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lfunc_lfunctions • Show schema
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{'Lhash': '1206886903405495478868444764210', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.2996641030220093, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.205891660851936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '2280.1', 'coefficient_field': 'CDF', 'conductor': 2280, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.2996641030220093, 0], [7.0, 0]], [[1.0, 0], [5.011209116293987, 0], [11.0, 0]], [[1.0, 0], [-3.2996641030220095, 0], [13.0, 0]], [[1.0, 0], [-5.711545013271977, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.7115450132719774, 0], [23.0, 0]], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-2280-1.1-c1-0-9', 'leading_term': '2.14335511406528156232353686749', '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/2280/2/a/t/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.1433551140652813, 2.138151498740712, 2.122462362782638, 2.0960584639534354, 2.058576142373513, 2.0095437581722866, 1.9484164890580096, 1.8746175711670976, 1.787583876032775, 1.686813695122804, 1.5719147148002526, 1.4426503620485462, 1.2989829392599905, 1.1411122083793162, 0.969508307196248, 0.7849380729376683, 0.588484010252629, 0.38155527883793877, 0.16589020040937655, -0.05645009371664359, -0.28309712488353267, -0.5113997472850564, -0.7384579930896462, -0.9611658478265931, -1.1762625197907004, 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'6.81368976799422534631332608030676', '7.940183865920907529661633920006997', '8.009212005777289615762675737613694', '8.744562064318574499243171830765866'], 'prelabel': '2-2280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.952065895119842998882988728539', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.31341029416785165323438360657', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18714946018868992964988309019', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.205891660851936, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 2280, 'conductor_radical': 570, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2280/2/a/t/1/2'], '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': '2-2280-1.1-c1-0-9', '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': '2-2280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.952065895119842998882988728539', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1206886903405495478868444764210', 'Lhash_array': ['1206886903405495478868444764210'], 'label': '2-2280-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2280/2/a/t/1/2'}