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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.110', 'a10': [-0.27917848281287244, 0.9602392278668388], 'a2': [0.9969554894159722, -0.07797276526684974], 'a3': [0.6681633082368496, -0.7440146460426628], 'a4': [0.9878404957532815, -0.1554707527154578], 'a5': [-0.3532010288815979, 0.9355474510664762], 'a6': [0.6081161986220807, -0.7938480263711879], 'a7': [-0.8113047182536126, -0.5846235148704046], 'a8': [0.9727105204012866, -0.2320220754597679], 'a9': [-0.10711558705197749, -0.9942465745530684], 'algebraic': True, 'analytic_conductor': 103.91858227640239, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.110', 'coeff_info': ['x^322 - 1', '0.999809627498073 + 0.0195117595865944*I', '\\\\zeta_{322}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.589', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^318', 'a^279', 'a^314', 'a^99', 'a^275', 'a^193', 'a^310', 'a^236', 'a^95', 'a^6', 'a^271', 'a^155', 'a^189', 'a^56', 'a^306', 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-0.32019827606597023, 'root_number': '0.535300756973288217360561311341-0.844661529598586978250078491693*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.160099138033', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(322)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.32814059671944075163978481334-0.638238663510957762756483556385*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.810438187565', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.97339829424', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.11648691764', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 103.91858227640239, 'bad_primes': [967], 'central_character': '967.110', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/110'], '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': '1-967-967.110-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-967-967.110-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': -0.16009913803298512, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.810438187565', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.110', 'Lhash_array': ['dirichlet_L_967.110'], 'label': '1-967-967.110-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/110'}