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lfunc_lfunctions • Show schema
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{'Lhash': '2571732560952256261490644194857', 'a10': [-1.0440084130132756, 1.808275614868346], 'a2': [-0.766044443118978, 0.6427876096865394], 'a3': [0.0, 0.0], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [1.9620940034939642, -0.714143814104009], 'a6': [0.0, 0.0], 'a7': [-0.696712057679415, -3.951250426225711], 'a8': [0.5, 0.8660254037844386], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.766044443118978, -0.6427876096865394]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.37', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1781644518132005802104316047537', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9620940034939642, 0.714143814104009], [3.83022221559489, -3.2139380484326967]], 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{'__RealLiteral__': 0, 'data': '5.56646102629885148838068251510', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '27.22', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/e/b/37/2'], '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': '2-162-27.22-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': '2-162-27.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.02843136433597984, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02873927601914779256361266137', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2571732560952256261490644194857', 'Lhash_array': ['2571732560952256261490644194857'], 'label': '2-162-27.22-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/e/b/37/2'}