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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_783.211', 'a10': [0.6801727377709194, 0.7330518718298263], 'a2': [0.7497812029677342, -0.6616858375968594], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.12434370464748518, -0.9922392066001721], 'a5': [0.024930691738072875, 0.9996891820008162], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.12434370464748518, -0.9922392066001721], 'a8': [-0.5633200580636221, -0.8262387743159949], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 84.1450361141914, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '783.211', 'coeff_info': ['x^252 - 1', '0.999689182000816 + 0.0249306917380729*I', '\\\\zeta_{252}'], 'conductor': 783, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_783.475', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^223', 0, 'a^194', 'a^62', 0, 'a^184', 'a^165', 0, 'a^33', 'a^199', 0, 'a^38', 'a^155', 0, 'a^136', 'a^231', 0, 'a^75', 'a^4', 0, 'a^170', 'a^176', 0, 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'194.166127399474957777692507228292', '194.580163488675084592992177240742', '195.12289793367482019724590813041', '195.70434102639751289174678823458', '196.55318985328113117706528877763', '197.35050187406393619063925417865', '197.61448748081508272296649920601', '198.27472364399079497010044649646', '199.13223082043094425701956332875', '199.96798687719219506109215277836'], 'prelabel': '1-783-783.211-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 84.1450361141914, 'root_angle': -0.46588128437875126, 'root_number': '-0.977109713014392147952419274055-0.212736007137795589230744028704*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.465881284379', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(252)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.24189864115533036716737768541-0.797403881019520064308099273102*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.380103069523', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.53833467436', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.72037331308', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 84.1450361141914, 'bad_primes': [3, 29], 'central_character': '783.211', 'conductor': 783, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/783/211'], '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': '1-783-783.211-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-783-783.211-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 84.1450361141914, 'root_angle': -0.46588128437875126, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.380103069523', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_783.211', 'Lhash_array': ['dirichlet_L_783.211'], 'factors': ['1-783-783.211-r1-0-0'], 'label': '1-783-783.211-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/783/211'}
Lfunction data - 1-783-783.211-r1-0-0