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lfunc_lfunctions • Show schema
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{'Lhash': '1509183435702373746567468831468', 'a10': [-5.541527219586275, 4.392206287799381], 'a2': [1.4142135623730951, 0.0], 'a3': [2.014683183706685, 2.2228476486906374], 'a4': [2.0, 0.0], 'a5': [-3.918451475099289, 3.105758850473135], 'a6': [2.849192282283, 3.143581291867444], 'a7': [0.0, 2.6457513110645907], 'a8': [2.8284271247461903, 0.0], 'a9': [-0.8821033385789893, 8.956667555517946], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.722085551566235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4142135623730951, 0]]], [3, [[1.0, 0], [-2.014683183706685, -2.2228476486906374]]], [5, [[1.0, 0], [3.918451475099289, -3.105758850473135]]], [7, [[1.0, 0], [0, -2.6457513110645907]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.29', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': '3251604940503942326318527781617', 'degree': 2, 'euler_factors': [[[1.0, 0], 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{'__RealLiteral__': 0, 'data': '1.19053581123273122018751110119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10674738868592958035933662986', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12459473987616226743239742254', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.722085551566235, 'bad_primes': [2, 3, 5, 7], 'central_character': '15.14', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/c/a/29/22'], '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': '2-210-15.14-c2-0-8', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-210-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': -0.22385542938178296, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19053581123273122018751110119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1509183435702373746567468831468', 'Lhash_array': ['1509183435702373746567468831468'], 'label': '2-210-15.14-c2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/c/a/29/22'}