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lfunc_lfunctions • Show schema
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{'Lhash': '1158410526467517466815001827920', 'a10': [0.8990267069216518, 0.0], 'a2': [-0.8990267069216518, 0.0], 'a3': [-0.03421204435942975, 0.0], 'a4': [-1.1917509802416106, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.030757541577515594, 0.0], 'a7': [4.969989406729299, 0.0], 'a8': [2.869469373080569, 0.0], 'a9': [-2.9988295360207484, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.028705352606672, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [151, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 151], 'central_character': '755.1', 'coefficient_field': 'CDF', 'conductor': 755, 'conductor_radical': 755, 'conjugate': '1158410526467517466815001827920', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8990267069216518, 0], [2.0, 0]], [[1.0, 0], [0.03421204435942975, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.969989406729299, 0], [7.0, 0]], [[1.0, 0], [4.484511683243736, 0], [11.0, 0]], [[1.0, 0], 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'2.46018481839399139384085754564379', '4.06041655961473350929381549694752', '4.98537799544368685081112126546695', '5.61267737980436523266443508526212', '7.39111442385679109655513348542385', '7.895427218840449972076836687014125', '8.748417604523737099812185345315673', '9.025128677959796006571030753612714', '10.66270983180910586365919909549816'], 'prelabel': '2-755-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4553422068230475, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.913824776526714683837526822830', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.46018481839399139384085754564', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06041655961473350929381549695', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.028705352606672, 'bad_primes': [5, 151], 'central_character': '1.1', 'conductor': 755, 'conductor_radical': 755, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/755/2/a/k/1/8'], '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': '2-755-1.1-c1-0-10', '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': '2-755-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4553422068230475, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.913824776526714683837526822830', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1158410526467517466815001827920', 'Lhash_array': ['1158410526467517466815001827920'], 'label': '2-755-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/755/2/a/k/1/8'}