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lfunc_lfunctions • Show schema
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{'Lhash': '718567071015076778739986689123', 'a10': [-3.0594654735119544, 0.9437201161320816], 'a2': [0.8262387743159949, -0.5633200580636221], 'a3': [0.0, 0.0], 'a4': [0.36534102436639504, -0.9308737486442042], 'a5': [-3.0594654735119544, -0.9437201161320816], 'a6': [0.0, 0.0], 'a7': [-1.7683792353653467, 1.9679519506148193], 'a8': [-0.2225209339563144, -0.9749279121818236], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.042805458276933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8262387743159949, 0.5633200580636221]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.7683792353653467, -1.9679519506148193]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.37', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '1871090856083377009515299575694', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [0, 0]], [[1.0, 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'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56684947010296454199577054956', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10076903045794725051015293197', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59572879417347357898319095962', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.042805458276933, 'bad_primes': [2, 3, 7], 'central_character': '49.37', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/z/f/37/1'], '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': '2-882-49.37-c1-0-4', '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': '2-882-49.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.13433302854210097, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56684947010296454199577054956', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '718567071015076778739986689123', 'Lhash_array': ['718567071015076778739986689123'], 'label': '2-882-49.37-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/z/f/37/1'}