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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5200.2187', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.10452846326765347, -0.9945218953682733], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 24.14869847674626, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '5200.2187', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 5200, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_5200.2323', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^44', 0, 0, 0, 'a^55', 0, 'a^88', 0, 'a^77', 0, 0, 0, 0, 0, 'a^31', 0, 'a^61', 0, 'a^39', 0, 'a^17', 0, 0, 0, 'a^72', 0, 'a^59', 0, 'a^66', 0, 'a^1', 0, 0, 0, 'a^38', 0, 0, 0, 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'195.30549540006914010097346365274', '195.78415032832404280341979087567', '196.25425150096164795280710777574', '196.83657586486203469597025231081', '197.4619943311183357469265596420', '197.769394345292789246168119443', '198.571633616865392833736096838454', '198.83335849145086017527408198307', '199.59676157584420878866933256298'], 'prelabel': '1-5200-5200.2187-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.14869847674626, 'root_angle': 0.11018714236295002, 'root_number': '0.769763195192759420091004880920+0.638329556989674230149692855793*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.991259056664005122922823770376-0.181574779323391572122893798847*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.02432385347', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.62740091399', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.38026474435', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 24.14869847674626, 'bad_primes': [2, 5, 13], 'central_character': '5200.2187', 'conductor': 5200, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5200/2187'], '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': '1-5200-5200.2187-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': '1-5200-5200.2187-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.14869847674626, 'root_angle': 0.11018714236295002, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02432385347', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5200.2187', 'Lhash_array': ['dirichlet_L_5200.2187'], 'factors': ['1-5200-5200.2187-r0-0-0'], 'label': '1-5200-5200.2187-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5200/2187'}
Lfunction data - 1-5200-5200.2187-r0-0-0