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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3381.527', 'a10': [-0.44000023457108695, -0.8979976578908145], 'a2': [-0.9985206917896564, 0.054373045416879255], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.994087143864188, -0.10858522184874536], 'a5': [0.3905224711747844, 0.9205933953203986], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9867124733912889, 0.1624761362602058], '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': '3381.527', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.494', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^227', 0, 'a^454', 'a^86', 0, 0, 'a^219', 0, 'a^313', 'a^136', 0, 'a^192', 0, 0, 'a^446', 'a^316', 0, 'a^245', 'a^78', 0, 'a^363', 0, 0, 'a^172', 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'198.3053218930956021369368694938', '198.483861765874420143727943257642', '198.93710976528164450131327210579', '199.7250272021209724322562455317'], 'prelabel': '1-3381-3381.527-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.37274938456494, 'root_number': '0.389206118246263346880481113151-0.921150692080115452729235397553*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.599838777146372683233536711004+0.0991559253306599354968484079955*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.210783069127', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.68252729234', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.4489791733', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.527', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/527'], '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': '1-3381-3381.527-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': '1-3381-3381.527-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.18637469228247, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.210783069127', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3381.527', 'Lhash_array': ['dirichlet_L_3381.527'], 'label': '1-3381-3381.527-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/527'}
Lfunction data - 1-3381-3381.527-r0-0-0