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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.304', 'a10': [-0.9954719225730846, 0.09505604330418266], 'a2': [0.7104645782653688, 0.7037329628703004], 'a3': [0.10452846326765347, -0.9945218953682733], 'a4': [0.009519833939576644, 0.9999546853541729], 'a5': [-0.6403534686527224, 0.768080357244232], 'a6': [0.7741416106390825, -0.6330124538088704], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6969375686552934, 0.7171318047589635], 'a9': [-0.9781476007338057, -0.20791169081775934], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.304', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.404', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^253', 'a^82', 'a^119', 'a^294', 0, 'a^123', 'a^176', 'a^160', 0, 'a^5', 'a^126', 0, 'a^42', 'a^164', 'a^304', 'a^217', 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'unitary', 'types': ['DIR'], 'values': [[1, '0.909620965104518008864072985448+0.321610739043099199978361980299*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.00914565748', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.9106561088', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.80109724527', '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': '847.304', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/304'], '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': '1-847-847.304-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': '1-847-847.304-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.4190832452931613, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00914565748', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.304', 'Lhash_array': ['dirichlet_L_847.304'], 'label': '1-847-847.304-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/304'}