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lfunc_lfunctions • Show schema
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{'Lhash': '1185411354178301750034229520743', 'a10': [-4.268376810973857, 0.0], 'a2': [-2.3280368874569914, 0.0], 'a3': [-0.11379750862721817, 0.0], 'a4': [3.4197557493604362, 0.0], 'a5': [1.8334661422123673, 0.0], 'a6': [0.2649247977848691, 0.0], 'a7': [-3.176714332801582, 0.0], 'a8': [-3.305243755690238, 0.0], 'a9': [-2.9870501270302383, 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], [2.3280368874569914, 0], [2.0, 0]], [[1.0, 0], [0.11379750862721817, 0], [3.0, 0]], [[1.0, 0], [-1.8334661422123673, 0], [5.0, 0]], [[1.0, 0], [3.176714332801582, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.09110214610317086, 0], [13.0, 0]], [[1.0, 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'2.63431627473701723243690629757853', '3.50971505766680434056122421459825', '4.65717890716718127319642899466740', '5.78225981494583567427964830492826', '6.17828487056950250565145244087468', '6.80675577631515017163117434648651', '7.39186434464748997268794843925601'], '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': '0.935124673916360553437594558447', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.10760716536651364064622141193', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63431627473701723243690629758', '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': 365, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/4'], '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-c1-0-365', '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': '0.935124673916360553437594558447', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1185411354178301750034229520743', 'Lhash_array': ['1185411354178301750034229520743'], 'label': '2-9251-1.1-c1-0-365', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/4'}