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{'Lhash': '1769704714368739015981050240371,2201261570309892404890784622168,2297714212170065550586331483051,2670140577627241911972521242922,2699739505423796369439183921323', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -5, 'a8': 0, 'a9': -5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64728.415412762755, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 5, 10, 10, 5, 1]], [41, [1, -5, 10, -10, 5, -1]]], 'bad_primes': [2, 7, 41], 'central_character': '1148.1', 'coefficient_field': '1.1.1.1', 'conductor': 1993927854291968, 'conductor_radical': 574, 'degree': 10, 'euler_factors': [[1], [1, 2, 9, 16, 43, 59, 129, 144, 243, 162, 243], [1, 1, 16, 12, 127, 78, 635, 300, 2000, 625, 3125], [1, 5, 10, 10, 5, 1], [1, 2, 26, -10, 165, -728, 1815, -1210, 34606, 29282, 161051], [1, 1, 42, 4, 835, -131, 10855, 676, 92274, 28561, 371293], [1, 3, 56, 126, 1591, 3013, 27047, 36414, 275128, 250563, 1419857], [1, 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'4.42444775792775362180891023345518', '4.80117664371586015201548189837774', '5.11610541204964368398134841012338', '5.28817945300475455619323261393955', '5.29698381822689661785406536059001', '5.32067625999185495944569383974093', '5.90724539023125577759734534227310', '5.95967165021279489441086033901817', '6.05208525202265636199626020314295', '6.08292868938176301936981923247204', '6.13683345106680733233481946381461', '6.46950604836696087496423643144348', '6.62575798706271388719909980404654', '6.85715830092295999715027798375148', '6.97360024574155631895039442100173', '7.27796473910464256477323047123547', '7.59973106546992877440836095562660', '7.62383696023153298735126613388504', '7.69315626206760798510625186312771', '7.82740522116348636256908891488826', '7.85764476520480963629881409361248', '8.465458083015742341022419535424058', '8.492984645427314151263814567560129', '8.678248766289668269053567353988395', '8.682054597072575873915607896095190', '8.743018333029702541292137028428600', '9.237217540725257050599826072479221', '9.262182512388823240674563031203475', '9.352432201813224220589143961553679', '9.611390996742926292863363422752614', '9.651848276248134853251806835071784'], 'prelabel': '10-1148e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.027676692125993, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e5-0', 'trace_hash': 1197236871529083012, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39605086295081559782390318399', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73648919498288764681241678112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.81257691335166189049675046466', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64728.415412762755, 'bad_primes': [2, 7, 41], 'central_character': '1.1', 'conductor': 1993927854291968, 'conductor_radical': 574, 'degree': 10, 'dirichlet_coefficients': [1, 0, -2, 0, -1, 0, -5, 0, -5, 0, -2, 0, -1, 0, 2, 0, -3, 0, -4, 0, 10, 0, -8, 0, -15, 0, 12, 0, -9, 0, -11, 0, 4, 0, 5, 0, -11, 0, 2, 0, 5, 0, -27, 0, 5, 0, -3, 0, 15, 0, 6, 0, -19, 0, 2, 0, 8, 0, -15, 0, 0, 0, 25, 0, 1, 0, -21, 0, 16, 0, -16, 0, -10, 0, 30, 0, 10, 0, -14, 0, 10, 0, -2, 0, 3, 0, 18, 0, 6, 0, 5, 0, 22, 0, 4, 0, 20, 0, 10, 0], 'euler11': [1, 2, 26, -10, 165, -728, 1815, -1210, 34606, 29282, 161051], 'euler13': [1, 1, 42, 4, 835, -131, 10855, 676, 92274, 28561, 371293], 'euler17': [1, 3, 56, 126, 1591, 3013, 27047, 36414, 275128, 250563, 1419857], 'euler19': [1, 4, 39, 48, 441, -365, 8379, 17328, 267501, 521284, 2476099], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 8, 83, 574, 3355, 18011, 77165, 303646, 1009861, 2238728, 6436343], 'euler29': [1, 9, 68, 24, -1301, -16106, -37729, 20184, 1658452, 6365529, 20511149], 'euler3': [1, 2, 9, 16, 43, 59, 129, 144, 243, 162, 243], 'euler31': [1, 11, 112, 656, 5003, 25610, 155093, 630416, 3336592, 10158731, 28629151], 'euler37': [1, 11, 145, 663, 4956, 12852, 183372, 907647, 7344685, 20615771, 69343957], 'euler41': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler43': [1, 27, 382, 3986, 34437, 248301, 1480791, 7370114, 30371674, 92307627, 147008443], 'euler47': [1, 3, 167, 461, 13280, 29348, 624160, 1018349, 17338441, 14639043, 229345007], 'euler5': [1, 1, 16, 12, 127, 78, 635, 300, 2000, 625, 3125], 'euler53': [1, 19, 298, 2774, 25329, 175326, 1342437, 7792166, 44365346, 149919139, 418195493], 'euler59': [1, 15, 316, 3050, 36379, 253030, 2146361, 10617050, 64899764, 181760415, 714924299], 'euler61': [1, 0, 190, -30, 18957, -5364, 1156377, -111630, 43126390, 0, 844596301], 'euler67': [1, 21, 310, 3174, 31197, 258962, 2090199, 14248086, 93236530, 423173541, 1350125107], 'euler7': [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], 'euler71': [1, 16, 338, 4312, 46713, 451448, 3316623, 21736792, 120973918, 406586896, 1804229351], 'euler73': [1, 10, 222, 2492, 25941, 257572, 1893693, 13279868, 86361774, 283982410, 2073071593], 'euler79': [1, 14, 315, 3176, 45082, 346676, 3561478, 19821416, 155307285, 545301134, 3077056399], 'euler83': [1, 2, 114, 338, 12089, 78912, 1003387, 2328482, 65183718, 94916642, 3939040643], 'euler89': [1, -6, 305, -1284, 45117, -153431, 4015413, -10170564, 215015545, -376453446, 5584059449], 'euler97': [1, -20, 207, -2236, 33747, -423407, 3273459, -21038524, 188923311, -1770585620, 8587340257], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 9, 16, 43, 59, 129, 144, 243, 162, 243], [1, 1, 16, 12, 127, 78, 635, 300, 2000, 625, 3125], [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], [1, 2, 26, -10, 165, -728, 1815, -1210, 34606, 29282, 161051], [1, 1, 42, 4, 835, -131, 10855, 676, 92274, 28561, 371293], [1, 3, 56, 126, 1591, 3013, 27047, 36414, 275128, 250563, 1419857], [1, 4, 39, 48, 441, -365, 8379, 17328, 267501, 521284, 2476099], [1, 8, 83, 574, 3355, 18011, 77165, 303646, 1009861, 2238728, 6436343], [1, 9, 68, 24, -1301, -16106, -37729, 20184, 1658452, 6365529, 20511149], [1, 11, 112, 656, 5003, 25610, 155093, 630416, 3336592, 10158731, 28629151], [1, 11, 145, 663, 4956, 12852, 183372, 907647, 7344685, 20615771, 69343957], [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], [1, 27, 382, 3986, 34437, 248301, 1480791, 7370114, 30371674, 92307627, 147008443], [1, 3, 167, 461, 13280, 29348, 624160, 1018349, 17338441, 14639043, 229345007], [1, 19, 298, 2774, 25329, 175326, 1342437, 7792166, 44365346, 149919139, 418195493], [1, 15, 316, 3050, 36379, 253030, 2146361, 10617050, 64899764, 181760415, 714924299], [1, 0, 190, -30, 18957, -5364, 1156377, -111630, 43126390, 0, 844596301], [1, 21, 310, 3174, 31197, 258962, 2090199, 14248086, 93236530, 423173541, 1350125107], [1, 16, 338, 4312, 46713, 451448, 3316623, 21736792, 120973918, 406586896, 1804229351], [1, 10, 222, 2492, 25941, 257572, 1893693, 13279868, 86361774, 283982410, 2073071593], [1, 14, 315, 3176, 45082, 346676, 3561478, 19821416, 155307285, 545301134, 3077056399], [1, 2, 114, 338, 12089, 78912, 1003387, 2328482, 65183718, 94916642, 3939040643], [1, -6, 305, -1284, 45117, -153431, 4015413, -10170564, 215015545, -376453446, 5584059449], [1, -20, 207, -2236, 33747, -423407, 3273459, -21038524, 188923311, -1770585620, 8587340257]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1148/2/a/c'], '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': '10-1148e5-1.1-c1e5-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 5, 'prelabel': '10-1148e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.027676692125993, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 1197236871529083012, 'z1': {'__RealLiteral__': 0, 'data': '1.39605086295081559782390318399', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1769704714368739015981050240371,2201261570309892404890784622168,2297714212170065550586331483051,2670140577627241911972521242922,2699739505423796369439183921323', 'Lhash_array': ['1769704714368739015981050240371', '2201261570309892404890784622168', '2297714212170065550586331483051', '2670140577627241911972521242922', '2699739505423796369439183921323'], 'label': '10-1148e5-1.1-c1e5-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1148/2/a/c'}