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lfunc_lfunctions • Show schema
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{'Lhash': '3072118782174501938314463705701', 'a10': [-4.674825603429904, -8.09703546166443], 'a2': [1.8793852415718169, -0.6840402866513374], 'a3': [6.851777295098037, 2.493842987236679], 'a4': [3.064177772475912, -2.5711504387461575], 'a5': [-0.8117749469463108, -4.603804498237743], 'a6': [14.58301819879692, -5.550444545759499e-60], 'a7': [-0.6021583721178072, -3.4150098283223156], 'a8': [4.0, -6.928203230275509], 'a9': [20.044399292419005, 16.81924805343892], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.366141340424807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.8793852415718169, 0.6840402866513374]]], [37, [[1.0, 0], [185.04579047785109, -128.1056416651009]]]], 'bad_primes': [2, 37], 'central_character': '74.7', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '2893912734695954925779117694109', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8793852415718169, 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'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.42347440345264998547066957039', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57747021815766480492899964197', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.59985437920868564449942891716', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.366141340424807, 'bad_primes': [2, 37], 'central_character': '37.7', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/4/f/a/7/4'], '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': '2-74-37.7-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-74-37.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': 0.023928049233365795, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.42347440345264998547066957039', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3072118782174501938314463705701', 'Lhash_array': ['3072118782174501938314463705701'], 'label': '2-74-37.7-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/4/f/a/7/4'}