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lfunc_lfunctions • Show schema
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{'Lhash': '1315317170285917355090208699307', 'a10': [27.68425756213938, 0.0], 'a2': [2.0, 0.0], 'a3': [4.8584495495805555, 0.0], 'a4': [4.0, 0.0], 'a5': [13.84212878106969, 0.0], 'a6': [9.716899099161111, 0.0], 'a7': [-7.0, 0.0], 'a8': [8.0, 0.0], 'a9': [-3.3954679741804963, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 139.59851907358237, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [7, [[1.0, 0], [7.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 13], 'central_character': '2366.1', 'coefficient_field': 'CDF', 'conductor': 2366, 'conductor_radical': 182, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [-4.8584495495805555, 0], [27.0, 0]], [[1.0, 0], [-13.84212878106969, 0], [125.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [-51.84287715171713, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [105.7869747595911, 0], [4913.0, 0]], [[1.0, 0], [48.00583748410921, 0], 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'2.31171489352338095683790263841281', '2.55490594178410214649610257429770', '3.81361603470575608144026749623131', '4.43218996637030562210752056686361', '5.58777055477804964956959988488909', '6.46299305556435265890971565896836', '6.63230747865330644917204880995024', '7.913152434985545420071680723974356', '8.928817008330313148804380064486649'], 'prelabel': '2-2366-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.815181719871362, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03760229360448849598560500332', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31171489352338095683790263841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.55490594178410214649610257430', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 139.59851907358237, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 2366, 'conductor_radical': 182, 'degree': 2, 'index': 139, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2366/4/a/bg/1/9'], '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': '2-2366-1.1-c3-0-139', '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': '2-2366-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.815181719871362, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03760229360448849598560500332', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1315317170285917355090208699307', 'Lhash_array': ['1315317170285917355090208699307'], 'label': '2-2366-1.1-c3-0-139', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2366/4/a/bg/1/9'}