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lfunc_lfunctions • Show schema
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{'Lhash': '467527590990430149561377643158', 'a10': [1.4218059424114084e-60, -5.103991912157496], 'a2': [-1.020351903150442, -0.5891004459520546], 'a3': [-1.6195726175953429, 0.6139906646972485], 'a4': [-0.3059213291581808, -0.5298712852209714], 'a5': [2.1660108845737054, 3.7516409018288646], 'a6': [2.0142361770372985, 0.3276044080367106], 'a7': [0.0, 0.0], 'a8': [0.0, 3.077275349541537], 'a9': [2.246030927329262, -1.9888049360056546], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6195726175953429, -0.6139906646972485]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.146', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2352360483875494915140982145193', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.020351903150442, 0.5891004459520546], [1.0, 1.7320508075688772]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-21e2-63.20-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/2/o/e/146/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.41939481551684415, 0.2829806206096223, 0.14142566635565726, -0.007568990686839091, -0.1648089603710214, -0.32863201738439607, -0.494248888412865, -0.6534154982279604, -0.7944271005585996, -0.9024351566419239, -0.9601032138153113, -0.9486192217088706, -0.8490635989170638, -0.6440976123648072, -0.31989088224495266, 0.13184331471507893, 0.7118836722156938, 1.4118233090246888, 2.2129144118307336, 3.0856654489173114, 3.990386892897604, 4.878815233020151, 5.69684869272276, 6.388307433182562, 6.899496673972934, 7.18421781463759, 7.208757988512921, 6.9563112880304905, 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'8.957026005033486927570672866964993', '9.866425531884167193207769946102552', '10.39182712665075638994284053913178'], 'prelabel': '2-21e2-63.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.7076412342816265, 'root_number': '-0.6070350085435195 - 0.7946750898339328*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.353820617141', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36881423864450969108686488998', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84199974954492287517378194081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.28013924828747856457747471987', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '63.20', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/o/e/146/7'], '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': '2-21e2-63.20-c1-0-3', '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': '2-21e2-63.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.35382061714081325, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36881423864450969108686488998', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '467527590990430149561377643158', 'Lhash_array': ['467527590990430149561377643158'], 'label': '2-21e2-63.20-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/o/e/146/7'}