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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_67.17', 'a10': [-0.9954719225730846, -0.09505604330418266], 'a2': [0.9819286972627067, -0.18925124436041021], 'a3': [0.41541501300188644, -0.9096319953545183], 'a4': [0.9283679330160726, -0.3716624556603275], 'a5': [-0.9594929736144974, -0.28173255684142967], 'a6': [0.23575893550942723, -0.9718115683235417], 'a7': [-0.32706796331742166, 0.9450008187146685], 'a8': [0.8412535328311812, -0.5406408174555976], 'a9': [-0.6548607339452851, -0.7557495743542583], 'algebraic': True, 'analytic_conductor': 0.311146691911923, 'analytic_normalization': 0, 'bad_lfactors': [[67, [1]]], 'bad_primes': [67], 'central_character': '67.17', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 67, 'conductor_radical': 67, 'conjugate': 'dirichlet_L_67.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 'a^27', 'a^31', 'a^18', 'a^26', 'a^10', 'a^30', 'a^21', 'a^17', 'a^7', 'a^25', 'a^14', 'a^9', 'a^12', 'a^29', 'a^2', 'a^20', 'a^23', 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'189.64000703387315571000085129592', '190.657663262504975557017402230559', '191.12781043600615859858320410765', '192.27943278243892914940848479293', '192.68372178425994864382342839097', '193.87081444589681806898648608460', '194.63816791758761439565578561918', '195.62346109121911765266431665672', '196.10323177216699608108208114588', '196.34336963403044872629228524579', '197.63047292954466675315597338807', '198.41425120751730587588243379714', '199.56517131618765240648088446515'], 'prelabel': '1-67-67.17-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': -0.30374749176405225, 'root_number': '0.578220105607650603891360930864-0.815880818178168337957091506756*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.151873745882', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.50916675696013553719784493763-0.540770681369144411831267920382*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.99921564982', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.41222973148', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.05899313643', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.311146691911923, 'bad_primes': [67], 'central_character': '67.17', 'conductor': 67, 'conductor_radical': 67, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/67/17'], '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': '1-67-67.17-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': '1-67-67.17-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': -0.15187374588202612, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99921564982', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_67.17', 'Lhash_array': ['dirichlet_L_67.17'], 'label': '1-67-67.17-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/67/17'}
Lfunction data - 1-67-67.17-r0-0-0