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lfunc_lfunctions • Show schema
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{'Lhash': '1340915996054441192916682629461', 'a10': [2.5251530692560964, 6.784695659691032e-61], 'a2': [1.2625765346280482, 2.1868467064200257], 'a3': [-0.2598806580164295, -1.7124432964594616], 'a4': [-2.1881990115867427, 3.7900718651402365], 'a5': [0.5, -0.8660254037844386], 'a6': [3.4167317621781845, -2.7304098840363165], 'a7': [0.7993569302995448, 1.3845268166611053], 'a8': [-6.0007687619906465, 0.0], 'a9': [-2.8649240871778954, 0.890061781399417], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.2598806580164295, 1.7124432964594616]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.391', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2354330889367329959367190511253', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'6.19869986091414763881249546215293', '7.997004219965508362648807197349889', '9.303785997791341035856367731124394', '9.824336403893517542425290269867145', '10.70942205295751003626452418416671'], 'prelabel': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.6514374472784905, 'root_number': '-0.45800952995817934 - 0.888947282164408*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.325718723639', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05779620647284117390699219421', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88799888915988077487202246710', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54768059190340504073813725205', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.4', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/h/391/14'], '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': '2-585-9.4-c1-0-12', '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': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.32571872363924526, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05779620647284117390699219421', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1340915996054441192916682629461', 'Lhash_array': ['1340915996054441192916682629461'], 'label': '2-585-9.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/h/391/14'}