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lfunc_lfunctions • Show schema
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{'Lhash': '1443999631318999369420780805081', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-29.36896598090994, -50.868541244697944], 'a4': [0, 0], 'a5': [-209.19077625556108, 362.32905294940485], 'a6': [0, 0], 'a7': [505.91765731018774, 753.3859064395692], 'a8': [0, 0], 'a9': [-631.5723255756908, 1093.9153565515292], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.98712285422165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-505.91765731018774, -753.3859064395692]]]], 'bad_primes': [2, 7], 'central_character': '112.65', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '169845762571056821143773179063', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [29.36896598090994, 50.868541244697944], [-1093.5, 1893.9975580765674]], [[1.0, 0], [209.19077625556108, -362.32905294940485], [-39062.5, -67658.23467065927]], [[1.0, 0], [-505.91765731018774, 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'3.70075060836182266013730222143163', '4.75744391689488749798818379121307', '5.27126450823334650247892009029266', '7.37406325922400217079484553429931', '8.352398738613816440753789316558418', '9.726053006008497634470205543308737', '10.42552408005258549685646688367549', '11.80326470874091797820712192519029', '12.19074497175497856758105250504444'], 'prelabel': '2-112-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': 0.39579586353847285, 'root_number': '-0.7932099978069004286238650577026907694051171338893114180 + 0.6089481910468057357367627751859524247350325150774165210*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3957958635384729', 'prec': 60}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13911485630111315178738894960', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.70075060836182266013730222143', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75744391689488749798818379121', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.98712285422165, 'bad_primes': [2, 7], 'central_character': '7.2', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/8/i/d/65/2'], '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': '2-112-7.2-c7-0-15', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-112-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': 0.39579586353847285, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13911485630111315178738894960', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1443999631318999369420780805081', 'Lhash_array': ['1443999631318999369420780805081'], 'factors': ['2-112-7.2-c7-0-15'], 'label': '2-112-7.2-c7-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/8/i/d/65/2'}