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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4033.1236', 'a10': [0.44879918020046217, -0.8936326403234123], 'a2': [1.0, 0.0], 'a3': [0.28680323271109026, -0.9579895123154889], 'a4': [1.0, 0.0], 'a5': [0.44879918020046217, -0.8936326403234123], 'a6': [0.28680323271109026, -0.9579895123154889], 'a7': [-0.8354878114129364, 0.549508978070806], 'a8': [1.0, 0.0], 'a9': [-0.8354878114129364, -0.549508978070806], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.1236', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.819', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^0', 'a^86', 'a^0', 'a^89', 'a^86', 'a^44', 'a^0', 'a^64', 'a^89', 'a^73', 'a^86', 'a^8', 'a^44', 'a^67', 'a^0', 'a^90', 'a^64', 'a^12', 'a^89', 'a^22', 'a^73', 'a^102', 'a^86', 'a^70', 'a^8', 'a^42', 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'195.279602525862282590896633611164', '195.47773045026477359740151101378', '196.20294698448762258082802682883', '196.61721209445879598387829919148', '196.96587432931596780423316012111', '197.46620445938154521758661311148', '197.725408943180973384923818953921', '198.74774937963047063804919809561', '199.74105879660406333617525157202', '199.95622021200663707016503129260'], 'prelabel': '1-4033-4033.1236-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.6071352499620708, 'root_number': '-0.330256504310970488239171890790-0.943891223266906922094546270279*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.00670961701913373027482375445-1.14993738614992587016198207277*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.834367580155', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.44356237893', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.56040150091', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.1236', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/1236'], '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': '1-4033-4033.1236-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': '1-4033-4033.1236-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.3035676249810354, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.834367580155', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4033.1236', 'Lhash_array': ['dirichlet_L_4033.1236'], 'label': '1-4033-4033.1236-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/1236'}
Lfunction data - 1-4033-4033.1236-r0-0-0