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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3381.1121', 'a10': [0.37796670142890654, -0.9258191900208981], 'a2': [0.5910811325286766, -0.80661210923753], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.30124618953723425, -0.9535463980789276], 'a5': [0.9701859555740645, -0.24236173709321235], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9472030102919101, -0.3206344605527355], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.701297990361368, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.1121', 'coeff_info': ['x^154 - 1', '0.999167799344583 + 0.0407885860615856*I', '\\\\zeta_{154}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.2066', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^131', 0, 'a^108', 'a^148', 0, 0, 'a^85', 0, 'a^125', 'a^12', 0, 'a^26', 0, 0, 'a^62', 'a^46', 0, 'a^119', 'a^102', 0, 'a^143', 0, 0, 'a^142', 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'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.4021872754151172, 'root_number': '0.302474538427817853616841305006-0.953157465271546063745838267074*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(154)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.55896198549783621601588683507-0.806563398498354143784549198390*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.954001667738', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.70871712179', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.30967932391', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.1121', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/1121'], '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': '1-3381-3381.1121-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': '1-3381-3381.1121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.2010936377075586, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.954001667738', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3381.1121', 'Lhash_array': ['dirichlet_L_3381.1121'], 'label': '1-3381-3381.1121-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/1121'}
Lfunction data - 1-3381-3381.1121-r0-0-0