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lfunc_lfunctions • Show schema
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{'Lhash': '2204499458293649452940935700488', 'a10': [-2.884814231104576, 0.5608652268683132], 'a2': [-1.2695016514933024, 0.34016194230760693], 'a3': [-1.5994595056403402, -0.6646271810697774], 'a4': [-0.23612651141913893, 0.1363277049306471], 'a5': [2.23062697366804, 0.15589517101104033], 'a6': [2.256597356730198, 0.2996700519144375], 'a7': [1.2594340373219117, -2.32676296722185], 'a8': [2.1120689176797924, -2.1120689176797924], 'a9': [2.1165414203664827, 2.1260885249379977], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5994595056403402, 0.6646271810697774]]], [5, [[1.0, 0], [-2.23062697366804, -0.15589517101104033]]], [7, [[1.0, 0], [-1.2594340373219117, 2.32676296722185]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.23', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': 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4.661170708358693, 4.352301331896061], 'positive_zeros': ['1.73904343822875846850639853299544', '4.72969088619154278259603818389487', '5.65823479227484294269606180645320', '7.11672428074250424854903028499232', '9.124047381503724995983117002220206', '9.347623361032583298565125613893461', '10.50805149112917444510601830432536', '11.53331221984595996746831773781675', '12.44936103572861679069922631886948', '13.96956584825560252787638841650217'], 'prelabel': '2-105-105.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': 0.06409581414098914, 'root_number': '0.9199960666289926 + 0.3919275920207485*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.064095814141', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73904343822875846850639853300', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.72969088619154278259603818389', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.65823479227484294269606180645', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'bad_primes': [3, 5, 7], 'central_character': '105.23', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/2/x/a/23/4'], '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': '2-105-105.23-c1-0-3', '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': '2-105-105.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': 0.06409581414098914, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73904343822875846850639853300', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2204499458293649452940935700488', 'Lhash_array': ['2204499458293649452940935700488'], 'factors': ['2-105-105.23-c1-0-3'], 'label': '2-105-105.23-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/2/x/a/23/4'}