Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.15 | ||
Character | \(\chi\) | \(=\) | 43.7 |
Dual form | 43.7.d.a.37.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.38637i | 0.923297i | 0.887063 | + | 0.461648i | \(0.152742\pi\) | ||||
−0.887063 | + | 0.461648i | \(0.847258\pi\) | |||||||
\(3\) | −8.75832 | + | 5.05662i | −0.324382 | + | 0.187282i | −0.653344 | − | 0.757061i | \(-0.726635\pi\) |
0.328962 | + | 0.944343i | \(0.393301\pi\) | |||||||
\(4\) | 9.44147 | 0.147523 | ||||||||
\(5\) | 10.2848 | − | 5.93793i | 0.0822783 | − | 0.0475034i | −0.458296 | − | 0.888799i | \(-0.651540\pi\) |
0.540575 | + | 0.841296i | \(0.318207\pi\) | |||||||
\(6\) | −37.3501 | − | 64.6923i | −0.172917 | − | 0.299501i | ||||
\(7\) | 367.060 | + | 211.922i | 1.07015 | + | 0.617849i | 0.928221 | − | 0.372029i | \(-0.121338\pi\) |
0.141924 | + | 0.989878i | \(0.454671\pi\) | |||||||
\(8\) | 542.466i | 1.05950i | ||||||||
\(9\) | −313.361 | + | 542.757i | −0.429851 | + | 0.744523i | ||||
\(10\) | 43.8598 | + | 75.9673i | 0.0438598 | + | 0.0759673i | ||||
\(11\) | −1647.75 | −1.23798 | −0.618991 | − | 0.785398i | \(-0.712458\pi\) | ||||
−0.618991 | + | 0.785398i | \(0.712458\pi\) | |||||||
\(12\) | −82.6914 | + | 47.7419i | −0.0478538 | + | 0.0276284i | ||||
\(13\) | 1102.09 | − | 1908.88i | 0.501636 | − | 0.868858i | −0.498363 | − | 0.866969i | \(-0.666065\pi\) |
0.999998 | − | 0.00188971i | \(-0.000601514\pi\) | |||||||
\(14\) | −1565.34 | + | 2711.24i | −0.570458 | + | 0.988062i | ||||
\(15\) | −60.0517 | + | 104.013i | −0.0177931 | + | 0.0308185i | ||||
\(16\) | −3402.60 | −0.830714 | ||||||||
\(17\) | −2127.60 | + | 3685.11i | −0.433056 | + | 0.750074i | −0.997135 | − | 0.0756465i | \(-0.975898\pi\) |
0.564079 | + | 0.825721i | \(0.309231\pi\) | |||||||
\(18\) | −4009.01 | − | 2314.60i | −0.687416 | − | 0.396880i | ||||
\(19\) | −2140.56 | + | 1235.86i | −0.312081 | + | 0.180180i | −0.647857 | − | 0.761762i | \(-0.724335\pi\) |
0.335776 | + | 0.941942i | \(0.391001\pi\) | |||||||
\(20\) | 97.1035 | − | 56.0628i | 0.0121379 | − | 0.00700784i | ||||
\(21\) | −4286.44 | −0.462848 | ||||||||
\(22\) | − | 12170.9i | − | 1.14302i | ||||||
\(23\) | 1161.42 | + | 2011.64i | 0.0954567 | + | 0.165336i | 0.909799 | − | 0.415049i | \(-0.136236\pi\) |
−0.814342 | + | 0.580385i | \(0.802902\pi\) | |||||||
\(24\) | −2743.05 | − | 4751.10i | −0.198426 | − | 0.343685i | ||||
\(25\) | −7741.98 | + | 13409.5i | −0.495487 | + | 0.858208i | ||||
\(26\) | 14099.7 | + | 8140.48i | 0.802214 | + | 0.463159i | ||||
\(27\) | − | 13710.7i | − | 0.696578i | ||||||
\(28\) | 3465.58 | + | 2000.86i | 0.157871 | + | 0.0911468i | ||||
\(29\) | −12799.5 | − | 7389.81i | −0.524808 | − | 0.302998i | 0.214092 | − | 0.976814i | \(-0.431321\pi\) |
−0.738899 | + | 0.673816i | \(0.764654\pi\) | |||||||
\(30\) | −768.276 | − | 443.564i | −0.0284547 | − | 0.0164283i | ||||
\(31\) | 27047.2 | + | 46847.2i | 0.907900 | + | 1.57253i | 0.816977 | + | 0.576670i | \(0.195648\pi\) |
0.0909226 | + | 0.995858i | \(0.471018\pi\) | |||||||
\(32\) | 9584.92i | 0.292509i | ||||||||
\(33\) | 14431.6 | − | 8332.07i | 0.401580 | − | 0.231852i | ||||
\(34\) | −27219.6 | − | 15715.3i | −0.692541 | − | 0.399839i | ||||
\(35\) | 5033.51 | 0.117400 | ||||||||
\(36\) | −2958.59 | + | 5124.43i | −0.0634128 | + | 0.109834i | ||||
\(37\) | 58255.9 | − | 33634.1i | 1.15010 | − | 0.664009i | 0.201187 | − | 0.979553i | \(-0.435520\pi\) |
0.948911 | + | 0.315543i | \(0.102187\pi\) | |||||||
\(38\) | −9128.49 | − | 15811.0i | −0.166360 | − | 0.288143i | ||||
\(39\) | 22291.5i | 0.375790i | ||||||||
\(40\) | 3221.12 | + | 5579.15i | 0.0503301 | + | 0.0871742i | ||||
\(41\) | 124207. | 1.80216 | 0.901080 | − | 0.433652i | \(-0.142775\pi\) | ||||
0.901080 | + | 0.433652i | \(0.142775\pi\) | |||||||
\(42\) | − | 31661.2i | − | 0.427346i | ||||||
\(43\) | 41789.3 | − | 67638.9i | 0.525605 | − | 0.850729i | ||||
\(44\) | −15557.2 | −0.182631 | ||||||||
\(45\) | 7442.86i | 0.0816775i | ||||||||
\(46\) | −14858.7 | + | 8578.70i | −0.152654 | + | 0.0881349i | ||||
\(47\) | −82727.9 | −0.796817 | −0.398408 | − | 0.917208i | \(-0.630437\pi\) | ||||
−0.398408 | + | 0.917208i | \(0.630437\pi\) | |||||||
\(48\) | 29801.1 | − | 17205.7i | 0.269469 | − | 0.155578i | ||||
\(49\) | 30997.4 | + | 53689.1i | 0.263474 | + | 0.456350i | ||||
\(50\) | −99047.6 | − | 57185.2i | −0.792381 | − | 0.457481i | ||||
\(51\) | − | 43033.9i | − | 0.324414i | ||||||
\(52\) | 10405.4 | − | 18022.6i | 0.0740028 | − | 0.128177i | ||||
\(53\) | −69442.7 | − | 120278.i | −0.466443 | − | 0.807903i | 0.532822 | − | 0.846227i | \(-0.321131\pi\) |
−0.999265 | + | 0.0383238i | \(0.987798\pi\) | |||||||
\(54\) | 101273. | 0.643148 | ||||||||
\(55\) | −16946.8 | + | 9784.24i | −0.101859 | + | 0.0588084i | ||||
\(56\) | −114961. | + | 199118.i | −0.654613 | + | 1.13382i | ||||
\(57\) | 12498.5 | − | 21648.0i | 0.0674891 | − | 0.116894i | ||||
\(58\) | 54583.9 | − | 94542.1i | 0.279757 | − | 0.484553i | ||||
\(59\) | 218398. | 1.06339 | 0.531696 | − | 0.846936i | \(-0.321555\pi\) | ||||
0.531696 | + | 0.846936i | \(0.321555\pi\) | |||||||
\(60\) | −566.976 | + | 982.032i | −0.00262489 | + | 0.00454644i | ||||
\(61\) | −56523.7 | − | 32634.0i | −0.249024 | − | 0.143774i | 0.370293 | − | 0.928915i | \(-0.379257\pi\) |
−0.619317 | + | 0.785141i | \(0.712591\pi\) | |||||||
\(62\) | −346031. | + | 199781.i | −1.45191 | + | 0.838261i | ||||
\(63\) | −230045. | + | 132816.i | −0.920005 | + | 0.531165i | ||||
\(64\) | −288565. | −1.10079 | ||||||||
\(65\) | − | 26176.6i | − | 0.0953176i | ||||||
\(66\) | 61543.8 | + | 106597.i | 0.214068 | + | 0.370777i | ||||
\(67\) | 183226. | + | 317357.i | 0.609204 | + | 1.05517i | 0.991372 | + | 0.131079i | \(0.0418443\pi\) |
−0.382168 | + | 0.924093i | \(0.624822\pi\) | |||||||
\(68\) | −20087.7 | + | 34792.9i | −0.0638856 | + | 0.110653i | ||||
\(69\) | −20344.2 | − | 11745.7i | −0.0619290 | − | 0.0357547i | ||||
\(70\) | 37179.4i | 0.108395i | ||||||||
\(71\) | 119935. | + | 69244.7i | 0.335098 | + | 0.193469i | 0.658102 | − | 0.752929i | \(-0.271359\pi\) |
−0.323004 | + | 0.946398i | \(0.604693\pi\) | |||||||
\(72\) | −294428. | − | 169988.i | −0.788826 | − | 0.455429i | ||||
\(73\) | 414881. | + | 239532.i | 1.06649 | + | 0.615736i | 0.927219 | − | 0.374519i | \(-0.122192\pi\) |
0.139266 | + | 0.990255i | \(0.455526\pi\) | |||||||
\(74\) | 248434. | + | 430300.i | 0.613078 | + | 1.06188i | ||||
\(75\) | − | 156593.i | − | 0.371184i | ||||||
\(76\) | −20210.1 | + | 11668.3i | −0.0460391 | + | 0.0265807i | ||||
\(77\) | −604824. | − | 349195.i | −1.32482 | − | 0.764885i | ||||
\(78\) | −164653. | −0.346966 | ||||||||
\(79\) | 453069. | − | 784739.i | 0.918932 | − | 1.59164i | 0.117892 | − | 0.993026i | \(-0.462386\pi\) |
0.801040 | − | 0.598610i | \(-0.204280\pi\) | |||||||
\(80\) | −34995.1 | + | 20204.4i | −0.0683498 | + | 0.0394618i | ||||
\(81\) | −159110. | − | 275587.i | −0.299394 | − | 0.518566i | ||||
\(82\) | 917437.i | 1.66393i | ||||||||
\(83\) | −155641. | − | 269579.i | −0.272202 | − | 0.471467i | 0.697224 | − | 0.716854i | \(-0.254418\pi\) |
−0.969425 | + | 0.245387i | \(0.921085\pi\) | |||||||
\(84\) | −40470.3 | −0.0682807 | ||||||||
\(85\) | 50534.2i | 0.0822865i | ||||||||
\(86\) | 499606. | + | 308671.i | 0.785475 | + | 0.485289i | ||||
\(87\) | 149470. | 0.226984 | ||||||||
\(88\) | − | 893851.i | − | 1.31165i | ||||||
\(89\) | −579242. | + | 334425.i | −0.821656 | + | 0.474383i | −0.850987 | − | 0.525186i | \(-0.823996\pi\) |
0.0293312 | + | 0.999570i | \(0.490662\pi\) | |||||||
\(90\) | −54975.8 | −0.0754126 | ||||||||
\(91\) | 809068. | − | 467116.i | 1.07365 | − | 0.619870i | ||||
\(92\) | 10965.5 | + | 18992.9i | 0.0140821 | + | 0.0243908i | ||||
\(93\) | −473777. | − | 273535.i | −0.589013 | − | 0.340067i | ||||
\(94\) | − | 611059.i | − | 0.735699i | ||||||
\(95\) | −14676.8 | + | 25421.0i | −0.0171183 | + | 0.0296498i | ||||
\(96\) | −48467.3 | − | 83947.9i | −0.0547817 | − | 0.0948847i | ||||
\(97\) | 731097. | 0.801051 | 0.400525 | − | 0.916286i | \(-0.368828\pi\) | ||||
0.400525 | + | 0.916286i | \(0.368828\pi\) | |||||||
\(98\) | −396568. | + | 228958.i | −0.421346 | + | 0.243264i | ||||
\(99\) | 516342. | − | 894331.i | 0.532147 | − | 0.921706i | ||||
\(100\) | −73095.7 | + | 126605.i | −0.0730957 | + | 0.126605i | ||||
\(101\) | −239579. | + | 414962.i | −0.232533 | + | 0.402758i | −0.958553 | − | 0.284915i | \(-0.908035\pi\) |
0.726020 | + | 0.687674i | \(0.241368\pi\) | |||||||
\(102\) | 317865. | 0.299531 | ||||||||
\(103\) | −189620. | + | 328431.i | −0.173529 | + | 0.300561i | −0.939651 | − | 0.342134i | \(-0.888850\pi\) |
0.766122 | + | 0.642695i | \(0.222184\pi\) | |||||||
\(104\) | 1.03550e6 | + | 597848.i | 0.920559 | + | 0.531485i | ||||
\(105\) | −44085.1 | + | 25452.6i | −0.0380824 | + | 0.0219869i | ||||
\(106\) | 888420. | − | 512930.i | 0.745935 | − | 0.430666i | ||||
\(107\) | 2.24409e6 | 1.83185 | 0.915925 | − | 0.401349i | \(-0.131459\pi\) | ||||
0.915925 | + | 0.401349i | \(0.131459\pi\) | |||||||
\(108\) | − | 129450.i | − | 0.102761i | ||||||
\(109\) | −406627. | − | 704299.i | −0.313991 | − | 0.543848i | 0.665232 | − | 0.746637i | \(-0.268333\pi\) |
−0.979222 | + | 0.202789i | \(0.934999\pi\) | |||||||
\(110\) | −72270.1 | − | 125175.i | −0.0542976 | − | 0.0940462i | ||||
\(111\) | −340150. | + | 589156.i | −0.248714 | + | 0.430786i | ||||
\(112\) | −1.24896e6 | − | 721087.i | −0.888985 | − | 0.513255i | ||||
\(113\) | 1.01564e6i | 0.703890i | 0.936021 | + | 0.351945i | \(0.114480\pi\) | ||||
−0.936021 | + | 0.351945i | \(0.885520\pi\) | |||||||
\(114\) | 159901. | + | 92318.6i | 0.107928 | + | 0.0623124i | ||||
\(115\) | 23890.0 | + | 13792.9i | 0.0157080 | + | 0.00906904i | ||||
\(116\) | −120846. | − | 69770.7i | −0.0774212 | − | 0.0446991i | ||||
\(117\) | 690707. | + | 1.19634e6i | 0.431257 | + | 0.746959i | ||||
\(118\) | 1.61317e6i | 0.981826i | ||||||||
\(119\) | −1.56191e6 | + | 901771.i | −0.926864 | + | 0.535125i | ||||
\(120\) | −56423.3 | − | 32576.0i | −0.0326524 | − | 0.0188519i | ||||
\(121\) | 943532. | 0.532599 | ||||||||
\(122\) | 241047. | − | 417505.i | 0.132746 | − | 0.229923i | ||||
\(123\) | −1.08784e6 | + | 628066.i | −0.584589 | + | 0.337513i | ||||
\(124\) | 255366. | + | 442306.i | 0.133936 | + | 0.231984i | ||||
\(125\) | 369446.i | 0.189156i | ||||||||
\(126\) | −981031. | − | 1.69920e6i | −0.490423 | − | 0.849438i | ||||
\(127\) | −540650. | −0.263940 | −0.131970 | − | 0.991254i | \(-0.542130\pi\) | ||||
−0.131970 | + | 0.991254i | \(0.542130\pi\) | |||||||
\(128\) | − | 1.51801e6i | − | 0.723844i | ||||||
\(129\) | −23979.8 | + | 803716.i | −0.0111706 | + | 0.374398i | ||||
\(130\) | 193350. | 0.0880065 | ||||||||
\(131\) | − | 1.63580e6i | − | 0.727641i | −0.931469 | − | 0.363821i | \(-0.881472\pi\) | ||
0.931469 | − | 0.363821i | \(-0.118528\pi\) | |||||||
\(132\) | 136255. | − | 78667.0i | 0.0592422 | − | 0.0342035i | ||||
\(133\) | −1.04762e6 | −0.445296 | ||||||||
\(134\) | −2.34412e6 | + | 1.35338e6i | −0.974237 | + | 0.562476i | ||||
\(135\) | −81413.4 | − | 141012.i | −0.0330898 | − | 0.0573133i | ||||
\(136\) | −1.99905e6 | − | 1.15415e6i | −0.794707 | − | 0.458824i | ||||
\(137\) | 284343.i | 0.110581i | 0.998470 | + | 0.0552906i | \(0.0176085\pi\) | ||||
−0.998470 | + | 0.0552906i | \(0.982391\pi\) | |||||||
\(138\) | 86758.5 | − | 150270.i | 0.0330122 | − | 0.0571788i | ||||
\(139\) | −1.09554e6 | − | 1.89752e6i | −0.407927 | − | 0.706550i | 0.586730 | − | 0.809782i | \(-0.300415\pi\) |
−0.994657 | + | 0.103232i | \(0.967082\pi\) | |||||||
\(140\) | 47523.7 | 0.0173191 | ||||||||
\(141\) | 724558. | − | 418324.i | 0.258473 | − | 0.149230i | ||||
\(142\) | −511467. | + | 885888.i | −0.178629 | + | 0.309395i | ||||
\(143\) | −1.81598e6 | + | 3.14537e6i | −0.621016 | + | 1.07563i | ||||
\(144\) | 1.06624e6 | − | 1.84679e6i | 0.357083 | − | 0.618486i | ||||
\(145\) | −175521. | −0.0575737 | ||||||||
\(146\) | −1.76927e6 | + | 3.06447e6i | −0.568507 | + | 0.984683i | ||||
\(147\) | −542971. | − | 313484.i | −0.170932 | − | 0.0986879i | ||||
\(148\) | 550021. | − | 317555.i | 0.169666 | − | 0.0979566i | ||||
\(149\) | −2.19178e6 | + | 1.26542e6i | −0.662580 | + | 0.382541i | −0.793259 | − | 0.608884i | \(-0.791617\pi\) |
0.130680 | + | 0.991425i | \(0.458284\pi\) | |||||||
\(150\) | 1.15666e6 | 0.342713 | ||||||||
\(151\) | 1.95705e6i | 0.568421i | 0.958762 | + | 0.284211i | \(0.0917315\pi\) | ||||
−0.958762 | + | 0.284211i | \(0.908269\pi\) | |||||||
\(152\) | −670410. | − | 1.16118e6i | −0.190902 | − | 0.330651i | ||||
\(153\) | −1.33342e6 | − | 2.30954e6i | −0.372298 | − | 0.644840i | ||||
\(154\) | 2.57929e6 | − | 4.46746e6i | 0.706216 | − | 1.22320i | ||||
\(155\) | 556350. | + | 321209.i | 0.149401 | + | 0.0862567i | ||||
\(156\) | 210464.i | 0.0554376i | ||||||||
\(157\) | −1.16223e6 | − | 671011.i | −0.300325 | − | 0.173393i | 0.342264 | − | 0.939604i | \(-0.388806\pi\) |
−0.642589 | + | 0.766211i | \(0.722140\pi\) | |||||||
\(158\) | 5.79638e6 | + | 3.34654e6i | 1.46955 | + | 0.848447i | ||||
\(159\) | 1.21640e6 | + | 702291.i | 0.302612 | + | 0.174713i | ||||
\(160\) | 56914.6 | + | 98579.0i | 0.0138952 | + | 0.0240671i | ||||
\(161\) | 984524.i | 0.235911i | ||||||||
\(162\) | 2.03559e6 | − | 1.17525e6i | 0.478790 | − | 0.276430i | ||||
\(163\) | 1.46663e6 | + | 846757.i | 0.338654 | + | 0.195522i | 0.659677 | − | 0.751549i | \(-0.270693\pi\) |
−0.321022 | + | 0.947072i | \(0.604026\pi\) | |||||||
\(164\) | 1.17269e6 | 0.265860 | ||||||||
\(165\) | 98950.4 | − | 171387.i | 0.0220275 | − | 0.0381528i | ||||
\(166\) | 1.99121e6 | − | 1.14963e6i | 0.435304 | − | 0.251323i | ||||
\(167\) | 1.81216e6 | + | 3.13875e6i | 0.389087 | + | 0.673919i | 0.992327 | − | 0.123641i | \(-0.0394571\pi\) |
−0.603240 | + | 0.797560i | \(0.706124\pi\) | |||||||
\(168\) | − | 2.32525e6i | − | 0.490390i | ||||||
\(169\) | −15815.7 | − | 27393.6i | −0.00327664 | − | 0.00567530i | ||||
\(170\) | −373264. | −0.0759748 | ||||||||
\(171\) | − | 1.54908e6i | − | 0.309802i | ||||||
\(172\) | 394552. | − | 638610.i | 0.0775388 | − | 0.125502i | ||||
\(173\) | −3.82435e6 | −0.738618 | −0.369309 | − | 0.929307i | \(-0.620406\pi\) | ||||
−0.369309 | + | 0.929307i | \(0.620406\pi\) | |||||||
\(174\) | 1.10404e6i | 0.209574i | ||||||||
\(175\) | −5.68354e6 | + | 3.28139e6i | −1.06049 | + | 0.612272i | ||||
\(176\) | 5.60666e6 | 1.02841 | ||||||||
\(177\) | −1.91280e6 | + | 1.10436e6i | −0.344945 | + | 0.199154i | ||||
\(178\) | −2.47019e6 | − | 4.27850e6i | −0.437997 | − | 0.758632i | ||||
\(179\) | 7.83536e6 | + | 4.52375e6i | 1.36615 | + | 0.788750i | 0.990435 | − | 0.137983i | \(-0.0440621\pi\) |
0.375720 | + | 0.926733i | \(0.377395\pi\) | |||||||
\(180\) | 70271.6i | 0.0120493i | ||||||||
\(181\) | 2.23912e6 | − | 3.87826e6i | 0.377608 | − | 0.654036i | −0.613106 | − | 0.790001i | \(-0.710080\pi\) |
0.990714 | + | 0.135965i | \(0.0434135\pi\) | |||||||
\(182\) | 3.45029e6 | + | 5.97608e6i | 0.572324 | + | 0.991294i | ||||
\(183\) | 660070. | 0.107705 | ||||||||
\(184\) | −1.09125e6 | + | 630032.i | −0.175174 | + | 0.101137i | ||||
\(185\) | 399433. | − | 691839.i | 0.0630854 | − | 0.109267i | ||||
\(186\) | 2.02043e6 | − | 3.49949e6i | 0.313983 | − | 0.543834i | ||||
\(187\) | 3.50576e6 | − | 6.07216e6i | 0.536115 | − | 0.928578i | ||||
\(188\) | −781073. | −0.117549 | ||||||||
\(189\) | 2.90561e6 | − | 5.03266e6i | 0.430380 | − | 0.745440i | ||||
\(190\) | −187769. | − | 108409.i | −0.0273756 | − | 0.0158053i | ||||
\(191\) | 7.03116e6 | − | 4.05944e6i | 1.00908 | − | 0.582594i | 0.0981601 | − | 0.995171i | \(-0.468704\pi\) |
0.910923 | + | 0.412576i | \(0.135371\pi\) | |||||||
\(192\) | 2.52734e6 | − | 1.45916e6i | 0.357076 | − | 0.206158i | ||||
\(193\) | −1.28573e7 | −1.78845 | −0.894225 | − | 0.447617i | \(-0.852273\pi\) | ||||
−0.894225 | + | 0.447617i | \(0.852273\pi\) | |||||||
\(194\) | 5.40016e6i | 0.739608i | ||||||||
\(195\) | 132365. | + | 229263.i | 0.0178513 | + | 0.0309194i | ||||
\(196\) | 292661. | + | 506904.i | 0.0388684 | + | 0.0673221i | ||||
\(197\) | −6.07930e6 | + | 1.05297e7i | −0.795161 | + | 1.37726i | 0.127577 | + | 0.991829i | \(0.459280\pi\) |
−0.922737 | + | 0.385430i | \(0.874053\pi\) | |||||||
\(198\) | 6.60586e6 | + | 3.81390e6i | 0.851009 | + | 0.491330i | ||||
\(199\) | − | 1.40743e7i | − | 1.78594i | −0.450119 | − | 0.892969i | \(-0.648618\pi\) | ||
0.450119 | − | 0.892969i | \(-0.351382\pi\) | |||||||
\(200\) | −7.27420e6 | − | 4.19976e6i | −0.909276 | − | 0.524970i | ||||
\(201\) | −3.20951e6 | − | 1.85301e6i | −0.395230 | − | 0.228186i | ||||
\(202\) | −3.06507e6 | − | 1.76962e6i | −0.371866 | − | 0.214697i | ||||
\(203\) | −3.13213e6 | − | 5.42501e6i | −0.374414 | − | 0.648503i | ||||
\(204\) | − | 406303.i | − | 0.0478586i | ||||||
\(205\) | 1.27744e6 | − | 737530.i | 0.148279 | − | 0.0856088i | ||||
\(206\) | −2.42591e6 | − | 1.40060e6i | −0.277507 | − | 0.160219i | ||||
\(207\) | −1.45578e6 | −0.164129 | ||||||||
\(208\) | −3.74999e6 | + | 6.49517e6i | −0.416716 | + | 0.721773i | ||||
\(209\) | 3.52712e6 | − | 2.03639e6i | 0.386351 | − | 0.223060i | ||||
\(210\) | −188002. | − | 325629.i | −0.0203004 | − | 0.0351613i | ||||
\(211\) | − | 5.96969e6i | − | 0.635484i | −0.948177 | − | 0.317742i | \(-0.897075\pi\) | ||
0.948177 | − | 0.317742i | \(-0.102925\pi\) | |||||||
\(212\) | −655641. | − | 1.13560e6i | −0.0688111 | − | 0.119184i | ||||
\(213\) | −1.40058e6 | −0.144933 | ||||||||
\(214\) | 1.65757e7i | 1.69134i | ||||||||
\(215\) | 28159.2 | − | 943794.i | 0.00283338 | − | 0.0949646i | ||||
\(216\) | 7.43762e6 | 0.738028 | ||||||||
\(217\) | 2.29276e7i | 2.24378i | ||||||||
\(218\) | 5.20221e6 | − | 3.00350e6i | 0.502133 | − | 0.289907i | ||||
\(219\) | −4.84488e6 | −0.461265 | ||||||||
\(220\) | −160003. | + | 92377.6i | −0.0150266 | + | 0.00867559i | ||||
\(221\) | 4.68963e6 | + | 8.12268e6i | 0.434472 | + | 0.752528i | ||||
\(222\) | −4.35173e6 | − | 2.51247e6i | −0.397743 | − | 0.229637i | ||||
\(223\) | − | 7.69920e6i | − | 0.694274i | −0.937814 | − | 0.347137i | \(-0.887154\pi\) | ||
0.937814 | − | 0.347137i | \(-0.112846\pi\) | |||||||
\(224\) | −2.03126e6 | + | 3.51824e6i | −0.180726 | + | 0.313027i | ||||
\(225\) | −4.85207e6 | − | 8.40404e6i | −0.425971 | − | 0.737803i | ||||
\(226\) | −7.50190e6 | −0.649900 | ||||||||
\(227\) | −6.06085e6 | + | 3.49923e6i | −0.518151 | + | 0.299154i | −0.736178 | − | 0.676788i | \(-0.763371\pi\) |
0.218027 | + | 0.975943i | \(0.430038\pi\) | |||||||
\(228\) | 118004. | − | 204389.i | 0.00995619 | − | 0.0172446i | ||||
\(229\) | −3.90615e6 | + | 6.76565e6i | −0.325269 | + | 0.563382i | −0.981567 | − | 0.191120i | \(-0.938788\pi\) |
0.656298 | + | 0.754502i | \(0.272122\pi\) | |||||||
\(230\) | −101879. | + | 176460.i | −0.00837342 | + | 0.0145032i | ||||
\(231\) | 7.06300e6 | 0.572998 | ||||||||
\(232\) | 4.00872e6 | − | 6.94331e6i | 0.321027 | − | 0.556036i | ||||
\(233\) | −1.42628e7 | − | 8.23460e6i | −1.12755 | − | 0.650991i | −0.184232 | − | 0.982883i | \(-0.558980\pi\) |
−0.943317 | + | 0.331892i | \(0.892313\pi\) | |||||||
\(234\) | −8.83661e6 | + | 5.10182e6i | −0.689665 | + | 0.398178i | ||||
\(235\) | −850840. | + | 491232.i | −0.0655608 | + | 0.0378515i | ||||
\(236\) | 2.06200e6 | 0.156875 | ||||||||
\(237\) | 9.16400e6i | 0.688399i | ||||||||
\(238\) | −6.66082e6 | − | 1.15369e7i | −0.494080 | − | 0.855771i | ||||
\(239\) | 2.79188e6 | + | 4.83569e6i | 0.204505 | + | 0.354213i | 0.949975 | − | 0.312326i | \(-0.101108\pi\) |
−0.745470 | + | 0.666539i | \(0.767775\pi\) | |||||||
\(240\) | 204332. | − | 353914.i | 0.0147810 | − | 0.0256014i | ||||
\(241\) | 2.18954e7 | + | 1.26413e7i | 1.56424 | + | 0.903112i | 0.996820 | + | 0.0796806i | \(0.0253901\pi\) |
0.567416 | + | 0.823432i | \(0.307943\pi\) | |||||||
\(242\) | 6.96928e6i | 0.491747i | ||||||||
\(243\) | 1.14431e7 | + | 6.60669e6i | 0.797491 | + | 0.460431i | ||||
\(244\) | −533667. | − | 308113.i | −0.0367367 | − | 0.0212100i | ||||
\(245\) | 637604. | + | 368121.i | 0.0433563 | + | 0.0250318i | ||||
\(246\) | −4.63913e6 | − | 8.03521e6i | −0.311624 | − | 0.539749i | ||||
\(247\) | 5.44811e6i | 0.361539i | ||||||||
\(248\) | −2.54130e7 | + | 1.46722e7i | −1.66610 | + | 0.961924i | ||||
\(249\) | 2.72631e6 | + | 1.57404e6i | 0.176595 | + | 0.101957i | ||||
\(250\) | −2.72886e6 | −0.174647 | ||||||||
\(251\) | −2.32801e6 | + | 4.03223e6i | −0.147219 | + | 0.254991i | −0.930199 | − | 0.367057i | \(-0.880365\pi\) |
0.782980 | + | 0.622047i | \(0.213699\pi\) | |||||||
\(252\) | −2.17196e6 | + | 1.25398e6i | −0.135722 | + | 0.0783591i | ||||
\(253\) | −1.91374e6 | − | 3.31469e6i | −0.118174 | − | 0.204683i | ||||
\(254\) | − | 3.99345e6i | − | 0.243695i | ||||||
\(255\) | −255532. | − | 442595.i | −0.0154108 | − | 0.0266923i | ||||
\(256\) | −7.25554e6 | −0.432464 | ||||||||
\(257\) | − | 2.48316e7i | − | 1.46287i | −0.681913 | − | 0.731433i | \(-0.738852\pi\) | ||
0.681913 | − | 0.731433i | \(-0.261148\pi\) | |||||||
\(258\) | −5.93655e6 | − | 177124.i | −0.345680 | − | 0.0103138i | ||||
\(259\) | 2.85112e7 | 1.64103 | ||||||||
\(260\) | − | 247146.i | − | 0.0140615i | ||||||
\(261\) | 8.02175e6 | − | 4.63136e6i | 0.451178 | − | 0.260488i | ||||
\(262\) | 1.20827e7 | 0.671829 | ||||||||
\(263\) | 1.03290e7 | − | 5.96347e6i | 0.567796 | − | 0.327817i | −0.188472 | − | 0.982078i | \(-0.560354\pi\) |
0.756269 | + | 0.654261i | \(0.227020\pi\) | |||||||
\(264\) | 4.51987e6 | + | 7.82864e6i | 0.245648 | + | 0.425475i | ||||
\(265\) | −1.42841e6 | − | 824691.i | −0.0767564 | − | 0.0443153i | ||||
\(266\) | − | 7.73811e6i | − | 0.411140i | ||||||
\(267\) | 3.38213e6 | − | 5.85801e6i | 0.177687 | − | 0.307763i | ||||
\(268\) | 1.72992e6 | + | 2.99631e6i | 0.0898716 | + | 0.155662i | ||||
\(269\) | −1.02199e7 | −0.525037 | −0.262519 | − | 0.964927i | \(-0.584553\pi\) | ||||
−0.262519 | + | 0.964927i | \(0.584553\pi\) | |||||||
\(270\) | 1.04157e6 | − | 601350.i | 0.0529172 | − | 0.0305517i | ||||
\(271\) | 1.36163e7 | − | 2.35840e7i | 0.684147 | − | 1.18498i | −0.289556 | − | 0.957161i | \(-0.593508\pi\) |
0.973704 | − | 0.227817i | \(-0.0731589\pi\) | |||||||
\(272\) | 7.23939e6 | − | 1.25390e7i | 0.359745 | − | 0.623097i | ||||
\(273\) | −4.72406e6 | + | 8.18230e6i | −0.232181 | + | 0.402150i | ||||
\(274\) | −2.10027e6 | −0.102099 | ||||||||
\(275\) | 1.27569e7 | − | 2.20956e7i | 0.613404 | − | 1.06245i | ||||
\(276\) | −192079. | − | 110897.i | −0.00913595 | − | 0.00527464i | ||||
\(277\) | 7.82758e6 | − | 4.51926e6i | 0.368289 | − | 0.212632i | −0.304422 | − | 0.952537i | \(-0.598463\pi\) |
0.672711 | + | 0.739906i | \(0.265130\pi\) | |||||||
\(278\) | 1.40158e7 | − | 8.09204e6i | 0.652356 | − | 0.376638i | ||||
\(279\) | −3.39022e7 | −1.56105 | ||||||||
\(280\) | 2.73051e6i | 0.124385i | ||||||||
\(281\) | −3.45902e6 | − | 5.99120e6i | −0.155896 | − | 0.270019i | 0.777489 | − | 0.628896i | \(-0.216493\pi\) |
−0.933385 | + | 0.358877i | \(0.883160\pi\) | |||||||
\(282\) | 3.08990e6 | + | 5.35186e6i | 0.137783 | + | 0.238648i | ||||
\(283\) | −837525. | + | 1.45064e6i | −0.0369520 | + | 0.0640028i | −0.883910 | − | 0.467657i | \(-0.845098\pi\) |
0.846958 | + | 0.531660i | \(0.178432\pi\) | |||||||
\(284\) | 1.13237e6 | + | 653772.i | 0.0494347 | + | 0.0285411i | ||||
\(285\) | − | 296861.i | − | 0.0128238i | ||||||
\(286\) | −2.32329e7 | − | 1.34135e7i | −0.993127 | − | 0.573382i | ||||
\(287\) | 4.55913e7 | + | 2.63221e7i | 1.92857 | + | 1.11346i | ||||
\(288\) | −5.20229e6 | − | 3.00354e6i | −0.217780 | − | 0.125735i | ||||
\(289\) | 3.01541e6 | + | 5.22284e6i | 0.124926 | + | 0.216378i | ||||
\(290\) | − | 1.29646e6i | − | 0.0531576i | ||||||
\(291\) | −6.40319e6 | + | 3.69688e6i | −0.259847 | + | 0.150023i | ||||
\(292\) | 3.91709e6 | + | 2.26153e6i | 0.157331 | + | 0.0908351i | ||||
\(293\) | −2.10978e7 | −0.838755 | −0.419377 | − | 0.907812i | \(-0.637752\pi\) | ||||
−0.419377 | + | 0.907812i | \(0.637752\pi\) | |||||||
\(294\) | 2.31551e6 | − | 4.01059e6i | 0.0911182 | − | 0.157821i | ||||
\(295\) | 2.24618e6 | − | 1.29683e6i | 0.0874941 | − | 0.0505147i | ||||
\(296\) | 1.82453e7 | + | 3.16019e7i | 0.703521 | + | 1.21853i | ||||
\(297\) | 2.25919e7i | 0.862351i | ||||||||
\(298\) | −9.34690e6 | − | 1.61893e7i | −0.353198 | − | 0.611758i | ||||
\(299\) | 5.11998e6 | 0.191538 | ||||||||
\(300\) | − | 1.47847e6i | − | 0.0547581i | ||||||
\(301\) | 2.96733e7 | − | 1.59714e7i | 1.08810 | − | 0.585659i | ||||
\(302\) | −1.44555e7 | −0.524822 | ||||||||
\(303\) | − | 4.84583e6i | − | 0.174197i | ||||||
\(304\) | 7.28349e6 | − | 4.20513e6i | 0.259250 | − | 0.149678i | ||||
\(305\) | −775112. | −0.0273190 | ||||||||
\(306\) | 1.70592e7 | − | 9.84911e6i | 0.595379 | − | 0.343742i | ||||
\(307\) | 8.99820e6 | + | 1.55853e7i | 0.310986 | + | 0.538643i | 0.978576 | − | 0.205886i | \(-0.0660075\pi\) |
−0.667590 | + | 0.744529i | \(0.732674\pi\) | |||||||
\(308\) | −5.71043e6 | − | 3.29692e6i | −0.195441 | − | 0.112838i | ||||
\(309\) | − | 3.83534e6i | − | 0.129995i | ||||||
\(310\) | −2.37257e6 | + | 4.10941e6i | −0.0796405 | + | 0.137941i | ||||
\(311\) | −5.51625e6 | − | 9.55443e6i | −0.183385 | − | 0.317632i | 0.759646 | − | 0.650336i | \(-0.225372\pi\) |
−0.943031 | + | 0.332705i | \(0.892039\pi\) | |||||||
\(312\) | −1.20924e7 | −0.398151 | ||||||||
\(313\) | −2.66776e7 | + | 1.54023e7i | −0.869988 | + | 0.502288i | −0.867344 | − | 0.497709i | \(-0.834175\pi\) |
−0.00264387 | + | 0.999997i | \(0.500842\pi\) | |||||||
\(314\) | 4.95634e6 | − | 8.58463e6i | 0.160093 | − | 0.277289i | ||||
\(315\) | −1.57731e6 | + | 2.73198e6i | −0.0504643 | + | 0.0874068i | ||||
\(316\) | 4.27764e6 | − | 7.40909e6i | 0.135564 | − | 0.234803i | ||||
\(317\) | −2.84283e7 | −0.892428 | −0.446214 | − | 0.894926i | \(-0.647228\pi\) | ||||
−0.446214 | + | 0.894926i | \(0.647228\pi\) | |||||||
\(318\) | −5.18738e6 | + | 8.98481e6i | −0.161312 | + | 0.279401i | ||||
\(319\) | 2.10905e7 | + | 1.21766e7i | 0.649702 | + | 0.375106i | ||||
\(320\) | −2.96783e6 | + | 1.71348e6i | −0.0905709 | + | 0.0522911i | ||||
\(321\) | −1.96545e7 | + | 1.13475e7i | −0.594220 | + | 0.343073i | ||||
\(322\) | −7.27206e6 | −0.217816 | ||||||||
\(323\) | − | 1.05176e7i | − | 0.312112i | ||||||
\(324\) | −1.50223e6 | − | 2.60195e6i | −0.0441675 | − | 0.0765003i | ||||
\(325\) | 1.70648e7 | + | 2.95571e7i | 0.497108 | + | 0.861016i | ||||
\(326\) | −6.25447e6 | + | 1.08331e7i | −0.180525 | + | 0.312679i | ||||
\(327\) | 7.12274e6 | + | 4.11232e6i | 0.203706 | + | 0.117610i | ||||
\(328\) | 6.73780e7i | 1.90940i | ||||||||
\(329\) | −3.03661e7 | − | 1.75319e7i | −0.852710 | − | 0.492312i | ||||
\(330\) | 1.26593e6 | + | 730885.i | 0.0352264 | + | 0.0203379i | ||||
\(331\) | 2.37071e7 | + | 1.36873e7i | 0.653724 | + | 0.377428i | 0.789881 | − | 0.613260i | \(-0.210142\pi\) |
−0.136158 | + | 0.990687i | \(0.543475\pi\) | |||||||
\(332\) | −1.46948e6 | − | 2.54522e6i | −0.0401560 | − | 0.0695522i | ||||
\(333\) | 4.21584e7i | 1.14170i | ||||||||
\(334\) | −2.31840e7 | + | 1.33853e7i | −0.622227 | + | 0.359243i | ||||
\(335\) | 3.76888e6 | + | 2.17597e6i | 0.100249 | + | 0.0578785i | ||||
\(336\) | 1.45851e7 | 0.384495 | ||||||||
\(337\) | 1.73763e7 | − | 3.00967e7i | 0.454013 | − | 0.786373i | −0.544618 | − | 0.838684i | \(-0.683325\pi\) |
0.998631 | + | 0.0523113i | \(0.0166588\pi\) | |||||||
\(338\) | 202339. | − | 116821.i | 0.00523999 | − | 0.00302531i | ||||
\(339\) | −5.13571e6 | − | 8.89531e6i | −0.131826 | − | 0.228330i | ||||
\(340\) | 477117.i | 0.0121391i | ||||||||
\(341\) | −4.45672e7 | − | 7.71926e7i | −1.12396 | − | 1.94676i | ||||
\(342\) | 1.14421e7 | 0.286039 | ||||||||
\(343\) | − | 2.35887e7i | − | 0.584550i | ||||||
\(344\) | 3.66918e7 | + | 2.26693e7i | 0.901351 | + | 0.556881i | ||||
\(345\) | −278981. | −0.00679388 | ||||||||
\(346\) | − | 2.82481e7i | − | 0.681963i | ||||||
\(347\) | −5.19013e7 | + | 2.99652e7i | −1.24220 | + | 0.717182i | −0.969541 | − | 0.244930i | \(-0.921235\pi\) |
−0.272655 | + | 0.962112i | \(0.587902\pi\) | |||||||
\(348\) | 1.41122e6 | 0.0334854 | ||||||||
\(349\) | −6.34422e7 | + | 3.66284e7i | −1.49246 | + | 0.861671i | −0.999963 | − | 0.00864411i | \(-0.997248\pi\) |
−0.492495 | + | 0.870315i | \(0.663915\pi\) | |||||||
\(350\) | −2.42376e7 | − | 4.19808e7i | −0.565308 | − | 0.979143i | ||||
\(351\) | −2.61722e7 | − | 1.51105e7i | −0.605228 | − | 0.349428i | ||||
\(352\) | − | 1.57936e7i | − | 0.362120i | ||||||
\(353\) | 2.87769e7 | − | 4.98431e7i | 0.654215 | − | 1.13313i | −0.327875 | − | 0.944721i | \(-0.606333\pi\) |
0.982090 | − | 0.188412i | \(-0.0603341\pi\) | |||||||
\(354\) | −8.15719e6 | − | 1.41287e7i | −0.183879 | − | 0.318487i | ||||
\(355\) | 1.64468e6 | 0.0367618 | ||||||||
\(356\) | −5.46889e6 | + | 3.15747e6i | −0.121213 | + | 0.0699824i | ||||
\(357\) | 9.11983e6 | − | 1.57960e7i | 0.200439 | − | 0.347171i | ||||
\(358\) | −3.34141e7 | + | 5.78749e7i | −0.728250 | + | 1.26137i | ||||
\(359\) | 2.21746e7 | − | 3.84076e7i | 0.479262 | − | 0.830105i | −0.520456 | − | 0.853889i | \(-0.674238\pi\) |
0.999717 | + | 0.0237833i | \(0.00757118\pi\) | |||||||
\(360\) | −4.03750e6 | −0.0865377 | ||||||||
\(361\) | −2.04683e7 | + | 3.54521e7i | −0.435070 | + | 0.753564i | ||||
\(362\) | 2.86463e7 | + | 1.65389e7i | 0.603869 | + | 0.348644i | ||||
\(363\) | −8.26376e6 | + | 4.77108e6i | −0.172766 | + | 0.0997464i | ||||
\(364\) | 7.63879e6 | − | 4.41026e6i | 0.158387 | − | 0.0914450i | ||||
\(365\) | 5.68929e6 | 0.116998 | ||||||||
\(366\) | 4.87553e6i | 0.0994439i | ||||||||
\(367\) | −4.43801e6 | − | 7.68686e6i | −0.0897822 | − | 0.155507i | 0.817637 | − | 0.575734i | \(-0.195284\pi\) |
−0.907419 | + | 0.420227i | \(0.861950\pi\) | |||||||
\(368\) | −3.95186e6 | − | 6.84482e6i | −0.0792973 | − | 0.137347i | ||||
\(369\) | −3.89216e7 | + | 6.74141e7i | −0.774660 | + | 1.34175i | ||||
\(370\) | 5.11018e6 | + | 2.95036e6i | 0.100886 | + | 0.0582466i | ||||
\(371\) | − | 5.88657e7i | − | 1.15277i | ||||||
\(372\) | −4.47315e6 | − | 2.58257e6i | −0.0868930 | − | 0.0501677i | ||||
\(373\) | 1.08499e7 | + | 6.26417e6i | 0.209073 | + | 0.120708i | 0.600881 | − | 0.799339i | \(-0.294817\pi\) |
−0.391807 | + | 0.920047i | \(0.628150\pi\) | |||||||
\(374\) | 4.48513e7 | + | 2.58949e7i | 0.857353 | + | 0.494993i | ||||
\(375\) | −1.86815e6 | − | 3.23572e6i | −0.0354256 | − | 0.0613589i | ||||
\(376\) | − | 4.48771e7i | − | 0.844231i | ||||||
\(377\) | −2.82126e7 | + | 1.62885e7i | −0.526524 | + | 0.303989i | ||||
\(378\) | 3.71731e7 | + | 2.14619e7i | 0.688262 | + | 0.397368i | ||||
\(379\) | 5.18840e7 | 0.953051 | 0.476526 | − | 0.879161i | \(-0.341896\pi\) | ||||
0.476526 | + | 0.879161i | \(0.341896\pi\) | |||||||
\(380\) | −138571. | + | 240012.i | −0.00252535 | + | 0.00437403i | ||||
\(381\) | 4.73519e6 | − | 2.73386e6i | 0.0856175 | − | 0.0494313i | ||||
\(382\) | 2.99846e7 | + | 5.19348e7i | 0.537908 | + | 0.931683i | ||||
\(383\) | − | 3.63320e7i | − | 0.646685i | −0.946282 | − | 0.323342i | \(-0.895193\pi\) | ||
0.946282 | − | 0.323342i | \(-0.104807\pi\) | |||||||
\(384\) | 7.67600e6 | + | 1.32952e7i | 0.135563 | + | 0.234802i | ||||
\(385\) | −8.29399e6 | −0.145339 | ||||||||
\(386\) | − | 9.49686e7i | − | 1.65127i | ||||||
\(387\) | 2.36164e7 | + | 4.38768e7i | 0.407456 | + | 0.757012i | ||||
\(388\) | 6.90263e6 | 0.118173 | ||||||||
\(389\) | 2.84384e7i | 0.483122i | 0.970386 | + | 0.241561i | \(0.0776594\pi\) | ||||
−0.970386 | + | 0.241561i | \(0.922341\pi\) | |||||||
\(390\) | −1.69342e6 | + | 977699.i | −0.0285477 | + | 0.0164820i | ||||
\(391\) | −9.88418e6 | −0.165352 | ||||||||
\(392\) | −2.91245e7 | + | 1.68150e7i | −0.483505 | + | 0.279151i | ||||
\(393\) | 8.27164e6 | + | 1.43269e7i | 0.136274 | + | 0.236034i | ||||
\(394\) | −7.77760e7 | − | 4.49040e7i | −1.27162 | − | 0.734169i | ||||
\(395\) | − | 1.07612e7i | − | 0.174610i | ||||||
\(396\) | 4.87503e6 | − | 8.44380e6i | 0.0785040 | − | 0.135973i | ||||
\(397\) | 1.42184e6 | + | 2.46270e6i | 0.0227237 | + | 0.0393586i | 0.877164 | − | 0.480192i | \(-0.159433\pi\) |
−0.854440 | + | 0.519550i | \(0.826100\pi\) | |||||||
\(398\) | 1.03958e8 | 1.64895 | ||||||||
\(399\) | 9.17539e6 | − | 5.29742e6i | 0.144446 | − | 0.0833960i | ||||
\(400\) | 2.63429e7 | − | 4.56272e7i | 0.411608 | − | 0.712926i | ||||
\(401\) | 3.15930e7 | − | 5.47208e7i | 0.489957 | − | 0.848631i | −0.509976 | − | 0.860189i | \(-0.670346\pi\) |
0.999933 | + | 0.0115575i | \(0.00367896\pi\) | |||||||
\(402\) | 1.36870e7 | − | 2.37066e7i | 0.210684 | − | 0.364915i | ||||
\(403\) | 1.19234e8 | 1.82174 | ||||||||
\(404\) | −2.26197e6 | + | 3.91785e6i | −0.0343039 | + | 0.0594161i | ||||
\(405\) | −3.27283e6 | − | 1.88957e6i | −0.0492673 | − | 0.0284445i | ||||
\(406\) | 4.00711e7 | − | 2.31351e7i | 0.598761 | − | 0.345695i | ||||
\(407\) | −9.59914e7 | + | 5.54207e7i | −1.42380 | + | 0.822032i | ||||
\(408\) | 2.33444e7 | 0.343719 | ||||||||
\(409\) | 7.44168e7i | 1.08768i | 0.839189 | + | 0.543840i | \(0.183030\pi\) | ||||
−0.839189 | + | 0.543840i | \(0.816970\pi\) | |||||||
\(410\) | 5.44768e6 | + | 9.43565e6i | 0.0790423 | + | 0.136905i | ||||
\(411\) | −1.43782e6 | − | 2.49037e6i | −0.0207099 | − | 0.0358706i | ||||
\(412\) | −1.79029e6 | + | 3.10087e6i | −0.0255995 | + | 0.0443396i | ||||
\(413\) | 8.01652e7 | + | 4.62834e7i | 1.13798 | + | 0.657015i | ||||
\(414\) | − | 1.07529e7i | − | 0.151539i | ||||||
\(415\) | −3.20148e6 | − | 1.84837e6i | −0.0447926 | − | 0.0258610i | ||||
\(416\) | 1.82965e7 | + | 1.05635e7i | 0.254149 | + | 0.146733i | ||||
\(417\) | 1.91901e7 | + | 1.10794e7i | 0.264649 | + | 0.152795i | ||||
\(418\) | 1.50415e7 | + | 2.60526e7i | 0.205950 | + | 0.356716i | ||||
\(419\) | 1.19518e8i | 1.62476i | 0.583127 | + | 0.812381i | \(0.301829\pi\) | ||||
−0.583127 | + | 0.812381i | \(0.698171\pi\) | |||||||
\(420\) | −416228. | + | 240310.i | −0.00561803 | + | 0.00324357i | ||||
\(421\) | −7.45688e7 | − | 4.30523e7i | −0.999335 | − | 0.576966i | −0.0912834 | − | 0.995825i | \(-0.529097\pi\) |
−0.908051 | + | 0.418859i | \(0.862430\pi\) | |||||||
\(422\) | 4.40944e7 | 0.586740 | ||||||||
\(423\) | 2.59237e7 | − | 4.49012e7i | 0.342512 | − | 0.593249i | ||||
\(424\) | 6.52469e7 | − | 3.76703e7i | 0.855977 | − | 0.494199i | ||||
\(425\) | −3.29437e7 | − | 5.70602e7i | −0.429147 | − | 0.743304i | ||||
\(426\) | − | 1.03452e7i | − | 0.133816i | ||||||
\(427\) | −1.38317e7 | − | 2.39572e7i | −0.177661 | − | 0.307718i | ||||
\(428\) | 2.11876e7 | 0.270240 | ||||||||
\(429\) | − | 3.67309e7i | − | 0.465221i | ||||||
\(430\) | 6.97121e6 | + | 207995.i | 0.0876805 | + | 0.00261605i | ||||
\(431\) | 5.24388e6 | 0.0654969 | 0.0327485 | − | 0.999464i | \(-0.489574\pi\) | ||||
0.0327485 | + | 0.999464i | \(0.489574\pi\) | |||||||
\(432\) | 4.66523e7i | 0.578657i | ||||||||
\(433\) | −1.19440e8 | + | 6.89586e7i | −1.47125 | + | 0.849425i | −0.999478 | − | 0.0322980i | \(-0.989717\pi\) |
−0.471768 | + | 0.881723i | \(0.656384\pi\) | |||||||
\(434\) | −1.69352e8 | −2.07167 | ||||||||
\(435\) | 1.53727e6 | − | 887542.i | 0.0186759 | − | 0.0107825i | ||||
\(436\) | −3.83916e6 | − | 6.64961e6i | −0.0463208 | − | 0.0802300i | ||||
\(437\) | −4.97220e6 | − | 2.87070e6i | −0.0595805 | − | 0.0343988i | ||||
\(438\) | − | 3.57861e7i | − | 0.425885i | ||||||
\(439\) | −2.46820e7 | + | 4.27504e7i | −0.291734 | + | 0.505297i | −0.974220 | − | 0.225601i | \(-0.927565\pi\) |
0.682486 | + | 0.730898i | \(0.260899\pi\) | |||||||
\(440\) | −5.30762e6 | − | 9.19307e6i | −0.0623077 | − | 0.107920i | ||||
\(441\) | −3.88535e7 | −0.453017 | ||||||||
\(442\) | −5.99972e7 | + | 3.46394e7i | −0.694807 | + | 0.401147i | ||||
\(443\) | 6.69891e7 | − | 1.16028e8i | 0.770536 | − | 1.33461i | −0.166734 | − | 0.986002i | \(-0.553322\pi\) |
0.937270 | − | 0.348605i | \(-0.113345\pi\) | |||||||
\(444\) | −3.21151e6 | + | 5.56250e6i | −0.0366911 | + | 0.0635508i | ||||
\(445\) | −3.97159e6 | + | 6.87899e6i | −0.0450697 | + | 0.0780629i | ||||
\(446\) | 5.68692e7 | 0.641021 | ||||||||
\(447\) | 1.27975e7 | − | 2.21660e7i | 0.143286 | − | 0.248179i | ||||
\(448\) | −1.05920e8 | − | 6.11532e7i | −1.17800 | − | 0.680119i | ||||
\(449\) | 1.43977e8 | − | 8.31254e7i | 1.59058 | − | 0.918321i | 0.597371 | − | 0.801965i | \(-0.296212\pi\) |
0.993208 | − | 0.116356i | \(-0.0371213\pi\) | |||||||
\(450\) | 6.20754e7 | − | 3.58392e7i | 0.681211 | − | 0.393297i | ||||
\(451\) | −2.04662e8 | −2.23104 | ||||||||
\(452\) | 9.58914e6i | 0.103840i | ||||||||
\(453\) | −9.89604e6 | − | 1.71404e7i | −0.106455 | − | 0.184386i | ||||
\(454\) | −2.58466e7 | − | 4.47677e7i | −0.276208 | − | 0.478407i | ||||
\(455\) | 5.54740e6 | − | 9.60838e6i | 0.0588919 | − | 0.102004i | ||||
\(456\) | 1.17433e7 | + | 6.78001e6i | 0.123850 | + | 0.0715050i | ||||
\(457\) | 4.13956e7i | 0.433716i | 0.976203 | + | 0.216858i | \(0.0695808\pi\) | ||||
−0.976203 | + | 0.216858i | \(0.930419\pi\) | |||||||
\(458\) | −4.99737e7 | − | 2.88523e7i | −0.520169 | − | 0.300320i | ||||
\(459\) | 5.05257e7 | + | 2.91710e7i | 0.522485 | + | 0.301657i | ||||
\(460\) | 225556. | + | 130225.i | 0.00231730 | + | 0.00133789i | ||||
\(461\) | 630616. | + | 1.09226e6i | 0.00643669 | + | 0.0111487i | 0.869226 | − | 0.494415i | \(-0.164618\pi\) |
−0.862789 | + | 0.505564i | \(0.831284\pi\) | |||||||
\(462\) | 5.21699e7i | 0.529047i | ||||||||
\(463\) | −8.97451e7 | + | 5.18144e7i | −0.904207 | + | 0.522044i | −0.878563 | − | 0.477627i | \(-0.841497\pi\) |
−0.0256441 | + | 0.999671i | \(0.508164\pi\) | |||||||
\(464\) | 4.35517e7 | + | 2.51446e7i | 0.435965 | + | 0.251705i | ||||
\(465\) | −6.49693e6 | −0.0646174 | ||||||||
\(466\) | 6.08239e7 | − | 1.05350e8i | 0.601058 | − | 1.04106i | ||||
\(467\) | −5.28163e7 | + | 3.04935e7i | −0.518582 | + | 0.299403i | −0.736354 | − | 0.676596i | \(-0.763454\pi\) |
0.217772 | + | 0.976000i | \(0.430121\pi\) | |||||||
\(468\) | 6.52129e6 | + | 1.12952e7i | 0.0636203 | + | 0.110194i | ||||
\(469\) | 1.55319e8i | 1.50558i | ||||||||
\(470\) | −3.62843e6 | − | 6.28462e6i | −0.0349482 | − | 0.0605321i | ||||
\(471\) | 1.35722e7 | 0.129893 | ||||||||
\(472\) | 1.18474e8i | 1.12667i | ||||||||
\(473\) | −6.88585e7 | + | 1.11452e8i | −0.650690 | + | 1.05319i | ||||
\(474\) | −6.76887e7 | −0.635596 | ||||||||
\(475\) | − | 3.82719e7i | − | 0.357107i | ||||||
\(476\) | −1.47468e7 | + | 8.51405e6i | −0.136734 | + | 0.0789433i | ||||
\(477\) | 8.70426e7 | 0.802004 | ||||||||
\(478\) | −3.57182e7 | + | 2.06219e7i | −0.327044 | + | 0.188819i | ||||
\(479\) | −3.09836e7 | − | 5.36652e7i | −0.281920 | − | 0.488299i | 0.689938 | − | 0.723869i | \(-0.257638\pi\) |
−0.971858 | + | 0.235569i | \(0.924304\pi\) | |||||||
\(480\) | −996953. | − | 575591.i | −0.00901469 | − | 0.00520463i | ||||
\(481\) | − | 1.48272e8i | − | 1.33236i | ||||||
\(482\) | −9.33736e7 | + | 1.61728e8i | −0.833841 | + | 1.44425i | ||||
\(483\) | −4.97836e6 | − | 8.62278e6i | −0.0441820 | − | 0.0765255i | ||||
\(484\) | 8.90833e6 | 0.0785706 | ||||||||
\(485\) | 7.51918e6 | − | 4.34120e6i | 0.0659091 | − | 0.0380526i | ||||
\(486\) | −4.87995e7 | + | 8.45232e7i | −0.425115 | + | 0.736321i | ||||
\(487\) | −1.21687e7 | + | 2.10768e7i | −0.105356 | + | 0.182481i | −0.913883 | − | 0.405977i | \(-0.866931\pi\) |
0.808528 | + | 0.588458i | \(0.200265\pi\) | |||||||
\(488\) | 1.77028e7 | − | 3.06622e7i | 0.152329 | − | 0.263842i | ||||
\(489\) | −1.71269e7 | −0.146471 | ||||||||
\(490\) | −2.71908e6 | + | 4.70958e6i | −0.0231118 | + | 0.0400308i | ||||
\(491\) | 7.41246e7 | + | 4.27958e7i | 0.626207 | + | 0.361541i | 0.779282 | − | 0.626674i | \(-0.215584\pi\) |
−0.153075 | + | 0.988215i | \(0.548918\pi\) | |||||||
\(492\) | −1.02708e7 | + | 5.92987e6i | −0.0862403 | + | 0.0497909i | ||||
\(493\) | 5.44646e7 | − | 3.14452e7i | 0.454542 | − | 0.262430i | ||||
\(494\) | −4.02418e7 | −0.333808 | ||||||||
\(495\) | − | 1.22640e7i | − | 0.101115i | ||||||
\(496\) | −9.20311e7 | − | 1.59402e8i | −0.754205 | − | 1.30632i | ||||
\(497\) | 2.93490e7 | + | 5.08339e7i | 0.239069 | + | 0.414080i | ||||
\(498\) | −1.16264e7 | + | 2.01376e7i | −0.0941366 | + | 0.163049i | ||||
\(499\) | 1.39441e8 | + | 8.05061e7i | 1.12224 | + | 0.647928i | 0.941973 | − | 0.335688i | \(-0.108969\pi\) |
0.180272 | + | 0.983617i | \(0.442302\pi\) | |||||||
\(500\) | 3.48811e6i | 0.0279049i | ||||||||
\(501\) | −3.17430e7 | − | 1.83268e7i | −0.252426 | − | 0.145738i | ||||
\(502\) | −2.97836e7 | − | 1.71955e7i | −0.235432 | − | 0.135927i | ||||
\(503\) | 1.23803e8 | + | 7.14776e7i | 0.972807 | + | 0.561650i | 0.900091 | − | 0.435702i | \(-0.143500\pi\) |
0.0727162 | + | 0.997353i | \(0.476833\pi\) | |||||||
\(504\) | −7.20483e7 | − | 1.24791e8i | −0.562772 | − | 0.974750i | ||||
\(505\) | 5.69040e6i | 0.0441844i | ||||||||
\(506\) | 2.44836e7 | − | 1.41356e7i | 0.188983 | − | 0.109109i | ||||
\(507\) | 277038. | + | 159948.i | 0.00212577 | + | 0.00122731i | ||||
\(508\) | −5.10453e6 | −0.0389372 | ||||||||
\(509\) | 2.35970e7 | − | 4.08712e7i | 0.178939 | − | 0.309931i | −0.762579 | − | 0.646895i | \(-0.776067\pi\) |
0.941517 | + | 0.336965i | \(0.109400\pi\) | |||||||
\(510\) | 3.26917e6 | − | 1.88746e6i | 0.0246449 | − | 0.0142287i | ||||
\(511\) | 1.01524e8 | + | 1.75845e8i | 0.760863 | + | 1.31785i | ||||
\(512\) | − | 1.50745e8i | − | 1.12314i | ||||||
\(513\) | 1.69445e7 | + | 2.93487e7i | 0.125510 | + | 0.217389i | ||||
\(514\) | 1.83415e8 | 1.35066 | ||||||||
\(515\) | 4.50379e6i | 0.0329728i | ||||||||
\(516\) | −226405. | + | 7.58826e6i | −0.00164792 | + | 0.0552323i | ||||
\(517\) | 1.36315e8 | 0.986445 | ||||||||
\(518\) | 2.10594e8i | 1.51516i | ||||||||
\(519\) | 3.34949e7 | − | 1.93383e7i | 0.239595 | − | 0.138330i | ||||
\(520\) | 1.41999e7 | 0.100989 | ||||||||
\(521\) | −9.06862e7 | + | 5.23577e7i | −0.641251 | + | 0.370226i | −0.785096 | − | 0.619374i | \(-0.787387\pi\) |
0.143845 | + | 0.989600i | \(0.454053\pi\) | |||||||
\(522\) | 3.42090e7 | + | 5.92517e7i | 0.240507 | + | 0.416571i | ||||
\(523\) | −1.68736e8 | − | 9.74196e7i | −1.17951 | − | 0.680991i | −0.223609 | − | 0.974679i | \(-0.571784\pi\) |
−0.955901 | + | 0.293688i | \(0.905117\pi\) | |||||||
\(524\) | − | 1.54444e7i | − | 0.107344i | ||||||
\(525\) | 3.31855e7 | − | 5.74790e7i | 0.229335 | − | 0.397220i | ||||
\(526\) | 4.40484e7 | + | 7.62941e7i | 0.302673 | + | 0.524244i | ||||
\(527\) | −2.30183e8 | −1.57268 | ||||||||
\(528\) | −4.91049e7 | + | 2.83507e7i | −0.333598 | + | 0.192603i | ||||
\(529\) | 7.13201e7 | − | 1.23530e8i | 0.481776 | − | 0.834461i | ||||
\(530\) | 6.09148e6 | − | 1.05507e7i | 0.0409162 | − | 0.0708689i | ||||
\(531\) | −6.84375e7 | + | 1.18537e8i | −0.457099 | + | 0.791719i | ||||
\(532\) | −9.89107e6 | −0.0656914 | ||||||||
\(533\) | 1.36887e8 | − | 2.37096e8i | 0.904028 | − | 1.56582i | ||||
\(534\) | 4.32695e7 | + | 2.49816e7i | 0.284157 | + | 0.164058i | ||||
\(535\) | 2.30800e7 | − | 1.33253e7i | 0.150722 | − | 0.0870191i | ||||
\(536\) | −1.72155e8 | + | 9.93939e7i | −1.11796 | + | 0.645454i | ||||
\(537\) | −9.14995e7 | −0.590875 | ||||||||
\(538\) | − | 7.54880e7i | − | 0.484765i | ||||||
\(539\) | −5.10761e7 | − | 8.84664e7i | −0.326176 | − | 0.564953i | ||||
\(540\) | −768662. | − | 1.33136e6i | −0.00488151 | − | 0.00845503i | ||||
\(541\) | 1.22324e8 | − | 2.11871e8i | 0.772536 | − | 1.33807i | −0.163632 | − | 0.986521i | \(-0.552321\pi\) |
0.936169 | − | 0.351551i | \(-0.114346\pi\) | |||||||
\(542\) | 1.74201e8 | + | 1.00575e8i | 1.09409 | + | 0.631671i | ||||
\(543\) | 4.52894e7i | 0.282877i | ||||||||
\(544\) | −3.53215e7 | − | 2.03929e7i | −0.219403 | − | 0.126673i | ||||
\(545\) | −8.36415e6 | − | 4.82904e6i | −0.0516692 | − | 0.0298313i | ||||
\(546\) | −6.04376e7 | − | 3.48936e7i | −0.371303 | − | 0.214372i | ||||
\(547\) | −8.78331e7 | − | 1.52131e8i | −0.536656 | − | 0.929516i | −0.999081 | − | 0.0428576i | \(-0.986354\pi\) |
0.462425 | − | 0.886658i | \(-0.346980\pi\) | |||||||
\(548\) | 2.68462e6i | 0.0163133i | ||||||||
\(549\) | 3.54247e7 | − | 2.04524e7i | 0.214086 | − | 0.123603i | ||||
\(550\) | 1.63206e8 | + | 9.42271e7i | 0.980954 | + | 0.566354i | ||||
\(551\) | 3.65310e7 | 0.218377 | ||||||||
\(552\) | 6.37167e6 | − | 1.10361e7i | 0.0378823 | − | 0.0656140i | ||||
\(553\) | 3.32607e8 | − | 1.92031e8i | 1.96678 | − | 1.13552i | ||||
\(554\) | 3.33809e7 | + | 5.78174e7i | 0.196322 | + | 0.340040i | ||||
\(555\) | 8.07913e6i | 0.0472591i | ||||||||
\(556\) | −1.03435e7 | − | 1.79154e7i | −0.0601786 | − | 0.104232i | ||||
\(557\) | −9.14418e7 | −0.529150 | −0.264575 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264575 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(558\) | − | 2.50414e8i | − | 1.44131i | ||||||
\(559\) | −8.30590e7 | − | 1.54315e8i | −0.475501 | − | 0.883432i | ||||
\(560\) | −1.71270e7 | −0.0975256 | ||||||||
\(561\) | 7.09093e7i | 0.401619i | ||||||||
\(562\) | 4.42532e7 | − | 2.55496e7i | 0.249308 | − | 0.143938i | ||||
\(563\) | 2.74712e8 | 1.53940 | 0.769701 | − | 0.638404i | \(-0.220405\pi\) | ||||
0.769701 | + | 0.638404i | \(0.220405\pi\) | |||||||
\(564\) | 6.84089e6 | − | 3.94959e6i | 0.0381308 | − | 0.0220148i | ||||
\(565\) | 6.03080e6 | + | 1.04457e7i | 0.0334372 | + | 0.0579149i | ||||
\(566\) | −1.07149e7 | − | 6.18627e6i | −0.0590936 | − | 0.0341177i | ||||
\(567\) | − | 1.34876e8i | − | 0.739921i | ||||||
\(568\) | −3.75629e7 | + | 6.50609e7i | −0.204981 | + | 0.355038i | ||||
\(569\) | −9.27992e6 | − | 1.60733e7i | −0.0503741 | − | 0.0872506i | 0.839739 | − | 0.542990i | \(-0.182708\pi\) |
−0.890113 | + | 0.455740i | \(0.849375\pi\) | |||||||
\(570\) | 2.19272e6 | 0.0118402 | ||||||||
\(571\) | −7.84214e7 | + | 4.52766e7i | −0.421237 | + | 0.243201i | −0.695606 | − | 0.718423i | \(-0.744864\pi\) |
0.274370 | + | 0.961624i | \(0.411531\pi\) | |||||||
\(572\) | −1.71455e7 | + | 2.96969e7i | −0.0916141 | + | 0.158680i | ||||
\(573\) | −4.10541e7 | + | 7.11078e7i | −0.218219 | + | 0.377967i | ||||
\(574\) | −1.94425e8 | + | 3.36754e8i | −1.02806 | + | 1.78065i | ||||
\(575\) | −3.59668e7 | −0.189190 | ||||||||
\(576\) | 9.04249e7 | − | 1.56621e8i | 0.473174 | − | 0.819561i | ||||
\(577\) | 1.87405e8 | + | 1.08198e8i | 0.975557 | + | 0.563238i | 0.900926 | − | 0.433973i | \(-0.142889\pi\) |
0.0746313 | + | 0.997211i | \(0.476222\pi\) | |||||||
\(578\) | −3.85778e7 | + | 2.22729e7i | −0.199781 | + | 0.115344i | ||||
\(579\) | 1.12608e8 | − | 6.50143e7i | 0.580142 | − | 0.334945i | ||||
\(580\) | −1.65717e6 | −0.00849345 | ||||||||
\(581\) | − | 1.31935e8i | − | 0.672717i | ||||||
\(582\) | −2.73066e7 | − | 4.72963e7i | −0.138515 | − | 0.239916i | ||||
\(583\) | 1.14424e8 | + | 1.98189e8i | 0.577448 | + | 1.00017i | ||||
\(584\) | −1.29938e8 | + | 2.25059e8i | −0.652375 | + | 1.12995i | ||||
\(585\) | 1.42075e7 | + | 8.20273e6i | 0.0709662 | + | 0.0409724i | ||||
\(586\) | − | 1.55836e8i | − | 0.774419i | ||||||
\(587\) | −1.28260e8 | − | 7.40511e7i | −0.634129 | − | 0.366115i | 0.148220 | − | 0.988954i | \(-0.452646\pi\) |
−0.782350 | + | 0.622840i | \(0.785979\pi\) | |||||||
\(588\) | −5.12644e6 | − | 2.95975e6i | −0.0252165 | − | 0.0145587i | ||||
\(589\) | −1.15793e8 | − | 6.68529e7i | −0.566676 | − | 0.327171i | ||||
\(590\) | 9.57889e6 | + | 1.65911e7i | 0.0466401 | + | 0.0807830i | ||||
\(591\) | − | 1.22963e8i | − | 0.595678i | ||||||
\(592\) | −1.98222e8 | + | 1.14443e8i | −0.955403 | + | 0.551602i | ||||
\(593\) | 2.93213e8 | + | 1.69287e8i | 1.40611 | + | 0.811819i | 0.995010 | − | 0.0997707i | \(-0.0318109\pi\) |
0.411101 | + | 0.911590i | \(0.365144\pi\) | |||||||
\(594\) | −1.66873e8 | −0.796206 | ||||||||
\(595\) | −1.07093e7 | + | 1.85491e7i | −0.0508406 | + | 0.0880585i | ||||
\(596\) | −2.06936e7 | + | 1.19475e7i | −0.0977457 | + | 0.0564335i | ||||
\(597\) | 7.11682e7 | + | 1.23267e8i | 0.334474 | + | 0.579327i | ||||
\(598\) | 3.78181e7i | 0.176846i | ||||||||
\(599\) | 7.50798e6 | + | 1.30042e7i | 0.0349335 | + | 0.0605067i | 0.882964 | − | 0.469441i | \(-0.155545\pi\) |
−0.848030 | + | 0.529948i | \(0.822211\pi\) | |||||||
\(600\) | 8.49465e7 | 0.393271 | ||||||||
\(601\) | − | 1.76814e8i | − | 0.814503i | −0.913316 | − | 0.407252i | \(-0.866487\pi\) | ||
0.913316 | − | 0.407252i | \(-0.133513\pi\) | |||||||
\(602\) | 1.17971e8 | + | 2.19178e8i | 0.540737 | + | 1.00463i | ||||
\(603\) | −2.29664e8 | −1.04747 | ||||||||
\(604\) | 1.84774e7i | 0.0838552i | ||||||||
\(605\) | 9.70403e6 | − | 5.60263e6i | 0.0438214 | − | 0.0253003i | ||||
\(606\) | 3.57931e7 | 0.160836 | ||||||||
\(607\) | −1.85350e8 | + | 1.07012e8i | −0.828754 | + | 0.478481i | −0.853426 | − | 0.521214i | \(-0.825479\pi\) |
0.0246719 | + | 0.999696i | \(0.492146\pi\) | |||||||
\(608\) | −1.18456e7 | − | 2.05171e7i | −0.0527042 | − | 0.0912864i | ||||
\(609\) | 5.48644e7 | + | 3.16760e7i | 0.242906 | + | 0.140242i | ||||
\(610\) | − | 5.72527e6i | − | 0.0252236i | ||||||
\(611\) | −9.11739e7 | + | 1.57918e8i | −0.399712 | + | 0.692321i | ||||
\(612\) | −1.25894e7 | − | 2.18055e7i | −0.0549226 | − | 0.0951287i | ||||
\(613\) | 8.50719e7 | 0.369322 | 0.184661 | − | 0.982802i | \(-0.440881\pi\) | ||||
0.184661 | + | 0.982802i | \(0.440881\pi\) | |||||||
\(614\) | −1.15119e8 | + | 6.64641e7i | −0.497328 | + | 0.287132i | ||||
\(615\) | −7.45882e6 | + | 1.29191e7i | −0.0320660 | + | 0.0555400i | ||||
\(616\) | 1.89427e8 | − | 3.28097e8i | 0.810399 | − | 1.40365i | ||||
\(617\) | −1.30388e8 | + | 2.25838e8i | −0.555112 | + | 0.961483i | 0.442783 | + | 0.896629i | \(0.353991\pi\) |
−0.997895 | + | 0.0648535i | \(0.979342\pi\) | |||||||
\(618\) | 2.83292e7 | 0.120024 | ||||||||
\(619\) | −2.16275e8 | + | 3.74600e8i | −0.911874 | + | 1.57941i | −0.100459 | + | 0.994941i | \(0.532031\pi\) |
−0.811415 | + | 0.584471i | \(0.801302\pi\) | |||||||
\(620\) | 5.25276e6 | + | 3.03269e6i | 0.0220401 | + | 0.0127248i | ||||
\(621\) | 2.75811e7 | − | 1.59240e7i | 0.115169 | − | 0.0664931i | ||||
\(622\) | 7.05726e7 | − | 4.07451e7i | 0.293268 | − | 0.169319i | ||||
\(623\) | −2.83489e8 | −1.17239 | ||||||||
\(624\) | − | 7.58491e7i | − | 0.312174i | ||||||
\(625\) | −1.18775e8 | − | 2.05724e8i | −0.486501 | − | 0.842645i | ||||
\(626\) | −1.13767e8 | − | 1.97051e8i | −0.463761 | − | 0.803257i | ||||
\(627\) | −2.05945e7 | + | 3.56706e7i | −0.0835502 | + | 0.144713i | ||||
\(628\) | −1.09731e7 | − | 6.33533e6i | −0.0443048 | − | 0.0255794i | ||||
\(629\) | 2.86240e8i | 1.15021i | ||||||||
\(630\) | −2.01794e7 | − | 1.16506e7i | −0.0807024 | − | 0.0465936i | ||||
\(631\) | 2.25092e7 | + | 1.29957e7i | 0.0895924 | + | 0.0517262i | 0.544127 | − | 0.839003i | \(-0.316861\pi\) |
−0.454534 | + | 0.890729i | \(0.650194\pi\) | |||||||
\(632\) | 4.25694e8 | + | 2.45775e8i | 1.68635 | + | 0.973612i | ||||
\(633\) | 3.01865e7 | + | 5.22845e7i | 0.119015 | + | 0.206140i | ||||
\(634\) | − | 2.09982e8i | − | 0.823976i | ||||||
\(635\) | −5.56048e6 | + | 3.21034e6i | −0.0217166 | + | 0.0125381i | ||||
\(636\) | 1.14846e7 | + | 6.63065e6i | 0.0446422 | + | 0.0257742i | ||||
\(637\) | 1.36648e8 | 0.528671 | ||||||||
\(638\) | −8.99409e7 | + | 1.55782e8i | −0.346334 | + | 0.599868i | ||||
\(639\) | −7.51662e7 | + | 4.33972e7i | −0.288084 | + | 0.166326i | ||||
\(640\) | −9.01384e6 | − | 1.56124e7i | −0.0343851 | − | 0.0595567i | ||||
\(641\) | − | 2.39688e8i | − | 0.910065i | −0.890475 | − | 0.455033i | \(-0.849628\pi\) | ||
0.890475 | − | 0.455033i | \(-0.150372\pi\) | |||||||
\(642\) | −8.38172e7 | − | 1.45176e8i | −0.316758 | − | 0.548641i | ||||
\(643\) | 3.61153e6 | 0.0135850 | 0.00679249 | − | 0.999977i | \(-0.497838\pi\) | ||||
0.00679249 | + | 0.999977i | \(0.497838\pi\) | |||||||
\(644\) | 9.29535e6i | 0.0348023i | ||||||||
\(645\) | 4.52578e6 | + | 8.40844e6i | 0.0168661 | + | 0.0313355i | ||||
\(646\) | 7.76872e7 | 0.288172 | ||||||||
\(647\) | 5.83802e7i | 0.215552i | 0.994175 | + | 0.107776i | \(0.0343730\pi\) | ||||
−0.994175 | + | 0.107776i | \(0.965627\pi\) | |||||||
\(648\) | 1.49497e8 | − | 8.63119e7i | 0.549422 | − | 0.317209i | ||||
\(649\) | −3.59867e8 | −1.31646 | ||||||||
\(650\) | −2.18320e8 | + | 1.26047e8i | −0.794973 | + | 0.458978i | ||||
\(651\) | −1.15936e8 | − | 2.00808e8i | −0.420220 | − | 0.727842i | ||||
\(652\) | 1.38471e7 | + | 7.99463e6i | 0.0499593 | + | 0.0288440i | ||||
\(653\) | 3.63961e8i | 1.30712i | 0.756876 | + | 0.653559i | \(0.226725\pi\) | ||||
−0.756876 | + | 0.653559i | \(0.773275\pi\) | |||||||
\(654\) | −3.03751e7 | + | 5.26112e7i | −0.108589 | + | 0.188081i | ||||
\(655\) | −9.71329e6 | − | 1.68239e7i | −0.0345655 | − | 0.0598691i | ||||
\(656\) | −4.22626e8 | −1.49708 | ||||||||
\(657\) | −2.60015e8 | + | 1.50120e8i | −0.916859 | + | 0.529349i | ||||
\(658\) | 1.29497e8 | − | 2.24295e8i | 0.454550 | − | 0.787304i | ||||
\(659\) | 2.32501e8 | − | 4.02703e8i | 0.812396 | − | 1.40711i | −0.0987861 | − | 0.995109i | \(-0.531496\pi\) |
0.911182 | − | 0.412003i | \(-0.135171\pi\) | |||||||
\(660\) | 934237. | − | 1.61815e6i | 0.00324957 | − | 0.00562841i | ||||
\(661\) | 1.67832e8 | 0.581127 | 0.290563 | − | 0.956856i | \(-0.406157\pi\) | ||||
0.290563 | + | 0.956856i | \(0.406157\pi\) | |||||||
\(662\) | −1.01099e8 | + | 1.75109e8i | −0.348478 | + | 0.603581i | ||||
\(663\) | −8.21466e7 | − | 4.74274e7i | −0.281870 | − | 0.162738i | ||||
\(664\) | 1.46237e8 | − | 8.44302e7i | 0.499521 | − | 0.288399i | ||||
\(665\) | −1.07746e7 | + | 6.22069e6i | −0.0366382 | + | 0.0211531i | ||||
\(666\) | −3.11398e8 | −1.05413 | ||||||||
\(667\) | − | 3.43308e7i | − | 0.115693i | ||||||
\(668\) | 1.71095e7 | + | 2.96344e7i | 0.0573993 | + | 0.0994186i | ||||
\(669\) | 3.89319e7 | + | 6.74321e7i | 0.130025 | + | 0.225210i | ||||
\(670\) | −1.60725e7 | + | 2.78384e7i | −0.0534391 | + | 0.0925592i | ||||
\(671\) | 9.31371e7 | + | 5.37727e7i | 0.308287 | + | 0.177990i | ||||
\(672\) | − | 4.10852e7i | − | 0.135387i | ||||||
\(673\) | −2.73265e7 | − | 1.57769e7i | −0.0896476 | − | 0.0517580i | 0.454506 | − | 0.890744i | \(-0.349816\pi\) |
−0.544154 | + | 0.838986i | \(0.683149\pi\) | |||||||
\(674\) | 2.22305e8 | + | 1.28348e8i | 0.726055 | + | 0.419188i | ||||
\(675\) | 1.83854e8 | + | 1.06148e8i | 0.597809 | + | 0.345145i | ||||
\(676\) | −149323. | − | 258636.i | −0.000483379 | − | 0.000837238i | ||||
\(677\) | − | 4.80339e8i | − | 1.54804i | −0.633162 | − | 0.774019i | \(-0.718243\pi\) | ||
0.633162 | − | 0.774019i | \(-0.281757\pi\) | |||||||
\(678\) | 6.57041e7 | − | 3.79343e7i | 0.210816 | − | 0.121715i | ||||
\(679\) | 2.68356e8 | + | 1.54936e8i | 0.857241 | + | 0.494928i | ||||
\(680\) | −2.74131e7 | −0.0871829 | ||||||||
\(681\) | 3.53886e7 | − | 6.12948e7i | 0.112053 | − | 0.194081i | ||||
\(682\) | 5.70174e8 | − | 3.29190e8i | 1.79744 | − | 1.03775i | ||||
\(683\) | −8.28952e7 | − | 1.43579e8i | −0.260176 | − | 0.450638i | 0.706113 | − | 0.708100i | \(-0.250447\pi\) |
−0.966289 | + | 0.257462i | \(0.917114\pi\) | |||||||
\(684\) | − | 1.46256e7i | − | 0.0457029i | ||||||
\(685\) | 1.68841e6 | + | 2.92441e6i | 0.00525299 | + | 0.00909844i | ||||
\(686\) | 1.74235e8 | 0.539713 | ||||||||
\(687\) | − | 7.90077e7i | − | 0.243668i | ||||||
\(688\) | −1.42192e8 | + | 2.30148e8i | −0.436627 | + | 0.706712i | ||||
\(689\) | −3.06129e8 | −0.935938 | ||||||||
\(690\) | − | 2.06066e6i | − | 0.00627277i | ||||||
\(691\) | 8.37351e7 | − | 4.83445e7i | 0.253789 | − | 0.146525i | −0.367709 | − | 0.929941i | \(-0.619858\pi\) |
0.621498 | + | 0.783416i | \(0.286524\pi\) | |||||||
\(692\) | −3.61075e7 | −0.108963 | ||||||||
\(693\) | 3.79057e8 | − | 2.18849e8i | 1.13895 | − | 0.657573i | ||||
\(694\) | −2.21335e8 | − | 3.83363e8i | −0.662172 | − | 1.14692i | ||||
\(695\) | −2.25347e7 | − | 1.30104e7i | −0.0671271 | − | 0.0387558i | ||||
\(696\) | 8.10824e7i | 0.240491i | ||||||||
\(697\) | −2.64262e8 | + | 4.57716e8i | −0.780436 | + | 1.35175i | ||||
\(698\) | −2.70551e8 | − | 4.68608e8i | −0.795578 | − | 1.37798i | ||||
\(699\) | 1.66557e8 | 0.487676 | ||||||||
\(700\) | −5.36610e7 | + | 3.09812e7i | −0.156446 | + | 0.0903241i | ||||
\(701\) | 1.43958e8 | − | 2.49343e8i | 0.417910 | − | 0.723842i | −0.577819 | − | 0.816165i | \(-0.696096\pi\) |
0.995729 | + | 0.0923230i | \(0.0294292\pi\) | |||||||
\(702\) | 1.11612e8 | − | 1.93318e8i | 0.322626 | − | 0.558805i | ||||
\(703\) | −8.31337e7 | + | 1.43992e8i | −0.239283 | + | 0.414450i | ||||
\(704\) | 4.75483e8 | 1.36275 | ||||||||
\(705\) | 4.96795e6 | − | 8.60475e6i | 0.0141778 | − | 0.0245567i | ||||
\(706\) | 3.68160e8 | + | 2.12557e8i | 1.04622 | + | 0.604035i | ||||
\(707\) | −1.75879e8 | + | 1.01544e8i | −0.497687 | + | 0.287340i | ||||
\(708\) | −1.80597e7 | + | 1.04268e7i | −0.0508874 | + | 0.0293798i | ||||
\(709\) | 2.29466e8 | 0.643842 | 0.321921 | − | 0.946767i | \(-0.395671\pi\) | ||||
0.321921 | + | 0.946767i | \(0.395671\pi\) | |||||||
\(710\) | 1.21482e7i | 0.0339420i | ||||||||
\(711\) | 2.83949e8 | + | 4.91813e8i | 0.790007 | + | 1.36833i | ||||
\(712\) | −1.81415e8 | − | 3.14219e8i | −0.502611 | − | 0.870548i | ||||
\(713\) | −6.28265e7 | + | 1.08819e8i | −0.173330 | + | 0.300217i | ||||
\(714\) | 1.16675e8 | + | 6.73625e7i | 0.320541 | + | 0.185065i | ||||
\(715\) | 4.31326e7i | 0.118002i | ||||||||
\(716\) | 7.39773e7 | + | 4.27108e7i | 0.201539 | + | 0.116359i | ||||
\(717\) | −4.89045e7 | − | 2.82350e7i | −0.132676 | − | 0.0766003i | ||||
\(718\) | 2.83693e8 | + | 1.63790e8i | 0.766434 | + | 0.442501i | ||||
\(719\) | −4.48018e7 | − | 7.75991e7i | −0.120534 | − | 0.208771i | 0.799444 | − | 0.600740i | \(-0.205127\pi\) |
−0.919978 | + | 0.391969i | \(0.871794\pi\) | |||||||
\(720\) | − | 2.53251e7i | − | 0.0678507i | ||||||
\(721\) | −1.39203e8 | + | 8.03691e7i | −0.371402 | + | 0.214429i | ||||
\(722\) | −2.61862e8 | − | 1.51186e8i | −0.695763 | − | 0.401699i | ||||
\(723\) | −2.55690e8 | −0.676548 | ||||||||
\(724\) | 2.11405e7 | − | 3.66165e7i | 0.0557058 | − | 0.0964853i | ||||
\(725\) | 1.98188e8 | − | 1.14424e8i | 0.520071 | − | 0.300263i | ||||
\(726\) | −3.52410e7 | − | 6.10392e7i | −0.0920955 | − | 0.159514i | ||||
\(727\) | 1.86804e8i | 0.486163i | 0.970006 | + | 0.243082i | \(0.0781583\pi\) | ||||
−0.970006 | + | 0.243082i | \(0.921842\pi\) | |||||||
\(728\) | 2.53395e8 | + | 4.38892e8i | 0.656755 | + | 1.13753i | ||||
\(729\) | 9.83527e7 | 0.253865 | ||||||||
\(730\) | 4.20232e7i | 0.108024i | ||||||||
\(731\) | 1.60346e8 | + | 2.97907e8i | 0.410494 | + | 0.762656i | ||||
\(732\) | 6.23203e6 | 0.0158890 | ||||||||
\(733\) | 3.91699e8i | 0.994582i | 0.867584 | + | 0.497291i | \(0.165672\pi\) | ||||
−0.867584 | + | 0.497291i | \(0.834328\pi\) | |||||||
\(734\) | 5.67780e7 | − | 3.27808e7i | 0.143579 | − | 0.0828956i | ||||
\(735\) | −7.44579e6 | −0.0187520 | ||||||||
\(736\) | −1.92814e7 | + | 1.11321e7i | −0.0483622 | + | 0.0279219i | ||||
\(737\) | −3.01911e8 | − | 5.22926e8i | −0.754184 | − | 1.30628i | ||||
\(738\) | −4.97946e8 | − | 2.87489e8i | −1.23883 | − | 0.715241i | ||||
\(739\) | − | 1.26171e8i | − | 0.312627i | −0.987707 | − | 0.156314i | \(-0.950039\pi\) | ||
0.987707 | − | 0.156314i | \(-0.0499611\pi\) | |||||||
\(740\) | 3.77124e6 | − | 6.53197e6i | 0.00930655 | − | 0.0161194i | ||||
\(741\) | −2.75490e7 | − | 4.77163e7i | −0.0677098 | − | 0.117277i | ||||
\(742\) | 4.34804e8 | 1.06434 | ||||||||
\(743\) | −1.19957e8 | + | 6.92569e7i | −0.292454 | + | 0.168848i | −0.639048 | − | 0.769167i | \(-0.720671\pi\) |
0.346594 | + | 0.938015i | \(0.387338\pi\) | |||||||
\(744\) | 1.48384e8 | − | 2.57008e8i | 0.360302 | − | 0.624062i | ||||
\(745\) | −1.50280e7 | + | 2.60293e7i | −0.0363440 | + | 0.0629496i | ||||
\(746\) | −4.62695e7 | + | 8.01412e7i | −0.111450 | + | 0.193036i | ||||
\(747\) | 1.95088e8 | 0.468024 | ||||||||
\(748\) | 3.30996e7 | − | 5.73301e7i | 0.0790893 | − | 0.136987i | ||||
\(749\) | 8.23717e8 | + | 4.75573e8i | 1.96035 | + | 1.13181i | ||||
\(750\) | 2.39003e7 | − | 1.37988e7i | 0.0566525 | − | 0.0327083i | ||||
\(751\) | −5.91540e8 | + | 3.41526e8i | −1.39658 | + | 0.806313i | −0.994032 | − | 0.109087i | \(-0.965207\pi\) |
−0.402544 | + | 0.915401i | \(0.631874\pi\) | |||||||
\(752\) | 2.81490e8 | 0.661927 | ||||||||
\(753\) | − | 4.70874e7i | − | 0.110286i | ||||||
\(754\) | −1.20313e8 | − | 2.08389e8i | −0.280672 | − | 0.486138i | ||||
\(755\) | 1.16208e7 | + | 2.01278e7i | 0.0270020 | + | 0.0467687i | ||||
\(756\) | 2.74332e7 | − | 4.75157e7i | 0.0634909 | − | 0.109969i | ||||
\(757\) | −1.32355e8 | − | 7.64151e7i | −0.305107 | − | 0.176154i | 0.339628 | − | 0.940560i | \(-0.389699\pi\) |
−0.644735 | + | 0.764406i | \(0.723032\pi\) | |||||||
\(758\) | 3.83235e8i | 0.879949i | ||||||||
\(759\) | 3.35223e7 | + | 1.93541e7i | 0.0766670 | + | 0.0442637i | ||||
\(760\) | −1.37900e7 | − | 7.96169e6i | −0.0314141 | − | 0.0181370i | ||||
\(761\) | 1.00725e8 | + | 5.81537e7i | 0.228551 | + | 0.131954i | 0.609904 | − | 0.792476i | \(-0.291208\pi\) |
−0.381352 | + | 0.924430i | \(0.624541\pi\) | |||||||
\(762\) | 2.01933e7 | + | 3.49759e7i | 0.0456398 | + | 0.0790504i | ||||
\(763\) | − | 3.44693e8i | − | 0.775995i | ||||||
\(764\) | 6.63845e7 | − | 3.83271e7i | 0.148863 | − | 0.0859461i | ||||
\(765\) | −2.74278e7 | − | 1.58354e7i | −0.0612642 | − | 0.0353709i | ||||
\(766\) | 2.68362e8 | 0.597082 | ||||||||
\(767\) | 2.40695e8 | − | 4.16896e8i | 0.533435 | − | 0.923936i | ||||
\(768\) | 6.35463e7 | − | 3.66885e7i | 0.140284 | − | 0.0809928i | ||||
\(769\) | −8.68560e7 | − | 1.50439e8i | −0.190994 | − | 0.330812i | 0.754586 | − | 0.656202i | \(-0.227838\pi\) |
−0.945580 | + | 0.325390i | \(0.894505\pi\) | |||||||
\(770\) | − | 6.12625e7i | − | 0.134191i | ||||||
\(771\) | 1.25564e8 | + | 2.17483e8i | 0.273969 | + | 0.474528i | ||||
\(772\) | −1.21392e8 | −0.263837 | ||||||||
\(773\) | − | 8.64443e8i | − | 1.87153i | −0.352618 | − | 0.935767i | \(-0.614708\pi\) | ||
0.352618 | − | 0.935767i | \(-0.385292\pi\) | |||||||
\(774\) | −3.24091e8 | + | 1.74439e8i | −0.698946 | + | 0.376203i | ||||
\(775\) | −8.37597e8 | −1.79941 | ||||||||
\(776\) | 3.96596e8i | 0.848717i | ||||||||
\(777\) | −2.49710e8 | + | 1.44170e8i | −0.532321 | + | 0.307336i | ||||
\(778\) | −2.10057e8 | −0.446065 | ||||||||
\(779\) | −2.65872e8 | + | 1.53502e8i | −0.562420 | + | 0.324713i | ||||
\(780\) | 1.24972e6 | + | 2.16458e6i | 0.00263348 | + | 0.00456132i | ||||
\(781\) | −1.97624e8 | − | 1.14098e8i | −0.414846 | − | 0.239511i | ||||
\(782\) | − | 7.30082e7i | − | 0.152669i | ||||||
\(783\) | −1.01320e8 | + | 1.75491e8i | −0.211062 | + | 0.365570i | ||||
\(784\) | −1.05472e8 | − | 1.82683e8i | −0.218871 | − | 0.379096i | ||||
\(785\) | −1.59377e7 | −0.0329470 | ||||||||
\(786\) | −1.05824e8 | + | 6.10974e7i | −0.217929 | + | 0.125822i | ||||
\(787\) | −2.54639e8 | + | 4.41048e8i | −0.522397 | + | 0.904818i | 0.477264 | + | 0.878760i | \(0.341629\pi\) |
−0.999660 | + | 0.0260577i | \(0.991705\pi\) | |||||||
\(788\) | −5.73975e7 | + | 9.94154e7i | −0.117304 | + | 0.203177i | ||||
\(789\) | −6.03100e7 | + | 1.04460e8i | −0.122789 | + | 0.212676i | ||||
\(790\) | 7.94860e7 | 0.161217 | ||||||||
\(791\) | −2.15237e8 | + | 3.72801e8i | −0.434897 | + | 0.753265i | ||||
\(792\) | 4.85144e8 | + | 2.80098e8i | 0.976552 | + | 0.563812i | ||||
\(793\) | −1.24589e8 | + | 7.19314e7i | −0.249839 | + | 0.144244i | ||||
\(794\) | −1.81904e7 | + | 1.05022e7i | −0.0363397 | + | 0.0209807i | ||||
\(795\) | 1.66806e7 | 0.0331979 | ||||||||
\(796\) | − | 1.32882e8i | − | 0.263467i | ||||||
\(797\) | −4.37498e8 | − | 7.57769e8i | −0.864174 | − | 1.49679i | −0.867865 | − | 0.496800i | \(-0.834508\pi\) |
0.00369164 | − | 0.999993i | \(-0.498825\pi\) | |||||||
\(798\) | 3.91287e7 | + | 6.77729e7i | 0.0769993 | + | 0.133367i | ||||
\(799\) | 1.76012e8 | − | 3.04862e8i | 0.345066 | − | 0.597672i | ||||
\(800\) | −1.28529e8 | − | 7.42063e7i | −0.251033 | − | 0.144934i | ||||
\(801\) | − | 4.19184e8i | − | 0.815656i | ||||||
\(802\) | 4.04188e8 | + | 2.33358e8i | 0.783539 | + | 0.452376i | ||||
\(803\) | −6.83622e8 | − | 3.94689e8i | −1.32029 | − | 0.762270i | ||||
\(804\) | −3.03025e7 | − | 1.74951e7i | −0.0583055 | − | 0.0336627i | ||||
\(805\) | 5.84603e6 | + | 1.01256e7i | 0.0112066 | + | 0.0194104i | ||||
\(806\) | 8.80709e8i | 1.68201i | ||||||||
\(807\) | 8.95092e7 | − | 5.16782e7i | 0.170313 | − | 0.0983301i | ||||
\(808\) | −2.25103e8 | − | 1.29963e8i | −0.426724 | − | 0.246369i | ||||
\(809\) | 6.12490e8 | 1.15679 | 0.578393 | − | 0.815758i | \(-0.303680\pi\) | ||||
0.578393 | + | 0.815758i | \(0.303680\pi\) | |||||||
\(810\) | 1.39571e7 | − | 2.41744e7i | 0.0262627 | − | 0.0454883i | ||||
\(811\) | 2.72520e8 | − | 1.57340e8i | 0.510900 | − | 0.294968i | −0.222303 | − | 0.974978i | \(-0.571358\pi\) |
0.733204 | + | 0.680009i | \(0.238024\pi\) | |||||||
\(812\) | −2.95719e7 | − | 5.12200e7i | −0.0552346 | − | 0.0956691i | ||||
\(813\) | 2.75409e8i | 0.512515i | ||||||||
\(814\) | −4.09358e8 | − | 7.09029e8i | −0.758979 | − | 1.31459i | ||||
\(815\) | 2.01119e7 | 0.0371519 | ||||||||
\(816\) | 1.46427e8i | 0.269496i | ||||||||
\(817\) | −5.86075e6 | + | 1.96431e8i | −0.0107470 | + | 0.360200i | ||||
\(818\) | −5.49670e8 | −1.00425 | ||||||||
\(819\) | 5.85504e8i | 1.06581i | ||||||||
\(820\) | 1.20609e7 | − | 6.96337e6i | 0.0218745 | − | 0.0126293i | ||||
\(821\) | 9.34037e8 | 1.68785 | 0.843926 | − | 0.536459i | \(-0.180238\pi\) | ||||
0.843926 | + | 0.536459i | \(0.180238\pi\) | |||||||
\(822\) | 1.83948e7 | − | 1.06203e7i | 0.0331192 | − | 0.0191214i | ||||
\(823\) | −2.81087e8 | − | 4.86857e8i | −0.504244 | − | 0.873377i | −0.999988 | − | 0.00490807i | \(-0.998438\pi\) |
0.495743 | − | 0.868469i | \(-0.334896\pi\) | |||||||
\(824\) | −1.78163e8 | − | 1.02862e8i | −0.318445 | − | 0.183854i | ||||
\(825\) | 2.58027e8i | 0.459519i | ||||||||
\(826\) | −3.41867e8 | + | 5.92130e8i | −0.606620 | + | 1.05070i | ||||
\(827\) | −1.15326e8 | − | 1.99751e8i | −0.203897 | − | 0.353160i | 0.745884 | − | 0.666076i | \(-0.232027\pi\) |
−0.949781 | + | 0.312916i | \(0.898694\pi\) | |||||||
\(828\) | −1.37447e7 | −0.0242127 | ||||||||
\(829\) | −8.81519e8 | + | 5.08945e8i | −1.54728 | + | 0.893321i | −0.548930 | + | 0.835869i | \(0.684965\pi\) |
−0.998348 | + | 0.0574527i | \(0.981702\pi\) | |||||||
\(830\) | 1.36528e7 | − | 2.36473e7i | 0.0238774 | − | 0.0413568i | ||||
\(831\) | −4.57043e7 | + | 7.91622e7i | −0.0796442 | + | 0.137948i | ||||
\(832\) | −3.18025e8 | + | 5.50836e8i | −0.552194 | + | 0.956428i | ||||
\(833\) | −2.63801e8 | −0.456395 | ||||||||
\(834\) | −8.18368e7 | + | 1.41745e8i | −0.141075 | + | 0.244349i | ||||
\(835\) | 3.72754e7 | + | 2.15210e7i | 0.0640269 | + | 0.0369660i | ||||
\(836\) | 3.33012e7 | − | 1.92265e7i | 0.0569956 | − | 0.0329064i | ||||
\(837\) | 6.42310e8 | − | 3.70838e8i | 1.09539 | − | 0.632423i | ||||
\(838\) | −8.82802e8 | −1.50014 | ||||||||
\(839\) | − | 9.32919e8i | − | 1.57964i | −0.613339 | − | 0.789820i | \(-0.710174\pi\) | ||
0.613339 | − | 0.789820i | \(-0.289826\pi\) | |||||||
\(840\) | −1.38072e7 | − | 2.39147e7i | −0.0232952 | − | 0.0403485i | ||||
\(841\) | −1.88193e8 | − | 3.25960e8i | −0.316385 | − | 0.547994i | ||||
\(842\) | 3.18001e8 | − | 5.50793e8i | 0.532711 | − | 0.922683i | ||||
\(843\) | 6.05904e7 | + | 3.49819e7i | 0.101140 | + | 0.0583930i | ||||
\(844\) | − | 5.63626e7i | − | 0.0937484i | ||||||
\(845\) | −325322. | − | 187825.i | −0.000539193 | − | 0.000311303i | ||||
\(846\) | 3.31657e8 | + | 1.91482e8i | 0.547745 | + | 0.316241i | ||||
\(847\) | 3.46333e8 | + | 1.99955e8i | 0.569959 | + | 0.329066i | ||||
\(848\) | 2.36286e8 | + | 4.09259e8i | 0.387481 | + | 0.671137i | ||||
\(849\) | − | 1.69402e7i | − | 0.0276818i | ||||||
\(850\) | 4.21468e8 | − | 2.43335e8i | 0.686290 | − | 0.396230i | ||||
\(851\) | 1.35319e8 | + | 7.81267e7i | 0.219569 | + | 0.126768i | ||||
\(852\) | −1.32235e7 | −0.0213810 | ||||||||
\(853\) | 4.21313e8 | − | 7.29735e8i | 0.678825 | − | 1.17576i | −0.296510 | − | 0.955030i | \(-0.595823\pi\) |
0.975335 | − | 0.220729i | \(-0.0708438\pi\) | |||||||
\(854\) | 1.76957e8 | − | 1.02166e8i | 0.284115 | − | 0.164034i | ||||
\(855\) | −9.19830e6 | − | 1.59319e7i | −0.0147167 | − | 0.0254900i | ||||
\(856\) | 1.21735e9i | 1.94085i | ||||||||
\(857\) | 5.16896e8 | + | 8.95290e8i | 0.821222 | + | 1.42240i | 0.904772 | + | 0.425895i | \(0.140041\pi\) |
−0.0835501 | + | 0.996504i | \(0.526626\pi\) | |||||||
\(858\) | 2.71308e8 | 0.429537 | ||||||||
\(859\) | 8.08522e8i | 1.27559i | 0.770205 | + | 0.637797i | \(0.220154\pi\) | ||||
−0.770205 | + | 0.637797i | \(0.779846\pi\) | |||||||
\(860\) | 265864. | − | 8.91080e6i | 0.000417989 | − | 0.0140095i | ||||
\(861\) | −5.32404e8 | −0.834127 | ||||||||
\(862\) | 3.87332e7i | 0.0604731i | ||||||||
\(863\) | 1.02081e9 | − | 5.89366e8i | 1.58823 | − | 0.916965i | 0.594632 | − | 0.803998i | \(-0.297298\pi\) |
0.993599 | − | 0.112967i | \(-0.0360355\pi\) | |||||||
\(864\) | 1.31416e8 | 0.203755 | ||||||||
\(865\) | −3.93327e7 | + | 2.27087e7i | −0.0607722 | + | 0.0350869i | ||||
\(866\) | −5.09354e8 | − | 8.82227e8i | −0.784271 | − | 1.35840i | ||||
\(867\) | −5.28198e7 | − | 3.04955e7i | −0.0810475 | − | 0.0467928i | ||||
\(868\) | 2.16470e8i | 0.331009i | ||||||||
\(869\) | −7.46547e8 | + | 1.29306e9i | −1.13762 | + | 1.97042i | ||||
\(870\) | 6.55572e6 | + | 1.13548e7i | 0.00995548 | + | 0.0172434i | ||||
\(871\) | 8.07729e8 | 1.22239 | ||||||||
\(872\) | 3.82058e8 | − | 2.20581e8i | 0.576209 | − | 0.332674i | ||||
\(873\) | −2.29098e8 | + | 3.96809e8i | −0.344332 | + | 0.596401i | ||||
\(874\) | 2.12041e7 | − | 3.67265e7i | 0.0317603 | − | 0.0550105i | ||||
\(875\) | −7.82937e7 | + | 1.35609e8i | −0.116870 | + | 0.202424i | ||||
\(876\) | −4.57428e7 | −0.0680472 | ||||||||
\(877\) | 3.07167e8 | − | 5.32029e8i | 0.455382 | − | 0.788745i | −0.543328 | − | 0.839520i | \(-0.682836\pi\) |
0.998710 | + | 0.0507758i | \(0.0161694\pi\) | |||||||
\(878\) | −3.15771e8 | − | 1.82310e8i | −0.466539 | − | 0.269357i | ||||
\(879\) | 1.84782e8 | − | 1.06684e8i | 0.272077 | − | 0.157084i | ||||
\(880\) | 5.76633e7 | − | 3.32919e7i | 0.0846158 | − | 0.0488529i | ||||
\(881\) | 5.83393e8 | 0.853165 | 0.426583 | − | 0.904449i | \(-0.359717\pi\) | ||||
0.426583 | + | 0.904449i | \(0.359717\pi\) | |||||||
\(882\) | − | 2.86987e8i | − | 0.418269i | ||||||
\(883\) | −5.35300e8 | − | 9.27167e8i | −0.777527 | − | 1.34672i | −0.933363 | − | 0.358933i | \(-0.883141\pi\) |
0.155837 | − | 0.987783i | \(-0.450193\pi\) | |||||||
\(884\) | 4.42770e7 | + | 7.66900e7i | 0.0640946 | + | 0.111015i | ||||
\(885\) | −1.31152e7 | + | 2.27162e7i | −0.0189210 | + | 0.0327722i | ||||
\(886\) | 8.57030e8 | + | 4.94806e8i | 1.23224 | + | 0.711433i | ||||
\(887\) | 4.42565e8i | 0.634171i | 0.948397 | + | 0.317085i | \(0.102704\pi\) | ||||
−0.948397 | + | 0.317085i | \(0.897296\pi\) | |||||||
\(888\) | −3.19597e8 | − | 1.84520e8i | −0.456420 | − | 0.263514i | ||||
\(889\) | −1.98451e8 | − | 1.14576e8i | −0.282454 | − | 0.163075i | ||||
\(890\) | −5.08108e7 | − | 2.93356e7i | −0.0720753 | − | 0.0416127i | ||||
\(891\) | 2.62175e8 | + | 4.54100e8i | 0.370644 | + | 0.641975i | ||||
\(892\) | − | 7.26918e7i | − | 0.102421i | ||||||
\(893\) | 1.77084e8 | − | 1.02240e8i | 0.248671 | − | 0.143571i | ||||
\(894\) | 1.63726e8 | + | 9.45275e7i | 0.229143 | + | 0.132296i | ||||
\(895\) | 1.07447e8 | 0.149873 | ||||||||
\(896\) | 3.21700e8 | − | 5.57201e8i | 0.447226 | − | 0.774618i | ||||
\(897\) | −4.48425e7 | + | 2.58898e7i | −0.0621316 | + | 0.0358717i | ||||
\(898\) | 6.13995e8 | + | 1.06347e9i | 0.847883 | + | 1.46858i | ||||
\(899\) | − | 7.99496e8i | − | 1.10037i | ||||||
\(900\) | −4.58107e7 | − | 7.93465e7i | −0.0628405 | − | 0.108843i | ||||
\(901\) | 5.90985e8 | 0.807983 | ||||||||
\(902\) | − | 1.51171e9i | − | 2.05991i | ||||||
\(903\) | −1.79127e8 | + | 2.89930e8i | −0.243275 | + | 0.393758i | ||||
\(904\) | −5.50951e8 | −0.745775 | ||||||||
\(905\) | − | 5.31828e7i | − | 0.0717506i | ||||||
\(906\) | 1.26606e8 | − | 7.30959e7i | 0.170243 | − | 0.0982898i | ||||
\(907\) | 6.22160e8 | 0.833835 | 0.416917 | − | 0.908944i | \(-0.363110\pi\) | ||||
0.416917 | + | 0.908944i | \(0.363110\pi\) | |||||||
\(908\) | −5.72233e7 | + | 3.30379e7i | −0.0764391 | + | 0.0441321i | ||||
\(909\) | −1.50149e8 | − | 2.60066e8i | −0.199909 | − | 0.346252i | ||||
\(910\) | 7.09711e7 | + | 4.09752e7i | 0.0941797 | + | 0.0543747i | ||||
\(911\) | − | 1.23633e9i | − | 1.63523i | −0.575762 | − | 0.817617i | \(-0.695295\pi\) | ||
0.575762 | − | 0.817617i | \(-0.304705\pi\) | |||||||
\(912\) | −4.25275e7 | + | 7.36597e7i | −0.0560641 | + | 0.0971059i | ||||
\(913\) | 2.56459e8 | + | 4.44199e8i | 0.336981 | + | 0.583668i | ||||
\(914\) | −3.05763e8 | −0.400448 | ||||||||
\(915\) | 6.78869e6 | − | 3.91945e6i | 0.00886181 | − | 0.00511637i | ||||
\(916\) | −3.68798e7 | + | 6.38777e7i | −0.0479846 | + | 0.0831118i | ||||
\(917\) | 3.46663e8 | − | 6.00438e8i | 0.449572 | − | 0.778682i | ||||
\(918\) | −2.15468e8 | + | 3.73202e8i | −0.278519 | + | 0.482409i | ||||
\(919\) | 1.02974e9 | 1.32673 | 0.663365 | − | 0.748296i | \(-0.269128\pi\) | ||||
0.663365 | + | 0.748296i | \(0.269128\pi\) | |||||||
\(920\) | −7.48217e6 | + | 1.29595e7i | −0.00960869 | + | 0.0166427i | ||||
\(921\) | −1.57618e8 | − | 9.10010e7i | −0.201757 | − | 0.116484i | ||||
\(922\) | −8.06784e6 | + | 4.65797e6i | −0.0102935 | + | 0.00594297i | ||||
\(923\) | 2.64360e8 | − | 1.52628e8i | 0.336194 | − | 0.194102i | ||||
\(924\) | 6.66851e7 | 0.0845303 | ||||||||
\(925\) | 1.04158e9i | 1.31603i | ||||||||
\(926\) | −3.82720e8 | − | 6.62891e8i | −0.482002 | − | 0.834851i | ||||
\(927\) | −1.18839e8 | − | 2.05835e8i | −0.149183 | − | 0.258392i | ||||
\(928\) | 7.08308e7 | − | 1.22683e8i | 0.0886295 | − | 0.153511i | ||||
\(929\) | −9.96313e8 | − | 5.75222e8i | −1.24265 | − | 0.717444i | −0.273017 | − | 0.962009i | \(-0.588021\pi\) |
−0.969633 | + | 0.244565i | \(0.921355\pi\) | |||||||
\(930\) | − | 4.79888e7i | − | 0.0596610i | ||||||
\(931\) | −1.32704e8 | − | 7.66166e7i | −0.164450 | − | 0.0949454i | ||||
\(932\) | −1.34661e8 | − | 7.77468e7i | −0.166339 | − | 0.0960361i | ||||
\(933\) | 9.66263e7 | + | 5.57872e7i | 0.118974 | + | 0.0686894i | ||||
\(934\) | −2.25237e8 | − | 3.90121e8i | −0.276438 | − | 0.478805i | ||||
\(935\) | − | 8.32679e7i | − | 0.101869i | ||||||
\(936\) | −6.48973e8 | + | 3.74685e8i | −0.791406 | + | 0.456919i | ||||
\(937\) | −2.39111e8 | − | 1.38051e8i | −0.290657 | − | 0.167811i | 0.347581 | − | 0.937650i | \(-0.387003\pi\) |
−0.638238 | + | 0.769839i | \(0.720336\pi\) | |||||||
\(938\) | −1.14724e9 | −1.39010 | ||||||||
\(939\) | 1.55767e8 | − | 2.69797e8i | 0.188139 | − | 0.325867i | ||||
\(940\) | −8.03317e6 | + | 4.63796e6i | −0.00967172 | + | 0.00558397i | ||||
\(941\) | 7.07351e8 | + | 1.22517e9i | 0.848919 | + | 1.47037i | 0.882174 | + | 0.470924i | \(0.156079\pi\) |
−0.0332544 | + | 0.999447i | \(0.510587\pi\) | |||||||
\(942\) | 1.00249e8i | 0.119930i | ||||||||
\(943\) | 1.44256e8 | + | 2.49860e8i | 0.172028 | + | 0.297962i | ||||
\(944\) | −7.43123e8 | −0.883374 | ||||||||
\(945\) | − | 6.90132e7i | − | 0.0817780i | ||||||
\(946\) | −8.23228e8 | − | 5.08614e8i | −0.972404 | − | 0.600780i | ||||
\(947\) | −2.20679e8 | −0.259843 | −0.129921 | − | 0.991524i | \(-0.541473\pi\) | ||||
−0.129921 | + | 0.991524i | \(0.541473\pi\) | |||||||
\(948\) | 8.65216e7i | 0.101555i | ||||||||
\(949\) | 9.14475e8 | − | 5.27973e8i | 1.06997 | − | 0.617750i | ||||
\(950\) | 2.82690e8 | 0.329716 | ||||||||
\(951\) | 2.48984e8 | − | 1.43751e8i | 0.289488 | − | 0.167136i | ||||
\(952\) | −4.89181e8 | − | 8.47286e8i | −0.566968 | − | 0.982017i | ||||
\(953\) | −2.26275e8 | − | 1.30640e8i | −0.261431 | − | 0.150937i | 0.363556 | − | 0.931572i | \(-0.381562\pi\) |
−0.624987 | + | 0.780635i | \(0.714896\pi\) | |||||||
\(954\) | 6.42929e8i | 0.740488i | ||||||||
\(955\) | 4.82094e7 | − | 8.35010e7i | 0.0553505 | − | 0.0958698i | ||||
\(956\) | 2.63595e7 | + | 4.56560e7i | 0.0301692 | + | 0.0522545i | ||||
\(957\) | −2.46290e8 | −0.281003 | ||||||||
\(958\) | 3.96391e8 | − | 2.28856e8i | 0.450845 | − | 0.260295i | ||||
\(959\) | −6.02586e7 | + | 1.04371e8i | −0.0683225 | + | 0.118338i | ||||
\(960\) | 1.73288e7 | − | 3.00143e7i | 0.0195864 | − | 0.0339246i | ||||
\(961\) | −1.01935e9 | + | 1.76557e9i | −1.14856 | + | 1.98937i | ||||
\(962\) | 1.09519e9 | 1.23017 | ||||||||
\(963\) | −7.03212e8 | + | 1.21800e9i | −0.787422 | + | 1.36385i | ||||
\(964\) | 2.06725e8 | + | 1.19353e8i | 0.230761 | + | 0.133230i | ||||
\(965\) | −1.32234e8 | + | 7.63455e7i | −0.147151 | + | 0.0849575i | ||||
\(966\) | 6.36911e7 | − | 3.67721e7i | 0.0706557 | − | 0.0407931i | ||||
\(967\) | 6.66773e7 | 0.0737392 | 0.0368696 | − | 0.999320i | \(-0.488261\pi\) | ||||
0.0368696 | + | 0.999320i | \(0.488261\pi\) | |||||||
\(968\) | 5.11834e8i | 0.564291i | ||||||||
\(969\) | 5.31837e7 | + | 9.21168e7i | 0.0584530 | + | 0.101244i | ||||
\(970\) | 3.20658e7 | + | 5.55395e7i | 0.0351339 | + | 0.0608537i | ||||
\(971\) | 8.14090e7 | − | 1.41005e8i | 0.0889232 | − | 0.154019i | −0.818133 | − | 0.575029i | \(-0.804991\pi\) |
0.907056 | + | 0.421010i | \(0.138324\pi\) | |||||||
\(972\) | 1.08040e8 | + | 6.23768e7i | 0.117648 | + | 0.0679242i | ||||
\(973\) | − | 9.28673e8i | − | 1.00815i | ||||||
\(974\) | −1.55681e8 | − | 8.98827e7i | −0.168485 | − | 0.0972746i | ||||
\(975\) | −2.98918e8 | − | 1.72580e8i | −0.322506 | − | 0.186199i | ||||
\(976\) | 1.92328e8 | + | 1.11040e8i | 0.206868 | + | 0.119435i | ||||
\(977\) | −1.54252e8 | − | 2.67173e8i | −0.165405 | − | 0.286489i | 0.771394 | − | 0.636357i | \(-0.219560\pi\) |
−0.936799 | + | 0.349868i | \(0.886226\pi\) | |||||||
\(978\) | − | 1.26506e8i | − | 0.135237i | ||||||
\(979\) | 9.54448e8 | − | 5.51051e8i | 1.01720 | − | 0.587278i | ||||
\(980\) | 6.01992e6 | + | 3.47560e6i | 0.00639606 | + | 0.00369276i | ||||
\(981\) | 5.09684e8 | 0.539876 | ||||||||
\(982\) | −3.16106e8 | + | 5.47512e8i | −0.333809 | + | 0.578175i | ||||
\(983\) | 1.18203e9 | − | 6.82444e8i | 1.24442 | − | 0.718467i | 0.274430 | − | 0.961607i | \(-0.411511\pi\) |
0.969991 | + | 0.243140i | \(0.0781775\pi\) | |||||||
\(984\) | −3.40705e8 | − | 5.90118e8i | −0.357596 | − | 0.619375i | ||||
\(985\) | 1.44394e8i | 0.151091i | ||||||||
\(986\) | 2.32266e8 | + | 4.02296e8i | 0.242301 | + | 0.419677i | ||||
\(987\) | 3.54608e8 | 0.368805 | ||||||||
\(988\) | 5.14382e7i | 0.0533353i | ||||||||
\(989\) | 1.84600e8 | + | 5.50777e6i | 0.190829 | + | 0.00569360i | ||||
\(990\) | 9.05866e7 | 0.0933594 | ||||||||
\(991\) | 1.23381e9i | 1.26773i | 0.773442 | + | 0.633867i | \(0.218533\pi\) | ||||
−0.773442 | + | 0.633867i | \(0.781467\pi\) | |||||||
\(992\) | −4.49027e8 | + | 2.59246e8i | −0.459978 | + | 0.265569i | ||||
\(993\) | −2.76846e8 | −0.282742 | ||||||||
\(994\) | −3.75478e8 | + | 2.16782e8i | −0.382319 | + | 0.220732i | ||||
\(995\) | −8.35719e7 | − | 1.44751e8i | −0.0848381 | − | 0.146944i | ||||
\(996\) | 2.57404e7 | + | 1.48612e7i | 0.0260518 | + | 0.0150410i | ||||
\(997\) | − | 6.00877e8i | − | 0.606317i | −0.952940 | − | 0.303159i | \(-0.901959\pi\) | ||
0.952940 | − | 0.303159i | \(-0.0980412\pi\) | |||||||
\(998\) | −5.94648e8 | + | 1.02996e9i | −0.598230 | + | 1.03617i | ||||
\(999\) | −4.61148e8 | − | 7.98732e8i | −0.462535 | − | 0.801133i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.7.d.a.7.15 | ✓ | 42 | |
43.37 | odd | 6 | inner | 43.7.d.a.37.7 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.15 | ✓ | 42 | 1.1 | even | 1 | trivial | |
43.7.d.a.37.7 | yes | 42 | 43.37 | odd | 6 | inner |