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lfunc_lfunctions • Show schema
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{'Lhash': '1985675300690667188752637340100', 'a10': [0.4280750835771524, 0.0], 'a2': [1.5495770152866664, 0.0], 'a3': [0.6976902886950423, 0.0], 'a4': [0.40118892630473374, 0.0], 'a5': [0.2762528608479392, 0.0], 'a6': [1.0811248351505562, 0.0], 'a7': [3.526002539508255, 0.0], 'a8': [-2.477480891583981, 0.0], 'a9': [-2.5132282610606285, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.86960690988651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 29], 'central_character': '9251.1', 'coefficient_field': 'CDF', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5495770152866664, 0], [2.0, 0]], [[1.0, 0], [-0.6976902886950423, 0], [3.0, 0]], [[1.0, 0], [-0.2762528608479392, 0], [5.0, 0]], [[1.0, 0], [-3.526002539508255, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.6845181247291685, 0], [13.0, 0]], [[1.0, 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'4.67097109493216423506256340973577', '5.19336388151866625391474828410593', '5.72427837055926828267012563771169', '6.51666291992690290163837955881005', '7.42487422386343339977255851128687'], 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56642161517784452674033265796', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41569645631137037510990571912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13937315541030973409777361894', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.86960690988651, 'bad_primes': [11, 29], 'central_character': '1.1', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'index': 610, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/30'], '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': '2-9251-1.1-c1-0-610', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56642161517784452674033265796', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1985675300690667188752637340100', 'Lhash_array': ['1985675300690667188752637340100'], 'label': '2-9251-1.1-c1-0-610', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/30'}