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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2153.33', 'a10': [-0.45034466201332485, 0.8928547952473035], 'a2': [-0.6668129578506313, 0.7452251198413082], 'a3': [-0.8500362594859142, 0.5267241759775182], 'a4': [-0.1107209584849843, -0.9938515328519478], 'a5': [0.9656734779184064, -0.2597589922312008], 'a6': [0.17428710530192898, -0.9846948790998531], 'a7': [-0.5464334713713311, -0.837502514244033], 'a8': [0.81447329749749, 0.5802010407294743], 'a9': [0.445123284881609, -0.8954692966574599], 'algebraic': True, 'analytic_conductor': 9.998489965468211, 'analytic_normalization': 0, 'bad_lfactors': [[2153, [1]]], 'bad_primes': [2153], 'central_character': '2153.33', 'coeff_info': ['x^1076 - 1', '0.999982950801612 + 0.00583935836373736*I', '\\\\zeta_{1076}'], 'conductor': 2153, 'conductor_radical': 2153, 'conjugate': 'dirichlet_L_2153.261', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^394', 'a^443', 'a^788', 'a^1031', 'a^837', 'a^708', 'a^106', 'a^886', 'a^349', 'a^391', 'a^155', 'a^393', 'a^26', 'a^398', 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False, 'root_analytic_conductor': 9.998489965468211, 'root_angle': -0.016355090075984048, 'root_number': '0.998680285212063824210315212169-0.0513584260735359193886355762220*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00817754503799', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(1076)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.556810268902546597346914246823+0.160378570986450555706995311439*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.421213412513', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.53062663259', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.55495850053', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.998489965468211, 'bad_primes': [2153], 'central_character': '2153.33', 'conductor': 2153, 'conductor_radical': 2153, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2153/33'], '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': '1-2153-2153.33-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': '1-2153-2153.33-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.998489965468211, 'root_angle': -0.008177545037992024, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.421213412513', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2153.33', 'Lhash_array': ['dirichlet_L_2153.33'], 'label': '1-2153-2153.33-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2153/33'}
Lfunction data - 1-2153-2153.33-r0-0-0