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lfunc_lfunctions • Show schema
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{'Lhash': '2097024809831003191196009268658', 'a10': [-4.720154902454143, 1.4559749640162212], 'a2': [1.2987118118401135, 0.6254266457277375], 'a3': [-1.7256031144965196, -0.14931139018812895], 'a4': [0.048514277309314374, 0.060834979556249905], 'a5': [-2.512026233722261, 2.3308197228638767], 'a6': [-2.147677825410411, -1.2731506338364862], 'a7': [0.896803809589528, -2.4891249320003426], 'a8': [-0.6165524094852173, -2.7012926048930894], 'a9': [2.9554122175201765, 0.5153043998768807], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7256031144965196, 0.14931139018812895]]], [7, [[1.0, 0], [-0.896803809589528, 2.4891249320003426]]]], 'bad_primes': [3, 7], 'central_character': '441.184', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '894323307010578483210461867560', 'degree': 2, 'euler_factors': [[[1.0, 0], 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{'__RealLiteral__': 0, 'data': '0.135281548844', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65426088975420531367870868062', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80915940279879575389468187730', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34509180484814731934738985442', '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': '441.184', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/y/a/184/40'], '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': '2-21e2-441.184-c1-0-33', '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': '2-21e2-441.184-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.1352815488441435, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65426088975420531367870868062', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2097024809831003191196009268658', 'Lhash_array': ['2097024809831003191196009268658'], 'label': '2-21e2-441.184-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/y/a/184/40'}