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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1849.99', 'a10': [0.4417035444932268, 0.8971610662429127], 'a2': [0.5733389222111592, 0.8193183021742809], 'a3': [0.3588550983010642, -0.9333932817539098], 'a4': [-0.3425649605554927, 0.9394941446329582], 'a5': [0.9883063157076063, 0.1524815606309734], 'a6': [0.9704917941574053, -0.2411341482933108], 'a7': [0.9250402067486521, 0.3798692089369854], 'a8': [-0.966150572755548, 0.2579788184408293], 'a9': [-0.7424460368466671, -0.6699058757547044], 'algebraic': True, 'analytic_conductor': 8.586719900673815, 'analytic_normalization': 0, 'bad_lfactors': [[43, [1]]], 'bad_primes': [43], 'central_character': '1849.99', 'coeff_info': ['x^903 - 1', '0.999975792357992 + 0.00695806711708848*I', '\\\\zeta_{903}'], 'conductor': 1849, 'conductor_radical': 43, 'conjugate': 'dirichlet_L_1849.1214', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^138', 'a^730', 'a^276', 'a^22', 'a^868', 'a^56', 'a^414', 'a^557', 'a^160', 'a^606', 'a^103', 'a^680', 'a^194', 'a^752', 'a^552', 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'st_group': 'mu(903)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.86926801077306643116263527929+0.229077993951724826783669893598*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.89198608535', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.11924253488', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.83377207788', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.586719900673815, 'bad_primes': [43], 'central_character': '1849.99', 'conductor': 1849, 'conductor_radical': 43, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1849/99'], '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': '1-43e2-1849.99-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': '1-43e2-1849.99-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.586719900673815, 'root_angle': 0.0005408328826392644, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.89198608535', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1849.99', 'Lhash_array': ['dirichlet_L_1849.99'], 'label': '1-43e2-1849.99-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1849/99'}