/* 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([-21, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7,7,-w + 1]) primes_array = [ [3, 3, w],\ [3, 3, w + 2],\ [4, 2, 2],\ [5, 5, w + 2],\ [7, 7, w],\ [7, 7, w + 6],\ [17, 17, w + 8],\ [19, 19, w + 1],\ [19, 19, w - 2],\ [23, 23, w + 9],\ [23, 23, w + 13],\ [37, 37, w + 11],\ [37, 37, w + 25],\ [59, 59, 3*w + 10],\ [59, 59, 3*w - 13],\ [73, 73, w + 15],\ [73, 73, w + 57],\ [89, 89, -w - 10],\ [89, 89, w - 11],\ [97, 97, w + 22],\ [97, 97, w + 74],\ [101, 101, 3*w - 11],\ [101, 101, -3*w - 8],\ [107, 107, w + 18],\ [107, 107, w + 88],\ [113, 113, w + 28],\ [113, 113, w + 84],\ [121, 11, -11],\ [149, 149, 3*w - 8],\ [149, 149, -3*w - 5],\ [151, 151, -3*w - 17],\ [151, 151, 3*w - 20],\ [163, 163, w + 66],\ [163, 163, w + 96],\ [167, 167, w + 34],\ [167, 167, w + 132],\ [169, 13, -13],\ [173, 173, w + 68],\ [173, 173, w + 104],\ [179, 179, 3*w - 5],\ [179, 179, -3*w - 2],\ [191, 191, 3*w - 2],\ [191, 191, 3*w - 1],\ [193, 193, w + 24],\ [193, 193, w + 168],\ [197, 197, w + 85],\ [197, 197, w + 111],\ [227, 227, w + 26],\ [227, 227, w + 200],\ [229, 229, 3*w - 22],\ [229, 229, -3*w - 19],\ [233, 233, w + 102],\ [233, 233, w + 130],\ [239, 239, 2*w - 19],\ [239, 239, -2*w - 17],\ [251, 251, -w - 16],\ [251, 251, w - 17],\ [271, 271, -3*w - 20],\ [271, 271, 3*w - 23],\ [277, 277, w + 37],\ [277, 277, w + 239],\ [281, 281, 5*w - 31],\ [281, 281, -5*w - 26],\ [283, 283, w + 29],\ [283, 283, w + 253],\ [313, 313, w + 140],\ [313, 313, w + 172],\ [317, 317, w + 134],\ [317, 317, w + 182],\ [331, 331, -4*w - 1],\ [331, 331, 4*w - 5],\ [337, 337, w + 95],\ [337, 337, w + 241],\ [347, 347, w + 49],\ [347, 347, w + 297],\ [349, 349, -5*w - 11],\ [349, 349, 5*w - 16],\ [359, 359, -w - 19],\ [359, 359, w - 20],\ [367, 367, w + 33],\ [367, 367, w + 333],\ [389, 389, 4*w - 29],\ [389, 389, -4*w - 25],\ [397, 397, w + 150],\ [397, 397, w + 246],\ [409, 409, -3*w - 23],\ [409, 409, 3*w - 26],\ [421, 421, -5*w - 8],\ [421, 421, 5*w - 13],\ [461, 461, -5*w - 29],\ [461, 461, 5*w - 34],\ [487, 487, w + 38],\ [487, 487, w + 448],\ [491, 491, 2*w - 25],\ [491, 491, -2*w - 23],\ [503, 503, w + 136],\ [503, 503, w + 366],\ [509, 509, -6*w - 13],\ [509, 509, 6*w - 19],\ [547, 547, w + 52],\ [547, 547, w + 494],\ [569, 569, 6*w - 17],\ [569, 569, -6*w - 11],\ [599, 599, 9*w - 38],\ [599, 599, 9*w + 29],\ [607, 607, w + 252],\ [607, 607, w + 354],\ [617, 617, w + 286],\ [617, 617, w + 330],\ [631, 631, 8*w - 31],\ [631, 631, -8*w - 23],\ [643, 643, w + 191],\ [643, 643, w + 451],\ [653, 653, w + 44],\ [653, 653, w + 608],\ [659, 659, -5*w - 32],\ [659, 659, 5*w - 37],\ [661, 661, 7*w - 23],\ [661, 661, -7*w - 16],\ [673, 673, w + 124],\ [673, 673, w + 548],\ [677, 677, w + 315],\ [677, 677, w + 361],\ [683, 683, w + 45],\ [683, 683, w + 637],\ [701, 701, 6*w - 11],\ [701, 701, -6*w - 5],\ [739, 739, -3*w - 29],\ [739, 739, 3*w - 32],\ [743, 743, w + 268],\ [743, 743, w + 474],\ [761, 761, 6*w - 5],\ [761, 761, 6*w - 1],\ [769, 769, 7*w - 20],\ [769, 769, -7*w - 13],\ [787, 787, w + 287],\ [787, 787, w + 499],\ [823, 823, w + 192],\ [823, 823, w + 630],\ [827, 827, w + 149],\ [827, 827, w + 677],\ [829, 829, -9*w + 55],\ [829, 829, -9*w - 46],\ [841, 29, -29],\ [853, 853, w + 310],\ [853, 853, w + 542],\ [857, 857, w + 389],\ [857, 857, w + 467],\ [859, 859, 7*w - 17],\ [859, 859, -7*w - 10],\ [877, 877, w + 51],\ [877, 877, w + 825],\ [887, 887, w + 343],\ [887, 887, w + 543],\ [907, 907, w + 67],\ [907, 907, w + 839],\ [919, 919, -8*w - 17],\ [919, 919, 8*w - 25],\ [947, 947, w + 53],\ [947, 947, w + 893],\ [961, 31, -31],\ [971, 971, -w - 31],\ [971, 971, w - 32],\ [983, 983, w + 54],\ [983, 983, w + 928],\ [997, 997, w + 151],\ [997, 997, w + 845],\ [1013, 1013, w + 313],\ [1013, 1013, w + 699],\ [1019, 1019, 9*w - 31],\ [1019, 1019, -9*w - 22],\ [1021, 1021, -7*w - 1],\ [1021, 1021, 7*w - 8],\ [1039, 1039, 7*w - 2],\ [1039, 1039, 7*w - 5],\ [1069, 1069, 3*w - 37],\ [1069, 1069, -3*w - 34],\ [1093, 1093, w + 517],\ [1093, 1093, w + 575],\ [1109, 1109, 5*w - 43],\ [1109, 1109, -5*w - 38],\ [1117, 1117, w + 342],\ [1117, 1117, w + 774],\ [1153, 1153, w + 176],\ [1153, 1153, w + 976],\ [1163, 1163, w + 413],\ [1163, 1163, w + 749],\ [1171, 1171, -6*w - 41],\ [1171, 1171, 6*w - 47],\ [1181, 1181, 4*w - 41],\ [1181, 1181, -4*w - 37],\ [1187, 1187, w + 273],\ [1187, 1187, w + 913],\ [1193, 1193, w + 91],\ [1193, 1193, w + 1101],\ [1213, 1213, w + 60],\ [1213, 1213, w + 1152],\ [1217, 1217, w + 357],\ [1217, 1217, w + 859],\ [1249, 1249, 9*w - 59],\ [1249, 1249, -9*w - 50],\ [1259, 1259, 9*w - 26],\ [1259, 1259, -9*w - 17],\ [1279, 1279, 8*w - 13],\ [1279, 1279, -8*w - 5],\ [1291, 1291, 3*w - 40],\ [1291, 1291, -3*w - 37],\ [1297, 1297, w + 505],\ [1297, 1297, w + 791],\ [1301, 1301, -9*w - 16],\ [1301, 1301, 9*w - 25],\ [1303, 1303, w + 466],\ [1303, 1303, w + 836],\ [1361, 1361, 5*w - 46],\ [1361, 1361, -5*w - 41],\ [1367, 1367, w + 293],\ [1367, 1367, w + 1073],\ [1381, 1381, 11*w - 40],\ [1381, 1381, -11*w - 29],\ [1409, 1409, 7*w - 53],\ [1409, 1409, -7*w - 46],\ [1423, 1423, w + 65],\ [1423, 1423, w + 1357],\ [1429, 1429, -12*w + 73],\ [1429, 1429, -12*w - 61],\ [1433, 1433, w + 300],\ [1433, 1433, w + 1132],\ [1471, 1471, 9*w - 61],\ [1471, 1471, -9*w - 52],\ [1481, 1481, 9*w - 20],\ [1481, 1481, -9*w - 11],\ [1493, 1493, w + 468],\ [1493, 1493, w + 1024],\ [1511, 1511, -9*w - 10],\ [1511, 1511, 9*w - 19],\ [1523, 1523, w + 561],\ [1523, 1523, w + 961],\ [1531, 1531, 3*w - 43],\ [1531, 1531, -3*w - 40],\ [1549, 1549, 10*w - 29],\ [1549, 1549, -10*w - 19],\ [1553, 1553, w + 454],\ [1553, 1553, w + 1098],\ [1567, 1567, w + 409],\ [1567, 1567, w + 1157],\ [1579, 1579, -11*w - 26],\ [1579, 1579, 11*w - 37],\ [1619, 1619, -w - 40],\ [1619, 1619, w - 41],\ [1627, 1627, w + 193],\ [1627, 1627, w + 1433],\ [1637, 1637, w + 305],\ [1637, 1637, w + 1331],\ [1663, 1663, w + 397],\ [1663, 1663, w + 1265],\ [1681, 41, -41],\ [1693, 1693, w + 739],\ [1693, 1693, w + 953],\ [1697, 1697, w + 71],\ [1697, 1697, w + 1625],\ [1699, 1699, -13*w - 37],\ [1699, 1699, 13*w - 50],\ [1709, 1709, 9*w - 8],\ [1709, 1709, 9*w - 1],\ [1721, 1721, 9*w - 4],\ [1721, 1721, 9*w - 5],\ [1723, 1723, w + 329],\ [1723, 1723, w + 1393],\ [1759, 1759, -11*w - 23],\ [1759, 1759, 11*w - 34],\ [1789, 1789, 3*w - 46],\ [1789, 1789, -3*w - 43],\ [1801, 1801, 10*w - 23],\ [1801, 1801, -10*w - 13],\ [1811, 1811, -13*w - 67],\ [1811, 1811, 13*w - 80],\ [1847, 1847, w + 324],\ [1847, 1847, w + 1522],\ [1849, 43, -43],\ [1861, 1861, 14*w - 55],\ [1861, 1861, -14*w - 41],\ [1867, 1867, w + 788],\ [1867, 1867, w + 1078],\ [1871, 1871, -w - 43],\ [1871, 1871, w - 44],\ [1873, 1873, w + 178],\ [1873, 1873, w + 1694],\ [1877, 1877, w + 766],\ [1877, 1877, w + 1110],\ [1879, 1879, -3*w - 44],\ [1879, 1879, 3*w - 47],\ [1889, 1889, -8*w - 53],\ [1889, 1889, 8*w - 61],\ [1907, 1907, w + 447],\ [1907, 1907, w + 1459],\ [1933, 1933, w + 228],\ [1933, 1933, w + 1704],\ [1951, 1951, -13*w - 34],\ [1951, 1951, 13*w - 47],\ [2003, 2003, w + 118],\ [2003, 2003, w + 1884],\ [2017, 2017, w + 356],\ [2017, 2017, w + 1660],\ [2039, 2039, -7*w - 52],\ [2039, 2039, 7*w - 59],\ [2063, 2063, w + 653],\ [2063, 2063, w + 1409],\ [2089, 2089, -10*w - 1],\ [2089, 2089, 10*w - 11],\ [2099, 2099, -12*w - 25],\ [2099, 2099, 12*w - 37],\ [2113, 2113, w + 220],\ [2113, 2113, w + 1892],\ [2129, 2129, 15*w - 59],\ [2129, 2129, -15*w - 44],\ [2137, 2137, w + 560],\ [2137, 2137, w + 1576],\ [2141, 2141, -w - 46],\ [2141, 2141, w - 47],\ [2153, 2153, w + 80],\ [2153, 2153, w + 2072],\ [2161, 2161, -3*w - 47],\ [2161, 2161, 3*w - 50],\ [2203, 2203, w + 457],\ [2203, 2203, w + 1745],\ [2207, 2207, w + 81],\ [2207, 2207, w + 2125],\ [2209, 47, -47],\ [2213, 2213, w + 1065],\ [2213, 2213, w + 1147],\ [2237, 2237, w + 680],\ [2237, 2237, w + 1556],\ [2267, 2267, w + 359],\ [2267, 2267, w + 1907],\ [2269, 2269, -12*w - 67],\ [2269, 2269, 12*w - 79],\ [2273, 2273, w + 793],\ [2273, 2273, w + 1479],\ [2311, 2311, 9*w - 68],\ [2311, 2311, -9*w - 59],\ [2357, 2357, w + 497],\ [2357, 2357, w + 1859],\ [2371, 2371, -6*w - 53],\ [2371, 2371, 6*w - 59],\ [2377, 2377, w + 1071],\ [2377, 2377, w + 1305],\ [2381, 2381, -7*w - 55],\ [2381, 2381, 7*w - 62],\ [2383, 2383, w + 327],\ [2383, 2383, w + 2055],\ [2389, 2389, 11*w - 19],\ [2389, 2389, -11*w - 8],\ [2399, 2399, -11*w - 65],\ [2399, 2399, 11*w - 76],\ [2417, 2417, w + 255],\ [2417, 2417, w + 2161],\ [2437, 2437, w + 1175],\ [2437, 2437, w + 1261],\ [2477, 2477, w + 1172],\ [2477, 2477, w + 1304],\ [2531, 2531, -12*w - 17],\ [2531, 2531, 12*w - 29],\ [2543, 2543, w + 133],\ [2543, 2543, w + 2409],\ [2549, 2549, 5*w - 58],\ [2549, 2549, -5*w - 53],\ [2551, 2551, 11*w - 10],\ [2551, 2551, 11*w - 1],\ [2557, 2557, w + 807],\ [2557, 2557, w + 1749],\ [2609, 2609, 8*w - 67],\ [2609, 2609, -8*w - 59],\ [2647, 2647, w + 684],\ [2647, 2647, w + 1962],\ [2657, 2657, w + 1194],\ [2657, 2657, w + 1462],\ [2663, 2663, w + 89],\ [2663, 2663, w + 2573],\ [2671, 2671, 3*w - 55],\ [2671, 2671, -3*w - 52],\ [2683, 2683, w + 347],\ [2683, 2683, w + 2335],\ [2693, 2693, w + 1140],\ [2693, 2693, w + 1552],\ [2699, 2699, -12*w - 13],\ [2699, 2699, 12*w - 25],\ [2711, 2711, -15*w - 38],\ [2711, 2711, 15*w - 53],\ [2713, 2713, w + 950],\ [2713, 2713, w + 1762],\ [2719, 2719, 17*w - 67],\ [2719, 2719, -17*w - 50],\ [2729, 2729, 13*w - 86],\ [2729, 2729, -13*w - 73],\ [2741, 2741, -7*w - 58],\ [2741, 2741, 7*w - 65],\ [2777, 2777, w + 139],\ [2777, 2777, w + 2637],\ [2789, 2789, -17*w + 103],\ [2789, 2789, -17*w - 86],\ [2801, 2801, 15*w - 52],\ [2801, 2801, -15*w - 37],\ [2809, 53, -53],\ [2833, 2833, w + 991],\ [2833, 2833, w + 1841],\ [2887, 2887, w + 426],\ [2887, 2887, w + 2460],\ [2897, 2897, w + 879],\ [2897, 2897, w + 2017],\ [2909, 2909, -4*w - 55],\ [2909, 2909, 4*w - 59],\ [2917, 2917, w + 1411],\ [2917, 2917, w + 1505],\ [2927, 2927, w + 1151],\ [2927, 2927, w + 1775],\ [2939, 2939, -12*w - 5],\ [2939, 2939, 12*w - 17],\ [2953, 2953, w + 829],\ [2953, 2953, w + 2123],\ [2963, 2963, w + 1028],\ [2963, 2963, w + 1934],\ [2971, 2971, 9*w - 73],\ [2971, 2971, -9*w - 64],\ [3001, 3001, 3*w - 58],\ [3001, 3001, -3*w - 55],\ [3011, 3011, -12*w - 1],\ [3011, 3011, 12*w - 13],\ [3023, 3023, w + 731],\ [3023, 3023, w + 2291],\ [3037, 3037, w + 900],\ [3037, 3037, w + 2136],\ [3041, 3041, 18*w - 71],\ [3041, 3041, -18*w - 53],\ [3061, 3061, -17*w - 47],\ [3061, 3061, 17*w - 64],\ [3067, 3067, w + 567],\ [3067, 3067, w + 2499],\ [3079, 3079, -6*w - 59],\ [3079, 3079, 6*w - 65],\ [3083, 3083, w + 372],\ [3083, 3083, w + 2710],\ [3109, 3109, -9*w - 65],\ [3109, 3109, 9*w - 74],\ [3119, 3119, 7*w - 68],\ [3119, 3119, -7*w - 61],\ [3167, 3167, w + 718],\ [3167, 3167, w + 2448],\ [3181, 3181, 12*w - 85],\ [3181, 3181, -12*w - 73],\ [3203, 3203, w + 1311],\ [3203, 3203, w + 1891],\ [3209, 3209, 21*w - 89],\ [3209, 3209, 21*w + 68],\ [3221, 3221, 15*w - 47],\ [3221, 3221, -15*w - 32],\ [3229, 3229, 22*w - 95],\ [3229, 3229, 22*w + 73],\ [3251, 3251, -5*w - 59],\ [3251, 3251, 5*w - 64],\ [3253, 3253, w + 705],\ [3253, 3253, w + 2547],\ [3257, 3257, w + 1282],\ [3257, 3257, w + 1974],\ [3299, 3299, -15*w - 31],\ [3299, 3299, 15*w - 46],\ [3319, 3319, -13*w - 10],\ [3319, 3319, 13*w - 23],\ [3331, 3331, 6*w - 67],\ [3331, 3331, -6*w - 61],\ [3343, 3343, w + 760],\ [3343, 3343, w + 2582],\ [3373, 3373, w + 438],\ [3373, 3373, w + 2934],\ [3391, 3391, -9*w - 67],\ [3391, 3391, 9*w - 76],\ [3407, 3407, w + 154],\ [3407, 3407, w + 3252],\ [3449, 3449, 15*w - 44],\ [3449, 3449, -15*w - 29],\ [3457, 3457, w + 602],\ [3457, 3457, w + 2854],\ [3463, 3463, w + 713],\ [3463, 3463, w + 2749],\ [3469, 3469, -3*w - 59],\ [3469, 3469, 3*w - 62],\ [3511, 3511, -19*w - 55],\ [3511, 3511, 19*w - 74],\ [3533, 3533, w + 685],\ [3533, 3533, w + 2847],\ [3547, 3547, w + 309],\ [3547, 3547, w + 3237],\ [3571, 3571, 13*w - 2],\ [3571, 3571, 13*w - 11],\ [3593, 3593, w + 311],\ [3593, 3593, w + 3281],\ [3607, 3607, w + 1255],\ [3607, 3607, w + 2351],\ [3643, 3643, w + 289],\ [3643, 3643, w + 3353],\ [3659, 3659, 15*w - 41],\ [3659, 3659, -15*w - 26],\ [3671, 3671, -19*w - 97],\ [3671, 3671, -19*w + 116],\ [3677, 3677, w + 160],\ [3677, 3677, w + 3516],\ [3691, 3691, -17*w - 41],\ [3691, 3691, 17*w - 58],\ [3719, 3719, 13*w - 92],\ [3719, 3719, -13*w - 79],\ [3721, 61, -61],\ [3733, 3733, w + 649],\ [3733, 3733, w + 3083],\ [3739, 3739, 20*w - 79],\ [3739, 3739, -20*w - 59],\ [3761, 3761, -w - 61],\ [3761, 3761, w - 62],\ [3767, 3767, w + 604],\ [3767, 3767, w + 3162],\ [3797, 3797, w + 526],\ [3797, 3797, w + 3270],\ [3803, 3803, w + 489],\ [3803, 3803, w + 3313],\ [3821, 3821, -20*w + 121],\ [3821, 3821, -20*w - 101],\ [3847, 3847, w + 934],\ [3847, 3847, w + 2912],\ [3851, 3851, -15*w - 23],\ [3851, 3851, 15*w - 38],\ [3853, 3853, w + 1080],\ [3853, 3853, w + 2772],\ [3889, 3889, 19*w - 71],\ [3889, 3889, -19*w - 52],\ [3907, 3907, w + 1717],\ [3907, 3907, w + 2189],\ [3911, 3911, 15*w - 37],\ [3911, 3911, -15*w - 22],\ [3917, 3917, w + 108],\ [3917, 3917, w + 3808],\ [3919, 3919, 16*w - 47],\ [3919, 3919, -16*w - 31],\ [3929, 3929, 7*w - 74],\ [3929, 3929, -7*w - 67],\ [3931, 3931, 23*w - 97],\ [3931, 3931, 23*w + 74],\ [3947, 3947, w + 1111],\ [3947, 3947, w + 2835],\ [3967, 3967, w + 1564],\ [3967, 3967, w + 2402],\ [4007, 4007, w + 1764],\ [4007, 4007, w + 2242],\ [4021, 4021, -14*w - 5],\ [4021, 4021, 14*w - 19],\ [4057, 4057, w + 142],\ [4057, 4057, w + 3914],\ [4073, 4073, w + 1445],\ [4073, 4073, w + 2627],\ [4079, 4079, -15*w - 19],\ [4079, 4079, 15*w - 34],\ [4099, 4099, 3*w - 67],\ [4099, 4099, -3*w - 64],\ [4129, 4129, 14*w - 13],\ [4129, 4129, 14*w - 1],\ [4139, 4139, -w - 64],\ [4139, 4139, w - 65],\ [4153, 4153, w + 2020],\ [4153, 4153, w + 2132],\ [4177, 4177, w + 1773],\ [4177, 4177, w + 2403],\ [4201, 4201, -22*w - 67],\ [4201, 4201, 22*w - 89],\ [4229, 4229, -15*w - 16],\ [4229, 4229, 15*w - 31],\ [4231, 4231, -3*w - 65],\ [4231, 4231, 3*w - 68],\ [4241, 4241, -13*w - 82],\ [4241, 4241, 13*w - 95],\ [4243, 4243, w + 338],\ [4243, 4243, w + 3904],\ [4253, 4253, w + 437],\ [4253, 4253, w + 3815],\ [4259, 4259, -21*w - 61],\ [4259, 4259, 21*w - 82],\ [4271, 4271, 2*w - 67],\ [4271, 4271, -2*w - 65],\ [4273, 4273, w + 1366],\ [4273, 4273, w + 2906],\ [4339, 4339, 15*w - 103],\ [4339, 4339, -15*w - 88],\ [4357, 4357, w + 1916],\ [4357, 4357, w + 2440],\ [4363, 4363, w + 114],\ [4363, 4363, w + 4248],\ [4397, 4397, w + 175],\ [4397, 4397, w + 4221],\ [4421, 4421, -4*w - 67],\ [4421, 4421, 4*w - 71],\ [4423, 4423, w + 1415],\ [4423, 4423, w + 3007],\ [4441, 4441, -9*w - 74],\ [4441, 4441, 9*w - 83],\ [4447, 4447, w + 1198],\ [4447, 4447, w + 3248],\ [4457, 4457, w + 2170],\ [4457, 4457, w + 2286],\ [4483, 4483, w + 2166],\ [4483, 4483, w + 2316],\ [4489, 67, -67],\ [4493, 4493, w + 1266],\ [4493, 4493, w + 3226],\ [4517, 4517, w + 116],\ [4517, 4517, w + 4400],\ [4567, 4567, w + 692],\ [4567, 4567, w + 3874],\ [4583, 4583, w + 940],\ [4583, 4583, w + 3642],\ [4591, 4591, 19*w - 65],\ [4591, 4591, -19*w - 46],\ [4597, 4597, w + 975],\ [4597, 4597, w + 3621],\ [4639, 4639, -3*w - 68],\ [4639, 4639, 3*w - 71],\ [4649, 4649, -15*w - 4],\ [4649, 4649, 15*w - 19],\ [4663, 4663, w + 908],\ [4663, 4663, w + 3754],\ [4679, 4679, -21*w - 58],\ [4679, 4679, 21*w - 79],\ [4691, 4691, 15*w - 17],\ [4691, 4691, -15*w - 2],\ [4703, 4703, w + 181],\ [4703, 4703, w + 4521],\ [4723, 4723, w + 545],\ [4723, 4723, w + 4177],\ [4733, 4733, w + 418],\ [4733, 4733, w + 4314],\ [4751, 4751, 15*w - 2],\ [4751, 4751, 15*w - 13],\ [4759, 4759, -9*w - 76],\ [4759, 4759, 9*w - 85],\ [4783, 4783, w + 1655],\ [4783, 4783, w + 3127],\ [4787, 4787, w + 920],\ [4787, 4787, w + 3866],\ [4817, 4817, w + 858],\ [4817, 4817, w + 3958],\ [4861, 4861, -12*w - 83],\ [4861, 4861, 12*w - 95],\ [4871, 4871, 5*w - 76],\ [4871, 4871, -5*w - 71],\ [4903, 4903, w + 682],\ [4903, 4903, w + 4220],\ [4909, 4909, -21*w - 109],\ [4909, 4909, 21*w - 130],\ [4931, 4931, -10*w - 79],\ [4931, 4931, 10*w - 89],\ [4933, 4933, w + 2405],\ [4933, 4933, w + 2527],\ [4937, 4937, w + 530],\ [4937, 4937, w + 4406],\ [4951, 4951, -17*w - 26],\ [4951, 4951, 17*w - 43],\ [4957, 4957, w + 157],\ [4957, 4957, w + 4799],\ [4967, 4967, w + 854],\ [4967, 4967, w + 4112],\ [4987, 4987, w + 730],\ [4987, 4987, w + 4256],\ [4993, 4993, w + 533],\ [4993, 4993, w + 4459],\ [4999, 4999, -16*w - 13],\ [4999, 4999, 16*w - 29],\ [5003, 5003, w + 1554],\ [5003, 5003, w + 3448],\ [5011, 5011, 6*w - 79],\ [5011, 5011, -6*w - 73],\ [5041, 71, -71],\ [5051, 5051, 14*w - 103],\ [5051, 5051, -14*w - 89],\ [5077, 5077, w + 123],\ [5077, 5077, w + 4953],\ [5081, 5081, 21*w - 76],\ [5081, 5081, -21*w - 55],\ [5099, 5099, 2*w - 73],\ [5099, 5099, -2*w - 71],\ [5101, 5101, 22*w - 83],\ [5101, 5101, -22*w - 61],\ [5107, 5107, w + 2111],\ [5107, 5107, w + 2995],\ [5119, 5119, -15*w - 92],\ [5119, 5119, 15*w - 107],\ [5189, 5189, 27*w + 88],\ [5189, 5189, 27*w - 115],\ [5197, 5197, w + 2009],\ [5197, 5197, w + 3187],\ [5233, 5233, w + 2428],\ [5233, 5233, w + 2804],\ [5261, 5261, 11*w - 94],\ [5261, 5261, -11*w - 83],\ [5273, 5273, w + 2070],\ [5273, 5273, w + 3202],\ [5279, 5279, -7*w - 76],\ [5279, 5279, 7*w - 83],\ [5297, 5297, w + 549],\ [5297, 5297, w + 4747],\ [5333, 5333, w + 1894],\ [5333, 5333, w + 3438],\ [5351, 5351, 24*w - 95],\ [5351, 5351, -24*w - 71],\ [5381, 5381, -w - 73],\ [5381, 5381, w - 74],\ [5413, 5413, w + 1108],\ [5413, 5413, w + 4304],\ [5417, 5417, w + 1566],\ [5417, 5417, w + 3850],\ [5419, 5419, -9*w - 80],\ [5419, 5419, 9*w - 89],\ [5431, 5431, 16*w - 5],\ [5431, 5431, 16*w - 11],\ [5437, 5437, w + 1498],\ [5437, 5437, w + 3938],\ [5441, 5441, -18*w - 29],\ [5441, 5441, 18*w - 47],\ [5443, 5443, w + 2024],\ [5443, 5443, w + 3418],\ [5449, 5449, -25*w - 76],\ [5449, 5449, 25*w - 101],\ [5477, 5477, w + 853],\ [5477, 5477, w + 4623],\ [5503, 5503, w + 2598],\ [5503, 5503, w + 2904],\ [5521, 5521, 15*w - 109],\ [5521, 5521, -15*w - 94],\ [5573, 5573, w + 1913],\ [5573, 5573, w + 3659],\ [5591, 5591, 22*w - 137],\ [5591, 5591, -22*w - 115],\ [5647, 5647, w + 390],\ [5647, 5647, w + 5256],\ [5659, 5659, 18*w - 121],\ [5659, 5659, -18*w - 103],\ [5669, 5669, 19*w - 125],\ [5669, 5669, -19*w - 106],\ [5683, 5683, w + 1604],\ [5683, 5683, w + 4078],\ [5711, 5711, -21*w - 50],\ [5711, 5711, 21*w - 71],\ [5717, 5717, w + 1235],\ [5717, 5717, w + 4481],\ [5743, 5743, w + 1665],\ [5743, 5743, w + 4077],\ [5779, 5779, 19*w - 53],\ [5779, 5779, -19*w - 34],\ [5783, 5783, w + 1412],\ [5783, 5783, w + 4370],\ [5801, 5801, 11*w - 97],\ [5801, 5801, -11*w - 86],\ [5807, 5807, w + 2040],\ [5807, 5807, w + 3766],\ [5839, 5839, 23*w - 85],\ [5839, 5839, -23*w - 62],\ [5843, 5843, w + 1612],\ [5843, 5843, w + 4230],\ [5849, 5849, -17*w - 101],\ [5849, 5849, 17*w - 118],\ [5861, 5861, 18*w - 41],\ [5861, 5861, -18*w - 23],\ [5869, 5869, 17*w - 25],\ [5869, 5869, -17*w - 8],\ [5881, 5881, 29*w + 95],\ [5881, 5881, 29*w - 124],\ [5923, 5923, w + 2485],\ [5923, 5923, w + 3437],\ [5927, 5927, w + 2248],\ [5927, 5927, w + 3678],\ [5953, 5953, w + 1026],\ [5953, 5953, w + 4926],\ [5987, 5987, w + 2262],\ [5987, 5987, w + 3724],\ [6007, 6007, w + 2743],\ [6007, 6007, w + 3263],\ [6047, 6047, w + 1747],\ [6047, 6047, w + 4299],\ [6101, 6101, -18*w - 19],\ [6101, 6101, 18*w - 37],\ [6113, 6113, w + 135],\ [6113, 6113, w + 5977],\ [6121, 6121, 17*w - 4],\ [6121, 6121, 17*w - 13],\ [6143, 6143, w + 1501],\ [6143, 6143, w + 4641],\ [6217, 6217, w + 2514],\ [6217, 6217, w + 3702],\ [6221, 6221, -4*w - 79],\ [6221, 6221, 4*w - 83],\ [6241, 79, -79],\ [6263, 6263, w + 2028],\ [6263, 6263, w + 4234],\ [6269, 6269, 7*w - 89],\ [6269, 6269, -7*w - 82],\ [6271, 6271, 23*w - 82],\ [6271, 6271, -23*w - 59],\ [6287, 6287, w + 812],\ [6287, 6287, w + 5474],\ [6299, 6299, -w - 79],\ [6299, 6299, w - 80],\ [6311, 6311, 24*w - 89],\ [6311, 6311, -24*w - 65],\ [6317, 6317, w + 1383],\ [6317, 6317, w + 4933],\ [6353, 6353, w + 1454],\ [6353, 6353, w + 4898],\ [6359, 6359, 11*w - 100],\ [6359, 6359, -11*w - 89],\ [6379, 6379, 31*w - 134],\ [6379, 6379, 31*w + 103],\ [6397, 6397, w + 1904],\ [6397, 6397, w + 4492],\ [6451, 6451, -3*w - 80],\ [6451, 6451, 3*w - 83],\ [6469, 6469, 9*w - 95],\ [6469, 6469, -9*w - 86],\ [6481, 6481, 19*w - 44],\ [6481, 6481, -19*w - 25],\ [6529, 6529, 24*w - 149],\ [6529, 6529, -24*w - 125],\ [6571, 6571, -18*w - 107],\ [6571, 6571, 18*w - 125],\ [6581, 6581, 30*w + 97],\ [6581, 6581, 30*w - 127],\ [6607, 6607, w + 2130],\ [6607, 6607, w + 4476],\ [6637, 6637, w + 1450],\ [6637, 6637, w + 5186],\ [6653, 6653, w + 3218],\ [6653, 6653, w + 3434],\ [6679, 6679, 19*w - 41],\ [6679, 6679, -19*w - 22],\ [6689, 6689, 18*w - 23],\ [6689, 6689, -18*w - 5],\ [6703, 6703, w + 1711],\ [6703, 6703, w + 4991],\ [6719, 6719, 21*w - 62],\ [6719, 6719, -21*w - 41],\ [6737, 6737, w + 651],\ [6737, 6737, w + 6085],\ [6763, 6763, w + 1527],\ [6763, 6763, w + 5235],\ [6779, 6779, 5*w - 88],\ [6779, 6779, -5*w - 83],\ [6781, 6781, 3*w - 85],\ [6781, 6781, -3*w - 82],\ [6791, 6791, 7*w - 92],\ [6791, 6791, -7*w - 85],\ [6793, 6793, w + 2191],\ [6793, 6793, w + 4601],\ [6803, 6803, w + 1755],\ [6803, 6803, w + 5047],\ [6823, 6823, w + 1001],\ [6823, 6823, w + 5821],\ [6827, 6827, w + 2143],\ [6827, 6827, w + 4683],\ [6857, 6857, w + 143],\ [6857, 6857, w + 6713],\ [6863, 6863, w + 3179],\ [6863, 6863, w + 3683],\ [6869, 6869, 18*w - 5],\ [6869, 6869, 18*w - 13],\ [6889, 83, -83],\ [6907, 6907, w + 1826],\ [6907, 6907, w + 5080],\ [6911, 6911, 24*w - 85],\ [6911, 6911, -24*w - 61],\ [6947, 6947, w + 2586],\ [6947, 6947, w + 4360],\ [6949, 6949, -3*w - 83],\ [6949, 6949, 3*w - 86],\ [6961, 6961, -25*w - 67],\ [6961, 6961, 25*w - 92],\ [6967, 6967, w + 3203],\ [6967, 6967, w + 3763],\ [6971, 6971, 2*w - 85],\ [6971, 6971, -2*w - 83],\ [6977, 6977, w + 2761],\ [6977, 6977, w + 4215],\ [6991, 6991, -15*w - 101],\ [6991, 6991, 15*w - 116],\ [6997, 6997, w + 3166],\ [6997, 6997, w + 3830],\ [7019, 7019, -21*w - 38],\ [7019, 7019, 21*w - 59],\ [7027, 7027, w + 187],\ [7027, 7027, w + 6839],\ [7039, 7039, 18*w - 127],\ [7039, 7039, -18*w - 109],\ [7043, 7043, w + 3091],\ [7043, 7043, w + 3951],\ [7103, 7103, w + 3065],\ [7103, 7103, w + 4037],\ [7121, 7121, -13*w - 97],\ [7121, 7121, 13*w - 110],\ [7159, 7159, -27*w - 137],\ [7159, 7159, -27*w + 164],\ [7177, 7177, w + 2220],\ [7177, 7177, w + 4956],\ [7213, 7213, w + 1577],\ [7213, 7213, w + 5635],\ [7229, 7229, 4*w - 89],\ [7229, 7229, -4*w - 85],\ [7237, 7237, w + 2487],\ [7237, 7237, w + 4749],\ [7247, 7247, w + 2279],\ [7247, 7247, w + 4967],\ [7253, 7253, w + 2946],\ [7253, 7253, w + 4306],\ [7283, 7283, w + 572],\ [7283, 7283, w + 6710],\ [7307, 7307, w + 678],\ [7307, 7307, w + 6628],\ [7309, 7309, -26*w - 71],\ [7309, 7309, 26*w - 97],\ [7331, 7331, 7*w - 95],\ [7331, 7331, -7*w - 88],\ [7333, 7333, w + 2725],\ [7333, 7333, w + 4607],\ [7369, 7369, 22*w - 65],\ [7369, 7369, -22*w - 43],\ [7411, 7411, -20*w - 23],\ [7411, 7411, 20*w - 43],\ [7417, 7417, w + 882],\ [7417, 7417, w + 6534],\ [7457, 7457, w + 850],\ [7457, 7457, w + 6606],\ [7459, 7459, -23*w - 50],\ [7459, 7459, 23*w - 73],\ [7477, 7477, w + 1958],\ [7477, 7477, w + 5518],\ [7481, 7481, 27*w - 103],\ [7481, 7481, -27*w - 76],\ [7487, 7487, w + 1909],\ [7487, 7487, w + 5577],\ [7489, 7489, -19*w - 4],\ [7489, 7489, 19*w - 23],\ [7499, 7499, 14*w - 115],\ [7499, 7499, -14*w - 101],\ [7507, 7507, w + 1050],\ [7507, 7507, w + 6456],\ [7517, 7517, w + 2064],\ [7517, 7517, w + 5452],\ [7529, 7529, -11*w - 95],\ [7529, 7529, 11*w - 106],\ [7537, 7537, w + 1835],\ [7537, 7537, w + 5701],\ [7549, 7549, 12*w - 109],\ [7549, 7549, -12*w - 97],\ [7561, 7561, -19*w - 1],\ [7561, 7561, 19*w - 20],\ [7577, 7577, w + 529],\ [7577, 7577, w + 7047],\ [7591, 7591, -9*w - 92],\ [7591, 7591, 9*w - 101],\ [7643, 7643, w + 2687],\ [7643, 7643, w + 4955],\ [7649, 7649, 21*w - 52],\ [7649, 7649, -21*w - 31],\ [7669, 7669, 19*w - 8],\ [7669, 7669, 19*w - 11],\ [7673, 7673, w + 3760],\ [7673, 7673, w + 3912],\ [7687, 7687, w + 3512],\ [7687, 7687, w + 4174],\ [7699, 7699, -6*w - 89],\ [7699, 7699, 6*w - 95],\ [7723, 7723, w + 663],\ [7723, 7723, w + 7059],\ [7757, 7757, w + 902],\ [7757, 7757, w + 6854],\ [7793, 7793, w + 666],\ [7793, 7793, w + 7126],\ [7817, 7817, w + 3372],\ [7817, 7817, w + 4444],\ [7823, 7823, w + 3021],\ [7823, 7823, w + 4801],\ [7829, 7829, 19*w - 134],\ [7829, 7829, -19*w - 115],\ [7841, 7841, -5*w - 89],\ [7841, 7841, 5*w - 94],\ [7877, 7877, w + 3861],\ [7877, 7877, w + 4015],\ [7879, 7879, 25*w - 86],\ [7879, 7879, -25*w - 61],\ [7883, 7883, w + 1545],\ [7883, 7883, w + 6337],\ [7901, 7901, -17*w - 110],\ [7901, 7901, 17*w - 127],\ [7927, 7927, w + 2097],\ [7927, 7927, w + 5829],\ [7933, 7933, w + 597],\ [7933, 7933, w + 7335],\ [7963, 7963, w + 2575],\ [7963, 7963, w + 5387],\ [7993, 7993, w + 3454],\ [7993, 7993, w + 4538],\ [8009, 8009, -27*w - 73],\ [8009, 8009, 27*w - 100],\ [8011, 8011, -28*w - 79],\ [8011, 8011, 28*w - 107],\ [8017, 8017, w + 917],\ [8017, 8017, w + 7099],\ [8039, 8039, 21*w - 47],\ [8039, 8039, -21*w - 26],\ [8053, 8053, w + 155],\ [8053, 8053, w + 7897],\ [8059, 8059, 20*w - 31],\ [8059, 8059, -20*w - 11],\ [8087, 8087, w + 2839],\ [8087, 8087, w + 5247],\ [8101, 8101, 15*w - 121],\ [8101, 8101, -15*w - 106],\ [8111, 8111, 21*w - 46],\ [8111, 8111, -21*w - 25],\ [8123, 8123, w + 238],\ [8123, 8123, w + 7884],\ [8161, 8161, -23*w - 44],\ [8161, 8161, 23*w - 67],\ [8167, 8167, w + 2642],\ [8167, 8167, w + 5524],\ [8179, 8179, 9*w - 104],\ [8179, 8179, -9*w - 95],\ [8209, 8209, 35*w + 116],\ [8209, 8209, 35*w - 151],\ [8219, 8219, -23*w - 128],\ [8219, 8219, 23*w - 151],\ [8233, 8233, w + 471],\ [8233, 8233, w + 7761],\ [8273, 8273, w + 3775],\ [8273, 8273, w + 4497],\ [8293, 8293, w + 4067],\ [8293, 8293, w + 4225],\ [8311, 8311, 25*w - 83],\ [8311, 8311, -25*w - 58],\ [8329, 8329, -15*w - 107],\ [8329, 8329, 15*w - 122],\ [8353, 8353, w + 1130],\ [8353, 8353, w + 7222],\ [8387, 8387, w + 2157],\ [8387, 8387, w + 6229],\ [8389, 8389, 12*w - 113],\ [8389, 8389, -12*w - 101],\ [8419, 8419, 20*w - 19],\ [8419, 8419, 20*w - 1],\ [8431, 8431, -31*w - 94],\ [8431, 8431, 31*w - 125],\ [8443, 8443, w + 2895],\ [8443, 8443, w + 5547],\ [8501, 8501, -21*w - 19],\ [8501, 8501, 21*w - 40],\ [8521, 8521, -22*w - 31],\ [8521, 8521, 22*w - 53],\ [8527, 8527, w + 2091],\ [8527, 8527, w + 6435],\ [8537, 8537, w + 244],\ [8537, 8537, w + 8292],\ [8563, 8563, w + 734],\ [8563, 8563, w + 7828],\ [8573, 8573, w + 2788],\ [8573, 8573, w + 5784],\ [8581, 8581, 9*w - 106],\ [8581, 8581, -9*w - 97],\ [8597, 8597, w + 3930],\ [8597, 8597, w + 4666],\ [8647, 8647, w + 988],\ [8647, 8647, w + 7658],\ [8663, 8663, w + 3217],\ [8663, 8663, w + 5445],\ [8669, 8669, -21*w - 16],\ [8669, 8669, 21*w - 37],\ [8677, 8677, w + 1487],\ [8677, 8677, w + 7189],\ [8689, 8689, 34*w + 109],\ [8689, 8689, 34*w - 143],\ [8693, 8693, w + 1523],\ [8693, 8693, w + 7169],\ [8707, 8707, w + 704],\ [8707, 8707, w + 8002],\ [8719, 8719, 21*w - 145],\ [8719, 8719, -21*w - 124],\ [8783, 8783, w + 3740],\ [8783, 8783, w + 5042],\ [8803, 8803, w + 4296],\ [8803, 8803, w + 4506],\ [8819, 8819, 21*w - 34],\ [8819, 8819, -21*w - 13],\ [8821, 8821, -12*w - 103],\ [8821, 8821, 12*w - 115],\ [8831, 8831, -14*w - 107],\ [8831, 8831, 14*w - 121],\ [8837, 8837, w + 3385],\ [8837, 8837, w + 5451],\ [8839, 8839, -6*w - 95],\ [8839, 8839, 6*w - 101],\ [8849, 8849, -27*w - 68],\ [8849, 8849, 27*w - 95],\ [8861, 8861, -29*w - 149],\ [8861, 8861, 29*w - 178],\ [8863, 8863, w + 1164],\ [8863, 8863, w + 7698],\ [8867, 8867, w + 3890],\ [8867, 8867, w + 4976],\ [8929, 8929, 3*w - 97],\ [8929, 8929, -3*w - 94],\ [8941, 8941, -29*w - 80],\ [8941, 8941, 29*w - 109],\ [8951, 8951, 21*w - 31],\ [8951, 8951, -21*w - 10],\ [9001, 9001, 35*w - 148],\ [9001, 9001, 35*w + 113],\ [9007, 9007, w + 972],\ [9007, 9007, w + 8034],\ [9011, 9011, 27*w - 94],\ [9011, 9011, -27*w - 67],\ [9013, 9013, w + 164],\ [9013, 9013, w + 8848],\ [9029, 9029, -21*w - 8],\ [9029, 9029, 21*w - 29],\ [9059, 9059, -7*w - 97],\ [9059, 9059, 7*w - 104],\ [9067, 9067, w + 1154],\ [9067, 9067, w + 7912],\ [9091, 9091, -28*w - 73],\ [9091, 9091, 28*w - 101],\ [9157, 9157, w + 4495],\ [9157, 9157, w + 4661],\ [9161, 9161, 21*w - 25],\ [9161, 9161, -21*w - 4],\ [9173, 9173, w + 642],\ [9173, 9173, w + 8530],\ [9181, 9181, 26*w - 85],\ [9181, 9181, -26*w - 59],\ [9187, 9187, w + 2106],\ [9187, 9187, w + 7080],\ [9199, 9199, 9*w - 109],\ [9199, 9199, -9*w - 100],\ [9203, 9203, w + 498],\ [9203, 9203, w + 8704],\ [9239, 9239, -21*w - 1],\ [9239, 9239, 21*w - 22],\ [9277, 9277, w + 500],\ [9277, 9277, w + 8776],\ [9281, 9281, 21*w - 20],\ [9281, 9281, 21*w - 1],\ [9293, 9293, w + 1705],\ [9293, 9293, w + 7587],\ [9323, 9323, w + 3780],\ [9323, 9323, w + 5542],\ [9341, 9341, 21*w - 5],\ [9341, 9341, 21*w - 16],\ [9343, 9343, w + 4028],\ [9343, 9343, w + 5314],\ [9349, 9349, 23*w - 55],\ [9349, 9349, -23*w - 32],\ [9371, 9371, 21*w - 10],\ [9371, 9371, 21*w - 11],\ [9377, 9377, w + 2992],\ [9377, 9377, w + 6384],\ [9413, 9413, w + 2982],\ [9413, 9413, w + 6430],\ [9419, 9419, -11*w - 104],\ [9419, 9419, 11*w - 115],\ [9431, 9431, 24*w - 65],\ [9431, 9431, -24*w - 41],\ [9439, 9439, 32*w - 127],\ [9439, 9439, -32*w - 95],\ [9461, 9461, 4*w - 101],\ [9461, 9461, -4*w - 97],\ [9463, 9463, w + 1279],\ [9463, 9463, w + 8183],\ [9497, 9497, w + 4619],\ [9497, 9497, w + 4877],\ [9511, 9511, 3*w - 100],\ [9511, 9511, -3*w - 97],\ [9521, 9521, 30*w - 113],\ [9521, 9521, -30*w - 83],\ [9539, 9539, -10*w - 103],\ [9539, 9539, 10*w - 113],\ [9547, 9547, w + 3380],\ [9547, 9547, w + 6166],\ [9601, 9601, -23*w - 29],\ [9601, 9601, 23*w - 52],\ [9631, 9631, 37*w - 158],\ [9631, 9631, 37*w + 121],\ [9689, 9689, -16*w - 115],\ [9689, 9689, 16*w - 131],\ [9697, 9697, w + 1572],\ [9697, 9697, w + 8124],\ [9739, 9739, 15*w - 128],\ [9739, 9739, -15*w - 113],\ [9749, 9749, -13*w - 109],\ [9749, 9749, 13*w - 122],\ [9787, 9787, w + 4689],\ [9787, 9787, w + 5097],\ [9791, 9791, 27*w - 89],\ [9791, 9791, -27*w - 62],\ [9803, 9803, w + 1375],\ [9803, 9803, w + 8427],\ [9811, 9811, -21*w - 128],\ [9811, 9811, 21*w - 149],\ [9833, 9833, w + 4830],\ [9833, 9833, w + 5002],\ [9839, 9839, 24*w - 61],\ [9839, 9839, -24*w - 37],\ [9851, 9851, -29*w - 152],\ [9851, 9851, 29*w - 181],\ [9857, 9857, w + 3977],\ [9857, 9857, w + 5879],\ [9859, 9859, -25*w - 46],\ [9859, 9859, 25*w - 71],\ [9883, 9883, w + 3577],\ [9883, 9883, w + 6305],\ [9887, 9887, w + 2342],\ [9887, 9887, w + 7544],\ [9923, 9923, w + 4658],\ [9923, 9923, w + 5264],\ [9929, 9929, -23*w - 134],\ [9929, 9929, 23*w - 157],\ [9941, 9941, -27*w - 61],\ [9941, 9941, 27*w - 88],\ [9949, 9949, 38*w + 125],\ [9949, 9949, 38*w - 163],\ [9967, 9967, w + 3410],\ [9967, 9967, w + 6556],\ [9973, 9973, w + 2029],\ [9973, 9973, w + 7943]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 + 12*x^6 + 38*x^4 + 13*x^2 + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e^3 - 5*e, e^6 + 12*e^4 + 37*e^2 + 6, -4*e^7 - 47*e^5 - 142*e^3 - 27*e, -e^7 - 12*e^5 - 36*e^3 - 2*e, e^7 + 12*e^5 + 37*e^3 + 7*e, 4*e^7 + 47*e^5 + 142*e^3 + 27*e, -e^4 - 7*e^2 - 1, -2*e^4 - 12*e^2 - 5, -4*e^7 - 48*e^5 - 150*e^3 - 40*e, e^5 + 8*e^3 + 13*e, -3*e^7 - 34*e^5 - 97*e^3 - 8*e, -5*e^7 - 59*e^5 - 178*e^3 - 26*e, 2*e^6 + 28*e^4 + 97*e^2 + 11, e^6 + 12*e^4 + 38*e^2 + 12, 9*e^7 + 107*e^5 + 327*e^3 + 65*e, -e^5 - 2*e^3 + 25*e, 3*e^6 + 31*e^4 + 79*e^2 + 6, 5*e^6 + 59*e^4 + 177*e^2 + 33, -3*e^7 - 35*e^5 - 103*e^3 - 3*e, e^5 + 13*e^3 + 40*e, -3*e^6 - 38*e^4 - 125*e^2 - 33, e^6 + 14*e^4 + 51*e^2 + 5, 2*e^7 + 23*e^5 + 72*e^3 + 39*e, -9*e^7 - 106*e^5 - 323*e^3 - 73*e, 9*e^7 + 104*e^5 + 305*e^3 + 36*e, -5*e^7 - 58*e^5 - 170*e^3 - 21*e, -5*e^6 - 57*e^4 - 166*e^2 - 32, -6*e^6 - 68*e^4 - 196*e^2 - 29, 3*e^6 + 29*e^4 + 70*e^2 + 14, -10*e^6 - 115*e^4 - 338*e^2 - 61, 3*e^6 + 37*e^4 + 119*e^2 + 32, -14*e^7 - 165*e^5 - 501*e^3 - 99*e, e^7 + 13*e^5 + 38*e^3 - 18*e, 17*e^7 + 205*e^5 + 638*e^3 + 138*e, e^7 + 12*e^5 + 41*e^3 + 33*e, -3*e^6 - 28*e^4 - 64*e^2 - 19, 9*e^7 + 110*e^5 + 346*e^3 + 71*e, -8*e^7 - 94*e^5 - 288*e^3 - 76*e, -e^6 - 21*e^4 - 90*e^2 - 10, -e^6 - 7*e^4 - 5*e^2 + 16, 6*e^6 + 69*e^4 + 205*e^2 + 34, -e^6 - 13*e^4 - 43*e^2 - 4, -12*e^7 - 142*e^5 - 432*e^3 - 91*e, 5*e^7 + 55*e^5 + 148*e^3 - 11*e, 7*e^7 + 81*e^5 + 237*e^3 + 16*e, 13*e^7 + 154*e^5 + 475*e^3 + 127*e, -9*e^7 - 107*e^5 - 334*e^3 - 113*e, 9*e^7 + 111*e^5 + 356*e^3 + 92*e, 2*e^6 + 26*e^4 + 88*e^2 + 24, 5*e^6 + 57*e^4 + 165*e^2 + 28, -6*e^7 - 71*e^5 - 213*e^3 - 22*e, 17*e^7 + 203*e^5 + 626*e^3 + 131*e, -2*e^6 - 19*e^4 - 43*e^2 + 4, 7*e^6 + 84*e^4 + 258*e^2 + 46, 3*e^4 + 18*e^2 + 12, 3*e^6 + 31*e^4 + 80*e^2 + 4, -6*e^6 - 74*e^4 - 237*e^2 - 42, -3*e^6 - 34*e^4 - 95*e^2 - 12, 27*e^7 + 319*e^5 + 967*e^3 + 173*e, -4*e^7 - 49*e^5 - 163*e^3 - 75*e, -4*e^6 - 46*e^4 - 135*e^2 - 21, e^6 + 12*e^4 + 30*e^2 - 14, -9*e^7 - 107*e^5 - 324*e^3 - 45*e, -2*e^7 - 23*e^5 - 71*e^3 - 24*e, 10*e^7 + 121*e^5 + 372*e^3 + 52*e, 5*e^7 + 59*e^5 + 187*e^3 + 84*e, -12*e^7 - 141*e^5 - 427*e^3 - 85*e, -7*e^7 - 83*e^5 - 252*e^3 - 38*e, 4*e^6 + 55*e^4 + 185*e^2 + 16, -13*e^6 - 150*e^4 - 443*e^2 - 79, -8*e^7 - 96*e^5 - 298*e^3 - 67*e, 28*e^7 + 331*e^5 + 1010*e^3 + 210*e, 5*e^7 + 58*e^5 + 172*e^3 + 32*e, -29*e^7 - 340*e^5 - 1026*e^3 - 202*e, 5*e^6 + 55*e^4 + 149*e^2 + 19, 6*e^6 + 62*e^4 + 163*e^2 + 27, -10*e^6 - 116*e^4 - 347*e^2 - 61, -e^6 - 7*e^4 - e^2 + 20, 18*e^7 + 217*e^5 + 678*e^3 + 162*e, -6*e^7 - 71*e^5 - 223*e^3 - 90*e, -10*e^6 - 118*e^4 - 354*e^2 - 51, -6*e^6 - 70*e^4 - 213*e^2 - 44, 5*e^7 + 60*e^5 + 194*e^3 + 92*e, -26*e^7 - 308*e^5 - 936*e^3 - 166*e, -5*e^6 - 63*e^4 - 200*e^2 - 27, 3*e^6 + 43*e^4 + 157*e^2 + 37, -5*e^6 - 50*e^4 - 127*e^2 - 45, 2*e^6 + 19*e^4 + 46*e^2 + 36, -2*e^6 - 23*e^4 - 68*e^2 - 5, 4*e^6 + 57*e^4 + 206*e^2 + 60, 9*e^7 + 100*e^5 + 279*e^3 + 21*e, -26*e^7 - 308*e^5 - 940*e^3 - 200*e, 7*e^6 + 75*e^4 + 208*e^2 + 47, -9*e^6 - 105*e^4 - 311*e^2 - 38, -6*e^7 - 65*e^5 - 177*e^3 - 22*e, 24*e^7 + 281*e^5 + 848*e^3 + 177*e, -9*e^6 - 116*e^4 - 376*e^2 - 59, -7*e^6 - 81*e^4 - 248*e^2 - 69, -22*e^7 - 262*e^5 - 799*e^3 - 146*e, -11*e^7 - 125*e^5 - 361*e^3 - 54*e, 11*e^6 + 131*e^4 + 406*e^2 + 91, -10*e^6 - 118*e^4 - 353*e^2 - 80, 8*e^6 + 93*e^4 + 282*e^2 + 62, 7*e^4 + 50*e^2 + 43, -21*e^7 - 250*e^5 - 769*e^3 - 157*e, 16*e^7 + 194*e^5 + 611*e^3 + 146*e, -17*e^7 - 202*e^5 - 616*e^3 - 113*e, -7*e^7 - 82*e^5 - 258*e^3 - 105*e, -5*e^6 - 58*e^4 - 167*e^2 - 17, -4*e^6 - 47*e^4 - 148*e^2 - 53, -25*e^7 - 290*e^5 - 868*e^3 - 182*e, 5*e^7 + 53*e^5 + 137*e^3 - 5*e, -11*e^7 - 129*e^5 - 385*e^3 - 51*e, 3*e^5 + 10*e^3 - 47*e, -2*e^6 - 19*e^4 - 39*e^2 + 8, 6*e^6 + 81*e^4 + 278*e^2 + 53, -3*e^6 - 32*e^4 - 83*e^2 - 7, -5*e^6 - 60*e^4 - 186*e^2 - 9, -5*e^7 - 65*e^5 - 235*e^3 - 144*e, 6*e^7 + 66*e^5 + 188*e^3 + 49*e, 20*e^7 + 233*e^5 + 694*e^3 + 124*e, 12*e^7 + 145*e^5 + 456*e^3 + 116*e, 21*e^7 + 249*e^5 + 753*e^3 + 111*e, 16*e^7 + 186*e^5 + 549*e^3 + 55*e, 4*e^6 + 40*e^4 + 89*e^2 - 25, -4*e^6 - 46*e^4 - 138*e^2 - 24, 4*e^6 + 48*e^4 + 151*e^2 + 27, -8*e^6 - 96*e^4 - 297*e^2 - 49, 30*e^7 + 357*e^5 + 1093*e^3 + 217*e, -3*e^7 - 34*e^5 - 86*e^3 + 56*e, -e^6 - 8*e^4 - 18*e^2 - 14, 3*e^6 + 49*e^4 + 188*e^2 + 19, -3*e^6 - 20*e^4 - 5*e^2 + 32, -2*e^6 - 17*e^4 - 36*e^2 - 31, 2*e^7 + 22*e^5 + 59*e^3 - 8*e, e^5 + 6*e^3 - 17*e, -7*e^7 - 78*e^5 - 215*e^3 - 13*e, -18*e^7 - 208*e^5 - 611*e^3 - 90*e, 42*e^7 + 501*e^5 + 1533*e^3 + 267*e, 10*e^7 + 115*e^5 + 337*e^3 + 55*e, -19*e^6 - 218*e^4 - 639*e^2 - 120, 5*e^6 + 58*e^4 + 182*e^2 + 59, -9*e^6 - 93*e^4 - 247*e^2 - 81, -9*e^7 - 103*e^5 - 315*e^3 - 120*e, -4*e^7 - 52*e^5 - 178*e^3 - 69*e, -9*e^7 - 112*e^5 - 379*e^3 - 183*e, -25*e^7 - 292*e^5 - 865*e^3 - 100*e, -11*e^6 - 141*e^4 - 457*e^2 - 82, 14*e^6 + 173*e^4 + 543*e^2 + 89, -22*e^7 - 259*e^5 - 800*e^3 - 250*e, 4*e^3 + 27*e, -3*e^7 - 35*e^5 - 106*e^3 - 41*e, 5*e^7 + 53*e^5 + 141*e^3 + 21*e, -43*e^7 - 501*e^5 - 1503*e^3 - 302*e, -2*e^7 - 23*e^5 - 80*e^3 - 76*e, 8*e^6 + 83*e^4 + 221*e^2 + 66, -7*e^6 - 62*e^4 - 119*e^2 + 21, 8*e^7 + 95*e^5 + 280*e^3 + e, 15*e^7 + 175*e^5 + 514*e^3 + 57*e, 12*e^6 + 152*e^4 + 494*e^2 + 86, 2*e^6 + 20*e^4 + 54*e^2 + 33, -14*e^6 - 155*e^4 - 440*e^2 - 77, -17*e^7 - 196*e^5 - 570*e^3 - 55*e, -30*e^7 - 353*e^5 - 1074*e^3 - 250*e, -24*e^7 - 290*e^5 - 908*e^3 - 209*e, -e^7 - 7*e^5 + 10*e^3 + 84*e, -5*e^7 - 52*e^5 - 146*e^3 - 78*e, 10*e^7 + 118*e^5 + 355*e^3 + 43*e, -10*e^6 - 106*e^4 - 282*e^2 - 36, -10*e^6 - 109*e^4 - 292*e^2 - 28, 15*e^6 + 188*e^4 + 601*e^2 + 100, 10*e^6 + 127*e^4 + 411*e^2 + 86, -18*e^6 - 221*e^4 - 692*e^2 - 109, -18*e^6 - 197*e^4 - 547*e^2 - 93, -9*e^6 - 96*e^4 - 271*e^2 - 89, 12*e^6 + 151*e^4 + 483*e^2 + 94, -11*e^7 - 129*e^5 - 390*e^3 - 76*e, 3*e^7 + 38*e^5 + 117*e^3 - 27*e, -5*e^6 - 62*e^4 - 198*e^2 - 21, -e^6 - 26*e^4 - 122*e^2 - 37, -37*e^7 - 443*e^5 - 1377*e^3 - 328*e, -6*e^7 - 79*e^5 - 268*e^3 - 67*e, 19*e^7 + 222*e^5 + 673*e^3 + 166*e, 10*e^7 + 119*e^5 + 387*e^3 + 204*e, 10*e^7 + 115*e^5 + 329*e^3 + 5*e, e^7 + 5*e^5 - 21*e^3 - 79*e, -16*e^6 - 171*e^4 - 463*e^2 - 61, -e^6 - 8*e^4 - 18*e^2 - 19, -16*e^6 - 181*e^4 - 527*e^2 - 95, -5*e^6 - 69*e^4 - 248*e^2 - 67, -46*e^7 - 547*e^5 - 1681*e^3 - 367*e, -15*e^7 - 184*e^5 - 586*e^3 - 144*e, 3*e^7 + 39*e^5 + 146*e^3 + 101*e, -17*e^7 - 196*e^5 - 593*e^3 - 183*e, 47*e^7 + 553*e^5 + 1684*e^3 + 369*e, -16*e^7 - 187*e^5 - 566*e^3 - 129*e, 13*e^7 + 151*e^5 + 470*e^3 + 200*e, -5*e^7 - 54*e^5 - 131*e^3 + 71*e, -12*e^6 - 141*e^4 - 426*e^2 - 107, 7*e^6 + 79*e^4 + 230*e^2 + 78, e^6 + 19*e^4 + 92*e^2 + 74, -3*e^6 - 23*e^4 - 34*e^2 - 14, -9*e^6 - 108*e^4 - 338*e^2 - 94, 12*e^6 + 129*e^4 + 346*e^2 + 59, -6*e^6 - 63*e^4 - 164*e^2, 2*e^6 + 12*e^4 - 2*e^2 - 40, 34*e^7 + 407*e^5 + 1255*e^3 + 235*e, 8*e^7 + 105*e^5 + 370*e^3 + 176*e, -20*e^6 - 232*e^4 - 690*e^2 - 121, 5*e^6 + 56*e^4 + 165*e^2 + 21, 35*e^7 + 416*e^5 + 1274*e^3 + 279*e, -10*e^7 - 114*e^5 - 330*e^3 - 50*e, 6*e^6 + 44*e^4 + 48*e^2 - 23, -3*e^6 - 38*e^4 - 138*e^2 - 76, -19*e^7 - 218*e^5 - 638*e^3 - 91*e, e^5 - 11*e^3 - 114*e, e^6 + 7*e^4 - e^2 - 30, 13*e^6 + 149*e^4 + 437*e^2 + 38, 15*e^6 + 151*e^4 + 384*e^2 + 98, 22*e^6 + 257*e^4 + 777*e^2 + 152, -53*e^7 - 629*e^5 - 1927*e^3 - 405*e, 7*e^7 + 72*e^5 + 167*e^3 - 82*e, -7*e^6 - 107*e^4 - 405*e^2 - 105, -5*e^6 - 61*e^4 - 192*e^2 - 41, -32*e^7 - 375*e^5 - 1121*e^3 - 172*e, 36*e^7 + 429*e^5 + 1316*e^3 + 254*e, -13*e^6 - 174*e^4 - 590*e^2 - 97, 9*e^6 + 101*e^4 + 283*e^2 + 43, 2*e^6 - 3*e^4 - 94*e^2 - 47, 16*e^6 + 204*e^4 + 667*e^2 + 131, 20*e^7 + 233*e^5 + 703*e^3 + 151*e, 4*e^7 + 55*e^5 + 197*e^3 + 62*e, -10*e^6 - 121*e^4 - 381*e^2 - 93, 17*e^6 + 223*e^4 + 747*e^2 + 148, 10*e^7 + 123*e^5 + 393*e^3 + 106*e, 20*e^7 + 236*e^5 + 731*e^3 + 206*e, 10*e^6 + 141*e^4 + 503*e^2 + 119, -2*e^6 - 31*e^4 - 125*e^2 - 49, -e^6 - 3*e^4 + 19*e^2 - 19, 2*e^6 + 37*e^4 + 156*e^2 + 81, -6*e^7 - 71*e^5 - 212*e^3 - 6*e, -20*e^7 - 232*e^5 - 683*e^3 - 75*e, 28*e^7 + 331*e^5 + 1001*e^3 + 186*e, -7*e^5 - 67*e^3 - 157*e, 4*e^6 + 40*e^4 + 100*e^2 + 29, 2*e^6 + 23*e^4 + 67*e^2 - 4, -25*e^6 - 279*e^4 - 797*e^2 - 153, 22*e^6 + 252*e^4 + 731*e^2 + 111, 20*e^7 + 240*e^5 + 749*e^3 + 197*e, -34*e^7 - 404*e^5 - 1228*e^3 - 205*e, -25*e^7 - 304*e^5 - 947*e^3 - 170*e, 12*e^7 + 138*e^5 + 417*e^3 + 144*e, -31*e^7 - 379*e^5 - 1207*e^3 - 338*e, 5*e^7 + 62*e^5 + 202*e^3 + 86*e, 21*e^6 + 242*e^4 + 720*e^2 + 101, -15*e^7 - 173*e^5 - 516*e^3 - 122*e, 23*e^7 + 271*e^5 + 837*e^3 + 260*e, 29*e^7 + 343*e^5 + 1055*e^3 + 294*e, -27*e^7 - 307*e^5 - 885*e^3 - 107*e, 22*e^6 + 260*e^4 + 799*e^2 + 146, 6*e^6 + 67*e^4 + 185*e^2 + 24, -5*e^6 - 54*e^4 - 139*e^2 - 30, 14*e^6 + 150*e^4 + 402*e^2 + 41, 19*e^6 + 219*e^4 + 648*e^2 + 115, 8*e^6 + 99*e^4 + 319*e^2 + 105, 20*e^7 + 241*e^5 + 757*e^3 + 207*e, 25*e^7 + 300*e^5 + 937*e^3 + 253*e, -28*e^6 - 325*e^4 - 972*e^2 - 170, -16*e^6 - 163*e^4 - 419*e^2 - 97, 12*e^6 + 119*e^4 + 286*e^2 - 11, -7*e^6 - 71*e^4 - 175*e^2 - 31, -16*e^6 - 188*e^4 - 550*e^2 - 61, -17*e^6 - 198*e^4 - 594*e^2 - 141, -4*e^6 - 55*e^4 - 206*e^2 - 98, -14*e^6 - 148*e^4 - 386*e^2 - 15, 15*e^7 + 179*e^5 + 572*e^3 + 216*e, 27*e^7 + 318*e^5 + 958*e^3 + 145*e, -2*e^6 - 29*e^4 - 99*e^2 + 8, -23*e^6 - 276*e^4 - 851*e^2 - 126, -10*e^6 - 145*e^4 - 519*e^2 - 107, -64*e^7 - 762*e^5 - 2332*e^3 - 456*e, 8*e^7 + 87*e^5 + 225*e^3 - 36*e, e^6 + 37*e^4 + 190*e^2 + 31, -7*e^6 - 68*e^4 - 172*e^2 - 69, 15*e^7 + 175*e^5 + 516*e^3 + 52*e, 12*e^7 + 147*e^5 + 471*e^3 + 157*e, 41*e^7 + 479*e^5 + 1440*e^3 + 300*e, -27*e^7 - 325*e^5 - 1022*e^3 - 286*e, -25*e^6 - 277*e^4 - 787*e^2 - 135, 3*e^6 + 16*e^4 - 10*e^2 - 13, 3*e^6 + 23*e^4 + 28*e^2 - 22, 19*e^6 + 224*e^4 + 682*e^2 + 132, -3*e^7 - 30*e^5 - 77*e^3 - 17*e, -11*e^7 - 131*e^5 - 402*e^3 - 84*e, 66*e^7 + 776*e^5 + 2355*e^3 + 486*e, 42*e^7 + 498*e^5 + 1531*e^3 + 371*e, 6*e^6 + 67*e^4 + 196*e^2 + 32, 5*e^6 + 58*e^4 + 157*e^2 - 44, -18*e^7 - 203*e^5 - 588*e^3 - 112*e, 30*e^7 + 355*e^5 + 1080*e^3 + 191*e, -59*e^7 - 710*e^5 - 2210*e^3 - 501*e, 58*e^7 + 677*e^5 + 2033*e^3 + 392*e, 3*e^6 + 29*e^4 + 81*e^2 + 55, -23*e^6 - 266*e^4 - 778*e^2 - 145, 30*e^7 + 360*e^5 + 1113*e^3 + 219*e, -26*e^7 - 319*e^5 - 1028*e^3 - 324*e, -e^6 - 20*e^4 - 85*e^2 + 44, 5*e^6 + 48*e^4 + 104*e^2 + 6, -22*e^6 - 254*e^4 - 750*e^2 - 158, -26*e^6 - 300*e^4 - 886*e^2 - 132, -48*e^7 - 577*e^5 - 1778*e^3 - 318*e, 50*e^7 + 580*e^5 + 1730*e^3 + 341*e, -20*e^6 - 230*e^4 - 677*e^2 - 107, 8*e^6 + 78*e^4 + 180*e^2 + 5, -27*e^7 - 328*e^5 - 1050*e^3 - 336*e, -8*e^7 - 94*e^5 - 278*e^3 - 14*e, -10*e^6 - 118*e^4 - 346*e^2 - 16, -10*e^6 - 132*e^4 - 436*e^2 - 62, 63*e^7 + 736*e^5 + 2206*e^3 + 384*e, -15*e^7 - 177*e^5 - 535*e^3 - 112*e, 21*e^6 + 250*e^4 + 771*e^2 + 129, 23*e^6 + 252*e^4 + 699*e^2 + 117, 24*e^7 + 286*e^5 + 861*e^3 + 85*e, 31*e^7 + 369*e^5 + 1133*e^3 + 256*e, -16*e^7 - 191*e^5 - 598*e^3 - 165*e, -32*e^7 - 382*e^5 - 1167*e^3 - 169*e, -10*e^6 - 108*e^4 - 294*e^2 - 21, -5*e^7 - 65*e^5 - 209*e^3 + 7*e, -49*e^7 - 584*e^5 - 1783*e^3 - 327*e, 18*e^7 + 218*e^5 + 688*e^3 + 176*e, -58*e^7 - 673*e^5 - 2001*e^3 - 348*e, 20*e^7 + 237*e^5 + 710*e^3 + 91*e, -38*e^7 - 450*e^5 - 1360*e^3 - 210*e, 15*e^6 + 172*e^4 + 497*e^2 + 45, 26*e^6 + 289*e^4 + 816*e^2 + 108, 20*e^7 + 231*e^5 + 698*e^3 + 193*e, -18*e^7 - 217*e^5 - 691*e^3 - 216*e, -8*e^6 - 93*e^4 - 272*e^2 - 30, 9*e^6 + 132*e^4 + 471*e^2 + 70, 34*e^7 + 415*e^5 + 1321*e^3 + 373*e, -63*e^7 - 752*e^5 - 2315*e^3 - 498*e, 27*e^6 + 293*e^4 + 799*e^2 + 105, -3*e^6 - 48*e^4 - 186*e^2 - 29, 20*e^7 + 247*e^5 + 801*e^3 + 272*e, 47*e^7 + 553*e^5 + 1674*e^3 + 351*e, 17*e^6 + 198*e^4 + 583*e^2 + 54, 18*e^4 + 125*e^2 + 104, -82*e^7 - 965*e^5 - 2924*e^3 - 590*e, -37*e^7 - 439*e^5 - 1348*e^3 - 300*e, -2*e^6 - 41*e^4 - 172*e^2 - 3, -15*e^6 - 165*e^4 - 479*e^2 - 124, 3*e^6 + 39*e^4 + 123*e^2 + 12, -3*e^6 - 43*e^4 - 146*e^2 + 44, -23*e^7 - 278*e^5 - 877*e^3 - 244*e, -31*e^7 - 366*e^5 - 1102*e^3 - 149*e, 6*e^7 + 63*e^5 + 173*e^3 + 54*e, -84*e^7 - 987*e^5 - 2978*e^3 - 537*e, -36*e^7 - 438*e^5 - 1365*e^3 - 240*e, -2*e^5 - 7*e^3 + 28*e, -8*e^6 - 97*e^4 - 318*e^2 - 82, -17*e^6 - 191*e^4 - 564*e^2 - 138, -50*e^7 - 597*e^5 - 1827*e^3 - 299*e, -14*e^7 - 173*e^5 - 555*e^3 - 150*e, -12*e^6 - 144*e^4 - 448*e^2 - 91, -2*e^6 - 7*e^4 + 27*e^2 - 13, 13*e^6 + 147*e^4 + 400*e^2 + 3, 12*e^6 + 150*e^4 + 491*e^2 + 75, -30*e^7 - 358*e^5 - 1104*e^3 - 258*e, -16*e^7 - 198*e^5 - 633*e^3 - 153*e, 9*e^6 + 123*e^4 + 430*e^2 + 121, 17*e^6 + 188*e^4 + 542*e^2 + 131, 7*e^7 + 65*e^5 + 131*e^3 - 49*e, -8*e^5 - 46*e^3 + 15*e, 39*e^7 + 472*e^5 + 1490*e^3 + 400*e, 50*e^7 + 584*e^5 + 1743*e^3 + 252*e, -7*e^7 - 78*e^5 - 219*e^3 - 22*e, 23*e^7 + 278*e^5 + 892*e^3 + 313*e, -11*e^6 - 110*e^4 - 268*e^2 - 17, 13*e^6 + 142*e^4 + 403*e^2 + 81, -10*e^7 - 122*e^5 - 392*e^3 - 149*e, -74*e^7 - 891*e^5 - 2765*e^3 - 567*e, -34*e^7 - 402*e^5 - 1225*e^3 - 251*e, -17*e^7 - 203*e^5 - 635*e^3 - 188*e, 12*e^6 + 141*e^4 + 403*e^2 + 4, 7*e^6 + 108*e^4 + 413*e^2 + 117, -6*e^6 - 81*e^4 - 268*e^2 + 14, 16*e^6 + 173*e^4 + 490*e^2 + 120, 29*e^7 + 341*e^5 + 1064*e^3 + 393*e, 9*e^7 + 108*e^5 + 357*e^3 + 224*e, -e^6 + 15*e^4 + 120*e^2 - 6, 13*e^6 + 172*e^4 + 571*e^2 + 92, -9*e^6 - 104*e^4 - 305*e^2 - 45, 9*e^6 + 122*e^4 + 427*e^2 + 104, -10*e^6 - 133*e^4 - 449*e^2 - 59, 5*e^6 + 62*e^4 + 211*e^2 + 61, 32*e^7 + 377*e^5 + 1151*e^3 + 284*e, 19*e^7 + 226*e^5 + 690*e^3 + 111*e, -12*e^6 - 119*e^4 - 293*e^2 - 81, -23*e^6 - 301*e^4 - 1007*e^2 - 189, -11*e^6 - 123*e^4 - 349*e^2 - 75, -27*e^6 - 347*e^4 - 1128*e^2 - 181, 2*e^6 + 11*e^4 - 8*e^2 - 82, -6*e^7 - 72*e^5 - 233*e^3 - 96*e, -42*e^7 - 492*e^5 - 1480*e^3 - 264*e, e^7 + 9*e^5 + 39*e^3 + 134*e, -39*e^7 - 456*e^5 - 1364*e^3 - 219*e, -5*e^7 - 69*e^5 - 239*e^3 - 37*e, -61*e^7 - 720*e^5 - 2168*e^3 - 336*e, -7*e^6 - 86*e^4 - 284*e^2 - 40, e^6 - 29*e^4 - 222*e^2 - 102, -2*e^7 - 18*e^5 - 44*e^3 - 60*e, -32*e^7 - 380*e^5 - 1190*e^3 - 414*e, -30*e^7 - 364*e^5 - 1142*e^3 - 250*e, -30*e^7 - 355*e^5 - 1096*e^3 - 273*e, 29*e^6 + 354*e^4 + 1104*e^2 + 164, -6*e^6 - 54*e^4 - 126*e^2 - 63, -29*e^7 - 336*e^5 - 997*e^3 - 199*e, 5*e^7 + 68*e^5 + 265*e^3 + 203*e, -24*e^7 - 282*e^5 - 892*e^3 - 388*e, -68*e^7 - 786*e^5 - 2322*e^3 - 368*e, -28*e^6 - 317*e^4 - 904*e^2 - 118, -2*e^6 - 10*e^4 + 20*e^2 + 15, -32*e^6 - 387*e^4 - 1196*e^2 - 194, 3*e^6 + 24*e^4 + 19*e^2 - 75, 32*e^6 + 349*e^4 + 962*e^2 + 147, 14*e^6 + 153*e^4 + 420*e^2 + 98, -10*e^7 - 131*e^5 - 454*e^3 - 192*e, -17*e^7 - 204*e^5 - 630*e^3 - 107*e, 40*e^7 + 471*e^5 + 1405*e^3 + 142*e, -45*e^7 - 538*e^5 - 1663*e^3 - 377*e, 7*e^6 + 86*e^4 + 267*e^2 + 95, 12*e^6 + 136*e^4 + 412*e^2 + 105, -13*e^6 - 161*e^4 - 511*e^2 - 131, -2*e^6 - 29*e^4 - 107*e^2 - 13, 14*e^7 + 178*e^5 + 603*e^3 + 267*e, 4*e^7 + 36*e^5 + 86*e^3 + 82*e, -36*e^6 - 415*e^4 - 1231*e^2 - 212, -11*e^6 - 133*e^4 - 426*e^2 - 84, 49*e^7 + 577*e^5 + 1756*e^3 + 409*e, 53*e^7 + 624*e^5 + 1866*e^3 + 266*e, -20*e^6 - 240*e^4 - 737*e^2 - 132, e^6 + 15*e^4 + 42*e^2 + 23, 6*e^6 + 59*e^4 + 162*e^2 + 109, 16*e^6 + 209*e^4 + 687*e^2 + 134, 37*e^7 + 434*e^5 + 1312*e^3 + 258*e, 92*e^7 + 1096*e^5 + 3361*e^3 + 680*e, -8*e^6 - 66*e^4 - 128*e^2 - 98, -10*e^6 - 125*e^4 - 391*e^2 - 19, 59*e^7 + 697*e^5 + 2104*e^3 + 347*e, -6*e^7 - 63*e^5 - 163*e^3 - 10*e, -11*e^6 - 113*e^4 - 269*e^2 - 2, 7*e^6 + 78*e^4 + 203*e^2 + 27, 26*e^6 + 274*e^4 + 732*e^2 + 121, 9*e^6 + 83*e^4 + 164*e^2 - 48, 16*e^6 + 183*e^4 + 534*e^2 + 87, 6*e^6 + 56*e^4 + 119*e^2 + 44, -21*e^6 - 269*e^4 - 880*e^2 - 140, 12*e^6 + 140*e^4 + 432*e^2 + 136, 5*e^7 + 67*e^5 + 256*e^3 + 220*e, 25*e^7 + 299*e^5 + 908*e^3 + 95*e, -31*e^7 - 375*e^5 - 1196*e^3 - 414*e, -11*e^7 - 131*e^5 - 430*e^3 - 232*e, 24*e^6 + 292*e^4 + 897*e^2 + 149, -36*e^6 - 420*e^4 - 1238*e^2 - 209, -13*e^6 - 159*e^4 - 482*e^2 - 46, 2*e^6 + 15*e^4 - 12*e^2 - 80, -28*e^6 - 318*e^4 - 929*e^2 - 202, 26*e^6 + 313*e^4 + 967*e^2 + 157, -23*e^7 - 273*e^5 - 848*e^3 - 237*e, -61*e^7 - 718*e^5 - 2184*e^3 - 466*e, 35*e^7 + 409*e^5 + 1220*e^3 + 202*e, 19*e^7 + 220*e^5 + 645*e^3 + 65*e, -18*e^6 - 239*e^4 - 804*e^2 - 176, 14*e^6 + 164*e^4 + 484*e^2 + 81, 26*e^7 + 308*e^5 + 927*e^3 + 78*e, 54*e^7 + 638*e^5 + 1940*e^3 + 384*e, 16*e^6 + 147*e^4 + 306*e^2 - 20, -e^6 - 27*e^4 - 122*e^2 + 9, -29*e^7 - 329*e^5 - 951*e^3 - 143*e, 67*e^7 + 788*e^5 + 2395*e^3 + 557*e, -4*e^7 - 40*e^5 - 113*e^3 - 81*e, -47*e^7 - 550*e^5 - 1637*e^3 - 203*e, 31*e^6 + 387*e^4 + 1232*e^2 + 211, 14*e^6 + 152*e^4 + 429*e^2 + 76, 5*e^6 + 76*e^4 + 274*e^2 + 40, 10*e^6 + 98*e^4 + 254*e^2 + 108, -85*e^7 - 1006*e^5 - 3077*e^3 - 665*e, 23*e^7 + 281*e^5 + 893*e^3 + 236*e, -59*e^7 - 695*e^5 - 2099*e^3 - 405*e, -14*e^7 - 169*e^5 - 501*e^3 + 57*e, 12*e^6 + 138*e^4 + 412*e^2 + 108, 5*e^6 + 48*e^4 + 119*e^2 + 18, -4*e^7 - 43*e^5 - 137*e^3 - 137*e, 24*e^7 + 287*e^5 + 906*e^3 + 274*e, 21*e^7 + 252*e^5 + 796*e^3 + 248*e, -87*e^7 - 1042*e^5 - 3208*e^3 - 625*e, 82*e^7 + 967*e^5 + 2922*e^3 + 523*e, -23*e^7 - 269*e^5 - 837*e^3 - 340*e, 15*e^6 + 206*e^4 + 711*e^2 + 115, -9*e^4 - 59*e^2 - 80, 3*e^6 + 58*e^4 + 233*e^2 + 40, -4*e^6 - 35*e^4 - 65*e^2 - 22, 28*e^7 + 331*e^5 + 993*e^3 + 93*e, 41*e^7 + 479*e^5 + 1415*e^3 + 140*e, 4*e^6 + 63*e^4 + 238*e^2 + 81, -11*e^6 - 155*e^4 - 547*e^2 - 81, 24*e^6 + 275*e^4 + 811*e^2 + 155, -3*e^6 - 37*e^4 - 97*e^2 + 57, 13*e^6 + 182*e^4 + 632*e^2 + 120, -70*e^7 - 831*e^5 - 2541*e^3 - 479*e, 63*e^7 + 744*e^5 + 2257*e^3 + 377*e, -e^6 + 22*e^4 + 167*e^2 + 49, 2*e^6 + 33*e^4 + 124*e^2 - 17, 27*e^6 + 335*e^4 + 1066*e^2 + 215, -15*e^6 - 185*e^4 - 562*e^2 - 35, 26*e^7 + 322*e^5 + 1051*e^3 + 353*e, -13*e^7 - 164*e^5 - 572*e^3 - 313*e, 51*e^7 + 599*e^5 + 1837*e^3 + 527*e, 61*e^7 + 728*e^5 + 2228*e^3 + 364*e, 11*e^7 + 107*e^5 + 216*e^3 - 174*e, -e^7 - 19*e^5 - 82*e^3 - 13*e, 26*e^6 + 297*e^4 + 867*e^2 + 98, 23*e^6 + 253*e^4 + 695*e^2 + 57, 29*e^7 + 355*e^5 + 1150*e^3 + 427*e, -85*e^7 - 1006*e^5 - 3072*e^3 - 653*e, 20*e^6 + 231*e^4 + 685*e^2 + 111, 28*e^6 + 322*e^4 + 942*e^2 + 195, -47*e^7 - 556*e^5 - 1724*e^3 - 539*e, 27*e^7 + 335*e^5 + 1088*e^3 + 341*e, -21*e^6 - 248*e^4 - 761*e^2 - 94, -11*e^6 - 123*e^4 - 331*e^2 - 4, 60*e^7 + 722*e^5 + 2250*e^3 + 506*e, 31*e^7 + 367*e^5 + 1146*e^3 + 398*e, -7*e^6 - 97*e^4 - 345*e^2 - 93, -4*e^6 - 69*e^4 - 258*e^2 - 1, 33*e^7 + 393*e^5 + 1232*e^3 + 380*e, -28*e^7 - 342*e^5 - 1110*e^3 - 388*e, 27*e^6 + 315*e^4 + 932*e^2 + 169, -4*e^6 - 27*e^4 - 22*e^2 - 24, 17*e^6 + 212*e^4 + 679*e^2 + 139, -5*e^6 - 92*e^4 - 384*e^2 - 117, 40*e^6 + 468*e^4 + 1394*e^2 + 253, -10*e^6 - 87*e^4 - 161*e^2 + 28, 52*e^7 + 617*e^5 + 1883*e^3 + 376*e, 15*e^7 + 181*e^5 + 577*e^3 + 174*e, 38*e^7 + 449*e^5 + 1359*e^3 + 211*e, -78*e^7 - 917*e^5 - 2757*e^3 - 470*e, -8*e^7 - 79*e^5 - 199*e^3 - 80*e, -84*e^7 - 999*e^5 - 3052*e^3 - 574*e, -17*e^6 - 187*e^4 - 536*e^2 - 104, 3*e^6 + 28*e^4 + 54*e^2 + 51, -40*e^7 - 480*e^5 - 1493*e^3 - 370*e, 66*e^7 + 772*e^5 + 2299*e^3 + 316*e, e^7 + 22*e^5 + 107*e^3 + 92*e, -27*e^7 - 301*e^5 - 837*e^3 - 32*e, 28*e^6 + 356*e^4 + 1162*e^2 + 234, 25*e^6 + 271*e^4 + 755*e^2 + 134, -31*e^6 - 333*e^4 - 906*e^2 - 149, -36*e^6 - 418*e^4 - 1256*e^2 - 239, 9*e^6 + 103*e^4 + 307*e^2 + 13, -46*e^6 - 531*e^4 - 1568*e^2 - 278, 20*e^6 + 270*e^4 + 917*e^2 + 172, 7*e^6 + 51*e^4 + 50*e^2 + 6, 16*e^7 + 189*e^5 + 558*e^3 - 4*e, 38*e^7 + 464*e^5 + 1487*e^3 + 472*e, 104*e^7 + 1229*e^5 + 3735*e^3 + 698*e, 82*e^7 + 973*e^5 + 2951*e^3 + 468*e, 49*e^6 + 571*e^4 + 1716*e^2 + 296, 14*e^6 + 152*e^4 + 421*e^2 + 165, 12*e^6 + 147*e^4 + 462*e^2 + 87, 3*e^6 + 59*e^4 + 251*e^2 + 30, 5*e^6 + 57*e^4 + 171*e^2 + 36, 24*e^6 + 304*e^4 + 977*e^2 + 119, 18*e^6 + 227*e^4 + 741*e^2 + 94, 18*e^6 + 227*e^4 + 726*e^2 + 169, -52*e^7 - 605*e^5 - 1809*e^3 - 315*e, 38*e^7 + 451*e^5 + 1372*e^3 + 270*e, 88*e^7 + 1047*e^5 + 3200*e^3 + 567*e, -e^7 - 14*e^5 - 48*e^3 - 44*e, -23*e^6 - 232*e^4 - 578*e^2 - 39, -2*e^6 - 45*e^4 - 189*e^2 + 49, -2*e^6 - 54*e^4 - 263*e^2 - 49, 17*e^6 + 166*e^4 + 383*e^2 + 6, 59*e^7 + 697*e^5 + 2133*e^3 + 476*e, -21*e^7 - 263*e^5 - 867*e^3 - 284*e, -e^6 - 16*e^4 - 57*e^2 + 38, -9*e^6 - 132*e^4 - 479*e^2 - 126, -13*e^7 - 164*e^5 - 544*e^3 - 160*e, 30*e^7 + 370*e^5 + 1174*e^3 + 247*e, 69*e^7 + 811*e^5 + 2462*e^3 + 536*e, -7*e^7 - 76*e^5 - 170*e^3 + 165*e, 24*e^7 + 293*e^5 + 923*e^3 + 177*e, 7*e^7 + 91*e^5 + 318*e^3 + 132*e, 19*e^6 + 249*e^4 + 829*e^2 + 101, -12*e^6 - 146*e^4 - 460*e^2 - 89, -29*e^7 - 323*e^5 - 885*e^3 + 35*e, 39*e^7 + 467*e^5 + 1434*e^3 + 227*e, 37*e^6 + 443*e^4 + 1354*e^2 + 205, -4*e^6 - 50*e^4 - 180*e^2 - 37, -51*e^7 - 614*e^5 - 1909*e^3 - 393*e, -36*e^7 - 439*e^5 - 1367*e^3 - 216*e, -66*e^7 - 787*e^5 - 2406*e^3 - 407*e, 37*e^7 + 445*e^5 + 1397*e^3 + 347*e, -14*e^5 - 103*e^3 - 108*e, -69*e^7 - 819*e^5 - 2504*e^3 - 508*e, -44*e^6 - 483*e^4 - 1358*e^2 - 269, -22*e^7 - 271*e^5 - 850*e^3 - 115*e, 13*e^7 + 155*e^5 + 453*e^3 - 58*e, 92*e^7 + 1077*e^5 + 3232*e^3 + 585*e, 89*e^7 + 1066*e^5 + 3299*e^3 + 720*e, 16*e^7 + 187*e^5 + 588*e^3 + 260*e, -13*e^7 - 166*e^5 - 589*e^3 - 363*e, -59*e^7 - 710*e^5 - 2228*e^3 - 581*e, 8*e^7 + 103*e^5 + 358*e^3 + 134*e, -17*e^6 - 168*e^4 - 409*e^2 - 61, 21*e^6 + 217*e^4 + 568*e^2 + 119, 86*e^7 + 1022*e^5 + 3117*e^3 + 544*e, -38*e^7 - 459*e^5 - 1423*e^3 - 289*e, 18*e^6 + 217*e^4 + 668*e^2 + 194, 37*e^6 + 433*e^4 + 1304*e^2 + 228, 8*e^6 + 94*e^4 + 274*e^2 + 8, -15*e^6 - 187*e^4 - 603*e^2 - 71, 80*e^7 + 952*e^5 + 2911*e^3 + 570*e, 68*e^7 + 820*e^5 + 2555*e^3 + 569*e, -30*e^6 - 333*e^4 - 943*e^2 - 205, 16*e^6 + 212*e^4 + 721*e^2 + 135, -19*e^6 - 233*e^4 - 725*e^2 - 79, -22*e^6 - 264*e^4 - 797*e^2 - 153, -28*e^7 - 334*e^5 - 1056*e^3 - 339*e, 43*e^7 + 519*e^5 + 1620*e^3 + 370*e, -27*e^7 - 309*e^5 - 869*e^3 + 24*e, -6*e^7 - 84*e^5 - 319*e^3 - 195*e, -12*e^7 - 137*e^5 - 434*e^3 - 243*e, -59*e^7 - 706*e^5 - 2161*e^3 - 383*e, e^6 + 18*e^4 + 97*e^2 + 122, 23*e^6 + 263*e^4 + 760*e^2 + 127, -30*e^6 - 349*e^4 - 1054*e^2 - 220, 24*e^6 + 287*e^4 + 867*e^2 + 159, -25*e^7 - 296*e^5 - 887*e^3 - 95*e, -7*e^7 - 82*e^5 - 247*e^3 - 36*e, 97*e^7 + 1133*e^5 + 3392*e^3 + 574*e, -67*e^7 - 800*e^5 - 2460*e^3 - 479*e, -43*e^7 - 505*e^5 - 1563*e^3 - 498*e, -31*e^7 - 378*e^5 - 1206*e^3 - 331*e, 8*e^6 + 65*e^4 + 116*e^2 + 96, 25*e^6 + 318*e^4 + 1044*e^2 + 218, 2*e^6 + 23*e^4 + 92*e^2 + 68, -33*e^6 - 413*e^4 - 1328*e^2 - 246, -5*e^7 - 62*e^5 - 234*e^3 - 241*e, 14*e^7 + 166*e^5 + 509*e^3 + 73*e, -12*e^6 - 138*e^4 - 428*e^2 - 132, -12*e^6 - 157*e^4 - 508*e^2 - 13, 10*e^6 + 98*e^4 + 209*e^2 - 32, 19*e^6 + 251*e^4 + 830*e^2 + 85, -76*e^7 - 900*e^5 - 2740*e^3 - 505*e, 12*e^7 + 133*e^5 + 383*e^3 + 108*e, 82*e^7 + 983*e^5 + 3024*e^3 + 536*e, 62*e^7 + 731*e^5 + 2209*e^3 + 433*e, -6*e^6 - 53*e^4 - 90*e^2 + 39, e^6 - 3*e^4 - 42*e^2 + 59, 22*e^7 + 251*e^5 + 761*e^3 + 270*e, 85*e^7 + 1000*e^5 + 3024*e^3 + 532*e, -35*e^7 - 413*e^5 - 1258*e^3 - 247*e, 51*e^7 + 594*e^5 + 1749*e^3 + 159*e, 74*e^7 + 878*e^5 + 2710*e^3 + 674*e, 66*e^7 + 769*e^5 + 2342*e^3 + 657*e, 8*e^7 + 83*e^5 + 215*e^3 + 21*e, 30*e^7 + 349*e^5 + 1041*e^3 + 163*e, 3*e^6 + 36*e^4 + 88*e^2 - 45, -26*e^6 - 266*e^4 - 673*e^2 - 68, -24*e^7 - 294*e^5 - 932*e^3 - 251*e, 122*e^7 + 1445*e^5 + 4403*e^3 + 866*e, -20*e^6 - 239*e^4 - 753*e^2 - 172, e^6 + 14*e^4 + 56*e^2 + 90, -9*e^6 - 113*e^4 - 345*e^2 - 24, -8*e^6 - 117*e^4 - 402*e^2 - 11, -31*e^6 - 391*e^4 - 1269*e^2 - 207, 51*e^7 + 603*e^5 + 1862*e^3 + 543*e, 84*e^7 + 974*e^5 + 2880*e^3 + 438*e, 32*e^6 + 346*e^4 + 963*e^2 + 226, 15*e^6 + 174*e^4 + 540*e^2 + 108, -4*e^6 - 51*e^4 - 170*e^2 - 48, 13*e^6 + 167*e^4 + 548*e^2 + 64, -15*e^6 - 195*e^4 - 631*e^2 - 59, -10*e^6 - 105*e^4 - 246*e^2 + 46, -90*e^7 - 1071*e^5 - 3278*e^3 - 654*e, 37*e^7 + 436*e^5 + 1333*e^3 + 317*e, 17*e^6 + 202*e^4 + 589*e^2 + 24, 5*e^6 + 34*e^4 + 46*e^2 + 42, 22*e^6 + 264*e^4 + 818*e^2 + 186, -16*e^6 - 160*e^4 - 399*e^2 - 105, 15*e^7 + 168*e^5 + 466*e^3 + 26*e, 11*e^7 + 135*e^5 + 405*e^3 - 41*e, 23*e^7 + 281*e^5 + 907*e^3 + 300*e, -50*e^7 - 594*e^5 - 1781*e^3 - 156*e, -4*e^6 - 2*e^4 + 137*e^2 + 42, -15*e^6 - 184*e^4 - 572*e^2 - 136, -66*e^7 - 776*e^5 - 2338*e^3 - 407*e, 5*e^7 + 49*e^5 + 148*e^3 + 185*e, -e^6 + 20*e^4 + 177*e^2 + 96, 42*e^6 + 505*e^4 + 1544*e^2 + 241, -31*e^7 - 375*e^5 - 1206*e^3 - 424*e, -46*e^7 - 540*e^5 - 1615*e^3 - 248*e, -2*e^7 - 11*e^5 + 10*e^3 + 40*e, -2*e^7 - 33*e^5 - 147*e^3 - 95*e, -34*e^6 - 372*e^4 - 1037*e^2 - 207, 14*e^6 + 137*e^4 + 300*e^2 - 66, -13*e^6 - 127*e^4 - 308*e^2 - 92, -13*e^6 - 168*e^4 - 558*e^2 - 76, 24*e^7 + 289*e^5 + 925*e^3 + 371*e, -63*e^7 - 749*e^5 - 2292*e^3 - 435*e, -108*e^7 - 1281*e^5 - 3920*e^3 - 839*e, 31*e^7 + 371*e^5 + 1134*e^3 + 137*e, 28*e^6 + 325*e^4 + 945*e^2 + 118, -12*e^6 - 153*e^4 - 505*e^2 - 99, -18*e^6 - 251*e^4 - 857*e^2 - 82, 28*e^6 + 311*e^4 + 877*e^2 + 86, 25*e^7 + 295*e^5 + 900*e^3 + 238*e, 11*e^7 + 136*e^5 + 436*e^3 + 109*e, -45*e^6 - 530*e^4 - 1629*e^2 - 322, -14*e^6 - 142*e^4 - 355*e^2 - 80, 38*e^7 + 448*e^5 + 1409*e^3 + 580*e, 4*e^7 + 64*e^5 + 258*e^3 + 134*e, 42*e^6 + 495*e^4 + 1503*e^2 + 290, -43*e^6 - 503*e^4 - 1517*e^2 - 272, -43*e^7 - 526*e^5 - 1684*e^3 - 508*e, 81*e^7 + 946*e^5 + 2818*e^3 + 441*e, 25*e^7 + 291*e^5 + 848*e^3 + 68*e, -53*e^7 - 615*e^5 - 1846*e^3 - 443*e, -6*e^6 - 73*e^4 - 197*e^2 + 37, 24*e^6 + 258*e^4 + 703*e^2 + 81, 78*e^7 + 920*e^5 + 2774*e^3 + 438*e, -41*e^7 - 481*e^5 - 1442*e^3 - 216*e, 21*e^6 + 234*e^4 + 663*e^2 + 117, 28*e^6 + 359*e^4 + 1181*e^2 + 232, -e^7 - 19*e^5 - 80*e^3 + 21*e, 99*e^7 + 1187*e^5 + 3674*e^3 + 814*e, -32*e^6 - 381*e^4 - 1173*e^2 - 204, -16*e^6 - 208*e^4 - 694*e^2 - 77, 18*e^6 + 172*e^4 + 375*e^2 - 49, -e^6 - 39*e^4 - 201*e^2 - 13, 61*e^7 + 731*e^5 + 2283*e^3 + 559*e, 48*e^7 + 580*e^5 + 1822*e^3 + 466*e, -31*e^6 - 372*e^4 - 1150*e^2 - 167, 22*e^6 + 285*e^4 + 952*e^2 + 221, -62*e^7 - 739*e^5 - 2245*e^3 - 350*e, 26*e^7 + 306*e^5 + 893*e^3 + 16*e, -8*e^7 - 97*e^5 - 331*e^3 - 231*e, -24*e^7 - 277*e^5 - 808*e^3 - 74*e, 18*e^6 + 259*e^4 + 936*e^2 + 205, 28*e^6 + 313*e^4 + 871*e^2 + 81, -89*e^7 - 1064*e^5 - 3283*e^3 - 712*e, 49*e^7 + 577*e^5 + 1717*e^3 + 130*e, -9*e^6 - 87*e^4 - 181*e^2 + 14, -25*e^6 - 264*e^4 - 705*e^2 - 94, -11*e^7 - 119*e^5 - 313*e^3 + 8*e, -e^7 - 13*e^5 - 18*e^3 + 147*e, 6*e^6 + 92*e^4 + 367*e^2 + 156, 19*e^6 + 251*e^4 + 834*e^2 + 87, -35*e^7 - 420*e^5 - 1319*e^3 - 373*e, 46*e^7 + 548*e^5 + 1687*e^3 + 366*e, 20*e^6 + 189*e^4 + 432*e^2 + 68, -31*e^6 - 326*e^4 - 867*e^2 - 107, -11*e^6 - 164*e^4 - 615*e^2 - 180, -2*e^6 + 5*e^4 + 96*e^2 + 41, -12*e^6 - 163*e^4 - 568*e^2 - 92, -24*e^6 - 302*e^4 - 971*e^2 - 158, -33*e^6 - 428*e^4 - 1417*e^2 - 280, -20*e^6 - 206*e^4 - 525*e^2 - 17, -47*e^7 - 569*e^5 - 1822*e^3 - 644*e, 5*e^7 + 79*e^5 + 343*e^3 + 330*e, -34*e^7 - 400*e^5 - 1220*e^3 - 266*e, 52*e^7 + 616*e^5 + 1909*e^3 + 538*e, 21*e^7 + 256*e^5 + 826*e^3 + 302*e, 34*e^7 + 402*e^5 + 1218*e^3 + 236*e, 120*e^7 + 1419*e^5 + 4308*e^3 + 762*e, 50*e^7 + 597*e^5 + 1859*e^3 + 505*e, 13*e^7 + 134*e^5 + 340*e^3 + 32*e, 42*e^7 + 499*e^5 + 1512*e^3 + 183*e, 66*e^7 + 782*e^5 + 2393*e^3 + 480*e, -40*e^7 - 482*e^5 - 1487*e^3 - 262*e, 12*e^6 + 132*e^4 + 379*e^2 + 46, 9*e^6 + 87*e^4 + 227*e^2 + 101, -104*e^7 - 1244*e^5 - 3818*e^3 - 677*e, 49*e^7 + 578*e^5 + 1732*e^3 + 234*e, -18*e^6 - 222*e^4 - 720*e^2 - 149, 17*e^6 + 187*e^4 + 500*e^2 + 22, 41*e^7 + 500*e^5 + 1540*e^3 + 157*e, 84*e^7 + 987*e^5 + 2994*e^3 + 657*e, -13*e^7 - 149*e^5 - 423*e^3 - 9*e, 12*e^7 + 143*e^5 + 476*e^3 + 298*e, 27*e^6 + 306*e^4 + 898*e^2 + 136, -26*e^6 - 326*e^4 - 1024*e^2 - 157, 11*e^6 + 126*e^4 + 368*e^2 - 15, -29*e^7 - 356*e^5 - 1175*e^3 - 497*e, -72*e^7 - 843*e^5 - 2520*e^3 - 348*e, 19*e^6 + 195*e^4 + 493*e^2 + 122, 4*e^6 + 40*e^4 + 103*e^2 + 127, -3*e^6 - 6*e^4 + 86*e^2 + 96, 12*e^6 + 159*e^4 + 531*e^2 + 151, 62*e^7 + 752*e^5 + 2374*e^3 + 637*e, 6*e^7 + 89*e^5 + 360*e^3 + 295*e, -36*e^6 - 453*e^4 - 1461*e^2 - 219, 12*e^6 + 168*e^4 + 576*e^2 + 120, 10*e^6 + 105*e^4 + 299*e^2 + 186, -47*e^6 - 536*e^4 - 1554*e^2 - 258, 3*e^7 + 40*e^5 + 115*e^3 - 69*e, -80*e^7 - 942*e^5 - 2876*e^3 - 706*e, -62*e^7 - 725*e^5 - 2160*e^3 - 336*e, 47*e^7 + 559*e^5 + 1749*e^3 + 523*e, -31*e^6 - 341*e^4 - 957*e^2 - 167, -9*e^6 - 71*e^4 - 119*e^2 - 132, -11*e^6 - 157*e^4 - 579*e^2 - 158, 13*e^6 + 137*e^4 + 357*e^2 + 13, 5*e^7 + 50*e^5 + 127*e^3 + 60*e, -64*e^7 - 769*e^5 - 2356*e^3 - 348*e, -18*e^6 - 180*e^4 - 432*e^2 - 53, 10*e^6 + 142*e^4 + 510*e^2 + 175, -3*e^6 - 64*e^4 - 287*e^2 - 81, 30*e^6 + 345*e^4 + 1000*e^2 + 185, -11*e^6 - 109*e^4 - 272*e^2 - 37, 26*e^6 + 303*e^4 + 921*e^2 + 241, 33*e^6 + 424*e^4 + 1378*e^2 + 187, -9*e^6 - 118*e^4 - 375*e^2 - 31, -6*e^6 - 68*e^4 - 198*e^2 - 9, -2*e^6 - 14*e^4 - 2*e^2 - 13, -15*e^6 - 147*e^4 - 331*e^2 + 38, -11*e^6 - 84*e^4 - 135*e^2 - 110, -63*e^7 - 733*e^5 - 2191*e^3 - 428*e, -104*e^7 - 1238*e^5 - 3795*e^3 - 733*e, 31*e^7 + 359*e^5 + 1084*e^3 + 299*e, -74*e^7 - 875*e^5 - 2674*e^3 - 615*e, 18*e^7 + 226*e^5 + 755*e^3 + 283*e, -e^7 + 2*e^5 + 37*e^3 - 35*e, 22*e^6 + 269*e^4 + 858*e^2 + 106, -14*e^6 - 180*e^4 - 576*e^2 - 120, 2*e^6 + 60*e^4 + 281*e^2 + 13, -38*e^6 - 472*e^4 - 1489*e^2 - 215, -41*e^7 - 505*e^5 - 1621*e^3 - 466*e, -66*e^7 - 783*e^5 - 2383*e^3 - 440*e, -20*e^6 - 242*e^4 - 755*e^2 - 98, -14*e^6 - 144*e^4 - 391*e^2 - 96, 23*e^7 + 275*e^5 + 794*e^3 - 115*e, 74*e^7 + 870*e^5 + 2611*e^3 + 363*e, 96*e^7 + 1130*e^5 + 3430*e^3 + 747*e, -52*e^7 - 610*e^5 - 1845*e^3 - 406*e, 34*e^6 + 424*e^4 + 1370*e^2 + 260, 22*e^6 + 260*e^4 + 802*e^2 + 159, -9*e^6 - 113*e^4 - 347*e^2 + 29, -4*e^6 - 41*e^4 - 112*e^2 - 43, 50*e^6 + 558*e^4 + 1605*e^2 + 329, -e^6 - 10*e^4 - 14*e^2 + 82, 75*e^7 + 888*e^5 + 2678*e^3 + 391*e, 63*e^7 + 738*e^5 + 2223*e^3 + 454*e, 95*e^7 + 1136*e^5 + 3526*e^3 + 856*e, 32*e^7 + 381*e^5 + 1206*e^3 + 443*e, 50*e^7 + 594*e^5 + 1830*e^3 + 412*e, -93*e^7 - 1115*e^5 - 3463*e^3 - 820*e, -73*e^7 - 864*e^5 - 2641*e^3 - 557*e, 122*e^7 + 1435*e^5 + 4324*e^3 + 749*e, -67*e^7 - 799*e^5 - 2464*e^3 - 559*e, 6*e^7 + 59*e^5 + 127*e^3 - 43*e, -22*e^7 - 259*e^5 - 781*e^3 - 148*e, -104*e^7 - 1231*e^5 - 3744*e^3 - 646*e, 24*e^6 + 288*e^4 + 888*e^2 + 219, e^6 + 40*e^4 + 211*e^2 + 7, -e^6 - e^4 + 40*e^2 + 35, 73*e^7 + 860*e^5 + 2579*e^3 + 335*e, 66*e^7 + 794*e^5 + 2454*e^3 + 474*e, 7*e^6 + 57*e^4 + 80*e^2 + 12, -e^6 - 22*e^4 - 97*e^2 + 11, 5*e^7 + 57*e^5 + 218*e^3 + 334*e, 8*e^7 + 89*e^5 + 291*e^3 + 243*e, -10*e^6 - 170*e^4 - 662*e^2 - 57, -31*e^6 - 386*e^4 - 1216*e^2 - 206, -46*e^6 - 558*e^4 - 1726*e^2 - 312, 21*e^6 + 253*e^4 + 782*e^2 + 177, 45*e^7 + 509*e^5 + 1443*e^3 + 57*e, 25*e^7 + 301*e^5 + 979*e^3 + 431*e, 7*e^6 + 64*e^4 + 147*e^2 + 27, -22*e^6 - 254*e^4 - 769*e^2 - 90, 117*e^7 + 1398*e^5 + 4290*e^3 + 822*e, 62*e^7 + 744*e^5 + 2308*e^3 + 504*e, 57*e^4 + 355*e^2 + 140, -22*e^6 - 251*e^4 - 743*e^2 - 102, -74*e^7 - 843*e^5 - 2437*e^3 - 305*e, 8*e^7 + 84*e^5 + 185*e^3 - 153*e, -13*e^6 - 163*e^4 - 527*e^2 - 2, -28*e^6 - 286*e^4 - 747*e^2 - 189, -48*e^7 - 582*e^5 - 1814*e^3 - 372*e, -18*e^7 - 219*e^5 - 693*e^3 - 164*e, 11*e^6 + 110*e^4 + 270*e^2 - 19, -19*e^6 - 219*e^4 - 650*e^2 - 175, 77*e^7 + 906*e^5 + 2749*e^3 + 546*e, 78*e^7 + 906*e^5 + 2680*e^3 + 388*e, -43*e^7 - 529*e^5 - 1682*e^3 - 365*e, -21*e^7 - 260*e^5 - 845*e^3 - 270*e, -2*e^6 - 34*e^4 - 116*e^2 - 12, -23*e^6 - 243*e^4 - 620*e^2 + 17, -16*e^6 - 211*e^4 - 706*e^2 - 216, -47*e^6 - 577*e^4 - 1795*e^2 - 295, 90*e^7 + 1055*e^5 + 3182*e^3 + 625*e, -30*e^7 - 355*e^5 - 1055*e^3 - 62*e, -7*e^7 - 72*e^5 - 177*e^3 - 6*e, -111*e^7 - 1323*e^5 - 4076*e^3 - 933*e, -9*e^6 - 133*e^4 - 501*e^2 - 152, 21*e^6 + 257*e^4 + 824*e^2 + 243, -50*e^7 - 596*e^5 - 1793*e^3 - 144*e, -65*e^7 - 781*e^5 - 2440*e^3 - 631*e, -108*e^7 - 1270*e^5 - 3834*e^3 - 719*e, 86*e^7 + 1016*e^5 + 3068*e^3 + 491*e, -57*e^7 - 664*e^5 - 1994*e^3 - 406*e, 66*e^7 + 792*e^5 + 2454*e^3 + 504*e, -4*e^7 - 41*e^5 - 60*e^3 + 223*e, -68*e^7 - 804*e^5 - 2469*e^3 - 572*e, -71*e^7 - 831*e^5 - 2550*e^3 - 752*e, 48*e^7 + 581*e^5 + 1800*e^3 + 325*e, 38*e^6 + 415*e^4 + 1154*e^2 + 217, 31*e^6 + 354*e^4 + 1046*e^2 + 223, e^6 + 43*e^4 + 228*e^2 + 93, -34*e^6 - 452*e^4 - 1517*e^2 - 262, -60*e^7 - 705*e^5 - 2143*e^3 - 497*e, 66*e^7 + 768*e^5 + 2256*e^3 + 235*e, -24*e^6 - 254*e^4 - 669*e^2 - 149, -5*e^6 - 73*e^4 - 243*e^2 + 100, 21*e^6 + 267*e^4 + 856*e^2 + 167, -12*e^6 - 131*e^4 - 366*e^2 - 60, -98*e^7 - 1146*e^5 - 3440*e^3 - 644*e, -3*e^7 - 34*e^5 - 102*e^3 - 28*e, -110*e^7 - 1286*e^5 - 3860*e^3 - 716*e, 8*e^7 + 86*e^5 + 189*e^3 - 216*e, -12*e^6 - 169*e^4 - 597*e^2 - 145, 15*e^6 + 181*e^4 + 556*e^2 + 190, 76*e^7 + 891*e^5 + 2672*e^3 + 455*e, 24*e^7 + 298*e^5 + 945*e^3 + 174*e, 46*e^6 + 578*e^4 + 1856*e^2 + 346, 11*e^6 + 176*e^4 + 676*e^2 + 178, -47*e^7 - 557*e^5 - 1739*e^3 - 536*e, -100*e^7 - 1159*e^5 - 3442*e^3 - 610*e, 8*e^6 + 97*e^4 + 280*e^2 + 1, 58*e^6 + 663*e^4 + 1925*e^2 + 320, -36*e^6 - 391*e^4 - 1073*e^2 - 88, 53*e^6 + 567*e^4 + 1533*e^2 + 254, -34*e^7 - 396*e^5 - 1188*e^3 - 188*e, -25*e^7 - 303*e^5 - 981*e^3 - 405*e, -6*e^7 - 81*e^5 - 302*e^3 - 209*e, -34*e^7 - 404*e^5 - 1286*e^3 - 538*e, 24*e^6 + 268*e^4 + 746*e^2 + 82, -20*e^6 - 203*e^4 - 485*e^2 + 13, 59*e^7 + 692*e^5 + 2060*e^3 + 195*e, 29*e^7 + 356*e^5 + 1179*e^3 + 545*e, 5*e^6 + 31*e^4 + 3*e^2 - 3, -4*e^6 - 16*e^4 + 82*e^2 + 129, 5*e^6 + 94*e^4 + 389*e^2 + 32, -30*e^6 - 326*e^4 - 866*e^2 - 58, 50*e^7 + 595*e^5 + 1837*e^3 + 410*e, -139*e^7 - 1649*e^5 - 5041*e^3 - 978*e, -28*e^6 - 295*e^4 - 784*e^2 - 195, -47*e^6 - 517*e^4 - 1455*e^2 - 318, 86*e^7 + 1011*e^5 + 3072*e^3 + 668*e, -22*e^7 - 265*e^5 - 792*e^3 - 18*e, -19*e^6 - 219*e^4 - 616*e^2 - 71, 46*e^6 + 529*e^4 + 1569*e^2 + 276, 54*e^6 + 662*e^4 + 2092*e^2 + 379, -47*e^6 - 553*e^4 - 1677*e^2 - 326, 6*e^7 + 72*e^5 + 192*e^3 - 153*e, -49*e^7 - 569*e^5 - 1715*e^3 - 424*e, 57*e^7 + 649*e^5 + 1899*e^3 + 375*e, 57*e^7 + 670*e^5 + 2039*e^3 + 444*e, 42*e^6 + 503*e^4 + 1536*e^2 + 230, -14*e^6 - 171*e^4 - 528*e^2 - 196, -5*e^7 - 65*e^5 - 214*e^3 - 18*e, -8*e^7 - 102*e^5 - 344*e^3 - 149*e, -59*e^7 - 705*e^5 - 2139*e^3 - 215*e, 61*e^7 + 719*e^5 + 2214*e^3 + 599*e, -31*e^7 - 377*e^5 - 1229*e^3 - 502*e, -72*e^7 - 864*e^5 - 2649*e^3 - 441*e, 36*e^7 + 416*e^5 + 1196*e^3 + 9*e, -65*e^7 - 766*e^5 - 2315*e^3 - 471*e, 138*e^7 + 1635*e^5 + 4980*e^3 + 954*e, -73*e^7 - 847*e^5 - 2551*e^3 - 631*e, -16*e^6 - 158*e^4 - 373*e^2 + 9, 38*e^6 + 454*e^4 + 1383*e^2 + 202, -12*e^6 - 142*e^4 - 438*e^2 - 191, 33*e^6 + 358*e^4 + 987*e^2 + 164, 18*e^7 + 221*e^5 + 742*e^3 + 452*e, 30*e^7 + 348*e^5 + 982*e^3 - 83*e, 26*e^6 + 319*e^4 + 1008*e^2 + 165, 19*e^6 + 167*e^4 + 320*e^2 - 63, -57*e^7 - 661*e^5 - 2004*e^3 - 599*e, -37*e^7 - 415*e^5 - 1188*e^3 - 204*e, -25*e^6 - 308*e^4 - 981*e^2 - 161, 37*e^6 + 421*e^4 + 1212*e^2 + 150, -71*e^7 - 822*e^5 - 2425*e^3 - 376*e, -72*e^7 - 832*e^5 - 2440*e^3 - 287*e, -11*e^7 - 139*e^5 - 483*e^3 - 239*e, -71*e^7 - 843*e^5 - 2616*e^3 - 703*e, 77*e^7 + 927*e^5 + 2891*e^3 + 647*e, 160*e^7 + 1887*e^5 + 5726*e^3 + 1085*e, -52*e^7 - 643*e^5 - 2078*e^3 - 606*e, 97*e^7 + 1153*e^5 + 3537*e^3 + 712*e, 11*e^6 + 107*e^4 + 247*e^2 + 106, 41*e^6 + 446*e^4 + 1217*e^2 + 167, 23*e^6 + 257*e^4 + 729*e^2 + 107, -50*e^6 - 590*e^4 - 1783*e^2 - 296, -99*e^7 - 1163*e^5 - 3548*e^3 - 881*e, -19*e^7 - 228*e^5 - 677*e^3 + 35*e, 48*e^6 + 512*e^4 + 1394*e^2 + 255, 5*e^6 + 96*e^4 + 382*e^2 + 21, 89*e^7 + 1063*e^5 + 3232*e^3 + 459*e, -11*e^7 - 123*e^5 - 356*e^3 - 83*e, -14*e^6 - 146*e^4 - 407*e^2 - 130, -5*e^6 - 27*e^4 + 19*e^2 + 21, 122*e^7 + 1457*e^5 + 4466*e^3 + 839*e, -60*e^7 - 742*e^5 - 2381*e^3 - 601*e, 37*e^6 + 472*e^4 + 1538*e^2 + 250, 21*e^6 + 266*e^4 + 849*e^2 + 81, -62*e^6 - 673*e^4 - 1858*e^2 - 320, 4*e^6 + 48*e^4 + 131*e^2 - 81, -81*e^7 - 952*e^5 - 2856*e^3 - 479*e, -38*e^7 - 459*e^5 - 1421*e^3 - 274*e, 11*e^6 + 99*e^4 + 215*e^2 + 44, 25*e^6 + 291*e^4 + 866*e^2 + 202, -33*e^7 - 362*e^5 - 984*e^3 - 2*e, 73*e^7 + 862*e^5 + 2626*e^3 + 590*e, 30*e^6 + 384*e^4 + 1248*e^2 + 184, 10*e^6 + 64*e^4 + 13*e^2 - 61, -33*e^6 - 352*e^4 - 967*e^2 - 188, 26*e^6 + 294*e^4 + 829*e^2 + 166, 48*e^6 + 545*e^4 + 1589*e^2 + 312, 7*e^6 + 104*e^4 + 385*e^2 - 27, 116*e^7 + 1358*e^5 + 4071*e^3 + 680*e, -67*e^7 - 794*e^5 - 2401*e^3 - 383*e, 24*e^7 + 293*e^5 + 907*e^3 + 104*e, 35*e^7 + 400*e^5 + 1213*e^3 + 434*e, 54*e^7 + 641*e^5 + 1953*e^3 + 407*e, -41*e^7 - 494*e^5 - 1497*e^3 - 103*e, 12*e^6 + 118*e^4 + 301*e^2 + 152, 18*e^6 + 232*e^4 + 750*e^2 + 148, -40*e^6 - 449*e^4 - 1287*e^2 - 178, -33*e^6 - 419*e^4 - 1349*e^2 - 233, 126*e^7 + 1481*e^5 + 4485*e^3 + 921*e, -117*e^7 - 1378*e^5 - 4175*e^3 - 843*e, -131*e^7 - 1547*e^5 - 4700*e^3 - 941*e, -116*e^7 - 1383*e^5 - 4231*e^3 - 786*e, 14*e^6 + 132*e^4 + 293*e^2 + 80, 42*e^4 + 267*e^2 + 70, -34*e^6 - 417*e^4 - 1331*e^2 - 293, 26*e^6 + 331*e^4 + 1084*e^2 + 249, -16*e^6 - 192*e^4 - 564*e^2 - 11, -37*e^6 - 455*e^4 - 1413*e^2 - 183, -37*e^7 - 432*e^5 - 1270*e^3 - 94*e, 70*e^7 + 829*e^5 + 2516*e^3 + 478*e, 17*e^6 + 192*e^4 + 596*e^2 + 208, 16*e^6 + 185*e^4 + 537*e^2 + 65, -6*e^6 - 65*e^4 - 185*e^2 + 86, 7*e^6 + 104*e^4 + 382*e^2 + 32, -74*e^7 - 882*e^5 - 2710*e^3 - 589*e, -87*e^7 - 1040*e^5 - 3192*e^3 - 546*e, 65*e^7 + 781*e^5 + 2434*e^3 + 626*e, -113*e^7 - 1339*e^5 - 4099*e^3 - 935*e, -82*e^7 - 989*e^5 - 3091*e^3 - 733*e, -110*e^7 - 1301*e^5 - 3953*e^3 - 751*e, 51*e^7 + 585*e^5 + 1705*e^3 + 232*e, -4*e^7 - 38*e^5 - 23*e^3 + 302*e, 23*e^6 + 236*e^4 + 592*e^2 + 51, 45*e^6 + 547*e^4 + 1680*e^2 + 250, -13*e^7 - 140*e^5 - 370*e^3 + 15*e, 62*e^7 + 726*e^5 + 2193*e^3 + 497*e, -3*e^7 - 32*e^5 - 52*e^3 + 180*e, 51*e^7 + 621*e^5 + 2001*e^3 + 724*e, -113*e^7 - 1343*e^5 - 4106*e^3 - 800*e, 51*e^7 + 592*e^5 + 1727*e^3 + 142*e, 38*e^6 + 453*e^4 + 1374*e^2 + 254, 33*e^6 + 353*e^4 + 934*e^2 + 89, -145*e^7 - 1726*e^5 - 5285*e^3 - 996*e, -8*e^7 - 82*e^5 - 185*e^3 + 142*e, 12*e^6 + 143*e^4 + 462*e^2 + 171, 36*e^6 + 393*e^4 + 1108*e^2 + 201, 9*e^7 + 108*e^5 + 363*e^3 + 210*e, 25*e^7 + 298*e^5 + 887*e^3 + 65*e, 128*e^7 + 1488*e^5 + 4459*e^3 + 922*e, -7*e^7 - 105*e^5 - 423*e^3 - 287*e, -23*e^6 - 303*e^4 - 1007*e^2 - 77, 30*e^6 + 300*e^4 + 740*e^2 + 70, -104*e^7 - 1239*e^5 - 3801*e^3 - 800*e, -84*e^7 - 997*e^5 - 3072*e^3 - 698*e, -77*e^7 - 896*e^5 - 2702*e^3 - 627*e, 51*e^7 + 604*e^5 + 1812*e^3 + 210*e, 26*e^6 + 284*e^4 + 814*e^2 + 256, 9*e^6 + 120*e^4 + 406*e^2 - 20, 8*e^6 + 107*e^4 + 337*e^2 + 15, -19*e^6 - 256*e^4 - 851*e^2 - 117, 9*e^6 + 112*e^4 + 363*e^2 + 77, -16*e^6 - 230*e^4 - 817*e^2 - 96, 115*e^7 + 1351*e^5 + 4086*e^3 + 843*e, -43*e^7 - 514*e^5 - 1536*e^3 - 57*e, 25*e^6 + 289*e^4 + 874*e^2 + 200, 3*e^6 + 59*e^4 + 296*e^2 + 205, -19*e^6 - 209*e^4 - 552*e^2 + 28, -63*e^6 - 732*e^4 - 2168*e^2 - 344, 14*e^6 + 182*e^4 + 604*e^2 + 43, 27*e^6 + 323*e^4 + 996*e^2 + 97, -48*e^7 - 562*e^5 - 1684*e^3 - 334*e, 55*e^7 + 667*e^5 + 2066*e^3 + 315*e, -163*e^7 - 1922*e^5 - 5823*e^3 - 1061*e, -75*e^7 - 886*e^5 - 2712*e^3 - 638*e, 13*e^6 + 155*e^4 + 434*e^2 - 63, 22*e^6 + 244*e^4 + 715*e^2 + 168, -16*e^6 - 134*e^4 - 250*e^2 - 65, 28*e^6 + 308*e^4 + 886*e^2 + 223, -5*e^6 - 41*e^4 - 35*e^2 + 58, 35*e^6 + 416*e^4 + 1275*e^2 + 321, -6*e^6 - 92*e^4 - 338*e^2 - 95, 24*e^6 + 277*e^4 + 822*e^2 + 66, 58*e^7 + 702*e^5 + 2210*e^3 + 559*e, -113*e^7 - 1329*e^5 - 3983*e^3 - 599*e, 15*e^6 + 139*e^4 + 286*e^2 + 24, -53*e^6 - 607*e^4 - 1751*e^2 - 270, 29*e^7 + 321*e^5 + 874*e^3 - 2*e, 30*e^7 + 349*e^5 + 1056*e^3 + 283*e, -18*e^6 - 229*e^4 - 764*e^2 - 178, -52*e^6 - 652*e^4 - 2100*e^2 - 345, 39*e^6 + 482*e^4 + 1519*e^2 + 251, 19*e^6 + 205*e^4 + 589*e^2 + 133, 82*e^7 + 974*e^5 + 3019*e^3 + 860*e, -50*e^7 - 593*e^5 - 1874*e^3 - 688*e, -8*e^6 - 54*e^4 - 74*e^2 - 176, 3*e^6 + 56*e^4 + 240*e^2 + 114, 94*e^7 + 1136*e^5 + 3544*e^3 + 745*e, -82*e^7 - 983*e^5 - 3049*e^3 - 715*e, 39*e^6 + 503*e^4 + 1643*e^2 + 306, 9*e^6 + 110*e^4 + 338*e^2 + 39, -98*e^7 - 1145*e^5 - 3479*e^3 - 896*e, -5*e^7 - 58*e^5 - 139*e^3 + 205*e, 36*e^6 + 432*e^4 + 1317*e^2 + 253, -39*e^6 - 490*e^4 - 1583*e^2 - 315, -26*e^7 - 313*e^5 - 987*e^3 - 302*e, -8*e^7 - 104*e^5 - 397*e^3 - 423*e, -23*e^6 - 259*e^4 - 733*e^2 - 42, -10*e^6 - 156*e^4 - 586*e^2 - 45, 47*e^7 + 554*e^5 + 1705*e^3 + 469*e, -76*e^7 - 901*e^5 - 2727*e^3 - 456*e, -16*e^6 - 194*e^4 - 626*e^2 - 148, -21*e^6 - 202*e^4 - 496*e^2 - 180, 101*e^7 + 1194*e^5 + 3673*e^3 + 923*e, -80*e^7 - 937*e^5 - 2827*e^3 - 532*e, -25*e^6 - 275*e^4 - 760*e^2 - 63, -23*e^6 - 274*e^4 - 832*e^2 - 149, 41*e^7 + 487*e^5 + 1549*e^3 + 659*e, 146*e^7 + 1722*e^5 + 5203*e^3 + 903*e, 91*e^7 + 1071*e^5 + 3254*e^3 + 690*e, -79*e^7 - 927*e^5 - 2827*e^3 - 698*e, -32*e^6 - 391*e^4 - 1223*e^2 - 192, 24*e^6 + 252*e^4 + 691*e^2 + 220, -26*e^7 - 296*e^5 - 866*e^3 - 130*e, 41*e^7 + 499*e^5 + 1555*e^3 + 283*e, -17*e^6 - 196*e^4 - 588*e^2 - 159, -33*e^6 - 382*e^4 - 1132*e^2 - 203, -38*e^6 - 386*e^4 - 962*e^2 - 107, -13*e^6 - 116*e^4 - 262*e^2 - 162, 98*e^7 + 1159*e^5 + 3545*e^3 + 822*e, -11*e^7 - 106*e^5 - 235*e^3 + 58*e, -2*e^7 - 35*e^5 - 151*e^3 - 127*e, -29*e^7 - 340*e^5 - 1044*e^3 - 277*e, 20*e^6 + 259*e^4 + 862*e^2 + 83, -41*e^6 - 416*e^4 - 1052*e^2 - 182, 26*e^6 + 304*e^4 + 920*e^2 + 204, 49*e^6 + 567*e^4 + 1672*e^2 + 251, -17*e^6 - 188*e^4 - 519*e^2 - 83, 7*e^6 + 114*e^4 + 442*e^2 + 60, -59*e^6 - 709*e^4 - 2176*e^2 - 389, 33*e^6 + 322*e^4 + 787*e^2 + 225, -38*e^7 - 427*e^5 - 1204*e^3 - 94*e, -64*e^7 - 757*e^5 - 2280*e^3 - 346*e, -50*e^7 - 583*e^5 - 1760*e^3 - 459*e, -132*e^7 - 1583*e^5 - 4871*e^3 - 897*e, -53*e^6 - 652*e^4 - 2054*e^2 - 358, 6*e^6 + 30*e^4 - 38*e^2 - 15, 8*e^6 + 91*e^4 + 261*e^2 - 20, 20*e^6 + 246*e^4 + 764*e^2 + 235, -15*e^6 - 145*e^4 - 350*e^2 - 40, 47*e^6 + 550*e^4 + 1648*e^2 + 260, -45*e^7 - 541*e^5 - 1694*e^3 - 410*e, 4*e^7 + 48*e^5 + 127*e^3 - 99*e, 28*e^6 + 293*e^4 + 791*e^2 + 188, 21*e^6 + 276*e^4 + 928*e^2 + 155, -28*e^6 - 340*e^4 - 1042*e^2 - 113, 23*e^6 + 259*e^4 + 702*e^2 + 3, -41*e^6 - 455*e^4 - 1289*e^2 - 245, -3*e^6 - 79*e^4 - 362*e^2 - 31, 30*e^7 + 373*e^5 + 1197*e^3 + 292*e, 65*e^7 + 765*e^5 + 2370*e^3 + 723*e, 14*e^6 + 189*e^4 + 679*e^2 + 244, -11*e^6 - 164*e^4 - 596*e^2 - 178, 9*e^6 + 110*e^4 + 391*e^2 + 215, 27*e^6 + 307*e^4 + 883*e^2 + 48, 145*e^7 + 1699*e^5 + 5107*e^3 + 906*e, 111*e^7 + 1319*e^5 + 4054*e^3 + 909*e, -37*e^6 - 460*e^4 - 1452*e^2 - 312, 10*e^6 + 139*e^4 + 481*e^2 + 124, -9*e^7 - 110*e^5 - 365*e^3 - 198*e, -98*e^7 - 1158*e^5 - 3519*e^3 - 683*e, 31*e^4 + 177*e^2 - 42, -17*e^6 - 191*e^4 - 556*e^2 - 195, -24*e^7 - 278*e^5 - 839*e^3 - 264*e, -112*e^7 - 1326*e^5 - 4051*e^3 - 806*e, 59*e^6 + 704*e^4 + 2151*e^2 + 381, -32*e^6 - 403*e^4 - 1293*e^2 - 202, -11*e^6 - 114*e^4 - 287*e^2 - 37, -13*e^6 - 129*e^4 - 305*e^2 - 87, 52*e^7 + 612*e^5 + 1832*e^3 + 225*e, 84*e^7 + 992*e^5 + 2979*e^3 + 394*e, -12*e^6 - 157*e^4 - 505*e^2 - 55, -44*e^6 - 468*e^4 - 1243*e^2 - 124, 45*e^7 + 532*e^5 + 1643*e^3 + 482*e, 16*e^7 + 202*e^5 + 700*e^3 + 420*e, 70*e^7 + 836*e^5 + 2564*e^3 + 526*e, 58*e^7 + 682*e^5 + 2055*e^3 + 369*e, 13*e^7 + 137*e^5 + 374*e^3 + 121*e, 131*e^7 + 1540*e^5 + 4641*e^3 + 838*e, -39*e^6 - 432*e^4 - 1239*e^2 - 231, 7*e^6 + 74*e^4 + 230*e^2 + 133, -37*e^6 - 409*e^4 - 1124*e^2 - 95, 2*e^6 + 14*e^4 + 27*e^2 + 12, -20*e^6 - 267*e^4 - 871*e^2 - 74, 37*e^6 + 409*e^4 + 1177*e^2 + 275, -121*e^7 - 1449*e^5 - 4470*e^3 - 894*e, 15*e^7 + 183*e^5 + 593*e^3 + 253*e, 73*e^7 + 861*e^5 + 2611*e^3 + 484*e, 83*e^7 + 991*e^5 + 3047*e^3 + 565*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7,7,-w + 1])] = -e^7 - 12*e^5 - 37*e^3 - 7*e # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]