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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.192', 'a10': [-0.6691306063588582, 0.7431448254773942], 'a2': [-0.9945218953682733, 0.10452846326765347], 'a3': [-0.25881904510252074, 0.9659258262890683], 'a4': [0.9781476007338057, -0.20791169081775934], 'a5': [0.7431448254773942, -0.6691306063588582], 'a6': [0.15643446504023087, -0.9876883405951378], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9510565162951535, 0.30901699437494745], 'a9': [-0.8660254037844386, -0.5], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.192', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.145', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^58', 'a^35', 'a^116', 'a^106', 'a^93', 0, 'a^54', 'a^70', 'a^44', 'a^59', 'a^31', 'a^3', 0, 'a^21', 'a^112', 'a^29', 'a^8', 'a^37', 'a^102', 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'193.83240259164798018096808746695', '194.43623110934610170499138414773', '195.57131884364873285602760935347', '196.50892431522601260441064554111', '196.88493314683809471411953923801', '197.6246257653963942270592894481', '198.25179435731914482322921743483', '198.9653106906262710109540733253', '199.62489030523325520482100897951'], 'prelabel': '1-287-287.192-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.39705781087975656, 'root_number': '0.317794435994783007549998409566+0.948159636585927320577898438008*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19852890544', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(120)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.679638155894147753062212338368+0.233617684916481352028671109136*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.27360309259', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.72126383202', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.23908984334', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.192', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/192'], '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': '1-287-287.192-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': '1-287-287.192-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.19852890543987828, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27360309259', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.192', 'Lhash_array': ['dirichlet_L_287.192'], 'label': '1-287-287.192-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/192'}
Lfunction data - 1-287-287.192-r0-0-0