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lfunc_lfunctions • Show schema
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{'Lhash': '1165887356906585251378294824797', 'a10': [-1.8109981442393683, 1.3115966306611055], 'a2': [-0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.23037692955090902, -2.2241687144483206], 'a6': [0, 0], 'a7': [-0.4327134586813507, 0.7494816955549555], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.34249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.23037692955090902, 2.2241687144483206]]], [13, [[1.0, 0], [1.354858446012866, -3.341310909099541]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.829', 'coefficient_field': 'CDF', 'conductor': 1170, 'conductor_radical': 390, 'conjugate': '1216688068919800083248270665109', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.23037692955090902, 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'7.35441979444720853597462968217882', '7.935798235331537344126753088661372', '9.185340349844614380060998849174499', '9.845968185952774603085543921790366'], 'prelabel': '2-1170-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.2605173119005568, 'root_number': '0.6833614948154054809852143269282954590572132137157368745 + 0.7300801787500154752653080383466982384652119069339841957*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1302586559502784', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.919722955755061711518566904380', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.83617440901365159023148120406', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50641203756179497083227463010', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.34249703648981, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.49', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1170/2/bj/c/829/4'], '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': '2-1170-65.49-c1-0-18', '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': '2-1170-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.1302586559502784, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.919722955755061711518566904380', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1165887356906585251378294824797', 'Lhash_array': ['1165887356906585251378294824797'], 'label': '2-1170-65.49-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/bj/c/829/4'}