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lfunc_lfunctions • Show schema
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{'Lhash': '3357097558182661456872987046761', 'a10': [12.92205671642167, -1.5285668180785632], 'a2': [1.1965440952767938, 1.6025861062851627], 'a3': [-1.8679582911129915, 1.078466222209079], 'a4': [-1.1365644561164776, 3.8351298852962796], 'a5': [3.2530376794212397, -5.6344265396935445], 'a6': [-3.9634294472646974, -1.7031316143181112], 'a7': [2.3966903284599175, -6.576919907484559], 'a8': [-7.506075358842479, 2.767459612601012], 'a9': [-2.173821215108155, 3.765168791138438], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7629447402088314, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1965440952767938, -1.6025861062851627]]], [7, [[1.0, 0], [-2.3966903284599175, 6.576919907484559]]]], 'bad_primes': [2, 7], 'central_character': '28.23', 'coefficient_field': 'CDF', 'conductor': 28, 'conductor_radical': 14, 'conjugate': '5813916867699356988425268110402', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'6.62554897490320417107988604327458', '9.337226413794549213702993290903139', '10.75588145909543120886002167785680', '11.77052236243200125098021501065173', '12.83860537581552110621678902304718', '14.46228199640345065256911722043194', '14.99092087930229121921047168867477', '17.20091412504267350249826152248438'], 'prelabel': '2-28-28.23-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8734670802089975, 'root_angle': -0.3172300478692407, 'root_number': '0.5431538077361945 - 0.839633218221905*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.158615023935', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.64828301866322266445469852119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.40680002699864825858586071695', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.62554897490320417107988604327', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7629447402088314, 'bad_primes': [2, 7], 'central_character': '28.23', 'conductor': 28, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/28/3/g/a/23/5'], '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': '2-28-28.23-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-28-28.23-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8734670802089975, 'root_angle': -0.15861502393462035, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.64828301866322266445469852119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3357097558182661456872987046761', 'Lhash_array': ['3357097558182661456872987046761'], 'label': '2-28-28.23-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/28/3/g/a/23/5'}