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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.99', 'a10': [-0.14582564136906345, -0.9893103063848578], 'a2': [-0.4073307573478526, 0.913280709376052], 'a3': [0.5606300178972284, 0.8280664122113355], 'a4': [-0.6681633082368496, -0.7440146460426628], 'a5': [-0.8441187494686053, 0.5361562615465363], 'a6': [-0.984618930136869, 0.1747156616223271], 'a7': [-0.9770525020210205, 0.21299861101533926], 'a8': [0.951657690100178, -0.30716061087514734], 'a9': [-0.3713879660651067, 0.9284777749962695], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.99', 'coeff_info': ['x^161 - 1', '0.999238582475670 + 0.0390160901682098*I', '\\\\zeta_{161}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.547', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^51', 'a^25', 'a^102', 'a^66', 'a^76', 'a^75', 'a^153', 'a^50', 'a^117', 'a^4', 'a^127', 'a^157', 'a^126', 'a^91', 'a^43', 'a^24', 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4.490729120579545, 'root_angle': -0.9676072672044614, 'root_number': '-0.994826432783943887063901783803-0.101589215147933765663819962351*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.483803633602', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(161)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.538788744632541432915760165899+0.701746516616479566080895863552*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.29379306466', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.16541625544', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.64152090724', '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': '967.99', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/99'], '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': '1-967-967.99-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': '1-967-967.99-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.4838036336022307, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29379306466', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.99', 'Lhash_array': ['dirichlet_L_967.99'], 'label': '1-967-967.99-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/99'}