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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1052', 'a10': [0.8973131243109986, -0.4413945592542282], 'a2': [-0.055786122057162574, -0.9984427417663084], 'a3': [-0.24467175910276207, -0.9696059665129748], 'a4': [-0.9937758171716468, 0.11139849731852668], 'a5': [0.3906495744662157, 0.9205394668178897], 'a6': [-0.9544467510209387, 0.2983812987865934], 'a7': [0.9904643552931577, -0.13776923057674942], 'a8': [0.1666639201255505, 0.9860137614295168], 'a9': [-0.88027146059512, 0.4744703949265267], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1052', 'coeff_info': ['x^591 - 1', '0.999943486697302 + 0.0106312469467839*I', '\\\\zeta_{591}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.4257', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^438', 'a^420', 'a^285', 'a^110', 'a^267', 'a^578', 'a^132', 'a^249', 'a^548', 'a^27', 'a^114', 'a^74', 'a^425', 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'0.999998588298549934867938543439+0.00168029786265092892515174283115*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(591)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.971322201518512134277371758665-0.394487288345315765148237273611*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12912647684', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.76343425931', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.13181348283', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1052', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1052'], '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': '1-4729-4729.1052-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': '1-4729-4729.1052-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.0002674278365504087, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12912647684', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1052', 'Lhash_array': ['dirichlet_L_4729.1052'], 'factors': ['1-4729-4729.1052-r0-0-0'], 'label': '1-4729-4729.1052-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1052'}
Lfunction data - 1-4729-4729.1052-r0-0-0