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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.129', 'a10': [0.23575893550942723, 0.9718115683235417], 'a2': [-0.6403534686527224, 0.768080357244232], 'a3': [-0.9135454576426009, -0.4067366430758002], 'a4': [-0.17989487036885388, -0.983685841930732], 'a5': [0.595460324452688, -0.8033847160624227], 'a6': [0.8973984286913584, -0.4412211012432213], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8707460771197771, 0.49173292464560375], 'a9': [0.6691306063588582, 0.7431448254773942], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.129', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.348', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^119', 'a^187', 'a^238', 'a^281', 'a^306', 0, 'a^27', 'a^44', 'a^70', 0, 'a^95', 'a^84', 0, 'a^138', 'a^146', 'a^166', 'a^163', 'a^32', 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'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.510690527942649479029467151956+0.0955799875452282727778552247639*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.39543149063', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.90991434303', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.14452890269', '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': '847.129', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/129'], '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': '1-847-847.129-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': '1-847-847.129-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.4379415480952685, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39543149063', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.129', 'Lhash_array': ['dirichlet_L_847.129'], 'label': '1-847-847.129-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/129'}