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lfunc_lfunctions • Show schema
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{'Lhash': '988892738310234384410156819867', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-2.2491405381295495, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-2.2491405381295495, 0.0], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [2.0586331602576786, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.63329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '8470.1', 'coefficient_field': 'CDF', 'conductor': 8470, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.2491405381295495, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [-1.0586331602576788, 0], [17.0, 0]], [[1.0, 0], [-5.190507377871871, 0], [19.0, 0]], [[1.0, 0], [-5.307773698387228, 0], 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'4.59247218907234723711885998001499', '5.12721651179225672728411577684636', '5.61620848537844090051851065473199', '6.18074621043972761885763368860630', '6.92448700348144580472243040666139', '7.49126556573530054347421464969553'], 'prelabel': '2-8470-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.223946164222168, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78009882070989663670040713975', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64528506913175141783428740936', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75856274864874794228793228801', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.63329051202452, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 8470, 'conductor_radical': 770, 'degree': 2, 'index': 66, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8470/2/a/cn/1/1'], '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': '2-8470-1.1-c1-0-66', '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': '2-8470-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.223946164222168, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78009882070989663670040713975', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '988892738310234384410156819867', 'Lhash_array': ['988892738310234384410156819867'], 'label': '2-8470-1.1-c1-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8470/2/a/cn/1/1'}