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lfunc_lfunctions • Show schema
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{'Lhash': '1318929039377175340633782787299', 'a10': [-22.85296814364614, 0.0], 'a2': [-1.5818397066602703, 0.0], 'a3': [4.983870055146895, 0.0], 'a4': [-5.49778314243295, 0.0], 'a5': [14.447082120536406, 0.0], 'a6': [-7.883683546066469, 0.0], 'a7': [-29.410388515696095, 0.0], 'a8': [21.35132932659008, 0.0], 'a9': [-2.1610392734100916, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0, 0]]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': 'CDF', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5818397066602703, 0], [8.0, 0]], [[1.0, 0], [-4.983870055146895, 0], [27.0, 0]], [[1.0, 0], [-14.447082120536406, 0], [125.0, 0]], [[1.0, 0], [29.410388515696095, 0], [343.0, 0]], [[1.0, 0], [-13.532354219476389, 0], [1331.0, 0]], [[1.0, 0], [-45.765573516909285, 0], [2197.0, 0]], [[1.0, 0], 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['1.04045155592535806375875552208964', '2.73467890646142650795429502929083', '3.73607373124081558355553741559407', '5.49284447568122218835737753598868', '6.43924335829186201567622937286100', '7.73182356196945111656420594085063', '8.993217889524200190052808463707354', '9.352244247847217596049160288849364', '9.854284944989156302440815141108271', '11.04197517416543006860455541524676'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04045155592535806375875552209', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73467890646142650795429502929', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73607373124081558355553741559', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/c/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': '2-17e2-1.1-c3-0-18', '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': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04045155592535806375875552209', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1318929039377175340633782787299', 'Lhash_array': ['1318929039377175340633782787299'], 'label': '2-17e2-1.1-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/c/1/2'}