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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.1345', 'a10': [-0.4326580234465083, 0.9015581150138691], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [0.9781476007338057, 0.20791169081775934], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.9539552099769126, 0.29994909127701064], 'a6': [-0.3450003671949707, 0.9386025498768558], 'a7': [0.0475819158237423, 0.998867339183008], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 403.10093290463846, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1345', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.3051', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^90', 'a^11', 'a^180', 'a^16', 'a^101', 'a^80', 'a^270', 'a^22', 'a^106', 0, 'a^191', 'a^103', 'a^170', 'a^27', 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'193.91234190817049223722036925632', '194.30525864791875154966752993166', '195.23832523514327338924296201537', '195.80460187219410952801502180883', '196.21340098048232119816922601245', '196.63194353746013856916232745791', '197.06736373104478770358066959123', '197.69036329907723805625691084604', '198.15512978251714995024838790504', '198.4815597154630482064160435151', '199.01747485246172306629777348794', '199.69937487029582989241571848342'], 'prelabel': '1-3751-3751.1345-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 403.10093290463846, 'root_angle': -0.921663105765043, 'root_number': '-0.969869289926703159019836860073-0.243625861634335959993986270963*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.05602039938311313770556293109+1.17990771621550172482600470647*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17555638107', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.06158881915', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.75188125095', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 403.10093290463846, 'bad_primes': [11, 31], 'central_character': '3751.1345', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1345'], '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': '1-3751-3751.1345-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': '1-3751-3751.1345-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 403.10093290463846, 'root_angle': -0.4608315528825215, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17555638107', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.1345', 'Lhash_array': ['dirichlet_L_3751.1345'], 'label': '1-3751-3751.1345-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1345'}
Lfunction data - 1-3751-3751.1345-r1-0-0