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lfunc_lfunctions • Show schema
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{'Lhash': '1838858856470018129464643118106', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.148961141749635, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.2899029626458398, 0.0], 'a8': [0.0, 0.0], 'a9': [6.915956272249165, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.970080404256084, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '2000.1', 'coefficient_field': 'CDF', 'conductor': 2000, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.148961141749635, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.2899029626458398, 0], [7.0, 0]], [[1.0, 0], [-2.65626205220811, 0], [11.0, 0]], [[1.0, 0], [-5.53399026099906, 0], [13.0, 0]], [[1.0, 0], [5.8923300297078995, 0], [17.0, 0]], [[1.0, 0], [6.95418433570738, 0], [19.0, 0]], [[1.0, 0], [-1.4740290598543706, 0], [23.0, 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'6.43625093345871499108157574963047', '6.71760480128137579176872292621489', '8.049955111713297745633251537606310', '8.398402391386411377682193546413273', '8.948518493765603056019573985337989'], 'prelabel': '2-2000-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.99625830049261, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45060386208861312274167088956', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21693885149667966053706826182', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30747257186227308522299180264', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.970080404256084, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 2000, 'conductor_radical': 10, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2000/2/a/r/1/4'], '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': '2-2000-1.1-c1-0-34', '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': '2-2000-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.99625830049261, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45060386208861312274167088956', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1838858856470018129464643118106', 'Lhash_array': ['1838858856470018129464643118106'], 'label': '2-2000-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2000/2/a/r/1/4'}