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lfunc_lfunctions • Show schema
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{'Lhash': '3104916972785476131511785217703', 'a10': [-45.2401335802848, -256.5695470909458], 'a2': [0.6945927106677214, -3.939231012048832], 'a3': [0.8932159109382622, 0.749497141429974], 'a4': [-15.035081932574535, -5.472322293210699], 'a5': [61.20395310209232, -22.276417148586205], 'a6': [3.572863643753049, -2.997988565719896], 'a7': [-47.26214716521049, -81.86044016494196], 'a8': [-32.0, 55.42562584220407], 'a9': [-41.960418474522506, -237.96935843811056], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0945851528932655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6945927106677214, 3.939231012048832]]], [19, [[1.0, 0], [-1046.6465337337272, -1175.0021418802496]]]], 'bad_primes': [2, 19], 'central_character': '38.17', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '1323068808785877529481195271418', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6945927106677214, 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'data': '0.303367165852', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.44934761378763437776912287314', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.05979323233986313699346990498', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.30081529557679980365895166354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0945851528932655, 'bad_primes': [2, 19], 'central_character': '19.17', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/6/e/b/17/3'], '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': '2-38-19.17-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-38-19.17-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.468721359913521, 'root_angle': 0.30336716585179535, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.44934761378763437776912287314', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3104916972785476131511785217703', 'Lhash_array': ['3104916972785476131511785217703'], 'label': '2-38-19.17-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/6/e/b/17/3'}