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lfunc_lfunctions • Show schema
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{'Lhash': '1911856423066043283485479694344', 'a10': [3.768734305276283, 0.0], 'a2': [1.0, 0.0], 'a3': [2.6016791318831545, 0.0], 'a4': [-1.0, 0.0], 'a5': [3.768734305276283, 0.0], 'a6': [2.6016791318831545, 0.0], 'a7': [0.1670551733931289, 0.0], 'a8': [-3.0, 0.0], 'a9': [3.768734305276283, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0], [2.0, 0]], [[1.0, 0], [-2.6016791318831545, 0], [3.0, 0]], [[1.0, 0], [-3.768734305276283, 0], [5.0, 0]], [[1.0, 0], [-0.1670551733931289, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.370413437159438, 0], [17.0, 0]], [[1.0, 0], [3.370413437159437, 0], [19.0, 0]], 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'4.20376448758559288954064020819910', '5.09044550278763172614169077777475', '6.02327506898658858389252976493900', '6.58302359384078998077300083996002', '8.062442496978053488398885439126587', '8.415223831717115387485642193811034', '9.407750181247093254240824399636146'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50818878855248461912936282843', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50825995326670552262391988283', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22029146313498483787054389142', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 83, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/h/1/3'], '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': '2-1859-1.1-c1-0-83', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50818878855248461912936282843', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1911856423066043283485479694344', 'Lhash_array': ['1911856423066043283485479694344'], 'label': '2-1859-1.1-c1-0-83', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/h/1/3'}