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lfunc_lfunctions • Show schema
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{'Lhash': '2020562378037542968463336087783', 'a10': -3351936000, 'a2': -512, 'a3': -13092, 'a4': 262144, 'a5': 6546750, 'a6': 6703104, 'a7': 96674264, 'a8': -134217728, 'a9': -990861003, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.576333931127615, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '9.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 512]]], 'bad_primes': [2], 'central_character': '2.1', 'coefficient_field': '1.1.1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[1, 512], [1, 13092, 1162261467], [1, -6546750, 19073486328125], [1, -96674264, 11398895185373143], [1, -11799694452, 61159090448414546291], [1, -34401727958, 1461920290375446110677], [1, 400697609166, 239072435685151324847153], [1, -814875924620, 1978419655660313589123979], [1, 4937767258872, 74615470927590710561908487], [1, 96707212093050, 6103261246589991489578849669], [1, 58447954952608, 21670662219970396194714277471], [1, -246079341597854, 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'17.02733753345267717043357454376115', '17.95973734111144147904455991615987', '20.41705539767213077963378096591080', '22.10964121529051679758370773498306', '24.57417224366458349927386855492287'], 'prelabel': '2-2-1.1-c19-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1392367636911103, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c19-0', 'trace_hash': 2129424881682018929, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59394266659421640919546674373', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.03429904126089929688409579929', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.083581288116968962779107853524', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.576333931127615, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'dirichlet_coefficients': [1, -512, -13092, 262144, 6546750, 6703104, 96674264, -134217728, -990861003, -3351936000, 11799694452, -3431989248, 34401727958, -49497223168, -85710051000, 68719476736, -400697609166, 507320833536, 814875924620, 1716191232000, -1265659464288, -6041443559424, -4937767258872, 1757178494976, 23786449234375, -17613684714496, 28188679377240, 25342578262016, -96707212093050, 43883546112000, -58447954952608, -35184372088832, -154481599765584, 205157175892992, 632902237842000, -259748266770432, 246079341597854, -417216473405440, -450387422426136, -878689910784000, -2049265663743558, 648017645715456, 5698694101737428, 3093219102425088, -6486919271390250, 2528136836542464, -241487233520496, -899675389427712, -2052981865431447, -12178662008000000, 5245933099201272, 9018206573821952, -16046376246286002, 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'ModularForm/GL2/Q/holomorphic/2/20/a/a'], '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': '2-2-1.1-c19-0-0', 'motivic_weight': 19, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [19], 'order_of_vanishing': 0, 'prelabel': '2-2-1.1-c19-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1392367636911103, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c19-0', 'trace_hash': 2129424881682018929, 'z1': {'__RealLiteral__': 0, 'data': '1.59394266659421640919546674373', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10030743
{'Lhash': '2020562378037542968463336087783', 'Lhash_array': ['2020562378037542968463336087783'], 'label': '2-2-1.1-c19-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/20/a/a'}
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id: 24549771
{'Lhash': '2020562378037542968463336087783', 'Lhash_array': ['2020562378037542968463336087783'], 'label': '2-2-1.1-c19-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/20/a/a/1/1'}