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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_19.4', 'a10': [0.766044443118978, -0.6427876096865394], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [-0.9396926207859084, 0.3420201433256687], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.17364817766693036, -0.984807753012208], 'a6': [-0.9396926207859084, -0.3420201433256687], 'a7': [-0.5, -0.8660254037844386], 'a8': [-0.5, 0.8660254037844386], 'a9': [0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.4', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^4', 'a^2', 'a^7', 'a^5', 'a^6', 'a^3', 'a^8', 'a^8', 'a^3', 'a^6', 'a^5', 'a^7', 'a^2', 'a^4', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^4', 'a^2', 'a^7', 'a^5', 'a^6', 'a^3', 'a^8', 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0.08823562904964981, 'root_angle': 0.2653722833530496, 'root_number': '0.672147008506699151826663266315+0.740417719233876316090497923481*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.132686141677', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(9)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.934659887923669869670655683509+0.317963967924892247959840358356*I']], 'z1': {'__RealLiteral__': 0, 'data': '4.27062371722', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.58954103717', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.42932535066', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.4', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/4'], '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': '1-19-19.4-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': '1-19-19.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': 0.1326861416765248, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.27062371722', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_19.4', 'Lhash_array': ['dirichlet_L_19.4'], 'label': '1-19-19.4-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/19/4'}