Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 311.5 | ||
Character | \(\chi\) | \(=\) | 630.311 |
Dual form | 630.2.t.b.551.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 1.16177 | + | 1.28464i | 0.670747 | + | 0.741686i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.363801 | − | 1.69341i | −0.148521 | − | 0.691333i | ||||
\(7\) | −1.57438 | − | 2.12634i | −0.595058 | − | 0.803683i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.300592 | + | 2.98490i | −0.100197 | + | 0.994968i | ||||
\(10\) | 0.866025 | + | 0.500000i | 0.273861 | + | 0.158114i | ||||
\(11\) | − | 5.66323i | − | 1.70753i | −0.520660 | − | 0.853764i | \(-0.674314\pi\) | ||
0.520660 | − | 0.853764i | \(-0.325686\pi\) | |||||||
\(12\) | −0.531646 | + | 1.64844i | −0.153473 | + | 0.475863i | ||||
\(13\) | 2.43404 | + | 1.40529i | 0.675080 | + | 0.389758i | 0.797999 | − | 0.602659i | \(-0.205892\pi\) |
−0.122919 | + | 0.992417i | \(0.539225\pi\) | |||||||
\(14\) | 0.300277 | + | 2.62866i | 0.0802524 | + | 0.702538i | ||||
\(15\) | −1.16177 | − | 1.28464i | −0.299967 | − | 0.331692i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.51050 | − | 6.08036i | 0.851420 | − | 1.47470i | −0.0285066 | − | 0.999594i | \(-0.509075\pi\) |
0.879927 | − | 0.475109i | \(-0.157591\pi\) | |||||||
\(18\) | 1.75277 | − | 2.43471i | 0.413132 | − | 0.573866i | ||||
\(19\) | 3.76339 | − | 2.17279i | 0.863381 | − | 0.498473i | −0.00176228 | − | 0.999998i | \(-0.500561\pi\) |
0.865143 | + | 0.501525i | \(0.167228\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 0.902526 | − | 4.49282i | 0.196947 | − | 0.980414i | ||||
\(22\) | −2.83161 | + | 4.90450i | −0.603702 | + | 1.04564i | ||||
\(23\) | 4.07471i | 0.849636i | 0.905279 | + | 0.424818i | \(0.139662\pi\) | ||||
−0.905279 | + | 0.424818i | \(0.860338\pi\) | |||||||
\(24\) | 1.28464 | − | 1.16177i | 0.262226 | − | 0.237145i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.40529 | − | 2.43404i | −0.275600 | − | 0.477354i | ||||
\(27\) | −4.18374 | + | 3.08161i | −0.805161 | + | 0.593056i | ||||
\(28\) | 1.05428 | − | 2.42662i | 0.199240 | − | 0.458588i | ||||
\(29\) | 5.28540 | − | 3.05152i | 0.981473 | − | 0.566654i | 0.0787587 | − | 0.996894i | \(-0.474904\pi\) |
0.902715 | + | 0.430240i | \(0.141571\pi\) | |||||||
\(30\) | 0.363801 | + | 1.69341i | 0.0664207 | + | 0.309174i | ||||
\(31\) | 0.319228 | − | 0.184307i | 0.0573351 | − | 0.0331024i | −0.471058 | − | 0.882102i | \(-0.656128\pi\) |
0.528394 | + | 0.849000i | \(0.322795\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 7.27520 | − | 6.57936i | 1.26645 | − | 1.14532i | ||||
\(34\) | −6.08036 | + | 3.51050i | −1.04277 | + | 0.602045i | ||||
\(35\) | 1.57438 | + | 2.12634i | 0.266118 | + | 0.359418i | ||||
\(36\) | −2.73530 | + | 1.23213i | −0.455883 | + | 0.205355i | ||||
\(37\) | 0.783876 | + | 1.35771i | 0.128868 | + | 0.223207i | 0.923238 | − | 0.384227i | \(-0.125532\pi\) |
−0.794370 | + | 0.607434i | \(0.792199\pi\) | |||||||
\(38\) | −4.34559 | −0.704947 | ||||||||
\(39\) | 1.02249 | + | 4.75948i | 0.163730 | + | 0.762126i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 1.39596 | − | 2.41787i | 0.218012 | − | 0.377609i | −0.736188 | − | 0.676777i | \(-0.763376\pi\) |
0.954200 | + | 0.299169i | \(0.0967093\pi\) | |||||||
\(42\) | −3.02802 | + | 3.43963i | −0.467234 | + | 0.530747i | ||||
\(43\) | 3.18170 | + | 5.51086i | 0.485204 | + | 0.840399i | 0.999855 | − | 0.0170011i | \(-0.00541188\pi\) |
−0.514651 | + | 0.857400i | \(0.672079\pi\) | |||||||
\(44\) | 4.90450 | − | 2.83161i | 0.739381 | − | 0.426882i | ||||
\(45\) | 0.300592 | − | 2.98490i | 0.0448097 | − | 0.444963i | ||||
\(46\) | 2.03736 | − | 3.52880i | 0.300392 | − | 0.520294i | ||||
\(47\) | −2.59337 | + | 4.49185i | −0.378282 | + | 0.655204i | −0.990812 | − | 0.135243i | \(-0.956818\pi\) |
0.612530 | + | 0.790447i | \(0.290152\pi\) | |||||||
\(48\) | −1.69341 | + | 0.363801i | −0.244423 | + | 0.0525101i | ||||
\(49\) | −2.04268 | + | 6.69533i | −0.291812 | + | 0.956476i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 11.8894 | − | 2.55424i | 1.66485 | − | 0.357666i | ||||
\(52\) | 2.81058i | 0.389758i | ||||||||
\(53\) | −3.02705 | − | 1.74767i | −0.415797 | − | 0.240060i | 0.277481 | − | 0.960731i | \(-0.410501\pi\) |
−0.693277 | + | 0.720671i | \(0.743834\pi\) | |||||||
\(54\) | 5.16403 | − | 0.576883i | 0.702735 | − | 0.0785038i | ||||
\(55\) | 5.66323i | 0.763630i | ||||||||
\(56\) | −2.12634 | + | 1.57438i | −0.284145 | + | 0.210385i | ||||
\(57\) | 7.16344 | + | 2.31031i | 0.948820 | + | 0.306008i | ||||
\(58\) | −6.10305 | −0.801370 | ||||||||
\(59\) | −5.32873 | − | 9.22962i | −0.693741 | − | 1.20159i | −0.970603 | − | 0.240685i | \(-0.922628\pi\) |
0.276862 | − | 0.960910i | \(-0.410705\pi\) | |||||||
\(60\) | 0.531646 | − | 1.64844i | 0.0686352 | − | 0.212813i | ||||
\(61\) | 12.6860 | + | 7.32427i | 1.62428 | + | 0.937777i | 0.985758 | + | 0.168171i | \(0.0537861\pi\) |
0.638519 | + | 0.769606i | \(0.279547\pi\) | |||||||
\(62\) | −0.368613 | −0.0468139 | ||||||||
\(63\) | 6.82018 | − | 4.06020i | 0.859262 | − | 0.511537i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.43404 | − | 1.40529i | −0.301905 | − | 0.174305i | ||||
\(66\) | −9.59019 | + | 2.06029i | −1.18047 | + | 0.253604i | ||||
\(67\) | −1.36579 | − | 2.36562i | −0.166858 | − | 0.289007i | 0.770455 | − | 0.637494i | \(-0.220029\pi\) |
−0.937314 | + | 0.348487i | \(0.886696\pi\) | |||||||
\(68\) | 7.02099 | 0.851420 | ||||||||
\(69\) | −5.23453 | + | 4.73387i | −0.630164 | + | 0.569891i | ||||
\(70\) | −0.300277 | − | 2.62866i | −0.0358900 | − | 0.314185i | ||||
\(71\) | − | 9.06430i | − | 1.07573i | −0.843030 | − | 0.537867i | \(-0.819230\pi\) | ||
0.843030 | − | 0.537867i | \(-0.180770\pi\) | |||||||
\(72\) | 2.98490 | + | 0.300592i | 0.351774 | + | 0.0354252i | ||||
\(73\) | −14.3736 | − | 8.29858i | −1.68230 | − | 0.971275i | −0.960129 | − | 0.279559i | \(-0.909812\pi\) |
−0.722169 | − | 0.691716i | \(-0.756855\pi\) | |||||||
\(74\) | − | 1.56775i | − | 0.182248i | ||||||
\(75\) | 1.16177 | + | 1.28464i | 0.134149 | + | 0.148337i | ||||
\(76\) | 3.76339 | + | 2.17279i | 0.431690 | + | 0.249237i | ||||
\(77\) | −12.0420 | + | 8.91605i | −1.37231 | + | 1.01608i | ||||
\(78\) | 1.49423 | − | 4.63307i | 0.169189 | − | 0.524592i | ||||
\(79\) | 4.37159 | − | 7.57182i | 0.491842 | − | 0.851896i | −0.508114 | − | 0.861290i | \(-0.669657\pi\) |
0.999956 | + | 0.00939423i | \(0.00299032\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −8.81929 | − | 1.79448i | −0.979921 | − | 0.199386i | ||||
\(82\) | −2.41787 | + | 1.39596i | −0.267010 | + | 0.154158i | ||||
\(83\) | −8.34157 | − | 14.4480i | −0.915606 | − | 1.58588i | −0.806011 | − | 0.591901i | \(-0.798378\pi\) |
−0.109595 | − | 0.993976i | \(-0.534956\pi\) | |||||||
\(84\) | 4.34216 | − | 1.46480i | 0.473769 | − | 0.159823i | ||||
\(85\) | −3.51050 | + | 6.08036i | −0.380767 | + | 0.659507i | ||||
\(86\) | − | 6.36340i | − | 0.686183i | ||||||
\(87\) | 10.0605 | + | 3.24466i | 1.07860 | + | 0.347864i | ||||
\(88\) | −5.66323 | −0.603702 | ||||||||
\(89\) | −0.332109 | − | 0.575230i | −0.0352035 | − | 0.0609742i | 0.847887 | − | 0.530177i | \(-0.177875\pi\) |
−0.883090 | + | 0.469203i | \(0.844541\pi\) | |||||||
\(90\) | −1.75277 | + | 2.43471i | −0.184758 | + | 0.256640i | ||||
\(91\) | −0.843953 | − | 7.38805i | −0.0884703 | − | 0.774479i | ||||
\(92\) | −3.52880 | + | 2.03736i | −0.367903 | + | 0.212409i | ||||
\(93\) | 0.607637 | + | 0.195972i | 0.0630090 | + | 0.0203213i | ||||
\(94\) | 4.49185 | − | 2.59337i | 0.463299 | − | 0.267486i | ||||
\(95\) | −3.76339 | + | 2.17279i | −0.386116 | + | 0.222924i | ||||
\(96\) | 1.64844 | + | 0.531646i | 0.168243 | + | 0.0542609i | ||||
\(97\) | 1.68214 | − | 0.971182i | 0.170795 | − | 0.0986085i | −0.412166 | − | 0.911109i | \(-0.635227\pi\) |
0.582961 | + | 0.812500i | \(0.301894\pi\) | |||||||
\(98\) | 5.11668 | − | 4.77698i | 0.516863 | − | 0.482548i | ||||
\(99\) | 16.9042 | + | 1.70232i | 1.69893 | + | 0.171090i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 6.28513 | 0.625393 | 0.312697 | − | 0.949853i | \(-0.398768\pi\) | ||||
0.312697 | + | 0.949853i | \(0.398768\pi\) | |||||||
\(102\) | −11.5737 | − | 3.73268i | −1.14596 | − | 0.369590i | ||||
\(103\) | 5.60402i | 0.552181i | 0.961132 | + | 0.276090i | \(0.0890389\pi\) | ||||
−0.961132 | + | 0.276090i | \(0.910961\pi\) | |||||||
\(104\) | 1.40529 | − | 2.43404i | 0.137800 | − | 0.238677i | ||||
\(105\) | −0.902526 | + | 4.49282i | −0.0880775 | + | 0.438455i | ||||
\(106\) | 1.74767 | + | 3.02705i | 0.169748 | + | 0.294013i | ||||
\(107\) | −1.38444 | + | 0.799307i | −0.133839 | + | 0.0772720i | −0.565425 | − | 0.824800i | \(-0.691288\pi\) |
0.431586 | + | 0.902072i | \(0.357954\pi\) | |||||||
\(108\) | −4.76062 | − | 2.08242i | −0.458091 | − | 0.200381i | ||||
\(109\) | 2.63446 | − | 4.56303i | 0.252336 | − | 0.437059i | −0.711833 | − | 0.702349i | \(-0.752135\pi\) |
0.964169 | + | 0.265290i | \(0.0854679\pi\) | |||||||
\(110\) | 2.83161 | − | 4.90450i | 0.269984 | − | 0.467626i | ||||
\(111\) | −0.833489 | + | 2.58435i | −0.0791113 | + | 0.245295i | ||||
\(112\) | 2.62866 | − | 0.300277i | 0.248385 | − | 0.0283735i | ||||
\(113\) | 13.0916 | + | 7.55846i | 1.23156 | + | 0.711040i | 0.967355 | − | 0.253427i | \(-0.0815576\pi\) |
0.264203 | + | 0.964467i | \(0.414891\pi\) | |||||||
\(114\) | −5.04856 | − | 5.58251i | −0.472841 | − | 0.522850i | ||||
\(115\) | − | 4.07471i | − | 0.379969i | ||||||
\(116\) | 5.28540 | + | 3.05152i | 0.490737 | + | 0.283327i | ||||
\(117\) | −4.92631 | + | 6.84294i | −0.455437 | + | 0.632630i | ||||
\(118\) | 10.6575i | 0.981098i | ||||||||
\(119\) | −18.4558 | + | 2.10824i | −1.69184 | + | 0.193262i | ||||
\(120\) | −1.28464 | + | 1.16177i | −0.117271 | + | 0.106054i | ||||
\(121\) | −21.0722 | −1.91565 | ||||||||
\(122\) | −7.32427 | − | 12.6860i | −0.663108 | − | 1.14854i | ||||
\(123\) | 4.72788 | − | 1.01570i | 0.426298 | − | 0.0915829i | ||||
\(124\) | 0.319228 | + | 0.184307i | 0.0286676 | + | 0.0165512i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.93654 | + | 0.106144i | −0.707044 | + | 0.00945602i | ||||
\(127\) | −4.63451 | −0.411247 | −0.205623 | − | 0.978631i | \(-0.565922\pi\) | ||||
−0.205623 | + | 0.978631i | \(0.565922\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −3.38307 | + | 10.4897i | −0.297863 | + | 0.923564i | ||||
\(130\) | 1.40529 | + | 2.43404i | 0.123252 | + | 0.213479i | ||||
\(131\) | −3.71505 | −0.324585 | −0.162293 | − | 0.986743i | \(-0.551889\pi\) | ||||
−0.162293 | + | 0.986743i | \(0.551889\pi\) | |||||||
\(132\) | 9.33549 | + | 3.01083i | 0.812550 | + | 0.262059i | ||||
\(133\) | −10.5451 | − | 4.58147i | −0.914376 | − | 0.397264i | ||||
\(134\) | 2.73159i | 0.235973i | ||||||||
\(135\) | 4.18374 | − | 3.08161i | 0.360079 | − | 0.265223i | ||||
\(136\) | −6.08036 | − | 3.51050i | −0.521386 | − | 0.301022i | ||||
\(137\) | 21.0639i | 1.79961i | 0.436294 | + | 0.899804i | \(0.356291\pi\) | ||||
−0.436294 | + | 0.899804i | \(0.643709\pi\) | |||||||
\(138\) | 6.90017 | − | 1.48238i | 0.587382 | − | 0.126189i | ||||
\(139\) | −7.81740 | − | 4.51338i | −0.663063 | − | 0.382820i | 0.130380 | − | 0.991464i | \(-0.458380\pi\) |
−0.793443 | + | 0.608645i | \(0.791714\pi\) | |||||||
\(140\) | −1.05428 | + | 2.42662i | −0.0891030 | + | 0.205087i | ||||
\(141\) | −8.78330 | + | 1.88694i | −0.739688 | + | 0.158909i | ||||
\(142\) | −4.53215 | + | 7.84991i | −0.380329 | + | 0.658750i | ||||
\(143\) | 7.95849 | − | 13.7845i | 0.665522 | − | 1.15272i | ||||
\(144\) | −2.43471 | − | 1.75277i | −0.202892 | − | 0.146064i | ||||
\(145\) | −5.28540 | + | 3.05152i | −0.438928 | + | 0.253415i | ||||
\(146\) | 8.29858 | + | 14.3736i | 0.686795 | + | 1.18956i | ||||
\(147\) | −10.9742 | + | 5.15431i | −0.905137 | + | 0.425120i | ||||
\(148\) | −0.783876 | + | 1.35771i | −0.0644342 | + | 0.111603i | ||||
\(149\) | 8.86835i | 0.726524i | 0.931687 | + | 0.363262i | \(0.118337\pi\) | ||||
−0.931687 | + | 0.363262i | \(0.881663\pi\) | |||||||
\(150\) | −0.363801 | − | 1.69341i | −0.0297042 | − | 0.138267i | ||||
\(151\) | 13.4954 | 1.09824 | 0.549122 | − | 0.835742i | \(-0.314962\pi\) | ||||
0.549122 | + | 0.835742i | \(0.314962\pi\) | |||||||
\(152\) | −2.17279 | − | 3.76339i | −0.176237 | − | 0.305251i | ||||
\(153\) | 17.0940 | + | 12.3062i | 1.38197 | + | 0.994897i | ||||
\(154\) | 14.8867 | − | 1.70054i | 1.19960 | − | 0.137033i | ||||
\(155\) | −0.319228 | + | 0.184307i | −0.0256410 | + | 0.0148039i | ||||
\(156\) | −3.61058 | + | 3.26524i | −0.289078 | + | 0.261429i | ||||
\(157\) | −2.88573 | + | 1.66608i | −0.230306 | + | 0.132967i | −0.610713 | − | 0.791852i | \(-0.709117\pi\) |
0.380407 | + | 0.924819i | \(0.375784\pi\) | |||||||
\(158\) | −7.57182 | + | 4.37159i | −0.602381 | + | 0.347785i | ||||
\(159\) | −1.27161 | − | 5.91904i | −0.100845 | − | 0.469411i | ||||
\(160\) | −0.866025 | + | 0.500000i | −0.0684653 | + | 0.0395285i | ||||
\(161\) | 8.66424 | − | 6.41513i | 0.682838 | − | 0.505583i | ||||
\(162\) | 6.74049 | + | 5.96371i | 0.529583 | + | 0.468553i | ||||
\(163\) | 7.01305 | + | 12.1470i | 0.549304 | + | 0.951423i | 0.998322 | + | 0.0579002i | \(0.0184405\pi\) |
−0.449018 | + | 0.893523i | \(0.648226\pi\) | |||||||
\(164\) | 2.79192 | 0.218012 | ||||||||
\(165\) | −7.27520 | + | 6.57936i | −0.566374 | + | 0.512202i | ||||
\(166\) | 16.6831i | 1.29486i | ||||||||
\(167\) | −9.43447 | + | 16.3410i | −0.730061 | + | 1.26450i | 0.226796 | + | 0.973942i | \(0.427175\pi\) |
−0.956857 | + | 0.290560i | \(0.906158\pi\) | |||||||
\(168\) | −4.49282 | − | 0.902526i | −0.346629 | − | 0.0696314i | ||||
\(169\) | −2.55031 | − | 4.41727i | −0.196178 | − | 0.339790i | ||||
\(170\) | 6.08036 | − | 3.51050i | 0.466342 | − | 0.269243i | ||||
\(171\) | 5.35433 | + | 11.8865i | 0.409456 | + | 0.908981i | ||||
\(172\) | −3.18170 | + | 5.51086i | −0.242602 | + | 0.420199i | ||||
\(173\) | −4.54360 | + | 7.86975i | −0.345444 | + | 0.598326i | −0.985434 | − | 0.170057i | \(-0.945605\pi\) |
0.639991 | + | 0.768383i | \(0.278938\pi\) | |||||||
\(174\) | −7.09032 | − | 7.84021i | −0.537516 | − | 0.594365i | ||||
\(175\) | −1.57438 | − | 2.12634i | −0.119012 | − | 0.160737i | ||||
\(176\) | 4.90450 | + | 2.83161i | 0.369691 | + | 0.213441i | ||||
\(177\) | 5.66599 | − | 17.5682i | 0.425882 | − | 1.32050i | ||||
\(178\) | 0.664218i | 0.0497853i | ||||||||
\(179\) | 12.1711 | + | 7.02701i | 0.909714 | + | 0.525224i | 0.880339 | − | 0.474345i | \(-0.157315\pi\) |
0.0293749 | + | 0.999568i | \(0.490648\pi\) | |||||||
\(180\) | 2.73530 | − | 1.23213i | 0.203877 | − | 0.0918376i | ||||
\(181\) | 3.34540i | 0.248662i | 0.992241 | + | 0.124331i | \(0.0396784\pi\) | ||||
−0.992241 | + | 0.124331i | \(0.960322\pi\) | |||||||
\(182\) | −2.96314 | + | 6.82022i | −0.219643 | + | 0.505548i | ||||
\(183\) | 5.32915 | + | 24.8060i | 0.393942 | + | 1.83372i | ||||
\(184\) | 4.07471 | 0.300392 | ||||||||
\(185\) | −0.783876 | − | 1.35771i | −0.0576317 | − | 0.0998211i | ||||
\(186\) | −0.428243 | − | 0.473535i | −0.0314003 | − | 0.0347213i | ||||
\(187\) | −34.4345 | − | 19.8807i | −2.51810 | − | 1.45382i | ||||
\(188\) | −5.18675 | −0.378282 | ||||||||
\(189\) | 13.1393 | + | 4.04446i | 0.955747 | + | 0.294191i | ||||
\(190\) | 4.34559 | 0.315262 | ||||||||
\(191\) | 5.35829 | + | 3.09361i | 0.387713 | + | 0.223846i | 0.681169 | − | 0.732127i | \(-0.261472\pi\) |
−0.293456 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(192\) | −1.16177 | − | 1.28464i | −0.0838433 | − | 0.0927108i | ||||
\(193\) | −1.04267 | − | 1.80595i | −0.0750528 | − | 0.129995i | 0.826056 | − | 0.563587i | \(-0.190579\pi\) |
−0.901109 | + | 0.433592i | \(0.857246\pi\) | |||||||
\(194\) | −1.94236 | −0.139454 | ||||||||
\(195\) | −1.02249 | − | 4.75948i | −0.0732222 | − | 0.340833i | ||||
\(196\) | −6.81967 | + | 1.57865i | −0.487119 | + | 0.112761i | ||||
\(197\) | 24.7197i | 1.76121i | 0.473853 | + | 0.880604i | \(0.342863\pi\) | ||||
−0.473853 | + | 0.880604i | \(0.657137\pi\) | |||||||
\(198\) | −13.7883 | − | 9.92635i | −0.979891 | − | 0.705435i | ||||
\(199\) | 5.60009 | + | 3.23321i | 0.396980 | + | 0.229196i | 0.685180 | − | 0.728374i | \(-0.259724\pi\) |
−0.288200 | + | 0.957570i | \(0.593057\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 1.45224 | − | 4.50286i | 0.102433 | − | 0.317607i | ||||
\(202\) | −5.44308 | − | 3.14256i | −0.382974 | − | 0.221110i | ||||
\(203\) | −14.8098 | − | 6.43433i | −1.03944 | − | 0.451601i | ||||
\(204\) | 8.15676 | + | 9.01943i | 0.571087 | + | 0.631487i | ||||
\(205\) | −1.39596 | + | 2.41787i | −0.0974981 | + | 0.168872i | ||||
\(206\) | 2.80201 | − | 4.85323i | 0.195225 | − | 0.338140i | ||||
\(207\) | −12.1626 | − | 1.22483i | −0.845361 | − | 0.0851314i | ||||
\(208\) | −2.43404 | + | 1.40529i | −0.168770 | + | 0.0974394i | ||||
\(209\) | −12.3050 | − | 21.3129i | −0.851157 | − | 1.47425i | ||||
\(210\) | 3.02802 | − | 3.43963i | 0.208953 | − | 0.237357i | ||||
\(211\) | 0.607035 | − | 1.05142i | 0.0417900 | − | 0.0723824i | −0.844374 | − | 0.535754i | \(-0.820027\pi\) |
0.886164 | + | 0.463372i | \(0.153361\pi\) | |||||||
\(212\) | − | 3.49533i | − | 0.240060i | ||||||
\(213\) | 11.6443 | − | 10.5306i | 0.797857 | − | 0.721545i | ||||
\(214\) | 1.59861 | 0.109279 | ||||||||
\(215\) | −3.18170 | − | 5.51086i | −0.216990 | − | 0.375838i | ||||
\(216\) | 3.08161 | + | 4.18374i | 0.209677 | + | 0.284667i | ||||
\(217\) | −0.894485 | − | 0.388622i | −0.0607216 | − | 0.0263814i | ||||
\(218\) | −4.56303 | + | 2.63446i | −0.309047 | + | 0.178428i | ||||
\(219\) | −6.03806 | − | 28.1058i | −0.408014 | − | 1.89922i | ||||
\(220\) | −4.90450 | + | 2.83161i | −0.330661 | + | 0.190907i | ||||
\(221\) | 17.0893 | − | 9.86653i | 1.14955 | − | 0.663695i | ||||
\(222\) | 2.01400 | − | 1.82136i | 0.135171 | − | 0.122242i | ||||
\(223\) | 1.79024 | − | 1.03360i | 0.119884 | − | 0.0692148i | −0.438859 | − | 0.898556i | \(-0.644617\pi\) |
0.558743 | + | 0.829341i | \(0.311284\pi\) | |||||||
\(224\) | −2.42662 | − | 1.05428i | −0.162135 | − | 0.0704421i | ||||
\(225\) | −0.300592 | + | 2.98490i | −0.0200395 | + | 0.198994i | ||||
\(226\) | −7.55846 | − | 13.0916i | −0.502781 | − | 0.870843i | ||||
\(227\) | −19.5582 | −1.29813 | −0.649063 | − | 0.760735i | \(-0.724839\pi\) | ||||
−0.649063 | + | 0.760735i | \(0.724839\pi\) | |||||||
\(228\) | 1.58093 | + | 7.35888i | 0.104700 | + | 0.487353i | ||||
\(229\) | 13.3285i | 0.880775i | 0.897808 | + | 0.440388i | \(0.145159\pi\) | ||||
−0.897808 | + | 0.440388i | \(0.854841\pi\) | |||||||
\(230\) | −2.03736 | + | 3.52880i | −0.134339 | + | 0.232682i | ||||
\(231\) | −25.4439 | − | 5.11121i | −1.67408 | − | 0.336293i | ||||
\(232\) | −3.05152 | − | 5.28540i | −0.200342 | − | 0.347003i | ||||
\(233\) | −15.4047 | + | 8.89393i | −1.00920 | + | 0.582661i | −0.910957 | − | 0.412502i | \(-0.864655\pi\) |
−0.0982415 | + | 0.995163i | \(0.531322\pi\) | |||||||
\(234\) | 7.68778 | − | 3.46300i | 0.502566 | − | 0.226384i | ||||
\(235\) | 2.59337 | − | 4.49185i | 0.169173 | − | 0.293016i | ||||
\(236\) | 5.32873 | − | 9.22962i | 0.346871 | − | 0.600797i | ||||
\(237\) | 14.8058 | − | 3.18078i | 0.961741 | − | 0.206614i | ||||
\(238\) | 17.0373 | + | 7.40209i | 1.10436 | + | 0.479806i | ||||
\(239\) | −3.40145 | − | 1.96383i | −0.220021 | − | 0.127029i | 0.385939 | − | 0.922524i | \(-0.373878\pi\) |
−0.605960 | + | 0.795495i | \(0.707211\pi\) | |||||||
\(240\) | 1.69341 | − | 0.363801i | 0.109309 | − | 0.0234832i | ||||
\(241\) | 11.1448i | 0.717903i | 0.933356 | + | 0.358951i | \(0.116866\pi\) | ||||
−0.933356 | + | 0.358951i | \(0.883134\pi\) | |||||||
\(242\) | 18.2490 | + | 10.5361i | 1.17309 | + | 0.677285i | ||||
\(243\) | −7.94071 | − | 13.4144i | −0.509397 | − | 0.860532i | ||||
\(244\) | 14.6485i | 0.937777i | ||||||||
\(245\) | 2.04268 | − | 6.69533i | 0.130502 | − | 0.427749i | ||||
\(246\) | −4.60231 | − | 1.48431i | −0.293433 | − | 0.0946363i | ||||
\(247\) | 12.2136 | 0.777135 | ||||||||
\(248\) | −0.184307 | − | 0.319228i | −0.0117035 | − | 0.0202710i | ||||
\(249\) | 8.86952 | − | 27.5012i | 0.562083 | − | 1.74281i | ||||
\(250\) | 0.866025 | + | 0.500000i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | −20.9221 | −1.32059 | −0.660295 | − | 0.751006i | \(-0.729569\pi\) | ||||
−0.660295 | + | 0.751006i | \(0.729569\pi\) | |||||||
\(252\) | 6.92632 | + | 3.87635i | 0.436317 | + | 0.244187i | ||||
\(253\) | 23.0760 | 1.45078 | ||||||||
\(254\) | 4.01361 | + | 2.31726i | 0.251836 | + | 0.145398i | ||||
\(255\) | −11.8894 | + | 2.55424i | −0.744546 | + | 0.159953i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 29.1778 | 1.82006 | 0.910030 | − | 0.414541i | \(-0.136058\pi\) | ||||
0.910030 | + | 0.414541i | \(0.136058\pi\) | |||||||
\(258\) | 8.17466 | − | 7.39279i | 0.508932 | − | 0.460255i | ||||
\(259\) | 1.65285 | − | 3.80434i | 0.102703 | − | 0.236390i | ||||
\(260\) | − | 2.81058i | − | 0.174305i | ||||||
\(261\) | 7.51975 | + | 16.6937i | 0.465461 | + | 1.03331i | ||||
\(262\) | 3.21733 | + | 1.85752i | 0.198767 | + | 0.114758i | ||||
\(263\) | 0.627322i | 0.0386824i | 0.999813 | + | 0.0193412i | \(0.00615687\pi\) | ||||
−0.999813 | + | 0.0193412i | \(0.993843\pi\) | |||||||
\(264\) | −6.57936 | − | 7.27520i | −0.404931 | − | 0.447758i | ||||
\(265\) | 3.02705 | + | 1.74767i | 0.185950 | + | 0.107358i | ||||
\(266\) | 6.84159 | + | 9.24022i | 0.419485 | + | 0.566554i | ||||
\(267\) | 0.353129 | − | 1.09492i | 0.0216111 | − | 0.0670082i | ||||
\(268\) | 1.36579 | − | 2.36562i | 0.0834291 | − | 0.144504i | ||||
\(269\) | 1.72988 | − | 2.99624i | 0.105472 | − | 0.182684i | −0.808459 | − | 0.588553i | \(-0.799698\pi\) |
0.913931 | + | 0.405869i | \(0.133031\pi\) | |||||||
\(270\) | −5.16403 | + | 0.576883i | −0.314273 | + | 0.0351080i | ||||
\(271\) | −3.95501 | + | 2.28343i | −0.240250 | + | 0.138708i | −0.615292 | − | 0.788300i | \(-0.710962\pi\) |
0.375042 | + | 0.927008i | \(0.377628\pi\) | |||||||
\(272\) | 3.51050 | + | 6.08036i | 0.212855 | + | 0.368676i | ||||
\(273\) | 8.51050 | − | 9.66738i | 0.515079 | − | 0.585096i | ||||
\(274\) | 10.5319 | − | 18.2419i | 0.636258 | − | 1.10203i | ||||
\(275\) | − | 5.66323i | − | 0.341506i | ||||||
\(276\) | −6.71692 | − | 2.16630i | −0.404311 | − | 0.130396i | ||||
\(277\) | 30.6143 | 1.83943 | 0.919717 | − | 0.392582i | \(-0.128418\pi\) | ||||
0.919717 | + | 0.392582i | \(0.128418\pi\) | |||||||
\(278\) | 4.51338 | + | 7.81740i | 0.270694 | + | 0.468856i | ||||
\(279\) | 0.454180 | + | 1.00827i | 0.0271910 | + | 0.0603634i | ||||
\(280\) | 2.12634 | − | 1.57438i | 0.127073 | − | 0.0940869i | ||||
\(281\) | 8.79291 | − | 5.07659i | 0.524541 | − | 0.302844i | −0.214250 | − | 0.976779i | \(-0.568731\pi\) |
0.738791 | + | 0.673935i | \(0.235397\pi\) | |||||||
\(282\) | 8.55004 | + | 2.75751i | 0.509147 | + | 0.164207i | ||||
\(283\) | 7.55807 | − | 4.36365i | 0.449280 | − | 0.259392i | −0.258246 | − | 0.966079i | \(-0.583144\pi\) |
0.707526 | + | 0.706687i | \(0.249811\pi\) | |||||||
\(284\) | 7.84991 | − | 4.53215i | 0.465806 | − | 0.268933i | ||||
\(285\) | −7.16344 | − | 2.31031i | −0.424325 | − | 0.136851i | ||||
\(286\) | −13.7845 | + | 7.95849i | −0.815095 | + | 0.470595i | ||||
\(287\) | −7.33900 | + | 0.838350i | −0.433207 | + | 0.0494862i | ||||
\(288\) | 1.23213 | + | 2.73530i | 0.0726040 | + | 0.161179i | ||||
\(289\) | −16.1472 | − | 27.9677i | −0.949833 | − | 1.64516i | ||||
\(290\) | 6.10305 | 0.358383 | ||||||||
\(291\) | 3.20187 | + | 1.03265i | 0.187697 | + | 0.0605350i | ||||
\(292\) | − | 16.5972i | − | 0.971275i | ||||||
\(293\) | −8.72722 | + | 15.1160i | −0.509849 | + | 0.883085i | 0.490085 | + | 0.871674i | \(0.336966\pi\) |
−0.999935 | + | 0.0114108i | \(0.996368\pi\) | |||||||
\(294\) | 12.0811 | + | 1.02334i | 0.704584 | + | 0.0596823i | ||||
\(295\) | 5.32873 | + | 9.22962i | 0.310250 | + | 0.537369i | ||||
\(296\) | 1.35771 | − | 0.783876i | 0.0789155 | − | 0.0455619i | ||||
\(297\) | 17.4519 | + | 23.6935i | 1.01266 | + | 1.37484i | ||||
\(298\) | 4.43418 | − | 7.68022i | 0.256865 | − | 0.444903i | ||||
\(299\) | −5.72616 | + | 9.91800i | −0.331152 | + | 0.573572i | ||||
\(300\) | −0.531646 | + | 1.64844i | −0.0306946 | + | 0.0951727i | ||||
\(301\) | 6.70880 | − | 15.4416i | 0.386689 | − | 0.890036i | ||||
\(302\) | −11.6874 | − | 6.74772i | −0.672534 | − | 0.388288i | ||||
\(303\) | 7.30186 | + | 8.07412i | 0.419481 | + | 0.463846i | ||||
\(304\) | 4.34559i | 0.249237i | ||||||||
\(305\) | −12.6860 | − | 7.32427i | −0.726399 | − | 0.419387i | ||||
\(306\) | −8.65078 | − | 19.2045i | −0.494532 | − | 1.09785i | ||||
\(307\) | 3.26532i | 0.186362i | 0.995649 | + | 0.0931808i | \(0.0297035\pi\) | ||||
−0.995649 | + | 0.0931808i | \(0.970297\pi\) | |||||||
\(308\) | −13.7425 | − | 5.97063i | −0.783052 | − | 0.340208i | ||||
\(309\) | −7.19914 | + | 6.51057i | −0.409545 | + | 0.370373i | ||||
\(310\) | 0.368613 | 0.0209358 | ||||||||
\(311\) | 13.2864 | + | 23.0127i | 0.753403 | + | 1.30493i | 0.946164 | + | 0.323687i | \(0.104923\pi\) |
−0.192761 | + | 0.981246i | \(0.561744\pi\) | |||||||
\(312\) | 4.75948 | − | 1.02249i | 0.269452 | − | 0.0578872i | ||||
\(313\) | 4.19978 | + | 2.42475i | 0.237386 | + | 0.137055i | 0.613975 | − | 0.789326i | \(-0.289570\pi\) |
−0.376589 | + | 0.926380i | \(0.622903\pi\) | |||||||
\(314\) | 3.33216 | 0.188044 | ||||||||
\(315\) | −6.82018 | + | 4.06020i | −0.384273 | + | 0.228766i | ||||
\(316\) | 8.74318 | 0.491842 | ||||||||
\(317\) | −19.6462 | − | 11.3428i | −1.10344 | − | 0.637073i | −0.166319 | − | 0.986072i | \(-0.553188\pi\) |
−0.937123 | + | 0.348999i | \(0.886522\pi\) | |||||||
\(318\) | −1.85828 | + | 5.76185i | −0.104207 | + | 0.323108i | ||||
\(319\) | −17.2815 | − | 29.9324i | −0.967577 | − | 1.67589i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −2.63522 | − | 0.849897i | −0.147084 | − | 0.0474366i | ||||
\(322\) | −10.7110 | + | 1.22354i | −0.596902 | + | 0.0681854i | ||||
\(323\) | − | 30.5103i | − | 1.69764i | ||||||
\(324\) | −2.85558 | − | 8.53497i | −0.158643 | − | 0.474165i | ||||
\(325\) | 2.43404 | + | 1.40529i | 0.135016 | + | 0.0779515i | ||||
\(326\) | − | 14.0261i | − | 0.776834i | ||||||
\(327\) | 8.92248 | − | 1.91684i | 0.493414 | − | 0.106002i | ||||
\(328\) | −2.41787 | − | 1.39596i | −0.133505 | − | 0.0770790i | ||||
\(329\) | 13.6342 | − | 1.55746i | 0.751676 | − | 0.0858656i | ||||
\(330\) | 9.59019 | − | 2.06029i | 0.527923 | − | 0.113415i | ||||
\(331\) | 5.18322 | − | 8.97760i | 0.284895 | − | 0.493453i | −0.687688 | − | 0.726006i | \(-0.741374\pi\) |
0.972584 | + | 0.232553i | \(0.0747078\pi\) | |||||||
\(332\) | 8.34157 | − | 14.4480i | 0.457803 | − | 0.792938i | ||||
\(333\) | −4.28827 | + | 1.93168i | −0.234996 | + | 0.105855i | ||||
\(334\) | 16.3410 | − | 9.43447i | 0.894138 | − | 0.516231i | ||||
\(335\) | 1.36579 | + | 2.36562i | 0.0746213 | + | 0.129248i | ||||
\(336\) | 3.43963 | + | 3.02802i | 0.187647 | + | 0.165192i | ||||
\(337\) | 13.0605 | − | 22.6214i | 0.711449 | − | 1.23227i | −0.252864 | − | 0.967502i | \(-0.581372\pi\) |
0.964313 | − | 0.264765i | \(-0.0852942\pi\) | |||||||
\(338\) | 5.10063i | 0.277438i | ||||||||
\(339\) | 5.49955 | + | 25.5992i | 0.298695 | + | 1.39036i | ||||
\(340\) | −7.02099 | −0.380767 | ||||||||
\(341\) | −1.04377 | − | 1.80786i | −0.0565233 | − | 0.0979013i | ||||
\(342\) | 1.30625 | − | 12.9712i | 0.0706339 | − | 0.701400i | ||||
\(343\) | 17.4525 | − | 6.19752i | 0.942348 | − | 0.334635i | ||||
\(344\) | 5.51086 | − | 3.18170i | 0.297126 | − | 0.171546i | ||||
\(345\) | 5.23453 | − | 4.73387i | 0.281818 | − | 0.254863i | ||||
\(346\) | 7.86975 | − | 4.54360i | 0.423080 | − | 0.244266i | ||||
\(347\) | −5.80811 | + | 3.35332i | −0.311796 | + | 0.180015i | −0.647730 | − | 0.761870i | \(-0.724281\pi\) |
0.335934 | + | 0.941886i | \(0.390948\pi\) | |||||||
\(348\) | 2.22029 | + | 10.3350i | 0.119020 | + | 0.554013i | ||||
\(349\) | −18.6240 | + | 10.7526i | −0.996920 | + | 0.575572i | −0.907335 | − | 0.420407i | \(-0.861887\pi\) |
−0.0895843 | + | 0.995979i | \(0.528554\pi\) | |||||||
\(350\) | 0.300277 | + | 2.62866i | 0.0160505 | + | 0.140508i | ||||
\(351\) | −14.5139 | + | 1.62138i | −0.774696 | + | 0.0865427i | ||||
\(352\) | −2.83161 | − | 4.90450i | −0.150926 | − | 0.261411i | ||||
\(353\) | 7.03656 | 0.374518 | 0.187259 | − | 0.982311i | \(-0.440040\pi\) | ||||
0.187259 | + | 0.982311i | \(0.440040\pi\) | |||||||
\(354\) | −13.6910 | + | 12.3815i | −0.727667 | + | 0.658068i | ||||
\(355\) | 9.06430i | 0.481083i | ||||||||
\(356\) | 0.332109 | − | 0.575230i | 0.0176017 | − | 0.0304871i | ||||
\(357\) | −24.1496 | − | 21.2597i | −1.27813 | − | 1.12518i | ||||
\(358\) | −7.02701 | − | 12.1711i | −0.371389 | − | 0.643265i | ||||
\(359\) | 5.90962 | − | 3.41192i | 0.311898 | − | 0.180074i | −0.335878 | − | 0.941906i | \(-0.609033\pi\) |
0.647775 | + | 0.761831i | \(0.275699\pi\) | |||||||
\(360\) | −2.98490 | − | 0.300592i | −0.157318 | − | 0.0158426i | ||||
\(361\) | −0.0579356 | + | 0.100347i | −0.00304924 | + | 0.00528144i | ||||
\(362\) | 1.67270 | − | 2.89720i | 0.0879152 | − | 0.152274i | ||||
\(363\) | −24.4810 | − | 27.0701i | −1.28492 | − | 1.42081i | ||||
\(364\) | 5.97627 | − | 4.42491i | 0.313241 | − | 0.231928i | ||||
\(365\) | 14.3736 | + | 8.29858i | 0.752346 | + | 0.434367i | ||||
\(366\) | 7.78784 | − | 24.1472i | 0.407077 | − | 1.26220i | ||||
\(367\) | − | 35.3498i | − | 1.84525i | −0.385703 | − | 0.922623i | \(-0.626041\pi\) | ||
0.385703 | − | 0.922623i | \(-0.373959\pi\) | |||||||
\(368\) | −3.52880 | − | 2.03736i | −0.183952 | − | 0.106205i | ||||
\(369\) | 6.79750 | + | 4.89360i | 0.353864 | + | 0.254751i | ||||
\(370\) | 1.56775i | 0.0815036i | ||||||||
\(371\) | 1.04957 | + | 9.18803i | 0.0544909 | + | 0.477019i | ||||
\(372\) | 0.134102 | + | 0.624215i | 0.00695286 | + | 0.0323640i | ||||
\(373\) | −17.4842 | −0.905300 | −0.452650 | − | 0.891688i | \(-0.649521\pi\) | ||||
−0.452650 | + | 0.891688i | \(0.649521\pi\) | |||||||
\(374\) | 19.8807 | + | 34.4345i | 1.02801 | + | 1.78056i | ||||
\(375\) | −1.16177 | − | 1.28464i | −0.0599934 | − | 0.0663384i | ||||
\(376\) | 4.49185 | + | 2.59337i | 0.231650 | + | 0.133743i | ||||
\(377\) | 17.1531 | 0.883431 | ||||||||
\(378\) | −9.35678 | − | 10.0723i | −0.481261 | − | 0.518062i | ||||
\(379\) | −11.0373 | −0.566948 | −0.283474 | − | 0.958980i | \(-0.591487\pi\) | ||||
−0.283474 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(380\) | −3.76339 | − | 2.17279i | −0.193058 | − | 0.111462i | ||||
\(381\) | −5.38423 | − | 5.95368i | −0.275842 | − | 0.305016i | ||||
\(382\) | −3.09361 | − | 5.35829i | −0.158283 | − | 0.274154i | ||||
\(383\) | 27.9589 | 1.42864 | 0.714318 | − | 0.699822i | \(-0.246737\pi\) | ||||
0.714318 | + | 0.699822i | \(0.246737\pi\) | |||||||
\(384\) | 0.363801 | + | 1.69341i | 0.0185651 | + | 0.0864166i | ||||
\(385\) | 12.0420 | − | 8.91605i | 0.613716 | − | 0.454404i | ||||
\(386\) | 2.08533i | 0.106141i | ||||||||
\(387\) | −17.4058 | + | 7.84053i | −0.884786 | + | 0.398557i | ||||
\(388\) | 1.68214 | + | 0.971182i | 0.0853975 | + | 0.0493043i | ||||
\(389\) | 13.7967i | 0.699523i | 0.936839 | + | 0.349761i | \(0.113737\pi\) | ||||
−0.936839 | + | 0.349761i | \(0.886263\pi\) | |||||||
\(390\) | −1.49423 | + | 4.63307i | −0.0756635 | + | 0.234605i | ||||
\(391\) | 24.7757 | + | 14.3043i | 1.25296 | + | 0.723398i | ||||
\(392\) | 6.69533 | + | 2.04268i | 0.338165 | + | 0.103171i | ||||
\(393\) | −4.31602 | − | 4.77249i | −0.217714 | − | 0.240740i | ||||
\(394\) | 12.3599 | − | 21.4079i | 0.622681 | − | 1.07851i | ||||
\(395\) | −4.37159 | + | 7.57182i | −0.219959 | + | 0.380979i | ||||
\(396\) | 6.97784 | + | 15.4906i | 0.350650 | + | 0.778433i | ||||
\(397\) | −18.2602 | + | 10.5425i | −0.916453 | + | 0.529114i | −0.882502 | − | 0.470309i | \(-0.844142\pi\) |
−0.0339514 | + | 0.999423i | \(0.510809\pi\) | |||||||
\(398\) | −3.23321 | − | 5.60009i | −0.162066 | − | 0.280707i | ||||
\(399\) | −6.36542 | − | 18.8692i | −0.318670 | − | 0.944643i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 20.6070i | 1.02907i | 0.857471 | + | 0.514533i | \(0.172035\pi\) | ||||
−0.857471 | + | 0.514533i | \(0.827965\pi\) | |||||||
\(402\) | −3.50910 | + | 3.17347i | −0.175018 | + | 0.158278i | ||||
\(403\) | 1.03602 | 0.0516077 | ||||||||
\(404\) | 3.14256 | + | 5.44308i | 0.156348 | + | 0.270803i | ||||
\(405\) | 8.81929 | + | 1.79448i | 0.438234 | + | 0.0891683i | ||||
\(406\) | 9.60849 | + | 12.9772i | 0.476861 | + | 0.644047i | ||||
\(407\) | 7.68904 | − | 4.43927i | 0.381132 | − | 0.220047i | ||||
\(408\) | −2.55424 | − | 11.8894i | −0.126454 | − | 0.588615i | ||||
\(409\) | −20.1815 | + | 11.6518i | −0.997909 | + | 0.576143i | −0.907629 | − | 0.419773i | \(-0.862110\pi\) |
−0.0902803 | + | 0.995916i | \(0.528776\pi\) | |||||||
\(410\) | 2.41787 | − | 1.39596i | 0.119410 | − | 0.0689416i | ||||
\(411\) | −27.0595 | + | 24.4713i | −1.33475 | + | 1.20708i | ||||
\(412\) | −4.85323 | + | 2.80201i | −0.239101 | + | 0.138045i | ||||
\(413\) | −11.2359 | + | 25.8616i | −0.552885 | + | 1.27257i | ||||
\(414\) | 9.92073 | + | 7.14204i | 0.487577 | + | 0.351012i | ||||
\(415\) | 8.34157 | + | 14.4480i | 0.409472 | + | 0.709226i | ||||
\(416\) | 2.81058 | 0.137800 | ||||||||
\(417\) | −3.28394 | − | 15.2860i | −0.160815 | − | 0.748560i | ||||
\(418\) | 24.6101i | 1.20372i | ||||||||
\(419\) | −6.50968 | + | 11.2751i | −0.318019 | + | 0.550824i | −0.980075 | − | 0.198630i | \(-0.936351\pi\) |
0.662056 | + | 0.749454i | \(0.269684\pi\) | |||||||
\(420\) | −4.34216 | + | 1.46480i | −0.211876 | + | 0.0714750i | ||||
\(421\) | 16.4495 | + | 28.4914i | 0.801701 | + | 1.38859i | 0.918496 | + | 0.395431i | \(0.129405\pi\) |
−0.116795 | + | 0.993156i | \(0.537262\pi\) | |||||||
\(422\) | −1.05142 | + | 0.607035i | −0.0511821 | + | 0.0295500i | ||||
\(423\) | −12.6282 | − | 9.09118i | −0.614004 | − | 0.442028i | ||||
\(424\) | −1.74767 | + | 3.02705i | −0.0848742 | + | 0.147006i | ||||
\(425\) | 3.51050 | − | 6.08036i | 0.170284 | − | 0.294941i | ||||
\(426\) | −15.3496 | + | 3.29760i | −0.743691 | + | 0.159769i | ||||
\(427\) | −4.39862 | − | 38.5060i | −0.212864 | − | 1.86344i | ||||
\(428\) | −1.38444 | − | 0.799307i | −0.0669195 | − | 0.0386360i | ||||
\(429\) | 26.9540 | − | 5.79061i | 1.30135 | − | 0.279573i | ||||
\(430\) | 6.36340i | 0.306870i | ||||||||
\(431\) | 22.8306 | + | 13.1813i | 1.09971 | + | 0.634919i | 0.936146 | − | 0.351613i | \(-0.114367\pi\) |
0.163567 | + | 0.986532i | \(0.447700\pi\) | |||||||
\(432\) | −0.576883 | − | 5.16403i | −0.0277553 | − | 0.248455i | ||||
\(433\) | 29.2742i | 1.40683i | 0.710780 | + | 0.703415i | \(0.248342\pi\) | ||||
−0.710780 | + | 0.703415i | \(0.751658\pi\) | |||||||
\(434\) | 0.580336 | + | 0.783799i | 0.0278570 | + | 0.0376235i | ||||
\(435\) | −10.0605 | − | 3.24466i | −0.482364 | − | 0.155570i | ||||
\(436\) | 5.26893 | 0.252336 | ||||||||
\(437\) | 8.85351 | + | 15.3347i | 0.423521 | + | 0.733560i | ||||
\(438\) | −8.82381 | + | 27.3594i | −0.421618 | + | 1.30728i | ||||
\(439\) | −11.0785 | − | 6.39616i | −0.528747 | − | 0.305272i | 0.211759 | − | 0.977322i | \(-0.432081\pi\) |
−0.740506 | + | 0.672050i | \(0.765414\pi\) | |||||||
\(440\) | 5.66323 | 0.269984 | ||||||||
\(441\) | −19.3709 | − | 8.10977i | −0.922424 | − | 0.386180i | ||||
\(442\) | −19.7331 | −0.938606 | ||||||||
\(443\) | 19.0694 | + | 11.0097i | 0.906014 | + | 0.523087i | 0.879146 | − | 0.476552i | \(-0.158113\pi\) |
0.0268674 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(444\) | −2.65485 | + | 0.570350i | −0.125994 | + | 0.0270676i | ||||
\(445\) | 0.332109 | + | 0.575230i | 0.0157435 | + | 0.0272685i | ||||
\(446\) | −2.06719 | −0.0978845 | ||||||||
\(447\) | −11.3926 | + | 10.3030i | −0.538853 | + | 0.487313i | ||||
\(448\) | 1.57438 | + | 2.12634i | 0.0743823 | + | 0.100460i | ||||
\(449\) | 15.8715i | 0.749025i | 0.927222 | + | 0.374512i | \(0.122190\pi\) | ||||
−0.927222 | + | 0.374512i | \(0.877810\pi\) | |||||||
\(450\) | 1.75277 | − | 2.43471i | 0.0826265 | − | 0.114773i | ||||
\(451\) | −13.6930 | − | 7.90564i | −0.644777 | − | 0.372262i | ||||
\(452\) | 15.1169i | 0.711040i | ||||||||
\(453\) | 15.6786 | + | 17.3368i | 0.736643 | + | 0.814552i | ||||
\(454\) | 16.9379 | + | 9.77912i | 0.794936 | + | 0.458957i | ||||
\(455\) | 0.843953 | + | 7.38805i | 0.0395651 | + | 0.346357i | ||||
\(456\) | 2.31031 | − | 7.16344i | 0.108190 | − | 0.335459i | ||||
\(457\) | 10.6090 | − | 18.3754i | 0.496270 | − | 0.859565i | −0.503721 | − | 0.863867i | \(-0.668036\pi\) |
0.999991 | + | 0.00430150i | \(0.00136921\pi\) | |||||||
\(458\) | 6.66427 | − | 11.5429i | 0.311401 | − | 0.539363i | ||||
\(459\) | 4.05029 | + | 36.2566i | 0.189051 | + | 1.69231i | ||||
\(460\) | 3.52880 | − | 2.03736i | 0.164531 | − | 0.0949922i | ||||
\(461\) | −13.3910 | − | 23.1938i | −0.623679 | − | 1.08024i | −0.988795 | − | 0.149282i | \(-0.952304\pi\) |
0.365115 | − | 0.930962i | \(-0.381030\pi\) | |||||||
\(462\) | 19.4794 | + | 17.1484i | 0.906266 | + | 0.797815i | ||||
\(463\) | 7.79895 | − | 13.5082i | 0.362448 | − | 0.627778i | −0.625915 | − | 0.779891i | \(-0.715274\pi\) |
0.988363 | + | 0.152113i | \(0.0486077\pi\) | |||||||
\(464\) | 6.10305i | 0.283327i | ||||||||
\(465\) | −0.607637 | − | 0.195972i | −0.0281785 | − | 0.00908797i | ||||
\(466\) | 17.7879 | 0.824007 | ||||||||
\(467\) | −11.6318 | − | 20.1469i | −0.538256 | − | 0.932288i | −0.998998 | − | 0.0447533i | \(-0.985750\pi\) |
0.460742 | − | 0.887534i | \(-0.347583\pi\) | |||||||
\(468\) | −8.38931 | − | 0.844840i | −0.387796 | − | 0.0390527i | ||||
\(469\) | −2.87986 | + | 6.62853i | −0.132980 | + | 0.306077i | ||||
\(470\) | −4.49185 | + | 2.59337i | −0.207194 | + | 0.119623i | ||||
\(471\) | −5.49286 | − | 1.77153i | −0.253097 | − | 0.0816276i | ||||
\(472\) | −9.22962 | + | 5.32873i | −0.424828 | + | 0.245274i | ||||
\(473\) | 31.2093 | − | 18.0187i | 1.43500 | − | 0.828500i | ||||
\(474\) | −14.4126 | − | 4.64828i | −0.661993 | − | 0.213502i | ||||
\(475\) | 3.76339 | − | 2.17279i | 0.172676 | − | 0.0996946i | ||||
\(476\) | −11.0537 | − | 14.9290i | −0.506644 | − | 0.684272i | ||||
\(477\) | 6.12652 | − | 8.51011i | 0.280514 | − | 0.389651i | ||||
\(478\) | 1.96383 | + | 3.40145i | 0.0898233 | + | 0.155579i | ||||
\(479\) | −18.9385 | −0.865320 | −0.432660 | − | 0.901557i | \(-0.642425\pi\) | ||||
−0.432660 | + | 0.901557i | \(0.642425\pi\) | |||||||
\(480\) | −1.64844 | − | 0.531646i | −0.0752406 | − | 0.0242662i | ||||
\(481\) | 4.40630i | 0.200910i | ||||||||
\(482\) | 5.57242 | − | 9.65172i | 0.253817 | − | 0.439624i | ||||
\(483\) | 18.3070 | + | 3.67753i | 0.832995 | + | 0.167334i | ||||
\(484\) | −10.5361 | − | 18.2490i | −0.478913 | − | 0.829502i | ||||
\(485\) | −1.68214 | + | 0.971182i | −0.0763819 | + | 0.0440991i | ||||
\(486\) | 0.169672 | + | 15.5875i | 0.00769646 | + | 0.707065i | ||||
\(487\) | 14.3962 | − | 24.9350i | 0.652355 | − | 1.12991i | −0.330195 | − | 0.943913i | \(-0.607115\pi\) |
0.982550 | − | 0.185999i | \(-0.0595521\pi\) | |||||||
\(488\) | 7.32427 | − | 12.6860i | 0.331554 | − | 0.574269i | ||||
\(489\) | −7.45692 | + | 23.1212i | −0.337213 | + | 1.04558i | ||||
\(490\) | −5.11668 | + | 4.77698i | −0.231148 | + | 0.215802i | ||||
\(491\) | −2.36612 | − | 1.36608i | −0.106782 | − | 0.0616504i | 0.445658 | − | 0.895203i | \(-0.352970\pi\) |
−0.552440 | + | 0.833553i | \(0.686303\pi\) | |||||||
\(492\) | 3.24356 | + | 3.58661i | 0.146231 | + | 0.161697i | ||||
\(493\) | − | 42.8494i | − | 1.92984i | ||||||
\(494\) | −10.5773 | − | 6.10681i | −0.475896 | − | 0.274759i | ||||
\(495\) | −16.9042 | − | 1.70232i | −0.759787 | − | 0.0765138i | ||||
\(496\) | 0.368613i | 0.0165512i | ||||||||
\(497\) | −19.2738 | + | 14.2706i | −0.864549 | + | 0.640124i | ||||
\(498\) | −21.4318 | + | 19.3819i | −0.960382 | + | 0.868525i | ||||
\(499\) | 24.1713 | 1.08205 | 0.541027 | − | 0.841005i | \(-0.318036\pi\) | ||||
0.541027 | + | 0.841005i | \(0.318036\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −31.9529 | + | 6.86454i | −1.42755 | + | 0.306685i | ||||
\(502\) | 18.1191 | + | 10.4610i | 0.808693 | + | 0.466899i | ||||
\(503\) | −14.6533 | −0.653358 | −0.326679 | − | 0.945135i | \(-0.605930\pi\) | ||||
−0.326679 | + | 0.945135i | \(0.605930\pi\) | |||||||
\(504\) | −4.06020 | − | 6.82018i | −0.180855 | − | 0.303795i | ||||
\(505\) | −6.28513 | −0.279684 | ||||||||
\(506\) | −19.9844 | − | 11.5380i | −0.888416 | − | 0.512927i | ||||
\(507\) | 2.71173 | − | 8.40808i | 0.120432 | − | 0.373416i | ||||
\(508\) | −2.31726 | − | 4.01361i | −0.102812 | − | 0.178075i | ||||
\(509\) | −38.5161 | −1.70720 | −0.853598 | − | 0.520932i | \(-0.825585\pi\) | ||||
−0.853598 | + | 0.520932i | \(0.825585\pi\) | |||||||
\(510\) | 11.5737 | + | 3.73268i | 0.512491 | + | 0.165286i | ||||
\(511\) | 4.98374 | + | 43.6282i | 0.220468 | + | 1.93000i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −9.04934 | + | 20.6877i | −0.399538 | + | 0.913384i | ||||
\(514\) | −25.2687 | − | 14.5889i | −1.11456 | − | 0.643489i | ||||
\(515\) | − | 5.60402i | − | 0.246943i | ||||||
\(516\) | −10.7759 | + | 2.31501i | −0.474381 | + | 0.101913i | ||||
\(517\) | 25.4384 | + | 14.6869i | 1.11878 | + | 0.645928i | ||||
\(518\) | −3.33358 | + | 2.46823i | −0.146469 | + | 0.108448i | ||||
\(519\) | −15.3884 | + | 3.30593i | −0.675476 | + | 0.145114i | ||||
\(520\) | −1.40529 | + | 2.43404i | −0.0616261 | + | 0.106740i | ||||
\(521\) | 12.7686 | − | 22.1158i | 0.559401 | − | 0.968911i | −0.438146 | − | 0.898904i | \(-0.644365\pi\) |
0.997547 | − | 0.0700066i | \(-0.0223020\pi\) | |||||||
\(522\) | 1.83453 | − | 18.2170i | 0.0802952 | − | 0.797337i | ||||
\(523\) | −10.7847 | + | 6.22654i | −0.471581 | + | 0.272268i | −0.716901 | − | 0.697175i | \(-0.754440\pi\) |
0.245320 | + | 0.969442i | \(0.421107\pi\) | |||||||
\(524\) | −1.85752 | − | 3.21733i | −0.0811463 | − | 0.140550i | ||||
\(525\) | 0.902526 | − | 4.49282i | 0.0393895 | − | 0.196083i | ||||
\(526\) | 0.313661 | − | 0.543277i | 0.0136763 | − | 0.0236880i | ||||
\(527\) | − | 2.58803i | − | 0.112736i | ||||||
\(528\) | 2.06029 | + | 9.59019i | 0.0896625 | + | 0.417359i | ||||
\(529\) | 6.39672 | 0.278118 | ||||||||
\(530\) | −1.74767 | − | 3.02705i | −0.0759138 | − | 0.131487i | ||||
\(531\) | 29.1513 | − | 13.1314i | 1.26506 | − | 0.569853i | ||||
\(532\) | −1.30488 | − | 11.4231i | −0.0565737 | − | 0.495252i | ||||
\(533\) | 6.79563 | − | 3.92346i | 0.294352 | − | 0.169944i | ||||
\(534\) | −0.853280 | + | 0.771667i | −0.0369250 | + | 0.0333933i | ||||
\(535\) | 1.38444 | − | 0.799307i | 0.0598546 | − | 0.0345571i | ||||
\(536\) | −2.36562 | + | 1.36579i | −0.102179 | + | 0.0589933i | ||||
\(537\) | 5.11287 | + | 23.7993i | 0.220637 | + | 1.02701i | ||||
\(538\) | −2.99624 | + | 1.72988i | −0.129177 | + | 0.0745803i | ||||
\(539\) | 37.9172 | + | 11.5682i | 1.63321 | + | 0.498277i | ||||
\(540\) | 4.76062 | + | 2.08242i | 0.204865 | + | 0.0896131i | ||||
\(541\) | 8.36504 | + | 14.4887i | 0.359641 | + | 0.622916i | 0.987901 | − | 0.155087i | \(-0.0495658\pi\) |
−0.628260 | + | 0.778004i | \(0.716232\pi\) | |||||||
\(542\) | 4.56686 | 0.196163 | ||||||||
\(543\) | −4.29763 | + | 3.88658i | −0.184429 | + | 0.166789i | ||||
\(544\) | − | 7.02099i | − | 0.301022i | ||||||
\(545\) | −2.63446 | + | 4.56303i | −0.112848 | + | 0.195459i | ||||
\(546\) | −12.2040 | + | 4.11694i | −0.522283 | + | 0.176189i | ||||
\(547\) | 16.1409 | + | 27.9569i | 0.690137 | + | 1.19535i | 0.971793 | + | 0.235836i | \(0.0757829\pi\) |
−0.281656 | + | 0.959515i | \(0.590884\pi\) | |||||||
\(548\) | −18.2419 | + | 10.5319i | −0.779253 | + | 0.449902i | ||||
\(549\) | −25.6756 | + | 35.6649i | −1.09581 | + | 1.52214i | ||||
\(550\) | −2.83161 | + | 4.90450i | −0.120740 | + | 0.209129i | ||||
\(551\) | 13.2607 | − | 22.9681i | 0.564923 | − | 0.978476i | ||||
\(552\) | 4.73387 | + | 5.23453i | 0.201487 | + | 0.222797i | ||||
\(553\) | −22.9828 | + | 2.62538i | −0.977329 | + | 0.111642i | ||||
\(554\) | −26.5128 | − | 15.3071i | −1.12642 | − | 0.650338i | ||||
\(555\) | 0.833489 | − | 2.58435i | 0.0353796 | − | 0.109699i | ||||
\(556\) | − | 9.02675i | − | 0.382820i | ||||||
\(557\) | 26.6920 | + | 15.4106i | 1.13097 | + | 0.652969i | 0.944180 | − | 0.329430i | \(-0.106857\pi\) |
0.186795 | + | 0.982399i | \(0.440190\pi\) | |||||||
\(558\) | 0.110802 | − | 1.10027i | 0.00469064 | − | 0.0465783i | ||||
\(559\) | 17.8848i | 0.756448i | ||||||||
\(560\) | −2.62866 | + | 0.300277i | −0.111081 | + | 0.0126890i | ||||
\(561\) | −14.4653 | − | 67.3326i | −0.610724 | − | 2.84279i | ||||
\(562\) | −10.1532 | −0.428286 | ||||||||
\(563\) | −20.5084 | − | 35.5216i | −0.864325 | − | 1.49705i | −0.867716 | − | 0.497061i | \(-0.834413\pi\) |
0.00339066 | − | 0.999994i | \(-0.498921\pi\) | |||||||
\(564\) | −6.02579 | − | 6.66309i | −0.253732 | − | 0.280567i | ||||
\(565\) | −13.0916 | − | 7.55846i | −0.550769 | − | 0.317987i | ||||
\(566\) | −8.72730 | −0.366836 | ||||||||
\(567\) | 10.0692 | + | 21.5780i | 0.422866 | + | 0.906192i | ||||
\(568\) | −9.06430 | −0.380329 | ||||||||
\(569\) | 14.1078 | + | 8.14517i | 0.591432 | + | 0.341463i | 0.765663 | − | 0.643241i | \(-0.222411\pi\) |
−0.174232 | + | 0.984705i | \(0.555744\pi\) | |||||||
\(570\) | 5.04856 | + | 5.58251i | 0.211461 | + | 0.233826i | ||||
\(571\) | −5.84580 | − | 10.1252i | −0.244639 | − | 0.423727i | 0.717391 | − | 0.696671i | \(-0.245336\pi\) |
−0.962030 | + | 0.272944i | \(0.912003\pi\) | |||||||
\(572\) | 15.9170 | 0.665522 | ||||||||
\(573\) | 2.25092 | + | 10.4775i | 0.0940334 | + | 0.437705i | ||||
\(574\) | 6.77494 | + | 2.94347i | 0.282780 | + | 0.122858i | ||||
\(575\) | 4.07471i | 0.169927i | ||||||||
\(576\) | 0.300592 | − | 2.98490i | 0.0125247 | − | 0.124371i | ||||
\(577\) | 30.4481 | + | 17.5792i | 1.26757 | + | 0.731833i | 0.974528 | − | 0.224266i | \(-0.0719984\pi\) |
0.293044 | + | 0.956099i | \(0.405332\pi\) | |||||||
\(578\) | 32.2943i | 1.34327i | ||||||||
\(579\) | 1.10866 | − | 3.43754i | 0.0460743 | − | 0.142859i | ||||
\(580\) | −5.28540 | − | 3.05152i | −0.219464 | − | 0.126708i | ||||
\(581\) | −17.5887 | + | 40.4837i | −0.729703 | + | 1.67955i | ||||
\(582\) | −2.25657 | − | 2.49523i | −0.0935380 | − | 0.103431i | ||||
\(583\) | −9.89744 | + | 17.1429i | −0.409910 | + | 0.709985i | ||||
\(584\) | −8.29858 | + | 14.3736i | −0.343398 | + | 0.594782i | ||||
\(585\) | 4.92631 | − | 6.84294i | 0.203678 | − | 0.282921i | ||||
\(586\) | 15.1160 | − | 8.72722i | 0.624436 | − | 0.360518i | ||||
\(587\) | −3.93572 | − | 6.81686i | −0.162444 | − | 0.281362i | 0.773300 | − | 0.634040i | \(-0.218605\pi\) |
−0.935745 | + | 0.352678i | \(0.885271\pi\) | |||||||
\(588\) | −9.95086 | − | 6.92678i | −0.410367 | − | 0.285656i | ||||
\(589\) | 0.800920 | − | 1.38723i | 0.0330014 | − | 0.0571600i | ||||
\(590\) | − | 10.6575i | − | 0.438760i | ||||||
\(591\) | −31.7559 | + | 28.7186i | −1.30626 | + | 1.18132i | ||||
\(592\) | −1.56775 | −0.0644342 | ||||||||
\(593\) | −3.43635 | − | 5.95193i | −0.141114 | − | 0.244416i | 0.786802 | − | 0.617205i | \(-0.211735\pi\) |
−0.927916 | + | 0.372788i | \(0.878402\pi\) | |||||||
\(594\) | −3.26702 | − | 29.2451i | −0.134048 | − | 1.19994i | ||||
\(595\) | 18.4558 | − | 2.10824i | 0.756613 | − | 0.0864295i | ||||
\(596\) | −7.68022 | + | 4.43418i | −0.314594 | + | 0.181631i | ||||
\(597\) | 2.35249 | + | 10.9503i | 0.0962811 | + | 0.448167i | ||||
\(598\) | 9.91800 | − | 5.72616i | 0.405577 | − | 0.234160i | ||||
\(599\) | −28.1842 | + | 16.2722i | −1.15157 | + | 0.664862i | −0.949271 | − | 0.314461i | \(-0.898176\pi\) |
−0.202304 | + | 0.979323i | \(0.564843\pi\) | |||||||
\(600\) | 1.28464 | − | 1.16177i | 0.0524451 | − | 0.0474290i | ||||
\(601\) | 28.7087 | − | 16.5750i | 1.17105 | − | 0.676107i | 0.217124 | − | 0.976144i | \(-0.430333\pi\) |
0.953927 | + | 0.300038i | \(0.0969992\pi\) | |||||||
\(602\) | −13.5308 | + | 10.0184i | −0.551473 | + | 0.408318i | ||||
\(603\) | 7.47171 | − | 3.36567i | 0.304271 | − | 0.137061i | ||||
\(604\) | 6.74772 | + | 11.6874i | 0.274561 | + | 0.475553i | ||||
\(605\) | 21.0722 | 0.856705 | ||||||||
\(606\) | −2.28653 | − | 10.6433i | −0.0928841 | − | 0.432355i | ||||
\(607\) | − | 26.2617i | − | 1.06593i | −0.846138 | − | 0.532964i | \(-0.821078\pi\) | ||
0.846138 | − | 0.532964i | \(-0.178922\pi\) | |||||||
\(608\) | 2.17279 | − | 3.76339i | 0.0881184 | − | 0.152626i | ||||
\(609\) | −8.93975 | − | 26.5004i | −0.362257 | − | 1.07385i | ||||
\(610\) | 7.32427 | + | 12.6860i | 0.296551 | + | 0.513642i | ||||
\(611\) | −12.6247 | + | 7.28889i | −0.510742 | + | 0.294877i | ||||
\(612\) | −2.11046 | + | 20.9570i | −0.0853101 | + | 0.847135i | ||||
\(613\) | 9.71301 | − | 16.8234i | 0.392305 | − | 0.679492i | −0.600448 | − | 0.799664i | \(-0.705011\pi\) |
0.992753 | + | 0.120172i | \(0.0383445\pi\) | |||||||
\(614\) | 1.63266 | − | 2.82785i | 0.0658888 | − | 0.114123i | ||||
\(615\) | −4.72788 | + | 1.01570i | −0.190646 | + | 0.0409571i | ||||
\(616\) | 8.91605 | + | 12.0420i | 0.359238 | + | 0.485185i | ||||
\(617\) | 15.6130 | + | 9.01417i | 0.628556 | + | 0.362897i | 0.780192 | − | 0.625540i | \(-0.215121\pi\) |
−0.151637 | + | 0.988436i | \(0.548454\pi\) | |||||||
\(618\) | 9.48993 | − | 2.03875i | 0.381741 | − | 0.0820105i | ||||
\(619\) | 15.9835i | 0.642432i | 0.947006 | + | 0.321216i | \(0.104092\pi\) | ||||
−0.947006 | + | 0.321216i | \(0.895908\pi\) | |||||||
\(620\) | −0.319228 | − | 0.184307i | −0.0128205 | − | 0.00740193i | ||||
\(621\) | −12.5567 | − | 17.0475i | −0.503882 | − | 0.684094i | ||||
\(622\) | − | 26.5728i | − | 1.06547i | ||||||
\(623\) | −0.700272 | + | 1.61181i | −0.0280558 | + | 0.0645757i | ||||
\(624\) | −4.63307 | − | 1.49423i | −0.185471 | − | 0.0598172i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.42475 | − | 4.19978i | −0.0969123 | − | 0.167857i | ||||
\(627\) | 13.0838 | − | 40.5682i | 0.522518 | − | 1.62014i | ||||
\(628\) | −2.88573 | − | 1.66608i | −0.115153 | − | 0.0664837i | ||||
\(629\) | 11.0072 | 0.438885 | ||||||||
\(630\) | 7.93654 | − | 0.106144i | 0.316199 | − | 0.00422886i | ||||
\(631\) | −43.0538 | −1.71395 | −0.856973 | − | 0.515362i | \(-0.827657\pi\) | ||||
−0.856973 | + | 0.515362i | \(0.827657\pi\) | |||||||
\(632\) | −7.57182 | − | 4.37159i | −0.301191 | − | 0.173893i | ||||
\(633\) | 2.05592 | − | 0.441680i | 0.0817155 | − | 0.0175552i | ||||
\(634\) | 11.3428 | + | 19.6462i | 0.450478 | + | 0.780251i | ||||
\(635\) | 4.63451 | 0.183915 | ||||||||
\(636\) | 4.49024 | − | 4.06076i | 0.178050 | − | 0.161020i | ||||
\(637\) | −14.3808 | + | 13.4261i | −0.569790 | + | 0.531962i | ||||
\(638\) | 34.5630i | 1.36836i | ||||||||
\(639\) | 27.0560 | + | 2.72466i | 1.07032 | + | 0.107786i | ||||
\(640\) | −0.866025 | − | 0.500000i | −0.0342327 | − | 0.0197642i | ||||
\(641\) | − | 8.31902i | − | 0.328582i | −0.986412 | − | 0.164291i | \(-0.947466\pi\) | ||
0.986412 | − | 0.164291i | \(-0.0525335\pi\) | |||||||
\(642\) | 1.85722 | + | 2.05364i | 0.0732986 | + | 0.0810508i | ||||
\(643\) | 11.2945 | + | 6.52086i | 0.445410 | + | 0.257158i | 0.705890 | − | 0.708322i | \(-0.250547\pi\) |
−0.260480 | + | 0.965479i | \(0.583881\pi\) | |||||||
\(644\) | 9.88779 | + | 4.29589i | 0.389633 | + | 0.169282i | ||||
\(645\) | 3.38307 | − | 10.4897i | 0.133208 | − | 0.413030i | ||||
\(646\) | −15.2552 | + | 26.4227i | −0.600206 | + | 1.03959i | ||||
\(647\) | −3.58732 | + | 6.21343i | −0.141032 | + | 0.244275i | −0.927886 | − | 0.372865i | \(-0.878375\pi\) |
0.786853 | + | 0.617140i | \(0.211709\pi\) | |||||||
\(648\) | −1.79448 | + | 8.81929i | −0.0704938 | + | 0.346454i | ||||
\(649\) | −52.2695 | + | 30.1778i | −2.05176 | + | 1.18458i | ||||
\(650\) | −1.40529 | − | 2.43404i | −0.0551200 | − | 0.0954707i | ||||
\(651\) | −0.539945 | − | 1.60058i | −0.0211621 | − | 0.0627316i | ||||
\(652\) | −7.01305 | + | 12.1470i | −0.274652 | + | 0.475711i | ||||
\(653\) | − | 21.2930i | − | 0.833261i | −0.909076 | − | 0.416631i | \(-0.863211\pi\) | ||
0.909076 | − | 0.416631i | \(-0.136789\pi\) | |||||||
\(654\) | −8.68551 | − | 2.80120i | −0.339630 | − | 0.109536i | ||||
\(655\) | 3.71505 | 0.145159 | ||||||||
\(656\) | 1.39596 | + | 2.41787i | 0.0545031 | + | 0.0944021i | ||||
\(657\) | 29.0910 | − | 40.4092i | 1.13495 | − | 1.57651i | ||||
\(658\) | −12.5863 | − | 5.46829i | −0.490664 | − | 0.213176i | ||||
\(659\) | 7.91663 | − | 4.57067i | 0.308388 | − | 0.178048i | −0.337817 | − | 0.941212i | \(-0.609688\pi\) |
0.646205 | + | 0.763164i | \(0.276355\pi\) | |||||||
\(660\) | −9.33549 | − | 3.01083i | −0.363383 | − | 0.117196i | ||||
\(661\) | −18.5903 | + | 10.7331i | −0.723078 | + | 0.417469i | −0.815884 | − | 0.578215i | \(-0.803749\pi\) |
0.0928066 | + | 0.995684i | \(0.470416\pi\) | |||||||
\(662\) | −8.97760 | + | 5.18322i | −0.348924 | + | 0.201451i | ||||
\(663\) | 32.5288 | + | 10.4910i | 1.26331 | + | 0.407437i | ||||
\(664\) | −14.4480 | + | 8.34157i | −0.560692 | + | 0.323716i | ||||
\(665\) | 10.5451 | + | 4.58147i | 0.408921 | + | 0.177662i | ||||
\(666\) | 4.67959 | + | 0.471255i | 0.181330 | + | 0.0182607i | ||||
\(667\) | 12.4341 | + | 21.5365i | 0.481450 | + | 0.833895i | ||||
\(668\) | −18.8689 | −0.730061 | ||||||||
\(669\) | 3.40765 | + | 1.09902i | 0.131747 | + | 0.0424904i | ||||
\(670\) | − | 2.73159i | − | 0.105530i | ||||||
\(671\) | 41.4790 | − | 71.8438i | 1.60128 | − | 2.77350i | ||||
\(672\) | −1.46480 | − | 4.34216i | −0.0565059 | − | 0.167502i | ||||
\(673\) | −17.7533 | − | 30.7497i | −0.684341 | − | 1.18531i | −0.973643 | − | 0.228076i | \(-0.926757\pi\) |
0.289302 | − | 0.957238i | \(-0.406577\pi\) | |||||||
\(674\) | −22.6214 | + | 13.0605i | −0.871344 | + | 0.503071i | ||||
\(675\) | −4.18374 | + | 3.08161i | −0.161032 | + | 0.118611i | ||||
\(676\) | 2.55031 | − | 4.41727i | 0.0980890 | − | 0.169895i | ||||
\(677\) | −6.78337 | + | 11.7491i | −0.260706 | + | 0.451556i | −0.966430 | − | 0.256931i | \(-0.917289\pi\) |
0.705724 | + | 0.708487i | \(0.250622\pi\) | |||||||
\(678\) | 8.03685 | − | 24.9193i | 0.308653 | − | 0.957021i | ||||
\(679\) | −4.71338 | − | 2.04780i | −0.180883 | − | 0.0785872i | ||||
\(680\) | 6.08036 | + | 3.51050i | 0.233171 | + | 0.134621i | ||||
\(681\) | −22.7221 | − | 25.1253i | −0.870714 | − | 0.962802i | ||||
\(682\) | 2.08754i | 0.0799361i | ||||||||
\(683\) | 17.5340 | + | 10.1233i | 0.670922 | + | 0.387357i | 0.796426 | − | 0.604736i | \(-0.206721\pi\) |
−0.125504 | + | 0.992093i | \(0.540055\pi\) | |||||||
\(684\) | −7.61682 | + | 10.5802i | −0.291237 | + | 0.404545i | ||||
\(685\) | − | 21.0639i | − | 0.804809i | ||||||
\(686\) | −18.2131 | − | 3.35906i | −0.695379 | − | 0.128249i | ||||
\(687\) | −17.1224 | + | 15.4847i | −0.653259 | + | 0.590777i | ||||
\(688\) | −6.36340 | −0.242602 | ||||||||
\(689\) | −4.91196 | − | 8.50776i | −0.187131 | − | 0.324120i | ||||
\(690\) | −6.90017 | + | 1.48238i | −0.262685 | + | 0.0564334i | ||||
\(691\) | 25.4972 | + | 14.7208i | 0.969958 | + | 0.560006i | 0.899224 | − | 0.437489i | \(-0.144132\pi\) |
0.0707348 | + | 0.997495i | \(0.477466\pi\) | |||||||
\(692\) | −9.08721 | −0.345444 | ||||||||
\(693\) | −22.9938 | − | 38.6242i | −0.873463 | − | 1.46721i | ||||
\(694\) | 6.70663 | 0.254580 | ||||||||
\(695\) | 7.81740 | + | 4.51338i | 0.296531 | + | 0.171202i | ||||
\(696\) | 3.24466 | − | 10.0605i | 0.122989 | − | 0.381343i | ||||
\(697\) | −9.80102 | − | 16.9759i | −0.371240 | − | 0.643007i | ||||
\(698\) | 21.5051 | 0.813982 | ||||||||
\(699\) | −29.3222 | − | 9.45685i | −1.10907 | − | 0.357691i | ||||
\(700\) | 1.05428 | − | 2.42662i | 0.0398481 | − | 0.0917177i | ||||
\(701\) | − | 41.6152i | − | 1.57178i | −0.618364 | − | 0.785892i | \(-0.712204\pi\) | ||
0.618364 | − | 0.785892i | \(-0.287796\pi\) | |||||||
\(702\) | 13.3801 | + | 5.85281i | 0.505000 | + | 0.220900i | ||||
\(703\) | 5.90006 | + | 3.40640i | 0.222525 | + | 0.128475i | ||||
\(704\) | 5.66323i | 0.213441i | ||||||||
\(705\) | 8.78330 | − | 1.88694i | 0.330798 | − | 0.0710664i | ||||
\(706\) | −6.09384 | − | 3.51828i | −0.229345 | − | 0.132412i | ||||
\(707\) | −9.89515 | − | 13.3643i | −0.372145 | − | 0.502618i | ||||
\(708\) | 18.0475 | − | 3.87719i | 0.678266 | − | 0.145714i | ||||
\(709\) | −11.1912 | + | 19.3838i | −0.420296 | + | 0.727973i | −0.995968 | − | 0.0897069i | \(-0.971407\pi\) |
0.575673 | + | 0.817680i | \(0.304740\pi\) | |||||||
\(710\) | 4.53215 | − | 7.84991i | 0.170088 | − | 0.294602i | ||||
\(711\) | 21.2871 | + | 15.3248i | 0.798327 | + | 0.574725i | ||||
\(712\) | −0.575230 | + | 0.332109i | −0.0215576 | + | 0.0124463i | ||||
\(713\) | 0.750996 | + | 1.30076i | 0.0281250 | + | 0.0487140i | ||||
\(714\) | 10.2844 | + | 30.4863i | 0.384882 | + | 1.14092i | ||||
\(715\) | −7.95849 | + | 13.7845i | −0.297630 | + | 0.515511i | ||||
\(716\) | 14.0540i | 0.525224i | ||||||||
\(717\) | −1.42888 | − | 6.65114i | −0.0533626 | − | 0.248391i | ||||
\(718\) | −6.82384 | −0.254664 | ||||||||
\(719\) | −13.3750 | − | 23.1661i | −0.498802 | − | 0.863951i | 0.501197 | − | 0.865333i | \(-0.332893\pi\) |
−0.999999 | + | 0.00138257i | \(0.999560\pi\) | |||||||
\(720\) | 2.43471 | + | 1.75277i | 0.0907361 | + | 0.0653220i | ||||
\(721\) | 11.9161 | − | 8.82284i | 0.443778 | − | 0.328580i | ||||
\(722\) | 0.100347 | − | 0.0579356i | 0.00373454 | − | 0.00215614i | ||||
\(723\) | −14.3171 | + | 12.9477i | −0.532459 | + | 0.481531i | ||||
\(724\) | −2.89720 | + | 1.67270i | −0.107674 | + | 0.0621655i | ||||
\(725\) | 5.28540 | − | 3.05152i | 0.196295 | − | 0.113331i | ||||
\(726\) | 7.66607 | + | 35.6839i | 0.284515 | + | 1.32435i | ||||
\(727\) | −9.55141 | + | 5.51451i | −0.354242 | + | 0.204522i | −0.666552 | − | 0.745458i | \(-0.732231\pi\) |
0.312310 | + | 0.949980i | \(0.398897\pi\) | |||||||
\(728\) | −7.38805 | + | 0.843953i | −0.273820 | + | 0.0312790i | ||||
\(729\) | 8.00735 | − | 25.7853i | 0.296569 | − | 0.955012i | ||||
\(730\) | −8.29858 | − | 14.3736i | −0.307144 | − | 0.531989i | ||||
\(731\) | 44.6773 | 1.65245 | ||||||||
\(732\) | −18.8181 | + | 17.0182i | −0.695536 | + | 0.629011i | ||||
\(733\) | − | 4.89952i | − | 0.180968i | −0.995898 | − | 0.0904839i | \(-0.971159\pi\) | ||
0.995898 | − | 0.0904839i | \(-0.0288414\pi\) | |||||||
\(734\) | −17.6749 | + | 30.6139i | −0.652393 | + | 1.12998i | ||||
\(735\) | 10.9742 | − | 5.15431i | 0.404790 | − | 0.190120i | ||||
\(736\) | 2.03736 | + | 3.52880i | 0.0750980 | + | 0.130073i | ||||
\(737\) | −13.3971 | + | 7.73481i | −0.493488 | + | 0.284915i | ||||
\(738\) | −3.44001 | − | 7.63673i | −0.126629 | − | 0.281112i | ||||
\(739\) | −5.60509 | + | 9.70830i | −0.206187 | + | 0.357126i | −0.950510 | − | 0.310693i | \(-0.899439\pi\) |
0.744324 | + | 0.667819i | \(0.232772\pi\) | |||||||
\(740\) | 0.783876 | − | 1.35771i | 0.0288159 | − | 0.0499105i | ||||
\(741\) | 14.1894 | + | 15.6901i | 0.521261 | + | 0.576390i | ||||
\(742\) | 3.68506 | − | 8.48185i | 0.135283 | − | 0.311379i | ||||
\(743\) | −33.4349 | − | 19.3036i | −1.22661 | − | 0.708182i | −0.260288 | − | 0.965531i | \(-0.583818\pi\) |
−0.966318 | + | 0.257349i | \(0.917151\pi\) | |||||||
\(744\) | 0.195972 | − | 0.607637i | 0.00718467 | − | 0.0222770i | ||||
\(745\) | − | 8.86835i | − | 0.324911i | ||||||
\(746\) | 15.1418 | + | 8.74212i | 0.554381 | + | 0.320072i | ||||
\(747\) | 45.6334 | − | 20.5558i | 1.66964 | − | 0.752098i | ||||
\(748\) | − | 39.7615i | − | 1.45382i | ||||||
\(749\) | 3.87923 | + | 1.68539i | 0.141744 | + | 0.0615828i | ||||
\(750\) | 0.363801 | + | 1.69341i | 0.0132841 | + | 0.0618347i | ||||
\(751\) | 39.0281 | 1.42416 | 0.712078 | − | 0.702100i | \(-0.247754\pi\) | ||||
0.712078 | + | 0.702100i | \(0.247754\pi\) | |||||||
\(752\) | −2.59337 | − | 4.49185i | −0.0945706 | − | 0.163801i | ||||
\(753\) | −24.3066 | − | 26.8773i | −0.885782 | − | 0.979464i | ||||
\(754\) | −14.8550 | − | 8.57656i | −0.540989 | − | 0.312340i | ||||
\(755\) | −13.4954 | −0.491149 | ||||||||
\(756\) | 3.06707 | + | 13.4012i | 0.111548 | + | 0.487398i | ||||
\(757\) | −51.3343 | −1.86578 | −0.932889 | − | 0.360163i | \(-0.882721\pi\) | ||||
−0.932889 | + | 0.360163i | \(0.882721\pi\) | |||||||
\(758\) | 9.55858 | + | 5.51865i | 0.347183 | + | 0.200446i | ||||
\(759\) | 26.8090 | + | 29.6444i | 0.973105 | + | 1.07602i | ||||
\(760\) | 2.17279 | + | 3.76339i | 0.0788155 | + | 0.136512i | ||||
\(761\) | 3.20178 | 0.116064 | 0.0580321 | − | 0.998315i | \(-0.481517\pi\) | ||||
0.0580321 | + | 0.998315i | \(0.481517\pi\) | |||||||
\(762\) | 1.68604 | + | 7.84815i | 0.0610788 | + | 0.284308i | ||||
\(763\) | −13.8502 | + | 1.58214i | −0.501411 | + | 0.0572773i | ||||
\(764\) | 6.18722i | 0.223846i | ||||||||
\(765\) | −17.0940 | − | 12.3062i | −0.618036 | − | 0.444931i | ||||
\(766\) | −24.2132 | − | 13.9795i | −0.874857 | − | 0.505099i | ||||
\(767\) | − | 29.9536i | − | 1.08156i | ||||||
\(768\) | 0.531646 | − | 1.64844i | 0.0191841 | − | 0.0594829i | ||||
\(769\) | 26.4700 | + | 15.2825i | 0.954533 | + | 0.551100i | 0.894486 | − | 0.447096i | \(-0.147542\pi\) |
0.0600465 | + | 0.998196i | \(0.480875\pi\) | |||||||
\(770\) | −14.8867 | + | 1.70054i | −0.536479 | + | 0.0612831i | ||||
\(771\) | 33.8978 | + | 37.4829i | 1.22080 | + | 1.34991i | ||||
\(772\) | 1.04267 | − | 1.80595i | 0.0375264 | − | 0.0649976i | ||||
\(773\) | 8.73288 | − | 15.1258i | 0.314100 | − | 0.544037i | −0.665146 | − | 0.746714i | \(-0.731631\pi\) |
0.979246 | + | 0.202676i | \(0.0649639\pi\) | |||||||
\(774\) | 18.9941 | + | 1.91279i | 0.682729 | + | 0.0687538i | ||||
\(775\) | 0.319228 | − | 0.184307i | 0.0114670 | − | 0.00662049i | ||||
\(776\) | −0.971182 | − | 1.68214i | −0.0348634 | − | 0.0603852i | ||||
\(777\) | 6.80743 | − | 2.29645i | 0.244215 | − | 0.0823845i | ||||
\(778\) | 6.89837 | − | 11.9483i | 0.247319 | − | 0.428368i | ||||
\(779\) | − | 12.1325i | − | 0.434693i | ||||||
\(780\) | 3.61058 | − | 3.26524i | 0.129280 | − | 0.116914i | ||||
\(781\) | −51.3332 | −1.83685 | ||||||||
\(782\) | −14.3043 | − | 24.7757i | −0.511519 | − | 0.885977i | ||||
\(783\) | −12.7091 | + | 29.0543i | −0.454187 | + | 1.03832i | ||||
\(784\) | −4.77698 | − | 5.11668i | −0.170607 | − | 0.182739i | ||||
\(785\) | 2.88573 | − | 1.66608i | 0.102996 | − | 0.0594649i | ||||
\(786\) | 1.35154 | + | 6.29111i | 0.0482077 | + | 0.224396i | ||||
\(787\) | 17.4903 | − | 10.0980i | 0.623461 | − | 0.359956i | −0.154754 | − | 0.987953i | \(-0.549459\pi\) |
0.778215 | + | 0.627997i | \(0.216125\pi\) | |||||||
\(788\) | −21.4079 | + | 12.3599i | −0.762625 | + | 0.440302i | ||||
\(789\) | −0.805883 | + | 0.728803i | −0.0286902 | + | 0.0259461i | ||||
\(790\) | 7.57182 | − | 4.37159i | 0.269393 | − | 0.155534i | ||||
\(791\) | −4.53927 | − | 39.7372i | −0.161398 | − | 1.41289i | ||||
\(792\) | 1.70232 | − | 16.9042i | 0.0604894 | − | 0.600664i | ||||
\(793\) | 20.5855 | + | 35.6551i | 0.731011 | + | 1.26615i | ||||
\(794\) | 21.0851 | 0.748281 | ||||||||
\(795\) | 1.27161 | + | 5.91904i | 0.0450992 | + | 0.209927i | ||||
\(796\) | 6.46643i | 0.229196i | ||||||||
\(797\) | −12.9050 | + | 22.3521i | −0.457118 | + | 0.791752i | −0.998807 | − | 0.0488273i | \(-0.984452\pi\) |
0.541689 | + | 0.840579i | \(0.317785\pi\) | |||||||
\(798\) | −3.92200 | + | 19.5239i | −0.138837 | + | 0.691140i | ||||
\(799\) | 18.2080 | + | 31.5373i | 0.644154 | + | 1.11571i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | 1.81683 | − | 0.818404i | 0.0641947 | − | 0.0289169i | ||||
\(802\) | 10.3035 | − | 17.8462i | 0.363830 | − | 0.630172i | ||||
\(803\) | −46.9968 | + | 81.4008i | −1.65848 | + | 2.87257i | ||||
\(804\) | 4.62571 | − | 0.993754i | 0.163136 | − | 0.0350470i | ||||
\(805\) | −8.66424 | + | 6.41513i | −0.305374 | + | 0.226104i | ||||
\(806\) | −0.897218 | − | 0.518009i | −0.0316031 | − | 0.0182461i | ||||
\(807\) | 5.85879 | − | 1.25866i | 0.206239 | − | 0.0443070i | ||||
\(808\) | − | 6.28513i | − | 0.221110i | ||||||
\(809\) | 32.1130 | + | 18.5405i | 1.12903 | + | 0.651848i | 0.943692 | − | 0.330827i | \(-0.107328\pi\) |
0.185342 | + | 0.982674i | \(0.440661\pi\) | |||||||
\(810\) | −6.74049 | − | 5.96371i | −0.236837 | − | 0.209543i | ||||
\(811\) | − | 8.95559i | − | 0.314473i | −0.987561 | − | 0.157237i | \(-0.949741\pi\) | ||
0.987561 | − | 0.157237i | \(-0.0502585\pi\) | |||||||
\(812\) | −1.83261 | − | 16.0428i | −0.0643118 | − | 0.562993i | ||||
\(813\) | −7.52819 | − | 2.42795i | −0.264025 | − | 0.0851519i | ||||
\(814\) | −8.87854 | −0.311193 | ||||||||
\(815\) | −7.01305 | − | 12.1470i | −0.245656 | − | 0.425489i | ||||
\(816\) | −3.73268 | + | 11.5737i | −0.130670 | + | 0.405160i | ||||
\(817\) | 23.9479 | + | 13.8263i | 0.837832 | + | 0.483723i | ||||
\(818\) | 23.3036 | 0.814790 | ||||||||
\(819\) | 22.3063 | − | 0.298325i | 0.779446 | − | 0.0104243i | ||||
\(820\) | −2.79192 | −0.0974981 | ||||||||
\(821\) | 26.4839 | + | 15.2905i | 0.924294 | + | 0.533641i | 0.885002 | − | 0.465586i | \(-0.154157\pi\) |
0.0392915 | + | 0.999228i | \(0.487490\pi\) | |||||||
\(822\) | 35.6698 | − | 7.66306i | 1.24413 | − | 0.267280i | ||||
\(823\) | 8.50650 | + | 14.7337i | 0.296518 | + | 0.513584i | 0.975337 | − | 0.220721i | \(-0.0708412\pi\) |
−0.678819 | + | 0.734306i | \(0.737508\pi\) | |||||||
\(824\) | 5.60402 | 0.195225 | ||||||||
\(825\) | 7.27520 | − | 6.57936i | 0.253290 | − | 0.229064i | ||||
\(826\) | 22.6614 | − | 16.7788i | 0.788491 | − | 0.583810i | ||||
\(827\) | 41.4119i | 1.44003i | 0.693956 | + | 0.720017i | \(0.255866\pi\) | ||||
−0.693956 | + | 0.720017i | \(0.744134\pi\) | |||||||
\(828\) | −5.02058 | − | 11.1456i | −0.174477 | − | 0.387335i | ||||
\(829\) | 5.80702 | + | 3.35269i | 0.201686 | + | 0.116444i | 0.597442 | − | 0.801912i | \(-0.296184\pi\) |
−0.395756 | + | 0.918356i | \(0.629517\pi\) | |||||||
\(830\) | − | 16.6831i | − | 0.579080i | ||||||
\(831\) | 35.5667 | + | 39.3283i | 1.23379 | + | 1.36428i | ||||
\(832\) | −2.43404 | − | 1.40529i | −0.0843850 | − | 0.0487197i | ||||
\(833\) | 33.5392 | + | 35.9242i | 1.16206 | + | 1.24470i | ||||
\(834\) | −4.79904 | + | 14.8801i | −0.166177 | + | 0.515254i | ||||
\(835\) | 9.43447 | − | 16.3410i | 0.326493 | − | 0.565503i | ||||
\(836\) | 12.3050 | − | 21.3129i | 0.425578 | − | 0.737123i | ||||
\(837\) | −0.767607 | + | 1.75483i | −0.0265324 | + | 0.0606557i | ||||
\(838\) | 11.2751 | − | 6.50968i | 0.389492 | − | 0.224873i | ||||
\(839\) | −20.6497 | − | 35.7663i | −0.712906 | − | 1.23479i | −0.963762 | − | 0.266765i | \(-0.914045\pi\) |
0.250856 | − | 0.968025i | \(-0.419288\pi\) | |||||||
\(840\) | 4.49282 | + | 0.902526i | 0.155017 | + | 0.0311401i | ||||
\(841\) | 4.12360 | − | 7.14229i | 0.142193 | − | 0.246286i | ||||
\(842\) | − | 32.8991i | − | 1.13378i | ||||||
\(843\) | 16.7369 | + | 5.39789i | 0.576449 | + | 0.185913i | ||||
\(844\) | 1.21407 | 0.0417900 | ||||||||
\(845\) | 2.55031 | + | 4.41727i | 0.0877335 | + | 0.151959i | ||||
\(846\) | 6.39075 | + | 14.1873i | 0.219718 | + | 0.487769i | ||||
\(847\) | 33.1755 | + | 44.8067i | 1.13992 | + | 1.53958i | ||||
\(848\) | 3.02705 | − | 1.74767i | 0.103949 | − | 0.0600151i | ||||
\(849\) | 14.3864 | + | 4.63983i | 0.493741 | + | 0.159239i | ||||
\(850\) | −6.08036 | + | 3.51050i | −0.208554 | + | 0.120409i | ||||
\(851\) | −5.53229 | + | 3.19407i | −0.189645 | + | 0.109491i | ||||
\(852\) | 14.9419 | + | 4.81900i | 0.511903 | + | 0.165096i | ||||
\(853\) | 26.9412 | − | 15.5545i | 0.922449 | − | 0.532576i | 0.0380332 | − | 0.999276i | \(-0.487891\pi\) |
0.884415 | + | 0.466701i | \(0.154557\pi\) | |||||||
\(854\) | −15.4437 | + | 35.5465i | −0.528472 | + | 1.21638i | ||||
\(855\) | −5.35433 | − | 11.8865i | −0.183114 | − | 0.406509i | ||||
\(856\) | 0.799307 | + | 1.38444i | 0.0273198 | + | 0.0473192i | ||||
\(857\) | −24.4533 | −0.835309 | −0.417654 | − | 0.908606i | \(-0.637148\pi\) | ||||
−0.417654 | + | 0.908606i | \(0.637148\pi\) | |||||||
\(858\) | −26.2382 | − | 8.46219i | −0.895756 | − | 0.288894i | ||||
\(859\) | − | 34.7993i | − | 1.18734i | −0.804710 | − | 0.593668i | \(-0.797679\pi\) | ||
0.804710 | − | 0.593668i | \(-0.202321\pi\) | |||||||
\(860\) | 3.18170 | − | 5.51086i | 0.108495 | − | 0.187919i | ||||
\(861\) | −9.60319 | − | 8.45399i | −0.327276 | − | 0.288111i | ||||
\(862\) | −13.1813 | − | 22.8306i | −0.448956 | − | 0.777614i | ||||
\(863\) | −7.18913 | + | 4.15065i | −0.244721 | + | 0.141290i | −0.617345 | − | 0.786693i | \(-0.711792\pi\) |
0.372624 | + | 0.927983i | \(0.378458\pi\) | |||||||
\(864\) | −2.08242 | + | 4.76062i | −0.0708454 | + | 0.161960i | ||||
\(865\) | 4.54360 | − | 7.86975i | 0.154487 | − | 0.267580i | ||||
\(866\) | 14.6371 | − | 25.3522i | 0.497389 | − | 0.861503i | ||||
\(867\) | 17.1691 | − | 53.2352i | 0.583094 | − | 1.80796i | ||||
\(868\) | −0.110686 | − | 0.968957i | −0.00375693 | − | 0.0328886i | ||||
\(869\) | −42.8809 | − | 24.7573i | −1.45464 | − | 0.839834i | ||||
\(870\) | 7.09032 | + | 7.84021i | 0.240385 | + | 0.265808i | ||||
\(871\) | − | 7.67735i | − | 0.260137i | ||||||
\(872\) | −4.56303 | − | 2.63446i | −0.154524 | − | 0.0892142i | ||||
\(873\) | 2.39325 | + | 5.31294i | 0.0809991 | + | 0.179816i | ||||
\(874\) | − | 17.7070i | − | 0.598949i | ||||||
\(875\) | 1.57438 | + | 2.12634i | 0.0532236 | + | 0.0718836i | ||||
\(876\) | 21.3213 | − | 19.2820i | 0.720382 | − | 0.651480i | ||||
\(877\) | 15.2655 | 0.515480 | 0.257740 | − | 0.966214i | \(-0.417022\pi\) | ||||
0.257740 | + | 0.966214i | \(0.417022\pi\) | |||||||
\(878\) | 6.39616 | + | 11.0785i | 0.215860 | + | 0.373881i | ||||
\(879\) | −29.5576 | + | 6.34994i | −0.996952 | + | 0.214178i | ||||
\(880\) | −4.90450 | − | 2.83161i | −0.165331 | − | 0.0954537i | ||||
\(881\) | −18.8162 | −0.633933 | −0.316967 | − | 0.948437i | \(-0.602664\pi\) | ||||
−0.316967 | + | 0.948437i | \(0.602664\pi\) | |||||||
\(882\) | 12.7208 | + | 16.7087i | 0.428332 | + | 0.562612i | ||||
\(883\) | −13.6066 | −0.457899 | −0.228949 | − | 0.973438i | \(-0.573529\pi\) | ||||
−0.228949 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(884\) | 17.0893 | + | 9.86653i | 0.574777 | + | 0.331847i | ||||
\(885\) | −5.66599 | + | 17.5682i | −0.190460 | + | 0.590547i | ||||
\(886\) | −11.0097 | − | 19.0694i | −0.369879 | − | 0.640649i | ||||
\(887\) | −10.4409 | −0.350571 | −0.175285 | − | 0.984518i | \(-0.556085\pi\) | ||||
−0.175285 | + | 0.984518i | \(0.556085\pi\) | |||||||
\(888\) | 2.58435 | + | 0.833489i | 0.0867250 | + | 0.0279701i | ||||
\(889\) | 7.29647 | + | 9.85457i | 0.244716 | + | 0.330512i | ||||
\(890\) | − | 0.664218i | − | 0.0222646i | ||||||
\(891\) | −10.1625 | + | 49.9457i | −0.340458 | + | 1.67324i | ||||
\(892\) | 1.79024 | + | 1.03360i | 0.0599418 | + | 0.0346074i | ||||
\(893\) | 22.5395i | 0.754254i | ||||||||
\(894\) | 15.0178 | − | 3.22631i | 0.502270 | − | 0.107904i | ||||
\(895\) | −12.1711 | − | 7.02701i | −0.406836 | − | 0.234887i | ||||
\(896\) | −0.300277 | − | 2.62866i | −0.0100316 | − | 0.0878172i | ||||
\(897\) | −19.3935 | + | 4.16636i | −0.647530 | + | 0.139111i | ||||
\(898\) | 7.93577 | − | 13.7452i | 0.264820 | − | 0.458682i | ||||
\(899\) | 1.12483 | − | 1.94827i | 0.0375153 | − | 0.0649783i | ||||
\(900\) | −2.73530 | + | 1.23213i | −0.0911766 | + | 0.0410710i | ||||
\(901\) | −21.2529 | + | 12.2704i | −0.708036 | + | 0.408785i | ||||
\(902\) | 7.90564 | + | 13.6930i | 0.263229 | + | 0.455926i | ||||
\(903\) | 27.6309 | − | 9.32111i | 0.919498 | − | 0.310187i | ||||
\(904\) | 7.55846 | − | 13.0916i | 0.251391 | − | 0.435422i | ||||
\(905\) | − | 3.34540i | − | 0.111205i | ||||||
\(906\) | −4.90965 | − | 22.8534i | −0.163112 | − | 0.759252i | ||||
\(907\) | −34.3521 | −1.14064 | −0.570321 | − | 0.821422i | \(-0.693181\pi\) | ||||
−0.570321 | + | 0.821422i | \(0.693181\pi\) | |||||||
\(908\) | −9.77912 | − | 16.9379i | −0.324531 | − | 0.562105i | ||||
\(909\) | −1.88926 | + | 18.7605i | −0.0626628 | + | 0.622246i | ||||
\(910\) | 2.96314 | − | 6.82022i | 0.0982272 | − | 0.226088i | ||||
\(911\) | −26.3197 | + | 15.1957i | −0.872010 | + | 0.503455i | −0.868016 | − | 0.496537i | \(-0.834605\pi\) |
−0.00399406 | + | 0.999992i | \(0.501271\pi\) | |||||||
\(912\) | −5.58251 | + | 5.04856i | −0.184855 | + | 0.167175i | ||||
\(913\) | −81.8225 | + | 47.2402i | −2.70793 | + | 1.56342i | ||||
\(914\) | −18.3754 | + | 10.6090i | −0.607804 | + | 0.350916i | ||||
\(915\) | −5.32915 | − | 24.8060i | −0.176176 | − | 0.820062i | ||||
\(916\) | −11.5429 | + | 6.66427i | −0.381387 | + | 0.220194i | ||||
\(917\) | 5.84888 | + | 7.89947i | 0.193147 | + | 0.260864i | ||||
\(918\) | 14.6206 | − | 33.4243i | 0.482553 | − | 1.10317i | ||||
\(919\) | −11.9867 | − | 20.7616i | −0.395406 | − | 0.684862i | 0.597747 | − | 0.801685i | \(-0.296063\pi\) |
−0.993153 | + | 0.116822i | \(0.962729\pi\) | |||||||
\(920\) | −4.07471 | −0.134339 | ||||||||
\(921\) | −4.19476 | + | 3.79354i | −0.138222 | + | 0.125001i | ||||
\(922\) | 26.7819i | 0.882016i | ||||||||
\(923\) | 12.7380 | − | 22.0628i | 0.419276 | − | 0.726206i | ||||
\(924\) | −8.29550 | − | 24.5907i | −0.272902 | − | 0.808973i | ||||
\(925\) | 0.783876 | + | 1.35771i | 0.0257737 | + | 0.0446413i | ||||
\(926\) | −13.5082 | + | 7.79895i | −0.443906 | + | 0.256289i | ||||
\(927\) | −16.7275 | − | 1.68453i | −0.549402 | − | 0.0553271i | ||||
\(928\) | 3.05152 | − | 5.28540i | 0.100171 | − | 0.173502i | ||||
\(929\) | 15.9915 | − | 27.6981i | 0.524665 | − | 0.908746i | −0.474923 | − | 0.880028i | \(-0.657524\pi\) |
0.999588 | − | 0.0287187i | \(-0.00914271\pi\) | |||||||
\(930\) | 0.428243 | + | 0.473535i | 0.0140426 | + | 0.0155278i | ||||
\(931\) | 6.86016 | + | 29.6355i | 0.224833 | + | 0.971263i | ||||
\(932\) | −15.4047 | − | 8.89393i | −0.504599 | − | 0.291330i | ||||
\(933\) | −14.1273 | + | 43.8037i | −0.462508 | + | 1.43407i | ||||
\(934\) | 23.2636i | 0.761210i | ||||||||
\(935\) | 34.4345 | + | 19.8807i | 1.12613 | + | 0.650170i | ||||
\(936\) | 6.84294 | + | 4.92631i | 0.223668 | + | 0.161021i | ||||
\(937\) | − | 19.4842i | − | 0.636522i | −0.948003 | − | 0.318261i | \(-0.896901\pi\) | ||
0.948003 | − | 0.318261i | \(-0.103099\pi\) | |||||||
\(938\) | 5.80830 | − | 4.30055i | 0.189648 | − | 0.140418i | ||||
\(939\) | 1.76425 | + | 8.21219i | 0.0575741 | + | 0.267995i | ||||
\(940\) | 5.18675 | 0.169173 | ||||||||
\(941\) | −4.96490 | − | 8.59946i | −0.161851 | − | 0.280334i | 0.773681 | − | 0.633575i | \(-0.218413\pi\) |
−0.935533 | + | 0.353240i | \(0.885080\pi\) | |||||||
\(942\) | 3.87119 | + | 4.28062i | 0.126130 | + | 0.139470i | ||||
\(943\) | 9.85214 | + | 5.68814i | 0.320830 | + | 0.185231i | ||||
\(944\) | 10.6575 | 0.346871 | ||||||||
\(945\) | −13.1393 | − | 4.04446i | −0.427423 | − | 0.131566i | ||||
\(946\) | −36.0374 | −1.17168 | ||||||||
\(947\) | 41.6103 | + | 24.0237i | 1.35215 | + | 0.780665i | 0.988551 | − | 0.150890i | \(-0.0482138\pi\) |
0.363601 | + | 0.931555i | \(0.381547\pi\) | |||||||
\(948\) | 10.1575 | + | 11.2318i | 0.329902 | + | 0.364793i | ||||
\(949\) | −23.3238 | − | 40.3981i | −0.757124 | − | 1.31138i | ||||
\(950\) | −4.34559 | −0.140989 | ||||||||
\(951\) | −8.25301 | − | 38.4159i | −0.267622 | − | 1.24572i | ||||
\(952\) | 2.10824 | + | 18.4558i | 0.0683285 | + | 0.598155i | ||||
\(953\) | − | 43.5664i | − | 1.41126i | −0.708583 | − | 0.705628i | \(-0.750665\pi\) | ||
0.708583 | − | 0.705628i | \(-0.249335\pi\) | |||||||
\(954\) | −9.56078 | + | 4.30671i | −0.309542 | + | 0.139435i | ||||
\(955\) | −5.35829 | − | 3.09361i | −0.173390 | − | 0.100107i | ||||
\(956\) | − | 3.92765i | − | 0.127029i | ||||||
\(957\) | 18.3753 | − | 56.9750i | 0.593988 | − | 1.84174i | ||||
\(958\) | 16.4012 | + | 9.46923i | 0.529898 | + | 0.305937i | ||||
\(959\) | 44.7891 | − | 33.1625i | 1.44631 | − | 1.07087i | ||||
\(960\) | 1.16177 | + | 1.28464i | 0.0374959 | + | 0.0414615i | ||||
\(961\) | −15.4321 | + | 26.7291i | −0.497808 | + | 0.862230i | ||||
\(962\) | 2.20315 | − | 3.81597i | 0.0710324 | − | 0.123032i | ||||
\(963\) | −1.96970 | − | 4.37269i | −0.0634728 | − | 0.140908i | ||||
\(964\) | −9.65172 | + | 5.57242i | −0.310861 | + | 0.179476i | ||||
\(965\) | 1.04267 | + | 1.80595i | 0.0335646 | + | 0.0581356i | ||||
\(966\) | −14.0155 | − | 12.3383i | −0.450942 | − | 0.396979i | ||||
\(967\) | 1.35974 | − | 2.35513i | 0.0437261 | − | 0.0757359i | −0.843334 | − | 0.537390i | \(-0.819410\pi\) |
0.887060 | + | 0.461654i | \(0.152744\pi\) | |||||||
\(968\) | 21.0722i | 0.677285i | ||||||||
\(969\) | 39.1947 | − | 35.4459i | 1.25912 | − | 1.13869i | ||||
\(970\) | 1.94236 | 0.0623655 | ||||||||
\(971\) | 5.40380 | + | 9.35966i | 0.173416 | + | 0.300366i | 0.939612 | − | 0.342241i | \(-0.111186\pi\) |
−0.766196 | + | 0.642607i | \(0.777853\pi\) | |||||||
\(972\) | 7.64683 | − | 13.5840i | 0.245272 | − | 0.435708i | ||||
\(973\) | 2.71053 | + | 23.7282i | 0.0868955 | + | 0.760692i | ||||
\(974\) | −24.9350 | + | 14.3962i | −0.798968 | + | 0.461284i | ||||
\(975\) | 1.02249 | + | 4.75948i | 0.0327460 | + | 0.152425i | ||||
\(976\) | −12.6860 | + | 7.32427i | −0.406069 | + | 0.234444i | ||||
\(977\) | −16.0175 | + | 9.24772i | −0.512446 | + | 0.295861i | −0.733839 | − | 0.679324i | \(-0.762273\pi\) |
0.221393 | + | 0.975185i | \(0.428940\pi\) | |||||||
\(978\) | 18.0185 | − | 16.2951i | 0.576167 | − | 0.521059i | ||||
\(979\) | −3.25766 | + | 1.88081i | −0.104115 | + | 0.0601109i | ||||
\(980\) | 6.81967 | − | 1.57865i | 0.217846 | − | 0.0504281i | ||||
\(981\) | 12.8283 | + | 9.23523i | 0.409576 | + | 0.294858i | ||||
\(982\) | 1.36608 | + | 2.36612i | 0.0435934 | + | 0.0755061i | ||||
\(983\) | 41.8397 | 1.33448 | 0.667239 | − | 0.744844i | \(-0.267476\pi\) | ||||
0.667239 | + | 0.744844i | \(0.267476\pi\) | |||||||
\(984\) | −1.01570 | − | 4.72788i | −0.0323794 | − | 0.150719i | ||||
\(985\) | − | 24.7197i | − | 0.787636i | ||||||
\(986\) | −21.4247 | + | 37.1087i | −0.682302 | + | 1.18178i | ||||
\(987\) | 17.8405 | + | 15.7056i | 0.567870 | + | 0.499914i | ||||
\(988\) | 6.10681 | + | 10.5773i | 0.194284 | + | 0.336509i | ||||
\(989\) | −22.4552 | + | 12.9645i | −0.714033 | + | 0.412247i | ||||
\(990\) | 13.7883 | + | 9.92635i | 0.438221 | + | 0.315480i | ||||
\(991\) | −6.08551 | + | 10.5404i | −0.193313 | + | 0.334827i | −0.946346 | − | 0.323155i | \(-0.895256\pi\) |
0.753034 | + | 0.657982i | \(0.228590\pi\) | |||||||
\(992\) | 0.184307 | − | 0.319228i | 0.00585174 | − | 0.0101355i | ||||
\(993\) | 17.5547 | − | 3.77132i | 0.557080 | − | 0.119679i | ||||
\(994\) | 23.8269 | − | 2.72180i | 0.755744 | − | 0.0863302i | ||||
\(995\) | −5.60009 | − | 3.23321i | −0.177535 | − | 0.102500i | ||||
\(996\) | 28.2515 | − | 6.06934i | 0.895182 | − | 0.192314i | ||||
\(997\) | 7.33233i | 0.232217i | 0.993237 | + | 0.116109i | \(0.0370420\pi\) | ||||
−0.993237 | + | 0.116109i | \(0.962958\pi\) | |||||||
\(998\) | −20.9329 | − | 12.0856i | −0.662620 | − | 0.382564i | ||||
\(999\) | −7.46348 | − | 3.26472i | −0.236134 | − | 0.103291i |
(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 | 630.2.t.b.311.5 | ✓ | 28 | |
3.2 | odd | 2 | 1890.2.t.b.1151.8 | 28 | |||
7.5 | odd | 6 | 630.2.bk.b.131.14 | yes | 28 | ||
9.2 | odd | 6 | 630.2.bk.b.101.7 | yes | 28 | ||
9.7 | even | 3 | 1890.2.bk.b.521.14 | 28 | |||
21.5 | even | 6 | 1890.2.bk.b.341.14 | 28 | |||
63.47 | even | 6 | inner | 630.2.t.b.551.5 | yes | 28 | |
63.61 | odd | 6 | 1890.2.t.b.1601.8 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.5 | ✓ | 28 | 1.1 | even | 1 | trivial | |
630.2.t.b.551.5 | yes | 28 | 63.47 | even | 6 | inner | |
630.2.bk.b.101.7 | yes | 28 | 9.2 | odd | 6 | ||
630.2.bk.b.131.14 | yes | 28 | 7.5 | odd | 6 | ||
1890.2.t.b.1151.8 | 28 | 3.2 | odd | 2 | |||
1890.2.t.b.1601.8 | 28 | 63.61 | odd | 6 | |||
1890.2.bk.b.341.14 | 28 | 21.5 | even | 6 | |||
1890.2.bk.b.521.14 | 28 | 9.7 | even | 3 |