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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.174', 'a10': [0.6403534686527224, 0.768080357244232], 'a2': [0.5163974616389619, 0.8563490302515889], 'a3': [0.9135454576426009, -0.4067366430758002], 'a4': [-0.4666673232256737, 0.8844329309978143], 'a5': [0.9884217748453624, -0.15173132508333165], 'a6': [0.8200610852841911, 0.5722759967030896], 'a7': [-0.9911314021003612, 0.13288545357025405], 'a8': [-0.9983691039261356, 0.057088810862767986], 'a9': [0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.174', 'coeff_info': ['x^165 - 1', '0.999275047800474 + 0.0380707084693900*I', '\\\\zeta_{165}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2436', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^154', 'a^54', 'a^161', 'a^16', 'a^79', 'a^81', 'a^143', 'a^23', 0, 'a^43', 'a^131', 'a^106', 'a^150', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.174-r0-0-0', 'leading_term': '3.31307103621365856286050388913+0.588939352434125970965284317780*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/3751/174', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.3650095470657093, 2.928751925968638, 1.235589188707836, -1.8352096782315357, -4.312436402451429, -4.132262237680426, -1.4624602184227424, 1.2035301141668209, 1.556257810205037, -0.04531355840570873, -1.103487427140999, -0.12807894543884515, 1.4024859469547764, 0.9186154520404248, -1.7330664867516614, -3.780491695320172, -2.942692320247344, -0.35858849890625044, 0.9798752877522452, 0.20234953535647143, -0.5934190691616245, 0.25211084945410156, 1.4074403773873703, 0.7456051313456311, -1.0688728653664898, 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{'__RealLiteral__': 0, 'data': '2.02474063668', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.80457825015', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.174', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/174'], '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': '1-3751-3751.174-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': '1-3751-3751.174-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.05599856730184882, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.759709931713', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.174', 'Lhash_array': ['dirichlet_L_3751.174'], 'factors': ['1-3751-3751.174-r0-0-0'], 'label': '1-3751-3751.174-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/174'}
Lfunction data - 1-3751-3751.174-r0-0-0