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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.358', 'a10': [-0.9070353005068484, 0.4210545851008527], 'a2': [0.7350596058898482, -0.678002489515386], 'a3': [0.2518156701278019, -0.9677752157800312], 'a4': [0.08062524842187778, -0.9967444854710311], 'a5': [-0.95220106743899, -0.3054719744396332], 'a6': [-0.47105447834912095, -0.8821041199468674], 'a7': [0.7004909112786141, -0.7136613224885154], 'a8': [-0.616530879230335, -0.7873307278110452], 'a9': [-0.873177736556172, -0.4874019289894534], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.358', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.430', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^223', 'a^200', 'a^193', 'a^139', 'a^170', 'a^221', 'a^163', 'a^147', 'a^109', 'a^173', 'a^140', 'a^98', 'a^191', 'a^86', 'a^133', 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'a^142'], [1, 'a^70'], [1, 'a^222'], [1, 'a^227'], [1, 'a^224']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-23e2-529.358-r0-0-0', 'leading_term': '-0.433324897834289950118888343746-1.52592434835339540972098359995*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/529/358', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-1.5862583597828033, -0.8271739929907387, -0.051154998196116366, 0.6294740036517457, 0.7619884691072498, 0.16406179548779504, -0.8310928666225748, -1.5430997215706896, -1.4194153830100382, -0.49226928612240145, 0.5619884393116127, 0.8913673119796688, 0.16679250931475925, -1.0549762751795455, -1.690204993809164, -1.0227717489236432, 0.5772058319723934, 1.799160136603532, 1.4215529299864929, -0.5721417907924679, -2.805671024383837, -3.5629758549868673, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.358', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/358'], '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': '1-23e2-529.358-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': '1-23e2-529.358-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.4119264478432721, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.645025563967', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.358', 'Lhash_array': ['dirichlet_L_529.358'], 'label': '1-23e2-529.358-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/358'}