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{'Lhash': 'dirichlet_L_160.109', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-5.8869658587496495e-30, 1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 0.7430368762075773, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '160.109', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 160, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_160.69', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^9', 0, 0, 0, 'a^10', 0, 'a^2', 0, 'a^3', 0, 'a^5', 0, 0, 0, 'a^0', 0, 'a^1', 0, 'a^3', 0, 'a^6', 0, 0, 0, 'a^11', 0, 'a^5', 0, 'a^0', 0, 'a^4', 0, 0, 0, 'a^11', 0, 'a^6', 0, 'a^2', 0, 'a^7', 0, 0, 0, 'a^0', 0, 'a^4', 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'198.4763025332574360439544664395', '199.170530904076727756492071573045', '199.68953276583179155762057635553'], 'prelabel': '1-160-160.109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7430368762075773, 'root_angle': 0.4375, 'root_number': '0.195090322016128267848284868477+0.980785280403230449126182236134*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21875', 'prec': 24}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13546994579039858714965927869+0.475896043564781519907876377039*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.22519308294', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.19049471852', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.75613378542', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7430368762075773, 'bad_primes': [2, 5], 'central_character': '160.109', 'conductor': 160, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/160/109'], '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': '1-160-160.109-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': '1-160-160.109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7430368762075773, 'root_angle': 0.21875, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22519308294', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_160.109', 'Lhash_array': ['dirichlet_L_160.109'], 'label': '1-160-160.109-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/160/109'}