# Stored data for newform 440.1.o.c, downloaded from the LMFDB on 14 January 2025.
{"Nk2": 440, "analytic_conductor": 0.21958860555852106, "analytic_rank": 0, "analytic_rank_proved": true, "artin_degree": 6, "artin_field": [-8, 2, 0, 1], "artin_field_label": "3.1.440.1", "artin_image": "6.1", "char_conductor": 440, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 15, "char_orbit_label": "o", "char_order": 2, "char_parity": -1, "char_values": [440, 2, [111, 221, 177, 321], [2, 1, 1, 1]], "cm_discs": [-440], "conrey_index": 109, "dim": 1, "embedded_related_objects": [["ArtinRepresentation/2.2e3_5_11.3t2.1c1"]], "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": [[3, [1, 1]], [7, [1, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008161344192952, "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, 440, 15, -1, 2, -440]], "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": true, "label": "440.1.o.c", "level": 440, "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": "440.1.o.a", "nf_label": "1.1.1.1", "prim_orbit_index": 15, "projective_field": [-8, 2, 0, 1], "projective_field_label": "3.1.440.1", "projective_image": "D3", "projective_image_type": "Dn", "qexp_display": "q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\\cdots", "related_objects": ["ArtinRepresentation/2.2e3_5_11.3t2.1"], "relative_dim": 1, "rm_discs": [], "self_twist_discs": [-440], "self_twist_type": 1, "space_label": "440.1.o", "trace_display": [1, -1, 1, -1], "trace_hash": 2101339153026504295, "trace_moments": [{"__RealLiteral__": 0, "data": "-0.001", "prec": 20}, {"__RealLiteral__": 0, "data": "0.999", "prec": 17}, {"__RealLiteral__": 0, "data": "0.991", "prec": 17}, {"__RealLiteral__": 0, "data": "2.983", "prec": 17}, {"__RealLiteral__": 0, "data": "4.960", "prec": 17}, {"__RealLiteral__": 0, "data": "10.921", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.497", "prec": 17}, "traces": [0, 1, 1, -1, 1, 1, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, -1, 0, -1, 1, 1, 1, 0, -1, 1, 0, 1, -1, -1, -1, -1, 1, -1, -1, -1, 0, -1, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 1, 0, -1, 1, 1, -1, 1, -1, 0, -1, -1, -1, 0, 1, 0, -1, 2, -1, 0, -1, -1, 0, 2, -1, -1, -1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 1, 1, -1, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 1, 2, 1, 0, 0, 1, -1, 0, 1, 2, 1, 1, -1, 0, 1, 0, -1, 0, 0, 1, -1, 1, -1, 0, -1, 1, 0, 2, 1, 0, 0, -1, -1, 1, 2, 1, -1, 0, 0, 2, -1, 0, -1, 0, 0, -1, 2, 0, -1, -1, -1, 0, -1, 0, -1, -1, 0, -1, 0, 1, 1, 0, -1, -1, 0, -1, 0, -1, 1, 1, -1, 0, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, -1, 1, -2, 2, 1, 1, 0, 0, 0, 0, -1, 1, -1, -1, 1, 0, 0, 1, 1, 2, -2, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 1, -1, -1, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 1, 0, 0, -1, -1, -1, -1, 1, 1, 2, 0, 1, 0, -1, 0, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 1, -1, 0, -1, 0, 0, -2, -1, -1, 0, 0, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1, 0, -1, -2, 0, 0, -1, 0, 0, 0, -1, 2, 1, -1, 1, 0, -1, -1, 0, 1, 0, 0, 0, 0, 1, 2, -1, 0, 1, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, 0, -1, 1, 1, 0, -1, -1, 0, 0, -1, 0, -1, -2, 2, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, -1, -1, 1, -1, -2, 0, 2, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 1, 0, -1, 0, -1, -1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, -2, 0, 1, 0, 0, 2, 1, -1, 0, 1, -1, 2, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, 1, 0, -1, 1, -1, -1, 0, -2, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 2, 0, 2, 0, -1, 2, 0, 1, -2, 1, -1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, -1, 1, -1, 1, -1, 1, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, -1, 0, 0, -1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 2, 0, 0, -1, 0, 1, 0, 0, -1, 2, 1, 1, -1, 1, 0, -1, -1, 0, 0, 0, 0, 1, -2, -1, -1, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0, 1, 0, 1, -1, 1, 0, -1, 0, 1, -1, 2, 1, 0, -1, 0, 1, -1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, -1, -1, -2, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, -1, 1, -1, -1, 1, 1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, -1, -1, 0, 1, 1, 0, 0, -2, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, -1, 0, 1, -1, 1, -1, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, -1, 2, 0, 0, -1, 0, -2, -2, 2, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, -1, 2, -1, 0, 1, 0, -1, 2, -2, 0, 0, 0, 2, 0, -1, -1, 1, 0, -1, -1, 1, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -1, -1, 0, 2, 1, 0, 0, 0, -1, 1, 0, -1, -1, 0, -1, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, -1, -2, 0, 0, 0, 1, 2, 0, -1, 0, 0, 2, 2, 1, -2, -1, -1, 0, 0, 1, 0, -1, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 0, 0, -1, 0, 1, -1, 0, 0, -1, -1, 1, 0, -1, 1, -1, -1, 0, 2, -2, 0, 0, -1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 1, 1, -1, 0, 2, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 1, -1, 0, 0, 0, -2, 0, 0, -1, 0, 1, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 2, -1, 0, 1, -1, 0, 0, 0, -1, 1, 0, 1, 0, 0, -2, 2, 1, 0, 0, 2, 1, 0, -1, -1, 1, 2, 0, 0, -1, 1, 0, -2, 1, 1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 1, 0, 2, 0, 0, 2, 1, 0, -1, 0, -2, -1, -1, 1, 2, -1, 0, 1, -1, -1, 0, 1, 0, -1, 0, 0, -1, 1, 1, 0, 0, 1, -1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 2, -1, 0, -1, 0, -2, 0, -1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 1, 1, -1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, -1, 0, 0, 0, 0, -1, -1, 0, 2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 2, 0, 1, 0, 1, -2, -1, 0, 1, 0, 0, 0, -1, 2, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, -2, 2, -1, 0, -1, 2, -1, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 2, 0, 1, -2, 0, 1, -1, -1, 0, 2, 1, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, -1, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1, -2, 1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, -1, 0, 0, 0, -1, 0, -1, 0, -2, 1, 1, 0, 0, 0, 1, -1, -2, 0, 0, 2, 0, -1, 0, 1, 0, -1, -2, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 1, -1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 2, 0, 1, 1, 0, 0, 2, 2, 1, 0, -1, 1, -1, 0, 0, 0, 1, 2, 1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, -1, 2, -1, 2, 0, 0, 0, 0, 1, -1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, -1, -1, 0, 0, 2, 1, 1, -1, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, -1, -1, 1, 2, -2, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, -2, 0, 2, 2, 0, 2, 0, 2, 0, 0, -1, 1, 0, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 2, 0, 1, 0, -1, 0, 2, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 2, 0, -2, -1, 0, 0, 0, 0, 0, 1, 2, 0, 0, -1, -1, 0, -1, 1, 1, 0, 0, 0, -1, 0, -1, 1, 1, 0, 0, -2, 0, 2, 0, -1, 0, 0, 2, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -1, -1, 0, -1, 0, -1, 2, 0, 0, 2, 0, 1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 1, 1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, -1, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, -1, -1, 0, 1, 0, 0, 2, 0, 2, -1, 1, -1, -2, -2, -1, 0, -1, 0, 0, -1, 0, 2, 1, 2, 0, 0, -1, -1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, -1, -1, 1, 2, 0, 0, -1, 0, 1, 2, 0, 0, 1, 0, -1, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 2, 1, 1, -1, 0, 0, -2, 0, 1, -1, 0, -1, 1, 1, -1, 0, 0, -1, 0, 1, 0, -1, -1, -1, -1, 0, 0, 2, -1, -2, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, -2, -1, 2, 0, 0, 2, 0, 0, -1, 1, 0, 0, -1, 0, -2, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0, 2, -1, 0, 0, 0, 1, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, -1, 2, 0, 0, 1, 0, -1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 1], "weight": 1, "weight_parity": -1, "id": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "fricke_eigenval": null, "sato_tate_group": null, "qexp": [[0], 1, 1, -1, 1, 1, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, -1, 0, -1, 1, 1, 1, 0, -1, 1, 0, 1, -1, -1, -1, -1, 1, -1, -1, -1, 0, -1, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 1, 0, -1, 1, 1, -1, 1, -1, 0, -1, -1, -1, 0, 1, 0, -1, 2, -1, 0, -1, -1, 0, 2, -1, -1, -1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 1, 1, -1, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 1, 2, 1, 0, 0, 1, -1, 0, 1, 2, 1, 1, -1, 0, 1, 0, -1, 0, 0, 1, -1, 1, -1, 0, -1, 1, 0, 2, 1, 0, 0, -1, -1, 1, 2, 1, -1, 0, 0, 2, -1, 0, -1, 0, 0, -1, 2, 0, -1, -1, -1, 0, -1, 0, -1, -1, 0, -1, 0, 1, 1, 0, -1, -1, 0, -1, 0, -1, 1, 1, -1, 0, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, -1, 1, -2, 2, 1, 1, 0, 0, 0, 0, -1, 1, -1, -1, 1, 0, 0, 1, 1, 2, -2, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 1, -1, -1, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 1, 0, 0, -1, -1, -1, -1, 1, 1, 2, 0, 1, 0, -1, 0, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 1, -1, 0, -1, 0, 0, -2, -1, -1, 0, 0, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1, 0, -1, -2, 0, 0, -1, 0, 0, 0, -1, 2, 1, -1, 1, 0, -1, -1, 0, 1, 0, 0, 0, 0, 1, 2, -1, 0, 1, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, 0, -1, 1, 1, 0, -1, -1, 0, 0, -1, 0, -1, -2, 2, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, -1, -1, 1, -1, -2, 0, 2, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 1, 0, -1, 0, -1, -1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, -2, 0, 1, 0, 0, 2, 1, -1, 0, 1, -1, 2, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, 1, 0, -1, 1, -1, -1, 0, -2, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 2, 0, 2, 0, -1, 2, 0, 1, -2, 1, -1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, -1, 1, -1, 1, -1, 1, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, -1, 0, 0, -1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 2, 0, 0, -1, 0, 1, 0, 0, -1, 2, 1, 1, -1, 1, 0, -1, -1, 0, 0, 0, 0, 1, -2, -1, -1, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0, 1, 0, 1, -1, 1, 0, -1, 0, 1, -1, 2, 1, 0, -1, 0, 1, -1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, -1, -1, -2, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, -1, 1, -1, -1, 1, 1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, -1, -1, 0, 1, 1, 0, 0, -2, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, -1, 0, 1, -1, 1, -1, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, -1, 2, 0, 0, -1, 0, -2, -2, 2, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, -1, 2, -1, 0, 1, 0, -1, 2, -2, 0, 0, 0, 2, 0, -1, -1, 1, 0, -1, -1, 1, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -1, -1, 0, 2, 1, 0, 0, 0, -1, 1, 0, -1, -1, 0, -1, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, -1, -2, 0, 0, 0, 1, 2, 0, -1, 0, 0, 2, 2, 1, -2, -1, -1, 0, 0, 1, 0, -1, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 0, 0, -1, 0, 1, -1, 0, 0, -1, -1, 1, 0, -1, 1, -1, -1, 0, 2, -2, 0, 0, -1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 1, 1, -1, 0, 2, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 1, -1, 0, 0, 0, -2, 0, 0, -1, 0, 1, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 2, -1, 0, 1, -1, 0, 0, 0, -1, 1, 0, 1, 0, 0, -2, 2, 1, 0, 0, 2, 1, 0, -1, -1, 1, 2, 0, 0, -1, 1, 0, -2, 1, 1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 1, 0, 2, 0, 0, 2, 1, 0, -1, 0, -2, -1, -1, 1, 2, -1, 0, 1, -1, -1, 0, 1, 0, -1, 0, 0, -1, 1, 1, 0, 0, 1, -1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 2, -1, 0, -1, 0, -2, 0, -1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 1, 1, -1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, -1, 0, 0, 0, 0, -1, -1, 0, 2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 2, 0, 1, 0, 1, -2, -1, 0, 1, 0, 0, 0, -1, 2, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, -2, 2, -1, 0, -1, 2, -1, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 2, 0, 1, -2, 0, 1, -1, -1, 0, 2, 1, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, -1, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1, -2, 1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, -1, 0, 0, 0, -1, 0, -1, 0, -2, 1, 1, 0, 0, 0, 1, -1, -2, 0, 0, 2, 0, -1, 0, 1, 0, -1, -2, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 1, -1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 2, 0, 1, 1, 0, 0, 2, 2, 1, 0, -1, 1, -1, 0, 0, 0, 1, 2, 1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, -1, 2, -1, 2, 0, 0, 0, 0, 1, -1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, -1, -1, 0, 0, 2, 1, 1, -1, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, -1, -1, 1, 2, -2, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, -2, 0, 2, 2, 0, 2, 0, 2, 0, 0, -1, 1, 0, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 2, 0, 1, 0, -1, 0, 2, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 2, 0, -2, -1, 0, 0, 0, 0, 0, 1, 2, 0, 0, -1, -1, 0, -1, 1, 1, 0, 0, 0, -1, 0, -1, 1, 1, 0, 0, -2, 0, 2, 0, -1, 0, 0, 2, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -1, -1, 0, -1, 0, -1, 2, 0, 0, 2, 0, 1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 1, 1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, -1, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, -1, -1, 0, 1, 0, 0, 2, 0, 2, -1, 1, -1, -2, -2, -1, 0, -1, 0, 0, -1, 0, 2, 1, 2, 0, 0, -1, -1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, -1, -1, 1, 2, 0, 0, -1, 0, 1, 2, 0, 0, 1, 0, -1, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 2, 1, 1, -1, 0, 0, -2, 0, 1, -1, 0, -1, 1, 1, -1, 0, 0, -1, 0, 1, 0, -1, -1, -1, -1, 0, 0, 2, -1, -2, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, -2, -1, 2, 0, 0, 2, 0, 0, -1, 1, 0, 0, -1, 0, -2, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0, 2, -1, 0, 0, 0, 1, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, -1, 2, 0, 0, 1, 0, -1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 1]}