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lfunc_lfunctions • Show schema
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{'Lhash': '2337905460549161463495045851153', 'a10': [0.0, 0.0], 'a2': [1.7071067811865475, 1.7071067811865475], 'a3': [0.2928932188134525, -1.7071067811865475], 'a4': [0.0, 3.8284271247461903], 'a5': [0.0, 0.0], 'a6': [3.414213562373095, -2.414213562373095], 'a7': [3.414213562373095, -3.414213562373095], 'a8': [-3.1213203435596424, 3.1213203435596424], 'a9': [-2.8284271247461903, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.2928932188134525, 1.7071067811865475]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.518', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '1699409278754972432820374256716', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7071067811865475, -1.7071067811865475], [0, 2.0]], [[1.0, 0], [-0.2928932188134525, 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{'__RealLiteral__': 0, 'data': '1.84428221792995801580173526048', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69835982543350375541197656656', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73810728991915115361972205034', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '15.8', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/k/h/518/2'], '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': '2-825-15.8-c1-0-45', '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': '2-825-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': -0.06106073359504349, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84428221792995801580173526048', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2337905460549161463495045851153', 'Lhash_array': ['2337905460549161463495045851153'], 'label': '2-825-15.8-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/k/h/518/2'}