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{'Lhash': 'dirichlet_L_847.101', 'a10': [-0.9954719225730846, 0.09505604330418266], 'a2': [-0.9884217748453624, -0.15173132508333165], 'a3': [0.9781476007338057, -0.20791169081775934], 'a4': [0.9539552099769126, 0.29994909127701064], 'a5': [0.9695231451106913, -0.2449997369277637], 'a6': [-0.9983691039261356, 0.057088810862767986], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8973984286913584, -0.4412211012432213], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.101', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.369', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^173', 'a^319', 'a^16', 'a^317', 'a^162', 0, 'a^189', 'a^308', 'a^160', 0, 'a^5', 'a^258', 0, 'a^306', 'a^32', 'a^172', 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'191.646353939579091730958577944112', '192.38642732822858940558940850093', '192.54450707604419136028172307546', '193.24321526795794883420686884925', '193.887206479575566274318024486039', '194.640055708611155645155356932712', '195.68252095569930777593794699990', '196.2951512335837896350137787360', '196.93213823487753439410667356466', '197.14749455722797965133450937724', '197.75837221096325119883734902787', '198.44927082399098402410351583660', '199.04464590720748529554382699384', '199.57588985069036793719891634680'], 'prelabel': '1-847-847.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.4381664905863227, 'root_number': '0.193036286517767121953476469245-0.981191618435171163005658157533*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.219083245293', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.06740733582362313321926041332-0.364765049599071901096575687586*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.814357443288', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.03243852294', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.54907883977', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.101', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/101'], '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': '1-847-847.101-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': '1-847-847.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.21908324529316134, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.814357443288', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.101', 'Lhash_array': ['dirichlet_L_847.101'], 'label': '1-847-847.101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/101'}