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lfunc_lfunctions • Show schema
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{'Lhash': '3567483123837152619138444413267', 'a10': [-2.1825070656623624, -1.4026121234953608], 'a2': [-0.14231483827328514, -0.9898214418809327], 'a3': [0.41541501300188644, -0.9096319953545183], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [1.698938694557896, -1.9606797731338517], 'a6': [-0.9594929736144974, -0.28173255684142967], 'a7': [-1.0401922273890771, 0.6684909532967672], 'a8': [0.41541501300188644, 0.9096319953545183], 'a9': [-0.6548607339452851, -0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.14231483827328514, 0.9898214418809327]]], [3, [[1.0, 0], [-0.41541501300188644, 0.9096319953545183]]], [23, [[1.0, 0], [-3.3519663355125062, -3.4299156965719813]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.49', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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1.0497311788708907, 'root_angle': 0.5380919728766936, 'root_number': '-0.11938403992350478 + 0.992848151033955*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.269045986438', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.81424796643085917373179591481', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.48902131847679200972959817240', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.96421444950631544619855469793', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '23.3', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/a/49/1'], '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': '2-138-23.3-c1-0-3', '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': '2-138-23.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': 0.2690459864383468, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.81424796643085917373179591481', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3567483123837152619138444413267', 'Lhash_array': ['3567483123837152619138444413267'], 'label': '2-138-23.3-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/a/49/1'}