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lfunc_lfunctions • Show schema
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{'Lhash': '1626809897915506106487365547696', 'a10': [-0.9240812563882914, -1.600555686386603], 'a2': [-0.7308293747957264, 0.26600013875302275], 'a3': [0.0, 0.0], 'a4': [-1.0687333849902712, 0.8967737891721824], 'a5': [0.41264844080801305, 2.3402456002480787], 'a6': [0.0, 0.0], 'a7': [-1.9161654854737584, -1.6078537521356644], 'a8': [1.3202521753559653, -2.2867438465198666], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.163', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '544637386588604378153349665199', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7308293747957264, -0.26600013875302275], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.41264844080801305, -2.3402456002480787], [-4.698463103929542, 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'2.55728499087470457597795258589', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45825288084052972659872001939', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/s/163/1'], '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': '2-3e6-27.7-c1-0-19', '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': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.14814814814814817, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28332672869212795329662540436', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1626809897915506106487365547696', 'Lhash_array': ['1626809897915506106487365547696'], 'factors': ['2-3e6-27.7-c1-0-19'], 'label': '2-3e6-27.7-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/s/163/1'}