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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1984.747', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9832549075639546, -0.18223552549214744], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9914448613738104, 0.1305261922200516], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9335804264972017, -0.35836794954530027], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9335804264972017, -0.35836794954530027], 'algebraic': True, 'analytic_conductor': 9.213657264973959, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '1984.747', 'coeff_info': ['x^240 - 1', '0.999657324975557 + 0.0261769483078731*I', '\\\\zeta_{240}'], 'conductor': 1984, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_1984.579', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^233', 0, 'a^355', 0, 'a^374', 0, 'a^226', 0, 'a^319', 0, 'a^133', 0, 'a^348', 0, 'a^236', 0, 'a^77', 0, 'a^367', 0, 'a^426', 0, 'a^230', 0, 'a^219', 0, 'a^297', 0, 0, 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'193.50738380626400743054255951739', '193.82959291436371480471012310133', '194.52318438858536323217785965904', '195.241493540715020028195280387050', '195.938675421584950186726304700926', '196.206257032801467380158550887571', '196.64247994075229111812907719556', '197.56457994955945856603173210906', '197.89014996116090294559244312377', '198.52764518394133134879490923969', '199.00099412831047111612113504041', '199.40129587038908700188766865519'], 'prelabel': '1-1984-1984.747-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.20150883825124233, 'root_number': '0.299986931970622318225813309452-0.953943311023696636753290566029*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.201508838251', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(240)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.03052234246463300809417474699-0.145412494389043868216907640687*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.450425916379', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.83429281894', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.88351406855', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.213657264973959, 'bad_primes': [2, 31], 'central_character': '1984.747', 'conductor': 1984, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1984/747'], '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': '1-1984-1984.747-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': '1-1984-1984.747-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.20150883825124233, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.450425916379', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1984.747', 'Lhash_array': ['dirichlet_L_1984.747'], 'factors': ['1-1984-1984.747-r0-0-0'], 'label': '1-1984-1984.747-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1984/747'}
Lfunction data - 1-1984-1984.747-r0-0-0