# Stored data for newform 1840.3.k.c, downloaded from the LMFDB on 16 April 2024. {"label": "1840.3.k.c", "space_label": "1840.3.k", "level": 1840, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007886499841840, "dim": 16, "is_polredabs": true, "trace_hash": 201380207886494777, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1156, 472, -2557, 12, 724, 8, -52, 0, 1]]], "qexp_display": "q-\\beta _{3}q^{3}-\\beta _{4}q^{5}-\\beta _{7}q^{7}+(4+\\beta _{2}+\\cdots)q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 23, "char_orbit_label": "k", "char_is_real": true, "Nk2": 16560, "analytic_conductor": 50.13636864229463, "hecke_ring_index": 64, "level_radical": 230, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [1840, 2, [1151, 1381, 737, 1201], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 5, 23], "conrey_indexes": [321], "field_disc": 328225278704249970452188416172583064601600000000, "field_disc_factorization": [[2, 16], [5, 8], [23, 2], [2293, 2], [67894428887071, 2]], "field_poly": [1535848276, 72566336, 327235800, -8913096, 38013345, -4237944, 1261236, 196544, 374528, 12360, -30106, 648, 2252, -16, -64, 0, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "13.514", "prec": 20}, {"__RealLiteral__": 0, "data": "6.255", "prec": 17}, {"__RealLiteral__": 0, "data": "1021.242", "prec": 27}, {"__RealLiteral__": 0, "data": "278.386", "prec": 24}, {"__RealLiteral__": 0, "data": "112691.368", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, -80, 0, -48, 0, 90, 0, -10, 0, 0, 0, -30, 0, 0, 0, -20, 0, 186, 0, 0, 0, 0, 0, 320, 0, 2, 0, 0, 0, 0, 0, 120, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, -232, 0, 238, 0, -280, 0, 0, 0, 324, 0, 0, 0, 704, 0, 0, 0, -30, 0, -724, 0, 0, 0, 0, 0, -380, 0, -80, 0, 0, 0, 0, 0, -158, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, -140, 0, 82, 0, 252, 0, -572, 0, 0, 0, -244, 0, 0, 0, -420, 0, -276, 0, 0, 0, 0, 0, 862, 0, -356, 0, 0, 0, 0, 0, 220, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, 0, 0, -814, 0, 192, 0, -340, 0, -100, 0, 696, 0, 0, 0, 72, 0, 0, 0, -1268, 0, -380, 0, 0, 0, 0, 0, 10, 0, -484, 0, 0, 0, 0, 0, -1020, 0, 0, 0, -672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274, 0, -648, 0, 150, 0, 2036, 0, -340, 0, 0, 0, -732, 0, 0, 0, 308, 0, -320, 0, 0, 0, 0, 0, 1684, 0, 984, 0, 0, 0, 0, 0, 1598, 0, 0, 0, -2552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 604, 0, -760, 0, -232, 0, -1022, 0, 690, 0, 0, 0, -550, 0, 0, 0, 314, 0, -1478, 0, 0, 0, 0, 0, -612, 0, -102, 0, 0, 0, 0, 0, -260, 0, 0, 0, 410, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 20, 0, 1852, 0, 480, 0, -716, 0, 0, 0, -844, 0, 0, 0, 450, 0, 68, 0, 0, 0, 0, 0, -1012, 0, 60, 0, 0, 0, 0, 0, -822, 0, 0, 0, -370, 0, 0, 0, 0, 0, 0, 0, 0, 0, 680, 0, -468, 0, -1390, 0, 1440, 0, -748, 0, 0, 0, -244, 0, 0, 0, -1380, 0, 1600, 0, 0, 0, 0, 0, 2394, 0, -378, 0, 0, 0, 0, 0, 1800, 0, 0, 0, -2300, 0, 0, 0, 0, 0, 0, 0, 0, 0, -530, 0, 2512, 0, 40, 0, 516, 0, 2260, 0, 0, 0, 2168, 0, 0, 0, -2564, 0, -1914, 0, 0, 0, 0, 0, 350, 0, -1972, 0, 0, 0, 0, 0, 2808, 0, 0, 0, 436, 0, 0, 0, 0, 0, 0, 0, 0, 0, -172, 0, 1632, 0, 1254, 0, -1524, 0, 520, 0, 0, 0, 1794, 0, 0, 0, -1680, 0, -400, 0, 0, 0, 0, 0, 1700, 0, 1152, 0, 0, 0, 0, 0, 1390, 0, 0, 0, 920, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1228, 0, 840, 0, -1700, 0, -2180, 0, 106, 0, 0, 0, 2540, 0, 0, 0, -1738, 0, 1200, 0, 0, 0, 0, 0, 3880, 0, 2572, 0, 0, 0, 0, 0, 980, 0, 0, 0, -284, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1492, 0, 3334, 0, -1048, 0, -450, 0, 1808, 0, 0, 0, 1996, 0, 0, 0, -1340, 0, -2068, 0, 0, 0, 0, 0, 4876, 0, 200, 0, 0, 0, 0, 0, 6496, 0, 0, 0, -230, 0, 0, 0, 0, 0, 0, 0, 0, 0, -70, 0, 2976, 0, -3196, 0, -3550, 0, 4436, 0, 0, 0, 3048, 0, 0, 0, -3408, 0, -4296, 0, 0, 0, 0, 0, -3268, 0, -526, 0, 0, 0, 0, 0, -3832, 0, 0, 0, 1132, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2076, 0, 908, 0, 400, 0, 7688, 0, -2946, 0, 0, 0, -1212, 0, 0, 0, -6260, 0, 198, 0, 0, 0, 0, 0, 220, 0, -1116, 0, 0, 0, 0, 0, -1932, 0, 0, 0, -6224, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3400, 0, -1680, 0, -4196, 0, -1492, 0, 240, 0, 0, 0, -1084, 0, 0, 0, -4088, 0, -1180, 0, 0, 0, 0, 0, 1288, 0, 156, 0, 0, 0, 0, 0, -748, 0, 0, 0, -2604, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1040, 0, -2540, 0, 2012, 0, 646, 0, -4028, 0, 0, 0, -450, 0, 0, 0, 5068, 0, 3764, 0, 0, 0, 0, 0, 3036, 0, 5974, 0, 0, 0, 0, 0, 1360, 0, 0, 0, 414, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1956, 0, -2158, 0, -3536, 0, 190, 0, -3520, 0, 0, 0, -1924, 0, 0, 0, 50, 0, 4812, 0, 0, 0, 0, 0, -1208, 0, 770, 0, 0, 0, 0, 0, -234, 0, 0, 0, -260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1440, 0, -5820, 0, -374, 0, 1402, 0, -2252, 0, 0, 0, -4312, 0, 0, 0, 4592, 0, 232, 0, 0, 0, 0, 0, 1662, 0, 1756, 0, 0, 0, 0, 0, 6960, 0, 0, 0, 238, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1754, 0, 1424, 0, 160, 0, -3816, 0, 1094, 0, 0, 0, 548, 0, 0, 0, 6604, 0, -5368, 0, 0, 0, 0, 0, 150, 0, -1448, 0, 0, 0, 0, 0, 2180, 0, 0, 0, 3828, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6160, 0, 7078, 0, -2054, 0, -6544, 0, 1920, 0, 0, 0, 6686, 0, 0, 0, 636, 0, -2940, 0, 0, 0, 0, 0, 2020, 0, 144, 0, 0, 0, 0, 0, -4822, 0, 0, 0, 4768, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2792, 0, 1360, 0, -2928, 0, 3260, 0, 2400, 0, 0, 0, 2400, 0, 0, 0, -7704, 0, 2250, 0, 0, 0, 0, 0, 10008, 0, 2564, 0, 0, 0, 0, 0, 100, 0, 0, 0, -5616, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7004, 0, 3786, 0, -3948, 0, 2580, 0, 4948, 0, 0, 0, -1788, 0, 0, 0, -3840, 0, -6580, 0, 0, 0, 0, 0, 1276, 0, -150, 0, 0, 0, 0, 0, -4674, 0, 0, 0, -930, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2390, 0, 5268, 0, 2064, 0, 484, 0, -1152, 0, 0, 0, 14100, 0, 0, 0, 3612, 0, -6196, 0, 0, 0, 0, 0, -5436, 0, 2558, 0, 0, 0, 0, 0, 4592, 0, 0, 0, -2206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1104, 0, 5768, 0, 650, 0, -32, 0, -13248, 0, 0, 0, 2372, 0, 0, 0, -5308, 0, 7026, 0, 0, 0, 0, 0, -2600, 0, 1720, 0, 0, 0, 0, 0, 3364, 0, 0, 0, -2504, 0, 0, 0, 0, 0, 0, 0, 0, 0, -494, 0, -498, 0, 988, 0, -2120, 0, -1980, 0, 0, 0, -7366, 0, 0, 0, -3764, 0, 3040, 0, 0, 0, 0, 0, -2750, 0, 4096, 0, 0, 0, 0, 0, 1704, 0, 0, 0, 2564, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4812, 0, -1600, 0, 1556, 0, -10472, 0, 4202, 0, 0, 0, -2700, 0, 0, 0, 5058, 0, -1608, 0, 0, 0, 0, 0, -10972, 0, -3272, 0, 0, 0, 0, 0, 1560, 0, 0, 0, 10496, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3398, 0, 8784, 0, 1296, 0, -10, 0, -11868, 0, 0, 0, -188, 0, 0, 0, 3220, 0, 4364, 0, 0, 0, 0, 0, -2636, 0, -2180, 0, 0, 0, 0, 0, 6246, 0, 0, 0, 2360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1720, 0, -11884, 0, -9140, 0, -6350, 0, -1308, 0, 0, 0, -8032, 0, 0, 0, -4916, 0, -248, 0, 0, 0, 0, 0, 6870, 0, 2108, 0, 0, 0, 0, 0, -1048, 0, 0, 0, -3092, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4432, 0, -10816, 0, -1210, 0, 8096, 0, 1138, 0, 0, 0, -15752, 0, 0, 0, 8188, 0, -2636, 0, 0, 0, 0, 0, 9100, 0, 944, 0, 0, 0, 0, 0, 11476, 0, 0, 0, -2124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5456, 0, 21972, 0, -690, 0, 180, 0, 8140, 0, 0, 0, 8630, 0, 0, 0, 8736, 0, -600, 0, 0, 0, 0, 0, -4938, 0, 4992, 0, 0, 0, 0, 0, -8952, 0, 0, 0, 5168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9484, 0, 3320, 0, 2868, 0, -1162, 0, -8514, 0, 0, 0, 4150, 0, 0, 0, -2712, 0, -1352, 0, 0, 0, 0, 0, 11624, 0, 890, 0, 0, 0, 0, 0, -4770, 0, 0, 0, 482, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9358, 0, -2962, 0, -9916, 0, 2080, 0, 18444, 0, 0, 0, 4588, 0, 0, 0, -3790, 0, -13264, 0, 0, 0, 0, 0, -4724, 0, -450, 0, 0, 0, 0, 0, -5322, 0, 0, 0, -7860, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 16420, 0, -2714, 0, 9328, 0, 5348, 0, 0, 0, 5440, 0, 0, 0, -7330, 0, 2468, 0, 0, 0, 0, 0, -8636, 0, -220, 0, 0, 0, 0, 0, -15184, 0, 0, 0, -8654, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6554, 0, 8664, 0, -300, 0, 6760, 0, -14460, 0, 0, 0, 10612, 0, 0, 0, -26328, 0, 7960, 0, 0, 0, 0, 0, -2530, 0, -7232, 0, 0, 0, 0, 0, 8196, 0, 0, 0, -20292, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6472, 0, -9524, 0, 11548, 0, -5568, 0, -4360, 0, 0, 0, -27104, 0, 0, 0, 736, 0, 7360, 0, 0, 0, 0, 0, -1952, 0, 12244, 0, 0, 0, 0, 0, 14014, 0, 0, 0, 8672, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3104, 0, -8860, 0, 1536, 0, -8168, 0, -10132, 0, 0, 0, -4080, 0, 0, 0, 14640, 0, 4676, 0, 0, 0, 0, 0, -9168, 0, -984, 0, 0, 0, 0, 0, 7890, 0, 0, 0, 16630, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2904, 0, 746, 0, -16556, 0, -3440, 0, -7440, 0, 0, 0, 4152, 0, 0, 0, 5240, 0, 7368, 0, 0, 0, 0, 0, -7352, 0, -3960, 0, 0, 0, 0, 0, -1274, 0, 0, 0, 3750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1160, 0, -20988, 0, -3856, 0, -3164, 0, 5264, 0, 0, 0, -27132, 0, 0, 0, 558, 0, -5076, 0, 0, 0, 0, 0, 4064, 0, -6560, 0, 0, 0, 0, 0, 6304, 0, 0, 0, 11352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1136, 0, -18544, 0, -1190, 0, 44, 0, 12336, 0, 0, 0, -14468, 0, 0, 0, 16464, 0, -626, 0, 0, 0, 0, 0, 5240, 0, -10696, 0, 0, 0, 0, 0, -8108, 0, 0, 0, 9696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9460, 0, 17714, 0, -200, 0, -4256, 0, 1400, 0, 0, 0, 11878, 0, 0, 0, 17640, 0, -5690, 0, 0, 0, 0, 0, 2794, 0, 8240, 0, 0, 0, 0, 0, -3528, 0, 0, 0, -3696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13206, 0, -40, 0, 2256, 0, 7848, 0, 1802, 0, 0, 0, 0, 0, 0, 0, -13700, 0, -10124, 0, 0, 0, 0, 0, 22316, 0, 3052, 0, 0, 0, 0, 0, -2260, 0, 0, 0, -5086, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8438, 0, 11096, 0, 1384, 0, 6110, 0, 27560, 0, 0, 0, 5418, 0, 0, 0, -1620, 0, -13476, 0, 0, 0, 0, 0, -1760, 0, -2720, 0, 0, 0, 0, 0, -12060, 0, 0, 0, -4840, 0, 0, 0, 0, 0, 0, 0, 0, 0, -780, 0, 19344, 0, 18276, 0, 1706, 0, 14256, 0, 0, 0, 35340, 0, 0, 0, 7948, 0, 5008, 0, 0, 0, 0, 0, -21138, 0, 3626, 0, 0, 0, 0, 0, -15108, 0, 0, 0, 2616, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 23, 2, -1, 2, 0]], "char_orbit_index": 11, "prim_orbit_index": 2, "minimal_twist": "460.3.f.a", "char_is_minimal": false, "conrey_index": 321, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -1, -6, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 0, -6, 0, 1, 3, 1, 1, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, -2, 0, -2, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 1, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -4, 0, -1, 0, -1, -1, 2, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -5, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [20, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -12, 0, 1, 1, 0, 4, 2, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, -8, 0, 1, 0, -1, 3, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, -8, 0, 0, 5, 0, 6, 1, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 1, 6, 0, -1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 6, 0, -2, 0, 0, -3, 2, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 8, 0, -2, -3, -2, -2, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 1, -1, 1, -1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, -6, 0, 2, 2, 0, 4, -1, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-15, 2, -1, -2, 10, 1, -3, -2, -1, -2, 0, -2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [16, 0, 1, -12, 0, -1, 0, 0, 0, 0, 0, 0, 1, -3, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-16, 0, -1, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, -5, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [21, 0, 0, -9, 0, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, -1, 6, 1, -3, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [44, 0, 5, 14, 0, -4, 0, 0, 0, 0, 0, 3, 2, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 8, 0, -1, -6, -3, -1, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-46, 0, -3, -5, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -12, 0, 0, 10, 0, 1, 0, 1, -5, 0, 0, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, -8, 0, -5, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-25, 0, 1, 2, 0, -3, 0, 0, 0, 0, 0, -3, 2, 5, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 8, 0, -2, 0, 0, 2, 4, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 12, 0, 0, 38, 0, -1, -5, 0, -10, -4, 0, 0, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}