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lfunc_lfunctions • Show schema
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{'Lhash': '43278928860381800287952476326', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.9318516525781366], 'a6': [0, 0], 'a7': [0, 3.9324421947611325], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.5183', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '1906796507832780135046717972392', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.9318516525781366], [-5.0, 0]], [[1.0, 0], [0, -3.9324421947611325], [-7.0, 0]], [[1.0, 0], [-2.0355818675378745, 0], [11.0, 0]], [[1.0, 0], [2.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [0, 4.760278777324326], [-17.0, 0]], [[1.0, 0], [0, -6.811189679153948], [-19.0, 0]], [[1.0, 0], [7.596894952617289, 0], 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'3.36194050675563085538246258782350', '4.15797797971645075261551575904794', '4.63299807758826628464137167368111', '5.89510128461360666038709859301016', '6.59467465852720617160105618577520', '7.06660154881910172592912404715753', '7.72401252798482248303514621931636'], 'prelabel': '2-72e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03414105499779655982440219703', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.33029211431380271398746108660', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.44018506500183144216965536872', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/c/k/5183/2'], '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': '2-72e2-12.11-c1-0-2', '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': '2-72e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.03414105499779655982440219703', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '43278928860381800287952476326', 'Lhash_array': ['43278928860381800287952476326'], 'factors': ['2-72e2-12.11-c1-0-2'], 'label': '2-72e2-12.11-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/c/k/5183/2'}