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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_5184.43', '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': [0.40939231452609254, 0.9123584453530141], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.62023549126826, 0.7844156649195757], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 557.0981701353361, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '5184.43', 'coeff_info': ['x^432 - 1', '0.999894231927107 + 0.0145438976515827*I', '\\\\zeta_{432}'], 'conductor': 5184, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_5184.4099', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^511', 0, 'a^494', 0, 0, 0, 'a^371', 0, 'a^193', 0, 0, 0, 'a^516', 0, 'a^321', 0, 0, 0, 'a^586', 0, 'a^590', 0, 0, 0, 'a^437', 0, 'a^64', 0, 0, 0, 'a^573', 0, 'a^183', 0, 0, 0, 'a^418', 0, 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'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.60152348181', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 557.0981701353361, 'bad_primes': [2, 3], 'central_character': '5184.43', 'conductor': 5184, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5184/43'], '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': '1-72e2-5184.43-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': '1-72e2-5184.43-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 557.0981701353361, 'root_angle': 0.3921682098765432, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00951692318', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_5184.43', 'Lhash_array': ['dirichlet_L_5184.43'], 'label': '1-72e2-5184.43-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5184/43'}