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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2268.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8936326403234123, -0.44879918020046217], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 243.73044943420956, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.83', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 2268, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_2268.1175', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^50', 0, 0, 0, 0, 0, 'a^40', 0, 'a^35', 0, 0, 0, 'a^6', 0, 'a^48', 0, 0, 0, 'a^38', 0, 'a^46', 0, 0, 0, 'a^37', 0, 'a^74', 0, 0, 0, 0, 0, 'a^42', 0, 0, 0, 'a^26', 0, 'a^49', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '2.19642921766', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 243.73044943420956, 'bad_primes': [2, 3, 7], 'central_character': '2268.83', 'conductor': 2268, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2268/83'], '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': '1-2268-2268.83-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': '1-2268-2268.83-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 243.73044943420956, 'root_angle': -0.42901234567901236, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32848447869', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2268.83', 'Lhash_array': ['dirichlet_L_2268.83'], 'label': '1-2268-2268.83-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2268/83'}