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lfunc_lfunctions • Show schema
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{'Lhash': '733976702469726691079655681960', 'a10': [1.9496858291468608, 3.3769549148794167], 'a2': [-0.8660254037844386, -0.5], 'a3': [-0.6628271480711836, 0.3826834323650898], 'a4': [0.5, 0.8660254037844386], 'a5': [-3.3769549148794167, -1.9496858291468608], 'a6': [0.7653668647301796, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [-1.2071067811865475, 2.0907702751760278], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [2.9736874854436204, -1.4687350812573376]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.901', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '707664996512540882781069649041', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0.6628271480711836, -0.3826834323650898], [1.5, 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'7.49804204608021184062194150779378', '8.285874754994530779090022153644197', '8.754253840733844515953330035933543', '10.06601881059316970329849271203287'], 'prelabel': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.13368552969536318, 'root_number': '0.9130948617205799828980577085716368944185477468835125108 + 0.4077471931227423174662174199115364124978195265468775721*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06684276484768159', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57900552592140184877073403687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64047028575001050303332540841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63389979434554026985783686010', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.54', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/1'], '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': '2-1078-77.54-c1-0-10', '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': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.06684276484768159, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57900552592140184877073403687', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '733976702469726691079655681960', 'Lhash_array': ['733976702469726691079655681960'], 'label': '2-1078-77.54-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/1'}