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lfunc_lfunctions • Show schema
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{'Lhash': '1075188355177730485475703708740', 'a10': [-257.5341601759314, -2.617450157847188e-59], 'a2': [-2.1680688750209796, 3.755205445845035], 'a3': [11.803977953601798, 10.181655291301249], 'a4': [6.598954706330528, 11.429724828210235], 'a5': [29.69626139914943, 51.43543353817325], 'a6': [-63.82604460024926, 22.2518323607373], 'a7': [-30.406286110200835, 52.66523241234369], 'a8': [-195.9843612272164, 0.0], 'a9': [35.66779105823456, 240.36806917938605], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.877998161485086, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-11.803977953601798, -10.181655291301249]]], [11, [[1.0, 0], [-60.5, 104.78907385791707]]]], 'bad_primes': [3, 11], 'central_character': '99.34', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '3195609070840191300790867667027', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1680688750209796, -3.755205445845035], 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['0.848174059148595226153950052473090', '1.79236527788585736357453379601240', '3.34662054576670836801282040959886', '5.41975005216408973386600153297515', '6.79822821816788654498401532536708', '8.172792281427691729961406153567780', '9.456672089140196505412152094983272', '9.825402489415426227874666430397700', '11.48177892059238104676572883556169', '12.42439475217699630834838718699172'], 'prelabel': '2-99-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9847205876303406, 'root_angle': -0.9913357139341024, 'root_number': '-0.9996295679963022 - 0.02721629635946536*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.495667856967', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.848174059148595226153950052473', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.79236527788585736357453379601', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34662054576670836801282040960', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.877998161485086, 'bad_primes': [3, 11], 'central_character': '9.7', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/6/e/a/34/8'], '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': '2-99-9.7-c5-0-16', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-99-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9847205876303406, 'root_angle': -0.4956678569670512, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.848174059148595226153950052473', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1075188355177730485475703708740', 'Lhash_array': ['1075188355177730485475703708740'], 'label': '2-99-9.7-c5-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/6/e/a/34/8'}