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lfunc_lfunctions • Show schema
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{'Lhash': '2190350254669823537191961887699', 'a10': [0.9594929736144974, -0.28173255684142967], 'a2': [0.6548607339452851, 0.7557495743542583], 'a3': [-1.715548851210605, -1.102516301099015], 'a4': [-0.14231483827328514, 0.9898214418809327], 'a5': [0.41541501300188644, -0.9096319953545183], 'a6': [-0.2902193545485554, -2.0185199482106935], 'a7': [3.10381476337417, 0.9113622436998841], 'a8': [-0.8412535328311812, 0.5406408174555976], 'a9': [0.4813206276953126, 1.0539451615192064], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6548607339452851, -0.7557495743542583]]], [5, [[1.0, 0], [-0.41541501300188644, 0.9096319953545183]]], [23, [[1.0, 0], [0.9916245812780161, 4.69219359040153]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.151', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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1.355197124587213, 'root_angle': 0.020865996923789785, 'root_number': '0.9978522065972829 + 0.06550552487335269*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0104329984619', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72788168464991073600816936026', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88249727204966637849229621630', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.71224787689084524347023239264', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '23.13', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/g/b/151/1'], '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': '2-230-23.13-c1-0-4', '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': '2-230-23.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.010432998461894893, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72788168464991073600816936026', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2190350254669823537191961887699', 'Lhash_array': ['2190350254669823537191961887699'], 'label': '2-230-23.13-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/g/b/151/1'}