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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1012', 'a10': [-0.9937758171716468, 0.11139849731852668], 'a2': [0.9994914186000327, -0.031888934521151754], 'a3': [-0.8309154635618966, 0.5563986811753946], 'a4': [0.9979661917102114, -0.06374543280437904], 'a5': [-0.9968227806620411, 0.07965139015231544], 'a6': [-0.8127499143005265, 0.5826127159653203], 'a7': [0.29076153153237394, -0.9567955538049643], 'a8': [0.99542587073459, -0.09553709160469198], 'a9': [0.38084101517256314, -0.9246405361881619], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1012', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2986', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^392', 'a^160', 'a^390', 'a^192', 'a^158', 'a^314', 'a^388', 'a^320', 'a^190', 'a^151', 'a^156', 'a^122', 'a^312', 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'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.7658131445452542, 'root_number': '-0.741347936615701576385187868242-0.671120880971261180986763929144*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(394)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11075927356321338692830995019-0.0320353804444484571737944287445*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.153305900616', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.25421861032', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.41470904147', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1012', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1012'], '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': '1-4729-4729.1012-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': '1-4729-4729.1012-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.3829065722726271, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.153305900616', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1012', 'Lhash_array': ['dirichlet_L_4729.1012'], 'label': '1-4729-4729.1012-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1012'}
Lfunction data - 1-4729-4729.1012-r0-0-0