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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4693.71', 'a10': [0.9973010051548273, -0.07342142137803533], 'a2': [-0.5996118745598817, -0.8002909470228841], 'a3': [0.15552711424444318, -0.9878316236762194], 'a4': [-0.28093119977356934, 0.959727909875389], 'a5': [-0.5392350263549461, 0.8421553219875657], 'a6': [-0.8838086101279943, 0.46784863007560784], 'a7': [0.1100082209940793, 0.9939306773179495], 'a8': [0.9365112411970548, -0.35063755519275436], 'a9': [-0.9516226334695919, -0.30726920357953036], 'algebraic': True, 'analytic_conductor': 21.7942003752635, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [19, [1]]], 'bad_primes': [13, 19], 'central_character': '4693.71', 'coeff_info': ['x^684 - 1', '0.999957809518312 + 0.00918581424472636*I', '\\\\zeta_{684}'], 'conductor': 4693, 'conductor_radical': 247, 'conjugate': 'dirichlet_L_4693.661', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^443', 'a^530', 'a^202', 'a^233', 'a^289', 'a^159', 'a^645', 'a^376', 'a^676', 'a^327', 'a^48', 0, 'a^602', 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(684)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.586408204423805743989960519639-0.256028410598519528346175352778*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.292393041943', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.44307508413', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.37317635357', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.7942003752635, 'bad_primes': [13, 19], 'central_character': '4693.71', 'conductor': 4693, 'conductor_radical': 247, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4693/71'], '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': '1-4693-4693.71-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': '1-4693-4693.71-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.7942003752635, 'root_angle': -0.34517296252637997, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.292393041943', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4693.71', 'Lhash_array': ['dirichlet_L_4693.71'], 'factors': ['1-4693-4693.71-r0-0-0'], 'label': '1-4693-4693.71-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4693/71'}
Lfunction data - 1-4693-4693.71-r0-0-0