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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_149.113', 'a10': [-0.6606747233900815, 0.7506723052527243], 'a2': [-0.3728564777803086, -0.9278890272965093], 'a3': [0.9677329469334989, -0.2519780613851252], 'a4': [-0.7219560939545244, 0.6919388689775462], 'a5': [-0.4502037448176733, -0.8929258581495685], 'a6': [-0.5946331763042866, -0.8039971303669405], 'a7': [0.6606747233900815, -0.7506723052527243], 'a8': [0.9112284903881357, 0.41190124824399266], 'a9': [0.8730141131611882, -0.48769494381363454], 'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'analytic_normalization': 0, 'bad_lfactors': [[149, [1]]], 'bad_primes': [149], 'central_character': '149.113', 'coeff_info': ['x^74 - 1', '0.996397488542527 + 0.0848059244755092*I', '\\\\zeta_{74}'], 'conductor': 149, 'conductor_radical': 149, 'conjugate': 'dirichlet_L_149.120', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^51', 'a^71', 'a^28', 'a^50', 'a^48', 'a^64', 'a^5', 'a^68', 'a^27', 'a^9', 'a^25', 'a^39', 'a^41', 'a^47', 'a^56', 'a^34', 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'st_group': 'mu(74)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.838932371818941367135074756752-0.697799497948335010547641700874*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.14597296896', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.34409593193', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.02805712479', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'bad_primes': [149], 'central_character': '149.113', 'conductor': 149, 'conductor_radical': 149, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/149/113'], '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': '1-149-149.113-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': '1-149-149.113-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6919530909683064, 'root_angle': -0.331918265854182, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14597296896', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_149.113', 'Lhash_array': ['dirichlet_L_149.113'], 'label': '1-149-149.113-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/149/113'}