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lfunc_lfunctions • Show schema
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{'Lhash': '2626400031367995977532211314288', 'a10': [-2.133610448091825, -0.3543900525937716], 'a2': [-0.4196750802245881, 0.8714642836945691], 'a3': [1.7706357185785582, -2.220306963546413], 'a4': [0.6636567789236931, 0.8321992785912967], 'a5': [0.6269764600919299, 2.146369147768061], 'a6': [1.191826530326061, 2.474853291224634], 'a7': [-1.3888589284004025, 0.15648681856939117], 'a8': [-2.8897548510513764, 0.6595676873397563], 'a9': [-1.1270493625975424, -4.937925895182488], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1578308293085662, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.6269764600919299, -2.146369147768061]]], [29, [[1.0, 0], [-3.2054632067105473, 4.327239955263047]]]], 'bad_primes': [5, 29], 'central_character': '145.47', 'coefficient_field': 'CDF', 'conductor': 145, 'conductor_radical': 145, 'conjugate': '2990470628993760978762474947236', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_number': '0.93135836382375 - 0.36410382878452024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0593123366766', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07186430621745110753848121104', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.67992502273573403014391451257', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.84482876834715088989897662262', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1578308293085662, 'bad_primes': [5, 29], 'central_character': '145.47', 'conductor': 145, 'conductor_radical': 145, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/145/2/t/a/47/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-145-145.47-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-145-145.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0760254780015974, 'root_angle': -0.05931233667664009, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07186430621745110753848121104', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2626400031367995977532211314288', 'Lhash_array': ['2626400031367995977532211314288'], 'factors': ['2-145-145.47-c1-0-8'], 'label': '2-145-145.47-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/145/2/t/a/47/5'}