-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '871891016964277294315530308478,983964080130495954399878965994,1870438942618016961894588738353,1983805728058825509447659459977', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24077.246635059513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 3, -2, 1]], [5, [1, -4, 6, -4, 1]], [13, [1, -10, 51, -130, 169]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1', 'coefficient_field': '1.1.1.1', 'conductor': 5922408960000, 'conductor_radical': 390, 'degree': 8, 'euler_factors': [[1], [1, -2, 3, -2, 1], [1, -4, 6, -4, 1], [1, 2, -11, 2, 148, 14, -539, 686, 2401], [1, -1, -7, 14, -68, 154, -847, -1331, 14641], [1, -10, 51, -130, 169], [1, 0, -34, 0, 867, 0, -9826, 0, 83521], [1, 3, -17, -36, 144, -684, -6137, 20577, 130321], [1, -2, 14, 112, -521, 2576, 7406, -24334, 279841], [1, -6, 26, 288, -1785, 8352, 21866, -146334, 707281], [1, 14, 169, 1274, 8560, 39494, 162409, 417074, 923521], [1, -7, -23, 14, 2002, 518, -31487, -354571, 1874161], [1, 2, -22, -112, -1169, -4592, -36982, 137842, 2825761], [1, 7, -35, -14, 3100, -602, -64715, 556549, 3418801], [1, -2, 161, -254, 10912, -11938, 355649, -207646, 4879681], [1, -22, 365, -3850, 33328, -204050, 1025285, -3275294, 7890481], [1, 14, 86, -112, -2945, -6608, 299366, 2875306, 12117361], [1, 1, -107, -14, 7882, -854, -398147, 226981, 13845841], [1, -3, -113, 36, 9792, 2412, -507257, -902289, 20151121], [1, -4, -130, -16, 15139, -1136, -655330, -1431644, 25411681], [1, -2, 37, -182, 11128, -13286, 197173, -778034, 28398241], [1, 18, 409, 4374, 52176, 345546, 2552569, 8874702, 38950081], [1, -8, -100, -200, 19798, -16600, -688900, -4574296, 47458321], [1, -19, 107, -1444, 24466, -128516, 847547, -13394411, 62742241], [1, -7, -29, 812, -8078, 78764, -272861, -6388711, 88529281], [1, 2, -142, -112, 10711, -11312, -1448542, 2060602, 104060401], [1, 32, 682, 10112, 119323, 1041536, 7235338, 34967264, 112550881], [1, 0, 14, 0, -11253, 0, 160286, 0, 131079601], [1, 10, 217, 2050, 38428, 223450, 2578177, 12950290, 141158161], [1, -26, 338, -2912, 25087, -329056, 4315922, -37515322, 163047361]], 'euler_factors_factorization': [[1], [[[1, -1, 1], 2]], [[[1, -1], 4]], [[[1, -4, 7], 2], [[1, 5, 7], 2]], [[[1, -1, -7, 14, -68, 154, -847, -1331, 14641], 1]], [[[1, -5, 13], 2]], [[[1, 0, -17, 0, 289], 2]], [[[1, 3, -17, -36, 144, -684, -6137, 20577, 130321], 1]], [[[1, -2, 14, 112, -521, 2576, 7406, -24334, 279841], 1]], [[[1, -6, 26, 288, -1785, 8352, 21866, -146334, 707281], 1]], [[[1, 7, 60, 217, 961], 2]], [[[1, -7, -23, 14, 2002, 518, -31487, -354571, 1874161], 1]], [[[1, 2, -22, -112, -1169, -4592, -36982, 137842, 2825761], 1]], [[[1, 7, -35, -14, 3100, -602, -64715, 556549, 3418801], 1]], [[[1, -1, 80, -47, 2209], 2]], [[[1, -11, 122, -583, 2809], 2]], [[[1, 14, 86, -112, -2945, -6608, 299366, 2875306, 12117361], 1]], [[[1, 1, -107, -14, 7882, -854, -398147, 226981, 13845841], 1]], [[[1, -3, -113, 36, 9792, 2412, -507257, -902289, 20151121], 1]], [[[1, -2, -67, -142, 5041], 2]], [[[1, -1, 18, -73, 5329], 2]], [[[1, 9, 164, 711, 6241], 2]], [[[1, -4, -58, -332, 6889], 2]], [[[1, -19, 107, -1444, 24466, -128516, 847547, -13394411, 62742241], 1]], [[[1, -7, -29, 812, -8078, 78764, -272861, -6388711, 88529281], 1]], [[[1, 2, -142, -112, 10711, -11312, -1448542, 2060602, 104060401], 1]], [[[1, 16, 213, 1648, 10609], 2]], [[[1, 0, 14, 0, -11253, 0, 160286, 0, 131079601], 1]], [[[1, 5, 96, 545, 11881], 2]], [[[1, -26, 338, -2912, 25087, -329056, 4315922, -37515322, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 7, 'label': '8-1560e4-1.1-c1e4-0-7', 'leading_term': '12.4085465609538693646883846370385571848681396437890508783570477021284841497887055106954695', 'load_key': 'CMFs-workshop', '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1560/2/bg/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [12.408546560953868, 12.391902209746844, 12.361206598400747, 12.31329324395283, 12.245084425999766, 12.154682075070845, 12.04262798359932, 11.909981956429652, 11.757774686198239, 11.586699905487286, 11.396954961074666, 11.188689677691219, 10.96218371880408, 10.717858195021256, 10.456296505267698, 10.178173017575071, 9.884222559495722, 9.5752417147837, 9.252060447855586, 8.915591850654655, 8.56684042120153, 8.206894139189076, 7.836926023869227, 7.458200179619613, 7.072061687122979, 6.679933048873176, 6.283321645014008, 5.8838097324826775, 5.483041666586227, 5.082726512484385, 4.684641776282311, 4.290604576746977, 3.902460317189064, 3.522087553228969, 3.1513835744116947, 2.792234648544577, 2.4465081725873996, 2.116044367968022, 1.802634822226371, 1.507997232836087, 1.2337669528371236, 0.9814729062321411, 0.7525209525686612, 0.5481752074615616, 0.36954047004546775, 0.21754005692128459, 0.09290378449106941, -0.003845877296730288, -0.07241249512434375, -0.1127363528833551, -0.1250027372103148, -0.1096505378970541, -0.06737696150020299, 0.0008624482701605413, 0.09385010340871344, 0.21011304179006957, 0.3479343999580549, 0.505362936675969, 0.6802214202971804, 0.8701315879552413, 1.0725375606828054, 1.2847263913827807, 1.503855468084507, 1.7269881455724319, 1.9511243155499391, 2.173235073205402, 2.390304633629041, 2.5993670801919073, 2.7975406650615597, 2.9820700779767058, 3.150374899062722, 3.300078064940021, 3.4290366812396287, 3.5353792030393913, 3.6175527460951646, 3.6743340301177483, 3.704843545733378, 3.7085689391102385, 3.685402542546507, 3.6356235468723694, 3.559888077826906, 3.4592337953999186, 3.3350963518691255, 3.189259230387809, 3.0238201413823442, 2.8411741420314387, 2.644001089838518, 2.4351925515728174, 2.2178004644472793, 1.9949979166043967, 1.7700449414696853, 1.5462070129651853, 1.3266955738078146, 1.1146169762578162, 0.9129318551138155, 0.7243823576534643, 0.5514378897031086, 0.3962534303037289, 0.2606371733601861, 0.1460031802544789, 0.05334168896449147, -0.01679693076376051, -0.06431201085526893, -0.08956070765426488, -0.09335023597500336, -0.07692064524860712, -0.04192143978918622, 0.009623085546077355, 0.07535740774227923, 0.15264491686739498, 0.23862517145674095, 0.3302777885636293, 0.42448944230067087, 0.5181259164794699, 0.6081075423689879, 0.6914787331985035, 0.7654784416647833, 0.8276090840012388, 0.8757065603637301, 0.9079897500437458, 0.9231074221100913, 0.9201765682417485, 0.8988245769238549, 0.8591968897969348, 0.8019546012300869, 0.7282688641997754, 0.6398187010885803, 0.538743243113183, 0.4275875148490501, 0.30925245963527387, 0.18694386207572347, 0.06407877597990276, -0.05580066828446272, -0.16910906431554698, -0.27230319666796254, -0.36198502408520233, -0.434992069322397, -0.4884847985060288, -0.5200272045770823, -0.5276610901971904, -0.5099700180574888, -0.4661332472360577, -0.3959613614837713, -0.2999151750033809, -0.1791156490532791, -0.03533252747554134, 0.1290455196767616, 0.31105701052747364, 0.5072246144740261, 0.7136301239356485, 0.9260114827901247, 1.1398607482482024, 1.3505237479581937, 1.553313730003331, 1.7436553344869246, 1.9171881633510297, 2.069863048404914, 2.1980580670202188, 2.2987227184560695, 2.369424962172922, 2.408404649774026, 2.414651562367149, 2.3879817312780593, 2.3290001606810136, 2.239085053321755, 2.120385974398989, 1.9758006330095716, 1.8088594771756457, 1.6236371397691143, 1.4246546938617617, 1.2167855963292153, 1.005091902902687, 0.7946817415966078, 0.5905684409690134, 0.39755200625821185, 0.22005850159729579, 0.062002785455208514, -0.07331973198914739, -0.18332369550305008, -0.2662299984109349, -0.32112197323673486, -0.3479731206742805, -0.3476593835109845, -0.3219391196952931, -0.2734010366022038, -0.2053934250907144, -0.1219294453835069, -0.02756058016615727, 0.0727606875448884, 0.1738344586823363, 0.2703838194897991, 0.35722113836515196, 0.42941794328056926, 0.48247924039169104, 0.5125016216297972, 0.5163030328207387, 0.49155539040484, 0.43687890244245253, 0.3519092554118939, 0.2373356380025383, 0.09491421220843345, -0.07257377573189314, -0.2613848028578716, -0.46689096094423105, -0.6837163080954597, -0.905894203715739, -1.1270444204597785, -1.3405537621963606, -1.5397850013091816, -1.7182836216680057, -1.870009674896015, -1.9895255636750042, -2.0721660956073857, -2.114202606701785, -2.113033354214007, -2.0672531545742716, -1.9767021522176365, -1.8425086918048557, -1.667127218073642, -1.4542410110397408, -1.2086592222781989, -0.9362020892665603, -0.6435512505285912, -0.3380277902817905, -0.027376921493618787, 0.28046194644955186, 0.5776246048802445, 0.8565613155431617, 1.1102590792859885, 1.332471274027659, 1.5179810237915465, 1.66272537567844, 1.7638965777789017, 1.8200527706985876, 1.8312492997347507, 1.7989507596132028, 1.725944112108231, 1.6162702336465695, 1.4751540527395848, 1.3087198489450171, 1.1237472703671372, 0.9274545063321089, 0.7272718605148355, 0.5304901561989187, 0.343977035415398, 0.17393026152276328, 0.025647292973755887, -0.09672326395931863, -0.19035196396245277, -0.2538441039801097, -0.2873139854370824, -0.2924008698186174, -0.2722123981749692, -0.2312119915893141, -0.17505931086307372, -0.11037554279612552, -0.04446748464826647, 0.014977117565959416, 0.06022902453548571, 0.08387778494515268, 0.07918080815098257, 0.04040468594044538, -0.03683681257700963, -0.15531514608972077, -0.3159693665859861, -0.5177375128212504, -0.7574426755725303, -1.0297978453209795, -1.32747969374213, -1.6412841237730031, -1.9603502851144488, -2.272477436275032, -2.5645150411304507, -2.822804203492215, -3.033670847037072, -3.1839217085500313, -3.261375805345339, -3.2553649201880512, -3.1572625086614634, -2.9608963966688697, -2.662897118218119, -2.2629895677241363, -1.7642447246473116, -1.1731171229478021, -0.49938267609024867, 0.24398513871076852, 1.0410808331340695, 1.8735023567338718, 2.7208240212936983, 3.5611704879377677, 4.371997147144323, 5.130768877846364, 5.815649889137999, 6.406315667394074, 6.884898914798758, 7.236533334561881, 7.449920284241534, 7.517934891559867, 7.438279567758505, 7.213540195490207, 6.851260085964473, 6.363938464354518, 5.769085255759852, 5.088620983115683, 4.348256397828747, 3.576860942409614, 2.8058565875672894, 2.068090733544111, 1.39676018967252, 0.8244337599616813, 0.38206403679191764, 0.09780106582411591, -0.004002768733891348, 0.09634070292917793, 0.41304951440843785, 0.9542155377088207, 1.7213616661117823, 2.7091909733161192, 3.905531020120938, 5.291487336386887, 6.841808023002694, 8.525533276595976, 10.306830394401821, 12.145830819858649, 13.999741412077572, 15.824100196509796, 17.574221432215886, 19.20628654129469, 20.678658184767045, 21.95306090335457, 22.99613579306277, 23.78020902480191, 24.283891579770803, 24.49273205837292, 24.40033484763006, 24.008122103918037, 23.324836032146816, 22.36646640520786, 21.156553720686006, 19.724678540137383, 18.105251370020504, 16.33681418113161, 14.461379857852352, 12.52239514731927, 10.563378138017267, 8.626969893937753, 6.7538104922647895, 4.980971509501842, 3.341008483294681, 1.8612569870757987, 0.5631441857618122, -0.5383832561819432, -1.435008843203509, -2.1249989683304036, -2.6130388743545825, -2.909778796968336, -3.0311405926607327, -2.9975047628167077, -2.8328653541953113, -2.5637530195678777, -2.2180981712309245, -1.8241643257801872, -1.4095305731779804, -1.0000465499820634, -0.618939781500891, -0.28608560861750343, -0.01738686006834814, 0.1756256896491917, 0.2859878642319594, 0.3113412365275487, 0.25381402465012126, 0.1196287663472641, -0.08139858592350831, -0.33646619252121585, -0.6305115051906811, -0.9470283791209565, -1.2688848295091093, -1.5791404561470612, -1.861859623596191, -2.1027964153173606, -2.2899941005131415, -2.4142572903051156, -2.469546376057854, -2.4531259213510452, -2.365562998556743, -2.210604283754402, -1.9949479152744514, -1.7278106483876332, -1.4204068036709623, -1.08538566238719, -0.7361667806124467, -0.38629684098530553, -0.04885316658562324, 0.26415386551708564, 0.5424330813783319, 0.7777287714607124, 0.9640677808569844, 1.0980013992278124, 1.1788144903217643, 1.2082660088868573, 1.1903385576566023, 1.130991681250568, 1.0378693133221133, 0.9196450131710739, 0.7854761449027596, 0.644509594006315, 0.5054196161465305, 0.37580295054428026, 0.2617520083487331, 0.16755361663253968, 0.09548303048015835, 0.045648795099831274, 0.016020391052001298, 0.0025862584757087802, -0.00038548902865067475, 1.7043497738675846e-05, -0.004190762127955028, -0.02137410482162422, -0.05972527019060524, -0.12670480764349182, -0.22851255156759379, -0.36961563675747194, -0.5523496144851263, -0.7766306214835974, -1.0397932241458783, -1.3365770014368936, -1.6592408674172199, -1.9978046425682925, -2.3404482882238633, -2.6740107931322568, -2.9846171351478294, -3.2583085258750417, -3.4817393098408784, -3.642827437512601, -3.731516567156189, -3.7403234790588136, -3.6647436074282482, -3.503597553381816, -3.2593922341816617, -2.938263227656327, -2.549743372680971, -2.1065123514222432, -1.6240301389065845, -1.1198046876600083, -0.6126658888490865, -0.12200693387805682, 0.3331336923280392, 0.7349333714046759, 1.0675487866657383, 1.3178947118037052, 1.4764312816267569, 1.5375137995247985, 1.4996558569954532, 1.365716855875894, 1.142965901533255, 0.8426194877971745, 0.47933376989067566, 0.07059925208030304, -0.363958886963103, -0.8036298734014916, -1.2276097724198554, -1.6159521427695103, -1.9505489525035316, -2.2160831553355376, -2.4007578278655406, -2.4968970565130135, -2.5014834879105337, -2.4162779555707488, -2.247716246777395, -2.006677692157574, -1.708099582033224, -1.3701225902155723, -1.0131767633505024, -0.6589918331285087, -0.3295280925248351, -0.0457421029899707, 0.17354332548337642, 0.31267961521878, 0.3601104705787553, 0.3091170501002564, 0.15830791092448812, -0.088164999592413, -0.42055402632581446, -0.8238839925064065, -1.278626499860983, -1.7615130560519245, -2.2465215742593165, -2.706287017090573, -3.113476347610455, -3.4421092449903687, -3.6690541800838843, -3.7754928635147205, -3.7479272356422064, -3.5791467709749027, -3.269168011168028, -2.825478987273406, -2.2629887025697304, -1.6038495139112305, -0.8768425492947751, -0.11622514094206529, 0.639491288076479, 1.3490850037844122, 1.9704902024907178, 2.4625325590850595, 2.7868091316988726, 2.909704843343215, 2.804045159363266, 2.4504014040084368, 1.8385794542999798, 0.9683883233525531, -0.15005722714511427, -1.4961932787133214, -3.03921655086469, -4.73919854619961, -6.548476375806863, -8.41286524474519, -10.273674942617237, -12.069951148554944, -13.740953357962361, -15.228147802750694, -16.47743766110506, -17.44130900312883, -18.08114645317221, -18.368410374235655, -18.285610139598603, -17.827183395991003, -17.000203193999727, -15.823700812347717, -14.327928118237637, -12.553424302970233, -10.54950561262041, -8.37227044061762, -6.082679731450334, -3.74428961204364, -1.4205067932387727, 0.8273450124165047, 2.941935075417659, 4.872024969318257, 6.57489035397487, 8.016904677107686, 9.174099661089768, 10.032865121454398, 10.590981304975115, 10.856292451230855, 10.845493610080814, 10.583356226268508, 10.102266054158786, 9.43953066291629, 8.635344457471101, 7.731381213361241, 6.7695730242407235, 5.789622838468123, 4.827468267599756, 3.9143295581607376, 3.075918848242299, 2.3314400959090213, 1.6933388389766464, 1.1674415577528041, 0.7533336297657973, 0.44491497891533716, 0.23130471853223983, 0.09790932140434382, 0.027596077793770688, 0.0019227222009543187, 0.0023474571340528013, 0.011355072402257195, 0.013458719949126018, -0.0039876095059293536, -0.050201755160987974, -0.13061498114819292, -0.24676139257218652, -0.3964248803358498, -0.5739854999497151, -0.7709596372668114, -0.9767532697513017, -1.179440981118409, -1.366583662347675, -1.5261017198466664, -1.6471942781814473, -1.7209535511506444, -1.7408892288500604, -1.7033727983792144, -1.6079950666970844, -1.457461871797964, -1.257371853309772, -1.015945800429773, -0.7436476140915781, -0.45243803681368366, -0.1550407525783744, 0.13565120290015284, 0.40729073514740405, 0.6488771554223328, 0.8512452094881391, 1.0074310815687673, 1.1131286363275914, 1.1668583288815997, 1.1697836869837652, 1.1255673257721468, 1.040247152150489, 0.9216440790906771, 0.7787649728488424, 0.6213086063427732, 0.459127035916107, 0.3015222907458455, 0.1567414974809795, 0.03157726130347233, -0.0689804478651466, -0.14194611755836414, -0.18638781117790718, -0.20336456195602923, -0.1957079845032565, -0.16768950302074181, -0.12464705426026512, -0.0725112286411957, -0.017310502069865952, 0.0352795214017795, 0.08035160126493596, 0.11413793314984536, 0.13424802660677787, 0.1397824198584923, 0.131359054685643, 0.11099671727234724, 0.08184993664910495, 0.0478907333641655, 0.013521297557525505, -0.016883869176529988, -0.03947602486900699, -0.051320372373980676, -0.05074938304738728, -0.03765742894703709, -0.013677196697855408, 0.017846437730930344, 0.051972818914315995, 0.0824123411810037, 0.1019750516979224, 0.10308167657021611, 0.07831330572043509, 0.021045566798141208, -0.07379504903525354, -0.20921518711994713, -0.38570799767538894, -0.6008427158183735, -0.8489168797501006, -1.1210580931980552, -1.4054351378605385, -1.687582022613987, -1.950935549107176, -2.1776903247424397, -2.3496565629437844, -2.4492133003770156, -2.4604452729512034, -2.3701247694451117, -2.1685814615415904, -1.850541583928229, -1.4158824743004093, -0.8698911044683394, -0.22336476551691792, 0.5075052233833302, 1.3015913910686483, 2.1335980629806413, 2.974995654099239, 3.7952337318626546, 4.563279579184669, 5.248869223960773, 5.823870036719621, 6.26370176240351, 6.548998828277582, 6.666268855137803, 6.608491959666018, 6.375665654872385, 5.975483000211446, 5.422573327573173, 4.737672957393013, 3.946910536573013, 3.081085037852065, 2.173706205552717, 1.2593339072097218, 0.37215484582690406, -0.45546859438227105, -1.1947964030795035, -1.8219703307460127, -2.318996295075441, -2.6745998973519147, -2.8845807398552665, -2.9517361250177534, -2.885543202441273, -2.7016574744901813, -2.4206898392770966, -2.066850844483309, -1.6666118405872643, -1.247332618811934, -0.8354881921544863, -0.45516683959948273, -0.12693266561936373, 0.13322660899103653, 0.3148070522836276, 0.41310689851339627, 0.4292195706305361, 0.36984983104133484, 0.24664483659145556, 0.07517020680444703, -0.12620551709408356, -0.33758254456463865, -0.5390013555563622, -0.7117926202914614, -0.8398368900818266, -0.9106965213483817, -0.9163967955819722, -0.8539310159028445, -0.7255023828850686, -0.5383131028528949, -0.30401196889234133, -0.037919091116610286, 0.2420631286893358, 0.5167902819299918, 0.7671627961795121, 0.9754922464371313, 1.1268078757770277, 1.210039227714967, 1.2187848450928562, 1.151858229288996, 1.0134349771445486, 0.8129572391705667, 0.5645195004649188, 0.28585599410949253, -0.002848371911960361, -0.2803150770814818, -0.52579325806845, -0.7206654317329055, -0.8498954694467753, -0.903404935239088, -0.877082432134526, -0.7733820831430387, -0.6015741380359616, -0.3776173750852062, -0.12335265455238871, 0.1346383830434625, 0.366502238389524, 0.541003377990751, 0.6275824702968372, 0.598402645141574, 0.4304084042815326, 0.10742169175743198, -0.378413251277236, -1.0255782985994, -1.822483035052707, -2.7471870306988166, -3.7681863659632975, -4.845608720283749, -5.932796258466284, -6.97855324580034, -7.929900883107612, -8.73470206687109, -9.344510584809797, -9.717854566352196, -9.82255417616152, -9.637619701377217, -9.155072388727312, -8.381310438506084, -7.3367968652817055, -6.055473232089218, -4.583701959705215, -2.978064039015425, -1.3025541874542224, 0.3743677171122601, 1.9833194428097631, 3.4580988543925546, 4.738764220377123, 5.774746726451862, 6.5278104713872604, 6.974839515456495, 7.108473277872547, 6.937419423225103, 6.486120707656325, 5.794063733348297, 4.912838078327339, 3.902806217168758, 2.8297509969505326, 1.7612944538046802, 0.7620951876862762, -0.11036481574901653, -0.8093611725390999, -1.3022844363451365, -1.5733696721017159, -1.6251510412157357, -1.4790124733801129, -1.1749219717031603, -0.7695626626951612, -0.3335530737688139, 0.05207823403511448, 0.3003097567441953, 0.32320516211961253, 0.03701873133257934, -0.6326621190879421, -1.7456822566848686, -3.3431569119630766, -5.444169115487469, -8.043237561511233, -11.108795310422035, -14.583638045900996, -18.38634148746497, -22.413755543386866, -26.545384993609282, -30.648415963906807, -34.582786599333524, -38.20739858997974, -41.388257617840466, -44.00357274136039, -45.948599505585776, -47.14141932925082, -47.52907799422205, -47.08808184656136, -45.82523216655468, -43.778816527406974, -41.018095768814284, -37.6384410995369, -33.757298186842085, -29.50962613294935, -25.041847974970644, -20.504706161409228, -16.047125288667406, -11.80965246475689, -7.917738549649834, -4.4771994050627235, -1.5705462943726143, 0.7462681992799771, 2.446678471637747, 3.5322627709301018, 4.031079761348558, 3.9957203513068618, 3.5007594510626836, 2.6367531357843967, 1.5049390384321852, 0.21226251064511417, -1.1340575292035646, -2.432600550981185, -3.592275303857587, -4.536197588381133, -5.205621621866682, -5.561662441734754, -5.585719738194719, -5.279429431458667, -4.664569609915367, -3.7797220262110693, -2.676703669231375, -1.417296250276, -0.07021908134501223, 1.2942048766736876, 2.608316972170682, 3.8104601375436866, 4.847708818163123, 5.678938551811147, 6.276501582281522, 6.627001306168271, 6.731061864842286, 6.602325570297127, 6.266122007801428, 5.757319260076533, 5.117200452544707, 4.390692126257406, 3.623749274739795, 2.860183418267198, 2.138808273088564, 1.4918946148734211, 0.9435625055965983, 0.5082579955482869, 0.19090859702811422, -0.012528222999538274, -0.11448470858499965, -0.13438175329126334, -0.09646721835817962, -0.027918876146180483, 0.0432156117110838, 0.09029345270126432, 0.08992104397199101, 0.023554987154775196, -0.12112716965432248, -0.3496217683472595, -0.6604631592962028, -1.045358461713953, -1.4899513312801869, -1.9749507104822457, -2.477170032870266, -2.970933502495982, -3.4302546054046337, -3.8311152543979934, -4.1546133456494525, -4.3862135030345675], 'positive_zeros': ['0.68780073689650834684624357753573', '0.77621079495670323449665891843353', '1.47551615743428101748592828330206', '1.56494678241911347016437634996577', '1.92670211967839181431227630219732', '2.12732362578530929528344508307026', '2.58451573962371584225282479066756', '2.74333738071149507649510473713488', '2.93823598035367074995142850477774', '3.28254181149445120485908300953295', '3.60633255523269079437272511480387', '3.76069167920619765663690776410991', '3.83183166030962414472027756744510', '4.17012792851454133035675836126594', '4.56764184793435272466297460972519', '4.57348439745308300746798002619037', '5.13410643810228361426802515514175', '5.36243694993734310049620528198361', '5.44380021352831010331254476974701', '5.74438790962042197793056864931557', '6.05842059470533065658400473251603', '6.07456118542516564663981529265344', '6.07952497016127975895791974655246', '6.52234710593637300417237023693887', '6.69675799879268460658796123634369', '6.96070544918012222249819345757931', '7.04124640380508050775812847136614', '7.31179768586817945817446621428238', '7.46890516091460673768715124479842', '7.83143918146693904888377338283745', '8.252534710614065019028372574405277', '8.254342228474161716755029859080473', '8.303622688866384038051745487151330', '8.621010851788106789204090017885437', '8.866512849496538238205779556407166', '8.998813165671571044460178041932130', '9.146790367494322776299970574576030', '9.235184059604811713806956552722812', '9.334895945440894987003511018368443', '9.614016375968031855275063112874302'], 'prelabel': '8-1560e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1212238343803722634, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68780073689650834684624357754', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.77621079495670323449665891843', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.47551615743428101748592828330', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 24077.246635059513, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 5922408960000, 'conductor_radical': 390, 'degree': 8, 'dirichlet_coefficients': [1, 0, 2, 0, 4, 0, -2, 0, 1, 0, 1, 0, 10, 0, 8, 0, 0, 0, -3, 0, -4, 0, 2, 0, 10, 0, -2, 0, 6, 0, -14, 0, 2, 0, -8, 0, 7, 0, 20, 0, -2, 0, -7, 0, 4, 0, 2, 0, 15, 0, 0, 0, 22, 0, 4, 0, -6, 0, -14, 0, -1, 0, -2, 0, 40, 0, 3, 0, 4, 0, 4, 0, 2, 0, 20, 0, -2, 0, -18, 0, -4, 0, 8, 0, 0, 0, 12, 0, 19, 0, -20, 0, -28, 0, -12, 0, 7, 0, 1, 0], 'euler11': [1, -1, -7, 14, -68, 154, -847, -1331, 14641], 'euler13': [1, -10, 51, -130, 169, 0, 0, 0, 0], 'euler17': [1, 0, -34, 0, 867, 0, -9826, 0, 83521], 'euler19': [1, 3, -17, -36, 144, -684, -6137, 20577, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -2, 14, 112, -521, 2576, 7406, -24334, 279841], 'euler29': [1, -6, 26, 288, -1785, 8352, 21866, -146334, 707281], 'euler3': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler31': [1, 14, 169, 1274, 8560, 39494, 162409, 417074, 923521], 'euler37': [1, -7, -23, 14, 2002, 518, -31487, -354571, 1874161], 'euler41': [1, 2, -22, -112, -1169, -4592, -36982, 137842, 2825761], 'euler43': [1, 7, -35, -14, 3100, -602, -64715, 556549, 3418801], 'euler47': [1, -2, 161, -254, 10912, -11938, 355649, -207646, 4879681], 'euler5': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler53': [1, -22, 365, -3850, 33328, -204050, 1025285, -3275294, 7890481], 'euler59': [1, 14, 86, -112, -2945, -6608, 299366, 2875306, 12117361], 'euler61': [1, 1, -107, -14, 7882, -854, -398147, 226981, 13845841], 'euler67': [1, -3, -113, 36, 9792, 2412, -507257, -902289, 20151121], 'euler7': [1, 2, -11, 2, 148, 14, -539, 686, 2401], 'euler71': [1, -4, -130, -16, 15139, -1136, -655330, -1431644, 25411681], 'euler73': [1, -2, 37, -182, 11128, -13286, 197173, -778034, 28398241], 'euler79': [1, 18, 409, 4374, 52176, 345546, 2552569, 8874702, 38950081], 'euler83': [1, -8, -100, -200, 19798, -16600, -688900, -4574296, 47458321], 'euler89': [1, -19, 107, -1444, 24466, -128516, 847547, -13394411, 62742241], 'euler97': [1, -7, -29, 812, -8078, 78764, -272861, -6388711, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 2, -11, 2, 148, 14, -539, 686, 2401], [1, -1, -7, 14, -68, 154, -847, -1331, 14641], [1, -10, 51, -130, 169, 0, 0, 0, 0], [1, 0, -34, 0, 867, 0, -9826, 0, 83521], [1, 3, -17, -36, 144, -684, -6137, 20577, 130321], [1, -2, 14, 112, -521, 2576, 7406, -24334, 279841], [1, -6, 26, 288, -1785, 8352, 21866, -146334, 707281], [1, 14, 169, 1274, 8560, 39494, 162409, 417074, 923521], [1, -7, -23, 14, 2002, 518, -31487, -354571, 1874161], [1, 2, -22, -112, -1169, -4592, -36982, 137842, 2825761], [1, 7, -35, -14, 3100, -602, -64715, 556549, 3418801], [1, -2, 161, -254, 10912, -11938, 355649, -207646, 4879681], [1, -22, 365, -3850, 33328, -204050, 1025285, -3275294, 7890481], [1, 14, 86, -112, -2945, -6608, 299366, 2875306, 12117361], [1, 1, -107, -14, 7882, -854, -398147, 226981, 13845841], [1, -3, -113, 36, 9792, 2412, -507257, -902289, 20151121], [1, -4, -130, -16, 15139, -1136, -655330, -1431644, 25411681], [1, -2, 37, -182, 11128, -13286, 197173, -778034, 28398241], [1, 18, 409, 4374, 52176, 345546, 2552569, 8874702, 38950081], [1, -8, -100, -200, 19798, -16600, -688900, -4574296, 47458321], [1, -19, 107, -1444, 24466, -128516, 847547, -13394411, 62742241], [1, -7, -29, 812, -8078, 78764, -272861, -6388711, 88529281]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/2/bg/g'], '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': '8-1560e4-1.1-c1e4-0-7', '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1560e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1212238343803722634, 'z1': {'__RealLiteral__': 0, 'data': '0.68780073689650834684624357754', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '871891016964277294315530308478,983964080130495954399878965994,1870438942618016961894588738353,1983805728058825509447659459977', 'Lhash_array': ['871891016964277294315530308478', '983964080130495954399878965994', '1870438942618016961894588738353', '1983805728058825509447659459977'], 'label': '8-1560e4-1.1-c1e4-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/2/bg/g'}