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lfunc_lfunctions • Show schema
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{'Lhash': '2047479007973714150748232199548', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8000978467980638, -1.3858101216807064], 'a4': [0.0, 0.0], 'a5': [0.0, 1.0], 'a6': [0.0, 0.0], 'a7': [3.751835525465145, 2.1661232505825025], 'a8': [0.0, 0.0], 'a9': [0.21968687109820387, -0.38050882249792384], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [3.112559630066801, 1.8198825646943315]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.101', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '1774540421405584927864989966000', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8000978467980638, 1.3858101216807064], [-1.5, 2.598076211353316]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-3.751835525465145, -2.1661232505825025], [3.5, 6.06217782649107]], 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False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.1724952379707715, 'root_number': '0.8567252351098564 + 0.51577308142822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0862476189854', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61517614365116339326544243150', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.03421503065901668692345532547', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69644018803483543420545100368', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '13.10', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/x/a/101/2'], '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': '2-260-13.10-c1-0-1', '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': '2-260-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.08624761898538574, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61517614365116339326544243150', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2047479007973714150748232199548', 'Lhash_array': ['2047479007973714150748232199548'], 'label': '2-260-13.10-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/x/a/101/2'}