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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3407.625', 'a10': [0.9891299371861311, 0.14704410005899704], 'a2': [0.9901880315436912, 0.13974141185643588], 'a3': [-0.6815560115289676, 0.7317659483391706], 'a4': [0.96094467562474, 0.27674054706252094], 'a5': [0.9999727755906733, 0.0073788940556741515], 'a6': [-0.7771266122120172, 0.6293442846263666], 'a7': [0.6747775246740069, 0.738021200369488], 'a8': [0.912843802014813, 0.4083089432318878], 'a9': [-0.07096280629745164, -0.9974789622455155], 'algebraic': True, 'analytic_conductor': 15.8220414827451, 'analytic_normalization': 0, 'bad_lfactors': [[3407, [1]]], 'bad_primes': [3407], 'central_character': '3407.625', 'coeff_info': ['x^1703 - 1', '0.999993193874507 + 0.00368947213884746*I', '\\\\zeta_{1703}'], 'conductor': 3407, 'conductor_radical': 3407, 'conjugate': 'dirichlet_L_3407.447', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^38', 'a^629', 'a^76', 'a^2', 'a^667', 'a^225', 'a^114', 'a^1258', 'a^40', 'a^911', 'a^705', 'a^53', 'a^263', 'a^631', 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{'__RealLiteral__': 0, 'data': '2.04243208207', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.09119355941', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.8220414827451, 'bad_primes': [3407], 'central_character': '3407.625', 'conductor': 3407, 'conductor_radical': 3407, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3407/625'], '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': '1-3407-3407.625-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': '1-3407-3407.625-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.8220414827451, 'root_angle': 0.2775326308002573, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36261878744', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3407.625', 'Lhash_array': ['dirichlet_L_3407.625'], 'label': '1-3407-3407.625-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3407/625'}