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lfunc_lfunctions • Show schema
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{'Lhash': '1329993713358793200381839830493', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.2111300269652547, -0.33302252754525874], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.4270509831248424, 1.7633557568774194], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.388032161702434, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.2111300269652547, 0.33302252754525874]]]], 'bad_primes': [2, 5], 'central_character': '800.609', 'coefficient_field': 'CDF', 'conductor': 800, 'conductor_radical': 10, 'conjugate': '1846747573664699160252907828247', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [2.4270509831248424, -1.7633557568774194]], [[1.0, 0], [-2.2111300269652547, 0.33302252754525874]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [0, 0], [3.3991869381244215, 10.46162167924669]], [[1.0, 0], [-2.6275594382443237, 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'2-800-25.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.527455669582047, 'root_angle': -0.15516723530086654, 'root_number': '0.8835196647316699 - 0.468394067033772*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0775836176504', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04918004465847250553674041552', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67507874919984967645003872521', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48748800990758407171795152784', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.388032161702434, 'bad_primes': [2, 5], 'central_character': '25.9', 'conductor': 800, 'conductor_radical': 10, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/800/2/bg/b/609/2'], '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': '2-800-25.9-c1-0-12', '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': '2-800-25.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.527455669582047, 'root_angle': -0.07758361765043327, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04918004465847250553674041552', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1329993713358793200381839830493', 'Lhash_array': ['1329993713358793200381839830493'], 'label': '2-800-25.9-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/800/2/bg/b/609/2'}