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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1441.219', 'a10': [0.4859834132426061, -0.873968032626518], 'a2': [0.9582458291091662, -0.2859456783986893], 'a3': [-0.44319154559924134, -0.8964269372957038], 'a4': [0.8364701380102267, -0.54801250735467], 'a5': [0.7155989607441211, -0.698511365248937], 'a6': [-0.6810158587867972, -0.7322686665977736], 'a7': [0.9068743608505454, 0.4214011077725291], 'a8': [0.6448422127361706, -0.7643157205458483], 'a9': [-0.6071625078187112, 0.7945776797137543], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.219', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.329', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^124', 'a^88', 'a^118', 'a^114', 'a^82', 'a^9', 'a^112', 'a^46', 'a^108', 0, 'a^76', 'a^87', 'a^3', 'a^72', 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'196.15183847071597377790129931241', '196.50967758010399966829231693491', '196.77571941807033550118195993582', '197.8677549353616152985147801692', '198.32579608438148903423907451985', '199.22567273935183700775806862767'], 'prelabel': '1-1441-1441.219-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.7196183817874996, 'root_number': '-0.636499772043992711744156718240-0.771276889442400778854862877395*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.359809190894', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(130)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.54826441574716004382627073427-1.18924716657646361521083556811*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.846618896607', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.90775067765', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.21967752026', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.219', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/219'], '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': '1-1441-1441.219-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': '1-1441-1441.219-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.3598091908937498, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.846618896607', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1441.219', 'Lhash_array': ['dirichlet_L_1441.219'], 'label': '1-1441-1441.219-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/219'}
Lfunction data - 1-1441-1441.219-r0-0-0