2579, 2579, 36*w - 115],\ [2579, 2579, 36*w + 79],\ [2591, 2591, 33*w - 103],\ [2591, 2591, 33*w + 70],\ [2593, 2593, 34*w + 73],\ [2593, 2593, 34*w - 107],\ [2617, 2617, 17*w - 16],\ [2617, 2617, 17*w - 1],\ [2657, 2657, -8*w - 53],\ [2657, 2657, 8*w - 61],\ [2663, 2663, 11*w - 67],\ [2663, 2663, -11*w - 56],\ [2671, 2671, 17*w - 10],\ [2671, 2671, 17*w - 7],\ [2689, 2689, -19*w - 16],\ [2689, 2689, 19*w - 35],\ [2711, 2711, 27*w - 77],\ [2711, 2711, 27*w + 50],\ [2713, 2713, -22*w - 31],\ [2713, 2713, 22*w - 53],\ [2729, 2729, -17*w - 65],\ [2729, 2729, 17*w - 82],\ [2731, 2731, 23*w + 35],\ [2731, 2731, 23*w - 58],\ [2741, 2741, 18*w - 25],\ [2741, 2741, -18*w - 7],\ [2749, 2749, 15*w + 62],\ [2749, 2749, -15*w + 77],\ [2791, 2791, 9*w - 64],\ [2791, 2791, -9*w - 55],\ [2801, 2801, 18*w - 23],\ [2801, 2801, -18*w - 5],\ [2803, 2803, -6*w - 53],\ [2803, 2803, 6*w - 59],\ [2819, 2819, 21*w - 46],\ [2819, 2819, -21*w - 25],\ [2833, 2833, -19*w - 13],\ [2833, 2833, 19*w - 32],\ [2837, 2837, 27*w - 76],\ [2837, 2837, 27*w + 49],\ [2861, 2861, 42*w - 137],\ [2861, 2861, 42*w + 95],\ [2879, 2879, 2*w - 55],\ [2879, 2879, -2*w - 53],\ [2887, 2887, -3*w - 53],\ [2887, 2887, 3*w - 56],\ [2897, 2897, -18*w - 1],\ [2897, 2897, 18*w - 19],\ [2927, 2927, 24*w - 61],\ [2927, 2927, 24*w + 37],\ [2939, 2939, 39*w + 86],\ [2939, 2939, 39*w - 125],\ [2953, 2953, 38*w + 83],\ [2953, 2953, 38*w - 121],\ [2957, 2957, 21*w - 44],\ [2957, 2957, -21*w - 23],\ [2963, 2963, 36*w - 113],\ [2963, 2963, 36*w + 77],\ [2969, 2969, -7*w - 55],\ [2969, 2969, 7*w - 62],\ [2971, 2971, 20*w - 37],\ [2971, 2971, -20*w - 17],\ [3001, 3001, 23*w - 55],\ [3001, 3001, -23*w - 32],\ [3023, 3023, -21*w - 22],\ [3023, 3023, 21*w - 43],\ [3037, 3037, 31*w - 92],\ [3037, 3037, 31*w + 61],\ [3041, 3041, 11*w - 70],\ [3041, 3041, -11*w - 59],\ [3061, 3061, 43*w + 97],\ [3061, 3061, 43*w - 140],\ [3067, 3067, 19*w - 26],\ [3067, 3067, -19*w - 7],\ [3083, 3083, 27*w - 74],\ [3083, 3083, 27*w + 47],\ [3109, 3109, 3*w - 58],\ [3109, 3109, -3*w - 55],\ [3119, 3119, -24*w - 35],\ [3119, 3119, 24*w - 59],\ [3181, 3181, 22*w - 47],\ [3181, 3181, -22*w - 25],\ [3191, 3191, 5*w - 61],\ [3191, 3191, -5*w - 56],\ [3203, 3203, 27*w + 46],\ [3203, 3203, 27*w - 73],\ [3209, 3209, -21*w - 19],\ [3209, 3209, 21*w - 40],\ [3229, 3229, -19*w - 1],\ [3229, 3229, 19*w - 20],\ [3253, 3253, -23*w - 29],\ [3253, 3253, 23*w - 52],\ [3257, 3257, 16*w + 67],\ [3257, 3257, -16*w + 83],\ [3259, 3259, 20*w - 31],\ [3259, 3259, -20*w - 11],\ [3319, 3319, 19*w - 14],\ [3319, 3319, 19*w - 5],\ [3323, 3323, -21*w - 17],\ [3323, 3323, 21*w - 38],\ [3329, 3329, -7*w - 58],\ [3329, 3329, 7*w - 65],\ [3331, 3331, 25*w - 62],\ [3331, 3331, -25*w - 37],\ [3371, 3371, -14*w - 65],\ [3371, 3371, 14*w - 79],\ [3407, 3407, -13*w - 64],\ [3407, 3407, 13*w - 77],\ [3413, 3413, -w - 58],\ [3413, 3413, w - 59],\ [3457, 3457, 3*w - 61],\ [3457, 3457, -3*w - 58],\ [3467, 3467, 19*w - 92],\ [3467, 3467, -19*w - 73],\ [3469, 3469, -15*w - 67],\ [3469, 3469, 15*w - 82],\ [3481, 59, -59],\ [3499, 3499, 35*w + 71],\ [3499, 3499, 35*w - 106],\ [3511, 3511, -6*w - 59],\ [3511, 3511, 6*w - 65],\ [3527, 3527, 21*w - 34],\ [3527, 3527, -21*w - 13],\ [3541, 3541, 9*w - 70],\ [3541, 3541, -9*w - 61],\ [3559, 3559, 41*w + 89],\ [3559, 3559, 41*w - 130],\ [3593, 3593, 33*w + 64],\ [3593, 3593, 33*w - 97],\ [3617, 3617, -21*w - 11],\ [3617, 3617, 21*w - 32],\ [3623, 3623, 48*w - 157],\ [3623, 3623, 48*w + 109],\ [3637, 3637, 34*w - 101],\ [3637, 3637, 34*w + 67],\ [3659, 3659, 21*w - 31],\ [3659, 3659, -21*w - 10],\ [3673, 3673, -9*w - 62],\ [3673, 3673, 9*w - 71],\ [3691, 3691, 20*w - 13],\ [3691, 3691, 20*w - 7],\ [3697, 3697, 24*w - 107],\ [3697, 3697, 46*w - 149],\ [3701, 3701, 30*w - 83],\ [3701, 3701, 30*w + 53],\ [3709, 3709, 12*w - 77],\ [3709, 3709, -12*w - 65],\ [3721, 61, -61],\ [3727, 3727, -18*w + 91],\ [3727, 3727, 18*w + 73],\ [3733, 3733, 37*w - 113],\ [3733, 3733, 37*w + 76],\ [3767, 3767, 39*w + 82],\ [3767, 3767, 39*w - 121],\ [3821, 3821, 4*w - 65],\ [3821, 3821, -4*w - 61],\ [3823, 3823, 3*w - 64],\ [3823, 3823, -3*w - 61],\ [3847, 3847, 32*w - 91],\ [3847, 3847, 32*w + 59],\ [3851, 3851, -11*w - 65],\ [3851, 3851, 11*w - 76],\ [3881, 3881, 27*w - 67],\ [3881, 3881, 27*w + 40],\ [3889, 3889, 25*w - 56],\ [3889, 3889, -25*w - 31],\ [3911, 3911, 33*w + 62],\ [3911, 3911, 33*w - 95],\ [3919, 3919, 31*w - 86],\ [3919, 3919, 31*w + 55],\ [3923, 3923, 21*w - 23],\ [3923, 3923, -21*w - 2],\ [3929, 3929, -5*w - 62],\ [3929, 3929, 5*w - 67],\ [3931, 3931, 21*w - 100],\ [3931, 3931, -21*w - 79],\ [3943, 3943, 9*w - 73],\ [3943, 3943, -9*w - 64],\ [3947, 3947, -21*w - 1],\ [3947, 3947, 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-5*w - 92],\ [8699, 8699, 5*w - 97],\ [8707, 8707, 31*w - 2],\ [8707, 8707, 31*w - 29],\ [8731, 8731, 43*w + 70],\ [8731, 8731, 43*w - 113],\ [8741, 8741, -33*w - 20],\ [8741, 8741, 33*w - 53],\ [8753, 8753, 32*w - 151],\ [8753, 8753, -32*w - 119],\ [8779, 8779, 31*w - 5],\ [8779, 8779, 31*w - 26],\ [8803, 8803, 21*w - 124],\ [8803, 8803, -21*w - 103],\ [8807, 8807, 51*w - 149],\ [8807, 8807, 51*w + 98],\ [8831, 8831, 45*w - 122],\ [8831, 8831, 45*w + 77],\ [8839, 8839, -15*w - 97],\ [8839, 8839, 15*w - 112],\ [8887, 8887, 31*w - 14],\ [8887, 8887, 31*w - 17],\ [8929, 8929, -34*w - 25],\ [8929, 8929, 34*w - 59],\ [8933, 8933, 31*w - 149],\ [8933, 8933, -31*w - 118],\ [8951, 8951, -33*w - 17],\ [8951, 8951, 33*w - 50],\ [8963, 8963, -36*w - 37],\ [8963, 8963, 36*w - 73],\ [9001, 9001, -38*w - 47],\ [9001, 9001, 38*w - 85],\ [9007, 9007, -27*w + 139],\ [9007, 9007, 27*w + 112],\ [9029, 9029, 45*w + 76],\ [9029, 9029, 45*w - 121],\ [9049, 9049, 15*w - 113],\ [9049, 9049, -15*w - 98],\ [9091, 9091, 47*w + 83],\ [9091, 9091, 47*w - 130],\ [9103, 9103, 18*w - 119],\ [9103, 9103, -18*w - 101],\ [9109, 9109, -33*w - 122],\ [9109, 9109, 33*w - 155],\ [9127, 9127, 56*w + 113],\ [9127, 9127, 56*w - 169],\ [9151, 9151, 9*w - 104],\ [9151, 9151, -9*w - 95],\ [9173, 9173, 57*w - 173],\ [9173, 9173, 57*w + 116],\ [9187, 9187, 71*w - 229],\ [9187, 9187, 71*w + 158],\ [9203, 9203, 33*w - 46],\ [9203, 9203, -33*w - 13],\ [9209, 9209, -8*w - 95],\ [9209, 9209, 8*w - 103],\ [9239, 9239, 39*w - 89],\ [9239, 9239, -39*w - 50],\ [9241, 9241, 37*w - 77],\ [9241, 9241, -37*w - 40],\ [9257, 9257, 69*w + 152],\ [9257, 9257, 69*w - 221],\ [9277, 9277, 12*w - 109],\ [9277, 9277, -12*w - 97],\ [9283, 9283, 68*w + 149],\ [9283, 9283, 68*w - 217],\ [9323, 9323, 63*w + 134],\ [9323, 9323, 63*w - 197],\ [9349, 9349, 55*w - 164],\ [9349, 9349, 55*w + 109],\ [9371, 9371, -33*w - 10],\ [9371, 9371, 33*w - 43],\ [9377, 9377, -39*w - 49],\ [9377, 9377, 39*w - 88],\ [9391, 9391, 32*w - 7],\ [9391, 9391, 32*w - 25],\ [9397, 9397, -34*w - 19],\ [9397, 9397, 34*w - 53],\ [9409, 97, -97],\ [9419, 9419, 45*w + 74],\ [9419, 9419, 45*w - 119],\ [9431, 9431, 48*w + 85],\ [9431, 9431, 48*w - 133],\ [9439, 9439, 35*w - 61],\ [9439, 9439, -35*w - 26],\ [9461, 9461, 57*w + 115],\ [9461, 9461, 57*w - 172],\ [9463, 9463, 32*w - 19],\ [9463, 9463, 32*w - 13],\ [9473, 9473, 33*w - 41],\ [9473, 9473, -33*w - 8],\ [9479, 9479, 10*w - 107],\ [9479, 9479, -10*w - 97],\ [9497, 9497, -w - 97],\ [9497, 9497, w - 98],\ [9521, 9521, 33*w - 40],\ [9521, 9521, -33*w - 7],\ [9539, 9539, 51*w - 146],\ [9539, 9539, 51*w + 95],\ [9547, 9547, 18*w - 121],\ [9547, 9547, -18*w - 103],\ [9587, 9587, -36*w - 31],\ [9587, 9587, 36*w - 67],\ [9613, 9613, 61*w - 188],\ [9613, 9613, 61*w + 127],\ [9619, 9619, 3*w - 100],\ [9619, 9619, -3*w - 97],\ [9623, 9623, 26*w - 139],\ [9623, 9623, -26*w - 113],\ [9629, 9629, 69*w + 151],\ [9629, 9629, 69*w - 220],\ [9631, 9631, 30*w + 119],\ [9631, 9631, -30*w + 149],\ [9661, 9661, 67*w - 212],\ [9661, 9661, 67*w + 145],\ [9697, 9697, -41*w - 56],\ [9697, 9697, 41*w - 97],\ [9719, 9719, -25*w - 112],\ [9719, 9719, 25*w - 137],\ [9721, 9721, 47*w + 80],\ [9721, 9721, 47*w - 127],\ [9743, 9743, 31*w - 152],\ [9743, 9743, 31*w + 121],\ [9767, 9767, -33*w - 1],\ [9767, 9767, 33*w - 34],\ [9769, 9769, 27*w - 142],\ [9769, 9769, -27*w - 115],\ [9817, 9817, -3*w - 98],\ [9817, 9817, 3*w - 101],\ [9833, 9833, 33*w - 32],\ [9833, 9833, 33*w - 1],\ [9839, 9839, -35*w - 128],\ [9839, 9839, 35*w - 163],\ [9851, 9851, 14*w - 115],\ [9851, 9851, -14*w - 101],\ [9883, 9883, 52*w - 149],\ [9883, 9883, 52*w + 97],\ [9907, 9907, -37*w - 34],\ [9907, 9907, 37*w - 71],\ [9923, 9923, -22*w - 109],\ [9923, 9923, 22*w - 131],\ [9941, 9941, 33*w - 5],\ [9941, 9941, 33*w - 28],\ [9949, 9949, 33*w - 158],\ [9949, 9949, -33*w - 125]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 1, -3, -1, -1, 4, 4, -6, 6, 2, 2, 0, 0, 6, 6, 4, 4, 0, 0, -6, -6, -12, -12, 14, 14, 4, 4, 0, 0, -6, -6, 12, 12, 6, 6, 8, 8, -2, -2, -22, -10, -10, -26, -26, 22, 22, 4, 4, 16, 16, -10, -10, -6, -6, 16, 16, 6, 6, 16, 16, 2, 14, 14, 4, 4, -18, -18, -14, -14, -2, -2, 32, 32, -22, 0, 0, -10, -10, 12, 12, -18, -18, -12, -12, -14, -14, 36, 36, 20, 20, -10, -10, 18, 18, -46, -4, -4, -6, -6, 48, 48, -6, -6, -26, -26, -6, -6, -20, -20, 18, 18, 12, 12, 34, 34, -18, -18, 20, 20, -48, -48, -18, -18, 36, 36, 0, 0, -32, -32, 18, 18, 14, 14, -44, -44, 44, 44, 38, 38, 24, 24, -8, -8, -54, -24, -24, 46, 46, -6, -6, 8, 8, 26, 26, 42, 42, 38, 38, 26, 26, -62, 12, 12, 24, 24, -14, -14, -22, -22, 32, 32, -26, -26, -24, -24, 46, 46, 24, 24, -34, -34, -2, -2, -32, -32, -60, -60, 6, 6, 28, 28, 18, 18, -6, -6, 32, 32, 6, 6, -14, -14, 44, 44, -48, -48, -36, -36, 28, 28, 28, 28, 10, 10, 30, 30, 38, 38, -8, -8, 2, 2, 20, 20, -14, -14, 8, 8, 8, 8, 46, 46, 4, 4, -16, -16, 10, 10, -36, -36, 48, 48, -62, -62, -72, -72, -54, -54, -20, -20, 42, 42, 64, 64, 44, 44, -10, -10, 12, 12, -18, -18, -10, -10, -34, -34, -28, -28, -66, -66, 28, 28, -62, -62, 56, 56, 52, 52, 10, 10, -64, -64, -40, -40, -70, 70, 70, -24, -24, 6, 6, -54, -54, 60, 60, -50, -50, -26, -26, -80, -80, 14, 14, 68, 68, -18, -18, -80, -80, -80, -80, -48, -48, -10, -10, 18, 18, -12, -12, -12, -12, -14, -14, -38, -38, -16, -16, 42, 42, 4, 4, 6, 6, -50, -50, -20, -20, -34, -34, -6, -6, 16, 16, -74, -74, -22, -22, -74, -74, 28, 28, -34, -34, 52, 52, -54, -54, 22, 22, 2, 2, -46, -46, -62, -62, -28, -28, 72, 72, -90, -90, -2, -2, 52, 52, 40, 40, 2, 2, -54, -54, 2, 2, 8, 8, 32, 32, 34, 34, 80, 80, 58, 58, 18, 18, 12, 12, -42, -42, -34, -34, -8, -8, 50, 50, -76, -76, 84, 84, 50, 50, 86, 86, 6, 6, -24, -24, -88, -88, 90, 90, 8, 8, -100, -100, 74, 74, -42, -42, 28, 28, -54, -54, -36, -36, 42, 42, 16, 16, -34, -34, -102, -102, -10, -10, -36, -36, -68, -68, -90, -90, 104, 104, 94, 94, -88, -88, -36, -36, 18, 18, -2, -2, -26, -26, -6, -6, 76, 76, -24, -24, -36, -36, -14, -14, 100, 100, -12, -12, 112, 112, -26, -26, 18, 18, -60, -60, 14, 14, 26, -100, -100, 56, 56, -104, -104, 86, 86, 72, 72, 42, 42, 106, 106, -112, -112, 22, 22, 12, 12, -70, -70, -20, -20, 50, 50, -114, -114, 62, 62, -118, 0, 0, 54, 54, -112, -112, 118, 118, -64, -64, -40, -40, 20, 20, 34, 34, -14, -14, -72, -72, -32, -32, 36, 36, 122, 122, -4, -4, 120, 120, -68, -68, -114, -114, -76, -76, 8, 8, -26, -26, 90, 90, 82, 82, 16, 16, -52, -52, -48, -48, -18, -18, -6, -6, 98, 98, -4, -4, -30, -30, 28, 28, -90, -90, -76, -76, -60, -60, 72, 72, 44, 44, 10, 10, 100, 100, 38, 38, 92, 92, -66, -66, 112, 112, 90, 90, 112, 112, 84, 84, -78, -78, -10, -10, -116, -116, -62, -62, -74, -74, 84, 84, 12, 12, 82, 82, 8, 8, -16, -16, 54, 54, 46, 46, -42, -42, -100, -100, 88, 88, -30, -30, -16, -16, -38, -38, -2, -2, -96, -96, 22, 22, 56, 56, -30, -30, 46, 46, 82, 82, 112, 112, 6, 6, -50, -50, -108, -108, 54, 54, 26, 26, -88, -88, -66, -66, -128, -128, -54, -54, 120, 120, 20, 20, 78, 78, -64, -64, 48, 48, -60, -60, -78, -78, -36, -36, -76, -76, -102, -102, 36, 36, -110, -110, -60, -60, 76, 76, 86, 86, -132, -132, 114, 114, -98, -98, -88, -88, -62, -62, 16, 16, -98, -98, -54, -54, -48, -48, -122, -122, -44, -44, 10, 10, -18, -18, -120, -120, 68, 68, 54, 54, 0, 0, -58, -58, 120, 120, -88, -88, -132, -132, 42, 42, 74, 74, 118, 118, -44, -44, 48, 48, 14, 14, 94, 94, -80, -80, -76, -76, 90, 90, -46, -46, -60, -60, -88, -88, 20, 20, 8, 8, -110, -110, 12, 12, 28, 28, 112, 112, 52, 52, -80, -80, -30, -30, 54, 54, -6, -6, 84, 84, -106, -106, -72, -72, 24, 24, 116, 116, -54, -54, 98, 138, 138, 8, 8, -18, -18, -56, -56, 108, 108, 62, 62, 0, 0, -90, -90, -20, -20, 130, 130, -24, -24, -94, -94, -86, -86, 112, 112, -58, -58, 14, 14, -130, -130, -52, -52, 50, 50, -92, -92, 42, 42, -38, -38, 82, 82, -112, -112, 76, 76, 86, 86, -68, -68, -154, -154, -66, -66, -74, -74, 94, 94, 42, 42, -110, -110, -50, -50, -18, -18, 34, 34, -6, -6, -86, -86, -120, -120, 84, 84, 60, 60, 132, 132, 150, 150, -88, -88, -104, -104, -102, -102, -128, -128, 22, 22, 44, 44, 36, 36, 96, 96, -110, -110, 32, 32, 16, 16, 10, 10, 40, 40, -118, -118, -12, -12, 132, 132, 20, 20, 140, 140, -42, -42, 6, 6, 56, 56, 98, 98, -108, -108, -62, -62, -42, -42, 18, 18, 20, 20, 4, 4, -108, -108, -46, -46, 22, 22, 100, 100, -98, -98, 136, 136, 38, 38, -90, -90, 86, 86, 28, 28, 74, 74, 150, 150, 136, 136, 68, 68, 24, 24, 54, 54, 76, 76, 160, 160, -126, -126, 56, 56, 82, 82, 102, 102, 86, 86, 60, 60, -24, -24, 18, 168, 168, -144, -144, 58, 58, 18, 18, -152, -152, 44, 44, -18, -18, 144, 144, -98, -98, 36, 36, -110, -110, 40, 40, -130, -130, 56, 56, 112, 112, -92, -92, 42, 42, -70, -70, -94, -94, -132, -132, 34, 34, -180, -180, 38, 38, 30, 30, -148, -148, -128, -128, 174, 174, 174, 174, 130, 130, 10, 10, -6, -6, -112, -112, -140, -140, 118, 118, -58, -58, 26, 26, 8, 8, 150, 150, 108, 108, 148, 148, -52, -52, -82, -82, 26, 26, -148, -148, 116, 116, -48, -48, 136, 136, -56, -56, 40, 40, 34, 34, -122, -122, -24, -24, 36, 36, -70, -70, -64, -64, 126, 126, -86, -86, -76, -76, 16, 16, -106, -106, 72, 72, 16, 16, 46, 46, -60, -60, -44, -44, 106, 106, 120, 120, -38, -38, -78, -78, -2, -2, -76, -76, -116, -116, -26, -26, 12, 12, 98, 98, -32, -32, 86, 86, 130, 148, 148, -32, -32, 16, 16, -138, -138, -40, -40, -14, -14, 160, 160, -126, -126, -30, -30, 132, 132, -164, -164, -84, -84, 110, 110, 100, 100, 120, 120, 14, 14, -16, -16, -2, -2, -30, -30, -168, -168, 138, 138, -48, -48, 96, 96, -54, -54, 42, 42, 2, 2, -40, -40, 116, 116, -52, -52, 132, 132, -84, -84, 38, 38, -66, -66] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, -w + 3])] = -1 AL_eigenvalues[ZF.ideal([3, 3, -w - 2])] = -1 AL_eigenvalues[ZF.ideal([7, 7, w + 1])] = 1 AL_eigenvalues[ZF.ideal([7, 7, -w + 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]