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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.849', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.44974419148406575, 0.8931574117849238], 'a3': [-0.6691306063588582, -0.7431448254773942], 'a4': [-0.595460324452688, 0.8033847160624227], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.362807705350641, -0.9318640292114523], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.985353835847693, -0.17052219263262378], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 455.11395650523696, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.849', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.424', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^58', 'a^209', 'a^116', 0, 'a^267', 0, 'a^174', 'a^88', 0, 0, 'a^325', 'a^138', 0, 0, 'a^232', 'a^92', 'a^146', 'a^139', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '1.71986751484', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.52785992104', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 455.11395650523696, 'bad_primes': [5, 7, 11], 'central_character': '4235.849', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/849'], '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': '1-4235-4235.849-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': '1-4235-4235.849-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 455.11395650523696, 'root_angle': 0.2720699476013532, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.485493485287', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.849', 'Lhash_array': ['dirichlet_L_4235.849'], 'label': '1-4235-4235.849-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/849'}