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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_19.9', 'a10': [-0.9396926207859084, -0.3420201433256687], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [0.17364817766693036, -0.984807753012208], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [0.17364817766693036, 0.984807753012208], 'a7': [-0.5, -0.8660254037844386], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.9', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^7', 'a^8', 'a^1', 'a^2', 'a^6', 'a^3', 'a^5', 'a^5', 'a^3', 'a^6', 'a^2', 'a^1', 'a^8', 'a^7', 'a^4', 'a^0', 0, 'a^0', 'a^4', 'a^7', 'a^8', 'a^1', 'a^2', 'a^6', 'a^3', 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0.08823562904964981, 'root_angle': -0.10608002469196787, 'root_number': '0.944980864034573771287316164987-0.327125612889713054142581920436*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.053040012346', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(9)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.680620362658866176300685916428-0.0715457394267178453903388447671*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.13818063441', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '6.38471570653', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.35639597685', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.9', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/9'], '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': '1-19-19.9-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': '1-19-19.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': -0.05304001234598393, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13818063441', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_19.9', 'Lhash_array': ['dirichlet_L_19.9'], 'label': '1-19-19.9-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/19/9'}
Lfunction data - 1-19-19.9-r0-0-0