Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(32,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.l (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: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.5 | ||
Character | \(\chi\) | \(=\) | 231.65 |
Dual form | 231.2.l.b.32.5 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.939478 | + | 1.62722i | −0.664311 | + | 1.15062i | 0.315161 | + | 0.949038i | \(0.397942\pi\) |
−0.979472 | + | 0.201582i | \(0.935392\pi\) | |||||||
\(3\) | −1.69195 | + | 0.370556i | −0.976847 | + | 0.213940i | ||||
\(4\) | −0.765237 | − | 1.32543i | −0.382618 | − | 0.662715i | ||||
\(5\) | 2.63713 | + | 1.52255i | 1.17936 | + | 0.680904i | 0.955867 | − | 0.293801i | \(-0.0949204\pi\) |
0.223494 | + | 0.974705i | \(0.428254\pi\) | |||||||
\(6\) | 0.986571 | − | 3.10131i | 0.402766 | − | 1.26610i | ||||
\(7\) | −0.738610 | + | 2.54056i | −0.279168 | + | 0.960242i | ||||
\(8\) | −0.882219 | −0.311911 | ||||||||
\(9\) | 2.72538 | − | 1.25392i | 0.908459 | − | 0.417974i | ||||
\(10\) | −4.95505 | + | 2.86080i | −1.56692 | + | 0.904664i | ||||
\(11\) | −0.988816 | + | 3.16579i | −0.298139 | + | 0.954522i | ||||
\(12\) | 1.78589 | + | 1.95899i | 0.515541 | + | 0.565513i | ||||
\(13\) | 1.24436i | 0.345123i | 0.984999 | + | 0.172561i | \(0.0552043\pi\) | ||||
−0.984999 | + | 0.172561i | \(0.944796\pi\) | |||||||
\(14\) | −3.44015 | − | 3.58868i | −0.919420 | − | 0.959116i | ||||
\(15\) | −5.02608 | − | 1.59887i | −1.29773 | − | 0.412826i | ||||
\(16\) | 2.35930 | − | 4.08643i | 0.589825 | − | 1.02161i | ||||
\(17\) | −2.83407 | − | 4.90876i | −0.687363 | − | 1.19055i | −0.972688 | − | 0.232117i | \(-0.925435\pi\) |
0.285325 | − | 0.958431i | \(-0.407899\pi\) | |||||||
\(18\) | −0.520020 | + | 5.61283i | −0.122570 | + | 1.32296i | ||||
\(19\) | 0.532275 | + | 0.307309i | 0.122112 | + | 0.0705015i | 0.559812 | − | 0.828620i | \(-0.310873\pi\) |
−0.437700 | + | 0.899121i | \(0.644207\pi\) | |||||||
\(20\) | − | 4.66044i | − | 1.04211i | ||||||
\(21\) | 0.308270 | − | 4.57220i | 0.0672700 | − | 0.997735i | ||||
\(22\) | −4.22248 | − | 4.58322i | −0.900236 | − | 0.977145i | ||||
\(23\) | −4.41744 | − | 2.55041i | −0.921101 | − | 0.531798i | −0.0371147 | − | 0.999311i | \(-0.511817\pi\) |
−0.883986 | + | 0.467513i | \(0.845150\pi\) | |||||||
\(24\) | 1.49267 | − | 0.326911i | 0.304690 | − | 0.0667305i | ||||
\(25\) | 2.13630 | + | 3.70019i | 0.427261 | + | 0.740037i | ||||
\(26\) | −2.02485 | − | 1.16905i | −0.397105 | − | 0.229269i | ||||
\(27\) | −4.14655 | + | 3.13147i | −0.798004 | + | 0.602653i | ||||
\(28\) | 3.93255 | − | 0.965157i | 0.743181 | − | 0.182397i | ||||
\(29\) | −1.47768 | −0.274398 | −0.137199 | − | 0.990544i | \(-0.543810\pi\) | ||||
−0.137199 | + | 0.990544i | \(0.543810\pi\) | |||||||
\(30\) | 7.32360 | − | 6.67645i | 1.33710 | − | 1.21895i | ||||
\(31\) | 3.18007 | + | 5.50805i | 0.571158 | + | 0.989275i | 0.996447 | + | 0.0842172i | \(0.0268390\pi\) |
−0.425289 | + | 0.905057i | \(0.639828\pi\) | |||||||
\(32\) | 3.55080 | + | 6.15016i | 0.627698 | + | 1.08721i | ||||
\(33\) | 0.499923 | − | 5.72277i | 0.0870255 | − | 0.996206i | ||||
\(34\) | 10.6502 | 1.82649 | ||||||||
\(35\) | −5.81594 | + | 5.57522i | −0.983073 | + | 0.942385i | ||||
\(36\) | −3.74754 | − | 2.65275i | −0.624591 | − | 0.442124i | ||||
\(37\) | −3.15832 | + | 5.47036i | −0.519224 | + | 0.899322i | 0.480526 | + | 0.876980i | \(0.340446\pi\) |
−0.999750 | + | 0.0223421i | \(0.992888\pi\) | |||||||
\(38\) | −1.00012 | + | 0.577420i | −0.162241 | + | 0.0936699i | ||||
\(39\) | −0.461104 | − | 2.10539i | −0.0738357 | − | 0.337132i | ||||
\(40\) | −2.32653 | − | 1.34322i | −0.367856 | − | 0.212382i | ||||
\(41\) | 10.3640 | 1.61859 | 0.809296 | − | 0.587401i | \(-0.199849\pi\) | ||||
0.809296 | + | 0.587401i | \(0.199849\pi\) | |||||||
\(42\) | 7.15037 | + | 4.79710i | 1.10333 | + | 0.740209i | ||||
\(43\) | − | 2.31140i | − | 0.352486i | −0.984347 | − | 0.176243i | \(-0.943606\pi\) | ||
0.984347 | − | 0.176243i | \(-0.0563944\pi\) | |||||||
\(44\) | 4.95271 | − | 1.11198i | 0.746649 | − | 0.167637i | ||||
\(45\) | 9.09633 | + | 0.842761i | 1.35600 | + | 0.125631i | ||||
\(46\) | 8.30018 | − | 4.79211i | 1.22379 | − | 0.706558i | ||||
\(47\) | 9.35776 | + | 5.40270i | 1.36497 | + | 0.788065i | 0.990280 | − | 0.139086i | \(-0.0444163\pi\) |
0.374689 | + | 0.927151i | \(0.377750\pi\) | |||||||
\(48\) | −2.47756 | + | 7.78827i | −0.357605 | + | 1.12414i | ||||
\(49\) | −5.90891 | − | 3.75297i | −0.844130 | − | 0.536138i | ||||
\(50\) | −8.02804 | −1.13534 | ||||||||
\(51\) | 6.61407 | + | 7.25518i | 0.926155 | + | 1.01593i | ||||
\(52\) | 1.64931 | − | 0.952228i | 0.228718 | − | 0.132050i | ||||
\(53\) | −2.58050 | + | 1.48985i | −0.354459 | + | 0.204647i | −0.666647 | − | 0.745373i | \(-0.732271\pi\) |
0.312189 | + | 0.950020i | \(0.398938\pi\) | |||||||
\(54\) | −1.20002 | − | 9.68931i | −0.163302 | − | 1.31855i | ||||
\(55\) | −7.42771 | + | 6.84309i | −1.00155 | + | 0.922722i | ||||
\(56\) | 0.651616 | − | 2.24133i | 0.0870758 | − | 0.299511i | ||||
\(57\) | −1.01446 | − | 0.322713i | −0.134368 | − | 0.0427444i | ||||
\(58\) | 1.38825 | − | 2.40451i | 0.182286 | − | 0.315728i | ||||
\(59\) | −5.38180 | + | 3.10718i | −0.700650 | + | 0.404521i | −0.807590 | − | 0.589745i | \(-0.799228\pi\) |
0.106939 | + | 0.994266i | \(0.465895\pi\) | |||||||
\(60\) | 1.72695 | + | 7.88522i | 0.222949 | + | 1.01798i | ||||
\(61\) | 8.24852 | + | 4.76229i | 1.05612 | + | 0.609749i | 0.924355 | − | 0.381533i | \(-0.124604\pi\) |
0.131760 | + | 0.991282i | \(0.457937\pi\) | |||||||
\(62\) | −11.9504 | −1.51771 | ||||||||
\(63\) | 1.17268 | + | 7.85015i | 0.147743 | + | 0.989026i | ||||
\(64\) | −3.90639 | −0.488299 | ||||||||
\(65\) | −1.89459 | + | 3.28153i | −0.234995 | + | 0.407024i | ||||
\(66\) | 8.84255 | + | 6.18990i | 1.08844 | + | 0.761924i | ||||
\(67\) | 2.31763 | + | 4.01426i | 0.283144 | + | 0.490420i | 0.972157 | − | 0.234329i | \(-0.0752893\pi\) |
−0.689013 | + | 0.724749i | \(0.741956\pi\) | |||||||
\(68\) | −4.33747 | + | 7.51272i | −0.525996 | + | 0.911051i | ||||
\(69\) | 8.41916 | + | 2.67826i | 1.01355 | + | 0.322424i | ||||
\(70\) | −3.60819 | − | 14.7016i | −0.431261 | − | 1.75718i | ||||
\(71\) | − | 7.90967i | − | 0.938705i | −0.883011 | − | 0.469353i | \(-0.844487\pi\) | ||
0.883011 | − | 0.469353i | \(-0.155513\pi\) | |||||||
\(72\) | −2.40438 | + | 1.10623i | −0.283359 | + | 0.130371i | ||||
\(73\) | −1.01586 | + | 0.586510i | −0.118898 | + | 0.0686458i | −0.558270 | − | 0.829660i | \(-0.688534\pi\) |
0.439372 | + | 0.898305i | \(0.355201\pi\) | |||||||
\(74\) | −5.93434 | − | 10.2786i | −0.689853 | − | 1.19486i | ||||
\(75\) | −4.98564 | − | 5.46890i | −0.575692 | − | 0.631495i | ||||
\(76\) | − | 0.940657i | − | 0.107901i | ||||||
\(77\) | −7.31254 | − | 4.85043i | −0.833342 | − | 0.552758i | ||||
\(78\) | 3.85913 | + | 1.22765i | 0.436961 | + | 0.139004i | ||||
\(79\) | −3.34216 | − | 1.92960i | −0.376022 | − | 0.217097i | 0.300064 | − | 0.953919i | \(-0.402992\pi\) |
−0.676086 | + | 0.736822i | \(0.736325\pi\) | |||||||
\(80\) | 12.4436 | − | 7.18429i | 1.39123 | − | 0.803228i | ||||
\(81\) | 5.85536 | − | 6.83482i | 0.650595 | − | 0.759424i | ||||
\(82\) | −9.73679 | + | 16.8646i | −1.07525 | + | 1.86238i | ||||
\(83\) | 15.6693 | 1.71993 | 0.859966 | − | 0.510352i | \(-0.170485\pi\) | ||||
0.859966 | + | 0.510352i | \(0.170485\pi\) | |||||||
\(84\) | −6.29602 | + | 3.09022i | −0.686952 | + | 0.337171i | ||||
\(85\) | − | 17.2600i | − | 1.87211i | ||||||
\(86\) | 3.76117 | + | 2.17151i | 0.405577 | + | 0.234160i | ||||
\(87\) | 2.50015 | − | 0.547562i | 0.268045 | − | 0.0587048i | ||||
\(88\) | 0.872352 | − | 2.79292i | 0.0929931 | − | 0.297726i | ||||
\(89\) | −1.19552 | − | 0.690235i | −0.126725 | − | 0.0731648i | 0.435297 | − | 0.900287i | \(-0.356643\pi\) |
−0.562022 | + | 0.827122i | \(0.689977\pi\) | |||||||
\(90\) | −9.91716 | + | 14.0100i | −1.04536 | + | 1.47678i | ||||
\(91\) | −3.16137 | − | 0.919095i | −0.331401 | − | 0.0963473i | ||||
\(92\) | 7.80668i | 0.813903i | ||||||||
\(93\) | −7.42156 | − | 8.14094i | −0.769580 | − | 0.844176i | ||||
\(94\) | −17.5828 | + | 10.1514i | −1.81353 | + | 1.04704i | ||||
\(95\) | 0.935785 | + | 1.62083i | 0.0960095 | + | 0.166293i | ||||
\(96\) | −8.28675 | − | 9.08999i | −0.845762 | − | 0.927743i | ||||
\(97\) | 9.19643 | 0.933756 | 0.466878 | − | 0.884322i | \(-0.345379\pi\) | ||||
0.466878 | + | 0.884322i | \(0.345379\pi\) | |||||||
\(98\) | 11.6582 | − | 6.08929i | 1.17766 | − | 0.615111i | ||||
\(99\) | 1.27476 | + | 9.86788i | 0.128118 | + | 0.991759i | ||||
\(100\) | 3.26956 | − | 5.66304i | 0.326956 | − | 0.566304i | ||||
\(101\) | 5.50095 | + | 9.52793i | 0.547365 | + | 0.948064i | 0.998454 | + | 0.0555851i | \(0.0177024\pi\) |
−0.451089 | + | 0.892479i | \(0.648964\pi\) | |||||||
\(102\) | −18.0196 | + | 3.94649i | −1.78420 | + | 0.390761i | ||||
\(103\) | −1.24322 | + | 2.15333i | −0.122499 | + | 0.212174i | −0.920752 | − | 0.390148i | \(-0.872424\pi\) |
0.798254 | + | 0.602321i | \(0.205757\pi\) | |||||||
\(104\) | − | 1.09780i | − | 0.107648i | ||||||
\(105\) | 7.77433 | − | 11.5881i | 0.758697 | − | 1.13088i | ||||
\(106\) | − | 5.59873i | − | 0.543797i | ||||||
\(107\) | 6.89744 | − | 11.9467i | 0.666800 | − | 1.15493i | −0.311994 | − | 0.950084i | \(-0.600997\pi\) |
0.978794 | − | 0.204848i | \(-0.0656699\pi\) | |||||||
\(108\) | 7.32364 | + | 3.09964i | 0.704718 | + | 0.298263i | ||||
\(109\) | −2.99294 | + | 1.72797i | −0.286671 | + | 0.165510i | −0.636440 | − | 0.771326i | \(-0.719594\pi\) |
0.349768 | + | 0.936836i | \(0.386260\pi\) | |||||||
\(110\) | −4.15706 | − | 18.5155i | −0.396361 | − | 1.76538i | ||||
\(111\) | 3.31663 | − | 10.4259i | 0.314801 | − | 0.989583i | ||||
\(112\) | 8.63922 | + | 9.01222i | 0.816329 | + | 0.851575i | ||||
\(113\) | 7.98997i | 0.751633i | 0.926694 | + | 0.375817i | \(0.122638\pi\) | ||||
−0.926694 | + | 0.375817i | \(0.877362\pi\) | |||||||
\(114\) | 1.47819 | − | 1.34757i | 0.138445 | − | 0.126211i | ||||
\(115\) | −7.76625 | − | 13.4515i | −0.724207 | − | 1.25436i | ||||
\(116\) | 1.13077 | + | 1.95856i | 0.104990 | + | 0.181847i | ||||
\(117\) | 1.56033 | + | 3.39134i | 0.144252 | + | 0.313530i | ||||
\(118\) | − | 11.6765i | − | 1.07491i | ||||||
\(119\) | 14.5643 | − | 3.57448i | 1.33510 | − | 0.327672i | ||||
\(120\) | 4.43410 | + | 1.41055i | 0.404776 | + | 0.128765i | ||||
\(121\) | −9.04449 | − | 6.26077i | −0.822226 | − | 0.569161i | ||||
\(122\) | −15.4986 | + | 8.94813i | −1.40318 | + | 0.810125i | ||||
\(123\) | −17.5354 | + | 3.84046i | −1.58112 | + | 0.346282i | ||||
\(124\) | 4.86702 | − | 8.42992i | 0.437071 | − | 0.757029i | ||||
\(125\) | − | 2.21498i | − | 0.198114i | ||||||
\(126\) | −13.8756 | − | 5.46683i | −1.23614 | − | 0.487024i | ||||
\(127\) | 11.9269i | 1.05834i | 0.848514 | + | 0.529172i | \(0.177498\pi\) | ||||
−0.848514 | + | 0.529172i | \(0.822502\pi\) | |||||||
\(128\) | −3.43163 | + | 5.94376i | −0.303316 | + | 0.525359i | ||||
\(129\) | 0.856503 | + | 3.91077i | 0.0754109 | + | 0.344324i | ||||
\(130\) | −3.55986 | − | 6.16585i | −0.312220 | − | 0.540781i | ||||
\(131\) | −1.54608 | + | 2.67789i | −0.135082 | + | 0.233968i | −0.925629 | − | 0.378433i | \(-0.876463\pi\) |
0.790547 | + | 0.612401i | \(0.209796\pi\) | |||||||
\(132\) | −7.96768 | + | 3.71666i | −0.693498 | + | 0.323494i | ||||
\(133\) | −1.17388 | + | 1.12530i | −0.101788 | + | 0.0975755i | ||||
\(134\) | −8.70946 | −0.752383 | ||||||||
\(135\) | −15.7028 | + | 1.94479i | −1.35148 | + | 0.167381i | ||||
\(136\) | 2.50027 | + | 4.33060i | 0.214396 | + | 0.371346i | ||||
\(137\) | 2.68265 | − | 1.54883i | 0.229194 | − | 0.132325i | −0.381006 | − | 0.924573i | \(-0.624422\pi\) |
0.610200 | + | 0.792247i | \(0.291089\pi\) | |||||||
\(138\) | −12.2677 | + | 11.1837i | −1.04430 | + | 0.952018i | ||||
\(139\) | − | 12.1764i | − | 1.03279i | −0.856351 | − | 0.516394i | \(-0.827274\pi\) | ||
0.856351 | − | 0.516394i | \(-0.172726\pi\) | |||||||
\(140\) | 11.8401 | + | 3.44225i | 1.00067 | + | 0.290923i | ||||
\(141\) | −17.8348 | − | 5.67352i | −1.50196 | − | 0.477797i | ||||
\(142\) | 12.8708 | + | 7.43096i | 1.08009 | + | 0.623592i | ||||
\(143\) | −3.93938 | − | 1.23044i | −0.329427 | − | 0.102895i | ||||
\(144\) | 1.30592 | − | 14.0954i | 0.108827 | − | 1.17462i | ||||
\(145\) | −3.89683 | − | 2.24983i | −0.323614 | − | 0.186839i | ||||
\(146\) | − | 2.20405i | − | 0.182409i | ||||||
\(147\) | 11.3883 | + | 4.16025i | 0.939287 | + | 0.343131i | ||||
\(148\) | 9.66744 | 0.794659 | ||||||||
\(149\) | −10.7473 | + | 18.6148i | −0.880452 | + | 1.52499i | −0.0296119 | + | 0.999561i | \(0.509427\pi\) |
−0.850840 | + | 0.525425i | \(0.823906\pi\) | |||||||
\(150\) | 13.5830 | − | 2.97484i | 1.10905 | − | 0.242894i | ||||
\(151\) | −19.8835 | + | 11.4797i | −1.61810 | + | 0.934208i | −0.630683 | + | 0.776040i | \(0.717225\pi\) |
−0.987412 | + | 0.158168i | \(0.949441\pi\) | |||||||
\(152\) | −0.469583 | − | 0.271114i | −0.0380882 | − | 0.0219902i | ||||
\(153\) | −13.8791 | − | 9.82450i | −1.12206 | − | 0.794264i | ||||
\(154\) | 14.7627 | − | 7.34226i | 1.18961 | − | 0.591657i | ||||
\(155\) | 19.3673i | 1.55562i | ||||||||
\(156\) | −2.43769 | + | 2.22228i | −0.195171 | + | 0.177925i | ||||
\(157\) | 5.67235 | + | 9.82480i | 0.452703 | + | 0.784105i | 0.998553 | − | 0.0537783i | \(-0.0171264\pi\) |
−0.545850 | + | 0.837883i | \(0.683793\pi\) | |||||||
\(158\) | 6.27977 | − | 3.62563i | 0.499592 | − | 0.288439i | ||||
\(159\) | 3.81400 | − | 3.47697i | 0.302470 | − | 0.275742i | ||||
\(160\) | 21.6250i | 1.70961i | ||||||||
\(161\) | 9.74225 | − | 9.33903i | 0.767797 | − | 0.736019i | ||||
\(162\) | 5.62080 | + | 15.9491i | 0.441612 | + | 1.25308i | ||||
\(163\) | 6.79598 | − | 11.7710i | 0.532302 | − | 0.921975i | −0.466986 | − | 0.884265i | \(-0.654660\pi\) |
0.999289 | − | 0.0377102i | \(-0.0120064\pi\) | |||||||
\(164\) | −7.93095 | − | 13.7368i | −0.619303 | − | 1.07266i | ||||
\(165\) | 10.0316 | − | 14.3305i | 0.780955 | − | 1.11563i | ||||
\(166\) | −14.7210 | + | 25.4975i | −1.14257 | + | 1.97899i | ||||
\(167\) | −6.57900 | −0.509099 | −0.254549 | − | 0.967060i | \(-0.581927\pi\) | ||||
−0.254549 | + | 0.967060i | \(0.581927\pi\) | |||||||
\(168\) | −0.271962 | + | 4.03368i | −0.0209823 | + | 0.311205i | ||||
\(169\) | 11.4516 | 0.880890 | ||||||||
\(170\) | 28.0859 | + | 16.2154i | 2.15409 | + | 1.24367i | ||||
\(171\) | 1.83599 | + | 0.170102i | 0.140402 | + | 0.0130080i | ||||
\(172\) | −3.06360 | + | 1.76877i | −0.233597 | + | 0.134867i | ||||
\(173\) | −1.14593 | + | 1.98481i | −0.0871234 | + | 0.150902i | −0.906294 | − | 0.422648i | \(-0.861101\pi\) |
0.819171 | + | 0.573550i | \(0.194434\pi\) | |||||||
\(174\) | −1.45783 | + | 4.58273i | −0.110518 | + | 0.347416i | ||||
\(175\) | −10.9784 | + | 2.69442i | −0.829893 | + | 0.203679i | ||||
\(176\) | 10.6039 | + | 11.5098i | 0.799296 | + | 0.867582i | ||||
\(177\) | 7.95434 | − | 7.25145i | 0.597885 | − | 0.545052i | ||||
\(178\) | 2.24633 | − | 1.29692i | 0.168370 | − | 0.0972083i | ||||
\(179\) | 12.2722 | − | 7.08537i | 0.917269 | − | 0.529585i | 0.0345062 | − | 0.999404i | \(-0.489014\pi\) |
0.882763 | + | 0.469819i | \(0.155681\pi\) | |||||||
\(180\) | −5.84383 | − | 12.7015i | −0.435573 | − | 0.946710i | ||||
\(181\) | 9.13748 | 0.679184 | 0.339592 | − | 0.940573i | \(-0.389711\pi\) | ||||
0.339592 | + | 0.940573i | \(0.389711\pi\) | |||||||
\(182\) | 4.46561 | − | 4.28078i | 0.331013 | − | 0.317313i | ||||
\(183\) | −15.7208 | − | 5.00101i | −1.16211 | − | 0.369685i | ||||
\(184\) | 3.89715 | + | 2.25002i | 0.287302 | + | 0.165874i | ||||
\(185\) | −16.6578 | + | 9.61738i | −1.22470 | + | 0.707084i | ||||
\(186\) | 20.2195 | − | 4.42830i | 1.48257 | − | 0.324699i | ||||
\(187\) | 18.3425 | − | 4.11823i | 1.34133 | − | 0.301154i | ||||
\(188\) | − | 16.5374i | − | 1.20611i | ||||||
\(189\) | −4.89302 | − | 12.8475i | −0.355915 | − | 0.934518i | ||||
\(190\) | −3.51660 | −0.255121 | ||||||||
\(191\) | −1.37505 | − | 0.793888i | −0.0994954 | − | 0.0574437i | 0.449427 | − | 0.893317i | \(-0.351628\pi\) |
−0.548922 | + | 0.835874i | \(0.684962\pi\) | |||||||
\(192\) | 6.60941 | − | 1.44753i | 0.476993 | − | 0.104467i | ||||
\(193\) | 11.2686 | − | 6.50595i | 0.811135 | − | 0.468309i | −0.0362150 | − | 0.999344i | \(-0.511530\pi\) |
0.847350 | + | 0.531035i | \(0.178197\pi\) | |||||||
\(194\) | −8.63984 | + | 14.9646i | −0.620305 | + | 1.07440i | ||||
\(195\) | 1.98956 | − | 6.25423i | 0.142476 | − | 0.447875i | ||||
\(196\) | −0.452577 | + | 10.7038i | −0.0323270 | + | 0.764554i | ||||
\(197\) | −0.114518 | −0.00815905 | −0.00407953 | − | 0.999992i | \(-0.501299\pi\) | ||||
−0.00407953 | + | 0.999992i | \(0.501299\pi\) | |||||||
\(198\) | −17.2548 | − | 7.19633i | −1.22625 | − | 0.511421i | ||||
\(199\) | −11.9254 | − | 20.6554i | −0.845370 | − | 1.46422i | −0.885299 | − | 0.465021i | \(-0.846047\pi\) |
0.0399293 | − | 0.999203i | \(-0.487287\pi\) | |||||||
\(200\) | −1.88469 | − | 3.26437i | −0.133268 | − | 0.230826i | ||||
\(201\) | −5.40882 | − | 5.93310i | −0.381509 | − | 0.418489i | ||||
\(202\) | −20.6721 | −1.45448 | ||||||||
\(203\) | 1.09143 | − | 3.75413i | 0.0766032 | − | 0.263488i | ||||
\(204\) | 4.55490 | − | 14.3184i | 0.318906 | − | 1.00249i | ||||
\(205\) | 27.3313 | + | 15.7798i | 1.90890 | + | 1.10211i | ||||
\(206\) | −2.33596 | − | 4.04601i | −0.162754 | − | 0.281899i | ||||
\(207\) | −15.2372 | − | 1.41171i | −1.05906 | − | 0.0981203i | ||||
\(208\) | 5.08497 | + | 2.93581i | 0.352579 | + | 0.203562i | ||||
\(209\) | −1.49920 | + | 1.38120i | −0.103702 | + | 0.0955396i | ||||
\(210\) | 11.5526 | + | 23.5374i | 0.797208 | + | 1.62423i | ||||
\(211\) | − | 5.75491i | − | 0.396184i | −0.980183 | − | 0.198092i | \(-0.936525\pi\) | ||
0.980183 | − | 0.198092i | \(-0.0634746\pi\) | |||||||
\(212\) | 3.94939 | + | 2.28018i | 0.271245 | + | 0.156603i | ||||
\(213\) | 2.93097 | + | 13.3828i | 0.200827 | + | 0.916971i | ||||
\(214\) | 12.9600 | + | 22.4473i | 0.885926 | + | 1.53447i | ||||
\(215\) | 3.51922 | − | 6.09547i | 0.240009 | − | 0.415708i | ||||
\(216\) | 3.65816 | − | 2.76265i | 0.248906 | − | 0.187974i | ||||
\(217\) | −16.3424 | + | 4.01087i | −1.10939 | + | 0.272276i | ||||
\(218\) | − | 6.49357i | − | 0.439800i | ||||||
\(219\) | 1.50146 | − | 1.36878i | 0.101459 | − | 0.0924935i | ||||
\(220\) | 14.7540 | + | 4.60832i | 0.994713 | + | 0.310693i | ||||
\(221\) | 6.10825 | − | 3.52660i | 0.410885 | − | 0.237225i | ||||
\(222\) | 13.8494 | + | 15.1918i | 0.929509 | + | 1.01961i | ||||
\(223\) | −10.9109 | −0.730650 | −0.365325 | − | 0.930880i | \(-0.619042\pi\) | ||||
−0.365325 | + | 0.930880i | \(0.619042\pi\) | |||||||
\(224\) | −18.2475 | + | 4.47845i | −1.21921 | + | 0.299229i | ||||
\(225\) | 10.4620 | + | 7.40564i | 0.697465 | + | 0.493710i | ||||
\(226\) | −13.0015 | − | 7.50640i | −0.864845 | − | 0.499318i | ||||
\(227\) | −4.04895 | − | 7.01299i | −0.268739 | − | 0.465469i | 0.699798 | − | 0.714341i | \(-0.253273\pi\) |
−0.968536 | + | 0.248872i | \(0.919940\pi\) | |||||||
\(228\) | 0.348566 | + | 1.59154i | 0.0230843 | + | 0.105402i | ||||
\(229\) | −0.452439 | + | 0.783647i | −0.0298980 | + | 0.0517848i | −0.880587 | − | 0.473884i | \(-0.842852\pi\) |
0.850689 | + | 0.525669i | \(0.176185\pi\) | |||||||
\(230\) | 29.1849 | 1.92439 | ||||||||
\(231\) | 14.1698 | + | 5.49698i | 0.932304 | + | 0.361675i | ||||
\(232\) | 1.30363 | 0.0855878 | ||||||||
\(233\) | −0.199109 | + | 0.344867i | −0.0130441 | + | 0.0225930i | −0.872474 | − | 0.488661i | \(-0.837486\pi\) |
0.859430 | + | 0.511254i | \(0.170819\pi\) | |||||||
\(234\) | −6.98436 | − | 0.647091i | −0.456582 | − | 0.0423016i | ||||
\(235\) | 16.4517 | + | 28.4953i | 1.07319 | + | 1.85883i | ||||
\(236\) | 8.23670 | + | 4.75546i | 0.536164 | + | 0.309554i | ||||
\(237\) | 6.36978 | + | 2.02632i | 0.413762 | + | 0.131624i | ||||
\(238\) | −7.86633 | + | 27.0575i | −0.509899 | + | 1.75387i | ||||
\(239\) | 18.8807 | 1.22129 | 0.610647 | − | 0.791903i | \(-0.290909\pi\) | ||||
0.610647 | + | 0.791903i | \(0.290909\pi\) | |||||||
\(240\) | −18.3917 | + | 16.7665i | −1.18718 | + | 1.08227i | ||||
\(241\) | 2.61969 | − | 1.51248i | 0.168749 | − | 0.0974274i | −0.413247 | − | 0.910619i | \(-0.635605\pi\) |
0.581996 | + | 0.813192i | \(0.302272\pi\) | |||||||
\(242\) | 18.6848 | − | 8.83554i | 1.20110 | − | 0.567970i | ||||
\(243\) | −7.37428 | + | 13.7339i | −0.473060 | + | 0.881030i | ||||
\(244\) | − | 14.5771i | − | 0.933204i | ||||||
\(245\) | −9.86849 | − | 18.8937i | −0.630475 | − | 1.20707i | ||||
\(246\) | 10.2249 | − | 32.1421i | 0.651913 | − | 2.04930i | ||||
\(247\) | −0.382402 | + | 0.662340i | −0.0243317 | + | 0.0421437i | ||||
\(248\) | −2.80552 | − | 4.85930i | −0.178151 | − | 0.308566i | ||||
\(249\) | −26.5117 | + | 5.80636i | −1.68011 | + | 0.367963i | ||||
\(250\) | 3.60427 | + | 2.08092i | 0.227954 | + | 0.131609i | ||||
\(251\) | 7.80267i | 0.492500i | 0.969206 | + | 0.246250i | \(0.0791985\pi\) | ||||
−0.969206 | + | 0.246250i | \(0.920802\pi\) | |||||||
\(252\) | 9.50744 | − | 7.56152i | 0.598912 | − | 0.476331i | ||||
\(253\) | 12.4421 | − | 11.4628i | 0.782229 | − | 0.720661i | ||||
\(254\) | −19.4078 | − | 11.2051i | −1.21775 | − | 0.703070i | ||||
\(255\) | 6.39580 | + | 29.2031i | 0.400521 | + | 1.82877i | ||||
\(256\) | −10.3543 | − | 17.9341i | −0.647142 | − | 1.12088i | ||||
\(257\) | −9.02456 | − | 5.21033i | −0.562937 | − | 0.325012i | 0.191387 | − | 0.981515i | \(-0.438702\pi\) |
−0.754323 | + | 0.656503i | \(0.772035\pi\) | |||||||
\(258\) | −7.16837 | − | 2.28036i | −0.446283 | − | 0.141969i | ||||
\(259\) | −11.5650 | − | 12.0644i | −0.718616 | − | 0.749643i | ||||
\(260\) | 5.79925 | 0.359654 | ||||||||
\(261\) | −4.02723 | + | 1.85289i | −0.249279 | + | 0.114691i | ||||
\(262\) | −2.90501 | − | 5.03163i | −0.179472 | − | 0.310855i | ||||
\(263\) | −15.4549 | − | 26.7686i | −0.952989 | − | 1.65062i | −0.738905 | − | 0.673809i | \(-0.764657\pi\) |
−0.214083 | − | 0.976815i | \(-0.568676\pi\) | |||||||
\(264\) | −0.441042 | + | 5.04873i | −0.0271442 | + | 0.310728i | ||||
\(265\) | −9.07348 | −0.557380 | ||||||||
\(266\) | −0.728272 | − | 2.96736i | −0.0446532 | − | 0.181940i | ||||
\(267\) | 2.27853 | + | 0.724834i | 0.139444 | + | 0.0443591i | ||||
\(268\) | 3.54708 | − | 6.14372i | 0.216672 | − | 0.375287i | ||||
\(269\) | −7.00519 | + | 4.04445i | −0.427114 | + | 0.246594i | −0.698116 | − | 0.715984i | \(-0.745978\pi\) |
0.271002 | + | 0.962579i | \(0.412645\pi\) | |||||||
\(270\) | 11.5878 | − | 27.3791i | 0.705213 | − | 1.66624i | ||||
\(271\) | −11.9023 | − | 6.87180i | −0.723014 | − | 0.417432i | 0.0928473 | − | 0.995680i | \(-0.470403\pi\) |
−0.815861 | + | 0.578248i | \(0.803736\pi\) | |||||||
\(272\) | −26.7457 | −1.62170 | ||||||||
\(273\) | 5.68944 | + | 0.383598i | 0.344341 | + | 0.0232164i | ||||
\(274\) | 5.82036i | 0.351621i | ||||||||
\(275\) | −13.8264 | + | 3.10429i | −0.833765 | + | 0.187196i | ||||
\(276\) | −2.89281 | − | 13.2085i | −0.174127 | − | 0.795058i | ||||
\(277\) | 23.6582 | − | 13.6590i | 1.42148 | − | 0.820692i | 0.425055 | − | 0.905167i | \(-0.360255\pi\) |
0.996426 | + | 0.0844752i | \(0.0269214\pi\) | |||||||
\(278\) | 19.8137 | + | 11.4394i | 1.18835 | + | 0.686092i | ||||
\(279\) | 15.5736 | + | 11.0239i | 0.932365 | + | 0.659986i | ||||
\(280\) | 5.13093 | − | 4.91857i | 0.306632 | − | 0.293941i | ||||
\(281\) | −0.129664 | −0.00773512 | −0.00386756 | − | 0.999993i | \(-0.501231\pi\) | ||||
−0.00386756 | + | 0.999993i | \(0.501231\pi\) | |||||||
\(282\) | 25.9875 | − | 23.6911i | 1.54753 | − | 1.41079i | ||||
\(283\) | 25.0814 | − | 14.4807i | 1.49093 | − | 0.860790i | 0.490986 | − | 0.871168i | \(-0.336637\pi\) |
0.999946 | + | 0.0103778i | \(0.00330341\pi\) | |||||||
\(284\) | −10.4837 | + | 6.05277i | −0.622094 | + | 0.359166i | ||||
\(285\) | −2.18391 | − | 2.39560i | −0.129363 | − | 0.141903i | ||||
\(286\) | 5.70316 | − | 5.25427i | 0.337235 | − | 0.310692i | ||||
\(287\) | −7.65499 | + | 26.3305i | −0.451859 | + | 1.55424i | ||||
\(288\) | 17.3891 | + | 12.3091i | 1.02466 | + | 0.725320i | ||||
\(289\) | −7.56392 | + | 13.1011i | −0.444936 | + | 0.770653i | ||||
\(290\) | 7.32197 | − | 4.22734i | 0.429961 | − | 0.248238i | ||||
\(291\) | −15.5599 | + | 3.40779i | −0.912137 | + | 0.199768i | ||||
\(292\) | 1.55475 | + | 0.897638i | 0.0909851 | + | 0.0525303i | ||||
\(293\) | −4.79018 | −0.279845 | −0.139923 | − | 0.990162i | \(-0.544685\pi\) | ||||
−0.139923 | + | 0.990162i | \(0.544685\pi\) | |||||||
\(294\) | −17.4687 | + | 14.6228i | −1.01879 | + | 0.852817i | ||||
\(295\) | −18.9233 | −1.10176 | ||||||||
\(296\) | 2.78633 | − | 4.82606i | 0.161952 | − | 0.280509i | ||||
\(297\) | −5.81343 | − | 16.2236i | −0.337329 | − | 0.941387i | ||||
\(298\) | −20.1937 | − | 34.9764i | −1.16979 | − | 2.02613i | ||||
\(299\) | 3.17362 | − | 5.49688i | 0.183535 | − | 0.317893i | ||||
\(300\) | −3.43345 | + | 10.7931i | −0.198230 | + | 0.623141i | ||||
\(301\) | 5.87226 | + | 1.70722i | 0.338471 | + | 0.0984028i | ||||
\(302\) | − | 43.1398i | − | 2.48242i | ||||||
\(303\) | −12.8380 | − | 14.0823i | −0.737521 | − | 0.809010i | ||||
\(304\) | 2.51159 | − | 1.45007i | 0.144050 | − | 0.0831671i | ||||
\(305\) | 14.5016 | + | 25.1175i | 0.830360 | + | 1.43823i | ||||
\(306\) | 29.0258 | − | 13.3545i | 1.65929 | − | 0.763426i | ||||
\(307\) | 14.6773i | 0.837677i | 0.908061 | + | 0.418839i | \(0.137563\pi\) | ||||
−0.908061 | + | 0.418839i | \(0.862437\pi\) | |||||||
\(308\) | −0.833080 | + | 13.4040i | −0.0474691 | + | 0.763763i | ||||
\(309\) | 1.30554 | − | 4.10400i | 0.0742697 | − | 0.233468i | ||||
\(310\) | −31.5148 | − | 18.1951i | −1.78992 | − | 1.03341i | ||||
\(311\) | 13.2520 | − | 7.65105i | 0.751453 | − | 0.433852i | −0.0747658 | − | 0.997201i | \(-0.523821\pi\) |
0.826219 | + | 0.563350i | \(0.190488\pi\) | |||||||
\(312\) | 0.406794 | + | 1.85741i | 0.0230302 | + | 0.105155i | ||||
\(313\) | 9.92967 | − | 17.1987i | 0.561258 | − | 0.972127i | −0.436129 | − | 0.899884i | \(-0.643651\pi\) |
0.997387 | − | 0.0722432i | \(-0.0230158\pi\) | |||||||
\(314\) | −21.3162 | −1.20294 | ||||||||
\(315\) | −8.85973 | + | 22.4873i | −0.499189 | + | 1.26702i | ||||
\(316\) | 5.90639i | 0.332261i | ||||||||
\(317\) | 15.6174 | + | 9.01672i | 0.877161 | + | 0.506429i | 0.869721 | − | 0.493543i | \(-0.164298\pi\) |
0.00743978 | + | 0.999972i | \(0.497632\pi\) | |||||||
\(318\) | 2.07464 | + | 9.47276i | 0.116340 | + | 0.531206i | ||||
\(319\) | 1.46115 | − | 4.67802i | 0.0818088 | − | 0.261919i | ||||
\(320\) | −10.3017 | − | 5.94767i | −0.575880 | − | 0.332485i | ||||
\(321\) | −7.24318 | + | 22.7691i | −0.404275 | + | 1.27085i | ||||
\(322\) | 6.04406 | + | 24.6266i | 0.336822 | + | 1.37239i | ||||
\(323\) | − | 3.48374i | − | 0.193841i | ||||||
\(324\) | −13.5398 | − | 2.53061i | −0.752212 | − | 0.140589i | ||||
\(325\) | −4.60435 | + | 2.65833i | −0.255404 | + | 0.147457i | ||||
\(326\) | 12.7693 | + | 22.1172i | 0.707229 | + | 1.22496i | ||||
\(327\) | 4.42358 | − | 4.03269i | 0.244625 | − | 0.223008i | ||||
\(328\) | −9.14336 | −0.504857 | ||||||||
\(329\) | −20.6376 | + | 19.7835i | −1.13779 | + | 1.09070i | ||||
\(330\) | 13.8945 | + | 29.7868i | 0.764870 | + | 1.63971i | ||||
\(331\) | −8.50642 | + | 14.7336i | −0.467555 | + | 0.809830i | −0.999313 | − | 0.0370671i | \(-0.988198\pi\) |
0.531757 | + | 0.846897i | \(0.321532\pi\) | |||||||
\(332\) | −11.9907 | − | 20.7686i | −0.658078 | − | 1.13982i | ||||
\(333\) | −1.74819 | + | 18.8691i | −0.0958004 | + | 1.03402i | ||||
\(334\) | 6.18083 | − | 10.7055i | 0.338200 | − | 0.585779i | ||||
\(335\) | 14.1148i | 0.771175i | ||||||||
\(336\) | −17.9566 | − | 12.0469i | −0.979615 | − | 0.657212i | ||||
\(337\) | 23.4102i | 1.27523i | 0.770354 | + | 0.637616i | \(0.220079\pi\) | ||||
−0.770354 | + | 0.637616i | \(0.779921\pi\) | |||||||
\(338\) | −10.7585 | + | 18.6343i | −0.585185 | + | 1.01357i | ||||
\(339\) | −2.96073 | − | 13.5186i | −0.160805 | − | 0.734230i | ||||
\(340\) | −22.8770 | + | 13.2080i | −1.24068 | + | 0.716305i | ||||
\(341\) | −20.5818 | + | 4.62100i | −1.11457 | + | 0.250241i | ||||
\(342\) | −2.00167 | + | 2.82776i | −0.108238 | + | 0.152908i | ||||
\(343\) | 13.8990 | − | 12.2400i | 0.750477 | − | 0.660897i | ||||
\(344\) | 2.03916i | 0.109944i | ||||||||
\(345\) | 18.1246 | + | 19.8815i | 0.975798 | + | 1.07038i | ||||
\(346\) | −2.15315 | − | 3.72937i | −0.115754 | − | 0.200492i | ||||
\(347\) | 11.4850 | + | 19.8925i | 0.616545 | + | 1.06789i | 0.990111 | + | 0.140283i | \(0.0448013\pi\) |
−0.373567 | + | 0.927603i | \(0.621865\pi\) | |||||||
\(348\) | −2.63896 | − | 2.89476i | −0.141463 | − | 0.155176i | ||||
\(349\) | − | 10.0181i | − | 0.536258i | −0.963383 | − | 0.268129i | \(-0.913595\pi\) | ||
0.963383 | − | 0.268129i | \(-0.0864053\pi\) | |||||||
\(350\) | 5.92959 | − | 20.3957i | 0.316950 | − | 1.09020i | ||||
\(351\) | −3.89667 | − | 5.15979i | −0.207989 | − | 0.275409i | ||||
\(352\) | −22.9812 | + | 5.15971i | −1.22490 | + | 0.275014i | ||||
\(353\) | −4.58642 | + | 2.64797i | −0.244110 | + | 0.140937i | −0.617064 | − | 0.786913i | \(-0.711678\pi\) |
0.372954 | + | 0.927850i | \(0.378345\pi\) | |||||||
\(354\) | 4.32680 | + | 19.7561i | 0.229967 | + | 1.05002i | ||||
\(355\) | 12.0429 | − | 20.8588i | 0.639168 | − | 1.10707i | ||||
\(356\) | 2.11277i | 0.111977i | ||||||||
\(357\) | −23.3174 | + | 11.4447i | −1.23409 | + | 0.605718i | ||||
\(358\) | 26.6262i | 1.40724i | ||||||||
\(359\) | −2.99188 | + | 5.18209i | −0.157905 | + | 0.273500i | −0.934113 | − | 0.356977i | \(-0.883807\pi\) |
0.776208 | + | 0.630477i | \(0.217141\pi\) | |||||||
\(360\) | −8.02495 | − | 0.743500i | −0.422952 | − | 0.0391859i | ||||
\(361\) | −9.31112 | − | 16.1273i | −0.490059 | − | 0.848807i | ||||
\(362\) | −8.58446 | + | 14.8687i | −0.451189 | + | 0.781483i | ||||
\(363\) | 17.6228 | + | 7.24142i | 0.924955 | + | 0.380076i | ||||
\(364\) | 1.20100 | + | 4.89349i | 0.0629495 | + | 0.256489i | ||||
\(365\) | −3.57196 | −0.186965 | ||||||||
\(366\) | 22.9071 | − | 20.8829i | 1.19737 | − | 1.09156i | ||||
\(367\) | −9.83094 | − | 17.0277i | −0.513171 | − | 0.888838i | −0.999883 | − | 0.0152759i | \(-0.995137\pi\) |
0.486712 | − | 0.873562i | \(-0.338196\pi\) | |||||||
\(368\) | −20.8441 | + | 12.0344i | −1.08658 | + | 0.627335i | ||||
\(369\) | 28.2459 | − | 12.9957i | 1.47042 | − | 0.676529i | ||||
\(370\) | − | 36.1412i | − | 1.87889i | ||||||
\(371\) | −1.87908 | − | 7.65634i | −0.0975569 | − | 0.397497i | ||||
\(372\) | −5.11099 | + | 16.0665i | −0.264992 | + | 0.833009i | ||||
\(373\) | −16.8118 | − | 9.70627i | −0.870480 | − | 0.502572i | −0.00297207 | − | 0.999996i | \(-0.500946\pi\) |
−0.867508 | + | 0.497424i | \(0.834279\pi\) | |||||||
\(374\) | −10.5311 | + | 33.7163i | −0.544549 | + | 1.74343i | ||||
\(375\) | 0.820774 | + | 3.74763i | 0.0423846 | + | 0.193527i | ||||
\(376\) | −8.25559 | − | 4.76637i | −0.425749 | − | 0.245807i | ||||
\(377\) | − | 1.83876i | − | 0.0947009i | ||||||
\(378\) | 25.5026 | + | 4.10790i | 1.31171 | + | 0.211288i | ||||
\(379\) | 2.78311 | 0.142959 | 0.0714795 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714795 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(380\) | 1.43219 | − | 2.48063i | 0.0734700 | − | 0.127254i | ||||
\(381\) | −4.41960 | − | 20.1798i | −0.226423 | − | 1.03384i | ||||
\(382\) | 2.58366 | − | 1.49168i | 0.132192 | − | 0.0763210i | ||||
\(383\) | 7.16366 | + | 4.13594i | 0.366046 | + | 0.211337i | 0.671730 | − | 0.740796i | \(-0.265552\pi\) |
−0.305684 | + | 0.952133i | \(0.598885\pi\) | |||||||
\(384\) | 3.60365 | − | 11.3281i | 0.183898 | − | 0.578087i | ||||
\(385\) | −11.8991 | − | 23.9249i | −0.606435 | − | 1.21933i | ||||
\(386\) | 24.4488i | 1.24441i | ||||||||
\(387\) | −2.89832 | − | 6.29944i | −0.147330 | − | 0.320219i | ||||
\(388\) | −7.03745 | − | 12.1892i | −0.357272 | − | 0.618814i | ||||
\(389\) | 16.7647 | − | 9.67910i | 0.850004 | − | 0.490750i | −0.0106482 | − | 0.999943i | \(-0.503390\pi\) |
0.860652 | + | 0.509193i | \(0.170056\pi\) | |||||||
\(390\) | 8.30789 | + | 9.11318i | 0.420686 | + | 0.461464i | ||||
\(391\) | 28.9122i | 1.46215i | ||||||||
\(392\) | 5.21295 | + | 3.31094i | 0.263294 | + | 0.167228i | ||||
\(393\) | 1.62358 | − | 5.10375i | 0.0818987 | − | 0.257450i | ||||
\(394\) | 0.107587 | − | 0.186346i | 0.00542015 | − | 0.00938797i | ||||
\(395\) | −5.87581 | − | 10.1772i | −0.295644 | − | 0.512070i | ||||
\(396\) | 12.1037 | − | 9.24087i | 0.608233 | − | 0.464371i | ||||
\(397\) | 7.01674 | − | 12.1534i | 0.352160 | − | 0.609959i | −0.634467 | − | 0.772950i | \(-0.718781\pi\) |
0.986628 | + | 0.162990i | \(0.0521139\pi\) | |||||||
\(398\) | 44.8146 | 2.24635 | ||||||||
\(399\) | 1.56916 | − | 2.33893i | 0.0785563 | − | 0.117093i | ||||
\(400\) | 20.1607 | 1.00804 | ||||||||
\(401\) | −11.1606 | − | 6.44358i | −0.557334 | − | 0.321777i | 0.194741 | − | 0.980855i | \(-0.437613\pi\) |
−0.752075 | + | 0.659078i | \(0.770947\pi\) | |||||||
\(402\) | 14.7360 | − | 3.22734i | 0.734962 | − | 0.160965i | ||||
\(403\) | −6.85398 | + | 3.95715i | −0.341421 | + | 0.197120i | ||||
\(404\) | 8.41906 | − | 14.5822i | 0.418864 | − | 0.725494i | ||||
\(405\) | 25.8477 | − | 9.10925i | 1.28438 | − | 0.452642i | ||||
\(406\) | 5.08344 | + | 5.30292i | 0.252287 | + | 0.263179i | ||||
\(407\) | −14.1950 | − | 15.4078i | −0.703622 | − | 0.763734i | ||||
\(408\) | −5.83506 | − | 6.40066i | −0.288878 | − | 0.316880i | ||||
\(409\) | 6.17168 | − | 3.56322i | 0.305170 | − | 0.176190i | −0.339593 | − | 0.940572i | \(-0.610289\pi\) |
0.644763 | + | 0.764382i | \(0.276956\pi\) | |||||||
\(410\) | −51.3544 | + | 29.6495i | −2.53621 | + | 1.46428i | ||||
\(411\) | −3.96497 | + | 3.61461i | −0.195578 | + | 0.178295i | ||||
\(412\) | 3.80544 | 0.187481 | ||||||||
\(413\) | −3.91894 | − | 15.9678i | −0.192838 | − | 0.785724i | ||||
\(414\) | 16.6122 | − | 23.4681i | 0.816444 | − | 1.15339i | ||||
\(415\) | 41.3220 | + | 23.8573i | 2.02842 | + | 1.17111i | ||||
\(416\) | −7.65300 | + | 4.41846i | −0.375219 | + | 0.216633i | ||||
\(417\) | 4.51203 | + | 20.6018i | 0.220955 | + | 1.00887i | ||||
\(418\) | −0.839056 | − | 3.73714i | −0.0410396 | − | 0.182789i | ||||
\(419\) | − | 27.8186i | − | 1.35903i | −0.733663 | − | 0.679514i | \(-0.762191\pi\) | ||
0.733663 | − | 0.679514i | \(-0.237809\pi\) | |||||||
\(420\) | −21.3084 | − | 1.43667i | −1.03975 | − | 0.0701025i | ||||
\(421\) | −17.5302 | −0.854369 | −0.427185 | − | 0.904164i | \(-0.640495\pi\) | ||||
−0.427185 | + | 0.904164i | \(0.640495\pi\) | |||||||
\(422\) | 9.36453 | + | 5.40661i | 0.455858 | + | 0.263190i | ||||
\(423\) | 32.2780 | + | 2.99051i | 1.56941 | + | 0.145403i | ||||
\(424\) | 2.27656 | − | 1.31438i | 0.110560 | − | 0.0638317i | ||||
\(425\) | 12.1089 | − | 20.9732i | 0.587367 | − | 1.01735i | ||||
\(426\) | −24.5303 | − | 7.80345i | −1.18850 | − | 0.378078i | ||||
\(427\) | −18.1913 | + | 17.4384i | −0.880340 | + | 0.843904i | ||||
\(428\) | −21.1127 | −1.02052 | ||||||||
\(429\) | 7.12117 | + | 0.622083i | 0.343813 | + | 0.0300345i | ||||
\(430\) | 6.61246 | + | 11.4531i | 0.318881 | + | 0.552318i | ||||
\(431\) | −6.45778 | − | 11.1852i | −0.311060 | − | 0.538772i | 0.667532 | − | 0.744581i | \(-0.267351\pi\) |
−0.978592 | + | 0.205809i | \(0.934017\pi\) | |||||||
\(432\) | 3.01359 | + | 24.3326i | 0.144991 | + | 1.17070i | ||||
\(433\) | 6.99731 | 0.336269 | 0.168135 | − | 0.985764i | \(-0.446226\pi\) | ||||
0.168135 | + | 0.985764i | \(0.446226\pi\) | |||||||
\(434\) | 8.82671 | − | 30.3608i | 0.423695 | − | 1.45737i | ||||
\(435\) | 7.42692 | + | 2.36261i | 0.356094 | + | 0.113279i | ||||
\(436\) | 4.58061 | + | 2.64462i | 0.219371 | + | 0.126654i | ||||
\(437\) | −1.56753 | − | 2.71504i | −0.0749851 | − | 0.129878i | ||||
\(438\) | 0.816724 | + | 3.72914i | 0.0390246 | + | 0.178185i | ||||
\(439\) | 10.1810 | + | 5.87802i | 0.485914 | + | 0.280543i | 0.722878 | − | 0.690976i | \(-0.242819\pi\) |
−0.236964 | + | 0.971519i | \(0.576152\pi\) | |||||||
\(440\) | 6.55286 | − | 6.03710i | 0.312396 | − | 0.287807i | ||||
\(441\) | −20.8099 | − | 2.81894i | −0.990949 | − | 0.134235i | ||||
\(442\) | 13.2526i | 0.630364i | ||||||||
\(443\) | 8.29921 | + | 4.79155i | 0.394307 | + | 0.227653i | 0.684025 | − | 0.729459i | \(-0.260228\pi\) |
−0.289717 | + | 0.957112i | \(0.593561\pi\) | |||||||
\(444\) | −16.3568 | + | 3.58233i | −0.776260 | + | 0.170010i | ||||
\(445\) | −2.10183 | − | 3.64048i | −0.0996364 | − | 0.172575i | ||||
\(446\) | 10.2506 | − | 17.7545i | 0.485379 | − | 0.840701i | ||||
\(447\) | 11.2860 | − | 35.4778i | 0.533810 | − | 1.67804i | ||||
\(448\) | 2.88530 | − | 9.92443i | 0.136318 | − | 0.468885i | ||||
\(449\) | − | 30.0895i | − | 1.42001i | −0.704197 | − | 0.710005i | \(-0.748693\pi\) | ||
0.704197 | − | 0.710005i | \(-0.251307\pi\) | |||||||
\(450\) | −21.8794 | + | 10.0665i | −1.03141 | + | 0.474541i | ||||
\(451\) | −10.2481 | + | 32.8104i | −0.482566 | + | 1.54498i | ||||
\(452\) | 10.5901 | − | 6.11422i | 0.498118 | − | 0.287589i | ||||
\(453\) | 29.3880 | − | 26.7911i | 1.38077 | − | 1.25875i | ||||
\(454\) | 15.2156 | 0.714104 | ||||||||
\(455\) | −6.93757 | − | 7.23710i | −0.325238 | − | 0.339281i | ||||
\(456\) | 0.894973 | + | 0.284704i | 0.0419109 | + | 0.0133325i | ||||
\(457\) | −35.4804 | − | 20.4846i | −1.65970 | − | 0.958230i | −0.972851 | − | 0.231434i | \(-0.925658\pi\) |
−0.686853 | − | 0.726796i | \(-0.741008\pi\) | |||||||
\(458\) | −0.850112 | − | 1.47244i | −0.0397231 | − | 0.0688025i | ||||
\(459\) | 27.1233 | + | 11.4796i | 1.26601 | + | 0.535820i | ||||
\(460\) | −11.8860 | + | 20.5872i | −0.554190 | + | 0.959884i | ||||
\(461\) | 5.45941 | 0.254270 | 0.127135 | − | 0.991885i | \(-0.459422\pi\) | ||||
0.127135 | + | 0.991885i | \(0.459422\pi\) | |||||||
\(462\) | −22.2570 | + | 17.8931i | −1.03549 | + | 0.832464i | ||||
\(463\) | 6.44042 | 0.299312 | 0.149656 | − | 0.988738i | \(-0.452183\pi\) | ||||
0.149656 | + | 0.988738i | \(0.452183\pi\) | |||||||
\(464\) | −3.48628 | + | 6.03842i | −0.161847 | + | 0.280327i | ||||
\(465\) | −7.17665 | − | 32.7684i | −0.332809 | − | 1.51960i | ||||
\(466\) | −0.374117 | − | 0.647990i | −0.0173306 | − | 0.0300176i | ||||
\(467\) | −2.59974 | − | 1.50096i | −0.120301 | − | 0.0694561i | 0.438642 | − | 0.898662i | \(-0.355460\pi\) |
−0.558943 | + | 0.829206i | \(0.688793\pi\) | |||||||
\(468\) | 3.30096 | − | 4.66328i | 0.152587 | − | 0.215560i | ||||
\(469\) | −11.9103 | + | 2.92312i | −0.549966 | + | 0.134977i | ||||
\(470\) | −61.8242 | −2.85174 | ||||||||
\(471\) | −13.2380 | − | 14.5211i | −0.609973 | − | 0.669099i | ||||
\(472\) | 4.74792 | − | 2.74122i | 0.218541 | − | 0.126175i | ||||
\(473\) | 7.31742 | + | 2.28555i | 0.336455 | + | 0.105090i | ||||
\(474\) | −9.28155 | + | 8.46138i | −0.426316 | + | 0.388644i | ||||
\(475\) | 2.62602i | 0.120490i | ||||||||
\(476\) | −15.8828 | − | 16.5686i | −0.727989 | − | 0.759420i | ||||
\(477\) | −5.16467 | + | 7.29615i | −0.236474 | + | 0.334068i | ||||
\(478\) | −17.7380 | + | 30.7232i | −0.811319 | + | 1.40525i | ||||
\(479\) | 10.7538 | + | 18.6261i | 0.491353 | + | 0.851049i | 0.999950 | − | 0.00995594i | \(-0.00316913\pi\) |
−0.508597 | + | 0.861005i | \(0.669836\pi\) | |||||||
\(480\) | −8.01328 | − | 36.5884i | −0.365755 | − | 1.67003i | ||||
\(481\) | −6.80709 | − | 3.93007i | −0.310377 | − | 0.179196i | ||||
\(482\) | 5.68377i | 0.258888i | ||||||||
\(483\) | −13.0227 | + | 19.4112i | −0.592556 | + | 0.883240i | ||||
\(484\) | −1.37704 | + | 16.7788i | −0.0625926 | + | 0.762673i | ||||
\(485\) | 24.2522 | + | 14.0020i | 1.10124 | + | 0.635798i | ||||
\(486\) | −15.4201 | − | 24.9023i | −0.699472 | − | 1.12959i | ||||
\(487\) | 16.6319 | + | 28.8073i | 0.753665 | + | 1.30539i | 0.946035 | + | 0.324063i | \(0.105049\pi\) |
−0.192371 | + | 0.981322i | \(0.561618\pi\) | |||||||
\(488\) | −7.27700 | − | 4.20138i | −0.329415 | − | 0.190188i | ||||
\(489\) | −7.13664 | + | 22.4342i | −0.322730 | + | 1.01451i | ||||
\(490\) | 40.0154 | + | 1.69194i | 1.80771 | + | 0.0764340i | ||||
\(491\) | −3.76057 | −0.169712 | −0.0848562 | − | 0.996393i | \(-0.527043\pi\) | ||||
−0.0848562 | + | 0.996393i | \(0.527043\pi\) | |||||||
\(492\) | 18.5090 | + | 20.3031i | 0.834450 | + | 0.915335i | ||||
\(493\) | 4.18784 | + | 7.25356i | 0.188611 | + | 0.326684i | ||||
\(494\) | −0.718517 | − | 1.24451i | −0.0323276 | − | 0.0559930i | ||||
\(495\) | −11.6626 | + | 27.9638i | −0.524195 | + | 1.25688i | ||||
\(496\) | 30.0110 | 1.34753 | ||||||||
\(497\) | 20.0950 | + | 5.84216i | 0.901385 | + | 0.262057i | ||||
\(498\) | 15.4589 | − | 48.5954i | 0.692730 | − | 2.17761i | ||||
\(499\) | −1.01365 | + | 1.75570i | −0.0453773 | + | 0.0785958i | −0.887822 | − | 0.460187i | \(-0.847782\pi\) |
0.842445 | + | 0.538783i | \(0.181116\pi\) | |||||||
\(500\) | −2.93580 | + | 1.69498i | −0.131293 | + | 0.0758020i | ||||
\(501\) | 11.1313 | − | 2.43789i | 0.497311 | − | 0.108917i | ||||
\(502\) | −12.6967 | − | 7.33044i | −0.566681 | − | 0.327173i | ||||
\(503\) | −12.6627 | −0.564602 | −0.282301 | − | 0.959326i | \(-0.591098\pi\) | ||||
−0.282301 | + | 0.959326i | \(0.591098\pi\) | |||||||
\(504\) | −1.03456 | − | 6.92555i | −0.0460828 | − | 0.308488i | ||||
\(505\) | 33.5018i | 1.49081i | ||||||||
\(506\) | 6.96348 | + | 31.0152i | 0.309564 | + | 1.37879i | ||||
\(507\) | −19.3755 | + | 4.24345i | −0.860495 | + | 0.188458i | ||||
\(508\) | 15.8083 | − | 9.12693i | 0.701381 | − | 0.404942i | ||||
\(509\) | 24.5196 | + | 14.1564i | 1.08681 | + | 0.627471i | 0.932726 | − | 0.360586i | \(-0.117423\pi\) |
0.154086 | + | 0.988057i | \(0.450757\pi\) | |||||||
\(510\) | −53.5287 | − | 17.0282i | −2.37029 | − | 0.754023i | ||||
\(511\) | −0.739737 | − | 3.01407i | −0.0327240 | − | 0.133335i | ||||
\(512\) | 25.1839 | 1.11298 | ||||||||
\(513\) | −3.16943 | + | 0.392534i | −0.139934 | + | 0.0173308i | ||||
\(514\) | 16.9568 | − | 9.78999i | 0.747930 | − | 0.431818i | ||||
\(515\) | −6.55709 | + | 3.78574i | −0.288940 | + | 0.166819i | ||||
\(516\) | 4.52802 | − | 4.12790i | 0.199335 | − | 0.181721i | ||||
\(517\) | −26.3569 | + | 24.2824i | −1.15918 | + | 1.06794i | ||||
\(518\) | 30.4965 | − | 7.48469i | 1.33994 | − | 0.328859i | ||||
\(519\) | 1.20337 | − | 3.78282i | 0.0528221 | − | 0.166047i | ||||
\(520\) | 1.67145 | − | 2.89503i | 0.0732978 | − | 0.126955i | ||||
\(521\) | −4.46847 | + | 2.57987i | −0.195767 | + | 0.113026i | −0.594680 | − | 0.803963i | \(-0.702721\pi\) |
0.398912 | + | 0.916989i | \(0.369388\pi\) | |||||||
\(522\) | 0.768422 | − | 8.29395i | 0.0336329 | − | 0.363016i | ||||
\(523\) | −1.50137 | − | 0.866814i | −0.0656502 | − | 0.0379031i | 0.466816 | − | 0.884355i | \(-0.345401\pi\) |
−0.532466 | + | 0.846452i | \(0.678735\pi\) | |||||||
\(524\) | 4.73247 | 0.206739 | ||||||||
\(525\) | 17.5765 | − | 8.62694i | 0.767103 | − | 0.376511i | ||||
\(526\) | 58.0781 | 2.53232 | ||||||||
\(527\) | 18.0251 | − | 31.2204i | 0.785186 | − | 1.35998i | ||||
\(528\) | −22.2062 | − | 15.5446i | −0.966401 | − | 0.676493i | ||||
\(529\) | 1.50921 | + | 2.61402i | 0.0656177 | + | 0.113653i | ||||
\(530\) | 8.52433 | − | 14.7646i | 0.370273 | − | 0.641332i | ||||
\(531\) | −10.7713 | + | 15.2166i | −0.467433 | + | 0.660344i | ||||
\(532\) | 2.38980 | + | 0.694778i | 0.103611 | + | 0.0301225i | ||||
\(533\) | 12.8966i | 0.558613i | ||||||||
\(534\) | −3.32010 | + | 3.02671i | −0.143675 | + | 0.130979i | ||||
\(535\) | 36.3789 | − | 21.0034i | 1.57280 | − | 0.908054i | ||||
\(536\) | −2.04466 | − | 3.54145i | −0.0883158 | − | 0.152968i | ||||
\(537\) | −18.1384 | + | 16.5356i | −0.782731 | + | 0.713565i | ||||
\(538\) | − | 15.1987i | − | 0.655262i | ||||||
\(539\) | 17.7239 | − | 14.9954i | 0.763424 | − | 0.645897i | ||||
\(540\) | 14.5940 | + | 19.3247i | 0.628028 | + | 0.831604i | ||||
\(541\) | 21.1393 | + | 12.2048i | 0.908850 | + | 0.524725i | 0.880061 | − | 0.474861i | \(-0.157502\pi\) |
0.0287892 | + | 0.999586i | \(0.490835\pi\) | |||||||
\(542\) | 22.3639 | − | 12.9118i | 0.960612 | − | 0.554610i | ||||
\(543\) | −15.4601 | + | 3.38595i | −0.663458 | + | 0.145305i | ||||
\(544\) | 20.1264 | − | 34.8600i | 0.862914 | − | 1.49461i | ||||
\(545\) | −10.5237 | −0.450785 | ||||||||
\(546\) | −5.96931 | + | 8.89761i | −0.255463 | + | 0.380783i | ||||
\(547\) | − | 22.7953i | − | 0.974657i | −0.873219 | − | 0.487329i | \(-0.837971\pi\) | ||
0.873219 | − | 0.487329i | \(-0.162029\pi\) | |||||||
\(548\) | −4.10572 | − | 2.37044i | −0.175388 | − | 0.101260i | ||||
\(549\) | 28.4519 | + | 2.63602i | 1.21430 | + | 0.112503i | ||||
\(550\) | 7.93825 | − | 25.4151i | 0.338488 | − | 1.08370i | ||||
\(551\) | −0.786530 | − | 0.454104i | −0.0335073 | − | 0.0193455i | ||||
\(552\) | −7.42754 | − | 2.36281i | −0.316137 | − | 0.100568i | ||||
\(553\) | 7.37081 | − | 7.06575i | 0.313439 | − | 0.300466i | ||||
\(554\) | 51.3295i | 2.18078i | ||||||||
\(555\) | 24.6203 | − | 22.4447i | 1.04507 | − | 0.952726i | ||||
\(556\) | −16.1389 | + | 9.31782i | −0.684443 | + | 0.395163i | ||||
\(557\) | 9.05269 | + | 15.6797i | 0.383575 | + | 0.664371i | 0.991570 | − | 0.129569i | \(-0.0413595\pi\) |
−0.607995 | + | 0.793941i | \(0.708026\pi\) | |||||||
\(558\) | −32.5694 | + | 14.9849i | −1.37877 | + | 0.634362i | ||||
\(559\) | 2.87621 | 0.121651 | ||||||||
\(560\) | 9.06120 | + | 36.9200i | 0.382906 | + | 1.56016i | ||||
\(561\) | −29.5085 | + | 13.7647i | −1.24585 | + | 0.581147i | ||||
\(562\) | 0.121817 | − | 0.210993i | 0.00513853 | − | 0.00890019i | ||||
\(563\) | −12.5996 | − | 21.8232i | −0.531011 | − | 0.919737i | −0.999345 | − | 0.0361860i | \(-0.988479\pi\) |
0.468335 | − | 0.883551i | \(-0.344854\pi\) | |||||||
\(564\) | 6.12802 | + | 27.9804i | 0.258036 | + | 1.17819i | ||||
\(565\) | −12.1651 | + | 21.0706i | −0.511790 | + | 0.886446i | ||||
\(566\) | 54.4173i | 2.28733i | ||||||||
\(567\) | 13.0395 | + | 19.9242i | 0.547606 | + | 0.836736i | ||||
\(568\) | 6.97806i | 0.292793i | ||||||||
\(569\) | 5.47239 | − | 9.47846i | 0.229415 | − | 0.397358i | −0.728220 | − | 0.685343i | \(-0.759652\pi\) |
0.957635 | + | 0.287986i | \(0.0929855\pi\) | |||||||
\(570\) | 5.94990 | − | 1.30310i | 0.249214 | − | 0.0545807i | ||||
\(571\) | −13.1413 | + | 7.58714i | −0.549946 | + | 0.317512i | −0.749100 | − | 0.662456i | \(-0.769514\pi\) |
0.199154 | + | 0.979968i | \(0.436181\pi\) | |||||||
\(572\) | 1.38369 | + | 6.16294i | 0.0578552 | + | 0.257686i | ||||
\(573\) | 2.62070 | + | 0.833683i | 0.109481 | + | 0.0348276i | ||||
\(574\) | −35.6539 | − | 37.1933i | −1.48817 | − | 1.55242i | ||||
\(575\) | − | 21.7938i | − | 0.908865i | ||||||
\(576\) | −10.6464 | + | 4.89831i | −0.443599 | + | 0.204096i | ||||
\(577\) | −0.568986 | − | 0.985512i | −0.0236872 | − | 0.0410274i | 0.853939 | − | 0.520373i | \(-0.174207\pi\) |
−0.877626 | + | 0.479346i | \(0.840874\pi\) | |||||||
\(578\) | −14.2123 | − | 24.6164i | −0.591152 | − | 1.02391i | ||||
\(579\) | −16.6551 | + | 15.1834i | −0.692164 | + | 0.631001i | ||||
\(580\) | 6.88663i | 0.285952i | ||||||||
\(581\) | −11.5735 | + | 39.8089i | −0.480150 | + | 1.65155i | ||||
\(582\) | 9.07293 | − | 28.5209i | 0.376085 | − | 1.18223i | ||||
\(583\) | −2.16492 | − | 9.64251i | −0.0896619 | − | 0.399352i | ||||
\(584\) | 0.896215 | − | 0.517430i | 0.0370856 | − | 0.0214114i | ||||
\(585\) | −1.04870 | + | 11.3191i | −0.0433582 | + | 0.467987i | ||||
\(586\) | 4.50027 | − | 7.79470i | 0.185904 | − | 0.321996i | ||||
\(587\) | − | 21.1025i | − | 0.870991i | −0.900191 | − | 0.435496i | \(-0.856573\pi\) | ||
0.900191 | − | 0.435496i | \(-0.143427\pi\) | |||||||
\(588\) | −3.20060 | − | 18.2779i | −0.131990 | − | 0.753768i | ||||
\(589\) | 3.90906i | 0.161070i | ||||||||
\(590\) | 17.7781 | − | 30.7925i | 0.731911 | − | 1.26771i | ||||
\(591\) | 0.193758 | − | 0.0424352i | 0.00797014 | − | 0.00174555i | ||||
\(592\) | 14.9028 | + | 25.8124i | 0.612502 | + | 1.06089i | ||||
\(593\) | −17.5906 | + | 30.4678i | −0.722359 | + | 1.25116i | 0.237692 | + | 0.971341i | \(0.423609\pi\) |
−0.960052 | + | 0.279823i | \(0.909724\pi\) | |||||||
\(594\) | 31.8609 | + | 5.78194i | 1.30727 | + | 0.237236i | ||||
\(595\) | 43.8502 | + | 12.7484i | 1.79768 | + | 0.522635i | ||||
\(596\) | 32.8969 | 1.34751 | ||||||||
\(597\) | 27.8312 | + | 30.5289i | 1.13905 | + | 1.24946i | ||||
\(598\) | 5.96310 | + | 10.3284i | 0.243849 | + | 0.422359i | ||||
\(599\) | 5.52855 | − | 3.19191i | 0.225890 | − | 0.130418i | −0.382784 | − | 0.923838i | \(-0.625035\pi\) |
0.608675 | + | 0.793420i | \(0.291701\pi\) | |||||||
\(600\) | 4.39843 | + | 4.82477i | 0.179565 | + | 0.196970i | ||||
\(601\) | 10.8370i | 0.442050i | 0.975268 | + | 0.221025i | \(0.0709402\pi\) | ||||
−0.975268 | + | 0.221025i | \(0.929060\pi\) | |||||||
\(602\) | −8.29489 | + | 7.95158i | −0.338075 | + | 0.324082i | ||||
\(603\) | 11.3500 | + | 8.03424i | 0.462207 | + | 0.327179i | ||||
\(604\) | 30.4312 | + | 17.5694i | 1.23823 | + | 0.714890i | ||||
\(605\) | −14.3192 | − | 30.2811i | −0.582157 | − | 1.23110i | ||||
\(606\) | 34.9761 | − | 7.66016i | 1.42081 | − | 0.311173i | ||||
\(607\) | −19.0804 | − | 11.0161i | −0.774450 | − | 0.447129i | 0.0600101 | − | 0.998198i | \(-0.480887\pi\) |
−0.834460 | + | 0.551069i | \(0.814220\pi\) | |||||||
\(608\) | 4.36477i | 0.177015i | ||||||||
\(609\) | −0.455524 | + | 6.75623i | −0.0184587 | + | 0.273776i | ||||
\(610\) | −54.4958 | −2.20647 | ||||||||
\(611\) | −6.72289 | + | 11.6444i | −0.271979 | + | 0.471082i | ||||
\(612\) | −2.40088 | + | 25.9138i | −0.0970498 | + | 1.04751i | ||||
\(613\) | −2.01225 | + | 1.16177i | −0.0812739 | + | 0.0469235i | −0.540086 | − | 0.841610i | \(-0.681608\pi\) |
0.458812 | + | 0.888533i | \(0.348275\pi\) | |||||||
\(614\) | −23.8832 | − | 13.7890i | −0.963849 | − | 0.556478i | ||||
\(615\) | −52.0905 | − | 16.5707i | −2.10049 | − | 0.668197i | ||||
\(616\) | 6.45126 | + | 4.27914i | 0.259929 | + | 0.172412i | ||||
\(617\) | − | 6.99701i | − | 0.281689i | −0.990032 | − | 0.140845i | \(-0.955018\pi\) | ||
0.990032 | − | 0.140845i | \(-0.0449818\pi\) | |||||||
\(618\) | 5.45160 | + | 5.98003i | 0.219295 | + | 0.240552i | ||||
\(619\) | 6.40585 | + | 11.0953i | 0.257473 | + | 0.445956i | 0.965564 | − | 0.260165i | \(-0.0837768\pi\) |
−0.708091 | + | 0.706121i | \(0.750444\pi\) | |||||||
\(620\) | 25.6699 | − | 14.8205i | 1.03093 | − | 0.595207i | ||||
\(621\) | 26.3037 | − | 3.25771i | 1.05553 | − | 0.130727i | ||||
\(622\) | 28.7520i | 1.15285i | ||||||||
\(623\) | 2.63661 | − | 2.52748i | 0.105634 | − | 0.101262i | ||||
\(624\) | −9.69139 | − | 3.08297i | −0.387966 | − | 0.123418i | ||||
\(625\) | 14.0539 | − | 24.3421i | 0.562157 | − | 0.973685i | ||||
\(626\) | 18.6574 | + | 32.3156i | 0.745700 | + | 1.29159i | ||||
\(627\) | 2.02475 | − | 2.89245i | 0.0808609 | − | 0.115514i | ||||
\(628\) | 8.68139 | − | 15.0366i | 0.346425 | − | 0.600026i | ||||
\(629\) | 35.8036 | 1.42758 | ||||||||
\(630\) | −28.2684 | − | 35.5431i | −1.12624 | − | 1.41607i | ||||
\(631\) | −40.1391 | −1.59791 | −0.798957 | − | 0.601388i | \(-0.794615\pi\) | ||||
−0.798957 | + | 0.601388i | \(0.794615\pi\) | |||||||
\(632\) | 2.94852 | + | 1.70233i | 0.117286 | + | 0.0677149i | ||||
\(633\) | 2.13252 | + | 9.73701i | 0.0847599 | + | 0.387011i | ||||
\(634\) | −29.3444 | + | 16.9420i | −1.16542 | + | 0.672853i | ||||
\(635\) | −18.1593 | + | 31.4529i | −0.720631 | + | 1.24817i | ||||
\(636\) | −7.52709 | − | 2.39448i | −0.298468 | − | 0.0949472i | ||||
\(637\) | 4.67003 | − | 7.35280i | 0.185033 | − | 0.291328i | ||||
\(638\) | 6.23946 | + | 6.77251i | 0.247023 | + | 0.268126i | ||||
\(639\) | −9.91811 | − | 21.5568i | −0.392354 | − | 0.852775i | ||||
\(640\) | −18.0993 | + | 10.4496i | −0.715438 | + | 0.413058i | ||||
\(641\) | −42.8336 | + | 24.7300i | −1.69183 | + | 0.976776i | −0.738781 | + | 0.673946i | \(0.764598\pi\) |
−0.953045 | + | 0.302830i | \(0.902069\pi\) | |||||||
\(642\) | −30.2456 | − | 33.1773i | −1.19370 | − | 1.30940i | ||||
\(643\) | −9.38943 | −0.370283 | −0.185141 | − | 0.982712i | \(-0.559274\pi\) | ||||
−0.185141 | + | 0.982712i | \(0.559274\pi\) | |||||||
\(644\) | −19.8334 | − | 5.76609i | −0.781544 | − | 0.227216i | ||||
\(645\) | −3.69563 | + | 11.6173i | −0.145515 | + | 0.457430i | ||||
\(646\) | 5.66883 | + | 3.27290i | 0.223037 | + | 0.128770i | ||||
\(647\) | 26.9444 | − | 15.5564i | 1.05929 | − | 0.611584i | 0.134058 | − | 0.990974i | \(-0.457199\pi\) |
0.925237 | + | 0.379390i | \(0.123866\pi\) | |||||||
\(648\) | −5.16571 | + | 6.02981i | −0.202928 | + | 0.236873i | ||||
\(649\) | −4.51509 | − | 20.1101i | −0.177233 | − | 0.789390i | ||||
\(650\) | − | 9.98975i | − | 0.391830i | ||||||
\(651\) | 26.1642 | − | 12.8419i | 1.02546 | − | 0.503316i | ||||
\(652\) | −20.8021 | −0.814675 | ||||||||
\(653\) | −40.2088 | − | 23.2146i | −1.57349 | − | 0.908456i | −0.995736 | − | 0.0922467i | \(-0.970595\pi\) |
−0.577756 | − | 0.816210i | \(-0.696071\pi\) | |||||||
\(654\) | 2.40623 | + | 10.9868i | 0.0940909 | + | 0.429617i | ||||
\(655\) | −8.15442 | + | 4.70796i | −0.318620 | + | 0.183955i | ||||
\(656\) | 24.4519 | − | 42.3519i | 0.954685 | − | 1.65356i | ||||
\(657\) | −2.03318 | + | 2.87227i | −0.0793218 | + | 0.112058i | ||||
\(658\) | −12.8035 | − | 52.1682i | −0.499133 | − | 2.03373i | ||||
\(659\) | −0.495294 | −0.0192939 | −0.00964695 | − | 0.999953i | \(-0.503071\pi\) | ||||
−0.00964695 | + | 0.999953i | \(0.503071\pi\) | |||||||
\(660\) | −26.6706 | − | 2.32986i | −1.03815 | − | 0.0906897i | ||||
\(661\) | 20.7038 | + | 35.8600i | 0.805283 | + | 1.39479i | 0.916100 | + | 0.400951i | \(0.131320\pi\) |
−0.110816 | + | 0.993841i | \(0.535346\pi\) | |||||||
\(662\) | −15.9832 | − | 27.6837i | −0.621204 | − | 1.07596i | ||||
\(663\) | −9.02803 | + | 8.23027i | −0.350620 | + | 0.319637i | ||||
\(664\) | −13.8238 | −0.536466 | ||||||||
\(665\) | −4.80899 | + | 1.18026i | −0.186485 | + | 0.0457686i | ||||
\(666\) | −29.0618 | − | 20.5718i | −1.12612 | − | 0.797141i | ||||
\(667\) | 6.52756 | + | 3.76869i | 0.252748 | + | 0.145924i | ||||
\(668\) | 5.03450 | + | 8.72000i | 0.194791 | + | 0.337387i | ||||
\(669\) | 18.4607 | − | 4.04311i | 0.713733 | − | 0.156316i | ||||
\(670\) | −22.9680 | − | 13.2606i | −0.887330 | − | 0.512300i | ||||
\(671\) | −23.2327 | + | 21.4041i | −0.896888 | + | 0.826296i | ||||
\(672\) | 29.2144 | − | 14.3390i | 1.12697 | − | 0.553140i | ||||
\(673\) | − | 16.3937i | − | 0.631930i | −0.948771 | − | 0.315965i | \(-0.897672\pi\) | ||
0.948771 | − | 0.315965i | \(-0.102328\pi\) | |||||||
\(674\) | −38.0936 | − | 21.9933i | −1.46731 | − | 0.847151i | ||||
\(675\) | −20.4453 | − | 8.65322i | −0.786941 | − | 0.333063i | ||||
\(676\) | −8.76317 | − | 15.1783i | −0.337045 | − | 0.583779i | ||||
\(677\) | −3.90912 | + | 6.77079i | −0.150239 | + | 0.260222i | −0.931315 | − | 0.364214i | \(-0.881338\pi\) |
0.781076 | + | 0.624436i | \(0.214671\pi\) | |||||||
\(678\) | 24.7793 | + | 7.88267i | 0.951645 | + | 0.302732i | ||||
\(679\) | −6.79258 | + | 23.3641i | −0.260675 | + | 0.896632i | ||||
\(680\) | 15.2271i | 0.583934i | ||||||||
\(681\) | 9.44933 | + | 10.3653i | 0.362099 | + | 0.397198i | ||||
\(682\) | 11.8168 | − | 37.8326i | 0.452488 | − | 1.44868i | ||||
\(683\) | 25.9035 | − | 14.9554i | 0.991171 | − | 0.572253i | 0.0855471 | − | 0.996334i | \(-0.472736\pi\) |
0.905624 | + | 0.424081i | \(0.139403\pi\) | |||||||
\(684\) | −1.17951 | − | 2.56364i | −0.0450997 | − | 0.0980234i | ||||
\(685\) | 9.43266 | 0.360403 | ||||||||
\(686\) | 6.85934 | + | 34.1160i | 0.261891 | + | 1.30256i | ||||
\(687\) | 0.475118 | − | 1.49354i | 0.0181269 | − | 0.0569822i | ||||
\(688\) | −9.44537 | − | 5.45329i | −0.360101 | − | 0.207905i | ||||
\(689\) | −1.85391 | − | 3.21106i | −0.0706283 | − | 0.122332i | ||||
\(690\) | −49.3793 | + | 10.8146i | −1.87984 | + | 0.411706i | ||||
\(691\) | −8.58042 | + | 14.8617i | −0.326415 | + | 0.565367i | −0.981798 | − | 0.189930i | \(-0.939174\pi\) |
0.655383 | + | 0.755297i | \(0.272507\pi\) | |||||||
\(692\) | 3.50763 | 0.133340 | ||||||||
\(693\) | −26.0115 | − | 4.04990i | −0.988095 | − | 0.153843i | ||||
\(694\) | −43.1594 | −1.63831 | ||||||||
\(695\) | 18.5391 | − | 32.1107i | 0.703229 | − | 1.21803i | ||||
\(696\) | −2.20568 | + | 0.483069i | −0.0836062 | + | 0.0183107i | ||||
\(697\) | −29.3724 | − | 50.8746i | −1.11256 | − | 1.92701i | ||||
\(698\) | 16.3017 | + | 9.41180i | 0.617029 | + | 0.356242i | ||||
\(699\) | 0.209090 | − | 0.657278i | 0.00790851 | − | 0.0248606i | ||||
\(700\) | 11.9724 | + | 12.4893i | 0.452513 | + | 0.472051i | ||||
\(701\) | 26.0963 | 0.985644 | 0.492822 | − | 0.870130i | \(-0.335965\pi\) | ||||
0.492822 | + | 0.870130i | \(0.335965\pi\) | |||||||
\(702\) | 12.0570 | − | 1.49325i | 0.455061 | − | 0.0563592i | ||||
\(703\) | −3.36218 | + | 1.94116i | −0.126807 | + | 0.0732122i | ||||
\(704\) | 3.86270 | − | 12.3668i | 0.145581 | − | 0.466092i | ||||
\(705\) | −38.3946 | − | 42.1162i | −1.44602 | − | 1.58619i | ||||
\(706\) | − | 9.95083i | − | 0.374505i | ||||||
\(707\) | −28.2693 | + | 6.93809i | −1.06318 | + | 0.260934i | ||||
\(708\) | −15.6982 | − | 4.99384i | −0.589976 | − | 0.187680i | ||||
\(709\) | −17.8611 | + | 30.9363i | −0.670786 | + | 1.16184i | 0.306895 | + | 0.951743i | \(0.400710\pi\) |
−0.977681 | + | 0.210093i | \(0.932623\pi\) | |||||||
\(710\) | 22.6280 | + | 39.1928i | 0.849213 | + | 1.47088i | ||||
\(711\) | −11.5282 | − | 1.06807i | −0.432342 | − | 0.0400558i | ||||
\(712\) | 1.05471 | + | 0.608938i | 0.0395270 | + | 0.0228209i | ||||
\(713\) | − | 32.4420i | − | 1.21496i | ||||||
\(714\) | 3.28313 | − | 48.6947i | 0.122868 | − | 1.82235i | ||||
\(715\) | −8.51525 | − | 9.24272i | −0.318452 | − | 0.345658i | ||||
\(716\) | −18.7823 | − | 10.8440i | −0.701928 | − | 0.405258i | ||||
\(717\) | −31.9452 | + | 6.99637i | −1.19302 | + | 0.261284i | ||||
\(718\) | −5.62161 | − | 9.73692i | −0.209797 | − | 0.363378i | ||||
\(719\) | 15.2790 | + | 8.82134i | 0.569811 | + | 0.328980i | 0.757074 | − | 0.653329i | \(-0.226628\pi\) |
−0.187263 | + | 0.982310i | \(0.559962\pi\) | |||||||
\(720\) | 24.9048 | − | 35.1831i | 0.928149 | − | 1.31120i | ||||
\(721\) | −4.55240 | − | 4.74896i | −0.169540 | − | 0.176860i | ||||
\(722\) | 34.9904 | 1.30221 | ||||||||
\(723\) | −3.87193 | + | 3.52978i | −0.143998 | + | 0.131274i | ||||
\(724\) | −6.99234 | − | 12.1111i | −0.259868 | − | 0.450105i | ||||
\(725\) | −3.15677 | − | 5.46768i | −0.117239 | − | 0.203065i | ||||
\(726\) | −28.3396 | + | 21.8730i | −1.05178 | + | 0.811784i | ||||
\(727\) | −9.23458 | −0.342492 | −0.171246 | − | 0.985228i | \(-0.554779\pi\) | ||||
−0.171246 | + | 0.985228i | \(0.554779\pi\) | |||||||
\(728\) | 2.78902 | + | 0.810843i | 0.103368 | + | 0.0300518i | ||||
\(729\) | 7.38773 | − | 25.9696i | 0.273620 | − | 0.961838i | ||||
\(730\) | 3.35577 | − | 5.81237i | 0.124203 | − | 0.215125i | ||||
\(731\) | −11.3461 | + | 6.55068i | −0.419651 | + | 0.242286i | ||||
\(732\) | 5.40163 | + | 24.6637i | 0.199650 | + | 0.911597i | ||||
\(733\) | −6.55078 | − | 3.78209i | −0.241958 | − | 0.139695i | 0.374118 | − | 0.927381i | \(-0.377945\pi\) |
−0.616077 | + | 0.787686i | \(0.711279\pi\) | |||||||
\(734\) | 36.9438 | 1.36362 | ||||||||
\(735\) | 23.6981 | + | 28.3103i | 0.874119 | + | 1.04424i | ||||
\(736\) | − | 36.2240i | − | 1.33523i | ||||||
\(737\) | −15.0000 | + | 3.36778i | −0.552533 | + | 0.124054i | ||||
\(738\) | −5.38951 | + | 58.1716i | −0.198391 | + | 2.14133i | ||||
\(739\) | −10.4826 | + | 6.05211i | −0.385607 | + | 0.222631i | −0.680255 | − | 0.732975i | \(-0.738131\pi\) |
0.294648 | + | 0.955606i | \(0.404798\pi\) | |||||||
\(740\) | 25.4943 | + | 14.7191i | 0.937189 | + | 0.541086i | ||||
\(741\) | 0.401571 | − | 1.26235i | 0.0147521 | − | 0.0463735i | ||||
\(742\) | 14.2239 | + | 4.13528i | 0.522177 | + | 0.151811i | ||||
\(743\) | 42.7206 | 1.56727 | 0.783633 | − | 0.621224i | \(-0.213364\pi\) | ||||
0.783633 | + | 0.621224i | \(0.213364\pi\) | |||||||
\(744\) | 6.54744 | + | 7.18209i | 0.240041 | + | 0.263308i | ||||
\(745\) | −56.6840 | + | 32.7265i | −2.07674 | + | 1.19901i | ||||
\(746\) | 31.5885 | − | 18.2377i | 1.15654 | − | 0.667728i | ||||
\(747\) | 42.7048 | − | 19.6481i | 1.56249 | − | 0.718887i | ||||
\(748\) | −19.4948 | − | 21.1602i | −0.712799 | − | 0.773695i | ||||
\(749\) | 25.2568 | + | 26.3473i | 0.922865 | + | 0.962710i | ||||
\(750\) | −6.86933 | − | 2.18524i | −0.250833 | − | 0.0797935i | ||||
\(751\) | 22.0949 | − | 38.2695i | 0.806255 | − | 1.39647i | −0.109186 | − | 0.994021i | \(-0.534824\pi\) |
0.915441 | − | 0.402453i | \(-0.131842\pi\) | |||||||
\(752\) | 44.1555 | − | 25.4932i | 1.61018 | − | 0.929641i | ||||
\(753\) | −2.89132 | − | 13.2017i | −0.105366 | − | 0.481097i | ||||
\(754\) | 2.99207 | + | 1.72747i | 0.108965 | + | 0.0629109i | ||||
\(755\) | −69.9138 | −2.54442 | ||||||||
\(756\) | −13.2841 | + | 16.3167i | −0.483139 | + | 0.593434i | ||||
\(757\) | 41.7862 | 1.51875 | 0.759373 | − | 0.650656i | \(-0.225506\pi\) | ||||
0.759373 | + | 0.650656i | \(0.225506\pi\) | |||||||
\(758\) | −2.61467 | + | 4.52875i | −0.0949692 | + | 0.164491i | ||||
\(759\) | −16.8038 | + | 24.0050i | −0.609939 | + | 0.871326i | ||||
\(760\) | −0.825567 | − | 1.42992i | −0.0299465 | − | 0.0518688i | ||||
\(761\) | −19.0611 | + | 33.0148i | −0.690965 | + | 1.19679i | 0.280556 | + | 0.959838i | \(0.409481\pi\) |
−0.971522 | + | 0.236950i | \(0.923852\pi\) | |||||||
\(762\) | 36.9891 | + | 11.7668i | 1.33997 | + | 0.426265i | ||||
\(763\) | −2.17941 | − | 8.88004i | −0.0788999 | − | 0.321479i | ||||
\(764\) | 2.43005i | 0.0879161i | ||||||||
\(765\) | −21.6427 | − | 47.0401i | −0.782495 | − | 1.70074i | ||||
\(766\) | −13.4602 | + | 7.77125i | −0.486337 | + | 0.280787i | ||||
\(767\) | −3.86645 | − | 6.69688i | −0.139609 | − | 0.241810i | ||||
\(768\) | 24.1645 | + | 26.5068i | 0.871961 | + | 0.956481i | ||||
\(769\) | 36.9953i | 1.33408i | 0.745020 | + | 0.667042i | \(0.232440\pi\) | ||||
−0.745020 | + | 0.667042i | \(0.767560\pi\) | |||||||
\(770\) | 50.1101 | + | 3.11443i | 1.80584 | + | 0.112236i | ||||
\(771\) | 17.1998 | + | 5.47151i | 0.619436 | + | 0.197052i | ||||
\(772\) | −17.2464 | − | 9.95719i | −0.620710 | − | 0.358367i | ||||
\(773\) | −36.9288 | + | 21.3208i | −1.32824 | + | 0.766857i | −0.985027 | − | 0.172402i | \(-0.944847\pi\) |
−0.343209 | + | 0.939259i | \(0.611514\pi\) | |||||||
\(774\) | 12.9735 | + | 1.20198i | 0.466323 | + | 0.0432041i | ||||
\(775\) | −13.5872 | + | 23.5337i | −0.488067 | + | 0.845356i | ||||
\(776\) | −8.11327 | −0.291249 | ||||||||
\(777\) | 24.0380 | + | 16.1268i | 0.862357 | + | 0.578545i | ||||
\(778\) | 36.3732i | 1.30404i | ||||||||
\(779\) | 5.51652 | + | 3.18496i | 0.197650 | + | 0.114113i | ||||
\(780\) | −9.81203 | + | 2.14895i | −0.351327 | + | 0.0769446i | ||||
\(781\) | 25.0404 | + | 7.82121i | 0.896015 | + | 0.279865i | ||||
\(782\) | −47.0466 | − | 27.1624i | −1.68238 | − | 0.971324i | ||||
\(783\) | 6.12726 | − | 4.62731i | 0.218970 | − | 0.165367i | ||||
\(784\) | −29.2771 | + | 15.2919i | −1.04561 | + | 0.546141i | ||||
\(785\) | 34.5457i | 1.23299i | ||||||||
\(786\) | 6.77963 | + | 7.43679i | 0.241821 | + | 0.265261i | ||||
\(787\) | 40.3211 | − | 23.2794i | 1.43729 | − | 0.829820i | 0.439630 | − | 0.898179i | \(-0.355110\pi\) |
0.997661 | + | 0.0683592i | \(0.0217764\pi\) | |||||||
\(788\) | 0.0876332 | + | 0.151785i | 0.00312180 | + | 0.00540712i | ||||
\(789\) | 36.0681 | + | 39.5642i | 1.28406 | + | 1.40852i | ||||
\(790\) | 22.0808 | 0.785598 | ||||||||
\(791\) | −20.2990 | − | 5.90147i | −0.721750 | − | 0.209832i | ||||
\(792\) | −1.12462 | − | 8.70563i | −0.0399615 | − | 0.309341i | ||||
\(793\) | −5.92599 | + | 10.2641i | −0.210438 | + | 0.364489i | ||||
\(794\) | 13.1841 | + | 22.8356i | 0.467888 | + | 0.810406i | ||||
\(795\) | 15.3519 | − | 3.36223i | 0.544474 | − | 0.119246i | ||||
\(796\) | −18.2515 | + | 31.6126i | −0.646908 | + | 1.12048i | ||||
\(797\) | − | 43.3952i | − | 1.53714i | −0.639768 | − | 0.768568i | \(-0.720970\pi\) | ||
0.639768 | − | 0.768568i | \(-0.279030\pi\) | |||||||
\(798\) | 2.33177 | + | 4.75075i | 0.0825438 | + | 0.168175i | ||||
\(799\) | − | 61.2466i | − | 2.16675i | ||||||
\(800\) | −15.1712 | + | 26.2772i | −0.536382 | + | 0.929040i | ||||
\(801\) | −4.12375 | − | 0.382059i | −0.145706 | − | 0.0134994i | ||||
\(802\) | 20.9703 | − | 12.1072i | 0.740487 | − | 0.427520i | ||||
\(803\) | −0.852265 | − | 3.79597i | −0.0300758 | − | 0.133957i | ||||
\(804\) | −3.72488 | + | 11.7092i | −0.131366 | + | 0.412953i | ||||
\(805\) | 39.9107 | − | 9.79520i | 1.40667 | − | 0.345235i | ||||
\(806\) | − | 14.8706i | − | 0.523795i | ||||||
\(807\) | 10.3537 | − | 9.43881i | 0.364468 | − | 0.332262i | ||||
\(808\) | −4.85304 | − | 8.40572i | −0.170729 | − | 0.295712i | ||||
\(809\) | −21.0777 | − | 36.5077i | −0.741053 | − | 1.28354i | −0.952016 | − | 0.306048i | \(-0.900993\pi\) |
0.210963 | − | 0.977494i | \(-0.432340\pi\) | |||||||
\(810\) | −9.46055 | + | 50.6179i | −0.332410 | + | 1.77853i | ||||
\(811\) | − | 37.2022i | − | 1.30635i | −0.757209 | − | 0.653173i | \(-0.773437\pi\) | ||
0.757209 | − | 0.653173i | \(-0.226563\pi\) | |||||||
\(812\) | −5.81104 | + | 1.42619i | −0.203927 | + | 0.0500495i | ||||
\(813\) | 22.6845 | + | 7.21626i | 0.795579 | + | 0.253085i | ||||
\(814\) | 38.4078 | − | 8.62326i | 1.34619 | − | 0.302245i | ||||
\(815\) | 35.8438 | − | 20.6944i | 1.25555 | − | 0.724894i | ||||
\(816\) | 45.2523 | − | 9.91077i | 1.58415 | − | 0.346946i | ||||
\(817\) | 0.710315 | − | 1.23030i | 0.0248508 | − | 0.0430428i | ||||
\(818\) | 13.3903i | 0.468180i | ||||||||
\(819\) | −9.76839 | + | 1.45923i | −0.341335 | + | 0.0509896i | ||||
\(820\) | − | 48.3010i | − | 1.68674i | ||||||
\(821\) | 10.8482 | − | 18.7896i | 0.378604 | − | 0.655761i | −0.612256 | − | 0.790660i | \(-0.709738\pi\) |
0.990859 | + | 0.134899i | \(0.0430710\pi\) | |||||||
\(822\) | −2.15677 | − | 9.84774i | −0.0752259 | − | 0.343479i | ||||
\(823\) | 9.74375 | + | 16.8767i | 0.339646 | + | 0.588284i | 0.984366 | − | 0.176135i | \(-0.0563595\pi\) |
−0.644720 | + | 0.764419i | \(0.723026\pi\) | |||||||
\(824\) | 1.09680 | − | 1.89971i | 0.0382087 | − | 0.0661794i | ||||
\(825\) | 22.2433 | − | 10.3758i | 0.774412 | − | 0.361238i | ||||
\(826\) | 29.6649 | + | 8.62439i | 1.03217 | + | 0.300081i | ||||
\(827\) | −38.2080 | −1.32862 | −0.664311 | − | 0.747457i | \(-0.731275\pi\) | ||||
−0.664311 | + | 0.747457i | \(0.731275\pi\) | |||||||
\(828\) | 9.78897 | + | 21.2761i | 0.340190 | + | 0.739397i | ||||
\(829\) | −7.92313 | − | 13.7233i | −0.275182 | − | 0.476629i | 0.694999 | − | 0.719010i | \(-0.255405\pi\) |
−0.970181 | + | 0.242382i | \(0.922071\pi\) | |||||||
\(830\) | −77.6423 | + | 44.8268i | −2.69500 | + | 1.55596i | ||||
\(831\) | −34.9669 | + | 31.8771i | −1.21299 | + | 1.10580i | ||||
\(832\) | − | 4.86094i | − | 0.168523i | ||||||
\(833\) | −1.67613 | + | 39.6416i | −0.0580745 | + | 1.37350i | ||||
\(834\) | −37.7627 | − | 12.0129i | −1.30761 | − | 0.415971i | ||||
\(835\) | −17.3497 | − | 10.0168i | −0.600411 | − | 0.346647i | ||||
\(836\) | 2.97792 | + | 0.930137i | 0.102994 | + | 0.0321694i | ||||
\(837\) | −30.4346 | − | 12.8811i | −1.05198 | − | 0.445235i | ||||
\(838\) | 45.2671 | + | 26.1350i | 1.56372 | + | 0.902817i | ||||
\(839\) | 20.1527i | 0.695748i | 0.937541 | + | 0.347874i | \(0.113096\pi\) | ||||
−0.937541 | + | 0.347874i | \(0.886904\pi\) | |||||||
\(840\) | −6.85866 | + | 10.2233i | −0.236646 | + | 0.352736i | ||||
\(841\) | −26.8165 | −0.924706 | ||||||||
\(842\) | 16.4692 | − | 28.5255i | 0.567567 | − | 0.983055i | ||||
\(843\) | 0.219385 | − | 0.0480478i | 0.00755603 | − | 0.00165485i | ||||
\(844\) | −7.62773 | + | 4.40387i | −0.262557 | + | 0.151587i | ||||
\(845\) | 30.1993 | + | 17.4356i | 1.03889 | + | 0.599802i | ||||
\(846\) | −35.1907 | + | 49.7140i | −1.20988 | + | 1.70920i | ||||
\(847\) | 22.5862 | − | 18.3538i | 0.776072 | − | 0.630644i | ||||
\(848\) | 14.0600i | 0.482823i | ||||||||
\(849\) | −37.0704 | + | 33.7947i | −1.27225 | + | 1.15983i | ||||
\(850\) | 22.7520 | + | 39.4077i | 0.780388 | + | 1.35167i | ||||
\(851\) | 27.9034 | − | 16.1100i | 0.956515 | − | 0.552244i | ||||
\(852\) | 15.4950 | − | 14.1258i | 0.530850 | − | 0.483941i | ||||
\(853\) | − | 20.6654i | − | 0.707570i | −0.935327 | − | 0.353785i | \(-0.884894\pi\) | ||
0.935327 | − | 0.353785i | \(-0.115106\pi\) | |||||||
\(854\) | −11.2858 | − | 45.9844i | −0.386194 | − | 1.57355i | ||||
\(855\) | 4.58276 | + | 3.24396i | 0.156727 | + | 0.110941i | ||||
\(856\) | −6.08505 | + | 10.5396i | −0.207983 | + | 0.360237i | ||||
\(857\) | −2.12306 | − | 3.67725i | −0.0725224 | − | 0.125612i | 0.827484 | − | 0.561490i | \(-0.189772\pi\) |
−0.900006 | + | 0.435877i | \(0.856438\pi\) | |||||||
\(858\) | −7.70245 | + | 11.0033i | −0.262957 | + | 0.375646i | ||||
\(859\) | 11.1034 | − | 19.2317i | 0.378844 | − | 0.656177i | −0.612050 | − | 0.790819i | \(-0.709655\pi\) |
0.990894 | + | 0.134642i | \(0.0429884\pi\) | |||||||
\(860\) | −10.7721 | −0.367327 | ||||||||
\(861\) | 3.19492 | − | 47.3864i | 0.108883 | − | 1.61493i | ||||
\(862\) | 24.2677 | 0.826563 | ||||||||
\(863\) | −15.9992 | − | 9.23715i | −0.544619 | − | 0.314436i | 0.202330 | − | 0.979317i | \(-0.435149\pi\) |
−0.746949 | + | 0.664881i | \(0.768482\pi\) | |||||||
\(864\) | −33.9826 | − | 14.3827i | −1.15611 | − | 0.489310i | ||||
\(865\) | −6.04393 | + | 3.48946i | −0.205500 | + | 0.118645i | ||||
\(866\) | −6.57381 | + | 11.3862i | −0.223387 | + | 0.386918i | ||||
\(867\) | 7.94308 | − | 24.9692i | 0.269761 | − | 0.847999i | ||||
\(868\) | 17.8219 | + | 18.5914i | 0.604915 | + | 0.631033i | ||||
\(869\) | 9.41349 | − | 8.67257i | 0.319331 | − | 0.294197i | ||||
\(870\) | −10.8219 | + | 9.86563i | −0.366897 | + | 0.334476i | ||||
\(871\) | −4.99517 | + | 2.88396i | −0.169255 | + | 0.0977194i | ||||
\(872\) | 2.64042 | − | 1.52445i | 0.0894160 | − | 0.0516244i | ||||
\(873\) | 25.0637 | − | 11.5316i | 0.848279 | − | 0.390286i | ||||
\(874\) | 5.89064 | 0.199254 | ||||||||
\(875\) | 5.62730 | + | 1.63601i | 0.190237 | + | 0.0553071i | ||||
\(876\) | −2.96319 | − | 0.942633i | −0.100117 | − | 0.0318486i | ||||
\(877\) | −13.8416 | − | 7.99143i | −0.467396 | − | 0.269851i | 0.247753 | − | 0.968823i | \(-0.420308\pi\) |
−0.715149 | + | 0.698972i | \(0.753641\pi\) | |||||||
\(878\) | −19.1297 | + | 11.0445i | −0.645596 | + | 0.372735i | ||||
\(879\) | 8.10474 | − | 1.77503i | 0.273366 | − | 0.0598702i | ||||
\(880\) | 10.4396 | + | 46.4977i | 0.351918 | + | 1.56744i | ||||
\(881\) | 12.5797i | 0.423819i | 0.977289 | + | 0.211910i | \(0.0679683\pi\) | ||||
−0.977289 | + | 0.211910i | \(0.932032\pi\) | |||||||
\(882\) | 24.1375 | − | 31.2141i | 0.812753 | − | 1.05103i | ||||
\(883\) | 4.39614 | 0.147942 | 0.0739710 | − | 0.997260i | \(-0.476433\pi\) | ||||
0.0739710 | + | 0.997260i | \(0.476433\pi\) | |||||||
\(884\) | −9.34851 | − | 5.39736i | −0.314424 | − | 0.181533i | ||||
\(885\) | 32.0173 | − | 7.01215i | 1.07625 | − | 0.235711i | ||||
\(886\) | −15.5938 | + | 9.00311i | −0.523885 | + | 0.302465i | ||||
\(887\) | 4.55516 | − | 7.88976i | 0.152947 | − | 0.264912i | −0.779362 | − | 0.626573i | \(-0.784457\pi\) |
0.932310 | + | 0.361661i | \(0.117790\pi\) | |||||||
\(888\) | −2.92600 | + | 9.19793i | −0.0981900 | + | 0.308662i | ||||
\(889\) | −30.3011 | − | 8.80936i | −1.01627 | − | 0.295456i | ||||
\(890\) | 7.89850 | 0.264758 | ||||||||
\(891\) | 15.8477 | + | 25.2952i | 0.530920 | + | 0.847422i | ||||
\(892\) | 8.34944 | + | 14.4617i | 0.279560 | + | 0.484212i | ||||
\(893\) | 3.32060 | + | 5.75145i | 0.111120 | + | 0.192465i | ||||
\(894\) | 47.1274 | + | 51.6955i | 1.57617 | + | 1.72895i | ||||
\(895\) | 43.1513 | 1.44239 | ||||||||
\(896\) | −12.5659 | − | 13.1084i | −0.419796 | − | 0.437921i | ||||
\(897\) | −3.33271 | + | 10.4764i | −0.111276 | + | 0.349798i | ||||
\(898\) | 48.9623 | + | 28.2684i | 1.63389 | + | 0.943328i | ||||
\(899\) | −4.69912 | − | 8.13912i | −0.156724 | − | 0.271455i | ||||
\(900\) | 1.80977 | − | 19.5337i | 0.0603255 | − | 0.651123i | ||||
\(901\) | 14.6266 | + | 8.44469i | 0.487284 | + | 0.281333i | ||||
\(902\) | −43.7620 | − | 47.5007i | −1.45711 | − | 1.58160i | ||||
\(903\) | −10.5682 | − | 0.712536i | −0.351687 | − | 0.0237117i | ||||
\(904\) | − | 7.04890i | − | 0.234443i | ||||||
\(905\) | 24.0967 | + | 13.9123i | 0.801003 | + | 0.462459i | ||||
\(906\) | 15.9857 | + | 72.9904i | 0.531090 | + | 2.42494i | ||||
\(907\) | 15.1268 | + | 26.2004i | 0.502278 | + | 0.869970i | 0.999997 | + | 0.00263193i | \(0.000837770\pi\) |
−0.497719 | + | 0.867338i | \(0.665829\pi\) | |||||||
\(908\) | −6.19682 | + | 10.7332i | −0.205649 | + | 0.356194i | ||||
\(909\) | 26.9394 | + | 19.0694i | 0.893525 | + | 0.632493i | ||||
\(910\) | 18.2941 | − | 4.48988i | 0.606443 | − | 0.148838i | ||||
\(911\) | 19.0232i | 0.630267i | 0.949047 | + | 0.315134i | \(0.102049\pi\) | ||||
−0.949047 | + | 0.315134i | \(0.897951\pi\) | |||||||
\(912\) | −3.71215 | + | 3.38412i | −0.122922 | + | 0.112060i | ||||
\(913\) | −15.4941 | + | 49.6058i | −0.512779 | + | 1.64171i | ||||
\(914\) | 66.6661 | − | 38.4897i | 2.20512 | − | 1.27313i | ||||
\(915\) | −33.8434 | − | 37.1239i | −1.11883 | − | 1.22728i | ||||
\(916\) | 1.38489 | 0.0457581 | ||||||||
\(917\) | −5.66139 | − | 5.90582i | −0.186956 | − | 0.195027i | ||||
\(918\) | −44.1615 | + | 33.3508i | −1.45755 | + | 1.10074i | ||||
\(919\) | 23.5991 | + | 13.6250i | 0.778463 | + | 0.449446i | 0.835885 | − | 0.548904i | \(-0.184955\pi\) |
−0.0574223 | + | 0.998350i | \(0.518288\pi\) | |||||||
\(920\) | 6.85153 | + | 11.8672i | 0.225888 | + | 0.391250i | ||||
\(921\) | −5.43875 | − | 24.8332i | −0.179213 | − | 0.818282i | ||||
\(922\) | −5.12899 | + | 8.88368i | −0.168914 | + | 0.292568i | ||||
\(923\) | 9.84246 | 0.323968 | ||||||||
\(924\) | −3.55740 | − | 22.9876i | −0.117030 | − | 0.756235i | ||||
\(925\) | −26.9885 | −0.887376 | ||||||||
\(926\) | −6.05063 | + | 10.4800i | −0.198836 | + | 0.344394i | ||||
\(927\) | −0.688150 | + | 7.42753i | −0.0226018 | + | 0.243952i | ||||
\(928\) | −5.24693 | − | 9.08796i | −0.172239 | − | 0.298327i | ||||
\(929\) | −16.4471 | − | 9.49571i | −0.539610 | − | 0.311544i | 0.205311 | − | 0.978697i | \(-0.434180\pi\) |
−0.744921 | + | 0.667153i | \(0.767513\pi\) | |||||||
\(930\) | 60.0638 | + | 19.1072i | 1.96957 | + | 0.626549i | ||||
\(931\) | −1.99184 | − | 3.81347i | −0.0652800 | − | 0.124982i | ||||
\(932\) | 0.609463 | 0.0199636 | ||||||||
\(933\) | −19.5866 | + | 17.8558i | −0.641236 | + | 0.584573i | ||||
\(934\) | 4.88479 | − | 2.82023i | 0.159835 | − | 0.0922809i | ||||
\(935\) | 54.6417 | + | 17.0670i | 1.78697 | + | 0.558151i | ||||
\(936\) | −1.37655 | − | 2.99191i | −0.0449939 | − | 0.0977935i | ||||
\(937\) | 33.4823i | 1.09382i | 0.837192 | + | 0.546909i | \(0.184196\pi\) | ||||
−0.837192 | + | 0.546909i | \(0.815804\pi\) | |||||||
\(938\) | 6.43289 | − | 22.1269i | 0.210041 | − | 0.722469i | ||||
\(939\) | −10.4274 | + | 32.7788i | −0.340286 | + | 1.06970i | ||||
\(940\) | 25.1790 | − | 43.6112i | 0.821247 | − | 1.42244i | ||||
\(941\) | −10.3259 | − | 17.8849i | −0.336613 | − | 0.583031i | 0.647180 | − | 0.762337i | \(-0.275948\pi\) |
−0.983793 | + | 0.179306i | \(0.942615\pi\) | |||||||
\(942\) | 36.0659 | − | 7.89884i | 1.17509 | − | 0.257358i | ||||
\(943\) | −45.7826 | − | 26.4326i | −1.49089 | − | 0.860763i | ||||
\(944\) | 29.3231i | 0.954385i | ||||||||
\(945\) | 6.65739 | − | 41.3304i | 0.216565 | − | 1.34448i | ||||
\(946\) | −10.5937 | + | 9.75985i | −0.344429 | + | 0.317320i | ||||
\(947\) | 34.0101 | + | 19.6358i | 1.10518 | + | 0.638077i | 0.937577 | − | 0.347778i | \(-0.113064\pi\) |
0.167604 | + | 0.985854i | \(0.446397\pi\) | |||||||
\(948\) | −2.18865 | − | 9.99331i | −0.0710840 | − | 0.324568i | ||||
\(949\) | −0.729828 | − | 1.26410i | −0.0236912 | − | 0.0410344i | ||||
\(950\) | −4.27312 | − | 2.46709i | −0.138638 | − | 0.0800429i | ||||
\(951\) | −29.7650 | − | 9.46870i | −0.965198 | − | 0.307043i | ||||
\(952\) | −12.8489 | + | 3.15347i | −0.416434 | + | 0.102205i | ||||
\(953\) | −7.71381 | −0.249875 | −0.124937 | − | 0.992165i | \(-0.539873\pi\) | ||||
−0.124937 | + | 0.992165i | \(0.539873\pi\) | |||||||
\(954\) | −7.02037 | − | 15.2586i | −0.227293 | − | 0.494017i | ||||
\(955\) | −2.41746 | − | 4.18717i | −0.0782273 | − | 0.135494i | ||||
\(956\) | −14.4482 | − | 25.0251i | −0.467290 | − | 0.809369i | ||||
\(957\) | −0.738725 | + | 8.45641i | −0.0238796 | + | 0.273357i | ||||
\(958\) | −40.4118 | −1.30565 | ||||||||
\(959\) | 1.95346 | + | 7.95941i | 0.0630806 | + | 0.257023i | ||||
\(960\) | 19.6338 | + | 6.24580i | 0.633679 | + | 0.201582i | ||||
\(961\) | −4.72573 | + | 8.18520i | −0.152443 | + | 0.264039i | ||||
\(962\) | 12.7902 | − | 7.38443i | 0.412373 | − | 0.238084i | ||||
\(963\) | 3.81787 | − | 41.2081i | 0.123029 | − | 1.32791i | ||||
\(964\) | −4.00937 | − | 2.31481i | −0.129133 | − | 0.0745551i | ||||
\(965\) | 39.6225 | 1.27549 | ||||||||
\(966\) | −19.3518 | − | 39.4273i | −0.622633 | − | 1.26855i | ||||
\(967\) | − | 15.1529i | − | 0.487283i | −0.969865 | − | 0.243642i | \(-0.921658\pi\) | ||
0.969865 | − | 0.243642i | \(-0.0783421\pi\) | |||||||
\(968\) | 7.97922 | + | 5.52337i | 0.256462 | + | 0.177528i | ||||
\(969\) | 1.29092 | + | 5.89431i | 0.0414703 | + | 0.189353i | ||||
\(970\) | −45.5688 | + | 26.3091i | −1.46313 | + | 0.844736i | ||||
\(971\) | −24.0452 | − | 13.8825i | −0.771648 | − | 0.445511i | 0.0618141 | − | 0.998088i | \(-0.480311\pi\) |
−0.833462 | + | 0.552576i | \(0.813645\pi\) | |||||||
\(972\) | 23.8464 | − | 0.735596i | 0.764873 | − | 0.0235943i | ||||
\(973\) | 30.9349 | + | 8.99360i | 0.991726 | + | 0.288321i | ||||
\(974\) | −62.5013 | −2.00267 | ||||||||
\(975\) | 6.80527 | − | 6.20392i | 0.217943 | − | 0.198684i | ||||
\(976\) | 38.9215 | − | 22.4713i | 1.24585 | − | 0.719289i | ||||
\(977\) | −44.2071 | + | 25.5230i | −1.41431 | + | 0.816553i | −0.995791 | − | 0.0916549i | \(-0.970784\pi\) |
−0.418520 | + | 0.908208i | \(0.637451\pi\) | |||||||
\(978\) | −29.8007 | − | 32.6893i | −0.952922 | − | 1.04529i | ||||
\(979\) | 3.36729 | − | 3.10226i | 0.107619 | − | 0.0991487i | ||||
\(980\) | −17.4905 | + | 27.5381i | −0.558713 | + | 0.879673i | ||||
\(981\) | −5.99014 | + | 8.46228i | −0.191250 | + | 0.270180i | ||||
\(982\) | 3.53298 | − | 6.11929i | 0.112742 | − | 0.195275i | ||||
\(983\) | −9.49000 | + | 5.47905i | −0.302684 | + | 0.174755i | −0.643648 | − | 0.765322i | \(-0.722580\pi\) |
0.340964 | + | 0.940076i | \(0.389247\pi\) | |||||||
\(984\) | 15.4701 | − | 3.38812i | 0.493168 | − | 0.108009i | ||||
\(985\) | −0.301998 | − | 0.174359i | −0.00962246 | − | 0.00555553i | ||||
\(986\) | −15.7375 | −0.501185 | ||||||||
\(987\) | 27.5869 | − | 41.1200i | 0.878102 | − | 1.30886i | ||||
\(988\) | 1.17051 | 0.0372390 | ||||||||
\(989\) | −5.89503 | + | 10.2105i | −0.187451 | + | 0.324675i | ||||
\(990\) | −34.5465 | − | 45.2490i | −1.09796 | − | 1.43811i | ||||
\(991\) | 9.46591 | + | 16.3954i | 0.300695 | + | 0.520818i | 0.976293 | − | 0.216451i | \(-0.0694482\pi\) |
−0.675599 | + | 0.737269i | \(0.736115\pi\) | |||||||
\(992\) | −22.5836 | + | 39.1159i | −0.717030 | + | 1.24193i | ||||
\(993\) | 8.93282 | − | 28.0805i | 0.283475 | − | 0.891108i | ||||
\(994\) | −28.3853 | + | 27.2105i | −0.900328 | + | 0.863064i | ||||
\(995\) | − | 72.6280i | − | 2.30246i | ||||||
\(996\) | 27.9836 | + | 30.6961i | 0.886695 | + | 0.972644i | ||||
\(997\) | −24.8780 | + | 14.3633i | −0.787895 | + | 0.454891i | −0.839221 | − | 0.543791i | \(-0.816989\pi\) |
0.0513262 | + | 0.998682i | \(0.483655\pi\) | |||||||
\(998\) | −1.90461 | − | 3.29888i | −0.0602893 | − | 0.104424i | ||||
\(999\) | −4.03420 | − | 32.5733i | −0.127636 | − | 1.03057i |
(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 | 231.2.l.b.65.5 | yes | 48 | |
3.2 | odd | 2 | inner | 231.2.l.b.65.20 | yes | 48 | |
7.4 | even | 3 | inner | 231.2.l.b.32.6 | yes | 48 | |
11.10 | odd | 2 | inner | 231.2.l.b.65.19 | yes | 48 | |
21.11 | odd | 6 | inner | 231.2.l.b.32.19 | yes | 48 | |
33.32 | even | 2 | inner | 231.2.l.b.65.6 | yes | 48 | |
77.32 | odd | 6 | inner | 231.2.l.b.32.20 | yes | 48 | |
231.32 | even | 6 | inner | 231.2.l.b.32.5 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.l.b.32.5 | ✓ | 48 | 231.32 | even | 6 | inner | |
231.2.l.b.32.6 | yes | 48 | 7.4 | even | 3 | inner | |
231.2.l.b.32.19 | yes | 48 | 21.11 | odd | 6 | inner | |
231.2.l.b.32.20 | yes | 48 | 77.32 | odd | 6 | inner | |
231.2.l.b.65.5 | yes | 48 | 1.1 | even | 1 | trivial | |
231.2.l.b.65.6 | yes | 48 | 33.32 | even | 2 | inner | |
231.2.l.b.65.19 | yes | 48 | 11.10 | odd | 2 | inner | |
231.2.l.b.65.20 | yes | 48 | 3.2 | odd | 2 | inner |