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lfunc_lfunctions • Show schema
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{'Lhash': '138424488953289811566120735854', 'a10': [0.0, -2.2786945359488016], 'a2': [0.0, 2.3482779597393497], 'a3': [0.0, 1.2986723964738611], 'a4': [-3.5144093761976025, 0.0], 'a5': [-0.9703683188346784, 0.0], 'a6': [-3.0496437655614503, 0.0], 'a7': [-2.5008325773456797, 0.0], 'a8': [0.0, -3.5562541601474478], 'a9': [1.3134500066368386, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.326021814819404, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[23, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [-3.856723295252245, -3.7584152809207585]]]], 'bad_primes': [23, 29], 'central_character': '667.231', 'coefficient_field': 'CDF', 'conductor': 667, 'conductor_radical': 667, 'conjugate': '3823710295378278429186486905238', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.3482779597393497], [-2.0, 0]], [[1.0, 0], [0, -1.2986723964738611], [-3.0, 0]], [[1.0, 0], [0.9703683188346784, 0], [5.0, 0]], [[1.0, 0], [2.5008325773456797, 0], 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['0.10919766766044814969609192920413', '1.65337204084669363181274030180813', '2.71418484472474981773269821718482', '3.76181754824389344781077883321705', '4.68253729484987698959073135538012', '6.19900959847650379293666540188911', '7.23172289308851523391457909169943', '8.079042901307751682566010193548947', '9.336838121646401108071796091192194', '9.971580119442306046744081417293795'], 'prelabel': '2-667-29.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3078175436588144, 'root_angle': 0.24589099077417886, 'root_number': '0.7161755365671795 + 0.6979201966003796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.122945495387', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10919766766044814969609192920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65337204084669363181274030181', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71418484472474981773269821718', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.326021814819404, 'bad_primes': [23, 29], 'central_character': '29.28', 'conductor': 667, 'conductor_radical': 667, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/667/2/c/a/231/23'], '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': '2-667-29.28-c1-0-0', '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': '2-667-29.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3078175436588144, 'root_angle': 0.12294549538708943, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10919766766044814969609192920', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '138424488953289811566120735854', 'Lhash_array': ['138424488953289811566120735854'], 'label': '2-667-29.28-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/667/2/c/a/231/23'}