# Stored data for newform 1045.2.b.c, downloaded from the LMFDB on 19 April 2024. {"label": "1045.2.b.c", "space_label": "1045.2.b", "level": 1045, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007268007773205, "dim": 20, "is_polredabs": true, "trace_hash": 1755655671497004675, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [4, 0, 276, 0, 2753, 0, 9095, 0, 13894, 0, 11551, 0, 5623, 0, 1640, 0, 281, 0, 26, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{7}q^{3}+(-1+\\beta _{2})q^{4}-\\beta _{11}q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 4180, "analytic_conductor": 8.3443670112238, "hecke_ring_index": 32, "level_radical": 1045, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [1045, 2, [837, 761, 496], [1, 2, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [5, 11, 19], "conrey_indexes": [419], "field_disc": 19561281735488561148431437524688175104, "field_disc_factorization": [[2, 22], [1493, 2], [1699, 2], [21739, 2], [39163, 2]], "field_poly": [4, 0, 276, 0, 2753, 0, 9095, 0, 13894, 0, 11551, 0, 5623, 0, 1640, 0, 281, 0, 26, 0, 1], "hecke_ring_index_factorization": [[2, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.200", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1138.606", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "147727.259", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 20, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 20, 0, 0, -12, 0, -8, 0, 0, -10, -6, 20, 0, 0, 24, -6, -4, 0, 0, 20, -6, -30, 0, 0, 38, 2, 8, 0, 0, 50, -20, -50, 0, 0, 28, 6, -12, 0, 0, 48, 12, -34, 0, 0, -12, -18, -36, 0, 0, -6, 26, -40, 0, 0, -6, 0, -40, 0, 0, 30, -30, -14, 0, 0, 36, 30, -8, 0, 0, -12, -54, -40, 0, 0, 50, -8, -12, 0, 0, 106, 8, 0, 0, 0, -30, -22, 56, 0, 0, 36, -64, -56, 0, 0, 28, 0, 66, 0, 0, -10, -48, -56, 0, 0, -6, -58, 48, 0, 0, 100, -6, 22, 0, 0, -8, 0, -102, 0, 0, -8, -24, 20, 0, 0, 92, -18, 26, 0, 0, 90, -76, -40, 0, 0, -10, 50, 22, 0, 0, 34, -146, -2, 0, 0, 58, 8, 36, 0, 0, 46, -6, -138, 0, 0, 24, -24, -28, 0, 0, 76, 8, -66, 0, 0, 46, -6, -32, 0, 0, -14, -24, -10, 0, 0, 42, -50, -4, 0, 0, 28, -100, -92, 0, 0, 108, -14, 132, 0, 0, 136, -6, -66, 0, 0, 16, -84, 92, 0, 0, 140, -56, 26, 0, 0, 56, -42, 36, 0, 0, 20, -168, -126, 0, 0, 66, -16, 22, 0, 0, -14, -6, 42, 0, 0, -2, 26, -110, 0, 0, 4, -110, -30, 0, 0, 46, 54, -6, 0, 0, 90, -66, -46, 0, 0, 64, 48, 164, 0, 0, 88, -124, 66, 0, 0, 110, 0, -60, 0, 0, 38, -56, -150, 0, 0, 38, -52, 24, 0, 0, 86, -88, -40, 0, 0, 40, 2, -8, 0, 0, 66, 38, -56, 0, 0, 4, -6, 8, 0, 0, 26, 34, -10, 0, 0, 272, -62, 178, 0, 0, -20, -116, 8, 0, 0, -4, -30, -58, 0, 0, -60, 18, 36, 0, 0, 60, -54, -202, 0, 0, 50, -124, -44, 0, 0, 164, 58, -116, 0, 0, -32, -20, -130, 0, 0, -186, 40, 150, 0, 0, -136, -8, -50, 0, 0, 2, 0, -8, 0, 0, 10, 140, -64, 0, 0, -26, 40, 104, 0, 0, 28, -102, 20, 0, 0, 230, -16, -46, 0, 0, 22, -44, 160, 0, 0, 28, -102, -98, 0, 0, 88, -6, 26, 0, 0, -12, 6, 38, 0, 0, -48, -128, -16, 0, 0, 4, -54, -12, 0, 0, -30, 104, -34, 0, 0, 148, 178, -12, 0, 0, 104, -72, 18, 0, 0, -138, 54, -52, 0, 0, 18, 62, -102, 0, 0, -90, -54, -30, 0, 0, 48, -98, -22, 0, 0, -234, 72, -86, 0, 0, 158, 12, 122, 0, 0, -234, 26, 220, 0, 0, -40, -164, -34, 0, 0, 66, 132, 38, 0, 0, 156, -66, -44, 0, 0, -20, 148, 38, 0, 0, -14, -58, 46, 0, 0, -44, 2, 14, 0, 0, -34, 58, -106, 0, 0, -12, -150, 236, 0, 0, -116, -16, -4, 0, 0, 8, -18, -238, 0, 0, 74, -130, 108, 0, 0, -142, -14, -36, 0, 0, -26, -8, -228, 0, 0, 36, 44, 0, 0, 0, -26, 104, -58, 0, 0, -166, 120, 194, 0, 0, 20, 4, -48, 0, 0, 234, 174, 114, 0, 0, -6, 136, -122, 0, 0, 16, 40, 474, 0, 0, 102, 26, 50, 0, 0, 42, -114, -126, 0, 0, 76, -140, -40, 0, 0, -162, 150, 102, 0, 0, 48, -20, -172, 0, 0, 54, -42, -30, 0, 0, -92, -114, -24, 0, 0, -20, -144, 52, 0, 0, -50, 74, -324, 0, 0, -6, 12, 94, 0, 0, 54, -78, 100, 0, 0, 250, 0, -82, 0, 0, -406, 206, -202, 0, 0, -250, 14, -40, 0, 0, -74, -20, 182, 0, 0, 164, 62, 302, 0, 0, 74, 90, -210, 0, 0, -84, -104, 128, 0, 0, 220, -34, 48, 0, 0, 130, 144, 28, 0, 0, 30, -104, -108, 0, 0, -248, 16, 38, 0, 0, -16, -30, -26, 0, 0, -202, 6, -338, 0, 0, -58, -60, -14, 0, 0, -80, 184, 132, 0, 0, 230, -24, 34, 0, 0, -12, 152, 104, 0, 0, -82, -266, 46, 0, 0, 258, -20, 152, 0, 0, 38, 96, -130, 0, 0, 36, 2, -160, 0, 0, -90, -36, -260, 0, 0, -254, 30, 194, 0, 0, -140, 66, -2, 0, 0, 108, 92, -8, 0, 0, -238, 310, 24, 0, 0, 116, -60, 102, 0, 0, 40, 38, 48, 0, 0, -238, 20, 254, 0, 0, 16, -58, -310, 0, 0, -378, 70, 2, 0, 0, -12, 12, -78, 0, 0, -82, 140, -108, 0, 0, -56, -54, -52, 0, 0, -284, -18, 168, 0, 0, -34, 246, -40, 0, 0, -32, 338, 264, 0, 0, 84, 24, -108, 0, 0, 52, 186, -30, 0, 0, 166, -140, -64, 0, 0, 400, 62, -148, 0, 0, -56, 96, -100, 0, 0, 50, 2, 100, 0, 0, -48, 188, -2, 0, 0, -118, -8, -118, 0, 0, -226, -76, 102, 0, 0, -314, 44, -12, 0, 0, -76, -8, 58, 0, 0, 248, 280, 274, 0, 0, 22, 100, -12, 0, 0, -308, -18, -10, 0, 0, 112, 8, 26, 0, 0, -270, 54, 168, 0, 0, 106, -176, -92, 0, 0, -36, 160, -136, 0, 0, 310, 8, 134, 0, 0, -324, 112, 6, 0, 0, -84, -150, 0, 0, 0, -218, 204, 180, 0, 0, 32, -168, -294, 0, 0, 84, 28, 442, 0, 0, -402, 136, -102, 0, 0, 50, 68, 126, 0, 0, 110, 336, -178, 0, 0, -30, -124, -2, 0, 0, -60, -146, -6, 0, 0, -152, -22, 336, 0, 0, 164, -32, -128, 0, 0, -366, 112, 56, 0, 0, -54, 26, 140, 0, 0, 110, -56, -54, 0, 0, 4, 138, 134, 0, 0, -460, 4, 360, 0, 0, -40, 196, 218, 0, 0, -240, 166, 148, 0, 0, 36, -306, -280, 0, 0, -188, 48, 270, 0, 0, -28, -64, -326, 0, 0, -250, -264, 144, 0, 0, 156, 152, -56, 0, 0, -318, 368, -190, 0, 0, 142, 264, 144, 0, 0, 156, 194, 10, 0, 0, -74, -302, -102, 0, 0, 58, 74, -6, 0, 0, -320, 128, -84, 0, 0, 28, -86, -172, 0, 0, 138, -2, 308, 0, 0, -260, 0, 68, 0, 0, -302, -28, 104, 0, 0, -104, 20, 66, 0, 0, -296, 160, 258, 0, 0, -40, 242, -318, 0, 0, -102, -136, 276, 0, 0, -148, -176, -88, 0, 0, 110, -160, -94, 0, 0, 6, 98, -386, 0, 0, -10, 30, -102, 0, 0, -186, -126, 218, 0, 0, -174, -48, 170, 0, 0, -108, 132, 420, 0, 0, -474, 148, -56, 0, 0, -346, -100, 146, 0, 0, 186, 250, 30, 0, 0, 184, 234, 78, 0, 0, 50, -238, 246, 0, 0, -104, -58, 278, 0, 0, -44, -30, -296, 0, 0, -6, -8, 248, 0, 0, -140, 46, 52, 0, 0, -174, -58, -300, 0, 0, -14, 56, -152, 0, 0, -568, 302, 48, 0, 0, 78, 60, -18, 0, 0, 46, 120, -188, 0, 0, 194, 422, -48, 0, 0, -176, -188, 134, 0, 0, -20, -84, 216, 0, 0, -238, 366, 506, 0, 0, 100, -76, -12, 0, 0, -144, 94, 284, 0, 0, -408, -6, 374, 0, 0, -304, -184, 36, 0, 0, 268, -238, 22, 0, 0, -240, 260, 178, 0, 0, 24, -132, -352, 0, 0, 78, 30, 86, 0, 0, -206, -198, 66, 0, 0, 230, 144, 102, 0, 0, -236, 42, -36, 0, 0, -8, -4, -236, 0, 0, -144, 192, 202, 0, 0, -154, 0, 162, 0, 0, -306, 254, -64, 0, 0, -446, 78, -102, 0, 0, -162, -194, -68, 0, 0, 128, 294, 460, 0, 0, -60, 328, -248, 0, 0, 30, 116, 350, 0, 0, 110, 264, 12, 0, 0, 228, -98, 98, 0, 0, -8, -112, -12, 0, 0, 234, -108, 628, 0, 0, 154, -24, 36, 0, 0, -238, 148, 92, 0, 0, -352, -54, 20, 0, 0, -570, -82, -74, 0, 0, 460, -14, -174, 0, 0, 78, 12, 664, 0, 0, -40, -156, -498, 0, 0, 172, -68, 476, 0, 0, -98, 86, -214, 0, 0, 92, 4, -476, 0, 0, -82, 72, 34, 0, 0, 190, -18, -508, 0, 0, -216, 246, 64, 0, 0, -74, 110, 26, 0, 0, -424, 292, 154, 0, 0, 370, 24, 90, 0, 0, 184, -108, -26, 0, 0, -326, -10, 50, 0, 0, -246, -340, 106, 0, 0, -264, 204, -48, 0, 0, 90, -394, 144, 0, 0, 0, -8, -70, 0, 0, 114, -76, -504, 0, 0, -48, -234, -32, 0, 0, 96, -90, -40, 0, 0, -12, 328, -312, 0, 0, 426, 232, 84, 0, 0, 80, -152, 36, 0, 0, -94, -228, 72, 0, 0, -34, 172, -172, 0, 0, -100, -334, -546, 0, 0, -10, -382, 42, 0, 0, -274, 422, 106, 0, 0, -6, 50, 30, 0, 0, -444, 80, 84, 0, 0, 70, 24, 22, 0, 0, 14, 90, 106, 0, 0, 252, 244, 144, 0, 0, -46, 150, 76, 0, 0, -368, -134, -82, 0, 0, 606, 8, 100, 0, 0, -124, -108, 0, 0, 0, 34, -52, 304, 0, 0, 132, -96, 168, 0, 0, 0, -146, -278, 0, 0, -466, 32, 414, 0, 0, 4, -294, -2, 0, 0, -330, 126, -394, 0, 0, -114, 218, -28, 0, 0, -102, -224, 60, 0, 0, 258, -12, 88, 0, 0, 338, 172, -254, 0, 0, 260, 196, 360, 0, 0, 58, 184, -140, 0, 0, 158, 244, -254, 0, 0, 40, 8, -30, 0, 0, 188, 100, -14, 0, 0, -234, 144, 36, 0, 0, -152, -142, 0, 0, 0, 194, -22, -296, 0, 0, 256, -184, -42, 0, 0, 124, -48, 74, 0, 0, 44, -144, 224, 0, 0, 56, 16, -230, 0, 0, 46, -90, 382, 0, 0, 110, 84, -124, 0, 0, 14, -6, -296, 0, 0, 260, 4, 48, 0, 0, -210, -24, -138, 0, 0, -40, 488, 154, 0, 0, 186, 132, 282, 0, 0, 576, 384, 304, 0, 0, -164, -46, -66, 0, 0, -148, -4, 180, 0, 0, 20, 218, 36, 0, 0, 24, -200, -156, 0, 0, 318, 24, -114, 0, 0, -244, -24, -150, 0, 0, -574, -64, -216, 0, 0, -550, -174, -28, 0, 0, 52, 280, 82, 0, 0, 156, 172, 214, 0, 0, -56, 570, -186, 0, 0, -604, 122, 516, 0, 0, 292, -406, -190, 0, 0, 134, 64, -472, 0, 0, 76, 278, -576, 0, 0, 662, -480, -234, 0, 0, 282, 8, 250, 0, 0, -494, 142, -70, 0, 0, -198, -192, -66, 0, 0, -706, 128, -300, 0, 0, 640, 94, 70, 0, 0, 2, 100, 28, 0, 0, -424, -336, -42, 0, 0, 478, -250, 446, 0, 0, -214, -148, -78, 0, 0, 46, 0, -486, 0, 0, -622, 84, 270, 0, 0, 274, -6, -78, 0, 0, -186, -306, 166, 0, 0, 66, 216, -32, 0, 0, -214, -88, -174, 0, 0, 26, 102, 498, 0, 0, 150, -2, -44, 0, 0, 416, 10, -404, 0, 0, 102, -544, -132, 0, 0, -54, 120, 326, 0, 0, -14, -108, 104, 0, 0, -116, 266, 260, 0, 0, -164, -24, -78, 0, 0, -274, -320, 136, 0, 0, 168, -262, -10, 0, 0, 182, 120, 314, 0, 0, 234, 94, -154, 0, 0, 150, -230, 622, 0, 0, -320, -48, 174, 0, 0, 136, -48, -300, 0, 0, -96, -220, -346, 0, 0, 42, -172, 160, 0, 0, -56, 206, -228, 0, 0, 514, -50, 60, 0, 0, -228, 152, -64, 0, 0, 40, -34, -4, 0, 0, -126, 230, -266, 0, 0, 586, -118, -62, 0, 0, -178, 544, -240, 0, 0, 94, -172, 106, 0, 0, 644, -96, 386, 0, 0, 40, 236, -608, 0, 0, 28, -52, 772, 0, 0, 914, -84, -6, 0, 0, 198, -100, 134, 0, 0, -410, 114, -76, 0, 0, -350, -310, -92, 0, 0, -82, -58, -540, 0, 0, 528, 104], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "1045.2.b.c", "char_is_minimal": true, "conrey_index": 419, "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, 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, 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], [-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, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 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, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 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, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0], [0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0], [0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 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, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0], [-2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, -1, 0, -1, -2, 0, 0, 1, -1, 0, -1, -1, -1, 0, 0, 0, 0], [2, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, -1, 0, -1], [0, 0, -1, 0, 0, -1, 0, 0, -1, 1, 0, 0, -1, 0, 1, -1, -1, 0, 1, 0], [0, 1, 0, 0, -1, 0, 1, -2, 0, 0, -1, 0, 0, 0, -1, -1, 0, -1, 0, 1], [0, 0, 0, -2, 1, 0, -1, 3, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 0, -1, 0], [-1, 1, -1, 2, -1, 0, 0, -1, -1, 1, 1, -1, -1, -1, 0, -1, 0, 1, 1, 1], [-4, 0, 3, 0, 0, -2, 0, 0, 1, 0, 0, 1, 2, -1, -1, 1, 0, 0, -2, 0], [0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 1, 0, 1, 0, 0, 0, -2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, -1, 0, -1, 0, 2, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, -1, 0, 0, -1, 0, -1, 0], [0, -2, 0, -1, 3, 0, -2, 3, 0, 0, -1, 2, 0, 2, 1, 1, 0, -1, 0, -1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, 0, 0, 1, 0, 0, -2, 0, 0, 1, -1, -1, 1, -1, 1, 0, 1, 0], [1, -1, -1, -1, -1, 0, 2, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 1, 1, 1], [-1, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0], [0, -3, 0, -4, 1, 0, -1, 4, 0, 0, -1, 0, 0, 0, 1, 1, 0, -1, 0, -2], [0, 0, 0, 0, 1, 0, -1, -1, 0, 0, -1, 1, 0, 1, 0, 0, 0, -2, 0, -2], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, -1, 2, -2, 0, 1, -4, 1, 0, 0, -1, 0, -1, -1, -1, 0, 0, 0, 1], [-2, 0, 1, 0, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, 2, -2, -1, 0, 1, 0], [0, 1, 0, 2, -2, 0, 2, -4, 0, 0, 1, -2, 0, -2, -2, -2, 0, 1, 0, 3], [0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [-3, 0, 4, 0, 0, -2, 0, 0, 1, -1, 0, 0, 3, 0, -1, 1, 1, 0, -1, 0], [3, 0, -2, -1, 2, 1, -1, 2, -1, 0, -1, 2, -1, 0, 1, 0, 0, -1, 0, 0], [-3, 0, 1, 0, 0, -1, 0, 0, 2, 0, 0, 1, -1, -1, -1, 1, 1, 0, -1, 0], [0, -2, 0, -3, -2, 0, 1, 2, 0, 0, 0, -1, 0, -1, 1, 1, 0, 1, 0, 0], [0, -1, 0, 0, -3, 0, 2, -4, 0, 0, 1, -3, 0, -3, -1, -1, 0, 0, 0, 2], [-1, 0, 2, 0, 0, -1, 0, 0, 2, 0, 0, 1, 2, -1, -1, 1, -1, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 1, 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, 5, 0, 3, -1, 0, -1, -3, 0, 0, 1, -1, 0, -1, -1, -1, 0, 1, 0, 2], [3, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 1, -1, -3, 0, 0, 0], [-2, -2, -1, -2, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, -1], [0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 1, 0], [0, -2, 0, 2, -1, 0, 2, -5, 0, 0, 2, -2, 0, -2, -1, -1, 0, 1, 0, 1], [0, 0, 0, -1, 0, 0, 1, -3, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0], [4, 0, -3, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 1, 0, 0, 0], [2, 2, -1, -1, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, 0, -1, 0, -1, 0, -1], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 3, -5, 0, 0, -5, 0, 0, 1, -3, 0, -3, -2, -2, 0, 1, 0, 2], [0, -1, 0, 0, 1, 0, -1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1], [-2, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 2, -2, -1, 0, 0, 0], [-4, 2, 2, 0, -2, 0, 0, 2, 1, 0, 1, -2, 1, 0, -1, 1, 1, 2, 0, 1], [-2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, -1, -1, -1, 1, 2, 0, -1, 0], [0, -3, 0, -1, 0, 0, 0, 3, 0, 0, 1, -1, 0, -1, 1, 1, 0, 2, 0, -1], [0, -2, 0, 1, -1, 0, -1, 2, 0, 0, 1, -1, 0, -1, 1, 1, 0, 4, 0, 1], [3, 0, 1, 0, 0, -2, 0, 0, -1, 2, 0, 1, -1, -1, 0, 0, -2, 0, -2, 0], [0, 1, -2, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 0, -1, 0, -1, -2, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -4, -1, 0, 0, 3, 0, 0, -1, -1, 0, -1, 1, 1, 0, 2, 0, 1], [6, 0, -2, 0, 0, -1, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0], [1, 0, -2, 0, 1, 1, -1, 3, 0, 0, -1, 1, 1, 3, 1, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 2, 0, 0, -2, 2, 0, -2, 0, 2, 0, 0, 1, 0, 2, 0], [0, -4, 0, -1, 2, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 1, 0, 2, 0, 2], [0, 3, 0, 1, -1, 0, 1, -4, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, -1], [-1, 0, 3, 0, 0, 0, 0, 0, 4, -1, 0, 1, 2, -1, -3, 3, 0, 0, -4, 0], [0, 1, -1, 0, 1, 2, 0, 0, 1, -1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, -2, 0, 0, -1, 0, -3, 0], [0, 0, 0, 2, 0, 0, -2, 4, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 3, 0, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, 1, -1, 1, 0, -1, 0], [-4, 1, 0, 0, 1, 0, -2, 1, 0, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1, -1], [-4, 0, 4, 0, 0, 1, 0, 0, 1, -1, 0, -1, 3, 1, -1, 1, 1, 0, -1, 0], [0, -6, 0, -4, -1, 0, 2, 3, 0, 0, 0, -1, 0, -1, 1, 1, 0, 3, 0, 0], [0, 0, 0, 2, 0, 0, 1, -5, 0, 0, -1, 1, 0, 1, -1, -1, 0, -1, 0, 1], [1, 0, -4, 0, 0, 0, 0, 0, -1, 1, 0, -1, -2, 1, 1, -1, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -2, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, -1, 1, 0, 0, 1, 0], [0, -2, 0, -2, 2, 0, -1, 2, 0, 0, 1, -1, 0, -1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 2, 4, 0, 0, -6, 0, 0, 0, 1, 0, 1, -1, -1, 0, -4, 0, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 3, -2, 0, -2, 0, 4, 0, 0, 0, 2, 0, -2, 0, 2, 0, 2, -2, 0]]}