# Stored data for newform 1100.3.e.b, downloaded from the LMFDB on 23 May 2024. {"Nk2": 9900, "analytic_conductor": 29.97282907963266, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 55, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": -1, "char_values": [1100, 2, [551, 177, 101], [2, 1, 1]], "cm_discs": [], "conrey_index": 549, "dim": 16, "field_disc": 1284935625715104104857600000000, "field_disc_factorization": [[2, 20], [5, 8], [691, 2], [1601, 4]], "field_poly": [92416, 0, 633600, 0, 1098976, 0, 712960, 0, 215801, 0, 32605, 0, 2456, 0, 85, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [1936, 0, 4200, 0, 793, 0, 50, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503874555610188, "hecke_ring_generator_nbound": 23, "hecke_ring_index": 838860800, "hecke_ring_index_factorization": [[2, 25], [5, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 55, 4, -1, 2, 0], [1, 1, 11, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1100.3.e.b", "level": 1100, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 5, 11], "level_radical": 110, "minimal_twist": "220.3.f.a", "prim_orbit_index": 4, "qexp_display": "q+(-\\beta _{9}+\\beta _{10})q^{3}-\\beta _{4}q^{7}+(-3+\\beta _{1}+\\cdots)q^{9}+\\cdots", "related_objects": [], "relative_dim": 16, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1100.3.e", "trace_display": [0, 0, 0, 0], "trace_hash": 1636122634740038049, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.225", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1994.645", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "435879.776", "prec": 34}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.758", "prec": 17}, "traces": [0, 16, 0, 0, 0, 0, 0, 0, 0, -56, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 488, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, -440, 0, 0, 0, 0, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, 0, 0, -440, 0, -144, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1512, 0, 0, 0, 0, 0, 0, 0, -808, 0, -960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1504, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 1648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, -56, 0, -304, 0, 0, 0, 0, 0, 0, 0, 280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -944, 0, 0, 0, 0, 0, 0, 0, 976, 0, -2424, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2888, 0, 3088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, 0, -2208, 0, -568, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -496, 0, 0, 0, 0, 0, 0, 0, 576, 0, -528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1840, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 840, 0, 1592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5072, 0, 0, 0, 0, 0, 0, 0, 2704, 0, -2688, 0, 0, 0, 0, 0, 0, 0, -1952, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7320, 0, 0, 0, 0, 0, 0, 0, -1776, 0, -5040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1488, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, -704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2000, 0, 0, 0, 0, 0, 0, 0, 3120, 0, -4240, 0, 0, 0, 0, 0, 0, 0, -672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5720, 0, 0, 0, 0, 0, 0, 0, -2448, 0, -4664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3896, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 800, 0, 4080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5512, 0, 0, 0, 0, 0, 0, 0, 3184, 0, -7848, 0, 0, 0, 0, 0, 0, 0, 1472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5216, 0, 0, 0, 0, 0, 0, 0, 144, 0, -7928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4352, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4384, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12480, 0, 0, 0, 0, 0, 0, 0, -7808, 0, -10024, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4400, 0, 0, 0, 0, 0, 0, 0, -1200, 0, -2528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3312, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5888, 0, -2552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368, 0, 0, 0, 0, 0, 0, 0, -288, 0, -25520, 0, 0, 0, 0, 0, 0, 0, 4624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, -4928, 0, -4688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2440, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11408, 0, -1624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7160, 0, 0, 0, 0, 0, 0, 0, -3640, 0, -11232, 0, 0, 0, 0, 0, 0, 0, 3632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 304, 0, 0, 0, 0, 0, 0, 0, 1592, 0, -10800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1840, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2760, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1120, 0, 3408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15536, 0, 0, 0, 0, 0, 0, 0, 8752, 0, -9696, 0, 0, 0, 0, 0, 0, 0, 2376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4432, 0, 0, 0, 0, 0, 0, 0, -9680, 0, -3792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5000, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2216, 0, 6896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23584, 0, 0, 0, 0, 0, 0, 0, -7280, 0, -11408, 0, 0, 0, 0, 0, 0, 0, -592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3536, 0, 0, 0, 0, 0, 0, 0, 2736, 0, -2272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5456, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14272, 0, -1224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6896, 0, 0, 0, 0, 0, 0, 0, 21328, 0, -9632, 0, 0, 0, 0, 0, 0, 0, -5200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6600, 0, 0, 0, 0, 0, 0, 0, -8752, 0, -1872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10152, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12896, 0, -624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12952, 0, 0, 0, 0, 0, 0, 0, -11352, 0, -22896, 0, 0, 0, 0, 0, 0, 0, 9392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7272, 0, 0, 0, 0, 0, 0, 0, 7032, 0, -5064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11656, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9992, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4448, 0, -4400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6808, 0, 0, 0, 0, 0, 0, 0, 36672, 0, -15992, 0, 0, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9504, 0, 0, 0, 0, 0, 0, 0, -4720, 0, 704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1880, 0, -18432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2144, 0, 0, 0, 0, 0, 0, 0, -26752, 0, -14584, 0, 0, 0, 0, 0, 0, 0, -4552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11504, 0, 0, 0, 0, 0, 0, 0, 5392, 0, 1904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5008, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30272, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2048, 0, -1224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 4624, 0, -5424, 0, 0, 0, 0, 0, 0, 0, -12256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1144, 0, 0, 0, 0, 0, 0, 0, 3928, 0, -10928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7248, 0, 22512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12984, 0, 0, 0, 0, 0, 0, 0, -7296, 0, 1568, 0, 0, 0, 0, 0, 0, 0, 12928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8248, 0, 0, 0, 0, 0, 0, 0, -16808, 0, -5760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3680, 0, -3264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 11688, 0, -6536, 0, 0, 0, 0, 0, 0, 0, -4688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8880, 0, 0, 0, 0, 0, 0, 0, 5328, 0, 1392, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 3, "weight_parity": -1, "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, 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, 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, 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], [-3, 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, 0], [3, 0, 0, 1, 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, 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, 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, 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, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 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, -2, 4, -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, 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, 3, 4, 2, -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, 2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -5, -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, 0, 2, -1, -1, -1, 0, 4, 3, -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, 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, -8, 7, 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, -5, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 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, 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, -6, 14, -5, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [27, -2, -7, -11, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 2, 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, 6, 5, -2, 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, 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, 3, 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, -4, 8, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -5, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 10, -4, 1, -3, 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, 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, -5, 15, 3, -5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10, -1, 6, 14, 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], [-24, -6, 7, 12, 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, -2, 3, 3, 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, 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, -3, 4, -19, 12, 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, 0, 3, 1, -1, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-27, 2, 2, -16, 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, -8, -4, -2, 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, 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, -2, -1, 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], [-26, 14, 3, -3, 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], [-10, -16, -2, -15, 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, 0, 0, -24, -12, 11, 6, 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, 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, 9, -17, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -2, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}