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lfunc_lfunctions • Show schema
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{'Lhash': '1897430096108277529094763856001', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.6012213982029341, 0.0], 'a4': [0.0, 0.0], 'a5': [1.8877376944726532, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.638532830342909, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.821900629278694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '5488.1', 'coefficient_field': 'CDF', 'conductor': 5488, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.6012213982029341, 0], [3.0, 0]], [[1.0, 0], [-1.8877376944726532, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.8030220507975379, 0], [11.0, 0]], [[1.0, 0], [2.5187274263178647, 0], [13.0, 0]], [[1.0, 0], [0.9311937754137837, 0], [17.0, 0]], [[1.0, 0], [0.9078442192707057, 0], [19.0, 0]], [[1.0, 0], [-3.0216698167382776, 0], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 120, 'label': '2-5488-1.1-c1-0-120', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5488/2/a/s/1/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.1206289230835884e-60, 0.21204761460123045, 0.4232444469815081, 0.6326979543805077, 0.8394348407882954, 1.0423674030290038, 1.2402674185319258, 1.4317492840250872, 1.6152635511245894, 1.7891014276221484, 1.951410268694785, 2.100219602267869, 2.2334768335804793, 2.3490914581600477, 2.4449863727812016, 2.519154698331774, 2.569720403506258, 2.5950009323136407, 2.593569983272611, 2.5643185594344096, 2.5065124050941283, 2.4198439690478977, 2.304477089148353, 2.1610826831663346, 1.9908638610243725, 1.7955690470343029, 1.5774919202653306, 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'6.36389714062532837994376477112098', '7.02901652473820224665279336513645', '7.997759703175819465395779285729163'], 'prelabel': '2-5488-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.619811223084741, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49680842320956724077629930955', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61561038442908930369024686884', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86047527550165093623372838264', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.821900629278694, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 5488, 'conductor_radical': 14, 'degree': 2, 'index': 120, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5488/2/a/s/1/6'], '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': '2-5488-1.1-c1-0-120', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5488-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.619811223084741, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49680842320956724077629930955', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1897430096108277529094763856001', 'Lhash_array': ['1897430096108277529094763856001'], 'factors': ['2-5488-1.1-c1-0-120'], 'label': '2-5488-1.1-c1-0-120', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5488/2/a/s/1/6'}