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lfunc_lfunctions • Show schema
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{'Lhash': '2437938271250236256185445076189', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-4.582907174201562e-80, 2.6459426906140066e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.30343152768086545, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 19], 'central_character': '608.463', 'coefficient_field': 'CDF', 'conductor': 608, 'conductor_radical': 38, 'conjugate': '1427193086787651771754625026299', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 1.7320508075688772], 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'3.83026987453406008490100688988183', '4.29070765762225192662841796840800', '5.61262967968093306371810311304277', '6.30017884713119662982360887260023', '7.50191829759378837732288657574188', '8.592155664383104785485620073556341', '9.369956775774070160574742727136722', '10.41801524758241042228149675412161', '10.72838366275460956136030641639198'], 'prelabel': '2-608-152.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5508461923993534, 'root_angle': 0.40108662139561013, 'root_number': '0.30576855776155245201166452061865 + 0.95210587073309245599954997573793*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20054331069780507', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92319419153140999332962519896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.83026987453406008490100688988', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29070765762225192662841796841', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.30343152768086545, 'bad_primes': [2, 19], 'central_character': '152.83', 'conductor': 608, 'conductor_radical': 38, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/608/1/o/a/463/1', 'ArtinRepresentation/2.608.12t18.a.b'], 'is_instance_Artin': True, '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': '2-608-152.83-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-608-152.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5508461923993534, 'root_angle': 0.20054331069780507, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92319419153140999332962519896', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603440
{'Lhash': '2437938271250236256185445076189', 'Lhash_array': ['2437938271250236256185445076189'], 'label': '2-608-152.83-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.608.12t18.a.b'}
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id: 19803185
{'Lhash': '2437938271250236256185445076189', 'Lhash_array': ['2437938271250236256185445076189'], 'label': '2-608-152.83-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/608/1/o/a/463/1'}