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lfunc_lfunctions • Show schema
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{'Lhash': '2182648746821121464038524562637', 'a10': [-1.1133407984528387, -1.928362829059618], 'a2': [-0.23395555688102196, 1.3268278963378768], 'a3': [0.0, 0.0], 'a4': [0.17364817766693036, 0.06320276790533177], 'a5': [-1.2660444431189781, 1.0623374252751794], 'a6': [0.0, 0.0], 'a7': [-2.266044443118978, 0.8247727268196405], 'a8': [-1.4717815070238645, 2.5492003478056238], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.649', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '3563991465670730007714906964767', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.23395555688102196, -1.3268278963378768], [-1.8793852415718169, -0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.2660444431189781, -1.0623374252751794], [0.8682408883346517, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92262555841052825930223146402', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.25', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/a/649/1'], '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': '2-3e6-27.25-c1-0-25', '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': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.25925925925925924, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72180626619681689135093834528', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2182648746821121464038524562637', 'Lhash_array': ['2182648746821121464038524562637'], 'label': '2-3e6-27.25-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/a/649/1'}