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lfunc_lfunctions • Show schema
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{'Lhash': '1919215922106972669271899161207', 'a10': [-1.1496065122027384, 0.0], 'a2': [1.8229715186913984, 0.0], 'a3': [0.0, 0.0], 'a4': [1.3232251579600238, 0.0], 'a5': [-0.6306223111088273, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.2337412616057466, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8229715186913984, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.6306223111088273, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.6082368019395883, 0], [11.0, 0]], [[1.0, 0], [4.346382678172989, 0], [13.0, 0]], [[1.0, 0], [-1.6748090689641812, 0], [17.0, 0]], [[1.0, 0], 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'4.81875917247986681868483345526365', '5.16289310999395099612536837109003', '5.91583626562855160802795882664427', '6.63690831134507308911297379104606', '7.45592824963754769267812834541923'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51399440962788534261189351418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47929709767864894918569567434', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46698042487706113217306921652', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 280, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/o/1/12'], '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': '2-8001-1.1-c1-0-280', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51399440962788534261189351418', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1919215922106972669271899161207', 'Lhash_array': ['1919215922106972669271899161207'], 'label': '2-8001-1.1-c1-0-280', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/o/1/12'}