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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_5184.11', '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': [0.5854294337699405, -0.8107233671702123], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9894416385809445, 0.14493185930724672], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.074394789125506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '5184.11', 'coeff_info': ['x^432 - 1', '0.999894231927107 + 0.0145438976515827*I', '\\\\zeta_{432}'], 'conductor': 5184, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_5184.3299', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^367', 0, 'a^638', 0, 0, 0, 'a^83', 0, 'a^697', 0, 0, 0, 'a^732', 0, 'a^537', 0, 0, 0, 'a^658', 0, 'a^302', 0, 0, 0, 'a^581', 0, 'a^352', 0, 0, 0, 'a^573', 0, 'a^399', 0, 0, 0, 'a^490', 0, 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{'__RealLiteral__': 0, 'data': '1.12140074138', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.17358051645', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.074394789125506, 'bad_primes': [2, 3], 'central_character': '5184.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5184/11'], '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': '1-72e2-5184.11-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': '1-72e2-5184.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.074394789125506, 'root_angle': 0.4755015432098766, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0694075578597', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_5184.11', 'Lhash_array': ['dirichlet_L_5184.11'], 'label': '1-72e2-5184.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5184/11'}