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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1005', 'a10': [-0.8309154635618966, 0.5563986811753946], 'a2': [-0.055786122057162574, 0.9984427417663084], 'a3': [-0.24467175910276207, 0.9696059665129748], 'a4': [-0.9937758171716468, -0.11139849731852668], 'a5': [0.6018857762173669, 0.7985821888742685], 'a6': [-0.9544467510209387, -0.2983812987865934], 'a7': [-0.6145438311858796, 0.7888826779384759], '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': '4729.1005', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.687', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^102', 'a^114', 'a^204', 'a^58', 'a^216', 'a^140', 'a^306', 'a^228', 'a^160', 'a^179', 'a^318', 'a^82', 'a^242', 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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(394)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.223541569427622283617647682321+0.661410660159099286699459218853*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.67750545363', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.75543975572', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.42992938244', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1005', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1005'], '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': '1-4729-4729.1005-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': '1-4729-4729.1005-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.006641892640483859, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67750545363', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1005', 'Lhash_array': ['dirichlet_L_4729.1005'], 'factors': ['1-4729-4729.1005-r0-0-0'], 'label': '1-4729-4729.1005-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1005'}
Lfunction data - 1-4729-4729.1005-r0-0-0