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lfunc_lfunctions • Show schema
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{'Lhash': '1918907802808503037605392692236', 'a10': [1.8378518563174846, -7.575728533787891], 'a2': [-0.6476442804977874, 1.8712452577090462], 'a3': [0.4582265217274104, 0.8888354486549235], 'a4': [-1.510009510951523, -1.1874846046865337], 'a5': [-3.918978010125827, 0.374217027111893], 'a6': [-1.9599969041483705, 0.28180501111388195], 'a7': [-1.0194112910543813, -2.4414750909380256], 'a8': [-0.13159576651938912, 0.08457146390256615], 'a9': [-0.5800569095711982, 0.8145759520503357], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.4582265217274104, -0.8888354486549235]]], [7, [[1.0, 0], [1.0194112910543813, 2.4414750909380256]]], [23, [[1.0, 0], [4.152033769919393, 2.4001282410423292]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.10', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '191508760297222592872289631978', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6476442804977874, -1.8712452577090462], [-1.572106189485575, -1.2363179724412103]], [[1.0, 0], [-0.4582265217274104, -0.8888354486549235]], [[1.0, 0], [3.918978010125827, -0.374217027111893], [4.909643486313533, -0.946256221802051]], [[1.0, 0], [1.0194112910543813, 2.4414750909380256]], [[1.0, 0], [-0.6456598485071859, 0.2234650462359461], [8.646584042170662, -6.799748848426657]], [[1.0, 0], [0.09765922289730289, 0.3325967691811853], [-10.936295926805355, 7.028330626922768]], [[1.0, 0], [-5.854825337722745, -2.343918488665279], [12.303478647786193, 11.731343195195905]], [[1.0, 0], [-1.616026747862088, 0.6469595169793507], [13.750946723996334, -13.111501218160127]], [[1.0, 0], [4.152033769919393, 2.4001282410423292]], [[1.0, 0], [0.9512967391453557, 6.616414152045888], [-27.825296234820424, 8.170244148401462]], [[1.0, 0], [4.911056991892171, -0.23394247787192993], [30.859629599765622, -2.9467373424296626]], 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[-3.7589713500756416, -78.91051979545763]], [[1.0, 0], [-5.090210942932103, -11.146007226209003], [-54.35344091745866, 62.72721467140344]], [[1.0, 0], [-0.12264537947429525, 2.574643364768672], [-88.59700110900452, -8.459987854072256]], [[1.0, 0], [6.549592231588107, -14.34160649930793], [-63.52149119269265, -73.30770871236305]], [[1.0, 0], [-1.0641945739191836, 11.144749788302617], [-99.17479842353337, -19.11437568040143]], [[1.0, 0], [4.0937472550481955, 0.7890051123616438], [95.62189710065547, 38.28123293301373]], [[1.0, 0], [-4.515332699417383, 8.758523514927358], [-62.0660893241182, -87.15962686938592]], [[1.0, 0], [-1.7553601072047507, 4.384677573981], [-78.88701015345265, -75.21861225155021]], [[1.0, 0], [-2.233400648636275, 1.9352526783882085], [16.08157672488122, -111.8498229325454]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-483-161.10-c1-0-19', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'2-483-161.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.18959985788385728, 'root_number': '0.8277865063459567 + 0.5610432246374207*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0947999289419', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51375134635917852585799959433', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17877649324743354382070619068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54206938507907269719791250968', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.10', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/10/5'], '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': '2-483-161.10-c1-0-19', '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': '2-483-161.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.09479992894192864, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51375134635917852585799959433', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1918907802808503037605392692236', 'Lhash_array': ['1918907802808503037605392692236'], 'label': '2-483-161.10-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/10/5'}