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lfunc_lfunctions • Show schema
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{'Lhash': '2612718037290414723385450853067', 'a10': [-0.8978773891157921, -0.5770307602665048], 'a2': [-0.14231483827328514, -0.9898214418809327], 'a3': [-0.41541501300188644, 0.9096319953545183], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [0.698938694557896, -0.8066182526008422], 'a6': [0.9594929736144974, 0.28173255684142967], 'a7': [3.7226992930514395, -2.3924335653762934], '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], [4.7849189724004875, -0.32334258544439715]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.49', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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[32.817786027149026, 71.86092763300695]], [[1.0, 0], [3.626899603231782, 4.18566527092624], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [-4.705036417762551, 10.302592662643104], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [7.84485221845382, -9.053442079585569], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-12.089353765605335, -13.951857988995956], [-14.373798665601798, 99.9719656299742]], [[1.0, 0], [-1.6263336050975428, 11.31139868132252], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [-6.174779844684519, -13.520881853563958], [-70.07009853214551, 80.86520445590564]], [[1.0, 0], [11.785448623936237, 3.4605199471516968], [91.69663507859875, 58.929849102660135]], [[1.0, 0], [-0.429024906448245, -2.983933767243366], [-108.4227060184382, 31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-138-23.3-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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1.0497311788708907, 'root_angle': 0.2629563038326001, 'root_number': '0.6777473818641024 + 0.7352948295591059*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.131478151916', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06107111598418183696851393998', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.55646159590577678250025061701', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.83411941093625982145067564158', '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': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/b/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-c1-0-1', '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': '2-138-23.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': 0.13147815191630005, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.06107111598418183696851393998', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2612718037290414723385450853067', 'Lhash_array': ['2612718037290414723385450853067'], 'label': '2-138-23.3-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/b/49/1'}