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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.149', 'a10': [0.16510106503159225, 0.9862766540506949], 'a2': [0.7797996589651528, -0.6260291461887629], 'a3': [-0.9982870823553307, -0.05850556556842369], 'a4': [0.21617501624433705, -0.9763546294004861], 'a5': [-0.4886921774348472, 0.8724562772506068], 'a6': [-0.8150901156300953, 0.5793341897403588], 'a7': [0.34100126366449335, 0.9400628373567474], 'a8': [-0.442653251076912, -0.8966928678823315], 'a9': [0.9931541975950378, 0.11681070070570036], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.149', 'coeff_info': ['x^483 - 1', '0.999915388507649 + 0.0130082983359933*I', '\\\\zeta_{483}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.649', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^431', 'a^246', 'a^379', 'a^160', 'a^194', 'a^94', 'a^327', 'a^9', 'a^108', 'a^78', 'a^142', 'a^244', 'a^42', 'a^406', 'a^275', 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0.6244196690067906, 'root_number': '-0.380998413772267048193961868386+0.924575691170288334904111984269*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.312209834503', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(483)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.907688788945571628248527132527-0.0389491994463657294920087286061*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.62340221369', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.38184237602', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.62244074932', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.149', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/149'], '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': '1-967-967.149-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': '1-967-967.149-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.3122098345033953, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62340221369', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.149', 'Lhash_array': ['dirichlet_L_967.149'], 'label': '1-967-967.149-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/149'}