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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1849.259', 'a10': [0.5209403404879303, -0.8535930890373464], 'a2': [-0.6940741952206338, 0.7199034737579958], 'a3': [0.9054482374931466, 0.4244566988758151], 'a4': [-0.03652202305765884, -0.9993328483702394], 'a5': [-0.9760758775559272, 0.21743017558155697], 'a6': [-0.934016108732548, 0.35723088980113277], 'a7': [0.8339978178898779, 0.5517677407704459], 'a8': [0.7447721827437819, 0.6673188112222395], 'a9': [0.6396730215588913, 0.768647139778532], 'algebraic': True, 'analytic_conductor': 8.586719900673815, 'analytic_normalization': 0, 'bad_lfactors': [[43, [1]]], 'bad_primes': [43], 'central_character': '1849.259', 'coeff_info': ['x^43 - 1', '0.989343368075110 + 0.145601167735005*I', '\\\\zeta_{43}'], 'conductor': 1849, 'conductor_radical': 43, 'conjugate': 'dirichlet_L_1849.1592', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^3', 'a^32', 'a^20', 'a^19', 'a^4', 'a^5', 'a^6', 'a^36', 'a^31', 'a^35', 'a^24', 'a^20', 'a^23', 'a^21', 'a^26', 'a^22', 'a^0', 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'191.85847349548552091384741800208', '192.255584661956425057765700315446', '192.98706312880683480732142829583', '193.58661593403837175135220423676', '194.4250094521095002837989034802', '195.21499540607980661494479375060', '195.640253334783271403169133233728', '195.97116478287173761405359881178', '196.80113205817504482259984010604', '197.21119171723003960373140928163', '197.96981688847101403411854468235', '198.220381739607853386352051835783', '198.91349598625038816167796204084', '199.27827155005613480982099967893', '199.70800951579233050188685822226'], 'prelabel': '1-43e2-1849.259-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.586719900673815, 'root_angle': 0.39697133585722016, 'root_number': '0.318052010124842912404679006256+0.948073266607358158101678890880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.198485667929', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(43)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.862191029831727617486515104696+0.410732368129995130293406160383*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.808101626043', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.16413547925', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93993610242', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.586719900673815, 'bad_primes': [43], 'central_character': '1849.259', 'conductor': 1849, 'conductor_radical': 43, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1849/259'], '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': '1-43e2-1849.259-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': '1-43e2-1849.259-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.586719900673815, 'root_angle': 0.19848566792861008, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.808101626043', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1849.259', 'Lhash_array': ['dirichlet_L_1849.259'], 'label': '1-43e2-1849.259-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1849/259'}
Lfunction data - 1-43e2-1849.259-r0-0-0