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{'Lhash': 'dirichlet_L_3168.2149', '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': [-0.052335956242943835, 0.9986295347545738], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.4067366430758002, 0.9135454576426009], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 14.712130148910031, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '3168.2149', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 3168, 'conductor_radical': 66, 'conjugate': 'dirichlet_L_3168.1741', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^31', 0, 'a^38', 0, 0, 0, 0, 0, 'a^169', 0, 0, 0, 'a^156', 0, 'a^177', 0, 0, 0, 'a^130', 0, 'a^62', 0, 0, 0, 'a^53', 0, 'a^64', 0, 0, 0, 'a^69', 0, 'a^63', 0, 0, 0, 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14.712130148910031, 'root_angle': -0.2760773740089394, 'root_number': '-0.163116828494780821233380756051-0.986606760701447990805128084592*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(120)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.695824260672092639821787567187+0.301013957764411524936202282264*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.97176901065', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.17625534881', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.36682578145', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.712130148910031, 'bad_primes': [2, 3, 11], 'central_character': '3168.2149', 'conductor': 3168, 'conductor_radical': 66, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3168/2149'], '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': '1-3168-3168.2149-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': '1-3168-3168.2149-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.712130148910031, 'root_angle': -0.2760773740089394, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97176901065', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3168.2149', 'Lhash_array': ['dirichlet_L_3168.2149'], 'factors': ['1-3168-3168.2149-r0-0-0'], 'label': '1-3168-3168.2149-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3168/2149'}