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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1157.58', 'a10': [-0.9718115683235417, 0.23575893550942723], 'a2': [0.9450008187146685, 0.32706796331742166], 'a3': [-0.9929278846732883, -0.1187190626573052], 'a4': [0.7860530947427875, 0.6181589862206052], 'a5': [-0.8412535328311812, 0.5406408174555976], 'a6': [-0.8994884619106032, -0.43694451236935955], 'a7': [-0.7399513643828839, -0.6726603737012525], 'a8': [0.5406408174555976, 0.8412535328311812], 'a9': [0.9718115683235417, 0.23575893550942723], 'algebraic': True, 'analytic_conductor': 5.373085411076043, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [89, [1]]], 'bad_primes': [13, 89], 'central_character': '1157.58', 'coeff_info': ['x^264 - 1', '0.999716794693129 + 0.0237976975461075*I', '\\\\zeta_{264}'], 'conductor': 1157, 'conductor_radical': 1157, 'conjugate': 'dirichlet_L_1157.778', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^137', 'a^28', 'a^108', 'a^151', 'a^163', 'a^42', 'a^10', 'a^122', 'a^134', 'a^165', 0, 'a^177', 'a^245', 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'199.33081871509831889044340629547', '199.95140872974043983096178584796'], 'prelabel': '1-1157-1157.58-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.373085411076043, 'root_angle': 0.4352381290624599, 'root_number': '0.202054677674756142048521742640+0.979374242682413208396518153323*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.217619064531', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(264)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.06038290218417848790267394483+0.328100211103287918503941678194*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.954309480725', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.77246067702', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.34901961501', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.373085411076043, 'bad_primes': [13, 89], 'central_character': '1157.58', 'conductor': 1157, 'conductor_radical': 1157, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1157/58'], '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': '1-1157-1157.58-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': '1-1157-1157.58-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.373085411076043, 'root_angle': 0.21761906453122995, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.954309480725', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1157.58', 'Lhash_array': ['dirichlet_L_1157.58'], 'label': '1-1157-1157.58-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1157/58'}
Lfunction data - 1-1157-1157.58-r0-0-0