Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(-1.50511 - 0.403293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.2.k.b.124.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.495361 | − | 0.285997i | 0.350273 | − | 0.202230i | −0.314533 | − | 0.949247i | \(-0.601848\pi\) |
0.664805 | + | 0.747017i | \(0.268514\pi\) | |||||||
\(3\) | 1.70828 | − | 0.285997i | 0.986273 | − | 0.165120i | ||||
\(4\) | −0.836412 | + | 1.44871i | −0.418206 | + | 0.724354i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.764419 | − | 0.630233i | 0.312073 | − | 0.257291i | ||||
\(7\) | 1.23669 | − | 0.714003i | 0.467425 | − | 0.269868i | −0.247736 | − | 0.968828i | \(-0.579687\pi\) |
0.715161 | + | 0.698960i | \(0.246353\pi\) | |||||||
\(8\) | 2.10083i | 0.742756i | ||||||||
\(9\) | 2.83641 | − | 0.977122i | 0.945471 | − | 0.325707i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.33641 | − | 2.31473i | −0.402943 | − | 0.697918i | 0.591136 | − | 0.806572i | \(-0.298679\pi\) |
−0.994080 | + | 0.108653i | \(0.965346\pi\) | |||||||
\(12\) | −1.01450 | + | 2.71400i | −0.292860 | + | 0.783465i | ||||
\(13\) | 4.04678 | + | 2.33641i | 1.12238 | + | 0.648004i | 0.942006 | − | 0.335595i | \(-0.108937\pi\) |
0.180370 | + | 0.983599i | \(0.442271\pi\) | |||||||
\(14\) | 0.408405 | − | 0.707378i | 0.109151 | − | 0.189055i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.07199 | − | 1.85675i | −0.267998 | − | 0.464187i | ||||
\(17\) | 2.67282i | 0.648255i | 0.946013 | + | 0.324127i | \(0.105071\pi\) | ||||
−0.946013 | + | 0.324127i | \(0.894929\pi\) | |||||||
\(18\) | 1.12559 | − | 1.29523i | 0.265305 | − | 0.305289i | ||||
\(19\) | −4.67282 | −1.07202 | −0.536010 | − | 0.844212i | \(-0.680069\pi\) | ||||
−0.536010 | + | 0.844212i | \(0.680069\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.90841 | − | 1.57340i | 0.416448 | − | 0.343345i | ||||
\(22\) | −1.32401 | − | 0.764419i | −0.282280 | − | 0.162975i | ||||
\(23\) | −5.12483 | − | 2.95882i | −1.06860 | − | 0.616957i | −0.140802 | − | 0.990038i | \(-0.544968\pi\) |
−0.927799 | + | 0.373081i | \(0.878301\pi\) | |||||||
\(24\) | 0.600830 | + | 3.58880i | 0.122644 | + | 0.732560i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.67282 | 0.524184 | ||||||||
\(27\) | 4.56592 | − | 2.48040i | 0.878712 | − | 0.477353i | ||||
\(28\) | 2.38880i | 0.451441i | ||||||||
\(29\) | −4.74482 | − | 8.21826i | −0.881090 | − | 1.52609i | −0.850130 | − | 0.526573i | \(-0.823477\pi\) |
−0.0309603 | − | 0.999521i | \(-0.509857\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.48040 | + | 6.02823i | −0.625098 | + | 1.08270i | 0.363424 | + | 0.931624i | \(0.381608\pi\) |
−0.988522 | + | 0.151078i | \(0.951726\pi\) | |||||||
\(32\) | −4.70079 | − | 2.71400i | −0.830990 | − | 0.479773i | ||||
\(33\) | −2.94497 | − | 3.57199i | −0.512653 | − | 0.621804i | ||||
\(34\) | 0.764419 | + | 1.32401i | 0.131097 | + | 0.227066i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.956844 | + | 4.92641i | −0.159474 | + | 0.821068i | ||||
\(37\) | − | 1.81681i | − | 0.298682i | −0.988786 | − | 0.149341i | \(-0.952285\pi\) | ||
0.988786 | − | 0.149341i | \(-0.0477152\pi\) | |||||||
\(38\) | −2.31473 | + | 1.33641i | −0.375499 | + | 0.216795i | ||||
\(39\) | 7.58123 | + | 2.83387i | 1.21397 | + | 0.453782i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.735581 | − | 1.27406i | 0.114879 | − | 0.198975i | −0.802853 | − | 0.596177i | \(-0.796685\pi\) |
0.917731 | + | 0.397202i | \(0.130019\pi\) | |||||||
\(42\) | 0.495361 | − | 1.32520i | 0.0764358 | − | 0.204483i | ||||
\(43\) | −0.408039 | + | 0.235581i | −0.0622254 | + | 0.0359258i | −0.530790 | − | 0.847503i | \(-0.678105\pi\) |
0.468565 | + | 0.883429i | \(0.344771\pi\) | |||||||
\(44\) | 4.47116 | 0.674053 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.38485 | −0.499069 | ||||||||
\(47\) | 6.02480 | − | 3.47842i | 0.878808 | − | 0.507380i | 0.00854274 | − | 0.999964i | \(-0.497281\pi\) |
0.870265 | + | 0.492584i | \(0.163947\pi\) | |||||||
\(48\) | −2.36228 | − | 2.86525i | −0.340966 | − | 0.413563i | ||||
\(49\) | −2.48040 | + | 4.29618i | −0.354343 | + | 0.613739i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.764419 | + | 4.56592i | 0.107040 | + | 0.639357i | ||||
\(52\) | −6.76956 | + | 3.90841i | −0.938769 | + | 0.541998i | ||||
\(53\) | 1.14399i | 0.157139i | 0.996909 | + | 0.0785693i | \(0.0250352\pi\) | ||||
−0.996909 | + | 0.0785693i | \(0.974965\pi\) | |||||||
\(54\) | 1.55239 | − | 2.53453i | 0.211254 | − | 0.344906i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | + | 2.59808i | 0.200446 | + | 0.347183i | ||||
\(57\) | −7.98247 | + | 1.33641i | −1.05730 | + | 0.177012i | ||||
\(58\) | −4.70079 | − | 2.71400i | −0.617244 | − | 0.356366i | ||||
\(59\) | −0.571993 | + | 0.990721i | −0.0744672 | + | 0.128981i | −0.900854 | − | 0.434121i | \(-0.857059\pi\) |
0.826387 | + | 0.563102i | \(0.190392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.26442 | + | 2.19004i | 0.161892 | + | 0.280406i | 0.935547 | − | 0.353201i | \(-0.114907\pi\) |
−0.773655 | + | 0.633607i | \(0.781574\pi\) | |||||||
\(62\) | 3.98153i | 0.505655i | ||||||||
\(63\) | 2.81009 | − | 3.23360i | 0.354039 | − | 0.407396i | ||||
\(64\) | 1.18319 | 0.147899 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.48040 | − | 0.927175i | −0.305316 | − | 0.114127i | ||||
\(67\) | 5.70751 | + | 3.29523i | 0.697283 | + | 0.402577i | 0.806335 | − | 0.591459i | \(-0.201448\pi\) |
−0.109051 | + | 0.994036i | \(0.534781\pi\) | |||||||
\(68\) | −3.87214 | − | 2.23558i | −0.469566 | − | 0.271104i | ||||
\(69\) | −9.60083 | − | 3.58880i | −1.15580 | − | 0.432040i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8745 | −1.52792 | −0.763960 | − | 0.645263i | \(-0.776748\pi\) | ||||
−0.763960 | + | 0.645263i | \(0.776748\pi\) | |||||||
\(72\) | 2.05277 | + | 5.95882i | 0.241921 | + | 0.702254i | ||||
\(73\) | 1.71203i | 0.200378i | 0.994968 | + | 0.100189i | \(0.0319447\pi\) | ||||
−0.994968 | + | 0.100189i | \(0.968055\pi\) | |||||||
\(74\) | −0.519602 | − | 0.899976i | −0.0604025 | − | 0.104620i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.90841 | − | 6.76956i | 0.448325 | − | 0.776521i | ||||
\(77\) | −3.30545 | − | 1.90841i | −0.376692 | − | 0.217483i | ||||
\(78\) | 4.56592 | − | 0.764419i | 0.516989 | − | 0.0865534i | ||||
\(79\) | −0.143987 | − | 0.249392i | −0.0161998 | − | 0.0280588i | 0.857812 | − | 0.513964i | \(-0.171823\pi\) |
−0.874012 | + | 0.485905i | \(0.838490\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.09046 | − | 5.54304i | 0.787829 | − | 0.615894i | ||||
\(82\) | − | 0.841495i | − | 0.0929276i | ||||||
\(83\) | 3.71007 | − | 2.14201i | 0.407233 | − | 0.235116i | −0.282367 | − | 0.959306i | \(-0.591120\pi\) |
0.689600 | + | 0.724190i | \(0.257786\pi\) | |||||||
\(84\) | 0.683190 | + | 4.08074i | 0.0745421 | + | 0.445245i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.134751 | + | 0.233396i | −0.0145306 | + | 0.0251677i | ||||
\(87\) | −10.4559 | − | 12.6821i | −1.12098 | − | 1.35966i | ||||
\(88\) | 4.86286 | − | 2.80757i | 0.518383 | − | 0.299288i | ||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.67282 | 0.699502 | ||||||||
\(92\) | 8.57293 | − | 4.94958i | 0.893790 | − | 0.516030i | ||||
\(93\) | −4.22143 | + | 11.2933i | −0.437742 | + | 1.17106i | ||||
\(94\) | 1.98963 | − | 3.44615i | 0.205215 | − | 0.355443i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.80644 | − | 3.29186i | −0.898804 | − | 0.335974i | ||||
\(97\) | 6.78555 | − | 3.91764i | 0.688968 | − | 0.397776i | −0.114257 | − | 0.993451i | \(-0.536449\pi\) |
0.803225 | + | 0.595675i | \(0.203115\pi\) | |||||||
\(98\) | 2.83754i | 0.286635i | ||||||||
\(99\) | −6.05239 | − | 5.25970i | −0.608288 | − | 0.528620i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.10083 | + | 3.63875i | 0.209040 | + | 0.362069i | 0.951413 | − | 0.307919i | \(-0.0996326\pi\) |
−0.742372 | + | 0.669988i | \(0.766299\pi\) | |||||||
\(102\) | 1.68450 | + | 2.04316i | 0.166790 | + | 0.202303i | ||||
\(103\) | −1.57340 | − | 0.908405i | −0.155032 | − | 0.0895078i | 0.420477 | − | 0.907303i | \(-0.361863\pi\) |
−0.575509 | + | 0.817795i | \(0.695196\pi\) | |||||||
\(104\) | −4.90841 | + | 8.50161i | −0.481309 | + | 0.833651i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.327176 | + | 0.566686i | 0.0317782 | + | 0.0550414i | ||||
\(107\) | 11.9176i | 1.15212i | 0.817407 | + | 0.576061i | \(0.195411\pi\) | ||||
−0.817407 | + | 0.576061i | \(0.804589\pi\) | |||||||
\(108\) | −0.225617 | + | 8.68932i | −0.0217100 | + | 0.836130i | ||||
\(109\) | 16.6521 | 1.59498 | 0.797491 | − | 0.603331i | \(-0.206160\pi\) | ||||
0.797491 | + | 0.603331i | \(0.206160\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.519602 | − | 3.10361i | −0.0493184 | − | 0.294582i | ||||
\(112\) | −2.65145 | − | 1.53081i | −0.250538 | − | 0.144648i | ||||
\(113\) | 17.4272 | + | 10.0616i | 1.63942 | + | 0.946518i | 0.981034 | + | 0.193836i | \(0.0620929\pi\) |
0.658384 | + | 0.752682i | \(0.271240\pi\) | |||||||
\(114\) | −3.57199 | + | 2.94497i | −0.334548 | + | 0.275821i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.8745 | 1.47391 | ||||||||
\(117\) | 13.7613 | + | 2.67282i | 1.27223 | + | 0.247103i | ||||
\(118\) | 0.654353i | 0.0602380i | ||||||||
\(119\) | 1.90841 | + | 3.30545i | 0.174943 | + | 0.303011i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.92801 | − | 3.33941i | 0.175273 | − | 0.303582i | ||||
\(122\) | 1.25269 | + | 0.723239i | 0.113413 | + | 0.0654790i | ||||
\(123\) | 0.892198 | − | 2.38683i | 0.0804468 | − | 0.215213i | ||||
\(124\) | −5.82209 | − | 10.0842i | −0.522839 | − | 0.905584i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.467210 | − | 2.40548i | 0.0416224 | − | 0.214297i | ||||
\(127\) | 2.18714i | 0.194078i | 0.995281 | + | 0.0970388i | \(0.0309371\pi\) | ||||
−0.995281 | + | 0.0970388i | \(0.969063\pi\) | |||||||
\(128\) | 9.98769 | − | 5.76640i | 0.882795 | − | 0.509682i | ||||
\(129\) | −0.629668 | + | 0.519136i | −0.0554391 | + | 0.0457074i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | 7.63798 | − | 1.27874i | 0.664801 | − | 0.111300i | ||||
\(133\) | −5.77883 | + | 3.33641i | −0.501089 | + | 0.289304i | ||||
\(134\) | 3.76970 | 0.325653 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.61515 | −0.481495 | ||||||||
\(137\) | −8.83490 | + | 5.10083i | −0.754816 | + | 0.435793i | −0.827431 | − | 0.561567i | \(-0.810199\pi\) |
0.0726153 | + | 0.997360i | \(0.476865\pi\) | |||||||
\(138\) | −5.78226 | + | 0.968056i | −0.492218 | + | 0.0824064i | ||||
\(139\) | 4.00000 | − | 6.92820i | 0.339276 | − | 0.587643i | −0.645021 | − | 0.764165i | \(-0.723151\pi\) |
0.984297 | + | 0.176522i | \(0.0564848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.29721 | − | 7.66518i | 0.782966 | − | 0.645524i | ||||
\(142\) | −6.37751 | + | 3.68206i | −0.535189 | + | 0.308992i | ||||
\(143\) | − | 12.4896i | − | 1.04444i | ||||||
\(144\) | −4.85488 | − | 4.21903i | −0.404574 | − | 0.351586i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.489634 | + | 0.848071i | 0.0405224 | + | 0.0701868i | ||||
\(147\) | −3.00851 | + | 8.04844i | −0.248138 | + | 0.663824i | ||||
\(148\) | 2.63203 | + | 1.51960i | 0.216351 | + | 0.124910i | ||||
\(149\) | −10.0381 | + | 17.3865i | −0.822351 | + | 1.42435i | 0.0815762 | + | 0.996667i | \(0.474005\pi\) |
−0.903927 | + | 0.427687i | \(0.859329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51960 | − | 2.63203i | −0.123663 | − | 0.214191i | 0.797546 | − | 0.603258i | \(-0.206131\pi\) |
−0.921210 | + | 0.389066i | \(0.872798\pi\) | |||||||
\(152\) | − | 9.81681i | − | 0.796248i | ||||||
\(153\) | 2.61168 | + | 7.58123i | 0.211141 | + | 0.612906i | ||||
\(154\) | −2.18319 | −0.175926 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.4465 | + | 8.61270i | −0.836388 | + | 0.689568i | ||||
\(157\) | −0.174643 | − | 0.100830i | −0.0139381 | − | 0.00804714i | 0.493015 | − | 0.870021i | \(-0.335895\pi\) |
−0.506953 | + | 0.861974i | \(0.669228\pi\) | |||||||
\(158\) | −0.142651 | − | 0.0823593i | −0.0113487 | − | 0.00655216i | ||||
\(159\) | 0.327176 | + | 1.95424i | 0.0259468 | + | 0.154982i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.45043 | −0.665987 | ||||||||
\(162\) | 1.92705 | − | 4.77365i | 0.151403 | − | 0.375054i | ||||
\(163\) | − | 17.8168i | − | 1.39552i | −0.716331 | − | 0.697760i | \(-0.754180\pi\) | ||
0.716331 | − | 0.697760i | \(-0.245820\pi\) | |||||||
\(164\) | 1.23050 | + | 2.13129i | 0.0960858 | + | 0.166425i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.22522 | − | 2.12214i | 0.0950952 | − | 0.164710i | ||||
\(167\) | −12.2117 | − | 7.05042i | −0.944968 | − | 0.545578i | −0.0534538 | − | 0.998570i | \(-0.517023\pi\) |
−0.891514 | + | 0.452993i | \(0.850356\pi\) | |||||||
\(168\) | 3.30545 | + | 4.00924i | 0.255021 | + | 0.309319i | ||||
\(169\) | 4.41764 | + | 7.65158i | 0.339819 | + | 0.588583i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.2541 | + | 4.56592i | −1.01356 | + | 0.349165i | ||||
\(172\) | − | 0.788172i | − | 0.0600976i | ||||||
\(173\) | −3.78140 | + | 2.18319i | −0.287494 | + | 0.165985i | −0.636811 | − | 0.771020i | \(-0.719747\pi\) |
0.349317 | + | 0.937005i | \(0.386414\pi\) | |||||||
\(174\) | −8.80644 | − | 3.29186i | −0.667615 | − | 0.249555i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.86525 | + | 4.96276i | −0.215976 | + | 0.374082i | ||||
\(177\) | −0.693779 | + | 1.85601i | −0.0521476 | + | 0.139507i | ||||
\(178\) | 1.48608 | − | 0.857990i | 0.111387 | − | 0.0643091i | ||||
\(179\) | 15.1625 | 1.13330 | 0.566648 | − | 0.823960i | \(-0.308240\pi\) | ||||
0.566648 | + | 0.823960i | \(0.308240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.20166 | 0.237978 | 0.118989 | − | 0.992896i | \(-0.462035\pi\) | ||||
0.118989 | + | 0.992896i | \(0.462035\pi\) | |||||||
\(182\) | 3.30545 | − | 1.90841i | 0.245017 | − | 0.141460i | ||||
\(183\) | 2.78632 | + | 3.37957i | 0.205971 | + | 0.249825i | ||||
\(184\) | 6.21598 | − | 10.7664i | 0.458248 | − | 0.793709i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.13870 | + | 6.80155i | 0.0834938 | + | 0.498714i | ||||
\(187\) | 6.18687 | − | 3.57199i | 0.452429 | − | 0.261210i | ||||
\(188\) | 11.6376i | 0.848757i | ||||||||
\(189\) | 3.87562 | − | 6.32757i | 0.281910 | − | 0.460263i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41877 | + | 2.45738i | 0.102659 | + | 0.177810i | 0.912779 | − | 0.408453i | \(-0.133932\pi\) |
−0.810121 | + | 0.586263i | \(0.800598\pi\) | |||||||
\(192\) | 2.02121 | − | 0.338388i | 0.145869 | − | 0.0244211i | ||||
\(193\) | −16.2710 | − | 9.39409i | −1.17121 | − | 0.676201i | −0.217249 | − | 0.976116i | \(-0.569708\pi\) |
−0.953966 | + | 0.299915i | \(0.903042\pi\) | |||||||
\(194\) | 2.24086 | − | 3.88129i | 0.160885 | − | 0.278660i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.14927 | − | 7.18675i | −0.296376 | − | 0.513339i | ||||
\(197\) | 5.83528i | 0.415747i | 0.978156 | + | 0.207873i | \(0.0666542\pi\) | ||||
−0.978156 | + | 0.207873i | \(0.933346\pi\) | |||||||
\(198\) | −4.50237 | − | 0.874485i | −0.319970 | − | 0.0621469i | ||||
\(199\) | −13.0761 | −0.926943 | −0.463472 | − | 0.886112i | \(-0.653396\pi\) | ||||
−0.463472 | + | 0.886112i | \(0.653396\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6924 | + | 3.99684i | 0.754186 | + | 0.281915i | ||||
\(202\) | 2.08134 | + | 1.20166i | 0.146442 | + | 0.0845486i | ||||
\(203\) | −11.7357 | − | 6.77563i | −0.823687 | − | 0.475556i | ||||
\(204\) | −7.25405 | − | 2.71157i | −0.507885 | − | 0.189848i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.03920 | −0.0724047 | ||||||||
\(207\) | −17.4272 | − | 3.38485i | −1.21128 | − | 0.235263i | ||||
\(208\) | − | 10.0185i | − | 0.694656i | ||||||
\(209\) | 6.24482 | + | 10.8163i | 0.431963 | + | 0.748182i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.19243 | + | 7.26149i | −0.288618 | + | 0.499902i | −0.973480 | − | 0.228771i | \(-0.926529\pi\) |
0.684862 | + | 0.728673i | \(0.259863\pi\) | |||||||
\(212\) | −1.65730 | − | 0.956844i | −0.113824 | − | 0.0657163i | ||||
\(213\) | −21.9932 | + | 3.68206i | −1.50695 | + | 0.252291i | ||||
\(214\) | 3.40841 | + | 5.90353i | 0.232994 | + | 0.403557i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.21090 | + | 9.59222i | 0.354557 | + | 0.652668i | ||||
\(217\) | 9.94006i | 0.674776i | ||||||||
\(218\) | 8.24879 | − | 4.76244i | 0.558679 | − | 0.322553i | ||||
\(219\) | 0.489634 | + | 2.92461i | 0.0330864 | + | 0.197627i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.24482 | + | 10.8163i | −0.420072 | + | 0.727586i | ||||
\(222\) | −1.14501 | − | 1.38880i | −0.0768482 | − | 0.0932104i | ||||
\(223\) | −7.93834 | + | 4.58321i | −0.531591 | + | 0.306914i | −0.741664 | − | 0.670772i | \(-0.765963\pi\) |
0.210073 | + | 0.977686i | \(0.432630\pi\) | |||||||
\(224\) | −7.75123 | −0.517901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.5104 | 0.765658 | ||||||||
\(227\) | −2.31473 | + | 1.33641i | −0.153634 | + | 0.0887008i | −0.574846 | − | 0.818261i | \(-0.694938\pi\) |
0.421212 | + | 0.906962i | \(0.361605\pi\) | |||||||
\(228\) | 4.74056 | − | 12.6821i | 0.313951 | − | 0.839890i | ||||
\(229\) | 1.27365 | − | 2.20603i | 0.0841654 | − | 0.145779i | −0.820870 | − | 0.571115i | \(-0.806511\pi\) |
0.905035 | + | 0.425336i | \(0.139844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.19243 | − | 2.31473i | −0.407432 | − | 0.152298i | ||||
\(232\) | 17.2652 | − | 9.96806i | 1.13351 | − | 0.654435i | ||||
\(233\) | 6.22013i | 0.407494i | 0.979024 | + | 0.203747i | \(0.0653121\pi\) | ||||
−0.979024 | + | 0.203747i | \(0.934688\pi\) | |||||||
\(234\) | 7.58123 | − | 2.61168i | 0.495600 | − | 0.170731i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.956844 | − | 1.65730i | −0.0622852 | − | 0.107881i | ||||
\(237\) | −0.317294 | − | 0.384851i | −0.0206105 | − | 0.0249987i | ||||
\(238\) | 1.89070 | + | 1.09159i | 0.122556 | + | 0.0707576i | ||||
\(239\) | 4.06163 | − | 7.03494i | 0.262725 | − | 0.455053i | −0.704240 | − | 0.709962i | \(-0.748712\pi\) |
0.966965 | + | 0.254909i | \(0.0820455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1821 | + | 22.8320i | 0.849131 | + | 1.47074i | 0.881985 | + | 0.471278i | \(0.156207\pi\) |
−0.0328536 | + | 0.999460i | \(0.510460\pi\) | |||||||
\(242\) | − | 2.20561i | − | 0.141782i | ||||||
\(243\) | 10.5272 | − | 11.4969i | 0.675319 | − | 0.737526i | ||||
\(244\) | −4.23030 | −0.270817 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.240665 | − | 1.43751i | −0.0153442 | − | 0.0916520i | ||||
\(247\) | −18.9099 | − | 10.9176i | −1.20321 | − | 0.694673i | ||||
\(248\) | −12.6643 | − | 7.31173i | −0.804183 | − | 0.464295i | ||||
\(249\) | 5.72522 | − | 4.72021i | 0.362821 | − | 0.299131i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.549569 | −0.0346885 | −0.0173443 | − | 0.999850i | \(-0.505521\pi\) | ||||
−0.0173443 | + | 0.999850i | \(0.505521\pi\) | |||||||
\(252\) | 2.33415 | + | 6.77563i | 0.147038 | + | 0.426825i | ||||
\(253\) | 15.8168i | 0.994394i | ||||||||
\(254\) | 0.625515 | + | 1.08342i | 0.0392483 | + | 0.0679801i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.11515 | − | 3.66355i | 0.132197 | − | 0.228972i | ||||
\(257\) | 15.5885 | + | 9.00000i | 0.972381 | + | 0.561405i | 0.899961 | − | 0.435970i | \(-0.143595\pi\) |
0.0724199 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(258\) | −0.163441 | + | 0.437242i | −0.0101754 | + | 0.0272215i | ||||
\(259\) | −1.29721 | − | 2.24683i | −0.0806046 | − | 0.139611i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.4885 | − | 18.6741i | −1.33010 | − | 1.15590i | ||||
\(262\) | − | 3.43196i | − | 0.212027i | ||||||
\(263\) | −10.3016 | + | 5.94761i | −0.635221 | + | 0.366745i | −0.782771 | − | 0.622309i | \(-0.786195\pi\) |
0.147550 | + | 0.989055i | \(0.452861\pi\) | |||||||
\(264\) | 7.50415 | − | 6.18687i | 0.461849 | − | 0.380776i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.90841 | + | 3.30545i | −0.117012 | + | 0.202670i | ||||
\(267\) | 5.12483 | − | 0.857990i | 0.313634 | − | 0.0525081i | ||||
\(268\) | −9.54766 | + | 5.51234i | −0.583216 | + | 0.336720i | ||||
\(269\) | −28.5737 | −1.74217 | −0.871084 | − | 0.491134i | \(-0.836583\pi\) | ||||
−0.871084 | + | 0.491134i | \(0.836583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3641 | −1.41927 | −0.709635 | − | 0.704570i | \(-0.751140\pi\) | ||||
−0.709635 | + | 0.704570i | \(0.751140\pi\) | |||||||
\(272\) | 4.96276 | − | 2.86525i | 0.300911 | − | 0.173731i | ||||
\(273\) | 11.3990 | − | 1.90841i | 0.689900 | − | 0.115502i | ||||
\(274\) | −2.91764 | + | 5.05350i | −0.176261 | + | 0.305293i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.2294 | − | 10.9071i | 0.796314 | − | 0.656529i | ||||
\(277\) | −13.0563 | + | 7.53807i | −0.784479 | + | 0.452919i | −0.838015 | − | 0.545647i | \(-0.816284\pi\) |
0.0535366 | + | 0.998566i | \(0.482951\pi\) | |||||||
\(278\) | − | 4.57595i | − | 0.274447i | ||||||
\(279\) | −3.98153 | + | 20.4993i | −0.238368 | + | 1.22726i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.32605 | − | 5.76088i | −0.198415 | − | 0.343665i | 0.749599 | − | 0.661892i | \(-0.230246\pi\) |
−0.948015 | + | 0.318226i | \(0.896913\pi\) | |||||||
\(282\) | 2.41326 | − | 6.45600i | 0.143707 | − | 0.384449i | ||||
\(283\) | 23.2934 | + | 13.4485i | 1.38465 | + | 0.799428i | 0.992706 | − | 0.120562i | \(-0.0384696\pi\) |
0.391943 | + | 0.919989i | \(0.371803\pi\) | |||||||
\(284\) | 10.7684 | − | 18.6514i | 0.638985 | − | 1.10675i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.57199 | − | 6.18687i | −0.211216 | − | 0.365838i | ||||
\(287\) | − | 2.10083i | − | 0.124008i | ||||||
\(288\) | −15.9853 | − | 3.10478i | −0.941943 | − | 0.182951i | ||||
\(289\) | 9.85601 | 0.579765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4712 | − | 8.63306i | 0.613830 | − | 0.506079i | ||||
\(292\) | −2.48023 | − | 1.43196i | −0.145144 | − | 0.0837991i | ||||
\(293\) | 10.7256 | + | 6.19243i | 0.626596 | + | 0.361765i | 0.779433 | − | 0.626486i | \(-0.215507\pi\) |
−0.152837 | + | 0.988251i | \(0.548841\pi\) | |||||||
\(294\) | 0.811528 | + | 4.84730i | 0.0473292 | + | 0.282701i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.81681 | 0.221848 | ||||||||
\(297\) | −11.8434 | − | 7.25405i | −0.687224 | − | 0.420923i | ||||
\(298\) | 11.4834i | 0.665217i | ||||||||
\(299\) | −13.8260 | − | 23.9474i | −0.799581 | − | 1.38491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.336412 | + | 0.582682i | −0.0193905 | + | 0.0335853i | ||||
\(302\) | −1.50550 | − | 0.869202i | −0.0866319 | − | 0.0500169i | ||||
\(303\) | 4.62947 | + | 5.61515i | 0.265956 | + | 0.322582i | ||||
\(304\) | 5.00924 | + | 8.67625i | 0.287299 | + | 0.497617i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.46193 | + | 3.00851i | 0.197905 | + | 0.171985i | ||||
\(307\) | − | 2.49359i | − | 0.142317i | −0.997465 | − | 0.0711583i | \(-0.977330\pi\) | ||
0.997465 | − | 0.0711583i | \(-0.0226695\pi\) | |||||||
\(308\) | 5.52944 | − | 3.19243i | 0.315069 | − | 0.181905i | ||||
\(309\) | −2.94761 | − | 1.10182i | −0.167684 | − | 0.0626802i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1101 | − | 20.9752i | 0.686699 | − | 1.18940i | −0.286201 | − | 0.958170i | \(-0.592392\pi\) |
0.972900 | − | 0.231228i | \(-0.0742742\pi\) | |||||||
\(312\) | −5.95348 | + | 15.9269i | −0.337049 | + | 0.901682i | ||||
\(313\) | 30.3837 | − | 17.5420i | 1.71739 | − | 0.991534i | 0.793770 | − | 0.608219i | \(-0.208116\pi\) |
0.923618 | − | 0.383315i | \(-0.125218\pi\) | |||||||
\(314\) | −0.115349 | −0.00650950 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.481728 | 0.0270993 | ||||||||
\(317\) | −9.06829 | + | 5.23558i | −0.509326 | + | 0.294060i | −0.732557 | − | 0.680706i | \(-0.761673\pi\) |
0.223231 | + | 0.974766i | \(0.428340\pi\) | |||||||
\(318\) | 0.720978 | + | 0.874485i | 0.0404304 | + | 0.0490387i | ||||
\(319\) | −12.6821 | + | 21.9660i | −0.710059 | + | 1.22986i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.40841 | + | 20.3586i | 0.190239 | + | 1.13631i | ||||
\(322\) | −4.18601 | + | 2.41679i | −0.233277 | + | 0.134683i | ||||
\(323\) | − | 12.4896i | − | 0.694942i | ||||||
\(324\) | 2.09970 | + | 14.9083i | 0.116650 | + | 0.828238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.09555 | − | 8.82575i | −0.282216 | − | 0.488813i | ||||
\(327\) | 28.4464 | − | 4.76244i | 1.57309 | − | 0.263364i | ||||
\(328\) | 2.67659 | + | 1.54533i | 0.147790 | + | 0.0853267i | ||||
\(329\) | 4.96721 | − | 8.60346i | 0.273851 | − | 0.474324i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.38880 | − | 14.5298i | −0.461090 | − | 0.798632i | 0.537925 | − | 0.842993i | \(-0.319208\pi\) |
−0.999016 | + | 0.0443606i | \(0.985875\pi\) | |||||||
\(332\) | 7.16641i | 0.393308i | ||||||||
\(333\) | −1.77525 | − | 5.15322i | −0.0972829 | − | 0.282395i | ||||
\(334\) | −8.06558 | −0.441329 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.96721 | − | 1.85675i | −0.270984 | − | 0.101294i | ||||
\(337\) | 23.5394 | + | 13.5905i | 1.28227 | + | 0.740320i | 0.977263 | − | 0.212030i | \(-0.0680074\pi\) |
0.305008 | + | 0.952350i | \(0.401341\pi\) | |||||||
\(338\) | 4.37665 | + | 2.52686i | 0.238058 | + | 0.137443i | ||||
\(339\) | 32.6481 | + | 12.2039i | 1.77320 | + | 0.662825i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.6050 | 1.00752 | ||||||||
\(342\) | −5.25970 | + | 6.05239i | −0.284412 | + | 0.327276i | ||||
\(343\) | 17.0801i | 0.922239i | ||||||||
\(344\) | −0.494917 | − | 0.857221i | −0.0266841 | − | 0.0462182i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.24877 | + | 2.16293i | −0.0671343 | + | 0.116280i | ||||
\(347\) | 20.4086 | + | 11.7829i | 1.09559 | + | 0.632539i | 0.935059 | − | 0.354492i | \(-0.115346\pi\) |
0.160530 | + | 0.987031i | \(0.448680\pi\) | |||||||
\(348\) | 27.1180 | − | 4.54005i | 1.45368 | − | 0.243372i | ||||
\(349\) | −5.35601 | − | 9.27689i | −0.286701 | − | 0.496580i | 0.686319 | − | 0.727300i | \(-0.259225\pi\) |
−0.973020 | + | 0.230720i | \(0.925892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.2725 | + | 0.630233i | 1.29557 | + | 0.0336393i | ||||
\(352\) | 14.5081i | 0.773285i | ||||||||
\(353\) | −23.6141 | + | 13.6336i | −1.25685 | + | 0.725644i | −0.972461 | − | 0.233064i | \(-0.925125\pi\) |
−0.284392 | + | 0.958708i | \(0.591792\pi\) | |||||||
\(354\) | 0.187143 | + | 1.11781i | 0.00994652 | + | 0.0594112i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.50924 | + | 4.34612i | −0.132989 | + | 0.230344i | ||||
\(357\) | 4.20543 | + | 5.10083i | 0.222575 | + | 0.269965i | ||||
\(358\) | 7.51089 | − | 4.33641i | 0.396963 | − | 0.229186i | ||||
\(359\) | 10.6807 | 0.563707 | 0.281854 | − | 0.959457i | \(-0.409051\pi\) | ||||
0.281854 | + | 0.959457i | \(0.409051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.83528 | 0.149225 | ||||||||
\(362\) | 1.58598 | − | 0.915664i | 0.0833571 | − | 0.0481262i | ||||
\(363\) | 2.33851 | − | 6.25603i | 0.122740 | − | 0.328356i | ||||
\(364\) | −5.58123 | + | 9.66697i | −0.292536 | + | 0.506687i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.34678 | + | 0.877227i | 0.122668 | + | 0.0458534i | ||||
\(367\) | −7.33624 | + | 4.23558i | −0.382949 | + | 0.221096i | −0.679100 | − | 0.734045i | \(-0.737630\pi\) |
0.296152 | + | 0.955141i | \(0.404297\pi\) | |||||||
\(368\) | 12.6873i | 0.661373i | ||||||||
\(369\) | 0.841495 | − | 4.33252i | 0.0438065 | − | 0.225542i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.816810 | + | 1.41476i | 0.0424067 | + | 0.0734505i | ||||
\(372\) | −12.8298 | − | 15.5614i | −0.665193 | − | 0.806822i | ||||
\(373\) | 8.76700 | + | 5.06163i | 0.453938 | + | 0.262081i | 0.709492 | − | 0.704714i | \(-0.248925\pi\) |
−0.255554 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(374\) | 2.04316 | − | 3.53885i | 0.105649 | − | 0.182990i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.30757 | + | 12.6571i | 0.376859 | + | 0.652740i | ||||
\(377\) | − | 44.3434i | − | 2.28380i | ||||||
\(378\) | 0.110165 | − | 4.24284i | 0.00566626 | − | 0.218228i | ||||
\(379\) | −11.9216 | −0.612371 | −0.306186 | − | 0.951972i | \(-0.599053\pi\) | ||||
−0.306186 | + | 0.951972i | \(0.599053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.625515 | + | 3.73624i | 0.0320461 | + | 0.191414i | ||||
\(382\) | 1.40561 | + | 0.811528i | 0.0719171 | + | 0.0415214i | ||||
\(383\) | 8.50161 | + | 4.90841i | 0.434412 | + | 0.250808i | 0.701224 | − | 0.712941i | \(-0.252637\pi\) |
−0.266813 | + | 0.963748i | \(0.585970\pi\) | |||||||
\(384\) | 15.4126 | − | 12.7070i | 0.786519 | − | 0.648453i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.7467 | −0.546993 | ||||||||
\(387\) | −0.927175 | + | 1.06691i | −0.0471309 | + | 0.0542341i | ||||
\(388\) | 13.1070i | 0.665409i | ||||||||
\(389\) | 4.61007 | + | 7.98487i | 0.233740 | + | 0.404849i | 0.958906 | − | 0.283725i | \(-0.0915703\pi\) |
−0.725166 | + | 0.688574i | \(0.758237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.90841 | − | 13.6978i | 0.399945 | − | 0.692725i | ||||
\(392\) | −9.02554 | − | 5.21090i | −0.455858 | − | 0.263190i | ||||
\(393\) | 3.63875 | − | 9.73445i | 0.183550 | − | 0.491038i | ||||
\(394\) | 1.66887 | + | 2.89057i | 0.0840765 | + | 0.145625i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.6821 | − | 4.36887i | 0.637297 | − | 0.219544i | ||||
\(397\) | − | 22.9793i | − | 1.15330i | −0.816993 | − | 0.576648i | \(-0.804360\pi\) | ||
0.816993 | − | 0.576648i | \(-0.195640\pi\) | |||||||
\(398\) | −6.47741 | + | 3.73973i | −0.324683 | + | 0.187456i | ||||
\(399\) | −8.91764 | + | 7.35224i | −0.446440 | + | 0.368072i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.53279 | − | 9.58307i | 0.276294 | − | 0.478556i | −0.694167 | − | 0.719814i | \(-0.744227\pi\) |
0.970461 | + | 0.241259i | \(0.0775602\pi\) | |||||||
\(402\) | 6.43969 | − | 1.07812i | 0.321183 | − | 0.0537718i | ||||
\(403\) | −28.1688 | + | 16.2633i | −1.40319 | + | 0.810132i | ||||
\(404\) | −7.02864 | −0.349688 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.75123 | −0.384687 | ||||||||
\(407\) | −4.20543 | + | 2.42801i | −0.208455 | + | 0.120352i | ||||
\(408\) | −9.59222 | + | 1.60591i | −0.474886 | + | 0.0795046i | ||||
\(409\) | −8.81681 | + | 15.2712i | −0.435963 | + | 0.755110i | −0.997374 | − | 0.0724270i | \(-0.976926\pi\) |
0.561411 | + | 0.827537i | \(0.310259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.6336 | + | 11.2404i | −0.672497 | + | 0.554447i | ||||
\(412\) | 2.63203 | − | 1.51960i | 0.129671 | − | 0.0748654i | ||||
\(413\) | 1.63362i | 0.0803852i | ||||||||
\(414\) | −9.60083 | + | 3.30741i | −0.471855 | + | 0.162550i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.6821 | − | 21.9660i | −0.621789 | − | 1.07697i | ||||
\(417\) | 4.85166 | − | 12.9793i | 0.237587 | − | 0.635597i | ||||
\(418\) | 6.18687 | + | 3.57199i | 0.302610 | + | 0.174712i | ||||
\(419\) | 18.5173 | − | 32.0730i | 0.904631 | − | 1.56687i | 0.0832199 | − | 0.996531i | \(-0.473480\pi\) |
0.821411 | − | 0.570336i | \(-0.193187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.52884 | − | 4.38007i | −0.123248 | − | 0.213472i | 0.797799 | − | 0.602924i | \(-0.205998\pi\) |
−0.921047 | + | 0.389452i | \(0.872664\pi\) | |||||||
\(422\) | 4.79608i | 0.233469i | ||||||||
\(423\) | 13.6900 | − | 15.7532i | 0.665630 | − | 0.765947i | ||||
\(424\) | −2.40332 | −0.116716 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.84150 | + | 8.11392i | −0.476822 | + | 0.393121i | ||||
\(427\) | 3.12739 | + | 1.80560i | 0.151345 | + | 0.0873790i | ||||
\(428\) | −17.2652 | − | 9.96806i | −0.834544 | − | 0.481824i | ||||
\(429\) | −3.57199 | − | 21.3357i | −0.172457 | − | 1.03010i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.23030 | −0.251935 | −0.125967 | − | 0.992034i | \(-0.540203\pi\) | ||||
−0.125967 | + | 0.992034i | \(0.540203\pi\) | |||||||
\(432\) | −9.50011 | − | 5.81879i | −0.457074 | − | 0.279957i | ||||
\(433\) | − | 34.3434i | − | 1.65044i | −0.564813 | − | 0.825219i | \(-0.691052\pi\) | ||
0.564813 | − | 0.825219i | \(-0.308948\pi\) | |||||||
\(434\) | 2.84283 | + | 4.92392i | 0.136460 | + | 0.236356i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.9280 | + | 24.1240i | −0.667031 | + | 1.15533i | ||||
\(437\) | 23.9474 | + | 13.8260i | 1.14556 | + | 0.661389i | ||||
\(438\) | 1.07898 | + | 1.30871i | 0.0515554 | + | 0.0625324i | ||||
\(439\) | −9.77365 | − | 16.9285i | −0.466471 | − | 0.807952i | 0.532796 | − | 0.846244i | \(-0.321141\pi\) |
−0.999267 | + | 0.0382924i | \(0.987808\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.83754 | + | 14.6094i | −0.135121 | + | 0.695685i | ||||
\(442\) | 7.14399i | 0.339805i | ||||||||
\(443\) | −9.09686 | + | 5.25208i | −0.432205 | + | 0.249534i | −0.700286 | − | 0.713863i | \(-0.746944\pi\) |
0.268081 | + | 0.963396i | \(0.413611\pi\) | |||||||
\(444\) | 4.93083 | + | 1.84315i | 0.234007 | + | 0.0874719i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.62156 | + | 4.54068i | −0.124135 | + | 0.215007i | ||||
\(447\) | −12.1753 | + | 32.5717i | −0.575873 | + | 1.54059i | ||||
\(448\) | 1.46324 | − | 0.844801i | 0.0691315 | − | 0.0399131i | ||||
\(449\) | −22.8560 | −1.07864 | −0.539321 | − | 0.842100i | \(-0.681319\pi\) | ||||
−0.539321 | + | 0.842100i | \(0.681319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.93216 | −0.185158 | ||||||||
\(452\) | −29.1527 | + | 16.8313i | −1.37123 | + | 0.791679i | ||||
\(453\) | −3.34865 | − | 4.06163i | −0.157333 | − | 0.190832i | ||||
\(454\) | −0.764419 | + | 1.32401i | −0.0358759 | + | 0.0621390i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.80757 | − | 16.7698i | −0.131477 | − | 0.785319i | ||||
\(457\) | −12.1472 | + | 7.01319i | −0.568222 | + | 0.328063i | −0.756439 | − | 0.654064i | \(-0.773063\pi\) |
0.188217 | + | 0.982127i | \(0.439729\pi\) | |||||||
\(458\) | − | 1.45704i | − | 0.0680832i | ||||||
\(459\) | 6.62967 | + | 12.2039i | 0.309446 | + | 0.569629i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0513 | + | 20.8734i | 0.561283 | + | 0.972171i | 0.997385 | + | 0.0722736i | \(0.0230255\pi\) |
−0.436102 | + | 0.899897i | \(0.643641\pi\) | |||||||
\(462\) | −3.72949 | + | 0.624385i | −0.173512 | + | 0.0290490i | ||||
\(463\) | −29.3930 | − | 16.9700i | −1.36601 | − | 0.788664i | −0.375591 | − | 0.926785i | \(-0.622560\pi\) |
−0.990415 | + | 0.138121i | \(0.955894\pi\) | |||||||
\(464\) | −10.1728 | + | 17.6198i | −0.472261 | + | 0.817981i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.77894 | + | 3.08121i | 0.0824077 | + | 0.142734i | ||||
\(467\) | − | 27.3720i | − | 1.26663i | −0.773896 | − | 0.633313i | \(-0.781695\pi\) | ||
0.773896 | − | 0.633313i | \(-0.218305\pi\) | |||||||
\(468\) | −15.3823 | + | 17.7005i | −0.711045 | + | 0.818207i | ||||
\(469\) | 9.41123 | 0.434570 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.327176 | − | 0.122299i | −0.0150755 | − | 0.00563523i | ||||
\(472\) | −2.08134 | − | 1.20166i | −0.0958013 | − | 0.0553109i | ||||
\(473\) | 1.09062 | + | 0.629668i | 0.0501466 | + | 0.0289521i | ||||
\(474\) | −0.267241 | − | 0.0998949i | −0.0122748 | − | 0.00458832i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.38485 | −0.292649 | ||||||||
\(477\) | 1.11781 | + | 3.24482i | 0.0511812 | + | 0.148570i | ||||
\(478\) | − | 4.64645i | − | 0.212524i | ||||||
\(479\) | 2.61515 | + | 4.52957i | 0.119489 | + | 0.206961i | 0.919565 | − | 0.392937i | \(-0.128541\pi\) |
−0.800076 | + | 0.599898i | \(0.795208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.24482 | − | 7.35224i | 0.193547 | − | 0.335233i | ||||
\(482\) | 13.0597 | + | 7.54005i | 0.594855 | + | 0.343440i | ||||
\(483\) | −14.4357 | + | 2.41679i | −0.656846 | + | 0.109968i | ||||
\(484\) | 3.22522 | + | 5.58624i | 0.146601 | + | 0.253920i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.92668 | − | 8.70585i | 0.0873958 | − | 0.394905i | ||||
\(487\) | − | 24.0185i | − | 1.08838i | −0.838962 | − | 0.544190i | \(-0.816837\pi\) | ||
0.838962 | − | 0.544190i | \(-0.183163\pi\) | |||||||
\(488\) | −4.60090 | + | 2.65633i | −0.208273 | + | 0.120246i | ||||
\(489\) | −5.09555 | − | 30.4360i | −0.230429 | − | 1.37636i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.38880 | + | 12.7978i | −0.333452 | + | 0.577556i | −0.983186 | − | 0.182606i | \(-0.941547\pi\) |
0.649734 | + | 0.760161i | \(0.274880\pi\) | |||||||
\(492\) | 2.71157 | + | 3.28890i | 0.122247 | + | 0.148275i | ||||
\(493\) | 21.9660 | − | 12.6821i | 0.989298 | − | 0.571171i | ||||
\(494\) | −12.4896 | −0.561935 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.9239 | 0.670101 | ||||||||
\(497\) | −15.9217 | + | 9.19243i | −0.714188 | + | 0.412337i | ||||
\(498\) | 1.48608 | − | 3.97560i | 0.0665929 | − | 0.178151i | ||||
\(499\) | 12.4280 | − | 21.5259i | 0.556354 | − | 0.963633i | −0.441443 | − | 0.897289i | \(-0.645533\pi\) |
0.997797 | − | 0.0663440i | \(-0.0211335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.8773 | − | 8.55155i | −1.02208 | − | 0.382055i | ||||
\(502\) | −0.272235 | + | 0.157175i | −0.0121504 | + | 0.00701506i | ||||
\(503\) | − | 38.9154i | − | 1.73515i | −0.497305 | − | 0.867576i | \(-0.665677\pi\) | ||
0.497305 | − | 0.867576i | \(-0.334323\pi\) | |||||||
\(504\) | 6.79326 | + | 5.90353i | 0.302596 | + | 0.262964i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.52355 | + | 7.83503i | 0.201097 | + | 0.348309i | ||||
\(507\) | 9.73487 | + | 11.8076i | 0.432341 | + | 0.524393i | ||||
\(508\) | −3.16853 | − | 1.82935i | −0.140581 | − | 0.0811644i | ||||
\(509\) | 1.01037 | − | 1.75001i | 0.0447837 | − | 0.0775676i | −0.842765 | − | 0.538282i | \(-0.819073\pi\) |
0.887548 | + | 0.460715i | \(0.152407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.22239 | + | 2.11725i | 0.0540755 | + | 0.0936615i | ||||
\(512\) | 20.6459i | 0.912428i | ||||||||
\(513\) | −21.3357 | + | 11.5905i | −0.941996 | + | 0.511732i | ||||
\(514\) | 10.2959 | 0.454132 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.225415 | − | 1.34642i | −0.00992333 | − | 0.0592726i | ||||
\(517\) | −16.1032 | − | 9.29721i | −0.708220 | − | 0.408891i | ||||
\(518\) | −1.28517 | − | 0.741995i | −0.0564672 | − | 0.0326014i | ||||
\(519\) | −5.83528 | + | 4.81096i | −0.256140 | + | 0.211178i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0290 | −1.00892 | −0.504460 | − | 0.863435i | \(-0.668308\pi\) | ||||
−0.504460 | + | 0.863435i | \(0.668308\pi\) | |||||||
\(522\) | −15.9853 | − | 3.10478i | −0.699657 | − | 0.135893i | ||||
\(523\) | 41.1170i | 1.79792i | 0.438028 | + | 0.898961i | \(0.355677\pi\) | ||||
−0.438028 | + | 0.898961i | \(0.644323\pi\) | |||||||
\(524\) | 5.01847 | + | 8.69225i | 0.219233 | + | 0.379723i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.40199 | + | 5.89242i | −0.148334 | + | 0.256922i | ||||
\(527\) | −16.1124 | − | 9.30249i | −0.701867 | − | 0.405223i | ||||
\(528\) | −3.47530 | + | 9.29721i | −0.151243 | + | 0.404609i | ||||
\(529\) | 6.00924 | + | 10.4083i | 0.261271 | + | 0.452535i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.654353 | + | 3.36900i | −0.0283965 | + | 0.146202i | ||||
\(532\) | − | 11.1625i | − | 0.483954i | ||||||
\(533\) | 5.95348 | − | 3.43724i | 0.257874 | − | 0.148883i | ||||
\(534\) | 2.29326 | − | 1.89070i | 0.0992389 | − | 0.0818185i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.92272 | + | 11.9905i | −0.299016 | + | 0.517911i | ||||
\(537\) | 25.9017 | − | 4.33641i | 1.11774 | − | 0.187130i | ||||
\(538\) | −14.1543 | + | 8.17198i | −0.610234 | + | 0.352319i | ||||
\(539\) | 13.2593 | 0.571120 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.20957 | 0.223977 | 0.111988 | − | 0.993710i | \(-0.464278\pi\) | ||||
0.111988 | + | 0.993710i | \(0.464278\pi\) | |||||||
\(542\) | −11.5737 | + | 6.68206i | −0.497132 | + | 0.287019i | ||||
\(543\) | 5.46932 | − | 0.915664i | 0.234711 | − | 0.0392949i | ||||
\(544\) | 7.25405 | − | 12.5644i | 0.311015 | − | 0.538694i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.10083 | − | 4.20543i | 0.218295 | − | 0.179976i | ||||
\(547\) | 34.6764 | − | 20.0204i | 1.48266 | − | 0.856013i | 0.482851 | − | 0.875702i | \(-0.339601\pi\) |
0.999806 | + | 0.0196900i | \(0.00626792\pi\) | |||||||
\(548\) | − | 17.0656i | − | 0.729005i | ||||||
\(549\) | 5.72635 | + | 4.97636i | 0.244394 | + | 0.212386i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.1717 | + | 38.4025i | 0.944546 | + | 1.63600i | ||||
\(552\) | 7.53946 | − | 20.1697i | 0.320901 | − | 0.858480i | ||||
\(553\) | −0.356133 | − | 0.205614i | −0.0151443 | − | 0.00874359i | ||||
\(554\) | −4.31173 | + | 7.46813i | −0.183188 | + | 0.317290i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.69129 | + | 11.5897i | 0.283774 | + | 0.491511i | ||||
\(557\) | − | 14.4033i | − | 0.610288i | −0.952306 | − | 0.305144i | \(-0.901295\pi\) | ||
0.952306 | − | 0.305144i | \(-0.0987047\pi\) | |||||||
\(558\) | 3.89044 | + | 11.2933i | 0.164695 | + | 0.478082i | ||||
\(559\) | −2.20166 | −0.0931203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.54731 | − | 7.87137i | 0.403088 | − | 0.332330i | ||||
\(562\) | −3.29518 | − | 1.90248i | −0.138999 | − | 0.0802511i | ||||
\(563\) | 25.4335 | + | 14.6840i | 1.07189 | + | 0.618858i | 0.928698 | − | 0.370836i | \(-0.120929\pi\) |
0.143196 | + | 0.989694i | \(0.454262\pi\) | |||||||
\(564\) | 3.32831 | + | 19.8802i | 0.140147 | + | 0.837107i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.3849 | 0.646674 | ||||||||
\(567\) | 4.81096 | − | 11.9176i | 0.202041 | − | 0.500494i | ||||
\(568\) | − | 27.0471i | − | 1.13487i | ||||||
\(569\) | 23.4033 | + | 40.5357i | 0.981118 | + | 1.69935i | 0.658056 | + | 0.752969i | \(0.271379\pi\) |
0.323062 | + | 0.946378i | \(0.395288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 18.0938 | + | 10.4465i | 0.756541 | + | 0.436789i | ||||
\(573\) | 3.12646 | + | 3.79213i | 0.130610 | + | 0.158418i | ||||
\(574\) | −0.600830 | − | 1.04067i | −0.0250782 | − | 0.0434367i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.35601 | − | 1.15612i | 0.139834 | − | 0.0481717i | ||||
\(577\) | 28.2386i | 1.17559i | 0.809010 | + | 0.587794i | \(0.200004\pi\) | ||||
−0.809010 | + | 0.587794i | \(0.799996\pi\) | |||||||
\(578\) | 4.88228 | − | 2.81879i | 0.203076 | − | 0.117246i | ||||
\(579\) | −30.4821 | − | 11.3942i | −1.26679 | − | 0.473528i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.05880 | − | 5.29801i | 0.126901 | − | 0.219798i | ||||
\(582\) | 2.71798 | − | 7.27119i | 0.112664 | − | 0.301401i | ||||
\(583\) | 2.64802 | − | 1.52884i | 0.109670 | − | 0.0633180i | ||||
\(584\) | −3.59668 | −0.148832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.08405 | 0.292639 | ||||||||
\(587\) | 15.6598 | − | 9.04118i | 0.646348 | − | 0.373169i | −0.140707 | − | 0.990051i | \(-0.544938\pi\) |
0.787056 | + | 0.616882i | \(0.211604\pi\) | |||||||
\(588\) | −9.14348 | − | 11.0903i | −0.377071 | − | 0.457355i | ||||
\(589\) | 16.2633 | − | 28.1688i | 0.670117 | − | 1.16068i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.66887 | + | 9.96827i | 0.0686482 | + | 0.410040i | ||||
\(592\) | −3.37336 | + | 1.94761i | −0.138644 | + | 0.0800462i | ||||
\(593\) | 7.73840i | 0.317778i | 0.987296 | + | 0.158889i | \(0.0507912\pi\) | ||||
−0.987296 | + | 0.158889i | \(0.949209\pi\) | |||||||
\(594\) | −7.94139 | − | 0.206197i | −0.325839 | − | 0.00846037i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.7919 | − | 29.0845i | −0.687824 | − | 1.19135i | ||||
\(597\) | −22.3377 | + | 3.73973i | −0.914220 | + | 0.153057i | ||||
\(598\) | −13.6978 | − | 7.90841i | −0.560143 | − | 0.323399i | ||||
\(599\) | −13.9608 | + | 24.1808i | −0.570423 | + | 0.988001i | 0.426100 | + | 0.904676i | \(0.359887\pi\) |
−0.996522 | + | 0.0833249i | \(0.973446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2201 | − | 33.2902i | −0.784006 | − | 1.35794i | −0.929591 | − | 0.368592i | \(-0.879840\pi\) |
0.145586 | − | 0.989346i | \(-0.453493\pi\) | |||||||
\(602\) | 0.384851i | 0.0156853i | ||||||||
\(603\) | 19.4087 | + | 3.76970i | 0.790383 | + | 0.153514i | ||||
\(604\) | 5.08405 | 0.206867 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.89917 | + | 1.45751i | 0.158393 | + | 0.0592074i | ||||
\(607\) | 0.554113 | + | 0.319917i | 0.0224907 | + | 0.0129850i | 0.511203 | − | 0.859460i | \(-0.329200\pi\) |
−0.488712 | + | 0.872445i | \(0.662533\pi\) | |||||||
\(608\) | 21.9660 | + | 12.6821i | 0.890838 | + | 0.514325i | ||||
\(609\) | −21.9857 | − | 8.21826i | −0.890905 | − | 0.333021i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.5081 | 1.31514 | ||||||||
\(612\) | −13.1674 | − | 2.55748i | −0.532261 | − | 0.103380i | ||||
\(613\) | − | 42.7467i | − | 1.72652i | −0.504757 | − | 0.863262i | \(-0.668418\pi\) | ||
0.504757 | − | 0.863262i | \(-0.331582\pi\) | |||||||
\(614\) | −0.713157 | − | 1.23522i | −0.0287807 | − | 0.0498496i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00924 | − | 6.94420i | 0.161537 | − | 0.279790i | ||||
\(617\) | −18.2753 | − | 10.5513i | −0.735737 | − | 0.424778i | 0.0847805 | − | 0.996400i | \(-0.472981\pi\) |
−0.820517 | + | 0.571622i | \(0.806314\pi\) | |||||||
\(618\) | −1.77525 | + | 0.297209i | −0.0714109 | + | 0.0119555i | ||||
\(619\) | −6.82605 | − | 11.8231i | −0.274362 | − | 0.475209i | 0.695612 | − | 0.718418i | \(-0.255133\pi\) |
−0.969974 | + | 0.243209i | \(0.921800\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.7386 | − | 0.798123i | −1.23350 | − | 0.0320276i | ||||
\(622\) | − | 13.8538i | − | 0.555485i | ||||||
\(623\) | 3.71007 | − | 2.14201i | 0.148641 | − | 0.0858178i | ||||
\(624\) | −2.86525 | − | 17.1143i | −0.114702 | − | 0.685121i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.0339 | − | 17.3793i | 0.401036 | − | 0.694615i | ||||
\(627\) | 13.7613 | + | 16.6913i | 0.549574 | + | 0.666586i | ||||
\(628\) | 0.292148 | − | 0.168672i | 0.0116580 | − | 0.00673073i | ||||
\(629\) | 4.85601 | 0.193622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2593 | 1.32403 | 0.662017 | − | 0.749489i | \(-0.269701\pi\) | ||||
0.662017 | + | 0.749489i | \(0.269701\pi\) | |||||||
\(632\) | 0.523930 | − | 0.302491i | 0.0208408 | − | 0.0120325i | ||||
\(633\) | −5.08506 | + | 13.6037i | −0.202113 | + | 0.540697i | ||||
\(634\) | −2.99472 | + | 5.18700i | −0.118935 | + | 0.206002i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.10478 | − | 1.16057i | −0.123113 | − | 0.0460196i | ||||
\(637\) | −20.0753 | + | 11.5905i | −0.795411 | + | 0.459231i | ||||
\(638\) | 14.5081i | 0.574381i | ||||||||
\(639\) | −36.5173 | + | 12.5799i | −1.44460 | + | 0.497655i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.1429 | − | 22.7641i | −0.519112 | − | 0.899128i | −0.999753 | − | 0.0222106i | \(-0.992930\pi\) |
0.480642 | − | 0.876917i | \(-0.340404\pi\) | |||||||
\(642\) | 7.51089 | + | 9.11007i | 0.296431 | + | 0.359546i | ||||
\(643\) | 17.8250 | + | 10.2913i | 0.702950 | + | 0.405848i | 0.808445 | − | 0.588571i | \(-0.200309\pi\) |
−0.105495 | + | 0.994420i | \(0.533643\pi\) | |||||||
\(644\) | 7.06804 | − | 12.2422i | 0.278520 | − | 0.482410i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.57199 | − | 6.18687i | −0.140538 | − | 0.243419i | ||||
\(647\) | 23.2527i | 0.914159i | 0.889426 | + | 0.457079i | \(0.151104\pi\) | ||||
−0.889426 | + | 0.457079i | \(0.848896\pi\) | |||||||
\(648\) | 11.6450 | + | 14.8959i | 0.457458 | + | 0.585165i | ||||
\(649\) | 3.05767 | 0.120024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.84283 | + | 16.9804i | 0.111419 | + | 0.665513i | ||||
\(652\) | 25.8114 | + | 14.9022i | 1.01085 | + | 0.583615i | ||||
\(653\) | 16.2459 | + | 9.37957i | 0.635751 | + | 0.367051i | 0.782976 | − | 0.622052i | \(-0.213701\pi\) |
−0.147225 | + | 0.989103i | \(0.547034\pi\) | |||||||
\(654\) | 12.7292 | − | 10.4947i | 0.497750 | − | 0.410375i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.15415 | −0.123149 | ||||||||
\(657\) | 1.67286 | + | 4.85601i | 0.0652645 | + | 0.189451i | ||||
\(658\) | − | 5.68242i | − | 0.221524i | ||||||
\(659\) | −0.140034 | − | 0.242545i | −0.00545494 | − | 0.00944823i | 0.863285 | − | 0.504717i | \(-0.168403\pi\) |
−0.868740 | + | 0.495268i | \(0.835070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8930 | − | 34.4556i | 0.773746 | − | 1.34017i | −0.161750 | − | 0.986832i | \(-0.551714\pi\) |
0.935496 | − | 0.353336i | \(-0.114953\pi\) | |||||||
\(662\) | −8.31097 | − | 4.79834i | −0.323015 | − | 0.186493i | ||||
\(663\) | −7.57443 | + | 20.2633i | −0.294167 | + | 0.786961i | ||||
\(664\) | 4.50000 | + | 7.79423i | 0.174634 | + | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.35319 | − | 2.04499i | −0.0911843 | − | 0.0792417i | ||||
\(667\) | 56.1562i | 2.17438i | ||||||||
\(668\) | 20.4280 | − | 11.7941i | 0.790382 | − | 0.456327i | ||||
\(669\) | −12.2501 | + | 10.0997i | −0.473616 | + | 0.390478i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.37957 | − | 5.85358i | 0.130467 | − | 0.225975i | ||||
\(672\) | −13.2412 | + | 2.21683i | −0.510792 | + | 0.0855159i | ||||
\(673\) | −29.0368 | + | 16.7644i | −1.11929 | + | 0.646221i | −0.941219 | − | 0.337797i | \(-0.890318\pi\) |
−0.178068 | + | 0.984018i | \(0.556985\pi\) | |||||||
\(674\) | 15.5473 | 0.598860 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.7799 | −0.568456 | ||||||||
\(677\) | 23.8048 | − | 13.7437i | 0.914891 | − | 0.528213i | 0.0328897 | − | 0.999459i | \(-0.489529\pi\) |
0.882002 | + | 0.471246i | \(0.156196\pi\) | |||||||
\(678\) | 19.6629 | − | 3.29193i | 0.755148 | − | 0.126426i | ||||
\(679\) | 5.59442 | − | 9.68981i | 0.214694 | − | 0.371861i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.57199 | + | 2.94497i | −0.136879 | + | 0.112851i | ||||
\(682\) | 9.21618 | − | 5.32096i | 0.352906 | − | 0.203750i | ||||
\(683\) | 34.5865i | 1.32342i | 0.749762 | + | 0.661708i | \(0.230168\pi\) | ||||
−0.749762 | + | 0.661708i | \(0.769832\pi\) | |||||||
\(684\) | 4.47116 | − | 23.0202i | 0.170959 | − | 0.880201i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.88485 | + | 8.46081i | 0.186504 | + | 0.323035i | ||||
\(687\) | 1.54483 | − | 4.13277i | 0.0589391 | − | 0.157675i | ||||
\(688\) | 0.874830 | + | 0.505083i | 0.0333526 | + | 0.0192561i | ||||
\(689\) | −2.67282 | + | 4.62947i | −0.101826 | + | 0.176369i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.3641 | − | 35.2717i | −0.774688 | − | 1.34180i | −0.934970 | − | 0.354727i | \(-0.884574\pi\) |
0.160282 | − | 0.987071i | \(-0.448760\pi\) | |||||||
\(692\) | − | 7.30418i | − | 0.277663i | ||||||
\(693\) | −11.2404 | − | 2.18319i | −0.426987 | − | 0.0829325i | ||||
\(694\) | 13.4795 | 0.511674 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 26.6429 | − | 21.9660i | 1.00989 | − | 0.832618i | ||||
\(697\) | 3.40535 | + | 1.96608i | 0.128987 | + | 0.0744706i | ||||
\(698\) | −5.30632 | − | 3.06360i | −0.200847 | − | 0.115959i | ||||
\(699\) | 1.77894 | + | 10.6257i | 0.0672856 | + | 0.401901i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.4712 | −0.735416 | −0.367708 | − | 0.929941i | \(-0.619857\pi\) | ||||
−0.367708 | + | 0.929941i | \(0.619857\pi\) | |||||||
\(702\) | 12.2039 | − | 6.62967i | 0.460606 | − | 0.250221i | ||||
\(703\) | 8.48963i | 0.320193i | ||||||||
\(704\) | −1.58123 | − | 2.73877i | −0.0595948 | − | 0.103221i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.79834 | + | 13.5071i | −0.293494 | + | 0.508347i | ||||
\(707\) | 5.19615 | + | 3.00000i | 0.195421 | + | 0.112827i | ||||
\(708\) | −2.10854 | − | 2.55748i | −0.0792436 | − | 0.0961158i | ||||
\(709\) | 7.54316 | + | 13.0651i | 0.283289 | + | 0.490671i | 0.972193 | − | 0.234182i | \(-0.0752410\pi\) |
−0.688904 | + | 0.724853i | \(0.741908\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.652092 | − | 0.566686i | −0.0244553 | − | 0.0212524i | ||||
\(712\) | 6.30249i | 0.236196i | ||||||||
\(713\) | 35.6729 | − | 20.5957i | 1.33596 | − | 0.771317i | ||||
\(714\) | 3.54203 | + | 1.32401i | 0.132557 | + | 0.0495499i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.6821 | + | 21.9660i | −0.473951 | + | 0.820907i | ||||
\(717\) | 4.92641 | − | 13.1792i | 0.183980 | − | 0.492188i | ||||
\(718\) | 5.29081 | − | 3.05465i | 0.197451 | − | 0.113999i | ||||
\(719\) | 3.43196 | 0.127990 | 0.0639952 | − | 0.997950i | \(-0.479616\pi\) | ||||
0.0639952 | + | 0.997950i | \(0.479616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.59442 | −0.0966211 | ||||||||
\(722\) | 1.40449 | − | 0.810881i | 0.0522696 | − | 0.0301779i | ||||
\(723\) | 29.0485 | + | 35.2333i | 1.08032 | + | 1.31034i | ||||
\(724\) | −2.67791 | + | 4.63827i | −0.0995236 | + | 0.172380i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.630798 | − | 3.76780i | −0.0234111 | − | 0.139836i | ||||
\(727\) | −30.9789 | + | 17.8857i | −1.14895 | + | 0.663344i | −0.948630 | − | 0.316388i | \(-0.897530\pi\) |
−0.200315 | + | 0.979732i | \(0.564197\pi\) | |||||||
\(728\) | 14.0185i | 0.519559i | ||||||||
\(729\) | 14.6952 | − | 22.6506i | 0.544268 | − | 0.838911i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.629668 | − | 1.09062i | −0.0232891 | − | 0.0403379i | ||||
\(732\) | −7.22652 | + | 1.20985i | −0.267100 | + | 0.0447174i | ||||
\(733\) | −19.0526 | − | 11.0000i | −0.703722 | − | 0.406294i | 0.105010 | − | 0.994471i | \(-0.466513\pi\) |
−0.808732 | + | 0.588177i | \(0.799846\pi\) | |||||||
\(734\) | −2.42272 | + | 4.19628i | −0.0894244 | + | 0.154888i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0605 | + | 27.8176i | 0.591998 | + | 1.02537i | ||||
\(737\) | − | 17.6151i | − | 0.648862i | ||||||
\(738\) | −0.822244 | − | 2.38683i | −0.0302672 | − | 0.0878603i | ||||
\(739\) | −6.08631 | −0.223889 | −0.111944 | − | 0.993714i | \(-0.535708\pi\) | ||||
−0.111944 | + | 0.993714i | \(0.535708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.4257 | − | 13.2422i | −1.30140 | − | 0.486463i | ||||
\(742\) | 0.809231 | + | 0.467210i | 0.0297078 | + | 0.0171518i | ||||
\(743\) | −22.0853 | − | 12.7509i | −0.810231 | − | 0.467787i | 0.0368054 | − | 0.999322i | \(-0.488282\pi\) |
−0.847036 | + | 0.531536i | \(0.821615\pi\) | |||||||
\(744\) | −23.7252 | − | 8.86850i | −0.869809 | − | 0.325135i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.79043 | 0.212003 | ||||||||
\(747\) | 8.43028 | − | 9.70081i | 0.308448 | − | 0.354934i | ||||
\(748\) | 11.9506i | 0.436958i | ||||||||
\(749\) | 8.50924 | + | 14.7384i | 0.310921 | + | 0.538530i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.19638 | − | 15.9286i | 0.335581 | − | 0.581243i | −0.648016 | − | 0.761627i | \(-0.724401\pi\) |
0.983596 | + | 0.180384i | \(0.0577342\pi\) | |||||||
\(752\) | −12.9171 | − | 7.45769i | −0.471038 | − | 0.271954i | ||||
\(753\) | −0.938816 | + | 0.157175i | −0.0342124 | + | 0.00572777i | ||||
\(754\) | −12.6821 | − | 21.9660i | −0.461853 | − | 0.799953i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.92518 | + | 10.9071i | 0.215497 | + | 0.396687i | ||||
\(757\) | − | 41.8986i | − | 1.52283i | −0.648264 | − | 0.761415i | \(-0.724505\pi\) | ||
0.648264 | − | 0.761415i | \(-0.275495\pi\) | |||||||
\(758\) | −5.90549 | + | 3.40954i | −0.214497 | + | 0.123840i | ||||
\(759\) | 4.52355 | + | 27.0195i | 0.164195 | + | 0.980745i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.98568 | − | 6.90340i | 0.144481 | − | 0.250248i | −0.784698 | − | 0.619878i | \(-0.787182\pi\) |
0.929179 | + | 0.369630i | \(0.120515\pi\) | |||||||
\(762\) | 1.37841 | + | 1.67189i | 0.0499345 | + | 0.0605663i | ||||
\(763\) | 20.5935 | − | 11.8896i | 0.745534 | − | 0.430434i | ||||
\(764\) | −4.74671 | −0.171730 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.61515 | 0.202884 | ||||||||
\(767\) | −4.62947 | + | 2.67282i | −0.167160 | + | 0.0965101i | ||||
\(768\) | 2.56550 | − | 6.86327i | 0.0925744 | − | 0.247657i | ||||
\(769\) | 3.01432 | − | 5.22095i | 0.108699 | − | 0.188272i | −0.806544 | − | 0.591174i | \(-0.798665\pi\) |
0.915244 | + | 0.402901i | \(0.131998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.2034 | + | 10.9162i | 1.05173 | + | 0.393139i | ||||
\(772\) | 27.2186 | − | 15.7147i | 0.979618 | − | 0.565583i | ||||
\(773\) | − | 44.4033i | − | 1.59708i | −0.601944 | − | 0.798538i | \(-0.705607\pi\) | ||
0.601944 | − | 0.798538i | \(-0.294393\pi\) | |||||||
\(774\) | −0.154153 | + | 0.793674i | −0.00554093 | + | 0.0285280i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.23030 | + | 14.2553i |