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lfunc_lfunctions • Show schema
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{'Lhash': '248826445845527549210261333594', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-4.0, 3.0], 'a6': [0, 0], 'a7': [3.4641016151377544, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.61857903394138, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [4.0, -3.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '720.559', 'coefficient_field': 'CDF', 'conductor': 720, 'conductor_radical': 30, 'conjugate': '2092740786947384542836458862880', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0, -3.0]], [[1.0, 0], [-3.4641016151377544, 0], [49.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-121.0, 0]], [[1.0, 0], [0, 6.0], [-169.0, 0]], [[1.0, 0], [0, -18.0], [-289.0, 0]], [[1.0, 0], [0, -13.856406460551018], [-361.0, 0]], [[1.0, 0], [6.928203230275509, 0], [529.0, 0]], [[1.0, 0], 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'7.44880672766954705033482671495126', '7.973049587284638204204255670355596', '9.056837631158755050813217789725846', '9.606396380395079037075115522952499'], 'prelabel': '2-720-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.4292865152235725, 'root_angle': -0.8714994313658002, 'root_number': '-0.9196152422706631880582339024517617100828415761431141885 - 0.3928203230275509174109785366023489467771221015241522512*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4357497156829001', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19628945531262993470294254129', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74212986364623220156922886584', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24086455862927495421069637014', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.61857903394138, 'bad_primes': [2, 3, 5], 'central_character': '20.19', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/3/j/d/559/4'], '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': '2-720-20.19-c2-0-3', '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': '2-720-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.4292865152235725, 'root_angle': -0.4357497156829001, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19628945531262993470294254129', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '248826445845527549210261333594', 'Lhash_array': ['248826445845527549210261333594'], 'label': '2-720-20.19-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/3/j/d/559/4'}