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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_896.299', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9469301294951057, 0.3214394653031616], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8968727415326883, 0.4422886902190013], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.7933533402912352, 0.6087614290087207], 'algebraic': True, 'analytic_conductor': 4.161006506762433, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '896.299', 'coeff_info': ['x^96 - 1', '0.997858923238603 + 0.0654031292301431*I', '\\\\zeta_{96}'], 'conductor': 896, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_896.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^101', 0, 'a^103', 0, 0, 0, 'a^106', 0, 'a^83', 0, 'a^105', 0, 'a^12', 0, 'a^116', 0, 'a^49', 0, 0, 0, 'a^82', 0, 'a^110', 0, 'a^111', 0, 'a^45', 0, 'a^152', 0, 'a^88', 0, 0, 0, 'a^127', 0, 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'195.0608456731738672007893598305', '195.85618028602263847643019399168', '196.70923921072791669639490820199', '196.89951120188745542803019805443', '197.68243848401788380730983314060', '197.93679036697929193237069846350', '198.5989759443085207655426986323', '199.471022923510963422274115498552', '199.844897679477650157377374498366'], 'prelabel': '1-896-896.299-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.161006506762433, 'root_angle': 0.11263954694605388, 'root_number': '0.759836237773813335764065802809+0.650114522038799717832588997632*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.112639546946', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(96)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.73808289634303057760409708629+0.363355246002487333128251127922*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.50932834012', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.21382322508', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.42951719383', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.161006506762433, 'bad_primes': [2, 7], 'central_character': '896.299', 'conductor': 896, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/896/299'], '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': '1-896-896.299-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': '1-896-896.299-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.161006506762433, 'root_angle': 0.11263954694605388, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50932834012', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_896.299', 'Lhash_array': ['dirichlet_L_896.299'], 'factors': ['1-896-896.299-r0-0-0'], 'label': '1-896-896.299-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/896/299'}
Lfunction data - 1-896-896.299-r0-0-0