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lfunc_lfunctions • Show schema
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{'Lhash': '2789035628514101628424996471226', 'a10': [247.47359318619675, 0.0], 'a2': [6.38986691902975, 0.0], 'a3': [-9.0, 0.0], 'a4': [8.83039924291075, 0.0], 'a5': [38.72906843320825, 0.0], 'a6': [-57.50880227126775, 0.0], 'a7': [0.0, 0.0], 'a8': [-148.05066540485126, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.1', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [-6.38986691902975, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [-38.72906843320825, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [576.3898669190297, 0], [161051.0, 0]], [[1.0, 0], [-391.49119772873223, 0], [371293.0, 0]], [[1.0, 0], [1329.700304016403, 0], [1419857.0, 0]], [[1.0, 0], [-942.4735931861967, 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['2.20016117060328781547685314761548', '3.75057735543581413636988354534630', '5.14360355813896893013133265669459', '5.71090857556082882098097954923748', '6.89014031001247425713127872382692', '8.494980513957656737553200337779346', '9.777799536130960735808623067692836', '10.82722374982454685967283686325982', '11.83882425796451419561152783904292'], 'prelabel': '2-147-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.20016117060328781547685314762', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75057735543581413636988354535', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.14360355813896893013133265669', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/a/i/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': '2-147-1.1-c5-0-30', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-147-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.20016117060328781547685314762', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2789035628514101628424996471226', 'Lhash_array': ['2789035628514101628424996471226'], 'label': '2-147-1.1-c5-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/a/i/1/2'}