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lfunc_lfunctions • Show schema
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{'Lhash': '2945126437413844962097357187618', 'a10': [-6.566383707620929, 0], 'a2': [-0.8875263367944495, -1.5372407083834736], 'a3': [0, 0], 'a4': [-0.5754059970075492, 0.9966324217969007], 'a5': [1.849630663169182, -3.2036542838463395], 'a6': [0, 0], 'a7': [0.04485034681353327, 0.07768307941812452], 'a8': [-1.5073534404031252, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.270631674670657, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 43], 'central_character': '1161.388', 'coefficient_field': 'CDF', 'conductor': 1161, 'conductor_radical': 129, 'conjugate': '325633823529556523662251037609', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8875263367944495, 1.5372407083834736], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.849630663169182, 3.2036542838463395], [-2.5, -4.330127018922194]], [[1.0, 0], 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'10.25984101306485049059923029839809'], 'prelabel': '2-1161-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.044771202351772, 'root_angle': -0.5698828083744848, 'root_number': '-0.2177839249564604479683788815720546964283646474186686031 - 0.9759970092323842792701008147891040646908375158622771729*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2849414041872424', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32329510740861930742845797885', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91492841254996246408199455268', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61764177651993399822280488812', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.270631674670657, 'bad_primes': [3, 43], 'central_character': '9.4', 'conductor': 1161, 'conductor_radical': 129, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1161/2/f/c/388/4'], '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': '2-1161-9.4-c1-0-41', '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': '2-1161-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.044771202351772, 'root_angle': -0.2849414041872424, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32329510740861930742845797885', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2945126437413844962097357187618', 'Lhash_array': ['2945126437413844962097357187618'], 'label': '2-1161-9.4-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1161/2/f/c/388/4'}