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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.3615', 'a10': [0.8925698396223906, -0.45090917200303204], 'a2': [-0.9998728465660103, -0.015946494912164058], 'a3': [0.29076153153237394, -0.9567955538049643], 'a4': [0.9994914186000327, 0.031888934521151754], 'a5': [-0.8852659254850125, 0.46508519775968393], 'a6': [-0.30598209563589956, 0.9520372666814378], 'a7': [0.11403941952393751, -0.9934762255809866], 'a8': [-0.9988558131018185, -0.047823264555078175], 'a9': [-0.8309154635618966, -0.5563986811753946], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.3615', 'coeff_info': ['x^591 - 1', '0.999943486697302 + 0.0106312469467839*I', '\\\\zeta_{591}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1074', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^297', 'a^471', 'a^3', 'a^250', 'a^177', 'a^454', 'a^300', 'a^351', 'a^547', 'a^330', 'a^474', 'a^7', 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0.22212027878342866, 'root_number': '0.766250266047571456801030292391+0.642542239687030973282156052166*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, '0.502134685726169283088661297802-0.211328911351431688059751393447*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.75189188229', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.4794640078', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.60137566423', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.3615', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/3615'], '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': '1-4729-4729.3615-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': '1-4729-4729.3615-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.11106013939171433, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75189188229', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.3615', 'Lhash_array': ['dirichlet_L_4729.3615'], 'label': '1-4729-4729.3615-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/3615'}
Lfunction data - 1-4729-4729.3615-r0-0-0