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lfunc_lfunctions • Show schema
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{'Lhash': '2809568561815843061908061732494', 'a10': [4.8103062975453845, 1.7882205619068108], 'a2': [-0.49278190110107484, 1.325581381110647], 'a3': [0.0, 0.0], 'a4': [-1.514331995894421, -1.3064450260957863], 'a5': [0.0, -3.6288275967749626], 'a6': [0.0, 0.0], 'a7': [0.0, -1.0], 'a8': [2.4780346018722255, -1.3635778349342442], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.49278190110107484, -1.325581381110647]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.323', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '290163344123923736054449009013', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.49278190110107484, -1.325581381110647]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.6288275967749626], [-5.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], 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['2.21635879895454222142971779082017', '2.79111141367310707582154023849822', '3.91518850073388062822822434020163', '5.11834843272155307464594035488314', '6.42995416233729523188766625985460', '7.34500524332865687739317110067881', '8.073793436978934694873392000706487', '9.259333347237088928408470024179418', '10.00446541898312368963398470993794', '10.60240168397235127436621458165747'], 'prelabel': '2-756-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.7265833805396592, 'root_number': '-0.653222513047893 + 0.7571659979472105*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.36329169027', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21635879895454222142971779082', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79111141367310707582154023850', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91518850073388062822822434020', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/e/b/323/10'], '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': '2-756-12.11-c1-0-42', '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': '2-756-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.3632916902698296, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21635879895454222142971779082', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2809568561815843061908061732494', 'Lhash_array': ['2809568561815843061908061732494'], 'label': '2-756-12.11-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/e/b/323/10'}