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lfunc_lfunctions • Show schema
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'4.68954254266858276279153071484569', '4.79391552263049069350081814569402', '4.80650297588467911747471524277852', '4.98383271797200123410532718372902', '5.12928294542882860652224217036446', '5.22899383114757614988045080719290', '5.32510307057814176720504526284212', '5.33746129542759409571953983880619', '5.39007694828148216289383228204038', '5.42933908728814879429013241725998', '5.71813219199148239867824515324077', '5.77996744896745212920392526647606', '5.82786902576711212135022154322758', '5.84633195006964052566540328967410', '5.89579057582780277381386422847671', '5.90885888452560631799178766528931', '5.91643966784355181435198118612524', '5.95437757061062299443747930336912', '6.24186231166216856208935413325964', '6.28758373854628865851792124571424', '6.32696473746518120507532525088879', '6.58308838388530123020309072349577', '6.61461363749700636128026995644009', '6.68697458908359533098745691365401', '6.72246849290892621464857911290897', '6.77141874264901820334812465432420', '6.88975705732638493328476624998250', '6.94370562971621409427536839056074', '7.05436312138060520180361610551037', '7.09310568123105913070308665772798', '7.45489338917912534227865401219958', '7.46107253766175738321934486581719', '7.50351884156608635540842139629152', '7.69728010616554460252419572770034', '7.73036405396747696469752259592172', '7.84256512378271421918596021570069'], 'prelabel': '16-91e16-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.131673746149824, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e8-0', 'trace_hash': 1718017626535124952, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.819433988137413312919178915922', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.955618115093120839516226605488', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.03453572755467412603791511356', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 365493058554671.1, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 22113743972843938840712550613441, 'conductor_radical': 91, 'degree': 16, 'dirichlet_coefficients': [1, 4, 0, 6, 0, 0, 0, -4, -10, 0, -4, 0, 0, 0, 0, -35, 0, -40, 0, 0, 0, -16, -12, 0, -26, 0, 0, 0, -8, 0, 0, -60, 0, 0, 0, -60, -8, 0, 0, 0, 0, 0, -32, -24, 0, -48, 0, 0, 0, -104, 0, 0, -4, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -14, 0, 0, 20, 0, 0, 0, 8, 40, 0, -32, 0, 0, 0, 0, -4, 0, 33, 0, 0, 0, 0, -128, 0, 16, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 40, -156], 'euler11': [1, 4, 82, 264, 2959, 7844, 62388, 136520, 845485, 1501720, 7548948, 10440364, 43322719, 42517464, 145268002, 77948684, 214358881], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, 0, 78, 0, 3142, 0, 85520, 0, 1694711, 0, 24715280, 0, 262422982, 0, 1882730382, 0, 6975757441], 'euler19': [1, 0, 58, 0, 1703, 0, 44478, 0, 996825, 0, 16056558, 0, 221936663, 0, 2728661098, 0, 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[[1, -4, 10, -12, 7, 4, 18, -80, 169, -160, 72, 32, 112, -384, 640, -512, 256], [1, 0, 10, 0, 67, 0, 306, 0, 1057, 0, 2754, 0, 5427, 0, 7290, 0, 6561], [1, 0, 26, 0, 311, 0, 2358, 0, 13281, 0, 58950, 0, 194375, 0, 406250, 0, 390625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 82, 264, 2959, 7844, 62388, 136520, 845485, 1501720, 7548948, 10440364, 43322719, 42517464, 145268002, 77948684, 214358881], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 78, 0, 3142, 0, 85520, 0, 1694711, 0, 24715280, 0, 262422982, 0, 1882730382, 0, 6975757441], [1, 0, 58, 0, 1703, 0, 44478, 0, 996825, 0, 16056558, 0, 221936663, 0, 2728661098, 0, 16983563041], [1, 12, 192, 1652, 15640, 103876, 719776, 3808732, 20685022, 87600836, 380761504, 1263859292, 4376713240, 10632838636, 28422890688, 40857905364, 78310985281], [1, 8, 78, 564, 6019, 34136, 231376, 1287216, 8857933, 37329264, 194587216, 832542904, 4257124339, 11568288036, 46396219038, 137999010472, 500246412961], [1, 0, 178, 0, 15406, 0, 835752, 0, 30991415, 0, 803157672, 0, 14227764526, 0, 157975655218, 0, 852891037441], [1, 8, 140, 592, 7168, 21264, 368548, 1445592, 18225486, 53486904, 504542212, 1077085392, 13433986048, 41051622544, 359201697260, 759455017064, 3512479453921], [1, 0, 152, 0, 6780, 0, -92120, 0, -15043642, 0, -154853720, 0, 19158659580, 0, 722015844632, 0, 7984925229121], [1, 32, 570, 7064, 70487, 619168, 5096592, 39067600, 271718389, 1679906800, 9423598608, 49228190176, 240981026087, 1038467641352, 3603176937930, 8698195555424, 11688200277601], [1, 0, 150, 0, 11494, 0, 707936, 0, 37180919, 0, 1563830624, 0, 56087053414, 0, 1616882299350, 0, 23811286661761], [1, 4, 268, 1024, 35706, 126340, 3137936, 9836596, 196115459, 521339588, 8814462224, 18809120180, 281737514586, 428232184832, 5940048782572, 4698844559348, 62259690411361], [1, 0, 278, 0, 36286, 0, 3136752, 0, 207469775, 0, 10919033712, 0, 439690561246, 0, 11726188352198, 0, 146830437604321], [1, 0, 380, 0, 67856, 0, 7443748, 0, 547986382, 0, 27698186308, 0, 939523386896, 0, 19577742257180, 0, 191707312997281], [1, -20, 624, -8816, 156098, -1693444, 21488928, -184739596, 1813198579, -12377552932, 96463797792, -509325297772, 3145549685858, -11902702943312, 56446030473456, -121214232106460, 406067677556641], [1, -8, 252, -2112, 43856, -321792, 4843124, -32159336, 410605134, -2283312856, 24414188084, -115172896512, 1114454681936, -3810532389312, 32281271548092, -72760961267128, 645753531245761], [1, 0, 156, 0, 7232, 0, 147460, 0, 11253390, 0, 785814340, 0, 205376078912, 0, 23608139301084, 0, 806460091894081], [1, 4, 80, -324, 3864, -48948, 583888, 689300, 111660830, 54454700, 3644045008, -24133272972, 150503112984, -996966273276, 19446996441680, 76815635944636, 1517108809906561], [1, 0, 314, 0, 46430, 0, 4837464, 0, 427877847, 0, 33325289496, 0, 2203489844030, 0, 102659277237866, 0, 2252292232139041], [1, 0, 106, 0, 17871, 0, 2077238, 0, 155830553, 0, 16453802198, 0, 1121266588911, 0, 52680016841866, 0, 3936588805702081], [1, 0, 412, 0, 82235, 0, 11265530, 0, 1213308829, 0, 105997371770, 0, 7280205423035, 0, 343184466030748, 0, 7837433594376961]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8281/2/a/cl'], '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': '16-91e16-1.1-c1e8-0-3', '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}, {'__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, 1, 1, 1], 'order_of_vanishing': 8, 'prelabel': '16-91e16-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.131673746149824, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 1718017626535124952, 'z1': {'__RealLiteral__': 0, 'data': '0.819433988137413312919178915922', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1038755986909803797248643338875,1211389877186763838552358975488,1311429835992230658603198398941,1388704671509192551478795325102,1910264148291608956259853414571,2138558317060995651372336611866,2212022805594200049364938670159,2395807971904914989388713955816', 'Lhash_array': ['1038755986909803797248643338875', '1211389877186763838552358975488', '1311429835992230658603198398941', '1388704671509192551478795325102', '1910264148291608956259853414571', '2138558317060995651372336611866', '2212022805594200049364938670159', '2395807971904914989388713955816'], 'factors': ['2-91e2-1.1-c1-0-216', '2-91e2-1.1-c1-0-271', '2-91e2-1.1-c1-0-303', '2-91e2-1.1-c1-0-323', '2-91e2-1.1-c1-0-433', '2-91e2-1.1-c1-0-469', '2-91e2-1.1-c1-0-476', '2-91e2-1.1-c1-0-490'], 'label': '16-91e16-1.1-c1e8-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8281/2/a/cl'}