Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (of order \(5\), degree \(4\), 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: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 24 x^{14} - 62 x^{13} + 148 x^{12} - 232 x^{11} + 432 x^{10} - 356 x^{9} + 424 x^{8} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 191.2 | ||
Root | \(0.253418 + 0.184119i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.191 |
Dual form | 418.2.f.f.267.2 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | ||||
\(3\) | −0.670482 | + | 2.06353i | −0.387103 | + | 1.19138i | 0.547840 | + | 0.836583i | \(0.315450\pi\) |
−0.934943 | + | 0.354797i | \(0.884550\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | −1.44869 | + | 1.05254i | −0.647875 | + | 0.470708i | −0.862547 | − | 0.505978i | \(-0.831132\pi\) |
0.214672 | + | 0.976686i | \(0.431132\pi\) | |||||||
\(6\) | 1.75534 | − | 1.27533i | 0.716616 | − | 0.520652i | ||||
\(7\) | 1.45655 | + | 4.48281i | 0.550526 | + | 1.69434i | 0.707476 | + | 0.706737i | \(0.249834\pi\) |
−0.156950 | + | 0.987606i | \(0.550166\pi\) | |||||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | −1.38156 | − | 1.00376i | −0.460521 | − | 0.334588i | ||||
\(10\) | 1.79068 | 0.566263 | ||||||||
\(11\) | 3.03398 | + | 1.33977i | 0.914779 | + | 0.403955i | ||||
\(12\) | −2.16972 | −0.626346 | ||||||||
\(13\) | −5.54899 | − | 4.03158i | −1.53901 | − | 1.11816i | −0.950951 | − | 0.309342i | \(-0.899891\pi\) |
−0.588062 | − | 0.808816i | \(-0.700109\pi\) | |||||||
\(14\) | 1.45655 | − | 4.48281i | 0.389280 | − | 1.19808i | ||||
\(15\) | −1.20062 | − | 3.69513i | −0.309999 | − | 0.954077i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 0.0745226 | − | 0.0541438i | 0.0180744 | − | 0.0131318i | −0.578711 | − | 0.815532i | \(-0.696444\pi\) |
0.596786 | + | 0.802401i | \(0.296444\pi\) | |||||||
\(18\) | 0.527710 | + | 1.62412i | 0.124382 | + | 0.382810i | ||||
\(19\) | −0.309017 | + | 0.951057i | −0.0708934 | + | 0.218187i | ||||
\(20\) | −1.44869 | − | 1.05254i | −0.323937 | − | 0.235354i | ||||
\(21\) | −10.2270 | −2.23172 | ||||||||
\(22\) | −1.66704 | − | 2.86722i | −0.355415 | − | 0.611294i | ||||
\(23\) | 4.91452 | 1.02475 | 0.512374 | − | 0.858763i | \(-0.328766\pi\) | ||||
0.512374 | + | 0.858763i | \(0.328766\pi\) | |||||||
\(24\) | 1.75534 | + | 1.27533i | 0.358308 | + | 0.260326i | ||||
\(25\) | −0.554210 | + | 1.70568i | −0.110842 | + | 0.341136i | ||||
\(26\) | 2.11952 | + | 6.52323i | 0.415673 | + | 1.27931i | ||||
\(27\) | −2.26842 | + | 1.64811i | −0.436558 | + | 0.317178i | ||||
\(28\) | −3.81331 | + | 2.77053i | −0.720647 | + | 0.523581i | ||||
\(29\) | −0.990376 | − | 3.04806i | −0.183908 | − | 0.566011i | 0.816020 | − | 0.578024i | \(-0.196176\pi\) |
−0.999928 | + | 0.0120130i | \(0.996176\pi\) | |||||||
\(30\) | −1.20062 | + | 3.69513i | −0.219202 | + | 0.674635i | ||||
\(31\) | −5.76130 | − | 4.18583i | −1.03476 | − | 0.751797i | −0.0655036 | − | 0.997852i | \(-0.520865\pi\) |
−0.969256 | + | 0.246056i | \(0.920865\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.79888 | + | 5.36242i | −0.835378 | + | 0.933477i | ||||
\(34\) | −0.0921150 | −0.0157976 | ||||||||
\(35\) | −6.82842 | − | 4.96114i | −1.15421 | − | 0.838585i | ||||
\(36\) | 0.527710 | − | 1.62412i | 0.0879516 | − | 0.270687i | ||||
\(37\) | 1.82728 | + | 5.62380i | 0.300403 | + | 0.924547i | 0.981353 | + | 0.192216i | \(0.0615674\pi\) |
−0.680949 | + | 0.732331i | \(0.738433\pi\) | |||||||
\(38\) | 0.809017 | − | 0.587785i | 0.131240 | − | 0.0953514i | ||||
\(39\) | 12.0398 | − | 8.74741i | 1.92791 | − | 1.40071i | ||||
\(40\) | 0.553351 | + | 1.70304i | 0.0874925 | + | 0.269274i | ||||
\(41\) | 1.11382 | − | 3.42797i | 0.173949 | − | 0.535360i | −0.825635 | − | 0.564205i | \(-0.809183\pi\) |
0.999584 | + | 0.0288450i | \(0.00918292\pi\) | |||||||
\(42\) | 8.27383 | + | 6.01129i | 1.27668 | + | 0.927562i | ||||
\(43\) | −7.91031 | −1.20631 | −0.603156 | − | 0.797624i | \(-0.706090\pi\) | ||||
−0.603156 | + | 0.797624i | \(0.706090\pi\) | |||||||
\(44\) | −0.336644 | + | 3.29950i | −0.0507510 | + | 0.497418i | ||||
\(45\) | 3.05796 | 0.455853 | ||||||||
\(46\) | −3.97593 | − | 2.88868i | −0.586218 | − | 0.425913i | ||||
\(47\) | 0.859197 | − | 2.64434i | 0.125327 | − | 0.385716i | −0.868634 | − | 0.495455i | \(-0.835001\pi\) |
0.993960 | + | 0.109739i | \(0.0350014\pi\) | |||||||
\(48\) | −0.670482 | − | 2.06353i | −0.0967757 | − | 0.297845i | ||||
\(49\) | −12.3109 | + | 8.94442i | −1.75871 | + | 1.27777i | ||||
\(50\) | 1.45094 | − | 1.05417i | 0.205194 | − | 0.149082i | ||||
\(51\) | 0.0617614 | + | 0.190082i | 0.00864833 | + | 0.0266168i | ||||
\(52\) | 2.11952 | − | 6.52323i | 0.293925 | − | 0.904609i | ||||
\(53\) | 5.88873 | + | 4.27841i | 0.808879 | + | 0.587685i | 0.913505 | − | 0.406826i | \(-0.133365\pi\) |
−0.104626 | + | 0.994512i | \(0.533365\pi\) | |||||||
\(54\) | 2.80392 | 0.381566 | ||||||||
\(55\) | −5.80545 | + | 1.25246i | −0.782807 | + | 0.168882i | ||||
\(56\) | 4.71351 | 0.629869 | ||||||||
\(57\) | −1.75534 | − | 1.27533i | −0.232501 | − | 0.168922i | ||||
\(58\) | −0.990376 | + | 3.04806i | −0.130043 | + | 0.400230i | ||||
\(59\) | 2.52234 | + | 7.76295i | 0.328380 | + | 1.01065i | 0.969892 | + | 0.243537i | \(0.0783076\pi\) |
−0.641512 | + | 0.767113i | \(0.721692\pi\) | |||||||
\(60\) | 3.14326 | − | 2.28371i | 0.405793 | − | 0.294826i | ||||
\(61\) | 9.80794 | − | 7.12588i | 1.25578 | − | 0.912376i | 0.257235 | − | 0.966349i | \(-0.417188\pi\) |
0.998542 | + | 0.0539729i | \(0.0171885\pi\) | |||||||
\(62\) | 2.20062 | + | 6.77281i | 0.279479 | + | 0.860148i | ||||
\(63\) | 2.48736 | − | 7.65532i | 0.313378 | − | 0.964480i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 12.2822 | 1.52341 | ||||||||
\(66\) | 7.03432 | − | 1.51758i | 0.865865 | − | 0.186801i | ||||
\(67\) | −10.7693 | −1.31568 | −0.657841 | − | 0.753157i | \(-0.728530\pi\) | ||||
−0.657841 | + | 0.753157i | \(0.728530\pi\) | |||||||
\(68\) | 0.0745226 | + | 0.0541438i | 0.00903719 | + | 0.00656590i | ||||
\(69\) | −3.29509 | + | 10.1413i | −0.396683 | + | 1.22086i | ||||
\(70\) | 2.60822 | + | 8.02729i | 0.311742 | + | 0.959444i | ||||
\(71\) | 8.70896 | − | 6.32743i | 1.03356 | − | 0.750928i | 0.0645448 | − | 0.997915i | \(-0.479440\pi\) |
0.969019 | + | 0.246987i | \(0.0794405\pi\) | |||||||
\(72\) | −1.38156 | + | 1.00376i | −0.162819 | + | 0.118295i | ||||
\(73\) | 1.81416 | + | 5.58341i | 0.212331 | + | 0.653488i | 0.999332 | + | 0.0365368i | \(0.0116326\pi\) |
−0.787001 | + | 0.616952i | \(0.788367\pi\) | |||||||
\(74\) | 1.82728 | − | 5.62380i | 0.212417 | − | 0.653753i | ||||
\(75\) | −3.14814 | − | 2.28726i | −0.363516 | − | 0.264110i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −1.58678 | + | 15.5522i | −0.180830 | + | 1.77234i | ||||
\(78\) | −14.8820 | −1.68505 | ||||||||
\(79\) | 11.3353 | + | 8.23559i | 1.27532 | + | 0.926576i | 0.999401 | − | 0.0346046i | \(-0.0110172\pi\) |
0.275921 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(80\) | 0.553351 | − | 1.70304i | 0.0618665 | − | 0.190406i | ||||
\(81\) | −3.46311 | − | 10.6584i | −0.384790 | − | 1.18426i | ||||
\(82\) | −2.91601 | + | 2.11860i | −0.322019 | + | 0.233961i | ||||
\(83\) | 1.62384 | − | 1.17979i | 0.178239 | − | 0.129498i | −0.495088 | − | 0.868843i | \(-0.664864\pi\) |
0.673328 | + | 0.739344i | \(0.264864\pi\) | |||||||
\(84\) | −3.16032 | − | 9.72647i | −0.344819 | − | 1.06124i | ||||
\(85\) | −0.0509719 | + | 0.156875i | −0.00552868 | + | 0.0170155i | ||||
\(86\) | 6.39958 | + | 4.64956i | 0.690084 | + | 0.501375i | ||||
\(87\) | 6.95380 | 0.745526 | ||||||||
\(88\) | 2.21175 | − | 2.47147i | 0.235773 | − | 0.263460i | ||||
\(89\) | −9.13077 | −0.967860 | −0.483930 | − | 0.875107i | \(-0.660791\pi\) | ||||
−0.483930 | + | 0.875107i | \(0.660791\pi\) | |||||||
\(90\) | −2.47394 | − | 1.79742i | −0.260776 | − | 0.189465i | ||||
\(91\) | 9.99040 | − | 30.7473i | 1.04728 | − | 3.22319i | ||||
\(92\) | 1.51867 | + | 4.67398i | 0.158332 | + | 0.487296i | ||||
\(93\) | 12.5004 | − | 9.08209i | 1.29623 | − | 0.941769i | ||||
\(94\) | −2.24941 | + | 1.63429i | −0.232009 | + | 0.168564i | ||||
\(95\) | −0.553351 | − | 1.70304i | −0.0567726 | − | 0.174728i | ||||
\(96\) | −0.670482 | + | 2.06353i | −0.0684308 | + | 0.210608i | ||||
\(97\) | 9.89309 | + | 7.18775i | 1.00449 | + | 0.729805i | 0.963046 | − | 0.269335i | \(-0.0868040\pi\) |
0.0414445 | + | 0.999141i | \(0.486804\pi\) | |||||||
\(98\) | 15.2172 | 1.53716 | ||||||||
\(99\) | −2.84682 | − | 4.89637i | −0.286116 | − | 0.492104i | ||||
\(100\) | −1.79346 | −0.179346 | ||||||||
\(101\) | −6.69584 | − | 4.86481i | −0.666261 | − | 0.484067i | 0.202511 | − | 0.979280i | \(-0.435090\pi\) |
−0.868771 | + | 0.495213i | \(0.835090\pi\) | |||||||
\(102\) | 0.0617614 | − | 0.190082i | 0.00611529 | − | 0.0188209i | ||||
\(103\) | 1.68167 | + | 5.17564i | 0.165700 | + | 0.509971i | 0.999087 | − | 0.0427182i | \(-0.0136018\pi\) |
−0.833388 | + | 0.552689i | \(0.813602\pi\) | |||||||
\(104\) | −5.54899 | + | 4.03158i | −0.544123 | + | 0.395329i | ||||
\(105\) | 14.8158 | − | 10.7643i | 1.44587 | − | 1.05049i | ||||
\(106\) | −2.24929 | − | 6.92262i | −0.218471 | − | 0.672384i | ||||
\(107\) | −0.630804 | + | 1.94141i | −0.0609821 | + | 0.187684i | −0.976907 | − | 0.213667i | \(-0.931459\pi\) |
0.915924 | + | 0.401351i | \(0.131459\pi\) | |||||||
\(108\) | −2.26842 | − | 1.64811i | −0.218279 | − | 0.158589i | ||||
\(109\) | 3.04609 | 0.291762 | 0.145881 | − | 0.989302i | \(-0.453398\pi\) | ||||
0.145881 | + | 0.989302i | \(0.453398\pi\) | |||||||
\(110\) | 5.43289 | + | 2.39910i | 0.518006 | + | 0.228745i | ||||
\(111\) | −12.8300 | −1.21777 | ||||||||
\(112\) | −3.81331 | − | 2.77053i | −0.360324 | − | 0.261791i | ||||
\(113\) | −2.60916 | + | 8.03017i | −0.245449 | + | 0.755415i | 0.750113 | + | 0.661310i | \(0.229999\pi\) |
−0.995562 | + | 0.0941054i | \(0.970001\pi\) | |||||||
\(114\) | 0.670482 | + | 2.06353i | 0.0627964 | + | 0.193267i | ||||
\(115\) | −7.11962 | + | 5.17271i | −0.663908 | + | 0.482357i | ||||
\(116\) | 2.59284 | − | 1.88381i | 0.240739 | − | 0.174907i | ||||
\(117\) | 3.61952 | + | 11.1397i | 0.334625 | + | 1.02987i | ||||
\(118\) | 2.52234 | − | 7.76295i | 0.232200 | − | 0.714638i | ||||
\(119\) | 0.351263 | + | 0.255207i | 0.0322002 | + | 0.0233948i | ||||
\(120\) | −3.88529 | −0.354676 | ||||||||
\(121\) | 7.41004 | + | 8.12965i | 0.673640 | + | 0.739059i | ||||
\(122\) | −12.1233 | −1.09759 | ||||||||
\(123\) | 6.32694 | + | 4.59679i | 0.570481 | + | 0.414478i | ||||
\(124\) | 2.20062 | − | 6.77281i | 0.197621 | − | 0.608216i | ||||
\(125\) | −3.75917 | − | 11.5695i | −0.336230 | − | 1.03481i | ||||
\(126\) | −6.51200 | + | 4.73125i | −0.580135 | + | 0.421493i | ||||
\(127\) | −1.86222 | + | 1.35298i | −0.165245 | + | 0.120058i | −0.667335 | − | 0.744758i | \(-0.732565\pi\) |
0.502089 | + | 0.864816i | \(0.332565\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | 5.30372 | − | 16.3232i | 0.466966 | − | 1.43717i | ||||
\(130\) | −9.93647 | − | 7.21927i | −0.871486 | − | 0.633172i | ||||
\(131\) | 10.0556 | 0.878559 | 0.439279 | − | 0.898350i | \(-0.355234\pi\) | ||||
0.439279 | + | 0.898350i | \(0.355234\pi\) | |||||||
\(132\) | −6.58290 | − | 2.90693i | −0.572968 | − | 0.253016i | ||||
\(133\) | −4.71351 | −0.408713 | ||||||||
\(134\) | 8.71257 | + | 6.33005i | 0.752651 | + | 0.546833i | ||||
\(135\) | 1.55155 | − | 4.77519i | 0.133537 | − | 0.410983i | ||||
\(136\) | −0.0284651 | − | 0.0876066i | −0.00244086 | − | 0.00751220i | ||||
\(137\) | −5.56726 | + | 4.04485i | −0.475643 | + | 0.345575i | −0.799636 | − | 0.600485i | \(-0.794974\pi\) |
0.323994 | + | 0.946059i | \(0.394974\pi\) | |||||||
\(138\) | 8.62667 | − | 6.26764i | 0.734351 | − | 0.533537i | ||||
\(139\) | 1.50444 | + | 4.63021i | 0.127605 | + | 0.392729i | 0.994367 | − | 0.105994i | \(-0.0338025\pi\) |
−0.866761 | + | 0.498723i | \(0.833802\pi\) | |||||||
\(140\) | 2.60822 | − | 8.02729i | 0.220435 | − | 0.678430i | ||||
\(141\) | 4.88060 | + | 3.54596i | 0.411020 | + | 0.298624i | ||||
\(142\) | −10.7649 | −0.903368 | ||||||||
\(143\) | −11.4341 | − | 19.6661i | −0.956170 | − | 1.64456i | ||||
\(144\) | 1.70770 | 0.142309 | ||||||||
\(145\) | 4.64295 | + | 3.37330i | 0.385576 | + | 0.280137i | ||||
\(146\) | 1.81416 | − | 5.58341i | 0.150141 | − | 0.462086i | ||||
\(147\) | −10.2028 | − | 31.4011i | −0.841515 | − | 2.58992i | ||||
\(148\) | −4.78389 | + | 3.47570i | −0.393233 | + | 0.285701i | ||||
\(149\) | 1.81184 | − | 1.31638i | 0.148432 | − | 0.107842i | −0.511091 | − | 0.859527i | \(-0.670758\pi\) |
0.659523 | + | 0.751685i | \(0.270758\pi\) | |||||||
\(150\) | 1.20248 | + | 3.70086i | 0.0981823 | + | 0.302174i | ||||
\(151\) | 1.74357 | − | 5.36614i | 0.141889 | − | 0.436690i | −0.854709 | − | 0.519108i | \(-0.826264\pi\) |
0.996598 | + | 0.0824177i | \(0.0262642\pi\) | |||||||
\(152\) | 0.809017 | + | 0.587785i | 0.0656199 | + | 0.0476757i | ||||
\(153\) | −0.157305 | −0.0127174 | ||||||||
\(154\) | 10.4251 | − | 11.6493i | 0.840077 | − | 0.938728i | ||||
\(155\) | 12.7521 | 1.02427 | ||||||||
\(156\) | 12.0398 | + | 8.74741i | 0.963954 | + | 0.700353i | ||||
\(157\) | −3.08996 | + | 9.50992i | −0.246606 | + | 0.758975i | 0.748762 | + | 0.662838i | \(0.230648\pi\) |
−0.995368 | + | 0.0961361i | \(0.969352\pi\) | |||||||
\(158\) | −4.32970 | − | 13.3255i | −0.344453 | − | 1.06012i | ||||
\(159\) | −12.7769 | + | 9.28298i | −1.01328 | + | 0.736188i | ||||
\(160\) | −1.44869 | + | 1.05254i | −0.114529 | + | 0.0832103i | ||||
\(161\) | 7.15826 | + | 22.0309i | 0.564150 | + | 1.73627i | ||||
\(162\) | −3.46311 | + | 10.6584i | −0.272088 | + | 0.837400i | ||||
\(163\) | 0.331429 | + | 0.240797i | 0.0259595 | + | 0.0188607i | 0.600689 | − | 0.799483i | \(-0.294893\pi\) |
−0.574730 | + | 0.818343i | \(0.694893\pi\) | |||||||
\(164\) | 3.60439 | 0.281455 | ||||||||
\(165\) | 1.30796 | − | 12.8195i | 0.101824 | − | 0.997995i | ||||
\(166\) | −2.00717 | −0.155787 | ||||||||
\(167\) | 12.9617 | + | 9.41720i | 1.00300 | + | 0.728725i | 0.962730 | − | 0.270464i | \(-0.0871771\pi\) |
0.0402735 | + | 0.999189i | \(0.487177\pi\) | |||||||
\(168\) | −3.16032 | + | 9.72647i | −0.243824 | + | 0.750413i | ||||
\(169\) | 10.5204 | + | 32.3786i | 0.809265 | + | 2.49066i | ||||
\(170\) | 0.133446 | − | 0.0969543i | 0.0102349 | − | 0.00743606i | ||||
\(171\) | 1.38156 | − | 1.00376i | 0.105651 | − | 0.0767597i | ||||
\(172\) | −2.44442 | − | 7.52315i | −0.186385 | − | 0.573635i | ||||
\(173\) | −5.90590 | + | 18.1765i | −0.449017 | + | 1.38193i | 0.429000 | + | 0.903304i | \(0.358866\pi\) |
−0.878018 | + | 0.478629i | \(0.841134\pi\) | |||||||
\(174\) | −5.62574 | − | 4.08734i | −0.426487 | − | 0.309861i | ||||
\(175\) | −8.45349 | −0.639024 | ||||||||
\(176\) | −3.24204 | + | 0.699432i | −0.244378 | + | 0.0527217i | ||||
\(177\) | −17.7103 | −1.33119 | ||||||||
\(178\) | 7.38695 | + | 5.36693i | 0.553675 | + | 0.402268i | ||||
\(179\) | −4.05533 | + | 12.4810i | −0.303110 | + | 0.932876i | 0.677266 | + | 0.735738i | \(0.263165\pi\) |
−0.980376 | + | 0.197138i | \(0.936835\pi\) | |||||||
\(180\) | 0.944960 | + | 2.90829i | 0.0704332 | + | 0.216771i | ||||
\(181\) | −10.7333 | + | 7.79816i | −0.797796 | + | 0.579633i | −0.910267 | − | 0.414022i | \(-0.864124\pi\) |
0.112470 | + | 0.993655i | \(0.464124\pi\) | |||||||
\(182\) | −26.1552 | + | 19.0029i | −1.93875 | + | 1.40859i | ||||
\(183\) | 8.12844 | + | 25.0168i | 0.600871 | + | 1.84929i | ||||
\(184\) | 1.51867 | − | 4.67398i | 0.111958 | − | 0.344571i | ||||
\(185\) | −8.56642 | − | 6.22387i | −0.629816 | − | 0.457588i | ||||
\(186\) | −15.4514 | −1.13295 | ||||||||
\(187\) | 0.298640 | − | 0.0644282i | 0.0218387 | − | 0.00471146i | ||||
\(188\) | 2.78042 | 0.202783 | ||||||||
\(189\) | −10.6922 | − | 7.76836i | −0.777745 | − | 0.565065i | ||||
\(190\) | −0.553351 | + | 1.70304i | −0.0401443 | + | 0.123551i | ||||
\(191\) | 6.72988 | + | 20.7124i | 0.486957 | + | 1.49870i | 0.829126 | + | 0.559061i | \(0.188838\pi\) |
−0.342169 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(192\) | 1.75534 | − | 1.27533i | 0.126681 | − | 0.0920392i | ||||
\(193\) | −1.22832 | + | 0.892423i | −0.0884161 | + | 0.0642380i | −0.631115 | − | 0.775689i | \(-0.717402\pi\) |
0.542699 | + | 0.839927i | \(0.317402\pi\) | |||||||
\(194\) | −3.77882 | − | 11.6300i | −0.271304 | − | 0.834987i | ||||
\(195\) | −8.23496 | + | 25.3446i | −0.589718 | + | 1.81496i | ||||
\(196\) | −12.3109 | − | 8.94442i | −0.879353 | − | 0.638887i | ||||
\(197\) | −12.8759 | −0.917370 | −0.458685 | − | 0.888599i | \(-0.651679\pi\) | ||||
−0.458685 | + | 0.888599i | \(0.651679\pi\) | |||||||
\(198\) | −0.574889 | + | 5.63456i | −0.0408556 | + | 0.400431i | ||||
\(199\) | 10.2537 | 0.726864 | 0.363432 | − | 0.931621i | \(-0.381605\pi\) | ||||
0.363432 | + | 0.931621i | \(0.381605\pi\) | |||||||
\(200\) | 1.45094 | + | 1.05417i | 0.102597 | + | 0.0745410i | ||||
\(201\) | 7.22064 | − | 22.2228i | 0.509304 | − | 1.56748i | ||||
\(202\) | 2.55758 | + | 7.87143i | 0.179951 | + | 0.553832i | ||||
\(203\) | 12.2214 | − | 8.87934i | 0.857771 | − | 0.623207i | ||||
\(204\) | −0.161693 | + | 0.117477i | −0.0113208 | + | 0.00822505i | ||||
\(205\) | 1.99449 | + | 6.13841i | 0.139301 | + | 0.428725i | ||||
\(206\) | 1.68167 | − | 5.17564i | 0.117167 | − | 0.360604i | ||||
\(207\) | −6.78971 | − | 4.93301i | −0.471918 | − | 0.342868i | ||||
\(208\) | 6.85893 | 0.475581 | ||||||||
\(209\) | −2.21175 | + | 2.47147i | −0.152990 | + | 0.170955i | ||||
\(210\) | −18.3133 | −1.26374 | ||||||||
\(211\) | −13.7872 | − | 10.0170i | −0.949149 | − | 0.689597i | 0.00145659 | − | 0.999999i | \(-0.499536\pi\) |
−0.950605 | + | 0.310402i | \(0.899536\pi\) | |||||||
\(212\) | −2.24929 | + | 6.92262i | −0.154482 | + | 0.475447i | ||||
\(213\) | 7.21765 | + | 22.2136i | 0.494545 | + | 1.52205i | ||||
\(214\) | 1.65147 | − | 1.19986i | 0.112892 | − | 0.0820207i | ||||
\(215\) | 11.4596 | − | 8.32589i | 0.781538 | − | 0.567821i | ||||
\(216\) | 0.866460 | + | 2.66669i | 0.0589552 | + | 0.181445i | ||||
\(217\) | 10.3726 | − | 31.9237i | 0.704140 | − | 2.16712i | ||||
\(218\) | −2.46434 | − | 1.79045i | −0.166906 | − | 0.121264i | ||||
\(219\) | −12.7379 | −0.860747 | ||||||||
\(220\) | −2.98514 | − | 5.13428i | −0.201258 | − | 0.346153i | ||||
\(221\) | −0.631810 | −0.0425001 | ||||||||
\(222\) | 10.3797 | + | 7.54131i | 0.696641 | + | 0.506139i | ||||
\(223\) | −1.83609 | + | 5.65091i | −0.122954 | + | 0.378413i | −0.993523 | − | 0.113634i | \(-0.963751\pi\) |
0.870569 | + | 0.492046i | \(0.163751\pi\) | |||||||
\(224\) | 1.45655 | + | 4.48281i | 0.0973201 | + | 0.299520i | ||||
\(225\) | 2.47778 | − | 1.80021i | 0.165185 | − | 0.120014i | ||||
\(226\) | 6.83087 | − | 4.96292i | 0.454383 | − | 0.330128i | ||||
\(227\) | 4.89684 | + | 15.0709i | 0.325015 | + | 1.00029i | 0.971434 | + | 0.237310i | \(0.0762657\pi\) |
−0.646419 | + | 0.762982i | \(0.723734\pi\) | |||||||
\(228\) | 0.670482 | − | 2.06353i | 0.0444037 | − | 0.136661i | ||||
\(229\) | −7.37474 | − | 5.35806i | −0.487337 | − | 0.354071i | 0.316823 | − | 0.948485i | \(-0.397384\pi\) |
−0.804159 | + | 0.594414i | \(0.797384\pi\) | |||||||
\(230\) | 8.80033 | 0.580277 | ||||||||
\(231\) | −31.0285 | − | 13.7018i | −2.04153 | − | 0.901514i | ||||
\(232\) | −3.20492 | −0.210414 | ||||||||
\(233\) | 5.29820 | + | 3.84937i | 0.347096 | + | 0.252180i | 0.747650 | − | 0.664093i | \(-0.231182\pi\) |
−0.400553 | + | 0.916273i | \(0.631182\pi\) | |||||||
\(234\) | 3.61952 | − | 11.1397i | 0.236616 | − | 0.728228i | ||||
\(235\) | 1.53855 | + | 4.73517i | 0.100364 | + | 0.308888i | ||||
\(236\) | −6.60356 | + | 4.79777i | −0.429855 | + | 0.312308i | ||||
\(237\) | −24.5945 | + | 17.8690i | −1.59758 | + | 1.16071i | ||||
\(238\) | −0.134170 | − | 0.412934i | −0.00869698 | − | 0.0267665i | ||||
\(239\) | 5.47862 | − | 16.8615i | 0.354382 | − | 1.09068i | −0.601984 | − | 0.798508i | \(-0.705623\pi\) |
0.956367 | − | 0.292169i | \(-0.0943769\pi\) | |||||||
\(240\) | 3.14326 | + | 2.28371i | 0.202897 | + | 0.147413i | ||||
\(241\) | 8.44210 | 0.543804 | 0.271902 | − | 0.962325i | \(-0.412347\pi\) | ||||
0.271902 | + | 0.962325i | \(0.412347\pi\) | |||||||
\(242\) | −1.21636 | − | 10.9325i | −0.0781907 | − | 0.702770i | ||||
\(243\) | 15.9040 | 1.02024 | ||||||||
\(244\) | 9.80794 | + | 7.12588i | 0.627889 | + | 0.456188i | ||||
\(245\) | 8.42043 | − | 25.9154i | 0.537961 | − | 1.65567i | ||||
\(246\) | −2.41667 | − | 7.43776i | −0.154082 | − | 0.474214i | ||||
\(247\) | 5.54899 | − | 4.03158i | 0.353074 | − | 0.256523i | ||||
\(248\) | −5.76130 | + | 4.18583i | −0.365843 | + | 0.265800i | ||||
\(249\) | 1.34577 | + | 4.14186i | 0.0852849 | + | 0.262480i | ||||
\(250\) | −3.75917 | + | 11.5695i | −0.237751 | + | 0.731721i | ||||
\(251\) | −16.8956 | − | 12.2754i | −1.06644 | − | 0.774813i | −0.0911704 | − | 0.995835i | \(-0.529061\pi\) |
−0.975269 | + | 0.221022i | \(0.929061\pi\) | |||||||
\(252\) | 8.04928 | 0.507057 | ||||||||
\(253\) | 14.9105 | + | 6.58431i | 0.937417 | + | 0.413952i | ||||
\(254\) | 2.30183 | 0.144430 | ||||||||
\(255\) | −0.289542 | − | 0.210364i | −0.0181318 | − | 0.0131735i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −7.99254 | − | 24.5985i | −0.498561 | − | 1.53441i | −0.811333 | − | 0.584585i | \(-0.801257\pi\) |
0.312771 | − | 0.949828i | \(-0.398743\pi\) | |||||||
\(258\) | −13.8853 | + | 10.0883i | −0.864462 | + | 0.628068i | ||||
\(259\) | −22.5489 | + | 16.3827i | −1.40112 | + | 1.01797i | ||||
\(260\) | 3.79539 | + | 11.6810i | 0.235380 | + | 0.724426i | ||||
\(261\) | −1.69127 | + | 5.20519i | −0.104687 | + | 0.322193i | ||||
\(262\) | −8.13512 | − | 5.91051i | −0.502590 | − | 0.365153i | ||||
\(263\) | 31.2182 | 1.92500 | 0.962498 | − | 0.271287i | \(-0.0874494\pi\) | ||||
0.962498 | + | 0.271287i | \(0.0874494\pi\) | |||||||
\(264\) | 3.61703 | + | 6.22108i | 0.222613 | + | 0.382881i | ||||
\(265\) | −13.0341 | −0.800681 | ||||||||
\(266\) | 3.81331 | + | 2.77053i | 0.233809 | + | 0.169872i | ||||
\(267\) | 6.12201 | − | 18.8416i | 0.374661 | − | 1.15309i | ||||
\(268\) | −3.32790 | − | 10.2422i | −0.203284 | − | 0.625644i | ||||
\(269\) | 17.3897 | − | 12.6343i | 1.06027 | − | 0.770329i | 0.0861290 | − | 0.996284i | \(-0.472550\pi\) |
0.974138 | + | 0.225955i | \(0.0725503\pi\) | |||||||
\(270\) | −4.06202 | + | 2.95123i | −0.247207 | + | 0.179606i | ||||
\(271\) | −1.09670 | − | 3.37529i | −0.0666197 | − | 0.205034i | 0.912205 | − | 0.409734i | \(-0.134378\pi\) |
−0.978825 | + | 0.204699i | \(0.934378\pi\) | |||||||
\(272\) | −0.0284651 | + | 0.0876066i | −0.00172595 | + | 0.00531193i | ||||
\(273\) | 56.7496 | + | 41.2310i | 3.43464 | + | 2.49541i | ||||
\(274\) | 6.88151 | 0.415727 | ||||||||
\(275\) | −3.96668 | + | 4.43249i | −0.239200 | + | 0.267289i | ||||
\(276\) | −10.6631 | −0.641846 | ||||||||
\(277\) | −13.1491 | − | 9.55341i | −0.790056 | − | 0.574009i | 0.117924 | − | 0.993023i | \(-0.462376\pi\) |
−0.907980 | + | 0.419014i | \(0.862376\pi\) | |||||||
\(278\) | 1.50444 | − | 4.63021i | 0.0902306 | − | 0.277701i | ||||
\(279\) | 3.75801 | + | 11.5660i | 0.224986 | + | 0.692436i | ||||
\(280\) | −6.82842 | + | 4.96114i | −0.408076 | + | 0.296485i | ||||
\(281\) | 3.62933 | − | 2.63686i | 0.216508 | − | 0.157302i | −0.474246 | − | 0.880393i | \(-0.657279\pi\) |
0.690753 | + | 0.723091i | \(0.257279\pi\) | |||||||
\(282\) | −1.86422 | − | 5.73748i | −0.111013 | − | 0.341662i | ||||
\(283\) | 5.44840 | − | 16.7684i | 0.323874 | − | 0.996780i | −0.648073 | − | 0.761578i | \(-0.724425\pi\) |
0.971947 | − | 0.235202i | \(-0.0755752\pi\) | |||||||
\(284\) | 8.70896 | + | 6.32743i | 0.516782 | + | 0.375464i | ||||
\(285\) | 3.88529 | 0.230144 | ||||||||
\(286\) | −2.30902 | + | 22.6310i | −0.136535 | + | 1.33820i | ||||
\(287\) | 16.9893 | 1.00285 | ||||||||
\(288\) | −1.38156 | − | 1.00376i | −0.0814093 | − | 0.0591473i | ||||
\(289\) | −5.25067 | + | 16.1599i | −0.308863 | + | 0.950582i | ||||
\(290\) | −1.77345 | − | 5.45811i | −0.104140 | − | 0.320511i | ||||
\(291\) | −21.4653 | + | 15.5954i | −1.25832 | + | 0.914221i | ||||
\(292\) | −4.74953 | + | 3.45074i | −0.277945 | + | 0.201939i | ||||
\(293\) | −4.74046 | − | 14.5896i | −0.276941 | − | 0.852335i | −0.988699 | − | 0.149911i | \(-0.952101\pi\) |
0.711759 | − | 0.702424i | \(-0.247899\pi\) | |||||||
\(294\) | −10.2028 | + | 31.4011i | −0.595041 | + | 1.83135i | ||||
\(295\) | −11.8249 | − | 8.59127i | −0.688471 | − | 0.500203i | ||||
\(296\) | 5.91321 | 0.343698 | ||||||||
\(297\) | −9.09042 | + | 1.96116i | −0.527480 | + | 0.113798i | ||||
\(298\) | −2.23956 | −0.129734 | ||||||||
\(299\) | −27.2706 | − | 19.8132i | −1.57710 | − | 1.14583i | ||||
\(300\) | 1.20248 | − | 3.70086i | 0.0694254 | − | 0.213669i | ||||
\(301\) | −11.5218 | − | 35.4604i | −0.664105 | − | 2.04391i | ||||
\(302\) | −4.56471 | + | 3.31646i | −0.262670 | + | 0.190841i | ||||
\(303\) | 14.5281 | − | 10.5553i | 0.834619 | − | 0.606386i | ||||
\(304\) | −0.309017 | − | 0.951057i | −0.0177233 | − | 0.0545468i | ||||
\(305\) | −6.70843 | + | 20.6464i | −0.384123 | + | 1.18221i | ||||
\(306\) | 0.127263 | + | 0.0924617i | 0.00727512 | + | 0.00528568i | ||||
\(307\) | −19.5442 | −1.11545 | −0.557724 | − | 0.830027i | \(-0.688325\pi\) | ||||
−0.557724 | + | 0.830027i | \(0.688325\pi\) | |||||||
\(308\) | −15.2814 | + | 3.29678i | −0.870736 | + | 0.187851i | ||||
\(309\) | −11.8076 | −0.671712 | ||||||||
\(310\) | −10.3166 | − | 7.49548i | −0.585946 | − | 0.425715i | ||||
\(311\) | −2.66109 | + | 8.18998i | −0.150896 | + | 0.464411i | −0.997722 | − | 0.0674594i | \(-0.978511\pi\) |
0.846826 | + | 0.531870i | \(0.178511\pi\) | |||||||
\(312\) | −4.59879 | − | 14.1536i | −0.260355 | − | 0.801290i | ||||
\(313\) | 2.33955 | − | 1.69978i | 0.132239 | − | 0.0960775i | −0.519699 | − | 0.854349i | \(-0.673956\pi\) |
0.651939 | + | 0.758272i | \(0.273956\pi\) | |||||||
\(314\) | 8.08962 | − | 5.87746i | 0.456524 | − | 0.331684i | ||||
\(315\) | 4.45408 | + | 13.7082i | 0.250959 | + | 0.772372i | ||||
\(316\) | −4.32970 | + | 13.3255i | −0.243565 | + | 0.749616i | ||||
\(317\) | 20.7713 | + | 15.0912i | 1.16663 | + | 0.847606i | 0.990602 | − | 0.136779i | \(-0.0436750\pi\) |
0.176028 | + | 0.984385i | \(0.443675\pi\) | |||||||
\(318\) | 15.7931 | 0.885635 | ||||||||
\(319\) | 1.07892 | − | 10.5746i | 0.0604079 | − | 0.592066i | ||||
\(320\) | 1.79068 | 0.100102 | ||||||||
\(321\) | −3.58323 | − | 2.60337i | −0.199996 | − | 0.145306i | ||||
\(322\) | 7.15826 | − | 22.0309i | 0.398914 | − | 1.22773i | ||||
\(323\) | 0.0284651 | + | 0.0876066i | 0.00158384 | + | 0.00487456i | ||||
\(324\) | 9.06654 | − | 6.58723i | 0.503697 | − | 0.365957i | ||||
\(325\) | 9.95189 | − | 7.23047i | 0.552032 | − | 0.401074i | ||||
\(326\) | −0.126595 | − | 0.389618i | −0.00701143 | − | 0.0215790i | ||||
\(327\) | −2.04235 | + | 6.28570i | −0.112942 | + | 0.347600i | ||||
\(328\) | −2.91601 | − | 2.11860i | −0.161010 | − | 0.116980i | ||||
\(329\) | 13.1055 | 0.722532 | ||||||||
\(330\) | −8.59326 | + | 9.60238i | −0.473044 | + | 0.528594i | ||||
\(331\) | 0.669770 | 0.0368139 | 0.0184069 | − | 0.999831i | \(-0.494141\pi\) | ||||
0.0184069 | + | 0.999831i | \(0.494141\pi\) | |||||||
\(332\) | 1.62384 | + | 1.17979i | 0.0891196 | + | 0.0647492i | ||||
\(333\) | 3.12046 | − | 9.60379i | 0.171000 | − | 0.526284i | ||||
\(334\) | −4.95091 | − | 15.2373i | −0.270902 | − | 0.833751i | ||||
\(335\) | 15.6014 | − | 11.3351i | 0.852397 | − | 0.619303i | ||||
\(336\) | 8.27383 | − | 6.01129i | 0.451374 | − | 0.327943i | ||||
\(337\) | 8.90772 | + | 27.4152i | 0.485235 | + | 1.49340i | 0.831641 | + | 0.555314i | \(0.187402\pi\) |
−0.346406 | + | 0.938085i | \(0.612598\pi\) | |||||||
\(338\) | 10.5204 | − | 32.3786i | 0.572237 | − | 1.76116i | ||||
\(339\) | −14.8211 | − | 10.7682i | −0.804972 | − | 0.584847i | ||||
\(340\) | −0.164949 | −0.00894559 | ||||||||
\(341\) | −11.8716 | − | 20.4185i | −0.642884 | − | 1.10572i | ||||
\(342\) | −1.70770 | −0.0923421 | ||||||||
\(343\) | −31.3345 | − | 22.7659i | −1.69191 | − | 1.22924i | ||||
\(344\) | −2.44442 | + | 7.52315i | −0.131794 | + | 0.405621i | ||||
\(345\) | −5.90046 | − | 18.1598i | −0.317670 | − | 0.977688i | ||||
\(346\) | 15.4618 | − | 11.2337i | 0.831234 | − | 0.603927i | ||||
\(347\) | 17.0753 | − | 12.4059i | 0.916648 | − | 0.665984i | −0.0260390 | − | 0.999661i | \(-0.508289\pi\) |
0.942688 | + | 0.333677i | \(0.108289\pi\) | |||||||
\(348\) | 2.14884 | + | 6.61346i | 0.115190 | + | 0.354519i | ||||
\(349\) | −2.11889 | + | 6.52127i | −0.113422 | + | 0.349076i | −0.991615 | − | 0.129231i | \(-0.958749\pi\) |
0.878193 | + | 0.478307i | \(0.158749\pi\) | |||||||
\(350\) | 6.83902 | + | 4.96884i | 0.365561 | + | 0.265595i | ||||
\(351\) | 19.2319 | 1.02652 | ||||||||
\(352\) | 3.03398 | + | 1.33977i | 0.161712 | + | 0.0714099i | ||||
\(353\) | 18.5941 | 0.989666 | 0.494833 | − | 0.868988i | \(-0.335229\pi\) | ||||
0.494833 | + | 0.868988i | \(0.335229\pi\) | |||||||
\(354\) | 14.3279 | + | 10.4098i | 0.761520 | + | 0.553276i | ||||
\(355\) | −5.95675 | + | 18.3330i | −0.316152 | + | 0.973014i | ||||
\(356\) | −2.82156 | − | 8.68388i | −0.149543 | − | 0.460245i | ||||
\(357\) | −0.762144 | + | 0.553730i | −0.0403369 | + | 0.0293065i | ||||
\(358\) | 10.6170 | − | 7.71370i | 0.561126 | − | 0.407682i | ||||
\(359\) | −9.36941 | − | 28.8361i | −0.494498 | − | 1.52191i | −0.817737 | − | 0.575592i | \(-0.804772\pi\) |
0.323239 | − | 0.946317i | \(-0.395228\pi\) | |||||||
\(360\) | 0.944960 | − | 2.90829i | 0.0498038 | − | 0.153280i | ||||
\(361\) | −0.809017 | − | 0.587785i | −0.0425798 | − | 0.0309361i | ||||
\(362\) | 13.2670 | 0.697300 | ||||||||
\(363\) | −21.7441 | + | 9.84007i | −1.14127 | + | 0.516470i | ||||
\(364\) | 32.3296 | 1.69453 | ||||||||
\(365\) | −8.50490 | − | 6.17917i | −0.445167 | − | 0.323432i | ||||
\(366\) | 8.12844 | − | 25.0168i | 0.424880 | − | 1.30765i | ||||
\(367\) | 4.41597 | + | 13.5910i | 0.230512 | + | 0.709443i | 0.997685 | + | 0.0680028i | \(0.0216627\pi\) |
−0.767173 | + | 0.641440i | \(0.778337\pi\) | |||||||
\(368\) | −3.97593 | + | 2.88868i | −0.207260 | + | 0.150583i | ||||
\(369\) | −4.97968 | + | 3.61795i | −0.259232 | + | 0.188343i | ||||
\(370\) | 3.27208 | + | 10.0704i | 0.170107 | + | 0.523537i | ||||
\(371\) | −10.6021 | + | 32.6298i | −0.550432 | + | 1.69406i | ||||
\(372\) | 12.5004 | + | 9.08209i | 0.648117 | + | 0.470884i | ||||
\(373\) | 23.0852 | 1.19530 | 0.597652 | − | 0.801755i | \(-0.296100\pi\) | ||||
0.597652 | + | 0.801755i | \(0.296100\pi\) | |||||||
\(374\) | −0.279475 | − | 0.123413i | −0.0144513 | − | 0.00638152i | ||||
\(375\) | 26.3945 | 1.36301 | ||||||||
\(376\) | −2.24941 | − | 1.63429i | −0.116004 | − | 0.0842821i | ||||
\(377\) | −6.79292 | + | 20.9064i | −0.349853 | + | 1.07674i | ||||
\(378\) | 4.08407 | + | 12.5695i | 0.210062 | + | 0.646504i | ||||
\(379\) | 14.7083 | − | 10.6862i | 0.755516 | − | 0.548915i | −0.142016 | − | 0.989864i | \(-0.545358\pi\) |
0.897532 | + | 0.440950i | \(0.145358\pi\) | |||||||
\(380\) | 1.44869 | − | 1.05254i | 0.0743163 | − | 0.0539940i | ||||
\(381\) | −1.54334 | − | 4.74990i | −0.0790674 | − | 0.243345i | ||||
\(382\) | 6.72988 | − | 20.7124i | 0.344331 | − | 1.05974i | ||||
\(383\) | −22.8700 | − | 16.6160i | −1.16860 | − | 0.849039i | −0.177761 | − | 0.984074i | \(-0.556886\pi\) |
−0.990841 | + | 0.135034i | \(0.956886\pi\) | |||||||
\(384\) | −2.16972 | −0.110723 | ||||||||
\(385\) | −14.0705 | − | 24.2005i | −0.717099 | − | 1.23337i | ||||
\(386\) | 1.51828 | 0.0772785 | ||||||||
\(387\) | 10.9286 | + | 7.94008i | 0.555531 | + | 0.403617i | ||||
\(388\) | −3.77882 | + | 11.6300i | −0.191841 | + | 0.590425i | ||||
\(389\) | −9.06759 | − | 27.9072i | −0.459745 | − | 1.41495i | −0.865473 | − | 0.500956i | \(-0.832982\pi\) |
0.405728 | − | 0.913994i | \(-0.367018\pi\) | |||||||
\(390\) | 21.5594 | − | 15.6638i | 1.09170 | − | 0.793169i | ||||
\(391\) | 0.366242 | − | 0.266091i | 0.0185217 | − | 0.0134568i | ||||
\(392\) | 4.70236 | + | 14.4724i | 0.237505 | + | 0.730965i | ||||
\(393\) | −6.74207 | + | 20.7500i | −0.340093 | + | 1.04670i | ||||
\(394\) | 10.4168 | + | 7.56826i | 0.524792 | + | 0.381284i | ||||
\(395\) | −25.0896 | −1.26240 | ||||||||
\(396\) | 3.77701 | − | 4.22055i | 0.189802 | − | 0.212090i | ||||
\(397\) | 2.08500 | 0.104643 | 0.0523216 | − | 0.998630i | \(-0.483338\pi\) | ||||
0.0523216 | + | 0.998630i | \(0.483338\pi\) | |||||||
\(398\) | −8.29540 | − | 6.02696i | −0.415811 | − | 0.302104i | ||||
\(399\) | 3.16032 | − | 9.72647i | 0.158214 | − | 0.486932i | ||||
\(400\) | −0.554210 | − | 1.70568i | −0.0277105 | − | 0.0852841i | ||||
\(401\) | −9.33009 | + | 6.77871i | −0.465923 | + | 0.338513i | −0.795850 | − | 0.605494i | \(-0.792976\pi\) |
0.329927 | + | 0.944006i | \(0.392976\pi\) | |||||||
\(402\) | −18.9039 | + | 13.7345i | −0.942839 | + | 0.685013i | ||||
\(403\) | 15.0939 | + | 46.4542i | 0.751880 | + | 2.31405i | ||||
\(404\) | 2.55758 | − | 7.87143i | 0.127244 | − | 0.391618i | ||||
\(405\) | 16.2353 | + | 11.7956i | 0.806738 | + | 0.586129i | ||||
\(406\) | −15.1064 | −0.749720 | ||||||||
\(407\) | −1.99065 | + | 19.5106i | −0.0986728 | + | 0.967105i | ||||
\(408\) | 0.199864 | 0.00989475 | ||||||||
\(409\) | 0.592468 | + | 0.430453i | 0.0292957 | + | 0.0212845i | 0.602337 | − | 0.798242i | \(-0.294236\pi\) |
−0.573041 | + | 0.819527i | \(0.694236\pi\) | |||||||
\(410\) | 1.99449 | − | 6.13841i | 0.0985008 | − | 0.303154i | ||||
\(411\) | −4.61393 | − | 14.2002i | −0.227588 | − | 0.700444i | ||||
\(412\) | −4.40266 | + | 3.19872i | −0.216904 | + | 0.157590i | ||||
\(413\) | −31.1259 | + | 22.6143i | −1.53161 | + | 1.11278i | ||||
\(414\) | 2.59344 | + | 7.98178i | 0.127461 | + | 0.392283i | ||||
\(415\) | −1.11067 | + | 3.41829i | −0.0545207 | + | 0.167797i | ||||
\(416\) | −5.54899 | − | 4.03158i | −0.272062 | − | 0.197664i | ||||
\(417\) | −10.5633 | −0.517286 | ||||||||
\(418\) | 3.24204 | − | 0.699432i | 0.158573 | − | 0.0342104i | ||||
\(419\) | 13.2156 | 0.645623 | 0.322812 | − | 0.946463i | \(-0.395372\pi\) | ||||
0.322812 | + | 0.946463i | \(0.395372\pi\) | |||||||
\(420\) | 14.8158 | + | 10.7643i | 0.722936 | + | 0.525244i | ||||
\(421\) | 3.21870 | − | 9.90614i | 0.156870 | − | 0.482796i | −0.841476 | − | 0.540295i | \(-0.818313\pi\) |
0.998346 | + | 0.0574993i | \(0.0183127\pi\) | |||||||
\(422\) | 5.26624 | + | 16.2078i | 0.256356 | + | 0.788984i | ||||
\(423\) | −3.84133 | + | 2.79089i | −0.186772 | + | 0.135698i | ||||
\(424\) | 5.88873 | − | 4.27841i | 0.285982 | − | 0.207778i | ||||
\(425\) | 0.0510510 | + | 0.157119i | 0.00247634 | + | 0.00762139i | ||||
\(426\) | 7.21765 | − | 22.2136i | 0.349696 | − | 1.07625i | ||||
\(427\) | 46.2298 | + | 33.5879i | 2.23722 | + | 1.62543i | ||||
\(428\) | −2.04132 | −0.0986711 | ||||||||
\(429\) | 48.2479 | − | 10.4089i | 2.32943 | − | 0.502548i | ||||
\(430\) | −14.1648 | −0.683089 | ||||||||
\(431\) | 9.13954 | + | 6.64027i | 0.440236 | + | 0.319850i | 0.785729 | − | 0.618571i | \(-0.212288\pi\) |
−0.345492 | + | 0.938422i | \(0.612288\pi\) | |||||||
\(432\) | 0.866460 | − | 2.66669i | 0.0416876 | − | 0.128301i | ||||
\(433\) | −6.86876 | − | 21.1399i | −0.330091 | − | 1.01592i | −0.969090 | − | 0.246709i | \(-0.920651\pi\) |
0.638998 | − | 0.769208i | \(-0.279349\pi\) | |||||||
\(434\) | −27.1559 | + | 19.7299i | −1.30353 | + | 0.947067i | ||||
\(435\) | −10.0739 | + | 7.31913i | −0.483007 | + | 0.350925i | ||||
\(436\) | 0.941293 | + | 2.89700i | 0.0450798 | + | 0.138741i | ||||
\(437\) | −1.51867 | + | 4.67398i | −0.0726478 | + | 0.223587i | ||||
\(438\) | 10.3052 | + | 7.48715i | 0.492400 | + | 0.357750i | ||||
\(439\) | 25.2534 | 1.20528 | 0.602641 | − | 0.798013i | \(-0.294115\pi\) | ||||
0.602641 | + | 0.798013i | \(0.294115\pi\) | |||||||
\(440\) | −0.602823 | + | 5.90835i | −0.0287384 | + | 0.281669i | ||||
\(441\) | 25.9864 | 1.23745 | ||||||||
\(442\) | 0.511145 | + | 0.371369i | 0.0243127 | + | 0.0176642i | ||||
\(443\) | −1.28871 | + | 3.96626i | −0.0612287 | + | 0.188442i | −0.976992 | − | 0.213276i | \(-0.931587\pi\) |
0.915763 | + | 0.401718i | \(0.131587\pi\) | |||||||
\(444\) | −3.96470 | − | 12.2021i | −0.188156 | − | 0.579086i | ||||
\(445\) | 13.2277 | − | 9.61046i | 0.627052 | − | 0.455580i | ||||
\(446\) | 4.80695 | − | 3.49245i | 0.227616 | − | 0.165372i | ||||
\(447\) | 1.50158 | + | 4.62140i | 0.0710225 | + | 0.218585i | ||||
\(448\) | 1.45655 | − | 4.48281i | 0.0688157 | − | 0.211793i | ||||
\(449\) | 6.93686 | + | 5.03992i | 0.327371 | + | 0.237849i | 0.739314 | − | 0.673361i | \(-0.235150\pi\) |
−0.411944 | + | 0.911209i | \(0.635150\pi\) | |||||||
\(450\) | −3.06270 | −0.144377 | ||||||||
\(451\) | 7.97198 | − | 8.90814i | 0.375386 | − | 0.419468i | ||||
\(452\) | −8.44342 | −0.397145 | ||||||||
\(453\) | 9.90417 | + | 7.19580i | 0.465339 | + | 0.338088i | ||||
\(454\) | 4.89684 | − | 15.0709i | 0.229820 | − | 0.707314i | ||||
\(455\) | 17.8896 | + | 55.0586i | 0.838678 | + | 2.58119i | ||||
\(456\) | −1.75534 | + | 1.27533i | −0.0822015 | + | 0.0597229i | ||||
\(457\) | 9.72307 | − | 7.06423i | 0.454826 | − | 0.330451i | −0.336672 | − | 0.941622i | \(-0.609301\pi\) |
0.791498 | + | 0.611171i | \(0.209301\pi\) | |||||||
\(458\) | 2.81690 | + | 8.66953i | 0.131625 | + | 0.405100i | ||||
\(459\) | −0.0798140 | + | 0.245642i | −0.00372540 | + | 0.0114656i | ||||
\(460\) | −7.11962 | − | 5.17271i | −0.331954 | − | 0.241179i | ||||
\(461\) | 3.00764 | 0.140080 | 0.0700398 | − | 0.997544i | \(-0.477687\pi\) | ||||
0.0700398 | + | 0.997544i | \(0.477687\pi\) | |||||||
\(462\) | 17.0489 | + | 29.3231i | 0.793186 | + | 1.36424i | ||||
\(463\) | 20.2752 | 0.942270 | 0.471135 | − | 0.882061i | \(-0.343844\pi\) | ||||
0.471135 | + | 0.882061i | \(0.343844\pi\) | |||||||
\(464\) | 2.59284 | + | 1.88381i | 0.120369 | + | 0.0874535i | ||||
\(465\) | −8.55003 | + | 26.3143i | −0.396498 | + | 1.22030i | ||||
\(466\) | −2.02373 | − | 6.22840i | −0.0937475 | − | 0.288525i | ||||
\(467\) | 17.3353 | − | 12.5948i | 0.802181 | − | 0.582819i | −0.109372 | − | 0.994001i | \(-0.534884\pi\) |
0.911553 | + | 0.411182i | \(0.134884\pi\) | |||||||
\(468\) | −9.47604 | + | 6.88474i | −0.438030 | + | 0.318247i | ||||
\(469\) | −15.6861 | − | 48.2769i | −0.724317 | − | 2.22922i | ||||
\(470\) | 1.53855 | − | 4.73517i | 0.0709680 | − | 0.218417i | ||||
\(471\) | −17.5523 | − | 12.7525i | −0.808765 | − | 0.587602i | ||||
\(472\) | 8.16245 | 0.375707 | ||||||||
\(473\) | −23.9997 | − | 10.5980i | −1.10351 | − | 0.487296i | ||||
\(474\) | 30.4005 | 1.39634 | ||||||||
\(475\) | −1.45094 | − | 1.05417i | −0.0665737 | − | 0.0483686i | ||||
\(476\) | −0.134170 | + | 0.412934i | −0.00614969 | + | 0.0189268i | ||||
\(477\) | −3.84113 | − | 11.8218i | −0.175873 | − | 0.541282i | ||||
\(478\) | −14.3432 | + | 10.4210i | −0.656043 | + | 0.476643i | ||||
\(479\) | −21.8499 | + | 15.8749i | −0.998349 | + | 0.725343i | −0.961734 | − | 0.273987i | \(-0.911658\pi\) |
−0.0366153 | + | 0.999329i | \(0.511658\pi\) | |||||||
\(480\) | −1.20062 | − | 3.69513i | −0.0548005 | − | 0.168659i | ||||
\(481\) | 12.5332 | − | 38.5732i | 0.571465 | − | 1.75879i | ||||
\(482\) | −6.82981 | − | 4.96214i | −0.311089 | − | 0.226020i | ||||
\(483\) | −50.2608 | −2.28695 | ||||||||
\(484\) | −5.44193 | + | 9.55957i | −0.247360 | + | 0.434526i | ||||
\(485\) | −21.8974 | −0.994310 | ||||||||
\(486\) | −12.8666 | − | 9.34815i | −0.583642 | − | 0.424041i | ||||
\(487\) | −0.741546 | + | 2.28224i | −0.0336027 | + | 0.103418i | −0.966451 | − | 0.256851i | \(-0.917315\pi\) |
0.932848 | + | 0.360269i | \(0.117315\pi\) | |||||||
\(488\) | −3.74630 | − | 11.5299i | −0.169587 | − | 0.521935i | ||||
\(489\) | −0.719110 | + | 0.522464i | −0.0325193 | + | 0.0236266i | ||||
\(490\) | −22.0450 | + | 16.0166i | −0.995890 | + | 0.723556i | ||||
\(491\) | −4.09373 | − | 12.5992i | −0.184747 | − | 0.568594i | 0.815197 | − | 0.579184i | \(-0.196629\pi\) |
−0.999944 | + | 0.0105906i | \(0.996629\pi\) | |||||||
\(492\) | −2.41667 | + | 7.43776i | −0.108952 | + | 0.335320i | ||||
\(493\) | −0.238839 | − | 0.173527i | −0.0107568 | − | 0.00781526i | ||||
\(494\) | −6.85893 | −0.308598 | ||||||||
\(495\) | 9.27777 | + | 4.09695i | 0.417005 | + | 0.184144i | ||||
\(496\) | 7.12135 | 0.319758 | ||||||||
\(497\) | 41.0498 | + | 29.8244i | 1.84133 | + | 1.33781i | ||||
\(498\) | 1.34577 | − | 4.14186i | 0.0603055 | − | 0.185601i | ||||
\(499\) | 9.12099 | + | 28.0715i | 0.408312 | + | 1.25665i | 0.918098 | + | 0.396353i | \(0.129724\pi\) |
−0.509787 | + | 0.860301i | \(0.670276\pi\) | |||||||
\(500\) | 9.84163 | − | 7.15036i | 0.440131 | − | 0.319774i | ||||
\(501\) | −28.1232 | + | 20.4327i | −1.25645 | + | 0.912867i | ||||
\(502\) | 6.45354 | + | 19.8619i | 0.288035 | + | 0.886482i | ||||
\(503\) | 9.26332 | − | 28.5096i | 0.413031 | − | 1.27118i | −0.500970 | − | 0.865465i | \(-0.667023\pi\) |
0.914000 | − | 0.405713i | \(-0.132977\pi\) | |||||||
\(504\) | −6.51200 | − | 4.73125i | −0.290068 | − | 0.210747i | ||||
\(505\) | 14.8206 | 0.659508 | ||||||||
\(506\) | −8.19271 | − | 14.0910i | −0.364211 | − | 0.626422i | ||||
\(507\) | −73.8680 | −3.28059 | ||||||||
\(508\) | −1.86222 | − | 1.35298i | −0.0826226 | − | 0.0600289i | ||||
\(509\) | −8.33496 | + | 25.6524i | −0.369441 | + | 1.13702i | 0.577713 | + | 0.816240i | \(0.303945\pi\) |
−0.947153 | + | 0.320781i | \(0.896055\pi\) | |||||||
\(510\) | 0.110595 | + | 0.340376i | 0.00489723 | + | 0.0150721i | ||||
\(511\) | −22.3869 | + | 16.2651i | −0.990340 | + | 0.719524i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | −0.866460 | − | 2.66669i | −0.0382552 | − | 0.117737i | ||||
\(514\) | −7.99254 | + | 24.5985i | −0.352536 | + | 1.08499i | ||||
\(515\) | −7.88376 | − | 5.72789i | −0.347400 | − | 0.252401i | ||||
\(516\) | 17.1632 | 0.755568 | ||||||||
\(517\) | 6.14958 | − | 6.87174i | 0.270458 | − | 0.302219i | ||||
\(518\) | 27.8720 | 1.22462 | ||||||||
\(519\) | −33.5479 | − | 24.3740i | −1.47259 | − | 1.06990i | ||||
\(520\) | 3.79539 | − | 11.6810i | 0.166439 | − | 0.512247i | ||||
\(521\) | −10.4935 | − | 32.2955i | −0.459727 | − | 1.41489i | −0.865495 | − | 0.500917i | \(-0.832996\pi\) |
0.405769 | − | 0.913976i | \(-0.367004\pi\) | |||||||
\(522\) | 4.42780 | − | 3.21699i | 0.193800 | − | 0.140804i | ||||
\(523\) | 30.0497 | − | 21.8324i | 1.31398 | − | 0.954665i | 0.313997 | − | 0.949424i | \(-0.398332\pi\) |
0.999986 | − | 0.00524074i | \(-0.00166819\pi\) | |||||||
\(524\) | 3.10734 | + | 9.56341i | 0.135745 | + | 0.417780i | ||||
\(525\) | 5.66791 | − | 17.4440i | 0.247368 | − | 0.761320i | ||||
\(526\) | −25.2561 | − | 18.3496i | −1.10122 | − | 0.800080i | ||||
\(527\) | −0.655983 | −0.0285751 | ||||||||
\(528\) | 0.730425 | − | 7.15900i | 0.0317877 | − | 0.311555i | ||||
\(529\) | 1.15247 | 0.0501074 | ||||||||
\(530\) | 10.5448 | + | 7.66127i | 0.458038 | + | 0.332784i | ||||
\(531\) | 4.30740 | − | 13.2568i | 0.186925 | − | 0.575297i | ||||
\(532\) | −1.45655 | − | 4.48281i | −0.0631496 | − | 0.194355i | ||||
\(533\) | −20.0007 | + | 14.5314i | −0.866326 | + | 0.629423i | ||||
\(534\) | −16.0276 | + | 11.6448i | −0.693584 | + | 0.503918i | ||||
\(535\) | −1.12957 | − | 3.47645i | −0.0488355 | − | 0.150300i | ||||
\(536\) | −3.32790 | + | 10.2422i | −0.143744 | + | 0.442397i | ||||
\(537\) | −23.0360 | − | 16.7366i | −0.994075 | − | 0.722238i | ||||
\(538\) | −21.4948 | −0.926707 | ||||||||
\(539\) | −49.3346 | + | 10.6434i | −2.12499 | + | 0.458442i | ||||
\(540\) | 5.02094 | 0.216067 | ||||||||
\(541\) | −5.89865 | − | 4.28562i | −0.253603 | − | 0.184253i | 0.453719 | − | 0.891145i | \(-0.350097\pi\) |
−0.707322 | + | 0.706891i | \(0.750097\pi\) | |||||||
\(542\) | −1.09670 | + | 3.37529i | −0.0471072 | + | 0.144981i | ||||
\(543\) | −8.89530 | − | 27.3769i | −0.381734 | − | 1.17486i | ||||
\(544\) | 0.0745226 | − | 0.0541438i | 0.00319513 | − | 0.00232140i | ||||
\(545\) | −4.41284 | + | 3.20612i | −0.189025 | + | 0.137335i | ||||
\(546\) | −21.6764 | − | 66.7131i | −0.927665 | − | 2.85506i | ||||
\(547\) | 7.17891 | − | 22.0944i | 0.306948 | − | 0.944689i | −0.671995 | − | 0.740556i | \(-0.734562\pi\) |
0.978943 | − | 0.204134i | \(-0.0654377\pi\) | |||||||
\(548\) | −5.56726 | − | 4.04485i | −0.237821 | − | 0.172787i | ||||
\(549\) | −20.7030 | −0.883582 | ||||||||
\(550\) | 5.81446 | − | 1.25440i | 0.247929 | − | 0.0534880i | ||||
\(551\) | 3.20492 | 0.136534 | ||||||||
\(552\) | 8.62667 | + | 6.26764i | 0.367175 | + | 0.266769i | ||||
\(553\) | −20.4081 | + | 62.8096i | −0.867840 | + | 2.67094i | ||||
\(554\) | 5.02253 | + | 15.4577i | 0.213387 | + | 0.656737i | ||||
\(555\) | 18.5868 | − | 13.5041i | 0.788964 | − | 0.573216i | ||||
\(556\) | −3.93869 | + | 2.86162i | −0.167038 | + | 0.121360i | ||||
\(557\) | −5.07224 | − | 15.6107i | −0.214917 | − | 0.661448i | −0.999159 | − | 0.0409929i | \(-0.986948\pi\) |
0.784242 | − | 0.620455i | \(-0.213052\pi\) | |||||||
\(558\) | 3.75801 | − | 11.5660i | 0.159089 | − | 0.489626i | ||||
\(559\) | 43.8942 | + | 31.8910i | 1.85653 | + | 1.34885i | ||||
\(560\) | 8.44039 | 0.356672 | ||||||||
\(561\) | −0.0672831 | + | 0.659451i | −0.00284070 | + | 0.0278420i | ||||
\(562\) | −4.48610 | −0.189235 | ||||||||
\(563\) | 14.7951 | + | 10.7493i | 0.623540 | + | 0.453028i | 0.854156 | − | 0.520016i | \(-0.174074\pi\) |
−0.230616 | + | 0.973045i | \(0.574074\pi\) | |||||||
\(564\) | −1.86422 | + | 5.73748i | −0.0784979 | + | 0.241592i | ||||
\(565\) | −4.67218 | − | 14.3795i | −0.196560 | − | 0.604949i | ||||
\(566\) | −14.2641 | + | 10.3635i | −0.599564 | + | 0.435609i | ||||
\(567\) | 42.7352 | − | 31.0489i | 1.79471 | − | 1.30393i | ||||
\(568\) | −3.32653 | − | 10.2380i | −0.139578 | − | 0.429577i | ||||
\(569\) | −6.69050 | + | 20.5912i | −0.280480 | + | 0.863229i | 0.707237 | + | 0.706977i | \(0.249941\pi\) |
−0.987717 | + | 0.156253i | \(0.950059\pi\) | |||||||
\(570\) | −3.14326 | − | 2.28371i | −0.131657 | − | 0.0956542i | ||||
\(571\) | 19.4212 | 0.812751 | 0.406375 | − | 0.913706i | \(-0.366793\pi\) | ||||
0.406375 | + | 0.913706i | \(0.366793\pi\) | |||||||
\(572\) | 15.1702 | − | 16.9517i | 0.634298 | − | 0.708784i | ||||
\(573\) | −47.2530 | −1.97402 | ||||||||
\(574\) | −13.7446 | − | 9.98606i | −0.573690 | − | 0.416810i | ||||
\(575\) | −2.72367 | + | 8.38260i | −0.113585 | + | 0.349579i | ||||
\(576\) | 0.527710 | + | 1.62412i | 0.0219879 | + | 0.0676718i | ||||
\(577\) | −29.7216 | + | 21.5940i | −1.23733 | + | 0.898971i | −0.997417 | − | 0.0718241i | \(-0.977118\pi\) |
−0.239910 | + | 0.970795i | \(0.577118\pi\) | |||||||
\(578\) | 13.7464 | − | 9.98736i | 0.571776 | − | 0.415419i | ||||
\(579\) | −1.01798 | − | 3.13302i | −0.0423058 | − | 0.130204i | ||||
\(580\) | −1.77345 | + | 5.45811i | −0.0736384 | + | 0.226636i | ||||
\(581\) | 7.65397 | + | 5.56093i | 0.317540 | + | 0.230706i | ||||
\(582\) | 26.5325 | 1.09981 | ||||||||
\(583\) | 12.1342 | + | 20.8701i | 0.502547 | + | 0.864353i | ||||
\(584\) | 5.87074 | 0.242933 | ||||||||
\(585\) | −16.9686 | − | 12.3284i | −0.701564 | − | 0.509716i | ||||
\(586\) | −4.74046 | + | 14.5896i | −0.195827 | + | 0.602692i | ||||
\(587\) | −0.442067 | − | 1.36054i | −0.0182461 | − | 0.0561556i | 0.941519 | − | 0.336960i | \(-0.109399\pi\) |
−0.959765 | + | 0.280805i | \(0.909399\pi\) | |||||||
\(588\) | 26.7113 | − | 19.4069i | 1.10156 | − | 0.800328i | ||||
\(589\) | 5.76130 | − | 4.18583i | 0.237390 | − | 0.172474i | ||||
\(590\) | 4.51670 | + | 13.9010i | 0.185950 | + | 0.572294i | ||||
\(591\) | 8.63305 | − | 26.5698i | 0.355116 | − | 1.09294i | ||||
\(592\) | −4.78389 | − | 3.47570i | −0.196617 | − | 0.142850i | ||||
\(593\) | −43.4676 | −1.78500 | −0.892499 | − | 0.451049i | \(-0.851050\pi\) | ||||
−0.892499 | + | 0.451049i | \(0.851050\pi\) | |||||||
\(594\) | 8.50704 | + | 3.75661i | 0.349048 | + | 0.154135i | ||||
\(595\) | −0.777486 | −0.0318738 | ||||||||
\(596\) | 1.81184 | + | 1.31638i | 0.0742160 | + | 0.0539211i | ||||
\(597\) | −6.87490 | + | 21.1588i | −0.281371 | + | 0.865971i | ||||
\(598\) | 10.4164 | + | 32.0585i | 0.425960 | + | 1.31097i | ||||
\(599\) | 36.3042 | − | 26.3765i | 1.48335 | − | 1.07772i | 0.506891 | − | 0.862010i | \(-0.330795\pi\) |
0.976458 | − | 0.215706i | \(-0.0692054\pi\) | |||||||
\(600\) | −3.14814 | + | 2.28726i | −0.128522 | + | 0.0933769i | ||||
\(601\) | 1.09693 | + | 3.37599i | 0.0447445 | + | 0.137709i | 0.970933 | − | 0.239351i | \(-0.0769348\pi\) |
−0.926189 | + | 0.377061i | \(0.876935\pi\) | |||||||
\(602\) | −11.5218 | + | 35.4604i | −0.469593 | + | 1.44526i | ||||
\(603\) | 14.8785 | + | 10.8099i | 0.605899 | + | 0.440211i | ||||
\(604\) | 5.64230 | 0.229582 | ||||||||
\(605\) | −19.2916 | − | 3.97802i | −0.784316 | − | 0.161730i | ||||
\(606\) | −17.9577 | −0.729484 | ||||||||
\(607\) | −24.3441 | − | 17.6870i | −0.988095 | − | 0.717893i | −0.0285923 | − | 0.999591i | \(-0.509102\pi\) |
−0.959503 | + | 0.281698i | \(0.909102\pi\) | |||||||
\(608\) | −0.309017 | + | 0.951057i | −0.0125323 | + | 0.0385704i | ||||
\(609\) | 10.1286 | + | 31.1726i | 0.410431 | + | 1.26318i | ||||
\(610\) | 17.5629 | − | 12.7602i | 0.711101 | − | 0.516645i | ||||
\(611\) | −15.4285 | + | 11.2095i | −0.624171 | + | 0.453487i | ||||
\(612\) | −0.0486100 | − | 0.149606i | −0.00196494 | − | 0.00604747i | ||||
\(613\) | 12.1716 | − | 37.4604i | 0.491608 | − | 1.51301i | −0.330570 | − | 0.943782i | \(-0.607241\pi\) |
0.822177 | − | 0.569231i | \(-0.192759\pi\) | |||||||
\(614\) | 15.8116 | + | 11.4878i | 0.638104 | + | 0.463610i | ||||
\(615\) | −14.0041 | −0.564698 | ||||||||
\(616\) | 14.3007 | + | 6.31501i | 0.576191 | + | 0.254439i | ||||
\(617\) | −2.17245 | −0.0874597 | −0.0437299 | − | 0.999043i | \(-0.513924\pi\) | ||||
−0.0437299 | + | 0.999043i | \(0.513924\pi\) | |||||||
\(618\) | 9.55256 | + | 6.94034i | 0.384260 | + | 0.279182i | ||||
\(619\) | −10.4598 | + | 32.1920i | −0.420416 | + | 1.29391i | 0.486900 | + | 0.873458i | \(0.338128\pi\) |
−0.907316 | + | 0.420450i | \(0.861872\pi\) | |||||||
\(620\) | 3.94061 | + | 12.1279i | 0.158259 | + | 0.487070i | ||||
\(621\) | −11.1482 | + | 8.09964i | −0.447362 | + | 0.325027i | ||||
\(622\) | 6.96681 | − | 5.06168i | 0.279344 | − | 0.202955i | ||||
\(623\) | −13.2995 | − | 40.9315i | −0.532831 | − | 1.63989i | ||||
\(624\) | −4.59879 | + | 14.1536i | −0.184099 | + | 0.566598i | ||||
\(625\) | 10.3685 | + | 7.53317i | 0.414741 | + | 0.301327i | ||||
\(626\) | −2.89185 | −0.115581 | ||||||||
\(627\) | −3.61703 | − | 6.22108i | −0.144450 | − | 0.248446i | ||||
\(628\) | −9.99933 | −0.399017 | ||||||||
\(629\) | 0.440668 | + | 0.320164i | 0.0175706 | + | 0.0127658i | ||||
\(630\) | 4.45408 | − | 13.7082i | 0.177455 | − | 0.546149i | ||||
\(631\) | −2.56932 | − | 7.90755i | −0.102283 | − | 0.314795i | 0.886800 | − | 0.462153i | \(-0.152923\pi\) |
−0.989083 | + | 0.147358i | \(0.952923\pi\) | |||||||
\(632\) | 11.3353 | − | 8.23559i | 0.450894 | − | 0.327594i | ||||
\(633\) | 29.9144 | − | 21.7341i | 1.18899 | − | 0.863852i | ||||
\(634\) | −7.93391 | − | 24.4181i | −0.315096 | − | 0.969766i | ||||
\(635\) | 1.27372 | − | 3.92011i | 0.0505460 | − | 0.155565i | ||||
\(636\) | −12.7769 | − | 9.28298i | −0.506638 | − | 0.368094i | ||||
\(637\) | 104.373 | 4.13542 | ||||||||
\(638\) | −7.08848 | + | 7.92088i | −0.280635 | + | 0.313591i | ||||
\(639\) | −18.3832 | −0.727229 | ||||||||
\(640\) | −1.44869 | − | 1.05254i | −0.0572646 | − | 0.0416051i | ||||
\(641\) | 6.31700 | − | 19.4417i | 0.249506 | − | 0.767902i | −0.745356 | − | 0.666666i | \(-0.767721\pi\) |
0.994863 | − | 0.101235i | \(-0.0322794\pi\) | |||||||
\(642\) | 1.36867 | + | 4.21233i | 0.0540171 | + | 0.166248i | ||||
\(643\) | −17.2527 | + | 12.5348i | −0.680381 | + | 0.494325i | −0.873484 | − | 0.486853i | \(-0.838145\pi\) |
0.193103 | + | 0.981178i | \(0.438145\pi\) | |||||||
\(644\) | −18.7406 | + | 13.6158i | −0.738482 | + | 0.536538i | ||||
\(645\) | 9.49727 | + | 29.2296i | 0.373955 | + | 1.15091i | ||||
\(646\) | 0.0284651 | − | 0.0876066i | 0.00111994 | − | 0.00344683i | ||||
\(647\) | 5.86761 | + | 4.26307i | 0.230679 | + | 0.167598i | 0.697121 | − | 0.716954i | \(-0.254464\pi\) |
−0.466441 | + | 0.884552i | \(0.654464\pi\) | |||||||
\(648\) | −11.2069 | −0.440247 | ||||||||
\(649\) | −2.74784 | + | 26.9320i | −0.107862 | + | 1.05717i | ||||
\(650\) | −12.3012 | −0.482493 | ||||||||
\(651\) | 58.9209 | + | 42.8085i | 2.30929 | + | 1.67780i | ||||
\(652\) | −0.126595 | + | 0.389618i | −0.00495783 | + | 0.0152586i | ||||
\(653\) | 6.68692 | + | 20.5802i | 0.261680 | + | 0.805367i | 0.992440 | + | 0.122733i | \(0.0391657\pi\) |
−0.730760 | + | 0.682634i | \(0.760834\pi\) | |||||||
\(654\) | 5.34693 | − | 3.88477i | 0.209082 | − | 0.151907i | ||||
\(655\) | −14.5674 | + | 10.5838i | −0.569196 | + | 0.413545i | ||||
\(656\) | 1.11382 | + | 3.42797i | 0.0434872 | + | 0.133840i | ||||
\(657\) | 3.09805 | − | 9.53481i | 0.120866 | − | 0.371988i | ||||
\(658\) | −10.6026 | − | 7.70324i | −0.413332 | − | 0.300304i | ||||
\(659\) | −13.1333 | −0.511602 | −0.255801 | − | 0.966729i | \(-0.582339\pi\) | ||||
−0.255801 | + | 0.966729i | \(0.582339\pi\) | |||||||
\(660\) | 12.5962 | − | 2.71749i | 0.490308 | − | 0.105778i | ||||
\(661\) | 9.99561 | 0.388784 | 0.194392 | − | 0.980924i | \(-0.437727\pi\) | ||||
0.194392 | + | 0.980924i | \(0.437727\pi\) | |||||||
\(662\) | −0.541855 | − | 0.393681i | −0.0210598 | − | 0.0153008i | ||||
\(663\) | 0.423617 | − | 1.30376i | 0.0164519 | − | 0.0506338i | ||||
\(664\) | −0.620251 | − | 1.90894i | −0.0240704 | − | 0.0740810i | ||||
\(665\) | 6.82842 | − | 4.96114i | 0.264795 | − | 0.192385i | ||||
\(666\) | −8.16947 | + | 5.93547i | −0.316560 | + | 0.229995i | ||||
\(667\) | −4.86722 | − | 14.9798i | −0.188459 | − | 0.580018i | ||||
\(668\) | −4.95091 | + | 15.2373i | −0.191557 | + | 0.589551i | ||||
\(669\) | −10.4298 | − | 7.57766i | −0.403238 | − | 0.292969i | ||||
\(670\) | −19.2844 | −0.745022 | ||||||||
\(671\) | 39.3041 | − | 8.47941i | 1.51732 | − | 0.327344i | ||||
\(672\) | −10.2270 | −0.394516 | ||||||||
\(673\) | −31.4666 | − | 22.8618i | −1.21295 | − | 0.881258i | −0.217452 | − | 0.976071i | \(-0.569775\pi\) |
−0.995495 | + | 0.0948130i | \(0.969775\pi\) | |||||||
\(674\) | 8.90772 | − | 27.4152i | 0.343113 | − | 1.05599i | ||||
\(675\) | −1.55396 | − | 4.78260i | −0.0598120 | − | 0.184082i | ||||
\(676\) | −27.5429 | + | 20.0111i | −1.05934 | + | 0.769657i | ||||
\(677\) | −7.18134 | + | 5.21755i | −0.276001 | + | 0.200527i | −0.717171 | − | 0.696897i | \(-0.754564\pi\) |
0.441170 | + | 0.897423i | \(0.354564\pi\) | |||||||
\(678\) | 5.66116 | + | 17.4233i | 0.217416 | + | 0.669136i | ||||
\(679\) | −17.8115 | + | 54.8182i | −0.683543 | + | 2.10373i | ||||
\(680\) | 0.133446 | + | 0.0969543i | 0.00511743 | + | 0.00371803i | ||||
\(681\) | −34.3826 | −1.31754 | ||||||||
\(682\) | −2.39736 | + | 23.4969i | −0.0917998 | + | 0.899742i | ||||
\(683\) | 15.0170 | 0.574610 | 0.287305 | − | 0.957839i | \(-0.407241\pi\) | ||||
0.287305 | + | 0.957839i | \(0.407241\pi\) | |||||||
\(684\) | 1.38156 | + | 1.00376i | 0.0528254 | + | 0.0383799i | ||||
\(685\) | 3.80789 | − | 11.7195i | 0.145492 | − | 0.447778i | ||||
\(686\) | 11.9687 | + | 36.8360i | 0.456968 | + | 1.40640i | ||||
\(687\) | 16.0012 | − | 11.6255i | 0.610482 | − | 0.443541i | ||||
\(688\) | 6.39958 | − | 4.64956i | 0.243982 | − | 0.177263i | ||||
\(689\) | −15.4277 | − | 47.4817i | −0.587750 | − | 1.80891i | ||||
\(690\) | −5.90046 | + | 18.1598i | −0.224627 | + | 0.691330i | ||||
\(691\) | 11.5883 | + | 8.41941i | 0.440841 | + | 0.320289i | 0.785969 | − | 0.618266i | \(-0.212165\pi\) |
−0.345128 | + | 0.938556i | \(0.612165\pi\) | |||||||
\(692\) | −19.1119 | −0.726525 | ||||||||
\(693\) | 17.8030 | − | 19.8936i | 0.676279 | − | 0.755695i | ||||
\(694\) | −21.1062 | −0.801180 | ||||||||
\(695\) | −7.05293 | − | 5.12426i | −0.267533 | − | 0.194374i | ||||
\(696\) | 2.14884 | − | 6.61346i | 0.0814517 | − | 0.250682i | ||||
\(697\) | −0.102599 | − | 0.315768i | −0.00388622 | − | 0.0119606i | ||||
\(698\) | 5.54733 | − | 4.03037i | 0.209969 | − | 0.152552i | ||||
\(699\) | −11.4956 | + | 8.35206i | −0.434805 | + | 0.315904i | ||||
\(700\) | −2.61227 | − | 8.03975i | −0.0987346 | − | 0.303874i | ||||
\(701\) | 6.27325 | − | 19.3071i | 0.236937 | − | 0.729218i | −0.759921 | − | 0.650015i | \(-0.774762\pi\) |
0.996858 | − | 0.0792031i | \(-0.0252376\pi\) | |||||||
\(702\) | −15.5589 | − | 11.3042i | −0.587235 | − | 0.426651i | ||||
\(703\) | −5.91321 | −0.223021 | ||||||||
\(704\) | −1.66704 | − | 2.86722i | −0.0628291 | − | 0.108063i | ||||
\(705\) | −10.8027 | −0.406854 | ||||||||
\(706\) | −15.0430 | − | 10.9294i | −0.566150 | − | 0.411332i | ||||
\(707\) | 12.0552 | − | 37.1020i | 0.453382 | − | 1.39537i | ||||
\(708\) | −5.47277 | − | 16.8435i | −0.205679 | − | 0.633016i | ||||
\(709\) | −4.24482 | + | 3.08404i | −0.159417 | + | 0.115824i | −0.664634 | − | 0.747169i | \(-0.731413\pi\) |
0.505217 | + | 0.862993i | \(0.331413\pi\) | |||||||
\(710\) | 15.5950 | − | 11.3304i | 0.585269 | − | 0.425223i | ||||
\(711\) | −7.39386 | − | 22.7559i | −0.277291 | − | 0.853415i | ||||
\(712\) | −2.82156 | + | 8.68388i | −0.105743 | + | 0.325442i | ||||
\(713\) | −28.3140 | − | 20.5713i | −1.06037 | − | 0.770402i | ||||
\(714\) | 0.942061 | 0.0352558 | ||||||||
\(715\) | 37.2638 | + | 16.4552i | 1.39359 | + | 0.615391i | ||||
\(716\) | −13.1233 | −0.490442 | ||||||||
\(717\) | 31.1208 | + | 22.6106i | 1.16223 | + | 0.844408i | ||||
\(718\) | −9.36941 | + | 28.8361i | −0.349663 | + | 1.07615i | ||||
\(719\) | 5.23852 | + | 16.1225i | 0.195364 | + | 0.601268i | 0.999972 | + | 0.00746203i | \(0.00237526\pi\) |
−0.804608 | + | 0.593806i | \(0.797625\pi\) | |||||||
\(720\) | −2.47394 | + | 1.79742i | −0.0921982 | + | 0.0669859i | ||||
\(721\) | −20.7520 | + | 15.0772i | −0.772844 | + | 0.561504i | ||||
\(722\) | 0.309017 | + | 0.951057i | 0.0115004 | + | 0.0353947i | ||||
\(723\) | −5.66028 | + | 17.4205i | −0.210508 | + | 0.647877i | ||||
\(724\) | −10.7333 | − | 7.79816i | −0.398898 | − | 0.289816i | ||||
\(725\) | 5.74790 | 0.213472 | ||||||||
\(726\) | 23.3752 | + | 4.82007i | 0.867534 | + | 0.178890i | ||||
\(727\) | −27.7361 | −1.02867 | −0.514337 | − | 0.857588i | \(-0.671962\pi\) | ||||
−0.514337 | + | 0.857588i | \(0.671962\pi\) | |||||||
\(728\) | −26.1552 | − | 19.0029i | −0.969376 | − | 0.704293i | ||||
\(729\) | −0.274029 | + | 0.843374i | −0.0101492 | + | 0.0312361i | ||||
\(730\) | 3.24858 | + | 9.99810i | 0.120235 | + | 0.370046i | ||||
\(731\) | −0.589497 | + | 0.428294i | −0.0218033 | + | 0.0158410i | ||||
\(732\) | −21.2805 | + | 15.4612i | −0.786551 | + | 0.571463i | ||||
\(733\) | −9.33566 | − | 28.7322i | −0.344821 | − | 1.06125i | −0.961680 | − | 0.274175i | \(-0.911595\pi\) |
0.616859 | − | 0.787074i | \(-0.288405\pi\) | |||||||
\(734\) | 4.41597 | − | 13.5910i | 0.162997 | − | 0.501652i | ||||
\(735\) | 47.8315 | + | 34.7516i | 1.76429 | + | 1.28183i | ||||
\(736\) | 4.91452 | 0.181151 | ||||||||
\(737\) | −32.6739 | − | 14.4284i | −1.20356 | − | 0.531477i | ||||
\(738\) | 6.15523 | 0.226577 | ||||||||
\(739\) | 19.6921 | + | 14.3071i | 0.724384 | + | 0.526296i | 0.887782 | − | 0.460264i | \(-0.152245\pi\) |
−0.163398 | + | 0.986560i | \(0.552245\pi\) | |||||||
\(740\) | 3.27208 | − | 10.0704i | 0.120284 | − | 0.370196i | ||||
\(741\) | 4.59879 | + | 14.1536i | 0.168941 | + | 0.519946i | ||||
\(742\) | 27.7566 | − | 20.1663i | 1.01898 | − | 0.740329i | ||||
\(743\) | −31.0815 | + | 22.5821i | −1.14027 | + | 0.828455i | −0.987157 | − | 0.159753i | \(-0.948930\pi\) |
−0.153114 | + | 0.988209i | \(0.548930\pi\) | |||||||
\(744\) | −4.77474 | − | 14.6951i | −0.175050 | − | 0.538750i | ||||
\(745\) | −1.23926 | + | 3.81406i | −0.0454031 | + | 0.139736i | ||||
\(746\) | −18.6763 | − | 13.5691i | −0.683788 | − | 0.496801i | ||||
\(747\) | −3.42766 | −0.125412 | ||||||||
\(748\) | 0.153560 | + | 0.264114i | 0.00561470 | + | 0.00965697i | ||||
\(749\) | −9.62180 | −0.351573 | ||||||||
\(750\) | −21.3536 | − | 15.5143i | −0.779724 | − | 0.566503i | ||||
\(751\) | −4.96528 | + | 15.2816i | −0.181186 | + | 0.557632i | −0.999862 | − | 0.0166233i | \(-0.994708\pi\) |
0.818676 | + | 0.574255i | \(0.194708\pi\) | |||||||
\(752\) | 0.859197 | + | 2.64434i | 0.0313317 | + | 0.0964291i | ||||
\(753\) | 36.6587 | − | 26.6341i | 1.33592 | − | 0.970602i | ||||
\(754\) | 17.7841 | − | 12.9209i | 0.647658 | − | 0.470551i | ||||
\(755\) | 3.12217 | + | 9.60905i | 0.113627 | + | 0.349709i | ||||
\(756\) | 4.08407 | − | 12.5695i | 0.148536 | − | 0.457147i | ||||
\(757\) | 20.5061 | + | 14.8985i | 0.745306 | + | 0.541496i | 0.894368 | − | 0.447331i | \(-0.147626\pi\) |
−0.149062 | + | 0.988828i | \(0.547626\pi\) | |||||||
\(758\) | −18.1805 | −0.660345 | ||||||||
\(759\) | −23.5842 | + | 26.3537i | −0.856051 | + | 0.956578i | ||||
\(760\) | −1.79068 | −0.0649548 | ||||||||
\(761\) | 26.3968 | + | 19.1784i | 0.956885 | + | 0.695218i | 0.952425 | − | 0.304772i | \(-0.0985804\pi\) |
0.00445971 | + | 0.999990i | \(0.498580\pi\) | |||||||
\(762\) | −1.54334 | + | 4.74990i | −0.0559091 | + | 0.172071i | ||||
\(763\) | 4.43679 | + | 13.6550i | 0.160623 | + | 0.494346i | ||||
\(764\) | −17.6191 | + | 12.8010i | −0.637435 | + | 0.463124i | ||||
\(765\) | 0.227887 | − | 0.165569i | 0.00823926 | − | 0.00598617i | ||||
\(766\) | 8.73556 | + | 26.8853i | 0.315629 | + | 0.971405i | ||||
\(767\) | 17.3005 | − | 53.2455i | 0.624685 | − | 1.92258i | ||||
\(768\) | 1.75534 | + | 1.27533i | 0.0633405 | + | 0.0460196i | ||||
\(769\) | −2.15033 | −0.0775430 | −0.0387715 | − | 0.999248i | \(-0.512344\pi\) | ||||
−0.0387715 | + | 0.999248i | \(0.512344\pi\) | |||||||
\(770\) | −2.84141 | + | 27.8490i | −0.102397 | + | 1.00361i | ||||
\(771\) | 56.1186 | 2.02106 | ||||||||
\(772\) | −1.22832 | − | 0.892423i | −0.0442080 | − | 0.0321190i | ||||
\(773\) | −4.62976 | + | 14.2489i | −0.166521 | + | 0.512499i | −0.999145 | − | 0.0413396i | \(-0.986837\pi\) |
0.832624 | + | 0.553838i | \(0.186837\pi\) | |||||||
\(774\) | −4.17435 | − | 12.8473i | −0.150044 | − | 0.461788i | ||||
\(775\) | 10.3327 | − | 7.50711i | 0.371160 | − | 0.269663i | ||||
\(776\) | 9.89309 | − | 7.18775i | 0.355141 | − | 0.258025i | ||||
\(777\) | −18.6876 | − | 57.5147i | −0.670415 | − | 2.06333i | ||||
\(778\) | −9.06759 | + | 27.9072i | −0.325089 | + | 1.00052i | ||||
\(779\) | 2.91601 | + | 2.11860i | 0.104477 | + | 0.0759069i | ||||
\(780\) | −26.6489 | −0.954183 | ||||||||
\(781\) | 34.9001 | − | 7.52930i | 1.24882 | − | 0.269419i | ||||
\(782\) | −0.452701 | −0.0161885 | ||||||||
\(783\) | 7.27012 | + | 5.28205i | 0.259813 | + | 0.188765i | ||||
\(784\) | 4.70236 | − | 14.4724i | 0.167941 | − | 0.516870i | ||||
\(785\) | −5.53314 | − | 17.0292i | −0.197486 | − | 0.607800i | ||||
\(786\) | 17.6510 | − | 12.8242i | 0.629590 | − | 0.457424i | ||||
\(787\) | 21.6713 | − | 15.7451i | 0.772499 | − | 0.561254i | −0.130219 | − | 0.991485i | \(-0.541568\pi\) |
0.902719 | + | 0.430232i | \(0.141568\pi\) | |||||||
\(788\) | −3.97887 | − | 12.2457i | −0.141741 | − | 0.436235i | ||||
\(789\) | −20.9312 | + | 64.4197i | −0.745172 | + | 2.29340i | ||||
\(790\) | 20.2979 | + | 14.7473i | 0.722168 | + | 0.524686i | ||||
\(791\) | −39.7981 | −1.41506 | ||||||||
\(792\) | −5.53644 | + | 1.19442i | −0.196729 | + | 0.0424420i | ||||
\(793\) | −83.1527 | −2.95284 | ||||||||
\(794\) | −1.68680 | − | 1.22553i | −0.0598623 | − | 0.0434925i | ||||
\(795\) | 8.73915 | − | 26.8963i | 0.309946 | − | 0.953915i | ||||
\(796\) | 3.16856 | + | 9.75182i | 0.112307 | + | 0.345644i | ||||
\(797\) | 10.6588 | − | 7.74404i | 0.377552 | − | 0.274308i | −0.382783 | − | 0.923838i | \(-0.625034\pi\) |
0.760336 | + | 0.649530i | \(0.225034\pi\) | |||||||
\(798\) | −8.27383 | + | 6.01129i | −0.292890 | + | 0.212797i | ||||
\(799\) | −0.0791450 | − | 0.243583i | −0.00279995 | − | 0.00861735i | ||||
\(800\) | −0.554210 | + | 1.70568i | −0.0195943 | + | 0.0603050i | ||||
\(801\) | 12.6147 | + | 9.16513i | 0.445719 | + | 0.323834i | ||||
\(802\) | 11.5326 | 0.407231 | ||||||||
\(803\) | −1.97635 | + | 19.3705i | −0.0697439 | + | 0.683570i | ||||
\(804\) | 23.3665 | 0.824072 | ||||||||
\(805\) | −33.5584 | − | 24.3816i | −1.18278 | − | 0.859338i | ||||
\(806\) | 15.0939 | − | 46.4542i | 0.531659 | − | 1.63628i | ||||
\(807\) | 14.4119 | + | 44.3552i | 0.507322 | + | 1.56138i | ||||
\(808\) | −6.69584 | + | 4.86481i | −0.235559 | + | 0.171143i | ||||
\(809\) | −7.59168 | + | 5.51568i | −0.266909 | + | 0.193921i | −0.713187 | − | 0.700973i | \(-0.752749\pi\) |
0.446278 | + | 0.894894i | \(0.352749\pi\) | |||||||
\(810\) | −6.20133 | − | 19.0857i | −0.217892 | − | 0.670604i | ||||
\(811\) | −15.1076 | + | 46.4963i | −0.530499 | + | 1.63271i | 0.222681 | + | 0.974891i | \(0.428519\pi\) |
−0.753179 | + | 0.657815i | \(0.771481\pi\) | |||||||
\(812\) | 12.2214 | + | 8.87934i | 0.428886 | + | 0.311604i | ||||
\(813\) | 7.70033 | 0.270062 | ||||||||
\(814\) | 13.0785 | − | 14.6143i | 0.458402 | − | 0.512232i | ||||
\(815\) | −0.733587 | −0.0256964 | ||||||||
\(816\) | −0.161693 | − | 0.117477i | −0.00566040 | − | 0.00411252i | ||||
\(817\) | 2.44442 | − | 7.52315i | 0.0855194 | − | 0.263202i | ||||
\(818\) | −0.226303 | − | 0.696488i | −0.00791249 | − | 0.0243521i | ||||
\(819\) | −44.6654 | + | 32.4513i | −1.56073 | + | 1.13394i | ||||
\(820\) | −5.22164 | + | 3.79375i | −0.182348 | + | 0.132483i | ||||
\(821\) | 8.26517 | + | 25.4376i | 0.288456 | + | 0.887777i | 0.985341 | + | 0.170594i | \(0.0545688\pi\) |
−0.696885 | + | 0.717183i | \(0.745431\pi\) | |||||||
\(822\) | −4.61393 | + | 14.2002i | −0.160929 | + | 0.495289i | ||||
\(823\) | 28.9371 | + | 21.0241i | 1.00868 | + | 0.732852i | 0.963933 | − | 0.266146i | \(-0.0857503\pi\) |
0.0447519 | + | 0.998998i | \(0.485750\pi\) | |||||||
\(824\) | 5.44199 | 0.189581 | ||||||||
\(825\) | −6.48699 | − | 11.1573i | −0.225848 | − | 0.388446i | ||||
\(826\) | 38.4738 | 1.33867 | ||||||||
\(827\) | −0.0316430 | − | 0.0229900i | −0.00110033 | − | 0.000799439i | 0.587235 | − | 0.809417i | \(-0.300216\pi\) |
−0.588335 | + | 0.808617i | \(0.700216\pi\) | |||||||
\(828\) | 2.59344 | − | 7.98178i | 0.0901282 | − | 0.277386i | ||||
\(829\) | 5.97065 | + | 18.3758i | 0.207369 | + | 0.638217i | 0.999608 | + | 0.0280053i | \(0.00891554\pi\) |
−0.792239 | + | 0.610211i | \(0.791084\pi\) | |||||||
\(830\) | 2.90777 | − | 2.11262i | 0.100930 | − | 0.0733302i | ||||
\(831\) | 28.5300 | − | 20.7283i | 0.989696 | − | 0.719056i | ||||
\(832\) | 2.11952 | + | 6.52323i | 0.0734813 | + | 0.226152i | ||||
\(833\) | −0.433158 | + | 1.33312i | −0.0150080 | + | 0.0461900i | ||||
\(834\) | 8.54587 | + | 6.20894i | 0.295919 | + | 0.214998i | ||||
\(835\) | −28.6894 | −0.992837 | ||||||||
\(836\) | −3.03398 | − | 1.33977i | −0.104932 | − | 0.0463368i | ||||
\(837\) | 19.9677 | 0.690186 | ||||||||
\(838\) | −10.6916 | − | 7.76792i | −0.369336 | − | 0.268338i | ||||
\(839\) | −8.05711 | + | 24.7972i | −0.278162 | + | 0.856096i | 0.710203 | + | 0.703997i | \(0.248603\pi\) |
−0.988365 | + | 0.152099i | \(0.951397\pi\) | |||||||
\(840\) | −5.65913 | − | 17.4170i | −0.195258 | − | 0.600944i | ||||
\(841\) | 15.1516 | − | 11.0083i | 0.522471 | − | 0.379597i | ||||
\(842\) | −8.42666 | + | 6.12233i | −0.290402 | + | 0.210989i | ||||
\(843\) | 3.00785 | + | 9.25720i | 0.103596 | + | 0.318835i | ||||
\(844\) | 5.26624 | − | 16.2078i | 0.181271 | − | 0.557896i | ||||
\(845\) | −49.3205 | − | 35.8335i | −1.69668 | − | 1.23271i | ||||
\(846\) | 4.74814 | 0.163244 | ||||||||
\(847\) | −25.6506 | + | 45.0591i | −0.881364 | + | 1.54825i | ||||
\(848\) | −7.27887 | −0.249957 | ||||||||
\(849\) | 30.9491 | + | 22.4859i | 1.06217 | + | 0.771713i | ||||
\(850\) | 0.0510510 | − | 0.157119i | 0.00175104 | − | 0.00538913i | ||||
\(851\) | 8.98021 | + | 27.6382i | 0.307838 | + | 0.947427i | ||||
\(852\) | −18.8960 | + | 13.7288i | −0.647368 | + | 0.470340i | ||||
\(853\) | 4.32562 | − | 3.14275i | 0.148106 | − | 0.107606i | −0.511264 | − | 0.859423i | \(-0.670823\pi\) |
0.659371 | + | 0.751818i | \(0.270823\pi\) | |||||||
\(854\) | −17.6582 | − | 54.3464i | −0.604251 | − | 1.85969i | ||||
\(855\) | −0.944960 | + | 2.90829i | −0.0323170 | + | 0.0994614i | ||||
\(856\) | 1.65147 | + | 1.19986i | 0.0564459 | + | 0.0410104i | ||||
\(857\) | 34.3568 | 1.17361 | 0.586803 | − | 0.809730i | \(-0.300386\pi\) | ||||
0.586803 | + | 0.809730i | \(0.300386\pi\) | |||||||
\(858\) | −45.1516 | − | 19.9384i | −1.54145 | − | 0.680686i | ||||
\(859\) | 18.8263 | 0.642346 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(860\) | 11.4596 | + | 8.32589i | 0.390769 | + | 0.283910i | ||||
\(861\) | −11.3910 | + | 35.0579i | −0.388205 | + | 1.19477i | ||||
\(862\) | −3.49100 | − | 10.7442i | −0.118904 | − | 0.365948i | ||||
\(863\) | 22.8506 | − | 16.6019i | 0.777842 | − | 0.565135i | −0.126489 | − | 0.991968i | \(-0.540371\pi\) |
0.904331 | + | 0.426833i | \(0.140371\pi\) | |||||||
\(864\) | −2.26842 | + | 1.64811i | −0.0771733 | + | 0.0560697i | ||||
\(865\) | −10.5756 | − | 32.5483i | −0.359581 | − | 1.10668i | ||||
\(866\) | −6.86876 | + | 21.1399i | −0.233410 | + | 0.718362i | ||||
\(867\) | −29.8260 | − | 21.6698i | −1.01294 | − | 0.735946i | ||||
\(868\) | 33.5666 | 1.13932 | ||||||||
\(869\) | 23.3573 | + | 40.1733i | 0.792342 | + | 1.36278i | ||||
\(870\) | 12.4520 | 0.422164 | ||||||||
\(871\) | 59.7589 | + | 43.4173i | 2.02485 | + | 1.47114i | ||||
\(872\) | 0.941293 | − | 2.89700i | 0.0318762 | − | 0.0981049i | ||||
\(873\) | −6.45312 | − | 19.8606i | −0.218405 | − | 0.672181i | ||||
\(874\) | 3.97593 | − | 2.88868i | 0.134488 | − | 0.0977111i | ||||
\(875\) | 46.3886 | − | 33.7033i | 1.56822 | − | 1.13938i | ||||
\(876\) | −3.93623 | − | 12.1145i | −0.132993 | − | 0.409310i | ||||
\(877\) | −3.36165 | + | 10.3461i | −0.113515 | + | 0.349363i | −0.991634 | − | 0.129079i | \(-0.958798\pi\) |
0.878120 | + | 0.478441i | \(0.158798\pi\) | |||||||
\(878\) | −20.4305 | − | 14.8436i | −0.689495 | − | 0.500947i | ||||
\(879\) | 33.2845 | 1.12266 | ||||||||
\(880\) | 3.96053 | − | 4.42562i | 0.133510 | − | 0.149188i | ||||
\(881\) | 29.2426 | 0.985208 | 0.492604 | − | 0.870254i | \(-0.336045\pi\) | ||||
0.492604 | + | 0.870254i | \(0.336045\pi\) | |||||||
\(882\) | −21.0234 | − | 15.2744i | −0.707896 | − | 0.514317i | ||||
\(883\) | −0.392996 | + | 1.20952i | −0.0132254 | + | 0.0407035i | −0.957451 | − | 0.288595i | \(-0.906812\pi\) |
0.944226 | + | 0.329298i | \(0.106812\pi\) | |||||||
\(884\) | −0.195240 | − | 0.600887i | −0.00656663 | − | 0.0202100i | ||||
\(885\) | 25.6567 | − | 18.6407i | 0.862441 | − | 0.626600i | ||||
\(886\) | 3.37390 | − | 2.45128i | 0.113348 | − | 0.0823524i | ||||
\(887\) | 4.75848 | + | 14.6451i | 0.159774 | + | 0.491735i | 0.998613 | − | 0.0526449i | \(-0.0167651\pi\) |
−0.838839 | + | 0.544380i | \(0.816765\pi\) | |||||||
\(888\) | −3.96470 | + | 12.2021i | −0.133047 | + | 0.409475i | ||||
\(889\) | −8.77759 | − | 6.37729i | −0.294391 | − | 0.213887i | ||||
\(890\) | −16.3503 | −0.548063 | ||||||||
\(891\) | 3.77272 | − | 36.9770i | 0.126391 | − | 1.23878i | ||||
\(892\) | −5.94172 | −0.198943 | ||||||||
\(893\) | 2.24941 | + | 1.63429i | 0.0752736 | + | 0.0546894i | ||||
\(894\) | 1.50158 | − | 4.62140i | 0.0502205 | − | 0.154563i | ||||
\(895\) | −7.26181 | − | 22.3496i | −0.242736 | − | 0.747063i | ||||
\(896\) | −3.81331 | + | 2.77053i | −0.127394 | + | 0.0925569i | ||||
\(897\) | 59.1697 | − | 42.9893i | 1.97562 | − | 1.43537i | ||||
\(898\) | −2.64964 | − | 8.15476i | −0.0884198 | − | 0.272128i | ||||
\(899\) | −7.05282 | + | 21.7063i | −0.235225 | + | 0.723947i | ||||
\(900\) | 2.47778 | + | 1.80021i | 0.0825926 | + | 0.0600070i | ||||
\(901\) | 0.670493 | 0.0223374 | ||||||||
\(902\) | −11.6855 | + | 2.52102i | −0.389086 | + | 0.0839409i | ||||
\(903\) | 80.8989 | 2.69215 | ||||||||
\(904\) | 6.83087 | + | 4.96292i | 0.227191 | + | 0.165064i | ||||
\(905\) | 7.34132 | − | 22.5943i | 0.244034 | − | 0.751059i | ||||
\(906\) | −3.78306 | − | 11.6431i | −0.125684 | − | 0.386814i | ||||
\(907\) | 12.6745 | − | 9.20857i | 0.420850 | − | 0.305766i | −0.357130 | − | 0.934055i | \(-0.616245\pi\) |
0.777980 | + | 0.628289i | \(0.216245\pi\) | |||||||
\(908\) | −12.8201 | + | 9.31434i | −0.425450 | + | 0.309107i | ||||
\(909\) | 4.36760 | + | 13.4421i | 0.144864 | + | 0.445846i | ||||
\(910\) | 17.8896 | − | 55.0586i | 0.593035 | − | 1.82517i | ||||
\(911\) | −23.4606 | − | 17.0451i | −0.777285 | − | 0.564730i | 0.126878 | − | 0.991918i | \(-0.459504\pi\) |
−0.904163 | + | 0.427188i | \(0.859504\pi\) | |||||||
\(912\) | 2.16972 | 0.0718468 | ||||||||
\(913\) | 6.50733 | − | 1.40388i | 0.215361 | − | 0.0464617i | ||||
\(914\) | −12.0184 | −0.397533 | ||||||||
\(915\) | −38.1066 | − | 27.6861i | −1.25977 | − | 0.915274i | ||||
\(916\) | 2.81690 | − | 8.66953i | 0.0930730 | − | 0.286449i | ||||
\(917\) | 14.6465 | + | 45.0772i | 0.483669 | + | 1.48858i | ||||
\(918\) | 0.208956 | − | 0.151815i | 0.00689657 | − | 0.00501065i | ||||
\(919\) | −2.11791 | + | 1.53875i | −0.0698634 | + | 0.0507587i | −0.622169 | − | 0.782883i | \(-0.713748\pi\) |
0.552305 | + | 0.833642i | \(0.313748\pi\) | |||||||
\(920\) | 2.71945 | + | 8.36961i | 0.0896577 | + | 0.275938i | ||||
\(921\) | 13.1040 | − | 40.3301i | 0.431793 | − | 1.32892i | ||||
\(922\) | −2.43323 | − | 1.76785i | −0.0801342 | − | 0.0582209i | ||||
\(923\) | −73.8355 | −2.43032 | ||||||||
\(924\) | 3.44287 | − | 33.7440i | 0.113262 | − | 1.11010i | ||||
\(925\) | −10.6051 | −0.348694 | ||||||||
\(926\) | −16.4030 | − | 11.9175i | −0.539036 | − | 0.391633i | ||||
\(927\) | 2.87179 | − | 8.83846i | 0.0943220 | − | 0.290293i | ||||
\(928\) | −0.990376 | − | 3.04806i | −0.0325107 | − | 0.100058i | ||||
\(929\) | 38.3315 | − | 27.8494i | 1.25761 | − | 0.913710i | 0.258976 | − | 0.965884i | \(-0.416615\pi\) |
0.998638 | + | 0.0521736i | \(0.0166149\pi\) | |||||||
\(930\) | 22.3843 | − | 16.2631i | 0.734009 | − | 0.533289i | ||||
\(931\) | −4.70236 | − | 14.4724i | −0.154114 | − | 0.474313i | ||||
\(932\) | −2.02373 | + | 6.22840i | −0.0662895 | + | 0.204018i | ||||
\(933\) | −15.1161 | − | 10.9825i | −0.494878 | − | 0.359550i | ||||
\(934\) | −21.4276 | −0.701132 | ||||||||
\(935\) | −0.364824 | + | 0.407666i | −0.0119310 | + | 0.0133321i | ||||
\(936\) | 11.7130 | 0.382852 | ||||||||
\(937\) | −3.86671 | − | 2.80933i | −0.126320 | − | 0.0917767i | 0.522831 | − | 0.852436i | \(-0.324876\pi\) |
−0.649151 | + | 0.760659i | \(0.724876\pi\) | |||||||
\(938\) | −15.6861 | + | 48.2769i | −0.512169 | + | 1.57630i | ||||
\(939\) | 1.93893 | + | 5.96741i | 0.0632746 | + | 0.194739i | ||||
\(940\) | −4.02797 | + | 2.92649i | −0.131378 | + | 0.0954517i | ||||
\(941\) | −21.8342 | + | 15.8634i | −0.711773 | + | 0.517133i | −0.883745 | − | 0.467968i | \(-0.844986\pi\) |
0.171972 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(942\) | 6.70437 | + | 20.6339i | 0.218440 | + | 0.672289i | ||||
\(943\) | 5.47387 | − | 16.8468i | 0.178254 | − | 0.548608i | ||||
\(944\) | −6.60356 | − | 4.79777i | −0.214928 | − | 0.156154i | ||||
\(945\) | 23.6662 | 0.769862 | ||||||||
\(946\) | 13.1868 | + | 22.6806i | 0.428741 | + | 0.737411i | ||||
\(947\) | −7.94684 | −0.258238 | −0.129119 | − | 0.991629i | \(-0.541215\pi\) | ||||
−0.129119 | + | 0.991629i | \(0.541215\pi\) | |||||||
\(948\) | −24.5945 | − | 17.8690i | −0.798792 | − | 0.580357i | ||||
\(949\) | 12.4432 | − | 38.2962i | 0.403923 | − | 1.24315i | ||||
\(950\) | 0.554210 | + | 1.70568i | 0.0179809 | + | 0.0553396i | ||||
\(951\) | −45.0679 | + | 32.7437i | −1.46143 | + | 1.06179i | ||||
\(952\) | 0.351263 | − | 0.255207i | 0.0113845 | − | 0.00827132i | ||||
\(953\) | −8.22934 | − | 25.3273i | −0.266574 | − | 0.820432i | −0.991327 | − | 0.131422i | \(-0.958046\pi\) |
0.724752 | − | 0.689010i | \(-0.241954\pi\) | |||||||
\(954\) | −3.84113 | + | 11.8218i | −0.124361 | + | 0.382744i | ||||
\(955\) | −31.5501 | − | 22.9225i | −1.02094 | − | 0.741755i | ||||
\(956\) | 17.7292 | 0.573403 | ||||||||
\(957\) | 21.0977 | + | 9.31648i | 0.681991 | + | 0.301159i | ||||
\(958\) | 27.0080 | 0.872589 | ||||||||
\(959\) | −26.2413 | − | 19.0654i | −0.847376 | − | 0.615655i | ||||
\(960\) | −1.20062 | + | 3.69513i | −0.0387498 | + | 0.119260i | ||||
\(961\) | 6.09186 | + | 18.7488i | 0.196512 | + | 0.604801i | ||||
\(962\) | −32.8123 | + | 23.8396i | −1.05791 | + | 0.768618i | ||||
\(963\) | 2.82022 | − | 2.04901i | 0.0908802 | − | 0.0660283i | ||||
\(964\) | 2.60875 | + | 8.02892i | 0.0840223 | + | 0.258594i | ||||
\(965\) | 0.840142 | − | 2.58569i | 0.0270451 | − | 0.0832364i | ||||
\(966\) | 40.6619 | + | 29.5426i | 1.30827 | + | 0.950517i | ||||
\(967\) | −37.0849 | −1.19257 | −0.596284 | − | 0.802773i | \(-0.703357\pi\) | ||||
−0.596284 | + | 0.802773i | \(0.703357\pi\) | |||||||
\(968\) | 10.0216 | − | 4.53517i | 0.322106 | − | 0.145766i | ||||
\(969\) | −0.199864 | −0.00642056 | ||||||||
\(970\) | 17.7154 | + | 12.8710i | 0.568806 | + | 0.413262i | ||||
\(971\) | 1.65904 | − | 5.10601i | 0.0532413 | − | 0.163860i | −0.920900 | − | 0.389798i | \(-0.872545\pi\) |
0.974142 | + | 0.225938i | \(0.0725448\pi\) | |||||||
\(972\) | 4.91461 | + | 15.1256i | 0.157636 | + | 0.485155i | ||||
\(973\) | −18.5650 | + | 13.4883i | −0.595168 | + | 0.432415i | ||||
\(974\) | 1.94139 | − | 1.41050i | 0.0622063 | − | 0.0451955i | ||||
\(975\) | 8.24774 | + | 25.3839i | 0.264139 | + | 0.812936i | ||||
\(976\) | −3.74630 | + | 11.5299i | −0.119916 | + | 0.369064i | ||||
\(977\) | 6.98946 | + | 5.07814i | 0.223613 | + | 0.162464i | 0.693951 | − | 0.720022i | \(-0.255868\pi\) |
−0.470339 | + | 0.882486i | \(0.655868\pi\) | |||||||
\(978\) | 0.888869 | 0.0284229 | ||||||||
\(979\) | −27.7025 | − | 12.2331i | −0.885377 | − | 0.390972i | ||||
\(980\) | 27.2491 | 0.870440 | ||||||||
\(981\) | −4.20836 | − | 3.05755i | −0.134363 | − | 0.0976202i | ||||
\(982\) | −4.09373 | + | 12.5992i | −0.130636 | + | 0.402056i | ||||
\(983\) | −10.1154 | − | 31.1319i | −0.322630 | − | 0.992952i | −0.972499 | − | 0.232906i | \(-0.925176\pi\) |
0.649870 | − | 0.760046i | \(-0.274824\pi\) | |||||||
\(984\) | 6.32694 | − | 4.59679i | 0.201695 | − | 0.146540i | ||||
\(985\) | 18.6532 | − | 13.5523i | 0.594341 | − | 0.431814i | ||||
\(986\) | 0.0912285 | + | 0.280772i | 0.00290531 | + | 0.00894161i | ||||
\(987\) | −8.78702 | + | 27.0437i | −0.279694 | + | 0.860810i | ||||
\(988\) | 5.54899 | + | 4.03158i | 0.176537 | + | 0.128262i | ||||
\(989\) | −38.8753 | −1.23616 | ||||||||
\(990\) | −5.09775 | − | 8.76784i | −0.162017 | − | 0.278660i | ||||
\(991\) | 33.6052 | 1.06750 | 0.533752 | − | 0.845641i | \(-0.320782\pi\) | ||||
0.533752 | + | 0.845641i | \(0.320782\pi\) | |||||||
\(992\) | −5.76130 | − | 4.18583i | −0.182921 | − | 0.132900i | ||||
\(993\) | −0.449069 | + | 1.38209i | −0.0142508 | + | 0.0438593i | ||||
\(994\) | −15.6796 | − | 48.2569i | −0.497327 | − | 1.53062i | ||||
\(995\) | −14.8544 | + | 10.7924i | −0.470917 | + | 0.342141i | ||||
\(996\) | −3.52328 | + | 2.55981i | −0.111639 | + | 0.0811108i | ||||
\(997\) | −2.91409 | − | 8.96865i | −0.0922902 | − | 0.284040i | 0.894248 | − | 0.447572i | \(-0.147711\pi\) |
−0.986538 | + | 0.163532i | \(0.947711\pi\) | |||||||
\(998\) | 9.12099 | − | 28.0715i | 0.288720 | − | 0.888588i | ||||
\(999\) | −13.4137 | − | 9.74559i | −0.424389 | − | 0.308337i |
(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 | 418.2.f.f.191.2 | ✓ | 16 | |
11.3 | even | 5 | inner | 418.2.f.f.267.2 | yes | 16 | |
11.5 | even | 5 | 4598.2.a.ca.1.3 | 8 | |||
11.6 | odd | 10 | 4598.2.a.bx.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.f.191.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
418.2.f.f.267.2 | yes | 16 | 11.3 | even | 5 | inner | |
4598.2.a.bx.1.3 | 8 | 11.6 | odd | 10 | |||
4598.2.a.ca.1.3 | 8 | 11.5 | even | 5 |