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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.2984', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.7104645782653688, -0.7037329628703004], 'a3': [0.10452846326765347, 0.9945218953682733], 'a4': [0.009519833939576644, -0.9999546853541729], 'a5': [1.0, -2.8163065144692913e-30], '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': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.2984', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.3084', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^289', 'a^77', 'a^248', 0, 'a^36', 0, 'a^207', 'a^154', 0, 0, 'a^325', 'a^39', 0, 0, 'a^166', 'a^191', 'a^113', 'a^172', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '1.92275605208', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.63284279852', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.2984', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/2984'], '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': '1-4235-4235.2984-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': '1-4235-4235.2984-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.07793005239864678, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.673937127994', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.2984', 'Lhash_array': ['dirichlet_L_4235.2984'], 'label': '1-4235-4235.2984-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/2984'}