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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3381.296', 'a10': [-0.12884055209943887, -0.991665322644042], 'a2': [0.9514758987623784, 0.3077232751585818], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8106127718513515, 0.5855825596032286], 'a5': [-0.42774718105107096, -0.9038984174689445], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5910811325286766, 0.80661210923753], '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': '3381.296', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.2867', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 0, 'a^46', 'a^314', 0, 0, 'a^69', 0, 'a^337', 'a^142', 0, 'a^282', 0, 0, 'a^92', 'a^262', 0, 'a^35', 'a^360', 0, 'a^165', 0, 0, 'a^166', 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'198.96883769078331462832469427329', '199.700603253908740990219883427439'], 'prelabel': '1-3381-3381.296-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.5556249996877646, 'root_number': '-0.173863024289094125595949481875-0.984769845590861837759568946328*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, '1.42018725192249077638665061521+0.0240776590059985719886372301097*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.279627246066', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.77988823731', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.41458265449', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.296', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/296'], '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': '1-3381-3381.296-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': '1-3381-3381.296-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.2778124998438823, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.279627246066', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3381.296', 'Lhash_array': ['dirichlet_L_3381.296'], 'label': '1-3381-3381.296-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/296'}
Lfunction data - 1-3381-3381.296-r0-0-0