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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1063.719', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, 0.0], 'a6': [-0.5, 0.8660254037844386], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 4.9365512463040915, 'analytic_normalization': 0, 'bad_lfactors': [[1063, [1]]], 'bad_primes': [1063], 'central_character': '1063.719', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 1063, 'conductor_radical': 1063, 'conjugate': 'dirichlet_L_1063.343', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^2', 'a^1', 'a^0', 'a^1', 'a^2', 'a^0', 'a^1', 'a^2', 'a^2', 'a^0', 'a^0', 'a^1', 'a^2', 'a^2', 'a^0', 'a^0', 'a^1', 'a^1', 'a^1', 'a^1', 'a^2', 'a^2', 'a^0', 'a^2', 'a^0', 'a^0', 'a^2', 'a^1', 'a^2', 'a^1', 'a^1', 'a^2', 'a^2', 'a^2', 'a^0', 'a^0', 'a^2', 'a^0', 'a^0', 'a^0', 'a^0', 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'190.291157088226606788117568640695', '190.86311196493665601289643316862', '191.48853155061262994646184071652', '192.14640212994077811771310433363', '192.5560109104539839743845208268', '193.60470365165288057215175879348', '193.98114268457250290489920311590', '194.43486720471233220503326633718', '194.719615518339285989200645292418', '195.7417324483464254507706854953', '196.4756134023287346810548574165', '196.97350663043001260970999392485', '197.62962868612679316595689671181', '198.04796216072075464789076780203', '199.01983199444097332621886328290', '199.73438795028866897973985155315'], 'prelabel': '1-1063-1063.719-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9365512463040915, 'root_angle': 0.4957680080793412, 'root_number': '-0.999646496423716133173280794654+0.0265872561162164338485958196082*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.495768008079', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(3)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.514850346315208062480410607449-0.573068657238036032700229802237*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.556153153271', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.37994751542', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.36847263576', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.9365512463040915, 'bad_primes': [1063], 'central_character': '1063.719', 'conductor': 1063, 'conductor_radical': 1063, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1063/719'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-1063-1063.719-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1063-1063.719-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9365512463040915, 'root_angle': 0.4957680080793412, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.556153153271', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1063.719', 'Lhash_array': ['dirichlet_L_1063.719'], 'factors': ['1-1063-1063.719-r0-0-0'], 'label': '1-1063-1063.719-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1063/719'}
Lfunction data - 1-1063-1063.719-r0-0-0