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lfunc_lfunctions • Show schema
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{'Lhash': '5259333205981419512092412822969', 'a10': [13.207704610577759, 33.652682512609594], 'a2': [-0.5829890818654211, -2.554242058499704], 'a3': [-4.152863934479077, -3.8532946172743356], 'a4': [1.023474719384833, -0.4928794478468933], 'a5': [-13.64461715903594, 2.056595130890502], 'a6': [-7.421172842958652, 12.853848415754754], 'a7': [9.34796996985882, 16.191158935423584], 'a8': [-14.923600866754796, -18.713603582019264], 'a9': [0.38068692394821835, 5.079913966110035], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.537082130246848, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-16.153377165812596, 281.50678216721354]]]], 'bad_primes': [43], 'central_character': '43.10', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '728010422186940876585690569571', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5829890818654211, 2.554242058499704], [-7.207750943219353, 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1.592822064841785, 'root_angle': -0.9439460907356338, 'root_number': '-0.984534678337807 - 0.17518980321431668*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.471973045368', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.14888235372942873660968726123', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.54795061870650394452019448718', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.43253506126836834701001592859', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.537082130246848, 'bad_primes': [43], 'central_character': '43.10', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/4/g/a/10/4'], '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': '2-43-43.10-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-43-43.10-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.592822064841785, 'root_angle': -0.4719730453678169, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.14888235372942873660968726123', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5259333205981419512092412822969', 'Lhash_array': ['5259333205981419512092412822969'], 'label': '2-43-43.10-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/4/g/a/10/4'}