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lfunc_lfunctions • Show schema
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{'Lhash': '2127417792109129956412267156158', 'a10': [0.7754287915815047, -2.0973102272163855], 'a2': [0.0, 1.0], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, 0.0], 'a5': [-2.0973102272163855, -0.7754287915815047], 'a6': [-0.7071067811865476, -0.7071067811865476], 'a7': [-0.9466810322084026, 0.0], 'a8': [0.0, -1.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [2.0973102272163855, 0.7754287915815047]]], [13, [[1.0, 0], [3.596805753149309, 0.25097484756850275]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.307', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '522558432064400115893072913195', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0.7071067811865476, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.151137938238', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67823672526649456327706386586', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33088769557465018672302078716', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29233759497532087483794310520', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.47', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/t/b/307/1'], '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': '2-390-65.47-c1-0-9', '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': '2-390-65.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.1511379382384958, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67823672526649456327706386586', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2127417792109129956412267156158', 'Lhash_array': ['2127417792109129956412267156158'], 'label': '2-390-65.47-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/t/b/307/1'}