Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(82,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.f (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 487.4 | ||
Character | \(\chi\) | \(=\) | 891.487 |
Dual form | 891.2.f.g.730.4 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10354 | + | 0.801770i | −0.780322 | + | 0.566937i | −0.905076 | − | 0.425251i | \(-0.860186\pi\) |
0.124754 | + | 0.992188i | \(0.460186\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0430645 | + | 0.132539i | −0.0215323 | + | 0.0662695i | ||||
\(5\) | 1.68064 | + | 1.22105i | 0.751603 | + | 0.546072i | 0.896323 | − | 0.443401i | \(-0.146228\pi\) |
−0.144720 | + | 0.989473i | \(0.546228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0320549 | + | 0.0986549i | −0.0121156 | + | 0.0372880i | −0.956932 | − | 0.290314i | \(-0.906240\pi\) |
0.944816 | + | 0.327602i | \(0.106240\pi\) | |||||||
\(8\) | −0.901773 | − | 2.77537i | −0.318825 | − | 0.981243i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.83366 | −0.896081 | ||||||||
\(11\) | −2.19825 | + | 2.48349i | −0.662797 | + | 0.748799i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.36047 | − | 3.89461i | 1.48673 | − | 1.08017i | 0.511415 | − | 0.859334i | \(-0.329121\pi\) |
0.975311 | − | 0.220836i | \(-0.0708786\pi\) | |||||||
\(14\) | −0.0437246 | − | 0.134570i | −0.0116859 | − | 0.0359655i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.99487 | + | 2.17590i | 0.748717 | + | 0.543975i | ||||
\(17\) | 3.06899 | + | 2.22975i | 0.744339 | + | 0.540794i | 0.894067 | − | 0.447933i | \(-0.147840\pi\) |
−0.149728 | + | 0.988727i | \(0.547840\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.03958 | + | 6.27717i | 0.467911 | + | 1.44008i | 0.855285 | + | 0.518158i | \(0.173382\pi\) |
−0.387374 | + | 0.921923i | \(0.626618\pi\) | |||||||
\(20\) | −0.234213 | + | 0.170166i | −0.0523716 | + | 0.0380502i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.434674 | − | 4.50312i | 0.0926728 | − | 0.960069i | ||||
\(23\) | −2.58108 | −0.538193 | −0.269096 | − | 0.963113i | \(-0.586725\pi\) | ||||
−0.269096 | + | 0.963113i | \(0.586725\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.211520 | − | 0.650992i | −0.0423040 | − | 0.130198i | ||||
\(26\) | −2.79292 | + | 8.59573i | −0.547737 | + | 1.68576i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0116952 | − | 0.00849706i | −0.00221018 | − | 0.00160579i | ||||
\(29\) | −3.07613 | + | 9.46735i | −0.571223 | + | 1.75804i | 0.0774731 | + | 0.996994i | \(0.475315\pi\) |
−0.648696 | + | 0.761048i | \(0.724685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.78160 | − | 1.29441i | 0.319984 | − | 0.232482i | −0.416185 | − | 0.909280i | \(-0.636633\pi\) |
0.736169 | + | 0.676798i | \(0.236633\pi\) | |||||||
\(32\) | 0.786868 | 0.139100 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.17450 | −0.887420 | ||||||||
\(35\) | −0.174336 | + | 0.126662i | −0.0294681 | + | 0.0214098i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00747 | − | 3.10068i | 0.165627 | − | 0.509748i | −0.833455 | − | 0.552588i | \(-0.813640\pi\) |
0.999082 | + | 0.0428396i | \(0.0136405\pi\) | |||||||
\(38\) | −7.28360 | − | 5.29185i | −1.18156 | − | 0.858451i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.87333 | − | 5.76550i | 0.296199 | − | 0.911606i | ||||
\(41\) | 0.443218 | + | 1.36409i | 0.0692191 | + | 0.213034i | 0.979682 | − | 0.200556i | \(-0.0642747\pi\) |
−0.910463 | + | 0.413590i | \(0.864275\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.82125 | 0.582735 | 0.291367 | − | 0.956611i | \(-0.405890\pi\) | ||||
0.291367 | + | 0.956611i | \(0.405890\pi\) | |||||||
\(44\) | −0.234492 | − | 0.398304i | −0.0353511 | − | 0.0600466i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.84833 | − | 2.06943i | 0.419964 | − | 0.305121i | ||||
\(47\) | −1.06159 | − | 3.26724i | −0.154849 | − | 0.476576i | 0.843297 | − | 0.537448i | \(-0.180612\pi\) |
−0.998146 | + | 0.0608726i | \(0.980612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.65441 | + | 4.10817i | 0.807773 | + | 0.586882i | ||||
\(50\) | 0.755367 | + | 0.548806i | 0.106825 | + | 0.0776129i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.285342 | + | 0.878191i | 0.0395697 | + | 0.121783i | ||||
\(53\) | −0.0511797 | + | 0.0371842i | −0.00703007 | + | 0.00510765i | −0.591295 | − | 0.806456i | \(-0.701383\pi\) |
0.584265 | + | 0.811563i | \(0.301383\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.72692 | + | 1.48966i | −0.907058 | + | 0.200865i | ||||
\(56\) | 0.302710 | 0.0404514 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.19600 | − | 12.9140i | −0.550962 | − | 1.69569i | ||||
\(59\) | −2.15302 | + | 6.62632i | −0.280299 | + | 0.862673i | 0.707469 | + | 0.706744i | \(0.249837\pi\) |
−0.987768 | + | 0.155929i | \(0.950163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.43265 | − | 2.49397i | −0.439506 | − | 0.319320i | 0.345932 | − | 0.938259i | \(-0.387563\pi\) |
−0.785439 | + | 0.618939i | \(0.787563\pi\) | |||||||
\(62\) | −0.928251 | + | 2.85686i | −0.117888 | + | 0.362822i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.85808 | + | 4.98268i | −0.857259 | + | 0.622835i | ||||
\(65\) | 13.7645 | 1.70728 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.43311 | −0.663761 | −0.331880 | − | 0.943322i | \(-0.607683\pi\) | ||||
−0.331880 | + | 0.943322i | \(0.607683\pi\) | |||||||
\(68\) | −0.427694 | + | 0.310738i | −0.0518655 | + | 0.0376825i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0908326 | − | 0.279554i | 0.0108566 | − | 0.0334131i | ||||
\(71\) | −9.57016 | − | 6.95313i | −1.13577 | − | 0.825185i | −0.149245 | − | 0.988800i | \(-0.547684\pi\) |
−0.986524 | + | 0.163616i | \(0.947684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.78107 | + | 11.6369i | −0.442540 | + | 1.36200i | 0.442618 | + | 0.896710i | \(0.354050\pi\) |
−0.885159 | + | 0.465289i | \(0.845950\pi\) | |||||||
\(74\) | 1.37424 | + | 4.22949i | 0.159753 | + | 0.491668i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.919803 | −0.105509 | ||||||||
\(77\) | −0.174543 | − | 0.296476i | −0.0198911 | − | 0.0337866i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6002 | + | 9.15460i | −1.41764 | + | 1.02997i | −0.425481 | + | 0.904967i | \(0.639895\pi\) |
−0.992156 | + | 0.125006i | \(0.960105\pi\) | |||||||
\(80\) | 2.37639 | + | 7.31378i | 0.265689 | + | 0.817706i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.58279 | − | 1.14997i | −0.174790 | − | 0.126993i | ||||
\(83\) | 3.98278 | + | 2.89366i | 0.437167 | + | 0.317620i | 0.784508 | − | 0.620119i | \(-0.212916\pi\) |
−0.347342 | + | 0.937739i | \(0.612916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.43521 | + | 7.49479i | 0.264135 | + | 0.812925i | ||||
\(86\) | −4.21690 | + | 3.06376i | −0.454721 | + | 0.330374i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.87492 | + | 3.86142i | 0.946070 | + | 0.411628i | ||||
\(89\) | 7.99493 | 0.847461 | 0.423731 | − | 0.905788i | \(-0.360720\pi\) | ||||
0.423731 | + | 0.905788i | \(0.360720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.212393 | + | 0.653678i | 0.0222648 | + | 0.0685240i | ||||
\(92\) | 0.111153 | − | 0.342094i | 0.0115885 | − | 0.0356658i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.79108 | + | 2.75438i | 0.391020 | + | 0.284093i | ||||
\(95\) | −4.23697 | + | 13.0401i | −0.434704 | + | 1.33788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.50008 | + | 1.81641i | −0.253844 | + | 0.184429i | −0.707429 | − | 0.706784i | \(-0.750145\pi\) |
0.453584 | + | 0.891213i | \(0.350145\pi\) | |||||||
\(98\) | −9.53369 | −0.963048 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0953908 | 0.00953908 | ||||||||
\(101\) | −2.02080 | + | 1.46820i | −0.201077 | + | 0.146091i | −0.683767 | − | 0.729700i | \(-0.739660\pi\) |
0.482690 | + | 0.875791i | \(0.339660\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.37288 | + | 13.4583i | −0.430873 | + | 1.32609i | 0.466385 | + | 0.884582i | \(0.345556\pi\) |
−0.897257 | + | 0.441508i | \(0.854444\pi\) | |||||||
\(104\) | −15.6429 | − | 11.3652i | −1.53391 | − | 1.11445i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0266657 | − | 0.0820687i | 0.00259001 | − | 0.00797122i | ||||
\(107\) | −1.56194 | − | 4.80716i | −0.150999 | − | 0.464726i | 0.846735 | − | 0.532015i | \(-0.178565\pi\) |
−0.997734 | + | 0.0672891i | \(0.978565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0865 | 1.54081 | 0.770403 | − | 0.637557i | \(-0.220055\pi\) | ||||
0.770403 | + | 0.637557i | \(0.220055\pi\) | |||||||
\(110\) | 6.22908 | − | 7.03735i | 0.593919 | − | 0.670985i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.310663 | + | 0.225710i | −0.0293549 | + | 0.0213276i | ||||
\(113\) | −3.15243 | − | 9.70217i | −0.296555 | − | 0.912703i | −0.982695 | − | 0.185233i | \(-0.940696\pi\) |
0.686139 | − | 0.727470i | \(-0.259304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.33786 | − | 3.15164i | −0.404507 | − | 0.293892i | ||||
\(116\) | −1.12232 | − | 0.815414i | −0.104205 | − | 0.0757093i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.93683 | − | 9.03865i | −0.270358 | − | 0.832075i | ||||
\(119\) | −0.318352 | + | 0.231296i | −0.0291833 | + | 0.0212029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.33541 | − | 10.9186i | −0.121401 | − | 0.992604i | ||||
\(122\) | 5.78767 | 0.523991 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0948356 | + | 0.291874i | 0.00851649 | + | 0.0262111i | ||||
\(125\) | 3.64914 | − | 11.2309i | 0.326389 | − | 1.00452i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.76775 | − | 2.01089i | −0.245598 | − | 0.178438i | 0.458175 | − | 0.888862i | \(-0.348503\pi\) |
−0.703774 | + | 0.710424i | \(0.748503\pi\) | |||||||
\(128\) | 3.08690 | − | 9.50049i | 0.272846 | − | 0.839733i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −15.1897 | + | 11.0360i | −1.33223 | + | 0.967919i | ||||
\(131\) | 17.7504 | 1.55086 | 0.775432 | − | 0.631431i | \(-0.217532\pi\) | ||||
0.775432 | + | 0.631431i | \(0.217532\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.684652 | −0.0593668 | ||||||||
\(134\) | 5.99567 | − | 4.35611i | 0.517947 | − | 0.376311i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.42086 | − | 10.5283i | 0.293336 | − | 0.902796i | ||||
\(137\) | 7.04789 | + | 5.12059i | 0.602142 | + | 0.437482i | 0.846639 | − | 0.532168i | \(-0.178623\pi\) |
−0.244496 | + | 0.969650i | \(0.578623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.18299 | + | 3.64088i | −0.100340 | + | 0.308815i | −0.988609 | − | 0.150509i | \(-0.951909\pi\) |
0.888268 | + | 0.459325i | \(0.151909\pi\) | |||||||
\(140\) | −0.00928000 | − | 0.0285609i | −0.000784303 | − | 0.00241384i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.1359 | 1.35409 | ||||||||
\(143\) | −2.11143 | + | 21.8740i | −0.176567 | + | 1.82919i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.7300 | + | 12.1550i | −1.38935 | + | 1.00942i | ||||
\(146\) | −5.15757 | − | 15.8734i | −0.426844 | − | 1.31369i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.367574 | + | 0.267058i | 0.0302144 | + | 0.0219521i | ||||
\(149\) | 8.37866 | + | 6.08745i | 0.686407 | + | 0.498704i | 0.875477 | − | 0.483260i | \(-0.160547\pi\) |
−0.189070 | + | 0.981964i | \(0.560547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.09496 | − | 9.52532i | −0.251865 | − | 0.775160i | −0.994431 | − | 0.105387i | \(-0.966392\pi\) |
0.742567 | − | 0.669772i | \(-0.233608\pi\) | |||||||
\(152\) | 15.5822 | − | 11.3212i | 1.26389 | − | 0.918268i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.430321 | + | 0.187230i | 0.0346763 | + | 0.0150874i | ||||
\(155\) | 4.57475 | 0.367453 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.58465 | + | 11.0324i | 0.286086 | + | 0.880482i | 0.986071 | + | 0.166324i | \(0.0531899\pi\) |
−0.699985 | + | 0.714157i | \(0.746810\pi\) | |||||||
\(158\) | 6.56500 | − | 20.2050i | 0.522283 | − | 1.60742i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.32244 | + | 0.960808i | 0.104548 | + | 0.0759585i | ||||
\(161\) | 0.0827364 | − | 0.254636i | 0.00652054 | − | 0.0200682i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4433 | − | 13.3999i | 1.44459 | − | 1.04956i | 0.457537 | − | 0.889191i | \(-0.348732\pi\) |
0.987057 | − | 0.160368i | \(-0.0512682\pi\) | |||||||
\(164\) | −0.199882 | −0.0156081 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.71521 | −0.521201 | ||||||||
\(167\) | −3.69706 | + | 2.68607i | −0.286087 | + | 0.207854i | −0.721568 | − | 0.692344i | \(-0.756578\pi\) |
0.435481 | + | 0.900198i | \(0.356578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.54942 | − | 29.3901i | 0.734571 | − | 2.26078i | ||||
\(170\) | −8.69645 | − | 6.31834i | −0.666988 | − | 0.484595i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.164560 | + | 0.506464i | −0.0125476 | + | 0.0386175i | ||||
\(173\) | −0.463595 | − | 1.42680i | −0.0352465 | − | 0.108477i | 0.931885 | − | 0.362753i | \(-0.118163\pi\) |
−0.967132 | + | 0.254275i | \(0.918163\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0710038 | 0.00536738 | ||||||||
\(176\) | −11.9873 | + | 2.65455i | −0.903575 | + | 0.200094i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.82274 | + | 6.41010i | −0.661292 | + | 0.480457i | ||||
\(179\) | 2.76184 | + | 8.50007i | 0.206430 | + | 0.635325i | 0.999652 | + | 0.0263926i | \(0.00840199\pi\) |
−0.793222 | + | 0.608933i | \(0.791598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9613 | − | 12.3231i | −1.26072 | − | 0.915967i | −0.261927 | − | 0.965088i | \(-0.584358\pi\) |
−0.998793 | + | 0.0491209i | \(0.984358\pi\) | |||||||
\(182\) | −0.758484 | − | 0.551071i | −0.0562225 | − | 0.0408481i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.32755 | + | 7.16346i | 0.171589 | + | 0.528098i | ||||
\(185\) | 5.47928 | − | 3.98093i | 0.402845 | − | 0.292684i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.2840 | + | 2.72024i | −0.898291 | + | 0.198924i | ||||
\(188\) | 0.478754 | 0.0349167 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.77945 | − | 17.7873i | −0.419286 | − | 1.29043i | ||||
\(191\) | 2.76336 | − | 8.50475i | 0.199950 | − | 0.615382i | −0.799933 | − | 0.600089i | \(-0.795132\pi\) |
0.999883 | − | 0.0152932i | \(-0.00486817\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.62654 | − | 3.36138i | −0.333026 | − | 0.241957i | 0.408688 | − | 0.912674i | \(-0.365987\pi\) |
−0.741713 | + | 0.670717i | \(0.765987\pi\) | |||||||
\(194\) | 1.30260 | − | 4.00898i | 0.0935209 | − | 0.287828i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.787998 | + | 0.572514i | −0.0562856 | + | 0.0408939i | ||||
\(197\) | −6.94318 | −0.494681 | −0.247341 | − | 0.968929i | \(-0.579557\pi\) | ||||
−0.247341 | + | 0.968929i | \(0.579557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0199 | 1.70273 | 0.851363 | − | 0.524576i | \(-0.175776\pi\) | ||||
0.851363 | + | 0.524576i | \(0.175776\pi\) | |||||||
\(200\) | −1.61600 | + | 1.17409i | −0.114269 | + | 0.0830210i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.05288 | − | 3.24043i | 0.0740805 | − | 0.227996i | ||||
\(203\) | −0.835395 | − | 0.606950i | −0.0586332 | − | 0.0425995i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.920733 | + | 2.83372i | −0.0643068 | + | 0.197916i | ||||
\(206\) | −5.96484 | − | 18.3579i | −0.415590 | − | 1.27905i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 24.5282 | 1.70072 | ||||||||
\(209\) | −20.0728 | − | 8.73352i | −1.38846 | − | 0.604110i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.27939 | + | 2.38262i | −0.225763 | + | 0.164026i | −0.694917 | − | 0.719090i | \(-0.744559\pi\) |
0.469154 | + | 0.883116i | \(0.344559\pi\) | |||||||
\(212\) | −0.00272433 | − | 0.00838463i | −0.000187108 | − | 0.000575859i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.57791 | + | 4.05259i | 0.381298 | + | 0.277029i | ||||
\(215\) | 6.42212 | + | 4.66594i | 0.437985 | + | 0.318215i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0705905 | + | 0.217255i | 0.00479200 | + | 0.0147482i | ||||
\(218\) | −17.7521 | + | 12.8977i | −1.20233 | + | 0.873540i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0922541 | − | 0.955731i | 0.00621977 | − | 0.0644354i | ||||
\(221\) | 25.1352 | 1.69078 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.12925 | − | 9.63083i | −0.209550 | − | 0.644928i | −0.999496 | − | 0.0317515i | \(-0.989891\pi\) |
0.789946 | − | 0.613176i | \(-0.210109\pi\) | |||||||
\(224\) | −0.0252230 | + | 0.0776284i | −0.00168528 | + | 0.00518676i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.2577 | + | 8.17923i | 0.748854 | + | 0.544074i | ||||
\(227\) | −2.02236 | + | 6.22419i | −0.134229 | + | 0.413114i | −0.995469 | − | 0.0950838i | \(-0.969688\pi\) |
0.861240 | + | 0.508198i | \(0.169688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5011 | + | 9.08257i | −0.826095 | + | 0.600193i | −0.918452 | − | 0.395533i | \(-0.870560\pi\) |
0.0923570 | + | 0.995726i | \(0.470560\pi\) | |||||||
\(230\) | 7.31390 | 0.482264 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 29.0494 | 1.90719 | ||||||||
\(233\) | 17.2087 | − | 12.5028i | 1.12738 | − | 0.819087i | 0.142066 | − | 0.989857i | \(-0.454625\pi\) |
0.985311 | + | 0.170770i | \(0.0546255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.20533 | − | 6.78730i | 0.143860 | − | 0.442754i | ||||
\(236\) | −0.785527 | − | 0.570719i | −0.0511334 | − | 0.0371506i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.165868 | − | 0.510490i | 0.0107516 | − | 0.0330902i | ||||
\(239\) | −5.35950 | − | 16.4949i | −0.346677 | − | 1.06696i | −0.960680 | − | 0.277659i | \(-0.910441\pi\) |
0.614002 | − | 0.789304i | \(-0.289559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6429 | 0.685572 | 0.342786 | − | 0.939414i | \(-0.388629\pi\) | ||||
0.342786 | + | 0.939414i | \(0.388629\pi\) | |||||||
\(242\) | 10.2279 | + | 10.9785i | 0.657476 | + | 0.705724i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.478374 | − | 0.347559i | 0.0306248 | − | 0.0222502i | ||||
\(245\) | 4.48671 | + | 13.8087i | 0.286646 | + | 0.882204i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.3802 | + | 25.7052i | 2.25119 | + | 1.63558i | ||||
\(248\) | −5.19905 | − | 3.77733i | −0.330140 | − | 0.239861i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.97761 | + | 15.3195i | 0.314812 | + | 0.968892i | ||||
\(251\) | 22.6506 | − | 16.4566i | 1.42969 | − | 1.03873i | 0.439619 | − | 0.898184i | \(-0.355113\pi\) |
0.990074 | − | 0.140548i | \(-0.0448866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.67386 | − | 6.41008i | 0.356712 | − | 0.402998i | ||||
\(254\) | 4.66660 | 0.292809 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.02841 | − | 3.16513i | −0.0642759 | − | 0.197821i | ||||
\(257\) | 5.55370 | − | 17.0925i | 0.346430 | − | 1.06620i | −0.614383 | − | 0.789008i | \(-0.710595\pi\) |
0.960814 | − | 0.277195i | \(-0.0894048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.273602 | + | 0.198784i | 0.0170008 | + | 0.0123518i | ||||
\(260\) | −0.592763 | + | 1.82434i | −0.0367616 | + | 0.113141i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.5884 | + | 14.2318i | −1.21017 | + | 0.879242i | ||||
\(263\) | 13.7602 | 0.848493 | 0.424247 | − | 0.905547i | \(-0.360539\pi\) | ||||
0.424247 | + | 0.905547i | \(0.360539\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.131418 | −0.00807296 | ||||||||
\(266\) | 0.755542 | − | 0.548933i | 0.0463252 | − | 0.0336573i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.233975 | − | 0.720100i | 0.0142923 | − | 0.0439871i | ||||
\(269\) | −11.5788 | − | 8.41248i | −0.705971 | − | 0.512918i | 0.175900 | − | 0.984408i | \(-0.443716\pi\) |
−0.881871 | + | 0.471490i | \(0.843716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.475672 | + | 1.46397i | −0.0288950 | + | 0.0889296i | −0.964464 | − | 0.264214i | \(-0.914887\pi\) |
0.935569 | + | 0.353144i | \(0.114887\pi\) | |||||||
\(272\) | 4.33950 | + | 13.3556i | 0.263121 | + | 0.809803i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.8832 | −0.717889 | ||||||||
\(275\) | 2.08170 | + | 0.905734i | 0.125531 | + | 0.0546178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3456 | − | 14.0554i | 1.16236 | − | 0.844507i | 0.172289 | − | 0.985046i | \(-0.444884\pi\) |
0.990075 | + | 0.140539i | \(0.0448836\pi\) | |||||||
\(278\) | −1.61367 | − | 4.96635i | −0.0967813 | − | 0.297862i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.508746 | + | 0.369625i | 0.0304034 | + | 0.0220893i | ||||
\(281\) | −12.3708 | − | 8.98791i | −0.737980 | − | 0.536174i | 0.154098 | − | 0.988056i | \(-0.450753\pi\) |
−0.892078 | + | 0.451882i | \(0.850753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.32988 | + | 19.4814i | 0.376272 | + | 1.15805i | 0.942616 | + | 0.333878i | \(0.108357\pi\) |
−0.566344 | + | 0.824169i | \(0.691643\pi\) | |||||||
\(284\) | 1.33370 | − | 0.968987i | 0.0791403 | − | 0.0574988i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.2078 | − | 25.8317i | −0.899258 | − | 1.52746i | ||||
\(287\) | −0.148781 | −0.00878227 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.806389 | − | 2.48181i | −0.0474347 | − | 0.145989i | ||||
\(290\) | 8.71669 | − | 26.8272i | 0.511861 | − | 1.57535i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.37952 | − | 1.00228i | −0.0807301 | − | 0.0586539i | ||||
\(293\) | −3.36576 | + | 10.3587i | −0.196630 | + | 0.605164i | 0.803324 | + | 0.595542i | \(0.203063\pi\) |
−0.999954 | + | 0.00962177i | \(0.996937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7095 | + | 8.50747i | −0.681755 | + | 0.495324i | ||||
\(296\) | −9.51404 | −0.552993 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.1269 | −0.818352 | ||||||||
\(299\) | −13.8358 | + | 10.0523i | −0.800145 | + | 0.581340i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.122490 | + | 0.376985i | −0.00706019 | + | 0.0217290i | ||||
\(302\) | 11.0525 | + | 8.03014i | 0.636002 | + | 0.462083i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.55022 | + | 23.2372i | −0.433035 | + | 1.33274i | ||||
\(305\) | −2.72377 | − | 8.38291i | −0.155963 | − | 0.480004i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2173 | 0.925568 | 0.462784 | − | 0.886471i | \(-0.346850\pi\) | ||||
0.462784 | + | 0.886471i | \(0.346850\pi\) | |||||||
\(308\) | 0.0468113 | − | 0.0103662i | 0.00266732 | − | 0.000590670i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.04843 | + | 3.66790i | −0.286732 | + | 0.208323i | ||||
\(311\) | 3.95563 | + | 12.1742i | 0.224303 | + | 0.690334i | 0.998362 | + | 0.0572201i | \(0.0182237\pi\) |
−0.774058 | + | 0.633114i | \(0.781776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.80832 | − | 7.12617i | −0.554399 | − | 0.402795i | 0.275006 | − | 0.961443i | \(-0.411320\pi\) |
−0.829405 | + | 0.558648i | \(0.811320\pi\) | |||||||
\(314\) | −12.8013 | − | 9.30066i | −0.722417 | − | 0.524867i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.670719 | − | 2.06426i | −0.0377309 | − | 0.116124i | ||||
\(317\) | 6.78257 | − | 4.92782i | 0.380947 | − | 0.276774i | −0.380789 | − | 0.924662i | \(-0.624348\pi\) |
0.761736 | + | 0.647888i | \(0.224348\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.7499 | − | 28.4511i | −0.937816 | − | 1.59296i | ||||
\(320\) | −17.6100 | −0.984432 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.112857 | + | 0.347337i | 0.00628926 | + | 0.0193564i | ||||
\(323\) | −7.73708 | + | 23.8123i | −0.430503 | + | 1.32495i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.66920 | − | 2.66583i | −0.203531 | − | 0.147874i | ||||
\(326\) | −9.60938 | + | 29.5746i | −0.532215 | + | 1.63799i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.38616 | − | 2.46019i | 0.186970 | − | 0.135841i | ||||
\(329\) | 0.356358 | 0.0196467 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.15077 | −0.448007 | −0.224003 | − | 0.974588i | \(-0.571913\pi\) | ||||
−0.224003 | + | 0.974588i | \(0.571913\pi\) | |||||||
\(332\) | −0.555039 | + | 0.403259i | −0.0304617 | + | 0.0221317i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.92625 | − | 5.92838i | 0.105400 | − | 0.324387i | ||||
\(335\) | −9.13109 | − | 6.63412i | −0.498884 | − | 0.362461i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.28005 | − | 28.5611i | 0.505517 | − | 1.55582i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.799900 | − | 0.600133i | \(-0.204886\pi\) | |||||||
\(338\) | 13.0259 | + | 40.0897i | 0.708517 | + | 2.18059i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.09822 | −0.0595596 | ||||||||
\(341\) | −0.701753 | + | 7.26999i | −0.0380020 | + | 0.393692i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.17399 | + | 0.852953i | −0.0633895 | + | 0.0460551i | ||||
\(344\) | −3.44590 | − | 10.6054i | −0.185790 | − | 0.571804i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.65556 | + | 1.20283i | 0.0890035 | + | 0.0646648i | ||||
\(347\) | −27.5191 | − | 19.9938i | −1.47730 | − | 1.07332i | −0.978413 | − | 0.206661i | \(-0.933740\pi\) |
−0.498892 | − | 0.866664i | \(-0.666260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.27633 | + | 22.3943i | 0.389493 | + | 1.19874i | 0.933168 | + | 0.359441i | \(0.117033\pi\) |
−0.543675 | + | 0.839296i | \(0.682967\pi\) | |||||||
\(350\) | −0.0783556 | + | 0.0569287i | −0.00418829 | + | 0.00304297i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.72973 | + | 1.95418i | −0.0921950 | + | 0.104158i | ||||
\(353\) | 15.8273 | 0.842404 | 0.421202 | − | 0.906967i | \(-0.361608\pi\) | ||||
0.421202 | + | 0.906967i | \(0.361608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.59381 | − | 23.3714i | −0.403038 | − | 1.24042i | ||||
\(356\) | −0.344298 | + | 1.05964i | −0.0182478 | + | 0.0561608i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.86291 | − | 7.16582i | −0.521271 | − | 0.378726i | ||||
\(359\) | 0.135487 | − | 0.416986i | 0.00715073 | − | 0.0220077i | −0.947417 | − | 0.320000i | \(-0.896317\pi\) |
0.954568 | + | 0.297992i | \(0.0963170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.8716 | + | 14.4376i | −1.04588 | + | 0.759873i | ||||
\(362\) | 28.5977 | 1.50306 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0957844 | −0.00502047 | ||||||||
\(365\) | −20.5639 | + | 14.9405i | −1.07636 | + | 0.782024i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.28173 | + | 13.1778i | −0.223504 | + | 0.687876i | 0.774936 | + | 0.632040i | \(0.217782\pi\) |
−0.998440 | + | 0.0558357i | \(0.982218\pi\) | |||||||
\(368\) | −7.73000 | − | 5.61617i | −0.402954 | − | 0.292763i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.85483 | + | 8.78625i | −0.148415 | + | 0.456775i | ||||
\(371\) | −0.00202784 | − | 0.00624107i | −0.000105280 | − | 0.000324020i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.01569 | 0.363259 | 0.181629 | − | 0.983367i | \(-0.441863\pi\) | ||||
0.181629 | + | 0.983367i | \(0.441863\pi\) | |||||||
\(374\) | 11.3748 | − | 12.8508i | 0.588179 | − | 0.664500i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.11049 | + | 5.89262i | −0.418267 | + | 0.303889i | ||||
\(377\) | 20.3821 | + | 62.7297i | 1.04973 | + | 3.23075i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.06973 | + | 5.86300i | 0.414514 | + | 0.301162i | 0.775427 | − | 0.631437i | \(-0.217535\pi\) |
−0.360913 | + | 0.932600i | \(0.617535\pi\) | |||||||
\(380\) | −1.54585 | − | 1.12313i | −0.0793006 | − | 0.0576153i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.76937 | + | 11.6009i | 0.192858 | + | 0.593555i | ||||
\(383\) | −15.2581 | + | 11.0857i | −0.779653 | + | 0.566451i | −0.904875 | − | 0.425678i | \(-0.860036\pi\) |
0.125222 | + | 0.992129i | \(0.460036\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0686690 | − | 0.711395i | 0.00349969 | − | 0.0362560i | ||||
\(386\) | 7.80064 | 0.397042 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.133081 | − | 0.409581i | −0.00675616 | − | 0.0207933i | ||||
\(389\) | 7.21474 | − | 22.2047i | 0.365802 | − | 1.12582i | −0.583675 | − | 0.811987i | \(-0.698386\pi\) |
0.949477 | − | 0.313836i | \(-0.101614\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.92131 | − | 5.75517i | −0.400598 | − | 0.291051i | ||||
\(392\) | 6.30271 | − | 19.3977i | 0.318335 | − | 0.979734i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.66209 | − | 5.56683i | 0.386011 | − | 0.280453i | ||||
\(395\) | −32.3547 | −1.62794 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.6991 | −1.39018 | −0.695090 | − | 0.718923i | \(-0.744636\pi\) | ||||
−0.695090 | + | 0.718923i | \(0.744636\pi\) | |||||||
\(398\) | −26.5070 | + | 19.2585i | −1.32868 | + | 0.965339i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.783017 | − | 2.40988i | 0.0391509 | − | 0.120494i | ||||
\(401\) | 12.2209 | + | 8.87901i | 0.610283 | + | 0.443397i | 0.849514 | − | 0.527566i | \(-0.176895\pi\) |
−0.239231 | + | 0.970963i | \(0.576895\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.50899 | − | 13.8772i | 0.224609 | − | 0.691274i | ||||
\(404\) | −0.107569 | − | 0.331062i | −0.00535174 | − | 0.0164710i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.40853 | 0.0699041 | ||||||||
\(407\) | 5.48582 | + | 9.31810i | 0.271922 | + | 0.461881i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.61125 | − | 5.52990i | 0.376352 | − | 0.273436i | −0.383488 | − | 0.923546i | \(-0.625277\pi\) |
0.759840 | + | 0.650110i | \(0.225277\pi\) | |||||||
\(410\) | −1.25593 | − | 3.86535i | −0.0620259 | − | 0.190896i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.59544 | − | 1.15915i | −0.0786017 | − | 0.0571075i | ||||
\(413\) | −0.584704 | − | 0.424812i | −0.0287714 | − | 0.0209036i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.16029 | + | 9.72636i | 0.155132 | + | 0.477448i | ||||
\(416\) | 4.21798 | − | 3.06454i | 0.206804 | − | 0.150252i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 29.1534 | − | 6.45593i | 1.42594 | − | 0.315770i | ||||
\(419\) | −20.1038 | −0.982137 | −0.491069 | − | 0.871121i | \(-0.663394\pi\) | ||||
−0.491069 | + | 0.871121i | \(0.663394\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.96940 | − | 12.2166i | −0.193457 | − | 0.595398i | −0.999991 | − | 0.00421133i | \(-0.998659\pi\) |
0.806534 | − | 0.591187i | \(-0.201341\pi\) | |||||||
\(422\) | 1.70863 | − | 5.25863i | 0.0831750 | − | 0.255986i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.149353 | + | 0.108511i | 0.00725320 | + | 0.00526976i | ||||
\(425\) | 0.802396 | − | 2.46952i | 0.0389219 | − | 0.119789i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.356076 | − | 0.258704i | 0.0172317 | − | 0.0125196i | ||||
\(428\) | 0.704401 | 0.0340485 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.8281 | −0.522177 | ||||||||
\(431\) | −12.3785 | + | 8.99352i | −0.596252 | + | 0.433202i | −0.844547 | − | 0.535482i | \(-0.820130\pi\) |
0.248295 | + | 0.968685i | \(0.420130\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.72241 | + | 11.4564i | −0.178887 | + | 0.550559i | −0.999790 | − | 0.0205099i | \(-0.993471\pi\) |
0.820902 | + | 0.571069i | \(0.193471\pi\) | |||||||
\(434\) | −0.252088 | − | 0.183153i | −0.0121006 | − | 0.00879162i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.692757 | + | 2.13209i | −0.0331771 | + | 0.102109i | ||||
\(437\) | −5.26431 | − | 16.2019i | −0.251826 | − | 0.775041i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.14815 | −0.197980 | −0.0989902 | − | 0.995088i | \(-0.531561\pi\) | ||||
−0.0989902 | + | 0.995088i | \(0.531561\pi\) | |||||||
\(440\) | 10.2005 | + | 17.3264i | 0.486290 | + | 0.826003i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.7378 | + | 20.1527i | −1.31935 | + | 0.958564i | ||||
\(443\) | −5.89970 | − | 18.1574i | −0.280303 | − | 0.862684i | −0.987767 | − | 0.155935i | \(-0.950161\pi\) |
0.707464 | − | 0.706749i | \(-0.249839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4366 | + | 9.76224i | 0.636954 | + | 0.462774i | ||||
\(446\) | 11.1750 | + | 8.11909i | 0.529150 | + | 0.384450i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.271731 | − | 0.836302i | −0.0128381 | − | 0.0395116i | ||||
\(449\) | 2.76223 | − | 2.00688i | 0.130358 | − | 0.0947104i | −0.520696 | − | 0.853742i | \(-0.674327\pi\) |
0.651053 | + | 0.759032i | \(0.274327\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.36199 | − | 1.89787i | −0.205398 | − | 0.0893673i | ||||
\(452\) | 1.42167 | 0.0668699 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.75861 | − | 8.49012i | −0.129468 | − | 0.398461i | ||||
\(455\) | −0.441220 | + | 1.35794i | −0.0206847 | + | 0.0636611i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.9018 | + | 17.3657i | 1.11808 | + | 0.812332i | 0.983917 | − | 0.178628i | \(-0.0571657\pi\) |
0.134162 | + | 0.990959i | \(0.457166\pi\) | |||||||
\(458\) | 6.51334 | − | 20.0460i | 0.304348 | − | 0.936688i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.604523 | − | 0.439212i | 0.0281860 | − | 0.0204784i | ||||
\(461\) | 40.7758 | 1.89912 | 0.949560 | − | 0.313586i | \(-0.101530\pi\) | ||||
0.949560 | + | 0.313586i | \(0.101530\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.7501 | −1.80087 | −0.900435 | − | 0.434990i | \(-0.856752\pi\) | ||||
−0.900435 | + | 0.434990i | \(0.856752\pi\) | |||||||
\(464\) | −29.8126 | + | 21.6601i | −1.38401 | + | 1.00555i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.96609 | + | 27.5948i | −0.415346 | + | 1.27830i | ||||
\(467\) | 22.7043 | + | 16.4956i | 1.05063 | + | 0.763327i | 0.972332 | − | 0.233603i | \(-0.0750515\pi\) |
0.0782979 | + | 0.996930i | \(0.475051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.174158 | − | 0.536003i | 0.00804187 | − | 0.0247503i | ||||
\(470\) | 3.00818 | + | 9.25823i | 0.138757 | + | 0.427050i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.3320 | 0.935858 | ||||||||
\(473\) | −8.40005 | + | 9.49001i | −0.386235 | + | 0.436351i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.65497 | − | 2.65549i | 0.167702 | − | 0.121842i | ||||
\(476\) | −0.0169461 | − | 0.0521547i | −0.000776723 | − | 0.00239051i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.1395 | + | 13.9057i | 0.875421 | + | 0.636031i | ||||
\(479\) | 12.8023 | + | 9.30143i | 0.584953 | + | 0.424993i | 0.840506 | − | 0.541802i | \(-0.182258\pi\) |
−0.255553 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.67540 | − | 20.5448i | −0.304372 | − | 0.936761i | ||||
\(482\) | −11.7449 | + | 8.53319i | −0.534967 | + | 0.388676i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.50465 | + | 0.293212i | 0.0683934 | + | 0.0133278i | ||||
\(485\) | −6.41966 | −0.291502 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.77582 | − | 5.46540i | −0.0804699 | − | 0.247661i | 0.902726 | − | 0.430217i | \(-0.141563\pi\) |
−0.983195 | + | 0.182556i | \(0.941563\pi\) | |||||||
\(488\) | −3.82622 | + | 11.7759i | −0.173205 | + | 0.533070i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.0227 | − | 11.6411i | −0.723830 | − | 0.525893i | ||||
\(491\) | −11.0256 | + | 33.9334i | −0.497580 | + | 1.53139i | 0.315317 | + | 0.948986i | \(0.397889\pi\) |
−0.812897 | + | 0.582407i | \(0.802111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.5504 | + | 22.1962i | −1.37592 | + | 0.999666i | ||||
\(494\) | −59.6532 | −2.68392 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.15214 | 0.366042 | ||||||||
\(497\) | 0.992731 | − | 0.721261i | 0.0445301 | − | 0.0323530i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.22074 | − | 25.3008i | 0.368011 | − | 1.13262i | −0.580064 | − | 0.814571i | \(-0.696972\pi\) |
0.948074 | − | 0.318049i | \(-0.103028\pi\) | |||||||
\(500\) | 1.33138 | + | 0.967306i | 0.0595412 | + | 0.0432592i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.8015 | + | 36.3211i | −0.526725 | + | 1.62109i | ||||
\(503\) | −9.97834 | − | 30.7102i | −0.444912 | − | 1.36930i | −0.882580 | − | 0.470162i | \(-0.844195\pi\) |
0.437668 | − | 0.899137i | \(-0.355805\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.18898 | −0.230906 | ||||||||
\(506\) | −1.12193 | + | 11.6229i | −0.0498758 | + | 0.516702i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.385713 | − | 0.280237i | 0.0171133 | − | 0.0124335i | ||||
\(509\) | −10.0215 | − | 30.8431i | −0.444197 | − | 1.36710i | −0.883362 | − | 0.468691i | \(-0.844726\pi\) |
0.439166 | − | 0.898406i | \(-0.355274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.02684 | − | 0.746041i | −0.0454246 | − | 0.0330029i | ||||
\(512\) | 19.8358 | + | 14.4116i | 0.876627 | + | 0.636907i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.57554 | + | 23.3151i | 0.334143 | + | 1.02839i | ||||
\(515\) | −23.7826 | + | 17.2790i | −1.04799 | + | 0.761406i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4478 | + | 4.54576i | 0.459493 | + | 0.199922i | ||||
\(518\) | −0.461311 | −0.0202688 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.4125 | − | 38.2017i | −0.544323 | − | 1.67525i | ||||
\(521\) | −4.14919 | + | 12.7699i | −0.181779 | + | 0.559460i | −0.999878 | − | 0.0156184i | \(-0.995028\pi\) |
0.818099 | + | 0.575078i | \(0.195028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.5065 | − | 10.5396i | −0.634325 | − | 0.460864i | 0.223571 | − | 0.974688i | \(-0.428229\pi\) |
−0.857896 | + | 0.513824i | \(0.828229\pi\) | |||||||
\(524\) | −0.764415 | + | 2.35263i | −0.0333936 | + | 0.102775i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.1850 | + | 11.0326i | −0.662098 | + | 0.481042i | ||||
\(527\) | 8.35390 | 0.363901 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.3380 | −0.710349 | ||||||||
\(530\) | 0.145026 | − | 0.105367i | 0.00629951 | − | 0.00457686i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.0294842 | − | 0.0907431i | 0.00127830 | − | 0.00393421i | ||||
\(533\) | 7.68843 | + | 5.58597i | 0.333023 | + | 0.241955i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.24475 | − | 9.98630i | 0.140283 | − | 0.431746i | ||||
\(536\) | 4.89944 | + | 15.0789i | 0.211623 | + | 0.651310i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.5226 | 0.841677 | ||||||||
\(539\) | −22.6324 | + | 5.01188i | −0.974846 | + | 0.215877i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9701 | + | 8.69682i | −0.514637 | + | 0.373906i | −0.814580 | − | 0.580052i | \(-0.803032\pi\) |
0.299943 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(542\) | −0.648841 | − | 1.99693i | −0.0278701 | − | 0.0857754i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.41489 | + | 1.75452i | 0.103537 | + | 0.0752244i | ||||
\(545\) | 27.0355 | + | 19.6425i | 1.15807 | + | 0.841391i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.16340 | + | 18.9690i | 0.263528 | + | 0.811056i | 0.992029 | + | 0.126011i | \(0.0402174\pi\) |
−0.728501 | + | 0.685045i | \(0.759783\pi\) | |||||||
\(548\) | −0.982193 | + | 0.713605i | −0.0419572 | + | 0.0304837i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.02344 | + | 0.669531i | −0.128920 | + | 0.0285489i | ||||
\(551\) | −65.7021 | −2.79900 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.499247 | − | 1.53652i | −0.0212301 | − | 0.0653397i | ||||
\(554\) | −10.0795 | + | 31.0214i | −0.428236 | + | 1.31798i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.431614 | − | 0.313586i | −0.0183045 | − | 0.0132990i | ||||
\(557\) | 4.01834 | − | 12.3672i | 0.170262 | − | 0.524014i | −0.829123 | − | 0.559066i | \(-0.811160\pi\) |
0.999385 | + | 0.0350524i | \(0.0111598\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.4837 | − | 14.8823i | 0.866367 | − | 0.629452i | ||||
\(560\) | −0.797716 | −0.0337096 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.8579 | 0.879838 | ||||||||
\(563\) | 35.3818 | − | 25.7064i | 1.49116 | − | 1.08339i | 0.517425 | − | 0.855728i | \(-0.326890\pi\) |
0.973739 | − | 0.227666i | \(-0.0731095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.54879 | − | 20.1551i | 0.275509 | − | 0.847931i | ||||
\(566\) | −22.6049 | − | 16.4234i | −0.950153 | − | 0.690327i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.6674 | + | 32.8309i | −0.447595 | + | 1.37755i | ||||
\(569\) | 0.121574 | + | 0.374166i | 0.00509664 | + | 0.0156858i | 0.953572 | − | 0.301164i | \(-0.0973750\pi\) |
−0.948476 | + | 0.316849i | \(0.897375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.5003 | 1.61119 | 0.805594 | − | 0.592468i | \(-0.201846\pi\) | ||||
0.805594 | + | 0.592468i | \(0.201846\pi\) | |||||||
\(572\) | −2.80823 | − | 1.22184i | −0.117418 | − | 0.0510877i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.164186 | − | 0.119288i | 0.00685300 | − | 0.00497899i | ||||
\(575\) | 0.545951 | + | 1.68026i | 0.0227677 | + | 0.0700718i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.0503581 | − | 0.0365873i | −0.00209643 | − | 0.00152315i | 0.586737 | − | 0.809778i | \(-0.300412\pi\) |
−0.588833 | + | 0.808255i | \(0.700412\pi\) | |||||||
\(578\) | 2.87973 | + | 2.09224i | 0.119781 | + | 0.0870259i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.890549 | − | 2.74083i | −0.0369780 | − | 0.113807i | ||||
\(581\) | −0.413141 | + | 0.300164i | −0.0171400 | + | 0.0124529i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0201592 | − | 0.208844i | 0.000834907 | − | 0.00864945i | ||||
\(584\) | 35.7065 | 1.47754 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.59107 | − | 14.1299i | −0.189655 | − | 0.583699i | ||||
\(587\) | −3.67814 | + | 11.3202i | −0.151813 | + | 0.467233i | −0.997824 | − | 0.0659326i | \(-0.978998\pi\) |
0.846011 | + | 0.533166i | \(0.178998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.7589 | + | 8.54334i | 0.484517 | + | 0.352022i | ||||
\(590\) | 6.10092 | − | 18.7767i | 0.251171 | − | 0.773025i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.76400 | − | 7.09396i | 0.401298 | − | 0.291560i | ||||
\(593\) | 29.3055 | 1.20343 | 0.601717 | − | 0.798709i | \(-0.294484\pi\) | ||||
0.601717 | + | 0.798709i | \(0.294484\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.817458 | −0.0335125 | ||||||||
\(596\) | −1.16765 | + | 0.848346i | −0.0478288 | + | 0.0347496i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.20876 | − | 22.1863i | 0.294788 | − | 0.907264i | ||||
\(599\) | −6.86622 | − | 4.98860i | −0.280546 | − | 0.203829i | 0.438609 | − | 0.898678i | \(-0.355471\pi\) |
−0.719156 | + | 0.694849i | \(0.755471\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.29121 | − | 19.3623i | 0.256624 | − | 0.789806i | −0.736882 | − | 0.676022i | \(-0.763703\pi\) |
0.993505 | − | 0.113785i | \(-0.0362974\pi\) | |||||||
\(602\) | −0.167082 | − | 0.514227i | −0.00680977 | − | 0.0209583i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.39576 | 0.0567927 | ||||||||
\(605\) | 11.0879 | − | 19.9809i | 0.450787 | − | 0.812337i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.6781 | + | 17.9297i | −1.00165 | + | 0.727743i | −0.962442 | − | 0.271488i | \(-0.912484\pi\) |
−0.0392104 | + | 0.999231i | \(0.512484\pi\) | |||||||
\(608\) | 1.60488 | + | 4.93930i | 0.0650863 | + | 0.200315i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.72696 | + | 7.06705i | 0.393833 | + | 0.286137i | ||||
\(611\) | −18.4152 | − | 13.3794i | −0.745001 | − | 0.541275i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6491 | + | 32.7746i | 0.430114 | + | 1.32376i | 0.898011 | + | 0.439972i | \(0.145012\pi\) |
−0.467897 | + | 0.883783i | \(0.654988\pi\) | |||||||
\(614\) | −17.8964 | + | 13.0025i | −0.722241 | + | 0.524739i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.665433 | + | 0.751777i | −0.0268110 | + | 0.0302900i | ||||
\(617\) | 0.224835 | 0.00905152 | 0.00452576 | − | 0.999990i | \(-0.498559\pi\) | ||||
0.00452576 | + | 0.999990i | \(0.498559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.183719 | + | 0.565428i | 0.00738427 | + | 0.0227265i | 0.954681 | − | 0.297632i | \(-0.0961967\pi\) |
−0.947296 | + | 0.320358i | \(0.896197\pi\) | |||||||
\(620\) | −0.197010 | + | 0.606333i | −0.00791210 | + | 0.0243509i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.1261 | − | 10.2632i | −0.566405 | − | 0.411517i | ||||
\(623\) | −0.256277 | + | 0.788739i | −0.0102675 | + | 0.0316002i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0775 | − | 12.4076i | 0.683102 | − | 0.496302i | ||||
\(626\) | 16.5374 | 0.660969 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.61660 | −0.0645092 | ||||||||
\(629\) | 10.0056 | − | 7.26953i | 0.398951 | − | 0.289855i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7136 | − | 32.9732i | 0.426504 | − | 1.31264i | −0.475044 | − | 0.879962i | \(-0.657568\pi\) |
0.901547 | − | 0.432681i | \(-0.142432\pi\) | |||||||
\(632\) | 36.7700 | + | 26.7150i | 1.46263 | + | 1.06266i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.53386 | + | 10.8761i | −0.140348 | + | 0.431946i | ||||
\(635\) | −2.19618 | − | 6.75914i | −0.0871527 | − | 0.268228i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.3100 | 1.83487 | ||||||||
\(638\) | 41.2955 | + | 17.9674i | 1.63490 | + | 0.711336i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.7886 | − | 12.1976i | 0.663626 | − | 0.482152i | ||||
\(641\) | −6.75129 | − | 20.7783i | −0.266660 | − | 0.820695i | −0.991306 | − | 0.131574i | \(-0.957997\pi\) |
0.724646 | − | 0.689121i | \(-0.242003\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.7049 | − | 17.9492i | −0.974267 | − | 0.707846i | −0.0178469 | − | 0.999841i | \(-0.505681\pi\) |
−0.956420 | + | 0.291994i | \(0.905681\pi\) | |||||||
\(644\) | 0.0301863 | + | 0.0219316i | 0.00118951 | + | 0.000864226i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5538 | − | 32.4812i | −0.415233 | − | 1.27796i | ||||
\(647\) | 21.6341 | − | 15.7181i | 0.850525 | − | 0.617943i | −0.0747658 | − | 0.997201i | \(-0.523821\pi\) |
0.925291 | + | 0.379259i | \(0.123821\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.7235 | − | 19.9133i | −0.460187 | − | 0.781665i | ||||
\(650\) | 6.18651 | 0.242655 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.981752 | + | 3.02152i | 0.0384484 | + | 0.118332i | ||||
\(653\) | 9.07240 | − | 27.9220i | 0.355030 | − | 1.09267i | −0.600962 | − | 0.799278i | \(-0.705216\pi\) |
0.955992 | − | 0.293393i | \(-0.0947844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.8320 | + | 21.6742i | 1.16563 | + | 0.846883i | ||||
\(656\) | −1.64073 | + | 5.04965i | −0.0640598 | + | 0.197156i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.393256 | + | 0.285717i | −0.0153307 | + | 0.0111384i | ||||
\(659\) | −36.5480 | −1.42371 | −0.711854 | − | 0.702328i | \(-0.752144\pi\) | ||||
−0.711854 | + | 0.702328i | \(0.752144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.81296 | −0.148307 | −0.0741535 | − | 0.997247i | \(-0.523625\pi\) | ||||
−0.0741535 | + | 0.997247i | \(0.523625\pi\) | |||||||
\(662\) | 8.99471 | − | 6.53504i | 0.349589 | − | 0.253992i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.43941 | − | 13.6631i | 0.172283 | − | 0.530232i | ||||
\(665\) | −1.15065 | − | 0.835996i | −0.0446203 | − | 0.0324185i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.93974 | − | 24.4360i | 0.307428 | − | 0.946166i | ||||
\(668\) | −0.196797 | − | 0.605679i | −0.00761431 | − | 0.0234344i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.3956 | 0.594783 | ||||||||
\(671\) | 13.7396 | − | 3.04259i | 0.530410 | − | 0.117458i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.1643 | + | 8.83787i | −0.468899 | + | 0.340675i | −0.797012 | − | 0.603964i | \(-0.793587\pi\) |
0.328113 | + | 0.944638i | \(0.393587\pi\) | |||||||
\(674\) | 12.6585 | + | 38.9588i | 0.487587 | + | 1.50064i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.48410 | + | 2.53134i | 0.134004 | + | 0.0973594i | ||||
\(677\) | −24.3918 | − | 17.7217i | −0.937455 | − | 0.681101i | 0.0103520 | − | 0.999946i | \(-0.496705\pi\) |
−0.947807 | + | 0.318846i | \(0.896705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0990582 | − | 0.304870i | −0.00380151 | − | 0.0116998i | ||||
\(680\) | 18.6048 | − | 13.5172i | 0.713463 | − | 0.518361i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.05445 | − | 8.58539i | −0.193545 | − | 0.328752i | ||||
\(683\) | −45.7767 | −1.75160 | −0.875798 | − | 0.482677i | \(-0.839664\pi\) | ||||
−0.875798 | + | 0.482677i | \(0.839664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.59242 | + | 17.2117i | 0.213675 | + | 0.657625i | ||||
\(686\) | 0.611674 | − | 1.88254i | 0.0233538 | − | 0.0718757i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.4441 | + | 8.31464i | 0.436303 | + | 0.316993i | ||||
\(689\) | −0.129529 | + | 0.398650i | −0.00493467 | + | 0.0151873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9896 | + | 14.5233i | −0.760440 | + | 0.552492i | −0.899045 | − | 0.437855i | \(-0.855738\pi\) |
0.138605 | + | 0.990348i | \(0.455738\pi\) | |||||||
\(692\) | 0.209071 | 0.00794768 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.3990 | 1.76128 | ||||||||
\(695\) | −6.43389 | + | 4.67450i | −0.244051 | + | 0.177314i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.68134 | + | 5.17463i | −0.0636852 | + | 0.196003i | ||||
\(698\) | −25.9848 | − | 18.8790i | −0.983539 | − | 0.714583i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.00305775 | + | 0.00941077i | −0.000115572 | + | 0.000355694i | ||||
\(701\) | −11.3822 | − | 35.0310i | −0.429902 | − | 1.32310i | −0.898222 | − | 0.439542i | \(-0.855141\pi\) |
0.468320 | − | 0.883559i | \(-0.344859\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.5183 | 0.811577 | ||||||||
\(704\) | 2.70133 | − | 27.9851i | 0.101810 | − | 1.05473i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.4661 | + | 12.6899i | −0.657347 | + | 0.477590i | ||||
\(707\) | −0.0800683 | − | 0.246425i | −0.00301128 | − | 0.00926776i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.59373 | − | 4.79063i | −0.247633 | − | 0.179916i | 0.457044 | − | 0.889444i | \(-0.348908\pi\) |
−0.704677 | + | 0.709528i | \(0.748908\pi\) | |||||||
\(710\) | 27.1185 | + | 19.7028i | 1.01774 | + | 0.739432i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.20962 | − | 22.1889i | −0.270192 | − | 0.831565i | ||||
\(713\) | −4.59845 | + | 3.34097i | −0.172213 | + | 0.125120i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.2578 | + | 34.1840i | −1.13158 | + | 1.27841i | ||||
\(716\) | −1.24553 | −0.0465476 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.184812 | + | 0.568791i | 0.00689710 | + | 0.0212271i | ||||
\(719\) | −10.8427 | + | 33.3703i | −0.404363 | + | 1.24450i | 0.517063 | + | 0.855947i | \(0.327025\pi\) |
−0.921426 | + | 0.388554i | \(0.872975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.18756 | − | 0.862812i | −0.0442270 | − | 0.0321328i | ||||
\(722\) | 10.3536 | − | 31.8650i | 0.385320 | − | 1.18589i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.36372 | − | 1.71734i | 0.0878469 | − | 0.0638245i | ||||
\(725\) | 6.81383 | 0.253059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5664 | 0.836940 | 0.418470 | − | 0.908231i | \(-0.362566\pi\) | ||||
0.418470 | + | 0.908231i | \(0.362566\pi\) | |||||||
\(728\) | 1.62267 | − | 1.17894i | 0.0601401 | − | 0.0436944i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.7142 | − | 32.9750i | 0.396552 | − | 1.22046i | ||||
\(731\) | 11.7274 | + | 8.52042i | 0.433752 | + | 0.315139i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6642 | + | 32.8209i | −0.393890 | + | 1.21227i | 0.535932 | + | 0.844261i | \(0.319960\pi\) |
−0.929823 | + | 0.368008i | \(0.880040\pi\) | |||||||
\(734\) | −5.84051 | − | 17.9752i | −0.215577 | − | 0.663478i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.03097 | −0.0748626 | ||||||||
\(737\) | 11.9433 | − | 13.4931i | 0.439938 | − | 0.497023i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.2345 | − | 12.5216i | 0.633983 | − | 0.460616i | −0.223795 | − | 0.974636i | \(-0.571845\pi\) |
0.857778 | + | 0.514021i | \(0.171845\pi\) | |||||||
\(740\) | 0.291666 | + | 0.897656i | 0.0107219 | + | 0.0329985i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.00724171 | + | 0.00526141i | 0.000265852 | + | 0.000193152i | ||||
\(743\) | −35.8054 | − | 26.0142i | −1.31357 | − | 0.954367i | −0.999988 | − | 0.00480648i | \(-0.998470\pi\) |
−0.313585 | − | 0.949560i | \(-0.601530\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.64837 | + | 20.4616i | 0.243577 | + | 0.749654i | ||||
\(746\) | −7.74211 | + | 5.62497i | −0.283459 | + | 0.205945i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.168464 | − | 1.74525i | 0.00615966 | − | 0.0638126i | ||||
\(749\) | 0.524318 | 0.0191582 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.71292 | − | 23.7379i | −0.281448 | − | 0.866209i | −0.987441 | − | 0.157990i | \(-0.949499\pi\) |
0.705992 | − | 0.708220i | \(-0.250501\pi\) | |||||||
\(752\) | 3.92986 | − | 12.0949i | 0.143307 | − | 0.441054i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −72.7873 | − | 52.8831i | −2.65076 | − | 1.92589i | ||||
\(755\) | 6.42942 | − | 19.7877i | 0.233990 | − | 0.720149i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.9524 | + | 23.9413i | −1.19768 | + | 0.870162i | −0.994054 | − | 0.108887i | \(-0.965271\pi\) |
−0.203622 | + | 0.979050i | \(0.565271\pi\) | |||||||
\(758\) | −13.6061 | −0.494194 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 40.0118 | 1.45138 | ||||||||
\(761\) | −15.6840 | + | 11.3951i | −0.568546 | + | 0.413073i | −0.834577 | − | 0.550892i | \(-0.814288\pi\) |
0.266031 | + | 0.963965i | \(0.414288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.515651 | + | 1.58701i | −0.0186678 | + | 0.0574537i | ||||
\(764\) | 1.00821 | + | 0.732507i | 0.0364757 | + | 0.0265012i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.94980 | − | 24.4670i | 0.287238 | − | 0.884028i | ||||
\(767\) | 14.2657 | + | 43.9053i | 0.515105 | + | 1.58533i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7672 | −0.388276 | −0.194138 | − | 0.980974i | \(-0.562191\pi\) | ||||
−0.194138 | + | 0.980974i | \(0.562191\pi\) | |||||||
\(770\) | 0.494596 | + | 0.840111i | 0.0178240 | + | 0.0302755i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.644754 | − | 0.468441i | 0.0232052 | − | 0.0168596i | ||||
\(773\) | −9.08010 | − | 27.9457i | −0.326589 | − | 1.00514i | −0.970718 | − | 0.240220i | \(-0.922780\pi\) |
0.644130 | − | 0.764916i | \(-0.277220\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.21949 | − | 0.886012i | −0.0438054 | − | 0.0318265i | ||||
\(776\) | 7.29573 | + | 5.30066i | 0.261901 | + | 0.190282i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.84129 | + | 30.2884i | 0.352827 | + | 1.08589i | ||||
\(779\) | −7.65862 | + | 5.56431i | −0.274398 | + | 0.199362i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.3056 | − | 8.48266i | 1.37068 | − | 0.303533i | ||||
\(782\) | 13.3558 | 0.477603 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.99525 | + | 24.6069i | 0.285545 | + | 0.878816i | ||||
\(785\) | −7.44667 | + | 22.9185i | −0.265783 | + | 0.817996i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.87784 | − | 2.09087i | −0.102584 | − | 0.0745315i | 0.535311 | − | 0.844655i | \(-0.320194\pi\) |
−0.637895 | + | 0.770124i | \(0.720194\pi\) | |||||||
\(788\) | 0.299005 | − | 0.920242i | 0.0106516 | − | 0.0327823i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 35.7047 | − | 25.9410i | 1.27032 | − | 0.922939i | ||||
\(791\) | 1.05822 | 0.0376259 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.1137 | −0.998346 | ||||||||
\(794\) | 30.5672 | − | 22.2084i | 1.08479 | − | 0.788145i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.03441 | + | 3.18358i | −0.0366636 | + | 0.112839i | ||||
\(797\) | 28.3276 | + | 20.5812i | 1.00341 | + | 0.729023i | 0.962817 | − | 0.270153i | \(-0.0870743\pi\) |
0.0405963 | + | 0.999176i | \(0.487074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.02712 | − | 12.3942i | 0.142469 | − | 0.438475i | ||||
\(800\) | −0.166438 | − | 0.512245i | −0.00588448 | − | 0.0181106i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.6052 | −0.727595 | ||||||||
\(803\) | −20.5884 | − | 34.9711i | −0.726550 | − | 1.23410i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.449974 | − | 0.326925i | 0.0158595 | − | 0.0115226i | ||||
\(806\) | 6.15050 | + | 18.9293i | 0.216642 | + | 0.666756i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.89710 | + | 4.28449i | 0.207459 | + | 0.150728i | ||||
\(809\) | −15.4959 | − | 11.2584i | −0.544807 | − | 0.395826i | 0.281060 | − | 0.959690i | \(-0.409314\pi\) |
−0.825867 | + | 0.563864i | \(0.809314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.91663 | − | 5.89877i | −0.0673019 | − | 0.207134i | 0.911750 | − | 0.410746i | \(-0.134732\pi\) |
−0.979052 | + | 0.203612i | \(0.934732\pi\) | |||||||
\(812\) | 0.116421 | − | 0.0845844i | 0.00408556 | − | 0.00296833i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.5248 | − | 5.88455i | −0.474044 | − | 0.206253i | ||||
\(815\) | 47.3585 | 1.65890 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.79372 | + | 23.9866i | 0.272668 | + | 0.839185i | ||||
\(818\) | −3.96563 | + | 12.2049i | −0.138655 | + | 0.426736i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.335928 | − | 0.244066i | −0.0117311 | − | 0.00852316i | ||||
\(821\) | 7.74584 | − | 23.8392i | 0.270332 | − | 0.831995i | −0.720085 | − | 0.693886i | \(-0.755897\pi\) |
0.990417 | − | 0.138110i | \(-0.0441026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.37823 | + | 1.72789i | −0.0829000 | + | 0.0602303i | −0.628463 | − | 0.777839i | \(-0.716316\pi\) |
0.545563 | + | 0.838070i | \(0.316316\pi\) | |||||||
\(824\) | 41.2953 | 1.43859 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.985847 | 0.0343020 | ||||||||
\(827\) | 26.1058 | − | 18.9670i | 0.907789 | − | 0.659547i | −0.0326657 | − | 0.999466i | \(-0.510400\pi\) |
0.940455 | + | 0.339919i | \(0.110400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.324911 | − | 0.999973i | 0.0112846 | − | 0.0347305i | −0.945256 | − | 0.326331i | \(-0.894188\pi\) |
0.956540 | + | 0.291600i | \(0.0941877\pi\) | |||||||
\(830\) | −11.2858 | − | 8.19963i | −0.391736 | − | 0.284613i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.3569 | + | 53.4190i | −0.601742 | + | 1.85197i | ||||
\(833\) | 8.19313 | + | 25.2159i | 0.283875 | + | 0.873678i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.49324 | −0.328527 | ||||||||
\(836\) | 2.02196 | − | 2.28432i | 0.0699308 | − | 0.0790048i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.1854 | − | 16.1187i | 0.766383 | − | 0.556810i | ||||
\(839\) | 0.728865 | + | 2.24322i | 0.0251632 | + | 0.0774444i | 0.962850 | − | 0.270039i | \(-0.0870364\pi\) |
−0.937686 | + | 0.347483i | \(0.887036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −56.7066 | − | 41.1998i | −1.95540 | − | 1.42068i | ||||
\(842\) | 14.1753 | + | 10.2989i | 0.488512 | + | 0.354925i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.174564 | − | 0.537254i | −0.00600875 | − | 0.0184930i | ||||
\(845\) | 51.9360 | − | 37.7337i | 1.78665 | − | 1.29808i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.11998 | + | 0.218251i | 0.0384831 | + | 0.00749921i | ||||
\(848\) | −0.234185 | −0.00804196 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.09451 | + | 3.36856i | 0.0375414 | + | 0.115541i | ||||
\(851\) | −2.60036 | + | 8.00310i | −0.0891393 | + | 0.274343i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.6595 | + | 17.1897i | 0.810087 | + | 0.588563i | 0.913856 | − | 0.406039i | \(-0.133090\pi\) |
−0.103769 | + | 0.994601i | \(0.533090\pi\) | |||||||
\(854\) | −0.185523 | + | 0.570982i | −0.00634848 | + | 0.0195386i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.9332 | + | 8.66994i | −0.407867 | + | 0.296333i | ||||
\(857\) | 28.2043 | 0.963439 | 0.481720 | − | 0.876325i | \(-0.340012\pi\) | ||||
0.481720 | + | 0.876325i | \(0.340012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6444 | 0.909095 | 0.454548 | − | 0.890722i | \(-0.349801\pi\) | ||||
0.454548 | + | 0.890722i | \(0.349801\pi\) | |||||||
\(860\) | −0.894986 | + | 0.650245i | −0.0305188 | + | 0.0221732i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.44948 | − | 19.8494i | 0.219670 | − | 0.676075i | ||||
\(863\) | −19.5825 | − | 14.2275i | −0.666596 | − | 0.484311i | 0.202288 | − | 0.979326i | \(-0.435162\pi\) |
−0.868884 | + | 0.495015i | \(0.835162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.963062 | − | 2.96400i | 0.0327451 | − | 0.100779i | ||||
\(866\) | −5.07756 | − | 15.6271i | −0.172542 | − | 0.531031i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.0318348 | −0.00108054 | ||||||||
\(869\) | 4.96310 | − | 51.4166i | 0.168362 | − | 1.74419i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.1240 | + | 21.1599i | −0.986830 | + | 0.716974i | ||||
\(872\) | −14.5064 | − | 44.6460i | −0.491248 | − | 1.51190i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.7996 | + | 13.6587i | 0.635905 | + | 0.462012i | ||||
\(875\) | 0.991009 | + | 0.720010i | 0.0335022 | + | 0.0243408i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.83286 | − | 8.71864i | −0.0956588 | − | 0.294408i | 0.891766 | − | 0.452497i | \(-0.149467\pi\) |
−0.987425 | + | 0.158089i | \(0.949467\pi\) | |||||||
\(878\) | 4.57766 | − | 3.32586i | 0.154489 | − | 0.112242i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −23.3876 | − | 10.1758i | −0.788395 | − | 0.343025i | ||||
\(881\) | −32.2415 | −1.08624 | −0.543122 | − | 0.839654i | \(-0.682758\pi\) | ||||
−0.543122 | + | 0.839654i | \(0.682758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.4868 | − | 41.5083i | −0.453869 | − | 1.39686i | −0.872458 | − | 0.488689i | \(-0.837475\pi\) |
0.418590 | − | 0.908175i | \(-0.362525\pi\) | |||||||
\(884\) | −1.08244 | + | 3.33140i | −0.0364063 | + | 0.112047i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.0686 | + | 15.3073i | 0.707814 | + | 0.514257i | ||||
\(887\) | −2.66422 | + | 8.19964i | −0.0894559 | + | 0.275317i | −0.985769 | − | 0.168104i | \(-0.946235\pi\) |
0.896313 | + | 0.443421i | \(0.146235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.287104 | − | 0.208593i | 0.00962916 | − | 0.00699600i | ||||
\(890\) | −22.6549 | −0.759393 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.41122 | 0.0472512 | ||||||||
\(893\) | 18.3438 | − | 13.3276i | 0.613852 | − | 0.445990i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.73739 | + | 17.6579i | −0.191780 | + | 0.590238i | ||||
\(896\) | 0.838320 | + | 0.609075i | 0.0280063 | + | 0.0203478i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.43918 | + | 4.42935i | −0.0480261 | + | 0.147809i | ||||
\(899\) | 6.77417 | + | 20.8487i | 0.225931 | + | 0.695345i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.239981 | −0.00799494 | ||||||||
\(902\) | 6.33530 | − | 1.40293i | 0.210942 | − | 0.0467126i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.0844 | + | 17.4983i | −0.801034 | + | 0.581985i | ||||
\(905\) | −13.4586 | − | 41.4212i | −0.447378 | − | 1.37689i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.79413 | + | 4.93622i | 0.225595 | + | 0.163905i | 0.694842 | − | 0.719163i | \(-0.255474\pi\) |
−0.469246 | + | 0.883067i | \(0.655474\pi\) | |||||||
\(908\) | −0.737856 | − | 0.536084i | −0.0244866 | − | 0.0177906i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.601848 | − | 1.85230i | −0.0199511 | − | 0.0614031i | ||||
\(911\) | 25.5548 | − | 18.5666i | 0.846667 | − | 0.615140i | −0.0775581 | − | 0.996988i | \(-0.524712\pi\) |
0.924225 | + | 0.381848i | \(0.124712\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.9415 | + | 3.53020i | −0.527586 | + | 0.116832i | ||||
\(914\) | −40.2999 | −1.33300 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.665441 | − | 2.04802i | −0.0219868 | − | 0.0676684i | ||||
\(917\) | −0.568989 | + | 1.75117i | −0.0187897 | + | 0.0578287i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.1386 | + | 24.0766i | 1.09314 | + | 0.794213i | 0.979927 | − | 0.199357i | \(-0.0638855\pi\) |
0.113214 | + | 0.993571i | \(0.463885\pi\) | |||||||
\(920\) | −4.83521 | + | 14.8812i | −0.159412 | + | 0.490620i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −44.9978 | + | 32.6928i | −1.48192 | + | 1.07668i | ||||
\(923\) | −78.3802 | −2.57992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.23161 | −0.0733750 | ||||||||
\(926\) | 42.7624 | − | 31.0687i | 1.40526 | − | 1.02098i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.42051 | + | 7.44955i | −0.0794570 | + | 0.244544i | ||||
\(929\) | 9.20018 | + | 6.68432i | 0.301848 | + | 0.219305i | 0.728391 | − | 0.685162i | \(-0.240269\pi\) |
−0.426543 | + | 0.904467i | \(0.640269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.2551 | + | 43.8726i | −0.467191 | + | 1.43787i | ||||
\(932\) | 0.916029 | + | 2.81925i | 0.0300055 | + | 0.0923476i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38.2809 | −1.25259 | ||||||||
\(935\) | −23.9664 | − | 10.4276i | −0.783785 | − | 0.341020i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.289552 | − | 0.210372i | 0.00945925 | − | 0.00687255i | −0.583046 | − | 0.812439i | \(-0.698139\pi\) |
0.592505 | + | 0.805567i | \(0.298139\pi\) | |||||||
\(938\) | 0.237561 | + | 0.731137i | 0.00775663 | + | 0.0238725i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.804610 | + | 0.584584i | 0.0262435 | + | 0.0190670i | ||||
\(941\) | −14.8500 | − | 10.7891i | −0.484095 | − | 0.351716i | 0.318814 | − | 0.947817i | \(-0.396716\pi\) |
−0.802909 | + | 0.596102i | \(0.796716\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.14398 | − | 3.52082i | −0.0372532 | − | 0.114654i | ||||
\(944\) | −20.8662 | + | 15.1602i | −0.679137 | + | 0.493422i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.66100 | − | 17.2075i | 0.0540036 | − | 0.559465i | ||||
\(947\) | 51.2153 | 1.66427 | 0.832137 | − | 0.554571i | \(-0.187117\pi\) | ||||
0.832137 | + | 0.554571i | \(0.187117\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.0530 | + | 77.1051i | 0.813254 | + | 2.50294i | ||||
\(950\) | −1.90432 | + | 5.86090i | −0.0617843 | + | 0.190153i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.929014 | + | 0.674968i | 0.0301095 | + | 0.0218759i | ||||
\(953\) | −5.01140 | + | 15.4235i | −0.162335 | + | 0.499616i | −0.998830 | − | 0.0483587i | \(-0.984601\pi\) |
0.836495 | + | 0.547975i | \(0.184601\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0290 | − | 10.9192i | 0.486326 | − | 0.353336i | ||||
\(956\) | 2.41702 | 0.0781719 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.5855 | −0.697396 | ||||||||
\(959\) | −0.731091 | + | 0.531169i | −0.0236082 | + | 0.0171523i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.08093 | + | 24.8705i | −0.260675 | + | 0.802275i | ||||
\(962\) | 23.8388 | + | 17.3199i | 0.768593 | + | 0.558416i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.458333 | + | 1.41060i | −0.0147619 | + | 0.0454325i | ||||
\(965\) | −3.67111 | − | 11.2985i | −0.118177 | − | 0.363712i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.5309 | 1.04612 | 0.523061 | − | 0.852295i | \(-0.324790\pi\) | ||||
0.523061 | + | 0.852295i | \(0.324790\pi\) | |||||||
\(968\) | −29.0991 | + | 13.5524i | −0.935279 | + | 0.435591i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.08436 | − | 5.14709i | 0.227465 | − | 0.165263i | ||||
\(971\) | −0.685761 | − | 2.11056i | −0.0220071 | − | 0.0677310i | 0.939450 | − | 0.342687i | \(-0.111337\pi\) |
−0.961457 | + | 0.274956i | \(0.911337\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.321270 | − | 0.233416i | −0.0102994 | − | 0.00748298i | ||||
\(974\) | 6.34168 | + | 4.60750i | 0.203201 | + | 0.147634i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.85372 | − | 14.9382i | −0.155364 | − | 0.478161i | ||||
\(977\) | −17.2791 | + | 12.5540i | −0.552806 | + | 0.401637i | −0.828819 | − | 0.559517i | \(-0.810987\pi\) |
0.276013 | + | 0.961154i | \(0.410987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5748 | + | 19.8553i | −0.561694 | + | 0.634578i | ||||
\(980\) | −2.02341 | −0.0646354 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.0396 | − | 46.2870i | −0.479931 | − | 1.47708i | ||||
\(983\) | 4.46743 | − | 13.7493i | 0.142489 | − | 0.438536i | −0.854191 | − | 0.519960i | \(-0.825947\pi\) |
0.996680 | + | 0.0814241i | \(0.0259468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.6690 | − | 8.47799i | −0.371804 | − | 0.270131i | ||||
\(986\) | 15.9174 | − | 48.9888i | 0.506914 | − | 1.56012i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.93058 | + | 3.58227i | −0.156863 | + | 0.113967i | ||||
\(989\) | −9.86295 | −0.313624 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.68782 | 0.148914 | 0.0744568 | − | 0.997224i | \(-0.476278\pi\) | ||||
0.0744568 | + | 0.997224i | \(0.476278\pi\) | |||||||
\(992\) | 1.40188 | − | 1.01853i | 0.0445098 | − | 0.0323382i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.517234 | + | 1.59188i | −0.0164057 | + | 0.0504915i | ||||
\(995\) | 40.3687 | + | 29.3296i | 1.27977 | + | 0.929811i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.4396 | − | 32.1297i | 0.330624 | − | 1.01756i | −0.638213 | − | 0.769860i | \(-0.720326\pi\) |
0.968838 | − | 0.247697i | \(-0.0796738\pi\) | |||||||
\(998\) | 11.2135 | + | 34.5117i | 0.354958 | + | 1.09245i | ||||
\(999\) | 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 | 891.2.f.g.487.4 | ✓ | 48 | |
3.2 | odd | 2 | inner | 891.2.f.g.487.9 | yes | 48 | |
9.2 | odd | 6 | 891.2.n.l.190.4 | 96 | |||
9.4 | even | 3 | 891.2.n.l.784.4 | 96 | |||
9.5 | odd | 6 | 891.2.n.l.784.9 | 96 | |||
9.7 | even | 3 | 891.2.n.l.190.9 | 96 | |||
11.2 | odd | 10 | 9801.2.a.cq.1.7 | 24 | |||
11.4 | even | 5 | inner | 891.2.f.g.730.4 | yes | 48 | |
11.9 | even | 5 | 9801.2.a.cr.1.18 | 24 | |||
33.2 | even | 10 | 9801.2.a.cq.1.18 | 24 | |||
33.20 | odd | 10 | 9801.2.a.cr.1.7 | 24 | |||
33.26 | odd | 10 | inner | 891.2.f.g.730.9 | yes | 48 | |
99.4 | even | 15 | 891.2.n.l.136.9 | 96 | |||
99.59 | odd | 30 | 891.2.n.l.136.4 | 96 | |||
99.70 | even | 15 | 891.2.n.l.433.4 | 96 | |||
99.92 | odd | 30 | 891.2.n.l.433.9 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
891.2.f.g.487.4 | ✓ | 48 | 1.1 | even | 1 | trivial | |
891.2.f.g.487.9 | yes | 48 | 3.2 | odd | 2 | inner | |
891.2.f.g.730.4 | yes | 48 | 11.4 | even | 5 | inner | |
891.2.f.g.730.9 | yes | 48 | 33.26 | odd | 10 | inner | |
891.2.n.l.136.4 | 96 | 99.59 | odd | 30 | |||
891.2.n.l.136.9 | 96 | 99.4 | even | 15 | |||
891.2.n.l.190.4 | 96 | 9.2 | odd | 6 | |||
891.2.n.l.190.9 | 96 | 9.7 | even | 3 | |||
891.2.n.l.433.4 | 96 | 99.70 | even | 15 | |||
891.2.n.l.433.9 | 96 | 99.92 | odd | 30 | |||
891.2.n.l.784.4 | 96 | 9.4 | even | 3 | |||
891.2.n.l.784.9 | 96 | 9.5 | odd | 6 | |||
9801.2.a.cq.1.7 | 24 | 11.2 | odd | 10 | |||
9801.2.a.cq.1.18 | 24 | 33.2 | even | 10 | |||
9801.2.a.cr.1.7 | 24 | 33.20 | odd | 10 | |||
9801.2.a.cr.1.18 | 24 | 11.9 | even | 5 |