Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(271,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bf (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.11 | ||
Character | \(\chi\) | \(=\) | 756.271 |
Dual form | 756.2.bf.b.703.11 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.434237 | + | 1.34590i | 0.307052 | + | 0.951693i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.62288 | + | 1.16888i | −0.811438 | + | 0.584438i | ||||
\(5\) | −0.421763 | − | 0.243505i | −0.188618 | − | 0.108899i | 0.402717 | − | 0.915324i | \(-0.368066\pi\) |
−0.591336 | + | 0.806426i | \(0.701399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.250520 | − | 2.63386i | −0.0946876 | − | 0.995507i | ||||
\(8\) | −2.27790 | − | 1.67665i | −0.805359 | − | 0.592787i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.144587 | − | 0.673389i | 0.0457226 | − | 0.212944i | ||||
\(11\) | 2.51153 | − | 1.45003i | 0.757254 | − | 0.437201i | −0.0710549 | − | 0.997472i | \(-0.522637\pi\) |
0.828309 | + | 0.560272i | \(0.189303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.17266i | − | 0.325239i | −0.986689 | − | 0.162619i | \(-0.948006\pi\) | ||
0.986689 | − | 0.162619i | \(-0.0519942\pi\) | |||||||
\(14\) | 3.43612 | − | 1.48090i | 0.918343 | − | 0.395786i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.26745 | − | 3.79388i | 0.316864 | − | 0.948471i | ||||
\(17\) | −0.0401295 | + | 0.0231688i | −0.00973282 | + | 0.00561925i | −0.504859 | − | 0.863202i | \(-0.668455\pi\) |
0.495126 | + | 0.868821i | \(0.335122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.38246 | − | 4.12654i | 0.546574 | − | 0.946693i | −0.451932 | − | 0.892052i | \(-0.649265\pi\) |
0.998506 | − | 0.0546412i | \(-0.0174015\pi\) | |||||||
\(20\) | 0.969097 | − | 0.0978105i | 0.216697 | − | 0.0218711i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.04219 | + | 2.75060i | 0.648597 | + | 0.586430i | ||||
\(23\) | 6.02414 | + | 3.47804i | 1.25612 | + | 0.725221i | 0.972318 | − | 0.233661i | \(-0.0750707\pi\) |
0.283802 | + | 0.958883i | \(0.408404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.38141 | − | 4.12472i | −0.476282 | − | 0.824945i | ||||
\(26\) | 1.57829 | − | 0.509215i | 0.309527 | − | 0.0998652i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.48523 | + | 3.98161i | 0.658646 | + | 0.752453i | ||||
\(29\) | 0.465824 | 0.0865013 | 0.0432506 | − | 0.999064i | \(-0.486229\pi\) | ||||
0.0432506 | + | 0.999064i | \(0.486229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.536070 | + | 0.928500i | 0.0962810 | + | 0.166764i | 0.910142 | − | 0.414295i | \(-0.135972\pi\) |
−0.813862 | + | 0.581059i | \(0.802639\pi\) | |||||||
\(32\) | 5.65655 | + | 0.0584175i | 0.999947 | + | 0.0103269i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.0486085 | − | 0.0439494i | −0.00833628 | − | 0.00753726i | ||||
\(35\) | −0.535699 | + | 1.17187i | −0.0905497 | + | 0.198082i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.196198 | − | 0.339825i | 0.0322547 | − | 0.0558668i | −0.849447 | − | 0.527673i | \(-0.823065\pi\) |
0.881702 | + | 0.471806i | \(0.156398\pi\) | |||||||
\(38\) | 6.58845 | + | 1.41465i | 1.06879 | + | 0.229486i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.552461 | + | 1.26183i | 0.0873517 | + | 0.199513i | ||||
\(41\) | − | 0.139187i | − | 0.0217373i | −0.999941 | − | 0.0108686i | \(-0.996540\pi\) | ||
0.999941 | − | 0.0108686i | \(-0.00345967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.47359i | − | 0.987213i | −0.869685 | − | 0.493607i | \(-0.835678\pi\) | ||
0.869685 | − | 0.493607i | \(-0.164322\pi\) | |||||||
\(44\) | −2.38099 | + | 5.28889i | −0.358948 | + | 0.797330i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.06518 | + | 9.61817i | −0.304494 | + | 1.41812i | ||||
\(47\) | 3.81879 | − | 6.61433i | 0.557027 | − | 0.964800i | −0.440715 | − | 0.897647i | \(-0.645275\pi\) |
0.997743 | − | 0.0671528i | \(-0.0213915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.87448 | + | 1.31967i | −0.982069 | + | 0.188524i | ||||
\(50\) | 4.51736 | − | 4.99624i | 0.638851 | − | 0.706575i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.37070 | + | 1.90309i | 0.190082 | + | 0.263911i | ||||
\(53\) | 5.03428 | + | 8.71964i | 0.691512 | + | 1.19773i | 0.971342 | + | 0.237685i | \(0.0763885\pi\) |
−0.279830 | + | 0.960049i | \(0.590278\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41236 | −0.190443 | ||||||||
\(56\) | −3.84542 | + | 6.41972i | −0.513866 | + | 0.857871i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.202278 | + | 0.626950i | 0.0265604 | + | 0.0823226i | ||||
\(59\) | 3.65438 | + | 6.32958i | 0.475760 | + | 0.824041i | 0.999614 | − | 0.0277670i | \(-0.00883963\pi\) |
−0.523854 | + | 0.851808i | \(0.675506\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0409 | − | 6.95182i | −1.54168 | − | 0.890090i | −0.998733 | − | 0.0503231i | \(-0.983975\pi\) |
−0.542948 | − | 0.839767i | \(-0.682692\pi\) | |||||||
\(62\) | −1.01688 | + | 1.12468i | −0.129144 | + | 0.142835i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.37766 | + | 7.63850i | 0.297208 | + | 0.954813i | ||||
\(65\) | −0.285550 | + | 0.494587i | −0.0354181 | + | 0.0613459i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.49182 | − | 2.01601i | 0.426594 | − | 0.246294i | −0.271300 | − | 0.962495i | \(-0.587454\pi\) |
0.697895 | + | 0.716200i | \(0.254120\pi\) | |||||||
\(68\) | 0.0380437 | − | 0.0845064i | 0.00461348 | − | 0.0102479i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.80984 | − | 0.212126i | −0.216317 | − | 0.0253540i | ||||
\(71\) | − | 6.95063i | − | 0.824888i | −0.910983 | − | 0.412444i | \(-0.864675\pi\) | ||
0.910983 | − | 0.412444i | \(-0.135325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.14246 | + | 4.12370i | −0.835961 | + | 0.482643i | −0.855889 | − | 0.517159i | \(-0.826990\pi\) |
0.0199280 | + | 0.999801i | \(0.493656\pi\) | |||||||
\(74\) | 0.542565 | + | 0.116498i | 0.0630719 | + | 0.0135426i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.956981 | + | 9.48167i | 0.109773 | + | 1.08762i | ||||
\(77\) | −4.44837 | − | 6.25176i | −0.506939 | − | 0.712454i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0015 | + | 6.92909i | 1.35028 | + | 0.779584i | 0.988288 | − | 0.152598i | \(-0.0487640\pi\) |
0.361990 | + | 0.932182i | \(0.382097\pi\) | |||||||
\(80\) | −1.45840 | + | 1.29149i | −0.163054 | + | 0.144393i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.187331 | − | 0.0604400i | 0.0206872 | − | 0.00667448i | ||||
\(83\) | −6.34905 | −0.696899 | −0.348450 | − | 0.937328i | \(-0.613292\pi\) | ||||
−0.348450 | + | 0.937328i | \(0.613292\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0225668 | 0.00244772 | ||||||||
\(86\) | 8.71279 | − | 2.81107i | 0.939524 | − | 0.303126i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.15221 | − | 0.907937i | −0.869029 | − | 0.0967864i | ||||
\(89\) | −9.16832 | − | 5.29333i | −0.971840 | − | 0.561092i | −0.0720434 | − | 0.997401i | \(-0.522952\pi\) |
−0.899797 | + | 0.436309i | \(0.856285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.08864 | + | 0.293776i | −0.323777 | + | 0.0307961i | ||||
\(92\) | −13.8418 | + | 1.39705i | −1.44311 | + | 0.145653i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.5605 | + | 2.26750i | 1.08923 | + | 0.233875i | ||||
\(95\) | −2.00967 | + | 1.16028i | −0.206188 | + | 0.119042i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.51277i | − | 0.864341i | −0.901792 | − | 0.432171i | \(-0.857748\pi\) | ||
0.901792 | − | 0.432171i | \(-0.142252\pi\) | |||||||
\(98\) | −4.76129 | − | 8.67929i | −0.480963 | − | 0.876741i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.68603 | + | 3.91034i | 0.868603 | + | 0.391034i | ||||
\(101\) | 15.8252 | − | 9.13670i | 1.57467 | − | 0.909136i | 0.579085 | − | 0.815267i | \(-0.303410\pi\) |
0.995585 | − | 0.0938690i | \(-0.0299235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.99009 | − | 15.5713i | 0.885820 | − | 1.53429i | 0.0410493 | − | 0.999157i | \(-0.486930\pi\) |
0.844771 | − | 0.535128i | \(-0.179737\pi\) | |||||||
\(104\) | −1.96615 | + | 2.67121i | −0.192797 | + | 0.261934i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.54966 | + | 10.5620i | −0.927545 | + | 1.02587i | ||||
\(107\) | −4.20572 | − | 2.42818i | −0.406583 | − | 0.234741i | 0.282738 | − | 0.959197i | \(-0.408757\pi\) |
−0.689320 | + | 0.724457i | \(0.742091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.83866 | + | 15.3090i | 0.846590 | + | 1.46634i | 0.884234 | + | 0.467045i | \(0.154681\pi\) |
−0.0376439 | + | 0.999291i | \(0.511985\pi\) | |||||||
\(110\) | −0.613299 | − | 1.90089i | −0.0584758 | − | 0.181243i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.3101 | − | 2.38786i | −0.974213 | − | 0.225632i | ||||
\(113\) | −17.4915 | −1.64546 | −0.822732 | − | 0.568430i | \(-0.807551\pi\) | ||||
−0.822732 | + | 0.568430i | \(0.807551\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.69384 | − | 2.93382i | −0.157951 | − | 0.273580i | ||||
\(116\) | −0.755974 | + | 0.544490i | −0.0701904 | + | 0.0505546i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.93209 | + | 7.66696i | −0.638151 | + | 0.705801i | ||||
\(119\) | 0.0710766 | + | 0.0998913i | 0.00651558 | + | 0.00915702i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29482 | + | 2.24269i | −0.117711 | + | 0.203881i | ||||
\(122\) | 4.12783 | − | 19.2246i | 0.373716 | − | 1.74051i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.95528 | − | 0.880241i | −0.175589 | − | 0.0790480i | ||||
\(125\) | 4.75459i | 0.425264i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.10449i | − | 0.630421i | −0.949022 | − | 0.315211i | \(-0.897925\pi\) | ||
0.949022 | − | 0.315211i | \(-0.102075\pi\) | |||||||
\(128\) | −9.24817 | + | 6.51701i | −0.817430 | + | 0.576028i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.789659 | − | 0.169553i | −0.0692577 | − | 0.0148707i | ||||
\(131\) | −7.34587 | + | 12.7234i | −0.641812 | + | 1.11165i | 0.343216 | + | 0.939256i | \(0.388484\pi\) |
−0.985028 | + | 0.172394i | \(0.944850\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.4656 | − | 5.24129i | −0.994194 | − | 0.454478i | ||||
\(134\) | 4.22961 | + | 3.82421i | 0.365383 | + | 0.330361i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.130257 | + | 0.0145071i | 0.0111694 | + | 0.00124397i | ||||
\(137\) | 5.97043 | + | 10.3411i | 0.510088 | + | 0.883498i | 0.999932 | + | 0.0116880i | \(0.00372050\pi\) |
−0.489844 | + | 0.871810i | \(0.662946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.39809 | −0.797135 | −0.398568 | − | 0.917139i | \(-0.630493\pi\) | ||||
−0.398568 | + | 0.917139i | \(0.630493\pi\) | |||||||
\(140\) | −0.500398 | − | 2.52797i | −0.0422913 | − | 0.213652i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.35483 | − | 3.01822i | 0.785040 | − | 0.253283i | ||||
\(143\) | −1.70040 | − | 2.94518i | −0.142195 | − | 0.246288i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.196467 | − | 0.113430i | −0.0163157 | − | 0.00941988i | ||||
\(146\) | −8.65159 | − | 7.82235i | −0.716011 | − | 0.647382i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0788082 | + | 0.780824i | 0.00647800 | + | 0.0641833i | ||||
\(149\) | −6.35996 | + | 11.0158i | −0.521028 | + | 0.902447i | 0.478673 | + | 0.877993i | \(0.341118\pi\) |
−0.999701 | + | 0.0244538i | \(0.992215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.87775 | + | 1.66147i | −0.234188 | + | 0.135209i | −0.612503 | − | 0.790468i | \(-0.709837\pi\) |
0.378314 | + | 0.925677i | \(0.376504\pi\) | |||||||
\(152\) | −12.3458 | + | 5.40529i | −1.00138 | + | 0.438427i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.48258 | − | 8.70180i | 0.522381 | − | 0.701211i | ||||
\(155\) | − | 0.522143i | − | 0.0419395i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.22021 | − | 4.74594i | 0.656045 | − | 0.378767i | −0.134724 | − | 0.990883i | \(-0.543015\pi\) |
0.790768 | + | 0.612116i | \(0.209681\pi\) | |||||||
\(158\) | −4.11433 | + | 19.1617i | −0.327318 | + | 1.52442i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.37150 | − | 1.40204i | −0.187484 | − | 0.110841i | ||||
\(161\) | 7.65152 | − | 16.7381i | 0.603024 | − | 1.31915i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.9144 | + | 6.87876i | 0.933205 | + | 0.538786i | 0.887824 | − | 0.460183i | \(-0.152216\pi\) |
0.0453814 | + | 0.998970i | \(0.485550\pi\) | |||||||
\(164\) | 0.162692 | + | 0.225883i | 0.0127041 | + | 0.0176385i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.75699 | − | 8.54517i | −0.213984 | − | 0.663234i | ||||
\(167\) | −11.0139 | −0.852280 | −0.426140 | − | 0.904657i | \(-0.640127\pi\) | ||||
−0.426140 | + | 0.904657i | \(0.640127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6249 | 0.894220 | ||||||||
\(170\) | 0.00979936 | + | 0.0303726i | 0.000751576 | + | 0.00232947i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.56683 | + | 10.5058i | 0.576965 | + | 0.801063i | ||||
\(173\) | 15.2097 | + | 8.78130i | 1.15637 | + | 0.667630i | 0.950431 | − | 0.310935i | \(-0.100642\pi\) |
0.205938 | + | 0.978565i | \(0.433975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.2674 | + | 7.30564i | −0.776140 | + | 0.552254i | ||||
\(176\) | −2.31800 | − | 11.3663i | −0.174726 | − | 0.856767i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.14305 | − | 14.6382i | 0.235582 | − | 1.09718i | ||||
\(179\) | −8.95722 | + | 5.17145i | −0.669494 | + | 0.386533i | −0.795885 | − | 0.605448i | \(-0.792994\pi\) |
0.126391 | + | 0.991981i | \(0.459661\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.4154i | − | 0.848503i | −0.905544 | − | 0.424252i | \(-0.860537\pi\) | ||
0.905544 | − | 0.424252i | \(-0.139463\pi\) | |||||||
\(182\) | −1.73659 | − | 4.02942i | −0.128725 | − | 0.298681i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.89093 | − | 18.0230i | −0.581727 | − | 1.32868i | ||||
\(185\) | −0.165498 | + | 0.0955503i | −0.0121677 | + | 0.00702500i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0671908 | + | 0.116378i | −0.00491348 | + | 0.00851040i | ||||
\(188\) | 1.53392 | + | 15.1979i | 0.111873 | + | 1.10842i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.43429 | − | 2.20097i | −0.176602 | − | 0.159675i | ||||
\(191\) | −12.6603 | − | 7.30943i | −0.916068 | − | 0.528892i | −0.0336895 | − | 0.999432i | \(-0.510726\pi\) |
−0.882379 | + | 0.470540i | \(0.844059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0358245 | + | 0.0620498i | 0.00257870 | + | 0.00446644i | 0.867312 | − | 0.497765i | \(-0.165846\pi\) |
−0.864733 | + | 0.502232i | \(0.832513\pi\) | |||||||
\(194\) | 11.4573 | − | 3.69656i | 0.822587 | − | 0.265398i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.61390 | − | 10.1771i | 0.686707 | − | 0.726934i | ||||
\(197\) | 1.90917 | 0.136023 | 0.0680113 | − | 0.997685i | \(-0.478335\pi\) | ||||
0.0680113 | + | 0.997685i | \(0.478335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.291782 | − | 0.505382i | −0.0206839 | − | 0.0358256i | 0.855498 | − | 0.517806i | \(-0.173251\pi\) |
−0.876182 | + | 0.481980i | \(0.839918\pi\) | |||||||
\(200\) | −1.49112 | + | 13.3885i | −0.105438 | + | 0.946711i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.1690 | + | 17.3316i | 1.34872 | + | 1.21945i | ||||
\(203\) | −0.116698 | − | 1.22692i | −0.00819060 | − | 0.0861126i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0338926 | + | 0.0587038i | −0.00236716 | + | 0.00410005i | ||||
\(206\) | 24.8612 | + | 5.33810i | 1.73216 | + | 0.371923i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.44895 | − | 1.48630i | −0.308479 | − | 0.103056i | ||||
\(209\) | − | 13.8186i | − | 0.955850i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89200i | 0.336779i | 0.985721 | + | 0.168390i | \(0.0538567\pi\) | ||||
−0.985721 | + | 0.168390i | \(0.946143\pi\) | |||||||
\(212\) | −18.3622 | − | 8.26643i | −1.26112 | − | 0.567741i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.44179 | − | 6.71487i | 0.0985589 | − | 0.459019i | ||||
\(215\) | −1.57635 | + | 2.73032i | −0.107506 | + | 0.186206i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.31125 | − | 1.64454i | 0.156898 | − | 0.111639i | ||||
\(218\) | −16.7663 | + | 18.5437i | −1.13555 | + | 1.25593i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.29209 | − | 1.65087i | 0.154532 | − | 0.111302i | ||||
\(221\) | 0.0271692 | + | 0.0470584i | 0.00182760 | + | 0.00316549i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3383 | −1.22803 | −0.614013 | − | 0.789296i | \(-0.710446\pi\) | ||||
−0.614013 | + | 0.789296i | \(0.710446\pi\) | |||||||
\(224\) | −1.26321 | − | 14.9132i | −0.0844021 | − | 0.996432i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.59547 | − | 23.5418i | −0.505243 | − | 1.56598i | ||||
\(227\) | −8.05581 | − | 13.9531i | −0.534683 | − | 0.926098i | −0.999179 | − | 0.0405227i | \(-0.987098\pi\) |
0.464496 | − | 0.885575i | \(-0.346236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0728 | + | 6.97024i | 0.797793 | + | 0.460606i | 0.842699 | − | 0.538385i | \(-0.180965\pi\) |
−0.0449057 | + | 0.998991i | \(0.514299\pi\) | |||||||
\(230\) | 3.21309 | − | 3.55371i | 0.211865 | − | 0.234325i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.06110 | − | 0.781025i | −0.0696646 | − | 0.0512768i | ||||
\(233\) | −1.82721 | + | 3.16482i | −0.119704 | + | 0.207334i | −0.919651 | − | 0.392738i | \(-0.871528\pi\) |
0.799946 | + | 0.600072i | \(0.204861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.22125 | + | 1.85979i | −0.210131 | + | 0.121319i | ||||
\(236\) | −13.3291 | − | 6.00060i | −0.867651 | − | 0.390606i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.103579 | + | 0.139038i | −0.00671405 | + | 0.00901251i | ||||
\(239\) | 16.3218i | 1.05577i | 0.849315 | + | 0.527886i | \(0.177015\pi\) | ||||
−0.849315 | + | 0.527886i | \(0.822985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.32608 | + | 1.34296i | −0.149836 | + | 0.0865079i | −0.573044 | − | 0.819525i | \(-0.694237\pi\) |
0.423208 | + | 0.906033i | \(0.360904\pi\) | |||||||
\(242\) | −3.58069 | − | 0.768832i | −0.230175 | − | 0.0494224i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.6667 | − | 2.79239i | 1.77118 | − | 0.178765i | ||||
\(245\) | 3.22075 | + | 1.11738i | 0.205766 | + | 0.0713869i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.83905 | − | 2.79383i | −0.307901 | − | 0.177767i | ||||
\(248\) | 0.335660 | − | 3.01383i | 0.0213144 | − | 0.191379i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.39919 | + | 2.06462i | −0.404720 | + | 0.130578i | ||||
\(251\) | 30.3569 | 1.91611 | 0.958055 | − | 0.286585i | \(-0.0925201\pi\) | ||||
0.958055 | + | 0.286585i | \(0.0925201\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1731 | 1.26827 | ||||||||
\(254\) | 9.56191 | − | 3.08503i | 0.599967 | − | 0.193572i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.7871 | − | 9.61715i | −0.799195 | − | 0.601072i | ||||
\(257\) | −20.1221 | − | 11.6175i | −1.25518 | − | 0.724678i | −0.283046 | − | 0.959106i | \(-0.591345\pi\) |
−0.972133 | + | 0.234428i | \(0.924678\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.944203 | − | 0.431625i | −0.0586699 | − | 0.0268199i | ||||
\(260\) | −0.114699 | − | 1.13643i | −0.00711333 | − | 0.0704781i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.3143 | − | 4.36180i | −1.25502 | − | 0.269473i | ||||
\(263\) | 8.24274 | − | 4.75895i | 0.508269 | − | 0.293449i | −0.223853 | − | 0.974623i | \(-0.571863\pi\) |
0.732122 | + | 0.681174i | \(0.238530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.90349i | − | 0.301219i | ||||||
\(266\) | 2.07545 | − | 17.7075i | 0.127254 | − | 1.08572i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.31034 | + | 7.35324i | −0.202211 | + | 0.449171i | ||||
\(269\) | 10.0770 | − | 5.81796i | 0.614405 | − | 0.354727i | −0.160282 | − | 0.987071i | \(-0.551240\pi\) |
0.774688 | + | 0.632344i | \(0.217907\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.94241 | + | 13.7567i | −0.482467 | + | 0.835657i | −0.999797 | − | 0.0201285i | \(-0.993592\pi\) |
0.517330 | + | 0.855786i | \(0.326926\pi\) | |||||||
\(272\) | 0.0370373 | + | 0.181612i | 0.00224572 | + | 0.0110118i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.3254 | + | 12.5261i | −0.684195 | + | 0.756727i | ||||
\(275\) | −11.9620 | − | 6.90624i | −0.721333 | − | 0.416462i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.38977 | + | 12.7995i | 0.444008 | + | 0.769045i | 0.997983 | − | 0.0634891i | \(-0.0202228\pi\) |
−0.553974 | + | 0.832534i | \(0.686889\pi\) | |||||||
\(278\) | −4.08100 | − | 12.6489i | −0.244762 | − | 0.758628i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.18509 | − | 1.77122i | 0.190346 | − | 0.105851i | ||||
\(281\) | −24.2255 | −1.44517 | −0.722586 | − | 0.691281i | \(-0.757047\pi\) | ||||
−0.722586 | + | 0.691281i | \(0.757047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1171 | + | 26.1836i | 0.898619 | + | 1.55645i | 0.829261 | + | 0.558861i | \(0.188761\pi\) |
0.0693572 | + | 0.997592i | \(0.477905\pi\) | |||||||
\(284\) | 8.12443 | + | 11.2800i | 0.482096 | + | 0.669345i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.22553 | − | 3.56747i | 0.190730 | − | 0.210949i | ||||
\(287\) | −0.366598 | + | 0.0348690i | −0.0216396 | + | 0.00205825i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.49893 | + | 14.7206i | −0.499937 | + | 0.865916i | ||||
\(290\) | 0.0673522 | − | 0.313680i | 0.00395506 | − | 0.0184199i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.77123 | − | 15.0409i | 0.396256 | − | 0.880202i | ||||
\(293\) | 27.6085i | 1.61290i | 0.591300 | + | 0.806452i | \(0.298615\pi\) | ||||
−0.591300 | + | 0.806452i | \(0.701385\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.55944i | − | 0.207239i | ||||||
\(296\) | −1.01669 | + | 0.445131i | −0.0590937 | + | 0.0258727i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.5878 | − | 3.77639i | −1.01884 | − | 0.218760i | ||||
\(299\) | 4.07857 | − | 7.06430i | 0.235870 | − | 0.408539i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0506 | + | 1.62176i | −0.982778 | + | 0.0934769i | ||||
\(302\) | −3.48580 | − | 3.15169i | −0.200585 | − | 0.181359i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.6360 | − | 14.2690i | −0.724722 | − | 0.818382i | ||||
\(305\) | 3.38561 | + | 5.86405i | 0.193859 | + | 0.335774i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.3244 | −1.04583 | −0.522913 | − | 0.852386i | \(-0.675155\pi\) | ||||
−0.522913 | + | 0.852386i | \(0.675155\pi\) | |||||||
\(308\) | 14.5267 | + | 4.94624i | 0.827735 | + | 0.281838i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.702750 | − | 0.226734i | 0.0399135 | − | 0.0128776i | ||||
\(311\) | 9.34254 | + | 16.1817i | 0.529767 | + | 0.917583i | 0.999397 | + | 0.0347196i | \(0.0110538\pi\) |
−0.469630 | + | 0.882863i | \(0.655613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.3438 | + | 14.0549i | 1.37599 | + | 0.794431i | 0.991675 | − | 0.128769i | \(-0.0411027\pi\) |
0.384320 | + | 0.923200i | \(0.374436\pi\) | |||||||
\(314\) | 9.95707 | + | 9.00270i | 0.561910 | + | 0.508051i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.5763 | + | 2.78326i | −1.55129 | + | 0.156571i | ||||
\(317\) | 3.14099 | − | 5.44035i | 0.176416 | − | 0.305561i | −0.764235 | − | 0.644938i | \(-0.776883\pi\) |
0.940650 | + | 0.339378i | \(0.110216\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.16993 | − | 0.675459i | 0.0655034 | − | 0.0378184i | ||||
\(320\) | 0.857204 | − | 3.80061i | 0.0479192 | − | 0.212461i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.8503 | + | 3.02985i | 1.44058 | + | 0.168847i | ||||
\(323\) | 0.220794i | 0.0122853i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.83692 | + | 2.79260i | −0.268304 | + | 0.154905i | ||||
\(326\) | −4.08444 | + | 19.0225i | −0.226216 | + | 1.05356i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.233368 | + | 0.317053i | −0.0128856 | + | 0.0175063i | ||||
\(329\) | −18.3779 | − | 8.40114i | −1.01321 | − | 0.463170i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2443 | + | 9.95600i | 0.947832 | + | 0.547231i | 0.892407 | − | 0.451232i | \(-0.149015\pi\) |
0.0554253 | + | 0.998463i | \(0.482349\pi\) | |||||||
\(332\) | 10.3037 | − | 7.42126i | 0.565490 | − | 0.407295i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.78264 | − | 14.8236i | −0.261694 | − | 0.811109i | ||||
\(335\) | −1.96363 | −0.107285 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.4718 | 1.49649 | 0.748243 | − | 0.663424i | \(-0.230898\pi\) | ||||
0.748243 | + | 0.663424i | \(0.230898\pi\) | |||||||
\(338\) | 5.04794 | + | 15.6459i | 0.274572 | + | 0.851022i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.0366232 | + | 0.0263778i | −0.00198617 | + | 0.00143054i | ||||
\(341\) | 2.69271 | + | 1.55464i | 0.145818 | + | 0.0841882i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.19803 | + | 17.7758i | 0.280667 | + | 0.959805i | ||||
\(344\) | −10.8540 | + | 14.7462i | −0.585207 | + | 0.795062i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.21413 | + | 24.2838i | −0.280313 | + | 1.30551i | ||||
\(347\) | 7.37788 | − | 4.25962i | 0.396065 | − | 0.228668i | −0.288720 | − | 0.957414i | \(-0.593230\pi\) |
0.684785 | + | 0.728745i | \(0.259896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.53420i | 0.296239i | 0.988969 | + | 0.148119i | \(0.0473220\pi\) | ||||
−0.988969 | + | 0.148119i | \(0.952678\pi\) | |||||||
\(350\) | −14.2911 | − | 10.6464i | −0.763892 | − | 0.569076i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.2913 | − | 8.05546i | 0.761729 | − | 0.429358i | ||||
\(353\) | 14.9667 | − | 8.64101i | 0.796595 | − | 0.459914i | −0.0456841 | − | 0.998956i | \(-0.514547\pi\) |
0.842279 | + | 0.539042i | \(0.181213\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.69251 | + | 2.93152i | −0.0898293 | + | 0.155589i | ||||
\(356\) | 21.0663 | − | 2.12621i | 1.11651 | − | 0.112689i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.8498 | − | 9.80986i | −0.573430 | − | 0.518467i | ||||
\(359\) | 20.8753 | + | 12.0523i | 1.10175 | + | 0.636098i | 0.936681 | − | 0.350183i | \(-0.113881\pi\) |
0.165073 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.85223 | − | 3.20815i | −0.0974857 | − | 0.168850i | ||||
\(362\) | 15.3640 | − | 4.95701i | 0.807514 | − | 0.260535i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.66909 | − | 4.08700i | 0.244727 | − | 0.214217i | ||||
\(365\) | 4.01657 | 0.210237 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.54588 | + | 4.40959i | 0.132894 | + | 0.230179i | 0.924791 | − | 0.380476i | \(-0.124240\pi\) |
−0.791897 | + | 0.610655i | \(0.790906\pi\) | |||||||
\(368\) | 20.8306 | − | 18.4466i | 1.08587 | − | 0.961598i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.200466 | − | 0.181252i | −0.0104217 | − | 0.00942283i | ||||
\(371\) | 21.7051 | − | 15.4441i | 1.12688 | − | 0.801816i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.30359 | + | 10.9181i | −0.326388 | + | 0.565320i | −0.981792 | − | 0.189958i | \(-0.939165\pi\) |
0.655405 | + | 0.755278i | \(0.272498\pi\) | |||||||
\(374\) | −0.185809 | − | 0.0398963i | −0.00960798 | − | 0.00206299i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.7888 | + | 8.66401i | −1.02053 | + | 0.446812i | ||||
\(377\) | − | 0.546255i | − | 0.0281336i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.1068i | − | 0.621883i | −0.950429 | − | 0.310942i | \(-0.899356\pi\) | ||
0.950429 | − | 0.310942i | \(-0.100644\pi\) | |||||||
\(380\) | 1.90521 | − | 4.23205i | 0.0977355 | − | 0.217099i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.34017 | − | 20.2135i | 0.222062 | − | 1.03421i | ||||
\(383\) | 0.646193 | − | 1.11924i | 0.0330189 | − | 0.0571905i | −0.849044 | − | 0.528323i | \(-0.822821\pi\) |
0.882063 | + | 0.471132i | \(0.156155\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.353824 | + | 3.71996i | 0.0180326 | + | 0.189587i | ||||
\(386\) | −0.0679563 | + | 0.0751604i | −0.00345888 | + | 0.00382556i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.95038 | + | 13.8152i | 0.505154 | + | 0.701359i | ||||
\(389\) | 15.0809 | + | 26.1208i | 0.764630 | + | 1.32438i | 0.940442 | + | 0.339954i | \(0.110412\pi\) |
−0.175812 | + | 0.984424i | \(0.556255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.322327 | −0.0163008 | ||||||||
\(392\) | 17.8720 | + | 8.52005i | 0.902673 | + | 0.430327i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.829031 | + | 2.56954i | 0.0417660 | + | 0.129452i | ||||
\(395\) | −3.37454 | − | 5.84487i | −0.169791 | − | 0.294087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.80099 | − | 2.19450i | −0.190766 | − | 0.110139i | 0.401575 | − | 0.915826i | \(-0.368463\pi\) |
−0.592341 | + | 0.805687i | \(0.701796\pi\) | |||||||
\(398\) | 0.553489 | − | 0.612165i | 0.0277439 | − | 0.0306850i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.6671 | + | 3.80690i | −0.933353 | + | 0.190345i | ||||
\(401\) | −6.56098 | + | 11.3640i | −0.327640 | + | 0.567489i | −0.982043 | − | 0.188657i | \(-0.939587\pi\) |
0.654403 | + | 0.756146i | \(0.272920\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.08882 | − | 0.628630i | 0.0542379 | − | 0.0313143i | ||||
\(404\) | −15.0027 | + | 33.3255i | −0.746413 | + | 1.65801i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.60063 | − | 0.689836i | 0.0794378 | − | 0.0342360i | ||||
\(407\) | − | 1.13797i | − | 0.0564072i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.8601 | + | 8.00213i | −0.685338 | + | 0.395680i | −0.801863 | − | 0.597508i | \(-0.796158\pi\) |
0.116525 | + | 0.993188i | \(0.462824\pi\) | |||||||
\(410\) | −0.0937266 | − | 0.0201246i | −0.00462883 | − | 0.000993885i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.61112 | + | 35.7786i | 0.177907 | + | 1.76268i | ||||
\(413\) | 15.7558 | − | 11.2108i | 0.775290 | − | 0.551649i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.67780 | + | 1.54603i | 0.131448 | + | 0.0758914i | ||||
\(416\) | 0.0685042 | − | 6.63324i | 0.00335869 | − | 0.325221i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.5984 | − | 6.00053i | 0.909676 | − | 0.293496i | ||||
\(419\) | 18.2612 | 0.892119 | 0.446059 | − | 0.895003i | \(-0.352827\pi\) | ||||
0.446059 | + | 0.895003i | \(0.352827\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6765 | 1.10518 | 0.552592 | − | 0.833452i | \(-0.313639\pi\) | ||||
0.552592 | + | 0.833452i | \(0.313639\pi\) | |||||||
\(422\) | −6.58413 | + | 2.12429i | −0.320510 | + | 0.103409i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.15222 | − | 28.3032i | 0.153085 | − | 1.37453i | ||||
\(425\) | 0.191129 | + | 0.110349i | 0.00927114 | + | 0.00535270i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.2937 | + | 33.4557i | −0.740112 | + | 1.61903i | ||||
\(428\) | 9.66361 | − | 0.975344i | 0.467108 | − | 0.0471450i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.35924 | − | 0.936000i | −0.210221 | − | 0.0451379i | ||||
\(431\) | −20.9603 | + | 12.1015i | −1.00962 | + | 0.582907i | −0.911082 | − | 0.412226i | \(-0.864751\pi\) |
−0.0985425 | + | 0.995133i | \(0.531418\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.0508i | − | 1.49221i | −0.665830 | − | 0.746103i | \(-0.731922\pi\) | ||
0.665830 | − | 0.746103i | \(-0.268078\pi\) | |||||||
\(434\) | 3.21701 | + | 2.39658i | 0.154422 | + | 0.115039i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.2384 | − | 14.5133i | −1.54394 | − | 0.695062i | ||||
\(437\) | 28.7045 | − | 16.5726i | 1.37312 | − | 0.792774i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.6459 | + | 30.5637i | −0.842195 | + | 1.45872i | 0.0458405 | + | 0.998949i | \(0.485403\pi\) |
−0.888035 | + | 0.459775i | \(0.847930\pi\) | |||||||
\(440\) | 3.21722 | + | 2.36804i | 0.153375 | + | 0.112892i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0515379 | + | 0.0570014i | −0.00245141 | + | 0.00271128i | ||||
\(443\) | 12.9852 | + | 7.49702i | 0.616947 | + | 0.356194i | 0.775679 | − | 0.631127i | \(-0.217407\pi\) |
−0.158733 | + | 0.987322i | \(0.550741\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.57791 | + | 4.46507i | 0.122205 | + | 0.211664i | ||||
\(446\) | −7.96318 | − | 24.6815i | −0.377068 | − | 1.16870i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.5231 | − | 8.17603i | 0.922381 | − | 0.386281i | ||||
\(449\) | −5.15686 | −0.243367 | −0.121684 | − | 0.992569i | \(-0.538829\pi\) | ||||
−0.121684 | + | 0.992569i | \(0.538829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.201825 | − | 0.349571i | −0.00950356 | − | 0.0164607i | ||||
\(452\) | 28.3866 | − | 20.4454i | 1.33519 | − | 0.961672i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.2813 | − | 16.9012i | 0.717185 | − | 0.793214i | ||||
\(455\) | 1.37421 | + | 0.628196i | 0.0644240 | + | 0.0294503i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.7402 | + | 22.0666i | −0.595961 | + | 1.03223i | 0.397450 | + | 0.917624i | \(0.369895\pi\) |
−0.993411 | + | 0.114610i | \(0.963438\pi\) | |||||||
\(458\) | −4.13876 | + | 19.2755i | −0.193391 | + | 0.900684i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.17817 | + | 2.78133i | 0.288058 | + | 0.129680i | ||||
\(461\) | − | 1.16194i | − | 0.0541170i | −0.999634 | − | 0.0270585i | \(-0.991386\pi\) | ||
0.999634 | − | 0.0270585i | \(-0.00861403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.3409i | − | 1.08474i | −0.840139 | − | 0.542371i | \(-0.817527\pi\) | ||
0.840139 | − | 0.542371i | \(-0.182473\pi\) | |||||||
\(464\) | 0.590410 | − | 1.76728i | 0.0274091 | − | 0.0820439i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.05296 | − | 1.08495i | −0.234074 | − | 0.0502595i | ||||
\(467\) | 9.08065 | − | 15.7281i | 0.420202 | − | 0.727812i | −0.575757 | − | 0.817621i | \(-0.695292\pi\) |
0.995959 | + | 0.0898092i | \(0.0286257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.18466 | − | 8.69194i | −0.285581 | − | 0.401357i | ||||
\(470\) | −3.90187 | − | 3.52788i | −0.179980 | − | 0.162729i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.28819 | − | 20.5453i | 0.105323 | − | 0.945674i | ||||
\(473\) | −9.38691 | − | 16.2586i | −0.431611 | − | 0.747571i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.6945 | −1.04129 | ||||||||
\(476\) | −0.232109 | − | 0.0790315i | −0.0106387 | − | 0.00362240i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.9675 | + | 7.08755i | −1.00477 | + | 0.324177i | ||||
\(479\) | 5.41667 | + | 9.38196i | 0.247494 | + | 0.428672i | 0.962830 | − | 0.270108i | \(-0.0870596\pi\) |
−0.715336 | + | 0.698781i | \(0.753726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.398500 | − | 0.230074i | −0.0181700 | − | 0.0104905i | ||||
\(482\) | −2.81756 | − | 2.54750i | −0.128336 | − | 0.116036i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.520100 | − | 5.15309i | −0.0236409 | − | 0.234232i | ||||
\(485\) | −2.07290 | + | 3.59037i | −0.0941257 | + | 0.163030i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.3315 | − | 8.85162i | 0.694734 | − | 0.401105i | −0.110649 | − | 0.993860i | \(-0.535293\pi\) |
0.805383 | + | 0.592754i | \(0.201960\pi\) | |||||||
\(488\) | 15.7722 | + | 36.0240i | 0.713974 | + | 1.63073i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.105312 | + | 4.82000i | −0.00475753 | + | 0.217746i | ||||
\(491\) | − | 2.86819i | − | 0.129440i | −0.997903 | − | 0.0647199i | \(-0.979385\pi\) | ||
0.997903 | − | 0.0647199i | \(-0.0206154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0186932 | + | 0.0107926i | −0.000841901 | + | 0.000486072i | ||||
\(494\) | 1.65891 | − | 7.72604i | 0.0746378 | − | 0.347611i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.20207 | − | 0.856955i | 0.188678 | − | 0.0384784i | ||||
\(497\) | −18.3070 | + | 1.74127i | −0.821182 | + | 0.0781067i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.5923 | − | 14.1984i | −1.10090 | − | 0.635606i | −0.164444 | − | 0.986386i | \(-0.552583\pi\) |
−0.936458 | + | 0.350781i | \(0.885916\pi\) | |||||||
\(500\) | −5.55753 | − | 7.71612i | −0.248540 | − | 0.345075i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.1821 | + | 40.8572i | 0.588345 | + | 1.82355i | ||||
\(503\) | −0.613623 | −0.0273601 | −0.0136800 | − | 0.999906i | \(-0.504355\pi\) | ||||
−0.0136800 | + | 0.999906i | \(0.504355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.89933 | −0.396015 | ||||||||
\(506\) | 8.75989 | + | 27.1509i | 0.389425 | + | 1.20700i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.30427 | + | 11.5297i | 0.368442 | + | 0.511548i | ||||
\(509\) | 8.62877 | + | 4.98182i | 0.382464 | + | 0.220816i | 0.678890 | − | 0.734240i | \(-0.262461\pi\) |
−0.296426 | + | 0.955056i | \(0.595795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6506 | + | 17.7792i | 0.559629 | + | 0.786505i | ||||
\(512\) | 7.39105 | − | 21.3863i | 0.326641 | − | 0.945148i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.89818 | − | 32.1270i | 0.304266 | − | 1.41706i | ||||
\(515\) | −7.58338 | + | 4.37827i | −0.334164 | + | 0.192929i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 22.1494i | − | 0.974131i | ||||||
\(518\) | 0.170915 | − | 1.45823i | 0.00750959 | − | 0.0640708i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.47971 | − | 0.647851i | 0.0648894 | − | 0.0284102i | ||||
\(521\) | −37.1542 | + | 21.4510i | −1.62776 | + | 0.939786i | −0.642997 | + | 0.765869i | \(0.722309\pi\) |
−0.984760 | + | 0.173917i | \(0.944357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.342559 | − | 0.593329i | 0.0149790 | − | 0.0259445i | −0.858439 | − | 0.512916i | \(-0.828565\pi\) |
0.873418 | + | 0.486972i | \(0.161899\pi\) | |||||||
\(524\) | −2.95067 | − | 29.2350i | −0.128901 | − | 1.27714i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.98436 | + | 9.02737i | 0.435339 | + | 0.393612i | ||||
\(527\) | −0.0430244 | − | 0.0248401i | −0.00187417 | − | 0.00108205i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.6935 | + | 21.9858i | 0.551892 | + | 0.955906i | ||||
\(530\) | 6.59960 | − | 2.12928i | 0.286668 | − | 0.0924900i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.7337 | − | 4.89590i | 1.07234 | − | 0.212264i | ||||
\(533\) | −0.163219 | −0.00706981 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.18255 | + | 2.04823i | 0.0511259 | + | 0.0885527i | ||||
\(536\) | −11.3342 | − | 1.26232i | −0.489562 | − | 0.0545240i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.2062 | + | 11.0362i | 0.526245 | + | 0.475805i | ||||
\(539\) | −15.3519 | + | 13.2826i | −0.661252 | + | 0.572122i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.951285 | + | 1.64767i | −0.0408989 | + | 0.0708390i | −0.885750 | − | 0.464162i | \(-0.846356\pi\) |
0.844851 | + | 0.535001i | \(0.179689\pi\) | |||||||
\(542\) | −21.9639 | − | 4.71601i | −0.943431 | − | 0.202570i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.228348 | + | 0.128711i | −0.00979033 | + | 0.00551844i | ||||
\(545\) | − | 8.60903i | − | 0.368770i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.8931i | − | 1.40641i | −0.710989 | − | 0.703203i | \(-0.751753\pi\) | ||
0.710989 | − | 0.703203i | \(-0.248247\pi\) | |||||||
\(548\) | −21.7767 | − | 9.80360i | −0.930255 | − | 0.418789i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.10076 | − | 19.0985i | 0.174857 | − | 0.814363i | ||||
\(551\) | 1.10981 | − | 1.92224i | 0.0472793 | − | 0.0818902i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2437 | − | 33.3463i | 0.648226 | − | 1.41803i | ||||
\(554\) | −14.0178 | + | 15.5039i | −0.595561 | + | 0.658696i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.2519 | − | 10.9852i | 0.646826 | − | 0.465876i | ||||
\(557\) | 11.8145 | + | 20.4633i | 0.500596 | + | 0.867058i | 1.00000 | 0.000688398i | \(0.000219124\pi\) | |
−0.499404 | + | 0.866369i | \(0.666448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.59135 | −0.321080 | ||||||||
\(560\) | 3.76696 | + | 3.51767i | 0.159183 | + | 0.148649i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.5196 | − | 32.6050i | −0.443743 | − | 1.37536i | ||||
\(563\) | 10.9592 | + | 18.9820i | 0.461877 | + | 0.799994i | 0.999055 | − | 0.0434752i | \(-0.0138429\pi\) |
−0.537178 | + | 0.843469i | \(0.680510\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.37728 | + | 4.25927i | 0.310364 | + | 0.179189i | ||||
\(566\) | −28.6760 | + | 31.7159i | −1.20534 | + | 1.33312i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.6538 | + | 15.8328i | −0.488983 | + | 0.664331i | ||||
\(569\) | 4.15511 | − | 7.19687i | 0.174191 | − | 0.301708i | −0.765690 | − | 0.643210i | \(-0.777602\pi\) |
0.939881 | + | 0.341502i | \(0.110936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.1031 | − | 12.7613i | 0.924988 | − | 0.534042i | 0.0397651 | − | 0.999209i | \(-0.487339\pi\) |
0.885223 | + | 0.465167i | \(0.154006\pi\) | |||||||
\(572\) | 6.20209 | + | 2.79210i | 0.259322 | + | 0.116744i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.206121 | − | 0.478262i | −0.00860331 | − | 0.0199623i | ||||
\(575\) | − | 33.1306i | − | 1.38164i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.3610 | − | 8.29131i | 0.597855 | − | 0.345172i | −0.170342 | − | 0.985385i | \(-0.554487\pi\) |
0.768197 | + | 0.640213i | \(0.221154\pi\) | |||||||
\(578\) | −23.5029 | − | 5.04646i | −0.977593 | − | 0.209905i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.451428 | − | 0.0455624i | 0.0187445 | − | 0.00189188i | ||||
\(581\) | 1.59056 | + | 16.7225i | 0.0659877 | + | 0.693768i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.2875 | + | 14.5997i | 1.04730 | + | 0.604659i | ||||
\(584\) | 23.1838 | + | 2.58205i | 0.959354 | + | 0.106846i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.1581 | + | 11.9886i | −1.53499 | + | 0.495245i | ||||
\(587\) | −27.4851 | −1.13443 | −0.567216 | − | 0.823569i | \(-0.691979\pi\) | ||||
−0.567216 | + | 0.823569i | \(0.691979\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.10866 | 0.210499 | ||||||||
\(590\) | 4.79064 | − | 1.54564i | 0.197228 | − | 0.0636331i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.04058 | − | 1.17506i | −0.0427677 | − | 0.0482948i | ||||
\(593\) | −31.4732 | − | 18.1711i | −1.29245 | − | 0.746197i | −0.313363 | − | 0.949633i | \(-0.601456\pi\) |
−0.979088 | + | 0.203437i | \(0.934789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.00565344 | − | 0.0594380i | −0.000231768 | − | 0.00243672i | ||||
\(596\) | −2.55465 | − | 25.3112i | −0.104643 | − | 1.03679i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.2789 | + | 2.42176i | 0.461228 | + | 0.0990331i | ||||
\(599\) | 27.8050 | − | 16.0532i | 1.13608 | − | 0.655918i | 0.190625 | − | 0.981663i | \(-0.438949\pi\) |
0.945458 | + | 0.325745i | \(0.105615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.7728i | − | 0.928923i | −0.885593 | − | 0.464462i | \(-0.846248\pi\) | ||
0.885593 | − | 0.464462i | \(-0.153752\pi\) | |||||||
\(602\) | −9.58671 | − | 22.2441i | −0.390725 | − | 0.906600i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.72818 | − | 6.06010i | 0.111008 | − | 0.246582i | ||||
\(605\) | 1.09221 | − | 0.630590i | 0.0444048 | − | 0.0256371i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.4667 | − | 38.9134i | 0.911893 | − | 1.57945i | 0.100506 | − | 0.994936i | \(-0.467954\pi\) |
0.811387 | − | 0.584509i | \(-0.198713\pi\) | |||||||
\(608\) | 13.7176 | − | 23.2028i | 0.556321 | − | 0.940999i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.42224 | + | 7.10306i | −0.260029 | + | 0.287595i | ||||
\(611\) | −7.75640 | − | 4.47816i | −0.313790 | − | 0.181167i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0988 | − | 26.1519i | −0.609836 | − | 1.05627i | −0.991267 | − | 0.131869i | \(-0.957902\pi\) |
0.381432 | − | 0.924397i | \(-0.375431\pi\) | |||||||
\(614\) | −7.95712 | − | 24.6627i | −0.321123 | − | 0.995305i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.349091 | + | 21.6993i | −0.0140653 | + | 0.874289i | ||||
\(617\) | 9.76529 | 0.393136 | 0.196568 | − | 0.980490i | \(-0.437020\pi\) | ||||
0.196568 | + | 0.980490i | \(0.437020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9884 | − | 41.5491i | −0.964174 | − | 1.67000i | −0.711819 | − | 0.702363i | \(-0.752128\pi\) |
−0.252355 | − | 0.967635i | \(-0.581205\pi\) | |||||||
\(620\) | 0.610320 | + | 0.847373i | 0.0245111 | + | 0.0340313i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.7221 | + | 19.6008i | −0.710591 | + | 0.785921i | ||||
\(623\) | −11.6451 | + | 25.4742i | −0.466550 | + | 1.02060i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.7493 | + | 18.6183i | −0.429971 | + | 0.744732i | ||||
\(626\) | −8.34547 | + | 38.8674i | −0.333552 | + | 1.55346i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.79297 | + | 17.3105i | −0.310973 | + | 0.690764i | ||||
\(629\) | 0.0181826i | 0.000724989i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.7354i | − | 0.506987i | −0.967337 | − | 0.253493i | \(-0.918420\pi\) | ||
0.967337 | − | 0.253493i | \(-0.0815796\pi\) | |||||||
\(632\) | −15.7206 | − | 35.9062i | −0.625333 | − | 1.42827i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.68609 | + | 1.86504i | 0.344969 | + | 0.0740704i | ||||
\(635\) | −1.72998 | + | 2.99641i | −0.0686521 | + | 0.118909i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.54753 | + | 8.06146i | 0.0613154 | + | 0.319407i | ||||
\(638\) | 1.41712 | + | 1.28129i | 0.0561045 | + | 0.0507269i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.48746 | − | 0.496658i | 0.216911 | − | 0.0196321i | ||||
\(641\) | −22.4179 | − | 38.8289i | −0.885452 | − | 1.53365i | −0.845195 | − | 0.534459i | \(-0.820515\pi\) |
−0.0402575 | − | 0.999189i | \(-0.512818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.9324 | 0.983236 | 0.491618 | − | 0.870811i | \(-0.336406\pi\) | ||||
0.491618 | + | 0.870811i | \(0.336406\pi\) | |||||||
\(644\) | 7.14730 | + | 36.1075i | 0.281643 | + | 1.42284i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.297167 | + | 0.0958772i | −0.0116919 | + | 0.00377224i | ||||
\(647\) | −23.4210 | − | 40.5664i | −0.920775 | − | 1.59483i | −0.798219 | − | 0.602367i | \(-0.794224\pi\) |
−0.122556 | − | 0.992462i | \(-0.539109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.3562 | + | 10.5979i | 0.720543 | + | 0.416006i | ||||
\(650\) | −5.85892 | − | 5.29734i | −0.229806 | − | 0.207779i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.3760 | + | 2.76304i | −1.07213 | + | 0.108209i | ||||
\(653\) | 12.1952 | − | 21.1227i | 0.477236 | − | 0.826597i | −0.522424 | − | 0.852686i | \(-0.674972\pi\) |
0.999660 | + | 0.0260892i | \(0.00830540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.19644 | − | 3.57751i | 0.242115 | − | 0.139785i | ||||
\(656\) | −0.528058 | − | 0.176413i | −0.0206172 | − | 0.00688776i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.32669 | − | 28.3829i | 0.129688 | − | 1.10648i | ||||
\(659\) | 36.2942i | 1.41382i | 0.707302 | + | 0.706911i | \(0.249912\pi\) | ||||
−0.707302 | + | 0.706911i | \(0.750088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1034 | + | 9.87464i | −0.665244 | + | 0.384079i | −0.794272 | − | 0.607562i | \(-0.792148\pi\) |
0.129028 | + | 0.991641i | \(0.458814\pi\) | |||||||
\(662\) | −5.91163 | + | 27.5323i | −0.229762 | + | 1.07007i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.4625 | + | 10.6452i | 0.561254 | + | 0.413113i | ||||
\(665\) | 3.55949 | + | 5.00252i | 0.138031 | + | 0.193989i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.80619 | + | 1.62015i | 0.108656 | + | 0.0627326i | ||||
\(668\) | 17.8742 | − | 12.8739i | 0.691573 | − | 0.498105i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.852681 | − | 2.64284i | −0.0329419 | − | 0.102102i | ||||
\(671\) | −40.3214 | −1.55659 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.01232 | −0.347399 | −0.173700 | − | 0.984799i | \(-0.555572\pi\) | ||||
−0.173700 | + | 0.984799i | \(0.555572\pi\) | |||||||
\(674\) | 11.9293 | + | 36.9743i | 0.459499 | + | 1.42420i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.8657 | + | 13.5880i | −0.725604 | + | 0.522616i | ||||
\(677\) | 14.1790 | + | 8.18626i | 0.544944 | + | 0.314624i | 0.747080 | − | 0.664734i | \(-0.231455\pi\) |
−0.202136 | + | 0.979357i | \(0.564788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4215 | + | 2.13262i | −0.860458 | + | 0.0818424i | ||||
\(680\) | −0.0514050 | − | 0.0378368i | −0.00197129 | − | 0.00145097i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.923105 | + | 4.29919i | −0.0353475 | + | 0.164624i | ||||
\(683\) | −18.9098 | + | 10.9176i | −0.723564 | + | 0.417750i | −0.816063 | − | 0.577963i | \(-0.803848\pi\) |
0.0924991 | + | 0.995713i | \(0.470514\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 5.81532i | − | 0.222192i | ||||||
\(686\) | −21.6673 | + | 14.7149i | −0.827260 | + | 0.561819i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.5601 | − | 8.20498i | −0.936343 | − | 0.312812i | ||||
\(689\) | 10.2252 | − | 5.90353i | 0.389549 | − | 0.224906i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.17352 | + | 10.6929i | −0.234852 | + | 0.406775i | −0.959230 | − | 0.282628i | \(-0.908794\pi\) |
0.724378 | + | 0.689403i | \(0.242127\pi\) | |||||||
\(692\) | −34.9477 | + | 3.52725i | −1.32851 | + | 0.134086i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.93676 | + | 8.08018i | 0.339235 | + | 0.306719i | ||||
\(695\) | 3.96377 | + | 2.28848i | 0.150354 | + | 0.0868071i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.00322478 | + | 0.00558548i | 0.000122147 | + | 0.000211565i | ||||
\(698\) | −7.44846 | + | 2.40315i | −0.281928 | + | 0.0909607i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.12328 | − | 23.8574i | 0.307031 | − | 0.901726i | ||||
\(701\) | 31.7226 | 1.19815 | 0.599074 | − | 0.800694i | \(-0.295536\pi\) | ||||
0.599074 | + | 0.800694i | \(0.295536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.934867 | − | 1.61924i | −0.0352592 | − | 0.0610707i | ||||
\(704\) | 17.0476 | + | 15.7366i | 0.642507 | + | 0.593097i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.1290 | + | 16.3913i | 0.682293 | + | 0.616896i | ||||
\(707\) | −28.0294 | − | 39.3926i | −1.05415 | − | 1.48151i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.7550 | + | 30.7526i | −0.666804 | + | 1.15494i | 0.311989 | + | 0.950086i | \(0.399005\pi\) |
−0.978793 | + | 0.204852i | \(0.934329\pi\) | |||||||
\(710\) | −4.68047 | − | 1.00497i | −0.175655 | − | 0.0377160i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.0094 | + | 27.4298i | 0.450073 | + | 1.02797i | ||||
\(713\) | 7.45789i | 0.279300i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.65622i | 0.0619393i | ||||||||
\(716\) | 8.49167 | − | 18.8625i | 0.317349 | − | 0.704925i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.15639 | + | 33.3295i | −0.267074 | + | 1.24385i | ||||
\(719\) | −6.27192 | + | 10.8633i | −0.233903 | + | 0.405132i | −0.958953 | − | 0.283564i | \(-0.908483\pi\) |
0.725050 | + | 0.688696i | \(0.241817\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.2649 | − | 19.7778i | −1.61127 | − | 0.736562i | ||||
\(722\) | 3.51354 | − | 3.88601i | 0.130760 | − | 0.144622i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.3432 | + | 18.5258i | 0.495898 | + | 0.688508i | ||||
\(725\) | −1.10932 | − | 1.92139i | −0.0411990 | − | 0.0713588i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.90679 | −0.330335 | −0.165167 | − | 0.986266i | \(-0.552816\pi\) | ||||
−0.165167 | + | 0.986266i | \(0.552816\pi\) | |||||||
\(728\) | 7.52817 | + | 4.50939i | 0.279013 | + | 0.167129i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.74414 | + | 5.40588i | 0.0645536 | + | 0.200081i | ||||
\(731\) | 0.149985 | + | 0.259782i | 0.00554740 | + | 0.00960837i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.4986 | − | 8.37078i | −0.535519 | − | 0.309182i | 0.207742 | − | 0.978184i | \(-0.433388\pi\) |
−0.743261 | + | 0.669002i | \(0.766722\pi\) | |||||||
\(734\) | −4.82934 | + | 5.34130i | −0.178254 | + | 0.197151i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.8727 | + | 20.0256i | 1.24856 | + | 0.738155i | ||||
\(737\) | 5.84654 | − | 10.1265i | 0.215360 | − | 0.373015i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0208 | − | 11.5590i | 0.736476 | − | 0.425205i | −0.0843103 | − | 0.996440i | \(-0.526869\pi\) |
0.820787 | + | 0.571235i | \(0.193535\pi\) | |||||||
\(740\) | 0.156896 | − | 0.348513i | 0.00576762 | − | 0.0128116i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.2113 | + | 22.5065i | 1.10909 | + | 0.826240i | ||||
\(743\) | − | 25.7365i | − | 0.944181i | −0.881550 | − | 0.472091i | \(-0.843499\pi\) | ||
0.881550 | − | 0.472091i | \(-0.156501\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.36479 | − | 3.09736i | 0.196551 | − | 0.113479i | ||||
\(746\) | −17.4320 | − | 3.74292i | −0.638229 | − | 0.137038i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.0269891 | − | 0.267405i | −0.000986818 | − | 0.00977729i | ||||
\(749\) | −5.34187 | + | 11.6856i | −0.195188 | + | 0.426983i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0832 | − | 11.0177i | −0.696355 | − | 0.402041i | 0.109633 | − | 0.993972i | \(-0.465032\pi\) |
−0.805988 | + | 0.591931i | \(0.798366\pi\) | |||||||
\(752\) | −20.2539 | − | 22.8714i | −0.738583 | − | 0.834034i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.735203 | − | 0.237204i | 0.0267745 | − | 0.00863846i | ||||
\(755\) | 1.61831 | 0.0588962 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.29374 | −0.192404 | −0.0962021 | − | 0.995362i | \(-0.530670\pi\) | ||||
−0.0962021 | + | 0.995362i | \(0.530670\pi\) | |||||||
\(758\) | 16.2945 | − | 5.25721i | 0.591842 | − | 0.190950i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.52321 | + | 0.726510i | 0.236622 | + | 0.0263533i | ||||
\(761\) | 36.0460 | + | 20.8112i | 1.30667 | + | 0.754405i | 0.981538 | − | 0.191265i | \(-0.0612589\pi\) |
0.325129 | + | 0.945670i | \(0.394592\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.1076 | − | 27.1150i | 1.37959 | − | 0.981630i | ||||
\(764\) | 29.0899 | − | 2.93604i | 1.05244 | − | 0.106222i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.78698 | + | 0.383694i | 0.0645663 | + | 0.0138634i | ||||
\(767\) | 7.42247 | − | 4.28537i | 0.268010 | − | 0.154736i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.29112i | − | 0.154742i | −0.997002 | − | 0.0773709i | \(-0.975347\pi\) | ||
0.997002 | − | 0.0773709i | \(-0.0246526\pi\) | |||||||
\(770\) | −4.85304 | + | 2.09156i | −0.174892 | + | 0.0753745i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.130667 | − | 0.0588248i | −0.00470282 | − | 0.00211715i | ||||
\(773\) | −40.4039 | + | 23.3272i | −1.45323 | + | 0.839021i | −0.998663 | − | 0.0516925i | \(-0.983538\pi\) |
−0.454564 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.55320 | − | 4.42228i | 0.0917138 | − | 0.158853i | ||||
\(776\) | −14.2730 | + | 19.3913i | −0.512370 | + | 0.696105i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.6073 | + | 31.6399i | −1.02562 | + | 1.13435i | ||||
\(779\) | −0.574359 | − | 0.331606i | −0.0205785 | − | 0.0118810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0786 | − | 17.4567i | −0.360642 | − | 0.624650i | ||||
\(782\) | −0.139967 | − | 0.433819i | −0.00500519 | − | 0.0155134i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.70641 | + | 27.7536i | −0.132372 | + | 0.991200i | ||||
\(785\) | −4.62264 | −0.164989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.1595 | + | 36.6493i | 0.754254 | + | 1.30641i | 0.945744 | + | 0.324912i | \(0.105335\pi\) |
−0.191490 | + | 0.981495i | \(0.561332\pi\) | |||||||
\(788\) | −3.09834 | + | 2.23158i | −0.110374 | + | 0.0794968i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.40124 | − | 7.07984i | 0.227746 | − | 0.251889i | ||||
\(791\) | 4.38197 | + | 46.0703i | 0.155805 | + | 1.63807i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.15216 | + | 14.1200i | −0.289492 | + | 0.501414i | ||||
\(794\) | 1.30304 | − | 6.06867i | 0.0462432 | − | 0.215369i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.06426 | + | 0.479115i | 0.0377215 | + | 0.0169818i | ||||
\(797\) | − | 7.72777i | − | 0.273732i | −0.990590 | − | 0.136866i | \(-0.956297\pi\) | ||
0.990590 | − | 0.136866i | \(-0.0437029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.353906i | 0.0125203i | ||||||||
\(800\) | −13.2296 | − | 23.4708i | −0.467738 | − | 0.829819i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.1437 | − | 3.89575i | −0.640677 | − | 0.137564i | ||||
\(803\) | −11.9590 | + | 20.7136i | −0.422023 | + | 0.730966i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.30294 | + | 5.19633i | −0.257395 | + | 0.183146i | ||||
\(806\) | 1.31888 | + | 1.19246i | 0.0464555 | + | 0.0420027i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −51.3674 | − | 5.72095i | −1.80710 | − | 0.201262i | ||||
\(809\) | 1.09641 | + | 1.89904i | 0.0385477 | + | 0.0667666i | 0.884656 | − | 0.466245i | \(-0.154394\pi\) |
−0.846108 | + | 0.533012i | \(0.821060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.83311 | −0.169713 | −0.0848567 | − | 0.996393i | \(-0.527043\pi\) | ||||
−0.0848567 | + | 0.996393i | \(0.527043\pi\) | |||||||
\(812\) | 1.62350 | + | 1.85473i | 0.0569737 | + | 0.0650882i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.53159 | − | 0.494150i | 0.0536823 | − | 0.0173199i | ||||
\(815\) | −3.35003 | − | 5.80242i | −0.117346 | − | 0.203250i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.7135 | − | 15.4231i | −0.934589 | − | 0.539585i | ||||
\(818\) | −16.7886 | − | 15.1794i | −0.587000 | − | 0.530737i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0136139 | − | 0.134885i | −0.000475418 | − | 0.00471040i | ||||
\(821\) | −19.6615 | + | 34.0547i | −0.686191 | + | 1.18852i | 0.286870 | + | 0.957970i | \(0.407385\pi\) |
−0.973061 | + | 0.230548i | \(0.925948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.3558 | − | 7.71099i | 0.465555 | − | 0.268788i | −0.248822 | − | 0.968549i | \(-0.580044\pi\) |
0.714377 | + | 0.699761i | \(0.246710\pi\) | |||||||
\(824\) | −46.5862 | + | 20.3966i | −1.62291 | + | 0.710549i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.9304 | + | 16.3375i | 0.763055 | + | 0.568453i | ||||
\(827\) | 10.7035i | 0.372196i | 0.982531 | + | 0.186098i | \(0.0595843\pi\) | ||||
−0.982531 | + | 0.186098i | \(0.940416\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.7020 | + | 13.6843i | −0.823203 | + | 0.475276i | −0.851520 | − | 0.524323i | \(-0.824319\pi\) |
0.0283169 | + | 0.999599i | \(0.490985\pi\) | |||||||
\(830\) | −0.917993 | + | 4.27538i | −0.0318640 | + | 0.148401i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.95740 | − | 2.78820i | 0.310542 | − | 0.0966634i | ||||
\(833\) | 0.245294 | − | 0.212231i | 0.00849893 | − | 0.00735336i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.64525 | + | 2.68194i | 0.160756 | + | 0.0928123i | ||||
\(836\) | 16.1522 | + | 22.4258i | 0.558635 | + | 0.775613i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.92970 | + | 24.5777i | 0.273927 | + | 0.849023i | ||||
\(839\) | −9.67322 | −0.333957 | −0.166978 | − | 0.985961i | \(-0.553401\pi\) | ||||
−0.166978 | + | 0.985961i | \(0.553401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7830 | −0.992518 | ||||||||
\(842\) | 9.84697 | + | 30.5202i | 0.339349 | + | 1.05180i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.71814 | − | 7.93911i | −0.196827 | − | 0.273275i | ||||
\(845\) | −4.90294 | − | 2.83071i | −0.168666 | − | 0.0973794i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.23132 | + | 2.84854i | 0.214111 | + | 0.0978769i | ||||
\(848\) | 39.4620 | − | 8.04775i | 1.35513 | − | 0.276361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.0655224 | + | 0.305158i | −0.00224740 | + | 0.0104668i | ||||
\(851\) | 2.36385 | − | 1.36477i | 0.0810316 | − | 0.0467836i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.8757i | − | 1.39956i | −0.714359 | − | 0.699779i | \(-0.753282\pi\) | ||
0.714359 | − | 0.699779i | \(-0.246718\pi\) | |||||||
\(854\) | −51.6690 | − | 6.05600i | −1.76808 | − | 0.207232i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.50901 | + | 12.5827i | 0.188294 | + | 0.430067i | ||||
\(857\) | −21.4624 | + | 12.3913i | −0.733141 | + | 0.423279i | −0.819570 | − | 0.572979i | \(-0.805788\pi\) |
0.0864289 | + | 0.996258i | \(0.472454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.84935 | + | 4.93522i | −0.0972185 | + | 0.168387i | −0.910532 | − | 0.413438i | \(-0.864328\pi\) |
0.813314 | + | 0.581825i | \(0.197661\pi\) | |||||||
\(860\) | −0.633185 | − | 6.27354i | −0.0215914 | − | 0.213926i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.3891 | − | 22.9556i | −0.864755 | − | 0.781869i | ||||
\(863\) | 11.4093 | + | 6.58713i | 0.388375 | + | 0.224229i | 0.681456 | − | 0.731859i | \(-0.261347\pi\) |
−0.293081 | + | 0.956088i | \(0.594680\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.27658 | − | 7.40726i | −0.145408 | − | 0.251854i | ||||
\(866\) | 41.7912 | − | 13.4834i | 1.42012 | − | 0.458185i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.82860 | + | 5.37045i | −0.0620667 | + | 0.182285i | ||||
\(869\) | 40.1896 | 1.36334 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.36410 | − | 4.09474i | −0.0801044 | − | 0.138745i | ||||
\(872\) | 5.53432 | − | 49.6917i | 0.187416 | − | 1.68277i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34.7696 | + | 31.4369i | 1.17610 | + | 1.06337i | ||||
\(875\) | 12.5230 | − | 1.19112i | 0.423353 | − | 0.0402672i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.6431 | − | 25.3625i | 0.494461 | − | 0.856432i | −0.505519 | − | 0.862816i | \(-0.668699\pi\) |
0.999980 | + | 0.00638414i | \(0.00203215\pi\) | |||||||
\(878\) | −48.7981 | − | 10.4777i | −1.64685 | − | 0.353606i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.79010 | + | 5.35833i | −0.0603443 | + | 0.180629i | ||||
\(881\) | − | 41.7794i | − | 1.40758i | −0.710406 | − | 0.703792i | \(-0.751489\pi\) | ||
0.710406 | − | 0.703792i | \(-0.248511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.9004i | − | 0.535090i | −0.963545 | − | 0.267545i | \(-0.913788\pi\) | ||
0.963545 | − | 0.267545i | \(-0.0862124\pi\) | |||||||
\(884\) | −0.0990977 | − | 0.0446125i | −0.00333302 | − | 0.00150048i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.45155 | + | 20.7323i | −0.149553 | + | 0.696514i | ||||
\(887\) | 2.54513 | − | 4.40830i | 0.0854572 | − | 0.148016i | −0.820129 | − | 0.572179i | \(-0.806098\pi\) |
0.905586 | + | 0.424163i | \(0.139432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.7123 | + | 1.77982i | −0.627589 | + | 0.0596931i | ||||
\(890\) | −4.89009 | + | 5.40849i | −0.163916 | + | 0.181293i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.7608 | − | 21.4352i | 0.996467 | − | 0.717705i | ||||
\(893\) | −18.1962 | − | 31.5168i | −0.608913 | − | 1.05467i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.03710 | 0.168372 | ||||||||
\(896\) | 19.4818 | + | 22.7258i | 0.650840 | + | 0.759215i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.23930 | − | 6.94061i | −0.0747265 | − | 0.231611i | ||||
\(899\) | 0.249714 | + | 0.432517i | 0.00832842 | + | 0.0144253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.404046 | − | 0.233276i | −0.0134607 | − | 0.00777156i | ||||
\(902\) | 0.382847 | − | 0.423432i | 0.0127474 | − | 0.0140987i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.8439 | + | 29.3272i | 1.32519 | + | 0.975409i | ||||
\(905\) | −2.77972 | + | 4.81461i | −0.0924009 | + | 0.160043i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.1139 | − | 17.3863i | 0.999916 | − | 0.577302i | 0.0916923 | − | 0.995787i | \(-0.470772\pi\) |
0.908223 | + | 0.418486i | \(0.137439\pi\) | |||||||
\(908\) | 29.3830 | + | 13.2279i | 0.975109 | + | 0.438982i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.248753 | + | 2.12233i | −0.00824609 | + | 0.0703546i | ||||
\(911\) | − | 26.6242i | − | 0.882098i | −0.897483 | − | 0.441049i | \(-0.854606\pi\) | ||
0.897483 | − | 0.441049i | \(-0.145394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.9458 | + | 9.20632i | −0.527730 | + | 0.304685i | ||||
\(914\) | −35.2317 | − | 7.56482i | −1.16536 | − | 0.250222i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.7400 | + | 2.79979i | −0.916556 | + | 0.0925076i | ||||
\(917\) | 35.3521 | + | 16.1606i | 1.16743 | + | 0.533669i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.74511 | − | 1.00754i | −0.0575659 | − | 0.0332357i | 0.470941 | − | 0.882165i | \(-0.343915\pi\) |
−0.528507 | + | 0.848929i | \(0.677248\pi\) | |||||||
\(920\) | −1.06060 | + | 9.52293i | −0.0349669 | + | 0.313962i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.56385 | − | 0.504558i | 0.0515027 | − | 0.0166167i | ||||
\(923\) | −8.15076 | −0.268285 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.86891 | −0.0614494 | ||||||||
\(926\) | 31.4144 | − | 10.1355i | 1.03234 | − | 0.333072i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.63496 | + | 0.0272123i | 0.0864966 | + | 0.000893286i | ||||
\(929\) | −30.2534 | − | 17.4668i | −0.992581 | − | 0.573067i | −0.0865362 | − | 0.996249i | \(-0.527580\pi\) |
−0.906045 | + | 0.423182i | \(0.860913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.9325 | + | 31.5119i | −0.358298 | + | 1.03276i | ||||
\(932\) | −0.733949 | − | 7.27189i | −0.0240413 | − | 0.238199i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.1116 | + | 5.39187i | 0.821677 | + | 0.176427i | ||||
\(935\) | 0.0566772 | − | 0.0327226i | 0.00185354 | − | 0.00107014i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.1738i | 1.47576i | 0.674931 | + | 0.737881i | \(0.264174\pi\) | ||||
−0.674931 | + | 0.737881i | \(0.735826\pi\) | |||||||
\(938\) | 9.01285 | − | 12.0983i | 0.294280 | − | 0.395023i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.05382 | − | 6.78345i | 0.0996047 | − | 0.221252i | ||||
\(941\) | −0.227297 | + | 0.131230i | −0.00740966 | + | 0.00427797i | −0.503700 | − | 0.863878i | \(-0.668028\pi\) |
0.496291 | + | 0.868156i | \(0.334695\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.484096 | − | 0.838480i | 0.0157643 | − | 0.0273047i | ||||
\(944\) | 28.6455 | − | 5.84186i | 0.932330 | − | 0.190136i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.8063 | − | 19.6939i | 0.578931 | − | 0.640304i | ||||
\(947\) | −26.5793 | − | 15.3456i | −0.863711 | − | 0.498664i | 0.00154195 | − | 0.999999i | \(-0.499509\pi\) |
−0.865253 | + | 0.501335i | \(0.832843\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.83572 | + | 8.37571i | 0.156974 | + | 0.271887i | ||||
\(950\) | −9.85478 | − | 30.5444i | −0.319731 | − | 0.990991i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.00557782 | − | 0.346713i | 0.000180778 | − | 0.0112370i | ||||
\(953\) | −33.2031 | −1.07555 | −0.537777 | − | 0.843087i | \(-0.680736\pi\) | ||||
−0.537777 | + | 0.843087i | \(0.680736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.55977 | + | 6.16570i | 0.115191 | + | 0.199517i | ||||
\(956\) | −19.0782 | − | 26.4883i | −0.617034 | − | 0.856694i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.2750 | + | 11.3643i | −0.331971 | + | 0.367163i | ||||
\(959\) | 25.7413 | − | 18.3159i | 0.831230 | − | 0.591453i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9253 | − | 25.8513i | 0.481460 | − | 0.833913i | ||||
\(962\) | 0.136613 | − | 0.636247i | 0.00440457 | − | 0.0205134i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.20518 | − | 4.89837i | 0.0710242 | − | 0.157766i | ||||
\(965\) | − | 0.0348938i | − | 0.00112327i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.4179i | − | 1.01033i | −0.863022 | − | 0.505166i | \(-0.831431\pi\) | ||
0.863022 | − | 0.505166i | \(-0.168569\pi\) | |||||||
\(968\) | 6.70969 | − | 2.93767i | 0.215657 | − | 0.0944201i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.73240 | − | 1.23084i | −0.184056 | − | 0.0395199i | ||||
\(971\) | 0.674219 | − | 1.16778i | 0.0216367 | − | 0.0374759i | −0.855004 | − | 0.518621i | \(-0.826446\pi\) |
0.876641 | + | 0.481145i | \(0.159779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.35441 | + | 24.7533i | 0.0754788 | + | 0.793554i | ||||
\(974\) | 18.5709 | + | 16.7909i | 0.595048 | + | 0.538014i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −41.6357 | + | 36.8707i | −1.33273 | + | 1.18020i | ||||
\(977\) | −28.2780 | − | 48.9789i | −0.904694 | − | 1.56698i | −0.821328 | − | 0.570456i | \(-0.806766\pi\) |
−0.0833656 | − | 0.996519i | \(-0.526567\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.7020 | −0.981240 | ||||||||
\(980\) | −6.53296 | + | 1.95128i | −0.208688 | + | 0.0623315i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.86029 | − | 1.24548i | 0.123187 | − | 0.0397447i | ||||
\(983\) | 25.5636 | + | 44.2775i | 0.815353 | + | 1.41223i | 0.909074 | + | 0.416634i | \(0.136790\pi\) |
−0.0937214 | + | 0.995598i | \(0.529876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.805216 | − | 0.464892i | −0.0256563 | − | 0.0148127i | ||||
\(986\) | −0.0226430 | − | 0.0204727i | −0.000721099 | − | 0.000651982i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.1188 | − | 1.12222i | 0.353737 | − | 0.0357025i | ||||
\(989\) | 22.5154 | − | 38.9978i | 0.715948 | − | 1.24006i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.61700 | + | 3.82033i | −0.210196 | + | 0.121357i | −0.601402 | − | 0.798946i | \(-0.705391\pi\) |
0.391207 | + | 0.920303i | \(0.372058\pi\) | |||||||
\(992\) | 2.97807 | + | 5.28342i | 0.0945537 | + | 0.167749i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.2932 | − | 23.8832i | −0.326479 | − | 0.757530i | ||||
\(995\) | 0.284202i | 0.00900981i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.7883 | + | 7.96070i | −0.436681 | + | 0.252118i | −0.702189 | − | 0.711991i | \(-0.747794\pi\) |
0.265508 | + | 0.964109i | \(0.414460\pi\) | |||||||
\(998\) | 8.43064 | − | 39.2641i | 0.266867 | − | 1.24288i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.bf.b.271.11 | ✓ | 32 | |
3.2 | odd | 2 | 756.2.bf.c.271.6 | yes | 32 | ||
4.3 | odd | 2 | 756.2.bf.c.271.1 | yes | 32 | ||
7.3 | odd | 6 | 756.2.bf.c.703.1 | yes | 32 | ||
12.11 | even | 2 | inner | 756.2.bf.b.271.16 | yes | 32 | |
21.17 | even | 6 | inner | 756.2.bf.b.703.16 | yes | 32 | |
28.3 | even | 6 | inner | 756.2.bf.b.703.11 | yes | 32 | |
84.59 | odd | 6 | 756.2.bf.c.703.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bf.b.271.11 | ✓ | 32 | 1.1 | even | 1 | trivial | |
756.2.bf.b.271.16 | yes | 32 | 12.11 | even | 2 | inner | |
756.2.bf.b.703.11 | yes | 32 | 28.3 | even | 6 | inner | |
756.2.bf.b.703.16 | yes | 32 | 21.17 | even | 6 | inner | |
756.2.bf.c.271.1 | yes | 32 | 4.3 | odd | 2 | ||
756.2.bf.c.271.6 | yes | 32 | 3.2 | odd | 2 | ||
756.2.bf.c.703.1 | yes | 32 | 7.3 | odd | 6 | ||
756.2.bf.c.703.6 | yes | 32 | 84.59 | odd | 6 |