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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_896.173', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9978589232386035, 0.06540312923014306], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.7518398074789774, 0.6593458151000688], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9914448613738104, -0.1305261922200516], 'algebraic': True, 'analytic_conductor': 96.28857261598402, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '896.173', 'coeff_info': ['x^96 - 1', '0.997858923238603 + 0.0654031292301431*I', '\\\\zeta_{96}'], 'conductor': 896, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_896.549', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^143', 0, 'a^37', 0, 0, 0, 'a^94', 0, 'a^89', 0, 'a^75', 0, 'a^84', 0, 'a^92', 0, 'a^19', 0, 0, 0, 'a^70', 0, 'a^74', 0, 'a^141', 0, 'a^87', 0, 'a^152', 0, 'a^40', 0, 0, 0, 'a^109', 0, 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'1.27499522983', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.95849515537', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 96.28857261598402, 'bad_primes': [2, 7], 'central_character': '896.173', 'conductor': 896, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/896/173'], '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': '1-896-896.173-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-896-896.173-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 96.28857261598402, 'root_angle': -0.21548545305394612, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35651609236', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_896.173', 'Lhash_array': ['dirichlet_L_896.173'], 'label': '1-896-896.173-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/896/173'}