# Stored data for newform 2100.2.bi.l, downloaded from the LMFDB on 24 April 2024. {"label": "2100.2.bi.l", "space_label": "2100.2.bi", "level": 2100, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49541932396841012, "dim": 16, "is_polredabs": true, "trace_hash": 1597106384425536397, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [1475789056, 0, -559605872, 0, 144546913, 0, -19966919, 0, 1984747, 0, -101180, 0, 3715, 0, -74, 0, 1]], [13, [25, 0, 78, 0, 71, 0, 21, 0, 1]], [19, [6889, 27888, 40869, 13104, 596, -351, -12, 9, 1]], [37, [12837889, 1311378, 631993, -29376, 16836, -315, 148, -3, 1]]], "qexp_display": "q-\\beta _{2}q^{3}+(-1+\\beta _{7}+\\beta _{10})q^{7}+(-\\beta _{10}+\\cdots)q^{9}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "bi", "char_is_real": false, "Nk2": 8400, "analytic_conductor": 16.76858442446888, "hecke_ring_index": 64, "level_radical": 210, "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": "0.594", "prec": 17}, "analytic_rank_proved": true, "char_values": [2100, 6, [1051, 701, 1177, 1501], [6, 3, 6, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 5, 7], "conrey_indexes": [101, 1601], "field_disc": 6402342849063379745816961, "field_disc_factorization": [[3, 8], [7, 8], [3607, 4]], "field_poly": [6561, -6561, 6561, -4374, 2592, -972, 0, 153, -167, 51, 0, -36, 32, -18, 9, -3, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.104", "prec": 17}, {"__RealLiteral__": 0, "data": "14.320", "prec": 20}, {"__RealLiteral__": 0, "data": "9.260", "prec": 17}, {"__RealLiteral__": 0, "data": "1561.040", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "268027.574", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c6", "trace_display": [0, -3, 0, -6], "traces": [0, 16, 0, -3, 0, 0, 0, -6, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, -12, 0, 0, 0, 6, 0, 12, 0, 0, 0, -4, 0, 0, 0, 0, 0, -18, 0, -1, 0, 0, 0, 0, 0, -6, 0, 0, 0, 36, 0, -19, 0, 0, 0, -30, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -81, 0, 0, 0, 20, 0, 34, 0, 0, 0, 0, 0, -30, 0, 0, 0, 72, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 0, -27, 0, 0, 0, 60, 0, 32, 0, 0, 0, -80, 0, -6, 0, 0, 0, -74, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 31, 0, 0, 0, 6, 0, 0, 0, 0, 0, 72, 0, -69, 0, 0, 0, 18, 0, 0, 0, 0, 0, 124, 0, -3, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, -24, 0, 0, 0, 54, 0, 58, 0, 0, 0, -30, 0, 0, 0, 0, 0, 90, 0, 84, 0, 0, 0, 0, 0, 79, 0, 0, 0, 16, 0, -3, 0, 0, 0, -118, 0, -46, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, -121, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 57, 0, 0, 0, 24, 0, 67, 0, 0, 0, -60, 0, 0, 0, 0, 0, -40, 0, -61, 0, 0, 0, 0, 0, -78, 0, 0, 0, 12, 0, 47, 0, 0, 0, -72, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -108, 0, -1, 0, 0, 0, 0, 0, -183, 0, 0, 0, 26, 0, 36, 0, 0, 0, 0, 0, 6, 0, 0, 0, 168, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 36, 0, 11, 0, 0, 0, 196, 0, -114, 0, 0, 0, -126, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 212, 0, 0, 0, 58, 0, 0, 0, 0, 0, 270, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 42, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 44, 0, 0, 0, 84, 0, 58, 0, 0, 0, 50, 0, 0, 0, 0, 0, 108, 0, 42, 0, 0, 0, 0, 0, 80, 0, 0, 0, -128, 0, -174, 0, 0, 0, -94, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, -111, 0, 0, 0, 0, 0, 0, 0, 0, 0, -78, 0, -51, 0, 0, 0, 42, 0, 94, 0, 0, 0, 212, 0, 0, 0, 0, 0, -150, 0, -23, 0, 0, 0, 0, 0, -92, 0, 0, 0, -150, 0, 61, 0, 0, 0, -92, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 24, 0, -144, 0, 0, 0, 0, 0, -102, 0, 0, 0, 158, 0, -10, 0, 0, 0, 0, 0, 28, 0, 0, 0, -54, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, -174, 0, 0, 0, 70, 0, 1, 0, 0, 0, -116, 0, -168, 0, 0, 0, -98, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 183, 0, 0, 0, 100, 0, 0, 0, 0, 0, 210, 0, -120, 0, 0, 0, -94, 0, 0, 0, 0, 0, 40, 0, 111, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -60, 0, 0, 0, 210, 0, 146, 0, 0, 0, -36, 0, 0, 0, 0, 0, 282, 0, 30, 0, 0, 0, 0, 0, 234, 0, 0, 0, 192, 0, 54, 0, 0, 0, -130, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, -186, 0, 30, 0, 0, 0, -122, 0, 59, 0, 0, 0, 72, 0, 0, 0, 0, 0, -244, 0, -86, 0, 0, 0, 0, 0, 10, 0, 0, 0, -150, 0, 160, 0, 0, 0, -242, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, -68, 0, -95, 0, 0, 0, 0, 0, -339, 0, 0, 0, -40, 0, 16, 0, 0, 0, 0, 0, 162, 0, 0, 0, -228, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -69, 0, 0, 0, -116, 0, 96, 0, 0, 0, 212, 0, -219, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 260, 0, 0, 0, 124, 0, 0, 0, 0, 0, 192, 0, 39, 0, 0, 0, -12, 0, 0, 0, 0, 0, 20, 0, 300, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 230, 0, 0, 0, -42, 0, 28, 0, 0, 0, -148, 0, 0, 0, 0, 0, 18, 0, 63, 0, 0, 0, 0, 0, 135, 0, 0, 0, -104, 0, -282, 0, 0, 0, -318, 0, 93, 0, 0, 0, 0, 0, 0, 0, 0, 0, 300, 0, -114, 0, 0, 0, 0, 0, 0, 0, 0, 0, -78, 0, -252, 0, 0, 0, -38, 0, 89, 0, 0, 0, -172, 0, 0, 0, 0, 0, -192, 0, 35, 0, 0, 0, 0, 0, -122, 0, 0, 0, 6, 0, 4, 0, 0, 0, -272, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, -120, 0, 0, 0, 0, 0, -192, 0, 0, 0, 406, 0, -108, 0, 0, 0, 0, 0, -176, 0, 0, 0, 30, 0, 0, 0, 0, 0, -146, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, 22, 0, 107, 0, 0, 0, -84, 0, -414, 0, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 130, 0, 0, 0, 0, 0, 340, 0, 0, 0, 142, 0, 0, 0, 0, 0, 246, 0, -159, 0, 0, 0, -178, 0, 0, 0, 0, 0, 64, 0, 150, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -160, 0, 0, 0, 12, 0, 151, 0, 0, 0, -52, 0, 0, 0, 0, 0, 30, 0, 159, 0, 0, 0, 0, 0, 85, 0, 0, 0, -56, 0, -51, 0, 0, 0, -172, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, -307, 0, 0, 0, 0, 0, 0, 0, 0, 0, -348, 0, 15, 0, 0, 0, -122, 0, 111, 0, 0, 0, 144, 0, 0, 0, 0, 0, -376, 0, 22, 0, 0, 0, 0, 0, -228, 0, 0, 0, -306, 0, 209, 0, 0, 0, -120, 0, 0, 0, 0, 0, 366, 0, 0, 0, 0, 0, -50, 0, -142, 0, 0, 0, 0, 0, -180, 0, 0, 0, 298, 0, 15, 0, 0, 0, 0, 0, -48, 0, 0, 0, 240, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, -164, 0, 97, 0, 0, 0, -60, 0, -96, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 335, 0, 0, 0, 80, 0, 0, 0, 0, 0, 612, 0, 132, 0, 0, 0, -124, 0, 0, 0, 0, 0, -184, 0, 531, 0, 0, 0, 0, 0, 171, 0, 0, 0, 0, 0, -98, 0, 0, 0, 150, 0, 365, 0, 0, 0, -118, 0, 0, 0, 0, 0, 126, 0, -27, 0, 0, 0, 0, 0, 263, 0, 0, 0, -68, 0, -111, 0, 0, 0, -484, 0, 173, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, -336, 0, 0, 0, -108, 0, 51, 0, 0, 0, 300, 0, 0, 0, 0, 0, -306, 0, -1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 252, 0, -7, 0, 0, 0, -200, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, -78, 0, -155, 0, 0, 0, 0, 0, -507, 0, 0, 0, 72, 0, -47, 0, 0, 0, 0, 0, -190, 0, 0, 0, -366, 0, 0, 0, 0, 0, -278, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, -4, 0, 48, 0, 0, 0, -4, 0, -120, 0, 0, 0, -154, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 174, 0, 0, 0, 248, 0, 0, 0, 0, 0, 102, 0, -171, 0, 0, 0, 2, 0, 0, 0, 0, 0, 304, 0, 213, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, -154, 0, 0, 0, 78, 0, 237, 0, 0, 0, -190, 0, 0, 0, 0, 0, 138, 0, -147, 0, 0, 0, 0, 0, 244, 0, 0, 0, -36, 0, -6, 0, 0, 0, -342, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, -363, 0, 0, 0, 0, 0, 0, 0, 0, 0, -300, 0, 27, 0, 0, 0, -266, 0, 277, 0, 0, 0, -244, 0, 0, 0, 0, 0, -62, 0, -101, 0, 0, 0, 0, 0, 68, 0, 0, 0, -276, 0, 232, 0, 0, 0, -230, 0, 0, 0, 0, 0, 276, 0, 0, 0, 0, 0, -8, 0, -177, 0, 0, 0, 0, 0, -378, 0, 0, 0, 168, 0, 168, 0, 0, 0, 0, 0, 54, 0, 0, 0, 360, 0, 0, 0, 0, 0, -276, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, -10, 0, 124, 0, 0, 0, 432, 0, -111, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 530, 0, 0, 0, 244, 0, 0, 0, 0, 0, 318, 0, -147, 0, 0, 0, 122, 0, 0, 0, 0, 0, 324, 0, 321, 0, 0, 0, 0, 0, 109, 0, 0, 0, 0, 0, 100, 0, 0, 0, 540, 0, 31, 0, 0, 0, -186, 0, 0, 0, 0, 0, 378, 0, 312, 0, 0, 0, 0, 0, 35, 0, 0, 0, -44, 0, -420, 0, 0, 0, -254, 0, 201, 0, 0, 0, 0, 0, 0, 0, 0, 0, 492, 0, -157, 0, 0, 0, 0, 0, 0, 0, 0, 0, -306, 0, -147, 0, 0, 0, -8, 0, 161, 0, 0, 0, 644, 0, 0, 0, 0, 0, -70, 0, 16, 0, 0, 0, 0, 0, 162, 0, 0, 0, -210, 0, 54, 0, 0, 0, 10, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 138, 0, -125, 0, 0, 0, 0, 0, -219, 0, 0, 0, 320, 0, -206, 0, 0, 0, 0, 0, -124, 0, 0, 0, 90, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -228, 0, 0, 0, 140, 0, 166, 0, 0, 0, -212, 0, -132, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 402, 0, 0, 0, -32, 0, 0, 0, 0, 0, 540, 0, -255, 0, 0, 0, 8, 0, 0, 0, 0, 0, -508, 0, 210, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, 94, 0, 0, 0, 16, 0, 0, 0, 0, 0, 78, 0, 48, 0, 0, 0, 0, 0, 332, 0, 0, 0, -436, 0, 72, 0, 0, 0, -330, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -138, 0, -129, 0, 0, 0, 0, 0, 0, 0, 0, 0, -684, 0, 204, 0, 0, 0, -16, 0, 107, 0, 0, 0, -160, 0, 0, 0, 0, 0, -276, 0, -25, 0, 0, 0, 0, 0, -374, 0, 0, 0, -270, 0, 206, 0, 0, 0, -204, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, -248, 0, -76, 0, 0, 0, 0, 0, -399, 0, 0, 0, -44, 0, 176, 0, 0, 0, 0, 0, -128, 0, 0, 0, -66, 0, 0, 0, 0, 0, 16, 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, 3, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 21, 7, 1, 6, 0]], "char_orbit_index": 35, "prim_orbit_index": 7, "minimal_twist": "2100.2.bi.l", "char_is_minimal": true, "conrey_index": 101, "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, -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], [-1, 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, 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], [0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, 1, 0, -1, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -1, 0, 1, 1, -1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, 1, 1, -1, -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], [-1, 1, -1, -2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, -1, 1, 0, -1, 0, 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, 0, 0, 0, 0, 0, 0, 0, 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, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, 1, -1, 0, -1, -1, 0, -1, 0, 0, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, -2, 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, 0, 0], [-2, 3, 0, 0, 0, 2, -3, -3, 0, -3, 1, 0, -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, -1, 6, 6, -2, -1, 2, 0, 0, -2, -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, -2, 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, 2, 0, 2, 0, -1, 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, -1, 0, 0, 1, -1, 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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, -1, 1, -2, -1, 2, -2, 0, -1, -4, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, -2, 0, 0, -1, 0, -3, -3, 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, 1, 1, -3, -3, 1, 2, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -1, 0, -1, -1, 0, 1, -1, 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, 0, 0, 0, 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, 2, -2, 2, 0, 0, 1, -1, 0, -1, -1, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, -3, 2, 0, -1, -1, -1, 0, 0, -2, -4, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, -1, 2, -2, -1, 0, -2, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 3, 2, -1, 0, 3, 0, 0, -1, 2, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, 1, 1, 1, -3, -2, -1, 0, -1, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 3, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -3, 3, -2, -1, 0, 2, 2, 0, -2, 2, 2, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 3, 3, 1, -1, 0, 1, 0, 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, 2, -2, 1, -2, 1, 1, 0, 0, 0, 0, 1, 0, -2, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, -2, 3, -2, -1, 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], [2, -2, 2, 3, -1, 0, 3, 0, 0, 1, -2, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, -3, 1, 0, 1, 0, 1, -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, 0, 0, 0, 0, 0, 0, 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, 4, -1, 1, 0, 0, -1, 0, -4, 1, -1, -2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 1, -1, 2, 1, 2, 2, 0, -1, 4, 2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -2, -2, 0, -1, 1, 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, 1, -2, -3, -1, 1, 0, 0, -1, 1, 5, 0, 0, -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], [1, -1, 0, 0, 1, -1, -1, 2, 0, -2, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 4, 2, 5, -2, 3, 0, 0, 1, -1, 0, -1, -1, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}