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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_179.117', 'a10': [-0.32908887327600994, -0.9442989534495557], 'a2': [0.607593920324899, -0.7942478378845109], 'a3': [0.15817743084430402, 0.9874107050115952], 'a4': [-0.26165925596844064, -0.9651603150596496], 'a5': [0.5500550034448413, -0.8351284291564356], 'a6': [0.8803564628730913, 0.4743126587785523], 'a7': [0.9900485105144543, 0.14072649653889052], 'a8': [-0.9255590665712211, -0.37860324125370337], 'a9': [-0.9499598007429908, 0.31237217701379416], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.117', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.153', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^76', 'a^20', 'a^63', 'a^75', 'a^7', 'a^2', 'a^50', 'a^40', 'a^62', 'a^72', 'a^83', 'a^31', 'a^78', 'a^6', 'a^37', 'a^67', 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'0.572488191442197737142560287013-0.819912965295244952319552529429*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.152989117206', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.48373166064305438608276283092-0.514461262766399008807382880019*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.43568021115', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.85509503527', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.28761106108', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'bad_primes': [179], 'central_character': '179.117', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/117'], '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': '1-179-179.117-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': '1-179-179.117-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.15298911720614106, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43568021115', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_179.117', 'Lhash_array': ['dirichlet_L_179.117'], 'label': '1-179-179.117-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/117'}