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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1984.493', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.5664062369248328, -0.8241261886220157], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.7933533402912352, 0.6087614290087207], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.35836794954530027, 0.9335804264972017], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.35836794954530027, -0.9335804264972017], 'algebraic': True, 'analytic_conductor': 9.213657264973959, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '1984.493', 'coeff_info': ['x^240 - 1', '0.999657324975557 + 0.0261769483078731*I', '\\\\zeta_{240}'], 'conductor': 1984, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_1984.165', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^203', 0, 'a^265', 0, 'a^314', 0, 'a^166', 0, 'a^109', 0, 'a^343', 0, 'a^228', 0, 'a^236', 0, 'a^47', 0, 'a^277', 0, 'a^126', 0, 'a^290', 0, 'a^369', 0, 'a^387', 0, 0, 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'195.81621996691962991099674755333', '196.08997482321935660367239296621', '196.38087387623790651256978235369', '197.0295098887269812755023075540', '197.689823618469378027122783133831', '198.198108096338137048551432697705', '198.58332913229365424810166920165', '199.432515583311099794124533179286'], 'prelabel': '1-1984-1984.493-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': 0.32615530401029647, 'root_number': '-0.460446288668409265752845042909+0.887687566236842096837328474943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32615530401', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(240)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07107915903588316131507213956+0.0935476569361195320471002031178*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.55085260024', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.28641533221', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.80791366666', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.213657264973959, 'bad_primes': [2, 31], 'central_character': '1984.493', 'conductor': 1984, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1984/493'], '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': '1-1984-1984.493-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': '1-1984-1984.493-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': 0.32615530401029647, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55085260024', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1984.493', 'Lhash_array': ['dirichlet_L_1984.493'], 'factors': ['1-1984-1984.493-r0-0-0'], 'label': '1-1984-1984.493-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1984/493'}
Lfunction data - 1-1984-1984.493-r0-0-0