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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4033.1008', 'a10': [0.17364817766693036, -0.984807753012208], 'a2': [0.17364817766693036, -0.984807753012208], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [1.0, 0.0], 'a6': [-0.9396926207859084, 0.3420201433256687], 'a7': [1.0, 0.0], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.1008', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.4029', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^6', 'a^5', 'a^0', 'a^4', 'a^0', 'a^3', 'a^3', 'a^7', 'a^2', 'a^2', 'a^6', 'a^7', 'a^6', 'a^1', 'a^4', 'a^1', 'a^8', 'a^5', 'a^6', 'a^0', 'a^3', 'a^0', 'a^0', 'a^4', 'a^0', 'a^5', 'a^4', 'a^4', 'a^2', 'a^8', 'a^8', 'a^2', 'a^0', 'a^8', 0, 'a^6', 'a^3', 'a^3', 'a^8', 'a^4', 'a^3', 'a^7', 'a^3', 'a^1', 'a^2', 'a^7', 'a^0', 'a^7', 'a^1', 'a^2', 'a^5', 'a^7', 'a^2', 'a^3', 'a^5', 'a^2', 'a^6', 'a^2', 'a^3', 'a^0', 'a^3', 'a^6', 'a^6', 'a^6', 'a^4', 'a^0', 'a^0', 'a^7', 'a^2', 'a^6', 'a^8', 0, 'a^6', 'a^4', 'a^2', 'a^1', 'a^4', 'a^1', 'a^6', 'a^6', 'a^2', 'a^2', 'a^4', 'a^1', 'a^1', 'a^5', 'a^2', 'a^1', 'a^6', 'a^8', 'a^8', 'a^0', 'a^8', 'a^5', 'a^4', 'a^7', 'a^5', 'a^5'], 'euler_factors': [[1, 'a^7'], [1, 'a^6'], [1, 'a^0'], [1, 'a^0'], [1, 'a^2'], [1, 'a^6'], [1, 'a^4'], [1, 'a^8'], [1, 'a^3'], [1, 'a^4'], [1, 'a^2'], [0], [1, 'a^8'], [1, 'a^3'], [1, 'a^2'], [1, 'a^5'], [1, 'a^6'], [1, 'a^3'], [1, 'a^4'], [1, 'a^2'], [1, 'a^8'], [1, 'a^4'], [1, 'a^2'], [1, 'a^2'], [1, 'a^4'], [1, 'a^6']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4033-4033.1008-r0-0-0', 'leading_term': '1.32460765390448651887916923921-0.226995312073293714922509918228*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.1008', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/1008'], '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': '1-4033-4033.1008-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': '1-4033-4033.1008-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.05402336060038445, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12088529285', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4033.1008', 'Lhash_array': ['dirichlet_L_4033.1008'], 'label': '1-4033-4033.1008-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/1008'}