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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.101', 'a10': [0.9810224757821062, 0.19389404841393854], 'a2': [0.8475882078129211, -0.5306545297804217], 'a3': [-0.9679981841107131, 0.25095719865818134], 'a4': [0.436811540047039, -0.8995530437287921], 'a5': [0.7286123269840293, 0.6849263295909407], 'a6': [-0.6872922717875923, 0.7263809834660117], 'a7': [0.9593262165898075, 0.2822998585962907], 'a8': [-0.10711558705197749, -0.9942465745530684], 'a9': [0.8740409688832762, -0.48585222518126203], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.101', 'coeff_info': ['x^483 - 1', '0.999915388507649 + 0.0130082983359933*I', '\\\\zeta_{483}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.450', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^440', 'a^222', 'a^397', 'a^58', 'a^179', 'a^22', 'a^354', 'a^444', 'a^15', 'a^306', 'a^136', 'a^16', 'a^462', 'a^280', 'a^311', 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'0.372193311370605586273036730944-0.928155234306731385791254383297*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.189302921615', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(483)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.50380696853003943475155433220-0.510626017287227352238301889160*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.887202515743', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.04915770061', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.94132202437', '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': '967.101', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/101'], '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': '1-967-967.101-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': '1-967-967.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.1893029216145292, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887202515743', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.101', 'Lhash_array': ['dirichlet_L_967.101'], 'label': '1-967-967.101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/101'}