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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1588.1263', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.5272254676105024, -0.8497254299495144], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.0634239196565645, -0.9979866764718844], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8959937742913359, -0.4440666126057741], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.4440666126057741, -0.8959937742913359], 'algebraic': True, 'analytic_conductor': 7.374640996360204, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [397, [1]]], 'bad_primes': [2, 397], 'central_character': '1588.1263', 'coeff_info': ['x^396 - 1', '0.999874127673875 + 0.0158659638348079*I', '\\\\zeta_{396}'], 'conductor': 1588, 'conductor_radical': 794, 'conjugate': 'dirichlet_L_1588.987', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^332', 0, 'a^301', 0, 'a^227', 0, 'a^268', 0, 'a^362', 0, 'a^305', 0, 'a^237', 0, 'a^381', 0, 'a^314', 0, 'a^163', 0, 'a^428', 0, 'a^206', 0, 'a^204', 0, 'a^356', 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'198.3047101133535231004258993445', '199.03935843178209943359048699561', '199.79734516802396067927869377750'], 'prelabel': '1-1588-1588.1263-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.374640996360204, 'root_angle': -0.44489572953195067, 'root_number': '-0.940658642670197149077103159820-0.339354266173069283405743279046*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.444895729532', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(396)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.967098847918455749509706417148-0.849334386181556025389744598741*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.816001485448', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.05207476211', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.61790771989', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.374640996360204, 'bad_primes': [2, 397], 'central_character': '1588.1263', 'conductor': 1588, 'conductor_radical': 794, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1588/1263'], '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': '1-1588-1588.1263-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': '1-1588-1588.1263-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.374640996360204, 'root_angle': -0.44489572953195067, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.816001485448', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1588.1263', 'Lhash_array': ['dirichlet_L_1588.1263'], 'factors': ['1-1588-1588.1263-r0-0-0'], 'label': '1-1588-1588.1263-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1588/1263'}
Lfunction data - 1-1588-1588.1263-r0-0-0