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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3407.447', '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': '3407.447', 'coeff_info': ['x^1703 - 1', '0.999993193874507 + 0.00368947213884746*I', '\\\\zeta_{1703}'], 'conductor': 3407, 'conductor_radical': 3407, 'conjugate': 'dirichlet_L_3407.625', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1665', 'a^1074', 'a^1627', 'a^1701', 'a^1036', 'a^1478', 'a^1589', 'a^445', 'a^1663', 'a^792', 'a^998', 'a^1650', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.8220414827451, 'bad_primes': [3407], 'central_character': '3407.447', 'conductor': 3407, 'conductor_radical': 3407, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3407/447'], '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': '1-3407-3407.447-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': '1-3407-3407.447-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': '0.861194939052', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3407.447', 'Lhash_array': ['dirichlet_L_3407.447'], 'label': '1-3407-3407.447-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3407/447'}