-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '619788639481879510437064072619', 'a10': [-3708.7734142511054, -8953.771076453788], 'a2': [11.38452499666966, -11.38452499666966], 'a3': [-244.37567199548872, -101.22371765457038], 'a4': [0.0, 252.7851812004074], 'a5': [230.35645596706993, -556.129680175901], 'a6': [-3934.4848903048755, 1629.7170025162984], 'a7': [406.47837693441585, 981.3256104064698], 'a8': [8706.716012458573, 8706.716012458573], 'a9': [35555.24527333969, 35555.24527333969], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.755609214785846, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-38251.66246974862, -342234.84161508223]]]], 'bad_primes': [17], 'central_character': '17.9', 'coefficient_field': 'CDF', 'conductor': 17, 'conductor_radical': 17, 'conjugate': '2107470047327339106193079398676', 'degree': 2, 'euler_factors': [[[1.0, 0], [-11.38452499666966, 11.38452499666966], [0, -512.0]], [[1.0, 0], [244.37567199548872, 101.22371765457038], [13917.982774094815, 13917.982774094815]], [[1.0, 0], [-230.35645596706993, 556.129680175901], [-1381067.9320049756, -1381067.9320049756]], [[1.0, 0], [-406.47837693441585, -981.3256104064698], [-28534309.155036934, 28534309.155036934]], [[1.0, 0], [16492.665528376645, -6831.485741536834], [1667320801.9892619, -1667320801.9892619]], [[1.0, 0], [0, -37747.46400885021], [-10604499373.0, 0]], [[1.0, 0], [-38251.66246974862, -342234.84161508223]], [[1.0, 0], [121753.2140414616, -121753.2140414616], [0, -322687697779.0]], [[1.0, 0], [2329782.8091742173, -965027.6369436492], [1273607260872.6853, -1273607260872.6853]], [[1.0, 0], [-1215225.4499136007, 2933813.7625223612], [-10258101295200.104, -10258101295200.104]], [[1.0, 0], [-6184875.160267054, -2561859.1729670838], [18695636121820.582, 18695636121820.582]], [[1.0, 0], [12559905.810257649, 5202483.328737356], [91896827503900.53, 91896827503900.53]], [[1.0, 0], [-9845358.736566037, -23768798.588246167], [-231493985847939.25, 231493985847939.25]], [[1.0, 0], [-11535287.674100995, -11535287.674100995], [0, 502592611936843.0]], [[1.0, 0], [0, -4008666.5702277124], [-1119130473102767.0, 0]], [[1.0, 0], [69612537.98882526, -69612537.98882526], [0, -3299763591802133.0]], [[1.0, 0], [57346437.53409849, 57346437.53409849], [0, 8662995818654939.0]], [[1.0, 0], [-33375393.016454075, -80575326.46985571], [-8269010002429191.0, 8269010002429191.0]], [[1.0, 0], [158490152.08317825, 0], [27206534396294948, 0]], [[1.0, 0], [224828354.58536863, 93126953.67528692], [32419785765251604, 32419785765251604]], [[1.0, 0], [-142014500.74222422, 342853333.7455217], [-41628498180628056, -41628498180628056]], [[1.0, 0], [155554054.58179492, -64432599.089904144], [84747876255339790, -84747876255339790]], [[1.0, 0], [-388859626.6859207, 388859626.6859207], [0, -186940255267540400]], [[1.0, 0], [0, 154694897.04911652], [-350356403707485200, 0]], [[1.0, 0], [298031613.7941339, -719511964.0377384], [-537564536843271040, -537564536843271040]], [[1.0, 0], [-63914425.33952178, 0], [1093685272684361000, 0]], [[1.0, 0], [602387170.9389575, 0], [1304773183829244700, 0]], [[1.0, 0], [-223017265.63850546, 538411307.3478432], [-1299986976037170700, -1299986976037170700]], [[1.0, 0], [-834500249.5135194, -2014661820.1792703], [-1535760465907146200, 1535760465907146200]], [[1.0, 0], [-873654366.9200816, 361879487.60477805], [2124178425317454000, -2124178425317454000]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-17-17.9-c9-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/17/10/d/a/9/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.903451039917422, 0.6305277631947009, 0.2970274076153936, -0.0880409922081282, -0.513958058920349, -0.9684829565858805, -1.4380834086029477, -1.908217895424695, -2.3636800008680874, -2.789012066965936, -3.168990750242031, -3.489180839498377, -3.736546031184136, -3.9000966591972843, -3.971545211190054, -3.9459315758324096, -3.8221722525579382, -3.60348222878708, -3.29761594939468, -2.9168757852946503, -2.4778435091251287, -2.000803071094866, -1.5088415720457655, -1.0266393294679956, -0.5789882406733988, -0.18910846675790208, 0.12313570603840375, 0.34299221897826265, 0.46240002082818193, 0.4812294779677607, 0.40802608231961207, 0.26011763902965285, 0.06298104745077265, -0.1511821384226992, -0.34564423370265257, -0.4820284939105116, -0.5236868874905227, -0.4393228291371561, -0.20653913626798176, 0.18504890850109584, 0.7315034549633518, 1.4133939025690108, 2.1960302656334787, 3.0312495271052065, 3.8607559903670277, 4.620845977310161, 5.2481712080230105, 5.686034281343979, 5.890585844592551, 5.836227195332835, 5.519531038032675, 4.961086743573592, 4.204855008772075, 3.3148693927607042, 2.369426411274328, 1.4532290216517252, 0.648250409918158, 0.024323112445470783, -0.36940744119254687, -0.5110270770350192, -0.409409732488016, -0.10410381495295362, 0.3387089303327516, 0.8339339109516621, 1.2881940944529833, 1.612136289216127, 1.732844765347109, 1.6046520961971196, 1.2167295931997866, 0.5961766970169126, -0.19411563727990822, -1.062840620048229, -1.9021289388168723, -2.6023947629380513, -3.0681345297022324, -3.232355038121728, -3.0673649041730644, -2.5900832953888044, -1.8607659789371092, -0.9750274721154578, -0.050107984293926496, 0.79267543739337, 1.4466154887903406, 1.8364200148658758, 1.93026473534885, 1.7448709374690257, 1.3424632770782028, 0.8198128201022915, 0.2909746752498535, -0.13345912678830474, -0.3669860820984764, -0.3639111278208598, -0.12886797997527674, 0.28300193080452607, 0.7757374467677017, 1.2308040012880772, 1.5308746832382325, 1.5848607249700546, 1.349373894168865, 0.8421592978823946, 0.1442811181200951, -0.6101973066902483, -1.2559508343828318, -1.6261538690607602, -1.5850641416686853, -1.0573091607287963, -0.04797363226084312, 1.3510212802047765, 2.9703831503826996, 4.5879468382048785, 5.964424183725859, 6.884222058526757, 7.19383458963606, 6.830423535227857, 5.834788630649807, 4.345755741972602, 2.5765619213366096, 0.7773987199307995, -0.8088517032602512, -1.98912008471542, -2.65251263126446, -2.7860911213683313, -2.47097627112213, -1.8597700674766744, -1.140266187838007, -0.4934013153655298, -0.054701074890512666, 0.11225501029367412, 0.024489507749010948, -0.23139622846935418, -0.5271532859785296, -0.7309110078614078, -0.7459369306588556, -0.5403768074051999, -0.16016109234419668, 0.278827729774867, 0.6182125251052822, 0.6981232242175691, 0.4019633899928392, -0.3063022497927055, -1.3623394095271346, -2.605327814188644, -3.806217725539243, -4.715036851752145, -5.116909084189981, -4.883712965403399, -4.008655766338479, -2.6145444047199535, -0.9324899992365107, 0.7451681691869151, 2.1274924988819093, 2.9887068354493525, 3.2178626768426386, 2.8421392294692165, 2.0176270549799145, 0.9893273046394891, 0.029815913119154706, -0.628394848102347, -0.8498252282140638, -0.6276942829957433, -0.08182534464855411, 0.5771154158311536, 1.1081621654430114, 1.309747407054548, 1.0800788294061083, 0.45165372954943783, -0.4102509038378358, -1.245982716508141, -1.7678458705969073, -1.7376155467032746, -1.0349218683211356, 0.3020681573373675, 2.0754798655363382, 3.967752992147579, 5.613668050654149, 6.686486460680416, 6.976192890154749, 6.439523772890289, 5.208655644757668, 3.5562691290567296, 1.8263014938038618, 0.3488750481542442, -0.6379354728113117, -1.0388873616581857, -0.9120820097304341, -0.4377618802881084, 0.1442753948697133, 0.6095234204754849, 0.8135256212390735, 0.7275429461045253, 0.4351395071011003, 0.09176911353312064, -0.13899976786488466, -0.15146874516321504, 0.05622141738362179, 0.3724775872294848, 0.6040844500067242, 0.5412425165836826, 0.0362513207052312, -0.9294309531928855, -2.2130517504605844, -3.527227985962755, -4.504932446092852, -4.797216332300537, -4.176827918258374, -2.6171504901001326, -0.32120561437834805, 2.311296394612973, 4.773337866266543, 6.574124825524419, 7.363568279789671, 7.0229492530224205, 5.6955993238992395, 3.7479656002502035, 1.671207143177111, -0.04933035509923289, -1.0599909031674084, -1.2245836139345418, -0.6464324032913796, 0.3780328132866764, 1.4585834442328323, 2.2323218517197736, 2.469596979964285, 2.1331289390678916, 1.3739563797748153, 0.46797957141684865, -0.2843761714875768, -0.661485928972373, -0.5926254385636748, -0.1754732350179589, 0.36586126154958837, 0.7670589336005816, 0.8237864386720911, 0.4706646314783155, -0.18921206148987557, -0.9157122424146831, -1.4145993014022216, -1.4443118159099149, -0.9098007939250153, 0.09012166324313028, 1.2805969401897783, 2.2906181995323496, 2.770515473230738, 2.5087687221986723, 1.508712929406475, -0.002105043635112183, -1.6353383844466391, -2.959141917732268, -3.6319056087958654, -3.508588028205432, -2.6841407275470304, -1.4590629050958859, -0.23816791967087286, 0.6036183453626879, 0.8430599754194991, 0.47651557639844266, -0.2892754932302007], 'positive_zeros': ['0.48892702718737480788990845257587', '4.49503138394798039662728931426951', '5.67684614318556796160955415049731', '6.78114232699368646938169525452485', '10.02792520902196227726701045216304', '10.76794921961943713466115157108840', '12.26389053448711748829488993374964', '14.07227490242427214734983341955188', '15.58174062704935483107150350045370', '16.23367863859724204602837325529667'], 'prelabel': '2-17-17.9-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9589878699964025, 'root_angle': -0.3002415648924236, 'root_number': '0.5871711213141884 - 0.8094628307060422*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.150120782446', 'prec': 50}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48892702718737480788990845258', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.49503138394798039662728931427', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.67684614318556796160955415050', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.755609214785846, 'bad_primes': [17], 'central_character': '17.9', 'conductor': 17, 'conductor_radical': 17, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/17/10/d/a/9/8'], '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': '2-17-17.9-c9-0-1', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-17-17.9-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9589878699964025, 'root_angle': -0.1501207824462118, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48892702718737480788990845258', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '619788639481879510437064072619', 'Lhash_array': ['619788639481879510437064072619'], 'label': '2-17-17.9-c9-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/17/10/d/a/9/8'}