# Stored data for newform 1875.2.b.h, downloaded from the LMFDB on 19 April 2024. {"label": "1875.2.b.h", "space_label": "1875.2.b", "level": 1875, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525266144626515, "dim": 16, "is_polredabs": true, "trace_hash": 1503954479434468285, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 0, 130, 0, 761, 0, 1440, 0, 1286, 0, 610, 0, 156, 0, 20, 0, 1]]], "qexp_display": "q+(-\\beta _{1}-\\beta _{9})q^{2}-\\beta _{9}q^{3}+(-1-\\beta _{14}+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 7500, "analytic_conductor": 14.971950378990073, "hecke_ring_index": 256, "level_radical": 15, "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": "0.511", "prec": 17}, "analytic_rank_proved": true, "char_values": [1875, 2, [626, 1252], [2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 5], "conrey_indexes": [1249], "field_disc": 29637136000000000000, "field_disc_factorization": [[2, 16], [5, 12], [1361, 2]], "field_poly": [1, 0, 130, 0, 761, 0, 1440, 0, 1286, 0, 610, 0, 156, 0, 20, 0, 1], "hecke_ring_index_factorization": [[2, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.351", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1024.776", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "124638.606", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, -8, 0, -8, 0, 0, -16, 0, 4, 0, 0, -12, 0, 0, 0, 0, 28, 0, -16, 0, 0, 24, 0, 12, 0, 0, -4, 0, -44, 0, 0, 24, 0, 8, 0, 0, 32, 0, 16, 0, 0, -44, 0, -4, 0, 0, 0, 0, -32, 0, 0, 8, 0, 60, 0, 0, -28, 0, -40, 0, 0, -12, 0, -24, 0, 0, 28, 0, 32, 0, 0, -52, 0, -32, 0, 0, 60, 0, 16, 0, 0, 32, 0, 64, 0, 0, -32, 0, -24, 0, 0, -28, 0, 4, 0, 0, -4, 0, 24, 0, 0, -72, 0, 56, 0, 0, 28, 0, -56, 0, 0, -32, 0, 76, 0, 0, -52, 0, 4, 0, 0, -32, 0, 12, 0, 0, 40, 0, 40, 0, 0, -96, 0, 28, 0, 0, 72, 0, -20, 0, 0, 0, 0, 96, 0, 0, -36, 0, -88, 0, 0, -44, 0, -32, 0, 0, 88, 0, 56, 0, 0, -52, 0, 0, 0, 0, -12, 0, -28, 0, 0, 16, 0, 88, 0, 0, -60, 0, -44, 0, 0, -20, 0, -32, 0, 0, 16, 0, 24, 0, 0, 64, 0, -72, 0, 0, 124, 0, -32, 0, 0, -4, 0, -76, 0, 0, -32, 0, -44, 0, 0, 92, 0, -24, 0, 0, 48, 0, 4, 0, 0, 28, 0, 60, 0, 0, 52, 0, -92, 0, 0, -12, 0, -48, 0, 0, -52, 0, -76, 0, 0, 72, 0, -32, 0, 0, 24, 0, 132, 0, 0, 4, 0, -88, 0, 0, -12, 0, 4, 0, 0, 64, 0, -40, 0, 0, 8, 0, -116, 0, 0, 120, 0, 4, 0, 0, 44, 0, 68, 0, 0, 84, 0, -12, 0, 0, -72, 0, -32, 0, 0, 8, 0, -80, 0, 0, -148, 0, -4, 0, 0, 152, 0, -24, 0, 0, 0, 0, 44, 0, 0, -40, 0, 40, 0, 0, 136, 0, -60, 0, 0, -8, 0, -172, 0, 0, -72, 0, 12, 0, 0, -32, 0, -16, 0, 0, 84, 0, 92, 0, 0, -196, 0, 60, 0, 0, 56, 0, -32, 0, 0, 32, 0, 128, 0, 0, -8, 0, 44, 0, 0, -72, 0, 72, 0, 0, -16, 0, 156, 0, 0, -48, 0, -108, 0, 0, -140, 0, -32, 0, 0, -56, 0, 60, 0, 0, -28, 0, -104, 0, 0, -4, 0, 44, 0, 0, 80, 0, -20, 0, 0, 116, 0, 100, 0, 0, 152, 0, 32, 0, 0, 4, 0, 76, 0, 0, -192, 0, 28, 0, 0, -260, 0, -56, 0, 0, 20, 0, 96, 0, 0, -44, 0, -152, 0, 0, 80, 0, 0, 0, 0, 32, 0, 92, 0, 0, -16, 0, -28, 0, 0, -92, 0, 104, 0, 0, 32, 0, 52, 0, 0, 144, 0, -116, 0, 0, -132, 0, -8, 0, 0, -40, 0, 124, 0, 0, 20, 0, 36, 0, 0, 112, 0, -8, 0, 0, -64, 0, 20, 0, 0, 156, 0, 96, 0, 0, -72, 0, -16, 0, 0, -60, 0, -128, 0, 0, -148, 0, -124, 0, 0, -48, 0, -64, 0, 0, 4, 0, -24, 0, 0, 172, 0, 108, 0, 0, 20, 0, 28, 0, 0, 8, 0, -52, 0, 0, -116, 0, 176, 0, 0, 28, 0, 48, 0, 0, 40, 0, 116, 0, 0, -124, 0, -208, 0, 0, -44, 0, -8, 0, 0, -52, 0, -108, 0, 0, -12, 0, 44, 0, 0, 56, 0, 12, 0, 0, -16, 0, 56, 0, 0, -40, 0, 208, 0, 0, 0, 0, -164, 0, 0, 24, 0, -176, 0, 0, -96, 0, 24, 0, 0, 84, 0, 56, 0, 0, 20, 0, 168, 0, 0, -8, 0, 180, 0, 0, 112, 0, -28, 0, 0, -16, 0, 8, 0, 0, -272, 0, 52, 0, 0, -148, 0, -76, 0, 0, -32, 0, 236, 0, 0, 148, 0, -84, 0, 0, -8, 0, 48, 0, 0, -32, 0, -144, 0, 0, -80, 0, 152, 0, 0, 132, 0, 52, 0, 0, -8, 0, 36, 0, 0, -24, 0, 140, 0, 0, 88, 0, -36, 0, 0, 32, 0, -40, 0, 0, -108, 0, 44, 0, 0, -276, 0, -32, 0, 0, 20, 0, -40, 0, 0, 152, 0, -8, 0, 0, -32, 0, -60, 0, 0, -16, 0, -240, 0, 0, -96, 0, 96, 0, 0, 88, 0, 72, 0, 0, -16, 0, 60, 0, 0, 156, 0, 16, 0, 0, -48, 0, 104, 0, 0, -40, 0, 24, 0, 0, -12, 0, -36, 0, 0, -28, 0, -32, 0, 0, 16, 0, -12, 0, 0, 56, 0, -52, 0, 0, -156, 0, 0, 0, 0, -64, 0, -172, 0, 0, 40, 0, -152, 0, 0, -132, 0, 192, 0, 0, 36, 0, -4, 0, 0, 212, 0, -196, 0, 0, 140, 0, 32, 0, 0, 16, 0, 32, 0, 0, -40, 0, -68, 0, 0, -64, 0, 140, 0, 0, 24, 0, 88, 0, 0, 184, 0, -60, 0, 0, -60, 0, -64, 0, 0, -128, 0, -392, 0, 0, 20, 0, -32, 0, 0, 188, 0, 28, 0, 0, -48, 0, 16, 0, 0, 316, 0, 232, 0, 0, 20, 0, 48, 0, 0, -4, 0, -192, 0, 0, 160, 0, -276, 0, 0, -140, 0, -16, 0, 0, 96, 0, 48, 0, 0, 376, 0, 12, 0, 0, 68, 0, 4, 0, 0, -136, 0, -240, 0, 0, 120, 0, -24, 0, 0, 12, 0, 124, 0, 0, -24, 0, -8, 0, 0, 148, 0, -148, 0, 0, 160, 0, 40, 0, 0, -36, 0, -216, 0, 0, 148, 0, -24, 0, 0, 272, 0, 72, 0, 0, 16, 0, -244, 0, 0, 8, 0, 300, 0, 0, -328, 0, -20, 0, 0, -56, 0, -272, 0, 0, 48, 0, -204, 0, 0, -124, 0, 48, 0, 0, -36, 0, -64, 0, 0, 244, 0, -168, 0, 0, 88, 0, -28, 0, 0, -40, 0, -168, 0, 0, 232, 0, 32, 0, 0, -84, 0, 20, 0, 0, 56, 0, 52, 0, 0, -56, 0, -108, 0, 0, -160, 0, -144, 0, 0, -20, 0, -112, 0, 0, 28, 0, 200, 0, 0, 320, 0, 32, 0, 0, -40, 0, -172, 0, 0, 320, 0, 204, 0, 0, 196, 0, -52, 0, 0, -76, 0, -336, 0, 0, -72, 0, -84, 0, 0, -244, 0, -32, 0, 0, -48, 0, -16, 0, 0, 200, 0, 92, 0, 0, 260, 0, 52, 0, 0, -120, 0, -392, 0, 0, 24, 0, 336, 0, 0, 56, 0, 168, 0, 0, -4, 0, 224, 0, 0, -112, 0, 196, 0, 0, -132, 0, 16, 0, 0, -72, 0, 120, 0, 0, -100, 0, 0, 0, 0, -356, 0, 32, 0, 0, 120, 0, 112, 0, 0, -240, 0, 220, 0, 0, -24, 0, 28, 0, 0, -12, 0, 140, 0, 0, -84, 0, -184, 0, 0, -312, 0, 136, 0, 0, -124, 0, -232, 0, 0, 4, 0, 416, 0, 0, 124, 0, -40, 0, 0, -144, 0, 312, 0, 0, -92, 0, -60, 0, 0, 72, 0, 68, 0, 0, -40, 0, -256, 0, 0, -72, 0, -176, 0, 0, -80, 0, 40, 0, 0, -156, 0, 296, 0, 0, 88, 0, 264, 0, 0, -372, 0, 96, 0, 0, -24, 0, -24, 0, 0, 344, 0, 84, 0, 0, -208, 0, 128, 0, 0, -28, 0, 340, 0, 0, 284, 0, -280, 0, 0, -420, 0, 136, 0, 0, 20, 0, -324, 0, 0, 356, 0, -20, 0, 0, 208, 0, -72, 0, 0, -192, 0, -284, 0, 0, 84, 0, 44, 0, 0, -140, 0, 68, 0, 0, 20, 0, -8, 0, 0, 120, 0, 176, 0, 0, 188, 0, 208, 0, 0, -32, 0, -276, 0, 0, 84, 0, 28, 0, 0, 164, 0, 0, 0, 0, 16, 0, 272, 0, 0, 116, 0, 128, 0, 0, -144, 0, -140, 0, 0, -96, 0, -396, 0, 0, -48, 0, -160, 0, 0, -296, 0, 256, 0, 0, -68, 0, -96, 0, 0, -220, 0, 320, 0, 0, -4, 0, 36, 0, 0, -128, 0, -564, 0, 0, 196, 0, 16, 0, 0, -144, 0, 20, 0, 0, 88, 0, -120, 0, 0, -44, 0, 388, 0, 0, -160, 0, -56, 0, 0, -108, 0, -124, 0, 0, -212, 0, 48, 0, 0, -168, 0, 44, 0, 0, -40, 0, 228, 0, 0, -4, 0, 416, 0, 0, -104, 0, 160, 0, 0, 32, 0, -40, 0, 0, 220, 0, 488, 0, 0, -124, 0, 96, 0, 0, 68, 0, -308, 0, 0, 92, 0, -48, 0, 0, 60, 0, -88, 0, 0, -72, 0, 332, 0, 0, -512, 0, 56, 0, 0, 100, 0, -44, 0, 0, -56, 0, 48, 0, 0, 380, 0, -84, 0, 0, 48, 0, 128, 0, 0, -128, 0, 264, 0, 0, 104, 0, -136, 0, 0, -228, 0, 52, 0, 0, 8, 0, 120, 0, 0, -92, 0, 4, 0, 0, -144, 0, 68, 0, 0, 0, 0, -52, 0, 0, -52, 0, -80, 0, 0, -132, 0, 24, 0, 0, -148, 0, 100, 0, 0, -80, 0, 40, 0, 0, -32, 0, 12, 0, 0, 16, 0, -280, 0, 0, -88, 0, 28, 0, 0, -216, 0, 176, 0, 0, 28, 0, -184, 0, 0, 192, 0, -152, 0, 0, 64, 0, -216, 0, 0, 4, 0, 92, 0, 0, 12, 0, 56, 0, 0, 448, 0, -16, 0, 0, -40, 0, 356, 0, 0, 72, 0, 144, 0, 0, 92, 0, 148, 0, 0, -88, 0, -220, 0, 0, 248, 0, -164, 0, 0, -288, 0, 240, 0, 0, 116, 0, -388, 0, 0, -108, 0, -68, 0, 0, 312, 0, 60, 0, 0, -192, 0, -212, 0, 0, -64, 0, 92, 0, 0, 80, 0, -24, 0, 0, 44, 0, 336, 0, 0, 368, 0, -448, 0, 0, 44, 0, -56, 0, 0, 20, 0, 160, 0, 0, -24, 0, 4, 0, 0, 484, 0, 20, 0, 0, -40, 0, -452, 0, 0, 148, 0, 516, 0, 0, -304, 0, -92, 0, 0, 32, 0, 268, 0, 0, -248, 0, -304, 0, 0, -140, 0, -280, 0, 0, 44, 0, -112, 0, 0, -36, 0, -44, 0, 0, 64, 0, -16, 0, 0, -112, 0, -232, 0, 0, 408, 0, -56, 0, 0, 272, 0, -168, 0, 0, -24, 0, -300, 0, 0, 208, 0, -176, 0, 0, -200, 0, -32, 0, 0, 56, 0, -20, 0, 0, 48, 0, -12, 0, 0, -68, 0, -64, 0, 0, 56, 0, 220, 0, 0, 68, 0, -140, 0, 0, 16, 0, 0, 0, 0, 72, 0, -476, 0, 0, 348, 0, -28, 0, 0, -468, 0, 224, 0, 0, 40, 0, 172, 0, 0, -192, 0, -16, 0, 0, 180, 0, -124, 0, 0, 56, 0, 404, 0, 0, -112, 0, -116, 0, 0, -84, 0, -212, 0, 0, 32, 0, 136, 0, 0, 12, 0, -420, 0, 0, -60, 0, -32, 0, 0, -20, 0, -124, 0, 0, 60, 0, 108, 0, 0, 376, 0, 4, 0, 0, 144, 0, 76, 0, 0, 184, 0, 224, 0, 0, -88, 0, -148, 0, 0, 76, 0, 108, 0, 0, -456, 0, -196, 0, 0, -196, 0, 136, 0, 0, -20, 0, 316, 0, 0, 16, 0, 44, 0, 0, 96, 0, 32, 0, 0, -80, 0, -48, 0, 0, 180, 0, 252, 0, 0, 540, 0, -100, 0, 0, 44, 0, -436, 0, 0, 48, 0, 152, 0, 0, 172, 0, 192, 0, 0, 96, 0, 160, 0, 0, -172, 0, 168, 0, 0, 208, 0, -92, 0, 0, -40, 0, 348, 0, 0, 64, 0, 204, 0, 0, -472, 0, 268, 0, 0, 24, 0, -120, 0, 0, 240, 0, -148, 0, 0, 4, 0, 232, 0, 0, 296, 0, 56, 0, 0, -468, 0, -404, 0, 0, 440, 0, -48, 0, 0, -136, 0, -252, 0, 0, -220, 0, -304, 0, 0, 128, 0, -96, 0, 0, -4, 0, 52, 0, 0, -440, 0, -392, 0, 0, 336, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "75.2.i.a", "char_is_minimal": false, "conrey_index": 1249, "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, -1, 0, 0, 0, 0, 0, 0, 0, -1, 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, 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], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 1, -1, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, -1, 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], [2, 0, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, -1, 0, 1], [0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 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, 2, 0, 0, 0, 0, -1, -1, 1], [0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 1, -1, -1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0], [0, -1, 0, -1, 2, 0, 1, 0, 0, -3, 1, 1, 1, 0, 0, 0], [0, -1, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, -3, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 3, 0, 2, -1, 0, 3, 0, 0, 2, 0, 1, -1, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2], [0, -1, 0, 0, 0, 0, 2, 0, 0, -1, -1, -1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 1, 0, 0, -1, 0, 1, -2, 0, 0, 0], [4, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -3, 2, 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, 1, 1], [0, -1, 0, -1, -2, 0, 1, 0, 0, -3, 1, -3, 1, 0, 0, 0], [0, -3, 0, -1, 2, 0, 2, 0, 0, -5, -1, 0, -1, 0, 0, 0], [2, 0, 0, 0, 0, 2, 0, 0, -1, 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, -1, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 0, 2, 1], [0, 1, 0, 0, -1, 0, 1, 0, 0, 1, -1, -1, 0, 0, 0, 0], [0, 2, 0, 2, -1, 0, 2, 0, 0, 4, 0, -2, 0, 0, 0, 0], [-2, 0, 2, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -3, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 2, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, -2, -1, 3], [0, 0, 0, 3, -2, 0, 2, 0, 0, -2, -2, 0, -3, 0, 0, 0], [0, -1, 0, 0, 1, 0, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 0, 2, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 2], [0, -2, 0, 2, 3, 0, 4, 0, 0, -6, -2, 2, 1, 0, 0, 0], [0, -1, 0, -1, -2, 0, -2, 0, 0, 7, -1, -3, -1, 0, 0, 0], [1, 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], [4, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, -1, 2, 1], [0, -2, 0, -2, 0, 0, -1, 0, 0, -3, -1, 0, 1, 0, 0, 0], [0, 1, 0, -2, 0, 0, 3, 0, 0, 0, 0, -1, 1, 0, 0, 0], [-4, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, -2, 0, 0, 4, 0, -2, -4, 0, 0, 0, 0, 2, 2, 0], [0, 2, 0, -1, 2, 0, 2, 0, 0, -2, 1, 0, 1, 0, 0, 0], [0, -1, 0, -1, -1, 0, -1, 0, 0, 1, -1, -1, 1, 0, 0, 0], [1, 0, 0, 0, 0, -3, 0, -1, 4, 0, 0, 0, 0, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 1, -1, 0], [0, 0, 0, 0, -1, 0, 4, 0, 0, -4, 4, 2, 0, 0, 0, 0], [0, -2, 0, 2, 0, 0, 4, 0, 0, -4, -5, 0, 2, 0, 0, 0], [3, 0, 2, 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], [2, 0, -1, 0, 0, -1, 0, 2, 1, 0, 0, 0, 0, 0, -4, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0], [0, 4, 0, 0, 2, 0, 4, 0, 0, 4, 4, 0, -1, 0, 0, 0], [-2, 0, 0, 0, 0, -1, 0, 2, 2, 0, 0, 0, 0, -5, 2, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 4, -3, -5], [0, 1, 0, 0, 0, 0, 0, 0, 0, -7, 1, 4, -2, 0, 0, 0], [0, -3, 0, 0, 0, 0, 3, 0, 0, -4, -1, 0, 2, 0, 0, 0], [5, 0, 2, 0, 0, 3, 0, -3, -2, 0, 0, 0, 0, 1, -1, 3], [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, -3, 0, -1, -2, 0, -1, 0, 0, -3, -1, -1, 0, 0, 0, 0], [0, 0, 0, 1, 2, 0, 0, 0, 0, 0, -1, 3, 3, 0, 0, 0], [0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 3, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -2, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, -2, 4, 1], [0, 0, 0, 0, -1, 0, 1, 0, 0, -1, -1, 1, -2, 0, 0, 0], [0, 4, 0, -2, -2, 0, 0, 0, 0, 6, 2, 0, 3, 0, 0, 0], [-1, 0, 1, 0, 0, -1, 0, -2, 2, 0, 0, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 3, 1], [0, -2, 0, 1, 0, 0, 2, 0, 0, -2, -4, -1, 3, 0, 0, 0], [0, -2, 0, 0, 0, 0, -1, 0, 0, 2, -1, 0, -1, 0, 0, 0], [-3, 0, 0, 0, 0, -1, 0, -5, 2, 0, 0, 0, 0, 4, 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, 1, 0, 0, 0, 0, 2, -1, -1], [0, 2, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0], [0, -2, 0, 2, 0, 0, 2, 0, 0, -2, -2, 1, 2, 0, 0, 0], [-2, 0, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}