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lfunc_lfunctions • Show schema
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{'Lhash': '1962710250804512336947724071238', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7330518718298263, -0.6801727377709194], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8262387743159949, 0.5633200580636221], 'a8': [0.0, 0.0], 'a9': [0.07473009358642425, 0.9972037971811801], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7330518718298263, 0.6801727377709194]]], [7, [[1.0, 0], [-0.8262387743159949, -0.5633200580636221]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.53', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '1756075445517612960661970734975', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [0, 0], [-0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [-0.8262387743159949, 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'8.492331343020060675186011524153032', '9.240310357034639558975934851092929', '10.46958859416177443387350263633826', '10.82441330119665726532307599614202'], 'prelabel': '2-588-147.53-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': 0.163265306122449, 'root_number': '0.87131870412338935154662548438946 + 0.49071755200393788668756170322444*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08163265306122448', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54830538513620671623865839789', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.69269407874133238887112002482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30775460598029860799587350196', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'bad_primes': [2, 3, 7], 'central_character': '147.53', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/1/z/a/53/1'], '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': '2-588-147.53-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-588-147.53-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': 0.0816326530612245, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54830538513620671623865839789', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1962710250804512336947724071238', 'Lhash_array': ['1962710250804512336947724071238'], 'label': '2-588-147.53-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/1/z/a/53/1'}