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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.167', 'a10': [0.8412535328311812, -0.5406408174555976], 'a2': [-0.6106478796354381, -0.7919022459222751], 'a3': [-0.30901699437494745, 0.9510565162951535], 'a4': [-0.25421833419348694, 0.9671468547019572], 'a5': [-0.08557500847883974, 0.9963317308626913], 'a6': [0.9418443636395247, -0.33604939321543015], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9211236531148501, -0.3892701063173915], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.167', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.776', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^71', 'a^33', 'a^32', 'a^29', 'a^104', 0, 'a^103', 'a^66', 'a^100', 0, 'a^65', 'a^76', 0, 'a^62', 'a^64', 'a^14', 'a^27', 'a^8', 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'unitary', 'types': ['DIR'], 'values': [[1, '0.678578239540018660237453917642+0.181754432268895609219316470296*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.15698704961', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.82766302635', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.21179433258', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.167', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/167'], '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': '1-847-847.167-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': '1-847-847.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.25991735537190086, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15698704961', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.167', 'Lhash_array': ['dirichlet_L_847.167'], 'label': '1-847-847.167-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/167'}