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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3997.832', 'a10': [0.36093933060171474, 0.932589298472155], 'a2': [0.635723748209968, 0.7719166509163209], 'a3': [0.6098540056060092, -0.7925137802248651], 'a4': [-0.1917106319237384, 0.9814514932524179], 'a5': [0.9493389120835459, 0.31425408510316855], 'a6': [0.999453257340926, -0.03306336931730822], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8794737512064891, 0.47594739303707356], 'a9': [-0.2561561836926114, -0.9666354067361888], 'algebraic': True, 'analytic_conductor': 429.5373044041162, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [571, [1]]], 'bad_primes': [7, 571], 'central_character': '3997.832', 'coeff_info': ['x^570 - 1', '0.999939245894343 + 0.0110229088834436*I', '\\\\zeta_{570}'], 'conductor': 3997, 'conductor_radical': 3997, 'conjugate': 'dirichlet_L_3997.2820', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^80', 'a^487', 'a^160', 'a^29', 'a^567', 0, 'a^240', 'a^404', 'a^109', 'a^556', 'a^77', 'a^139', 0, 'a^516', 'a^320', 'a^491', 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'a^377'], [1, 'a^559'], [1, 'a^239']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-3997-3997.832-r1-0-0', 'leading_term': '5.76762695128683762799837095878+0.908852907439168660255681869630*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/3997/832', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [5.83879561695483, 4.016194903444735, 0.3707639803826411, -2.9665118463452735, -3.895918216415843, -2.178023581152462, 0.10121634697956435, 0.48923050878420615, -1.2044162391261493, -2.6945233901171406, -2.010659413315349, -0.06541116663603629, 0.3827223942324701, -1.654518393585576, -3.8470643511054647, -3.366374486632173, -0.5652531276602772, 1.4387649561036873, 0.8175777616649896, -0.8169371641112887, -1.0654451591392098, -0.17375586169931395, -0.14513671894162822, 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'191.99103528326702384864949967011', '192.67776363114359325256587105999', '193.35254359786037316320671709709', '193.49004881062080403872366940742', '194.42826842718635869555510878881', '194.81430037406221010644736273008', '195.327143119410400007230241921', '195.98519759704890258811202676711', '196.223972450483048498797951634967', '196.8228691976513964570092540082', '197.510174687367075639135298284939', '197.69886834918742534844209557565', '198.192009179664365627028299231107', '198.507853331133584812731169439241', '199.59180591140717349080164031233'], 'prelabel': '1-3997-3997.832-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 429.5373044041162, 'root_angle': 0.09949929806893727, 'root_number': '0.951541423677555897196287650565+0.307520599351799627342623161487*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(570)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.15043604007226132208614350260+0.515454401022870887755288174156*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.654798109503', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.85620360474', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.30660354503', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 429.5373044041162, 'bad_primes': [7, 571], 'central_character': '3997.832', 'conductor': 3997, 'conductor_radical': 3997, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3997/832'], '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': '1-3997-3997.832-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3997-3997.832-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 429.5373044041162, 'root_angle': 0.049749649034468636, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.654798109503', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3997.832', 'Lhash_array': ['dirichlet_L_3997.832'], 'label': '1-3997-3997.832-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3997/832'}
Lfunction data - 1-3997-3997.832-r1-0-0