# Stored data for newform 1008.5.f.a, downloaded from the LMFDB on 10 April 2026.
{"Nk2": 25200, "analytic_conductor": 104.19692278851508, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 2, "char_parity": -1, "char_values": [1008, 2, [127, 757, 785, 577], [2, 2, 2, 1]], "cm_discs": [-7], "conrey_index": 433, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 0, "hecke_cutters": [[5, [0, 1]], [11, [206, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 343681270768, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": false, "label": "1008.5.f.a", "level": 1008, "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, 3, 7], "level_radical": 42, "minimal_twist": "7.5.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 2, "qexp_display": "q-7^{2}q^{7}-206q^{11}-734q^{23}+5^{4}q^{25}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "4.2.1.d2", "self_twist_discs": [-7], "self_twist_type": 1, "space_label": "1008.5.f", "trace_display": [0, 0, 0, -49], "trace_hash": 943456282458756957, "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.064", "prec": 17}, {"__RealLiteral__": 0, "data": "2.884", "prec": 17}, {"__RealLiteral__": 0, "data": "0.193", "prec": 17}, {"__RealLiteral__": 0, "data": "9.518", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "traces": [0, 1, 0, 0, 0, 0, 0, -49, 0, 0, 0, -206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -734, 0, 625, 0, 0, 0, -1234, 0, 0, 0, 0, 0, 0, 0, -1294, 0, 0, 0, 0, 0, 334, 0, 0, 0, 0, 0, 2401, 0, 0, 0, 5582, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4946, 0, 0, 0, 2914, 0, 0, 0, 0, 0, 10094, 0, 3646, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11698, 0, -12526, 0, 0, 0, -23746, 0, 0, 0, 0, 0, 0, 0, 27795, 0, 0, 0, 0, 0, 32254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7262, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9806, 0, -29474, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35966, 0, 47662, 0, 0, 0, 0, 0, 28561, 0, 0, 0, 0, 0, -30625, 0, 0, 0, 52882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28162, 0, -70654, 0, 0, 0, -1906, 0, 0, 0, 0, 0, 60466, 0, 0, 0, 0, 0, 0, 0, 11758, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108254, 0, 0, 0, 0, 0, -64958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151204, 0, 0, 0, 0, 0, 63406, 0, 0, 0, 109666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128750, 0, 52658, 0, 0, 0, 144926, 0, 0, 0, 0, 0, 0, 0, 83521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -71506, 0, 254204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -182834, 0, 0, 0, 0, 0, -176062, 0, 0, 0, 0, 0, -117649, 0, 0, 0, 218866, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 169954, 0, 130321, 0, 0, 0, 0, 0, 0, 0, 0, 0, -273518, 0, -209614, 0, 0, 0, 0, 0, -89714, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140914, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196286, 0, 0, 0, 0, 0, 266564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -326926, 0, 0, 0, 0, 0, 0, 0, 0, 0, -345278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156302, 0, 0, 0, 0, 0, -396034, 0, 0, 0, 0, 0, 0, 0, 353186, 0, 0, 0, 0, 0, -25538, 0, 0, 0, 0, 0, 242354, 0, 0, 0, -68804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 315934, 0, 0, 0, 427954, 0, 0, 0, 0, 0, -142786, 0, 409198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258915, 0, 0, 0, 0, 0, 0, 0, 0, 0, -494606, 0, -579886, 0, 0, 0, 0, 0, -110546, 0, 0, 0, 0, 0, -178654, 0, 0, 0, -383506, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219806, 0, -615794, 0, 0, 0, -458750, 0, 0, 0, 0, 0, 0, 0, -1149892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -687326, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704014, 0, 0, 0, 450014, 0, 0, 0, 0, 0, 0, 0, 390625, 0, 0, 0, 0, 0, -215714, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -572818, 0, 0, 0, 0, 0, -486638, 0, 0, 0, 0, 0, 0, 0, 905756, 0, 0, 0, 0, 0, -706942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 857266, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -971602, 0, 0, 0, 0, 0, 0, 0, 904562, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -771250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1018876, 0, -410834, 0, 0, 0, -1091102, 0, 0, 0, 0, 0, -573202, 0, 484798, 0, 0, 0, 0, 0, 819506, 0, 0, 0, 0, 0, 613774, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -600284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1163554, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1278686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7118, 0, 967774, 0, 0, 0, -1288334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 815475, 0, 0, 0, 0, 0, -1361955, 0, 0, 0, 949796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1272706, 0, 0, 0, 0, 0, -751076, 0, 0, 0, 0, 0, 0, 0, -981742, 0, 0, 0, 0, 0, -1071506, 0, 0, 0, 0, 0, -1580446, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1544498, 0, 0, 0, 792514, 0, 0, 0, 0, 0, 0, 0, 1471966, 0, 0, 0, 0, 0, -808750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 438418, 0, 0, 0, 0, 0, -309346, 0, 0, 0, 0, 0, -355838, 0, 923521, 0, 0, 0, 0, 0, 1758622, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1882814, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -245156, 0, -12674, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2020034, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1633166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2011234, 0, 1730978, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480494, 0, 0, 0, 0, 0, 0, 0, 2181646, 0, 0, 0, 0, 0, 1444226, 0, 0, 0, 1791758, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1596796, 0, 208750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1330946, 0, 0, 0, 0, 0, -1001614, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1036094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2007506, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1762334, 0, 597794, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2335438, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2575666, 0, 0, 0, 0, 0, 0, 0, 1648366, 0, 0, 0, 0, 0, -2409788, 0, 0, 0, 0, 0, -1399489, 0, 0, 0, 2742226, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2580356, 0, 933314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -932014, 0, 0, 0, 0, 0, -4097188, 0, 0, 0, 0, 0, 1500625, 0, 0, 0, 2903918, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4891676, 0, 0, 0, -412156, 0, 0, 0, 0, 0, -2591218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1399378, 0, 0, 0, 0, 0, 2705246, 0, 0, 0, 0, 0, 0, 0, -1296574, 0, 0, 0, 0, 0, -3250466, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3488750, 0, -796226, 0, 0, 0, -2709724, 0, 0, 0, 0, 0, -1379938, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3462046, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1882334, 0, -199725, 0, 0, 0, -3748306, 0, 0, 0, 0, 0, 93394, 0, 3616754, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6644324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2917886, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2962834, 0, 3756094, 0, 0, 0, 0, 0, -4080718, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4049074, 0, 2444306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -698882, 0, 0, 0, 0, 0, -576142, 0, 0, 0, -1933474, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1801906, 0, 0, 0, 0, 0, -1850126, 0, 0, 0, 0, 0, 0, 0, -1495972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4522094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6888188, 0, 0, 0, 3630364, 0, 0, 0, 0, 0, 0, 0, 4117394, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4885682, 0, 0, 0, -2559422, 0, 0, 0, 0, 0, 0, 0, -432196, 0, 0, 0, 0, 0, 161618, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4985698, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1199122, 0, -264526, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5304446, 0, -2138876, 0, 0, 0, 0, 0, -2020036, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6071644, 0, -3918338, 0, 0, 0, -3603374, 0, 0, 0, 0, 0, 3182942, 0, -3091250, 0, 0, 0, 0, 0, 2825761, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5088274, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4549774, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1918094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6092782, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4714366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7408996, 0, 0, 0, 1821250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1537934, 0, -5795758, 0, 0, 0, -9818372, 0, 0, 0, 0, 0, 0, 0, 6229154, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3106894, 0, 0, 0, -2676164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -253922, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5373634, 0, 0, 0, 0, 0, 0, 0, -3307245, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5883566, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6875966, 0, 4693826, 0, 0, 0, -6217906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4385006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3849826, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6308750, 0, 0, 0, 0, 0, 0, 0, 695186, 0, 0, 0, 0, 0, -2580242, 0, 0, 0, 6103364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7223108, 0, 0, 0, 0, 0, -7101374, 0, -10893692, 0, 0, 0, 0, 0, 2278750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5743982, 0, -6040514, 0], "weight": 5, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 0, 0, 0, 0, -49, 0, 0, 0, -206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -734, 0, 625, 0, 0, 0, -1234, 0, 0, 0, 0, 0, 0, 0, -1294, 0, 0, 0, 0, 0, 334, 0, 0, 0, 0, 0, 2401, 0, 0, 0, 5582, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4946, 0, 0, 0, 2914, 0, 0, 0, 0, 0, 10094, 0, 3646, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11698, 0, -12526, 0, 0, 0, -23746, 0, 0, 0, 0, 0, 0, 0, 27795, 0, 0, 0, 0, 0, 32254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7262, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9806, 0, -29474, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35966, 0, 47662, 0, 0, 0, 0, 0, 28561, 0, 0, 0, 0, 0, -30625, 0, 0, 0, 52882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28162, 0, -70654, 0, 0, 0, -1906, 0, 0, 0, 0, 0, 60466, 0, 0, 0, 0, 0, 0, 0, 11758, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108254, 0, 0, 0, 0, 0, -64958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151204, 0, 0, 0, 0, 0, 63406, 0, 0, 0, 109666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128750, 0, 52658, 0, 0, 0, 144926, 0, 0, 0, 0, 0, 0, 0, 83521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -71506, 0, 254204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -182834, 0, 0, 0, 0, 0, -176062, 0, 0, 0, 0, 0, -117649, 0, 0, 0, 218866, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 169954, 0, 130321, 0, 0, 0, 0, 0, 0, 0, 0, 0, -273518, 0, -209614, 0, 0, 0, 0, 0, -89714, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140914, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196286, 0, 0, 0, 0, 0, 266564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -326926, 0, 0, 0, 0, 0, 0, 0, 0, 0, -345278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156302, 0, 0, 0, 0, 0, -396034, 0, 0, 0, 0, 0, 0, 0, 353186, 0, 0, 0, 0, 0, -25538, 0, 0, 0, 0, 0, 242354, 0, 0, 0, -68804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 315934, 0, 0, 0, 427954, 0, 0, 0, 0, 0, -142786, 0, 409198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258915, 0, 0, 0, 0, 0, 0, 0, 0, 0, -494606, 0, -579886, 0, 0, 0, 0, 0, -110546, 0, 0, 0, 0, 0, -178654, 0, 0, 0, -383506, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 219806, 0, -615794, 0, 0, 0, -458750, 0, 0, 0, 0, 0, 0, 0, -1149892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -687326, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704014, 0, 0, 0, 450014, 0, 0, 0, 0, 0, 0, 0, 390625, 0, 0, 0, 0, 0, -215714, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -572818, 0, 0, 0, 0, 0, -486638, 0, 0, 0, 0, 0, 0, 0, 905756, 0, 0, 0, 0, 0, -706942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 857266, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -971602, 0, 0, 0, 0, 0, 0, 0, 904562, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -771250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1018876, 0, -410834, 0, 0, 0, -1091102, 0, 0, 0, 0, 0, -573202, 0, 484798, 0, 0, 0, 0, 0, 819506, 0, 0, 0, 0, 0, 613774, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -600284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1163554, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1278686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7118, 0, 967774, 0, 0, 0, -1288334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 815475, 0, 0, 0, 0, 0, -1361955, 0, 0, 0, 949796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1272706, 0, 0, 0, 0, 0, -751076, 0, 0, 0, 0, 0, 0, 0, -981742, 0, 0, 0, 0, 0, -1071506, 0, 0, 0, 0, 0, -1580446, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1544498, 0, 0, 0, 792514, 0, 0, 0, 0, 0, 0, 0, 1471966, 0, 0, 0, 0, 0, -808750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 438418, 0, 0, 0, 0, 0, -309346, 0, 0, 0, 0, 0, -355838, 0, 923521, 0, 0, 0, 0, 0, 1758622, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1882814, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -245156, 0, -12674, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2020034, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1633166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2011234, 0, 1730978, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480494, 0, 0, 0, 0, 0, 0, 0, 2181646, 0, 0, 0, 0, 0, 1444226, 0, 0, 0, 1791758, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1596796, 0, 208750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1330946, 0, 0, 0, 0, 0, -1001614, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1036094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2007506, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1762334, 0, 597794, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2335438, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2575666, 0, 0, 0, 0, 0, 0, 0, 1648366, 0, 0, 0, 0, 0, -2409788, 0, 0, 0, 0, 0, -1399489, 0, 0, 0, 2742226, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2580356, 0, 933314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -932014, 0, 0, 0, 0, 0, -4097188, 0, 0, 0, 0, 0, 1500625, 0, 0, 0, 2903918, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4891676, 0, 0, 0, -412156, 0, 0, 0, 0, 0, -2591218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1399378, 0, 0, 0, 0, 0, 2705246, 0, 0, 0, 0, 0, 0, 0, -1296574, 0, 0, 0, 0, 0, -3250466, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3488750, 0, -796226, 0, 0, 0, -2709724, 0, 0, 0, 0, 0, -1379938, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3462046, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1882334, 0, -199725, 0, 0, 0, -3748306, 0, 0, 0, 0, 0, 93394, 0, 3616754, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6644324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2917886, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2962834, 0, 3756094, 0, 0, 0, 0, 0, -4080718, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4049074, 0, 2444306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -698882, 0, 0, 0, 0, 0, -576142, 0, 0, 0, -1933474, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1801906, 0, 0, 0, 0, 0, -1850126, 0, 0, 0, 0, 0, 0, 0, -1495972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4522094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6888188, 0, 0, 0, 3630364, 0, 0, 0, 0, 0, 0, 0, 4117394, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4885682, 0, 0, 0, -2559422, 0, 0, 0, 0, 0, 0, 0, -432196, 0, 0, 0, 0, 0, 161618, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4985698, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1199122, 0, -264526, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5304446, 0, -2138876, 0, 0, 0, 0, 0, -2020036, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6071644, 0, -3918338, 0, 0, 0, -3603374, 0, 0, 0, 0, 0, 3182942, 0, -3091250, 0, 0, 0, 0, 0, 2825761, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5088274, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4549774, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1918094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6092782, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4714366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7408996, 0, 0, 0, 1821250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1537934, 0, -5795758, 0, 0, 0, -9818372, 0, 0, 0, 0, 0, 0, 0, 6229154, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3106894, 0, 0, 0, -2676164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -253922, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5373634, 0, 0, 0, 0, 0, 0, 0, -3307245, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5883566, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6875966, 0, 4693826, 0, 0, 0, -6217906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4385006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3849826, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6308750, 0, 0, 0, 0, 0, 0, 0, 695186, 0, 0, 0, 0, 0, -2580242, 0, 0, 0, 6103364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7223108, 0, 0, 0, 0, 0, -7101374, 0, -10893692, 0, 0, 0, 0, 0, 2278750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5743982, 0, -6040514, 0]}