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lfunc_lfunctions • Show schema
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{'Lhash': '3260239588890326121949635152354', 'a10': [0.6105741170145174, 47.84253779070805], 'a2': [-1.3828401737285176, 2.4673372396011217], 'a3': [-1.4298723584170678, -4.9955445187321486], 'a4': [-4.175506107844966, -6.823866114113713], 'a5': [14.649918588748932, -8.458134440820299], 'a6': [14.302977963676156, 3.3800623323533947], 'a7': [-3.0896585860133468, -1.7838152163388443], 'a8': [22.610836572981782, -0.8660655113266696], 'a9': [-22.910930077269626, 14.285982045153986], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1240687602066632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3828401737285176, -2.4673372396011217]]], [3, [[1.0, 0], [1.4298723584170678, 4.9955445187321486]]]], 'bad_primes': [2, 3], 'central_character': '36.11', 'coefficient_field': 'CDF', 'conductor': 36, 'conductor_radical': 6, 'conjugate': '1595886615567395427427610943455', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'4.68027462035480779050176741585613', '6.77239480369149172293538434279104', '9.331954070308053389241586882915334', '9.713640726664929027620174987665692', '10.92010643376261291556324010948062', '12.10879268173700124986387256976812', '13.74805937437256989677561764838422', '14.76042111446063902575644085287870', '16.44708902808231566415560749305599'], 'prelabel': '2-6e2-36.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4574185260955974, 'root_angle': 0.20329040361575823, 'root_number': '0.8028978793583673 + 0.5961165954088484*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.101645201808', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.57187555332940204792177224237', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.68027462035480779050176741586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.77239480369149172293538434279', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1240687602066632, 'bad_primes': [2, 3], 'central_character': '36.11', 'conductor': 36, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/36/4/h/b/11/5'], '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': '2-6e2-36.11-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-6e2-36.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4574185260955974, 'root_angle': 0.10164520180787912, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.57187555332940204792177224237', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3260239588890326121949635152354', 'Lhash_array': ['3260239588890326121949635152354'], 'label': '2-6e2-36.11-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/36/4/h/b/11/5'}