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lfunc_lfunctions • Show schema
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{'Lhash': '545714427907577835056327250356', 'a10': [-1.675119439580559, 2.9013919780998325], 'a2': [0.08715574274765818, -0.9961946980917455], 'a3': [0.0, 0.0], 'a4': [-0.984807753012208, -0.17364817766693036], 'a5': [-3.036347584616659, -1.415872131527181], 'a6': [0.0, 0.0], 'a7': [-1.6304608452842748, 0.5934392158199878], 'a8': [-0.25881904510252074, 0.9659258262890683], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.08715574274765818, 0.9961946980917455]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-4.150577001784813, 4.446651611297538]]]], 'bad_primes': [2, 3, 37], 'central_character': '666.557', 'coefficient_field': 'CDF', 'conductor': 666, 'conductor_radical': 222, 'conjugate': '1707339430707237020469334766624', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.08715574274765818, 0.9961946980917455]], [[1.0, 0], [0, 0]], 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'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18422521082688788867308286986', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68454885456507905286486386586', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '111.2', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/666/2/bs/b/557/5'], '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': '2-666-111.2-c1-0-1', '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': '2-666-111.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': -0.104257554297091, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43049277759133843827155740965', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '545714427907577835056327250356', 'Lhash_array': ['545714427907577835056327250356'], 'label': '2-666-111.2-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/bs/b/557/5'}