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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_27.13', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.766044443118978, 0.6427876096865394], 'a8': [-0.5, 0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '27.13', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 27, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_27.25', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^8', 'a^2', 0, 'a^1', 'a^3', 0, 'a^6', 'a^7', 0, 'a^5', 'a^5', 0, 'a^7', 'a^6', 0, 'a^3', 'a^1', 0, 'a^2', 'a^8', 0, 'a^4', 'a^0', 0, 'a^0', 'a^4', 0, 'a^8', 'a^2', 0, 'a^1', 'a^3', 0, 'a^6', 'a^7', 0, 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'197.93145142604157479983797283464', '198.51368885630907873962757929892', '199.430451735185308184860173553103'], 'prelabel': '1-3e3-27.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': 0.24074074074074073, 'root_number': '0.727373641573048695987176417664+0.686241637868733585729604999617*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12037037037', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(9)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.670852783499706717776236350424+0.180368012925232183647443805559*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.46476458252', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.69563784338', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.29020343828', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'bad_primes': [3], 'central_character': '27.13', 'conductor': 27, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/27/13'], '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': '1-3e3-27.13-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': '1-3e3-27.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': 0.12037037037037036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46476458252', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_27.13', 'Lhash_array': ['dirichlet_L_27.13'], 'label': '1-3e3-27.13-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/27/13'}