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lfunc_lfunctions • Show schema
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{'Lhash': '1142736339459948760988226759158', 'a10': [-7.110772741062667, -11.083505999396962], 'a2': [1.173337024905397, 0.10265368817445698], 'a3': [-5.054649205050144, 1.2043759437509287], 'a4': [-6.512280029779635, -1.1482906751790753], 'a5': [-6.834416346240305, -8.8482062140438], 'a6': [-6.054440692768591, 0.89426050338186], 'a7': [27.462305421902837, 19.22931327303375], 'a8': [-16.62470918771563, -4.45457740125067], 'a9': [24.09895717222812, -12.1753958133243], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.965257850774987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [5.054649205050144, -1.2043759437509287]]], [5, [[1.0, 0], [6.834416346240305, 8.8482062140438]]]], 'bad_primes': [3, 5], 'central_character': '135.113', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '1391918274102451940534356227540', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.173337024905397, 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'data': '-0.0541796613758', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.901460023175320612340434449990', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.64529291243525642780793122744', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73991295996122469300397318705', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.965257850774987, 'bad_primes': [3, 5], 'central_character': '135.113', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/4/q/a/113/32'], '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': '2-135-135.113-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-135-135.113-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.822278840011204, 'root_angle': -0.0541796613757725, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.901460023175320612340434449990', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1142736339459948760988226759158', 'Lhash_array': ['1142736339459948760988226759158'], 'label': '2-135-135.113-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/4/q/a/113/32'}