Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(76,225)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.2 | ||
Root | \(-1.62241 - 0.606458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.2.e.b.151.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.285997 | + | 0.495361i | 0.202230 | + | 0.350273i | 0.949247 | − | 0.314533i | \(-0.101848\pi\) |
−0.747017 | + | 0.664805i | \(0.768514\pi\) | |||||||
\(3\) | −0.285997 | − | 1.70828i | −0.165120 | − | 0.986273i | ||||
\(4\) | 0.836412 | − | 1.44871i | 0.418206 | − | 0.724354i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.764419 | − | 0.630233i | 0.312073 | − | 0.257291i | ||||
\(7\) | 0.714003 | + | 1.23669i | 0.269868 | + | 0.467425i | 0.968828 | − | 0.247736i | \(-0.0796866\pi\) |
−0.698960 | + | 0.715161i | \(0.746353\pi\) | |||||||
\(8\) | 2.10083 | 0.742756 | ||||||||
\(9\) | −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 | \(0.965346\pi\) | |||||||
\(12\) | −2.71400 | − | 1.01450i | −0.783465 | − | 0.292860i | ||||
\(13\) | 2.33641 | − | 4.04678i | 0.648004 | − | 1.12238i | −0.335595 | − | 0.942006i | \(-0.608937\pi\) |
0.983599 | − | 0.180370i | \(-0.0577294\pi\) | |||||||
\(14\) | −0.408405 | + | 0.707378i | −0.109151 | + | 0.189055i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.07199 | − | 1.85675i | −0.267998 | − | 0.464187i | ||||
\(17\) | −2.67282 | −0.648255 | −0.324127 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324127 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(18\) | −1.29523 | − | 1.12559i | −0.305289 | − | 0.265305i | ||||
\(19\) | 4.67282 | 1.07202 | 0.536010 | − | 0.844212i | \(-0.319931\pi\) | ||||
0.536010 | + | 0.844212i | \(0.319931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.90841 | − | 1.57340i | 0.416448 | − | 0.343345i | ||||
\(22\) | 0.764419 | − | 1.32401i | 0.162975 | − | 0.282280i | ||||
\(23\) | −2.95882 | + | 5.12483i | −0.616957 | + | 1.06860i | 0.373081 | + | 0.927799i | \(0.378301\pi\) |
−0.990038 | + | 0.140802i | \(0.955032\pi\) | |||||||
\(24\) | −0.600830 | − | 3.58880i | −0.122644 | − | 0.732560i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.67282 | 0.524184 | ||||||||
\(27\) | 2.48040 | + | 4.56592i | 0.477353 | + | 0.878712i | ||||
\(28\) | 2.38880 | 0.451441 | ||||||||
\(29\) | 4.74482 | + | 8.21826i | 0.881090 | + | 1.52609i | 0.850130 | + | 0.526573i | \(0.176523\pi\) |
0.0309603 | + | 0.999521i | \(0.490143\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.48040 | + | 6.02823i | −0.625098 | + | 1.08270i | 0.363424 | + | 0.931624i | \(0.381608\pi\) |
−0.988522 | + | 0.151078i | \(0.951726\pi\) | |||||||
\(32\) | 2.71400 | − | 4.70079i | 0.479773 | − | 0.830990i | ||||
\(33\) | −3.57199 | + | 2.94497i | −0.621804 | + | 0.512653i | ||||
\(34\) | −0.764419 | − | 1.32401i | −0.131097 | − | 0.227066i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.956844 | + | 4.92641i | −0.159474 | + | 0.821068i | ||||
\(37\) | 1.81681 | 0.298682 | 0.149341 | − | 0.988786i | \(-0.452285\pi\) | ||||
0.149341 | + | 0.988786i | \(0.452285\pi\) | |||||||
\(38\) | 1.33641 | + | 2.31473i | 0.216795 | + | 0.375499i | ||||
\(39\) | −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 | \(0.130019\pi\) | |||||||
\(42\) | 1.32520 | + | 0.495361i | 0.204483 | + | 0.0764358i | ||||
\(43\) | 0.235581 | + | 0.408039i | 0.0359258 | + | 0.0622254i | 0.883429 | − | 0.468565i | \(-0.155229\pi\) |
−0.847503 | + | 0.530790i | \(0.821895\pi\) | |||||||
\(44\) | −4.47116 | −0.674053 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.38485 | −0.499069 | ||||||||
\(47\) | 3.47842 | + | 6.02480i | 0.507380 | + | 0.878808i | 0.999964 | + | 0.00854274i | \(0.00271927\pi\) |
−0.492584 | + | 0.870265i | \(0.663947\pi\) | |||||||
\(48\) | −2.86525 | + | 2.36228i | −0.413563 | + | 0.340966i | ||||
\(49\) | 2.48040 | − | 4.29618i | 0.354343 | − | 0.613739i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.764419 | + | 4.56592i | 0.107040 | + | 0.639357i | ||||
\(52\) | −3.90841 | − | 6.76956i | −0.541998 | − | 0.938769i | ||||
\(53\) | 1.14399 | 0.157139 | 0.0785693 | − | 0.996909i | \(-0.474965\pi\) | ||||
0.0785693 | + | 0.996909i | \(0.474965\pi\) | |||||||
\(54\) | −1.55239 | + | 2.53453i | −0.211254 | + | 0.344906i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | + | 2.59808i | 0.200446 | + | 0.347183i | ||||
\(57\) | −1.33641 | − | 7.98247i | −0.177012 | − | 1.05730i | ||||
\(58\) | −2.71400 | + | 4.70079i | −0.356366 | + | 0.617244i | ||||
\(59\) | 0.571993 | − | 0.990721i | 0.0744672 | − | 0.128981i | −0.826387 | − | 0.563102i | \(-0.809608\pi\) |
0.900854 | + | 0.434121i | \(0.142941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.26442 | + | 2.19004i | 0.161892 | + | 0.280406i | 0.935547 | − | 0.353201i | \(-0.114907\pi\) |
−0.773655 | + | 0.633607i | \(0.781574\pi\) | |||||||
\(62\) | −3.98153 | −0.505655 | ||||||||
\(63\) | −3.23360 | − | 2.81009i | −0.407396 | − | 0.354039i | ||||
\(64\) | −1.18319 | −0.147899 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.48040 | − | 0.927175i | −0.305316 | − | 0.114127i | ||||
\(67\) | −3.29523 | + | 5.70751i | −0.402577 | + | 0.697283i | −0.994036 | − | 0.109051i | \(-0.965219\pi\) |
0.591459 | + | 0.806335i | \(0.298552\pi\) | |||||||
\(68\) | −2.23558 | + | 3.87214i | −0.271104 | + | 0.469566i | ||||
\(69\) | 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 | \(0.776748\pi\) | |||||||
\(72\) | −5.95882 | + | 2.05277i | −0.702254 | + | 0.241921i | ||||
\(73\) | 1.71203 | 0.200378 | 0.100189 | − | 0.994968i | \(-0.468055\pi\) | ||||
0.100189 | + | 0.994968i | \(0.468055\pi\) | |||||||
\(74\) | 0.519602 | + | 0.899976i | 0.0604025 | + | 0.104620i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.90841 | − | 6.76956i | 0.448325 | − | 0.776521i | ||||
\(77\) | 1.90841 | − | 3.30545i | 0.217483 | − | 0.376692i | ||||
\(78\) | −0.764419 | − | 4.56592i | −0.0865534 | − | 0.516989i | ||||
\(79\) | 0.143987 | + | 0.249392i | 0.0161998 | + | 0.0280588i | 0.874012 | − | 0.485905i | \(-0.161510\pi\) |
−0.857812 | + | 0.513964i | \(0.828177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.09046 | − | 5.54304i | 0.787829 | − | 0.615894i | ||||
\(82\) | 0.841495 | 0.0929276 | ||||||||
\(83\) | −2.14201 | − | 3.71007i | −0.235116 | − | 0.407233i | 0.724190 | − | 0.689600i | \(-0.242214\pi\) |
−0.959306 | + | 0.282367i | \(0.908880\pi\) | |||||||
\(84\) | −0.683190 | − | 4.08074i | −0.0745421 | − | 0.445245i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.134751 | + | 0.233396i | −0.0145306 | + | 0.0251677i | ||||
\(87\) | 12.6821 | − | 10.4559i | 1.35966 | − | 1.12098i | ||||
\(88\) | −2.80757 | − | 4.86286i | −0.299288 | − | 0.518383i | ||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.67282 | 0.699502 | ||||||||
\(92\) | 4.94958 | + | 8.57293i | 0.516030 | + | 0.893790i | ||||
\(93\) | 11.2933 | + | 4.22143i | 1.17106 | + | 0.437742i | ||||
\(94\) | −1.98963 | + | 3.44615i | −0.205215 | + | 0.355443i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.80644 | − | 3.29186i | −0.898804 | − | 0.335974i | ||||
\(97\) | 3.91764 | + | 6.78555i | 0.397776 | + | 0.688968i | 0.993451 | − | 0.114257i | \(-0.0364487\pi\) |
−0.595675 | + | 0.803225i | \(0.703115\pi\) | |||||||
\(98\) | 2.83754 | 0.286635 | ||||||||
\(99\) | 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 | \(0.766299\pi\) | |||||||
\(102\) | −2.04316 | + | 1.68450i | −0.202303 | + | 0.166790i | ||||
\(103\) | −0.908405 | + | 1.57340i | −0.0895078 | + | 0.155032i | −0.907303 | − | 0.420477i | \(-0.861863\pi\) |
0.817795 | + | 0.575509i | \(0.195196\pi\) | |||||||
\(104\) | 4.90841 | − | 8.50161i | 0.481309 | − | 0.833651i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.327176 | + | 0.566686i | 0.0317782 | + | 0.0550414i | ||||
\(107\) | −11.9176 | −1.15212 | −0.576061 | − | 0.817407i | \(-0.695411\pi\) | ||||
−0.576061 | + | 0.817407i | \(0.695411\pi\) | |||||||
\(108\) | 8.68932 | + | 0.225617i | 0.836130 | + | 0.0217100i | ||||
\(109\) | −16.6521 | −1.59498 | −0.797491 | − | 0.603331i | \(-0.793840\pi\) | ||||
−0.797491 | + | 0.603331i | \(0.793840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.519602 | − | 3.10361i | −0.0493184 | − | 0.294582i | ||||
\(112\) | 1.53081 | − | 2.65145i | 0.144648 | − | 0.250538i | ||||
\(113\) | 10.0616 | − | 17.4272i | 0.946518 | − | 1.63942i | 0.193836 | − | 0.981034i | \(-0.437907\pi\) |
0.752682 | − | 0.658384i | \(-0.228760\pi\) | |||||||
\(114\) | 3.57199 | − | 2.94497i | 0.334548 | − | 0.275821i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.8745 | 1.47391 | ||||||||
\(117\) | −2.67282 | + | 13.7613i | −0.247103 | + | 1.27223i | ||||
\(118\) | 0.654353 | 0.0602380 | ||||||||
\(119\) | −1.90841 | − | 3.30545i | −0.174943 | − | 0.303011i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.92801 | − | 3.33941i | 0.175273 | − | 0.303582i | ||||
\(122\) | −0.723239 | + | 1.25269i | −0.0654790 | + | 0.113413i | ||||
\(123\) | −2.38683 | − | 0.892198i | −0.215213 | − | 0.0804468i | ||||
\(124\) | 5.82209 | + | 10.0842i | 0.522839 | + | 0.905584i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.467210 | − | 2.40548i | 0.0416224 | − | 0.214297i | ||||
\(127\) | −2.18714 | −0.194078 | −0.0970388 | − | 0.995281i | \(-0.530937\pi\) | ||||
−0.0970388 | + | 0.995281i | \(0.530937\pi\) | |||||||
\(128\) | −5.76640 | − | 9.98769i | −0.509682 | − | 0.882795i | ||||
\(129\) | 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 | \(0.0822479\pi\) | |||||||
\(132\) | 1.27874 | + | 7.63798i | 0.111300 | + | 0.664801i | ||||
\(133\) | 3.33641 | + | 5.77883i | 0.289304 | + | 0.501089i | ||||
\(134\) | −3.76970 | −0.325653 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.61515 | −0.481495 | ||||||||
\(137\) | −5.10083 | − | 8.83490i | −0.435793 | − | 0.754816i | 0.561567 | − | 0.827431i | \(-0.310199\pi\) |
−0.997360 | + | 0.0726153i | \(0.976865\pi\) | |||||||
\(138\) | 0.968056 | + | 5.78226i | 0.0824064 | + | 0.492218i | ||||
\(139\) | −4.00000 | + | 6.92820i | −0.339276 | + | 0.587643i | −0.984297 | − | 0.176522i | \(-0.943515\pi\) |
0.645021 | + | 0.764165i | \(0.276849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.29721 | − | 7.66518i | 0.782966 | − | 0.645524i | ||||
\(142\) | −3.68206 | − | 6.37751i | −0.308992 | − | 0.535189i | ||||
\(143\) | −12.4896 | −1.04444 | ||||||||
\(144\) | 4.85488 | + | 4.21903i | 0.404574 | + | 0.351586i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.489634 | + | 0.848071i | 0.0405224 | + | 0.0701868i | ||||
\(147\) | −8.04844 | − | 3.00851i | −0.663824 | − | 0.248138i | ||||
\(148\) | 1.51960 | − | 2.63203i | 0.124910 | − | 0.216351i | ||||
\(149\) | 10.0381 | − | 17.3865i | 0.822351 | − | 1.42435i | −0.0815762 | − | 0.996667i | \(-0.525995\pi\) |
0.903927 | − | 0.427687i | \(-0.140671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51960 | − | 2.63203i | −0.123663 | − | 0.214191i | 0.797546 | − | 0.603258i | \(-0.206131\pi\) |
−0.921210 | + | 0.389066i | \(0.872798\pi\) | |||||||
\(152\) | 9.81681 | 0.796248 | ||||||||
\(153\) | 7.58123 | − | 2.61168i | 0.612906 | − | 0.211141i | ||||
\(154\) | 2.18319 | 0.175926 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.4465 | + | 8.61270i | −0.836388 | + | 0.689568i | ||||
\(157\) | 0.100830 | − | 0.174643i | 0.00804714 | − | 0.0139381i | −0.861974 | − | 0.506953i | \(-0.830772\pi\) |
0.870021 | + | 0.493015i | \(0.164105\pi\) | |||||||
\(158\) | −0.0823593 | + | 0.142651i | −0.00655216 | + | 0.0113487i | ||||
\(159\) | −0.327176 | − | 1.95424i | −0.0259468 | − | 0.154982i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.45043 | −0.665987 | ||||||||
\(162\) | 4.77365 | + | 1.92705i | 0.375054 | + | 0.151403i | ||||
\(163\) | −17.8168 | −1.39552 | −0.697760 | − | 0.716331i | \(-0.745820\pi\) | ||||
−0.697760 | + | 0.716331i | \(0.745820\pi\) | |||||||
\(164\) | −1.23050 | − | 2.13129i | −0.0960858 | − | 0.166425i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.22522 | − | 2.12214i | 0.0950952 | − | 0.164710i | ||||
\(167\) | 7.05042 | − | 12.2117i | 0.545578 | − | 0.944968i | −0.452993 | − | 0.891514i | \(-0.649644\pi\) |
0.998570 | − | 0.0534538i | \(-0.0170230\pi\) | |||||||
\(168\) | 4.00924 | − | 3.30545i | 0.309319 | − | 0.255021i | ||||
\(169\) | −4.41764 | − | 7.65158i | −0.339819 | − | 0.588583i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.2541 | + | 4.56592i | −1.01356 | + | 0.349165i | ||||
\(172\) | 0.788172 | 0.0600976 | ||||||||
\(173\) | 2.18319 | + | 3.78140i | 0.165985 | + | 0.287494i | 0.937005 | − | 0.349317i | \(-0.113586\pi\) |
−0.771020 | + | 0.636811i | \(0.780253\pi\) | |||||||
\(174\) | 8.80644 | + | 3.29186i | 0.667615 | + | 0.249555i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.86525 | + | 4.96276i | −0.215976 | + | 0.374082i | ||||
\(177\) | −1.85601 | − | 0.693779i | −0.139507 | − | 0.0521476i | ||||
\(178\) | −0.857990 | − | 1.48608i | −0.0643091 | − | 0.111387i | ||||
\(179\) | −15.1625 | −1.13330 | −0.566648 | − | 0.823960i | \(-0.691760\pi\) | ||||
−0.566648 | + | 0.823960i | \(0.691760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.20166 | 0.237978 | 0.118989 | − | 0.992896i | \(-0.462035\pi\) | ||||
0.118989 | + | 0.992896i | \(0.462035\pi\) | |||||||
\(182\) | 1.90841 | + | 3.30545i | 0.141460 | + | 0.245017i | ||||
\(183\) | 3.37957 | − | 2.78632i | 0.249825 | − | 0.205971i | ||||
\(184\) | −6.21598 | + | 10.7664i | −0.458248 | + | 0.793709i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.13870 | + | 6.80155i | 0.0834938 | + | 0.498714i | ||||
\(187\) | 3.57199 | + | 6.18687i | 0.261210 | + | 0.452429i | ||||
\(188\) | 11.6376 | 0.848757 | ||||||||
\(189\) | −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 | \(0.800598\pi\) | |||||||
\(192\) | 0.338388 | + | 2.02121i | 0.0244211 | + | 0.145869i | ||||
\(193\) | −9.39409 | + | 16.2710i | −0.676201 | + | 1.17121i | 0.299915 | + | 0.953966i | \(0.403042\pi\) |
−0.976116 | + | 0.217249i | \(0.930292\pi\) | |||||||
\(194\) | −2.24086 | + | 3.88129i | −0.160885 | + | 0.278660i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.14927 | − | 7.18675i | −0.296376 | − | 0.513339i | ||||
\(197\) | −5.83528 | −0.415747 | −0.207873 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207873 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(198\) | −0.874485 | + | 4.50237i | −0.0621469 | + | 0.319970i | ||||
\(199\) | 13.0761 | 0.926943 | 0.463472 | − | 0.886112i | \(-0.346604\pi\) | ||||
0.463472 | + | 0.886112i | \(0.346604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6924 | + | 3.99684i | 0.754186 | + | 0.281915i | ||||
\(202\) | −1.20166 | + | 2.08134i | −0.0845486 | + | 0.146442i | ||||
\(203\) | −6.77563 | + | 11.7357i | −0.475556 | + | 0.823687i | ||||
\(204\) | 7.25405 | + | 2.71157i | 0.507885 | + | 0.189848i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.03920 | −0.0724047 | ||||||||
\(207\) | 3.38485 | − | 17.4272i | 0.235263 | − | 1.21128i | ||||
\(208\) | −10.0185 | −0.694656 | ||||||||
\(209\) | −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 | \(0.259863\pi\) | |||||||
\(212\) | 0.956844 | − | 1.65730i | 0.0657163 | − | 0.113824i | ||||
\(213\) | 3.68206 | + | 21.9932i | 0.252291 | + | 1.50695i | ||||
\(214\) | −3.40841 | − | 5.90353i | −0.232994 | − | 0.403557i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.21090 | + | 9.59222i | 0.354557 | + | 0.652668i | ||||
\(217\) | −9.94006 | −0.674776 | ||||||||
\(218\) | −4.76244 | − | 8.24879i | −0.322553 | − | 0.558679i | ||||
\(219\) | −0.489634 | − | 2.92461i | −0.0330864 | − | 0.197627i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.24482 | + | 10.8163i | −0.420072 | + | 0.727586i | ||||
\(222\) | 1.38880 | − | 1.14501i | 0.0932104 | − | 0.0768482i | ||||
\(223\) | 4.58321 | + | 7.93834i | 0.306914 | + | 0.531591i | 0.977686 | − | 0.210073i | \(-0.0673702\pi\) |
−0.670772 | + | 0.741664i | \(0.734037\pi\) | |||||||
\(224\) | 7.75123 | 0.517901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.5104 | 0.765658 | ||||||||
\(227\) | −1.33641 | − | 2.31473i | −0.0887008 | − | 0.153634i | 0.818261 | − | 0.574846i | \(-0.194938\pi\) |
−0.906962 | + | 0.421212i | \(0.861605\pi\) | |||||||
\(228\) | −12.6821 | − | 4.74056i | −0.839890 | − | 0.313951i | ||||
\(229\) | −1.27365 | + | 2.20603i | −0.0841654 | + | 0.145779i | −0.905035 | − | 0.425336i | \(-0.860156\pi\) |
0.820870 | + | 0.571115i | \(0.193489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.19243 | − | 2.31473i | −0.407432 | − | 0.152298i | ||||
\(232\) | 9.96806 | + | 17.2652i | 0.654435 | + | 1.13351i | ||||
\(233\) | 6.22013 | 0.407494 | 0.203747 | − | 0.979024i | \(-0.434688\pi\) | ||||
0.203747 | + | 0.979024i | \(0.434688\pi\) | |||||||
\(234\) | −7.58123 | + | 2.61168i | −0.495600 | + | 0.170731i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.956844 | − | 1.65730i | −0.0622852 | − | 0.107881i | ||||
\(237\) | 0.384851 | − | 0.317294i | 0.0249987 | − | 0.0206105i | ||||
\(238\) | 1.09159 | − | 1.89070i | 0.0707576 | − | 0.122556i | ||||
\(239\) | −4.06163 | + | 7.03494i | −0.262725 | + | 0.455053i | −0.966965 | − | 0.254909i | \(-0.917954\pi\) |
0.704240 | + | 0.709962i | \(0.251288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1821 | + | 22.8320i | 0.849131 | + | 1.47074i | 0.881985 | + | 0.471278i | \(0.156207\pi\) |
−0.0328536 | + | 0.999460i | \(0.510460\pi\) | |||||||
\(242\) | 2.20561 | 0.141782 | ||||||||
\(243\) | −11.4969 | − | 10.5272i | −0.737526 | − | 0.675319i | ||||
\(244\) | 4.23030 | 0.270817 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.240665 | − | 1.43751i | −0.0153442 | − | 0.0916520i | ||||
\(247\) | 10.9176 | − | 18.9099i | 0.694673 | − | 1.20321i | ||||
\(248\) | −7.31173 | + | 12.6643i | −0.464295 | + | 0.804183i | ||||
\(249\) | −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 | \(0.505521\pi\) | |||||||
\(252\) | −6.77563 | + | 2.33415i | −0.426825 | + | 0.147038i | ||||
\(253\) | 15.8168 | 0.994394 | ||||||||
\(254\) | −0.625515 | − | 1.08342i | −0.0392483 | − | 0.0679801i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.11515 | − | 3.66355i | 0.132197 | − | 0.228972i | ||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 0.437242 | + | 0.163441i | 0.0272215 | + | 0.0101754i | ||||
\(259\) | 1.29721 | + | 2.24683i | 0.0806046 | + | 0.139611i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.4885 | − | 18.6741i | −1.33010 | − | 1.15590i | ||||
\(262\) | 3.43196 | 0.212027 | ||||||||
\(263\) | 5.94761 | + | 10.3016i | 0.366745 | + | 0.635221i | 0.989055 | − | 0.147550i | \(-0.0471387\pi\) |
−0.622309 | + | 0.782771i | \(0.713805\pi\) | |||||||
\(264\) | −7.50415 | + | 6.18687i | −0.461849 | + | 0.380776i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.90841 | + | 3.30545i | −0.117012 | + | 0.202670i | ||||
\(267\) | 0.857990 | + | 5.12483i | 0.0525081 | + | 0.313634i | ||||
\(268\) | 5.51234 | + | 9.54766i | 0.336720 | + | 0.583216i | ||||
\(269\) | 28.5737 | 1.74217 | 0.871084 | − | 0.491134i | \(-0.163417\pi\) | ||||
0.871084 | + | 0.491134i | \(0.163417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3641 | −1.41927 | −0.709635 | − | 0.704570i | \(-0.751140\pi\) | ||||
−0.709635 | + | 0.704570i | \(0.751140\pi\) | |||||||
\(272\) | 2.86525 | + | 4.96276i | 0.173731 | + | 0.300911i | ||||
\(273\) | −1.90841 | − | 11.3990i | −0.115502 | − | 0.689900i | ||||
\(274\) | 2.91764 | − | 5.05350i | 0.176261 | − | 0.305293i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.2294 | − | 10.9071i | 0.796314 | − | 0.656529i | ||||
\(277\) | −7.53807 | − | 13.0563i | −0.452919 | − | 0.784479i | 0.545647 | − | 0.838015i | \(-0.316284\pi\) |
−0.998566 | + | 0.0535366i | \(0.982951\pi\) | |||||||
\(278\) | −4.57595 | −0.274447 | ||||||||
\(279\) | 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 | \(0.896913\pi\) | |||||||
\(282\) | 6.45600 | + | 2.41326i | 0.384449 | + | 0.143707i | ||||
\(283\) | 13.4485 | − | 23.2934i | 0.799428 | − | 1.38465i | −0.120562 | − | 0.992706i | \(-0.538470\pi\) |
0.919989 | − | 0.391943i | \(-0.128197\pi\) | |||||||
\(284\) | −10.7684 | + | 18.6514i | −0.638985 | + | 1.10675i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.57199 | − | 6.18687i | −0.211216 | − | 0.365838i | ||||
\(287\) | 2.10083 | 0.124008 | ||||||||
\(288\) | −3.10478 | + | 15.9853i | −0.182951 | + | 0.941943i | ||||
\(289\) | −9.85601 | −0.579765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4712 | − | 8.63306i | 0.613830 | − | 0.506079i | ||||
\(292\) | 1.43196 | − | 2.48023i | 0.0837991 | − | 0.145144i | ||||
\(293\) | 6.19243 | − | 10.7256i | 0.361765 | − | 0.626596i | −0.626486 | − | 0.779433i | \(-0.715507\pi\) |
0.988251 | + | 0.152837i | \(0.0488408\pi\) | |||||||
\(294\) | −0.811528 | − | 4.84730i | −0.0473292 | − | 0.282701i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.81681 | 0.221848 | ||||||||
\(297\) | 7.25405 | − | 11.8434i | 0.420923 | − | 0.687224i | ||||
\(298\) | 11.4834 | 0.665217 | ||||||||
\(299\) | 13.8260 | + | 23.9474i | 0.799581 | + | 1.38491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.336412 | + | 0.582682i | −0.0193905 | + | 0.0335853i | ||||
\(302\) | 0.869202 | − | 1.50550i | 0.0500169 | − | 0.0866319i | ||||
\(303\) | 5.61515 | − | 4.62947i | 0.322582 | − | 0.265956i | ||||
\(304\) | −5.00924 | − | 8.67625i | −0.287299 | − | 0.497617i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.46193 | + | 3.00851i | 0.197905 | + | 0.171985i | ||||
\(307\) | 2.49359 | 0.142317 | 0.0711583 | − | 0.997465i | \(-0.477330\pi\) | ||||
0.0711583 | + | 0.997465i | \(0.477330\pi\) | |||||||
\(308\) | −3.19243 | − | 5.52944i | −0.181905 | − | 0.315069i | ||||
\(309\) | 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 | \(-0.0742742\pi\) | |||||||
\(312\) | −15.9269 | − | 5.95348i | −0.901682 | − | 0.337049i | ||||
\(313\) | −17.5420 | − | 30.3837i | −0.991534 | − | 1.71739i | −0.608219 | − | 0.793770i | \(-0.708116\pi\) |
−0.383315 | − | 0.923618i | \(-0.625218\pi\) | |||||||
\(314\) | 0.115349 | 0.00650950 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.481728 | 0.0270993 | ||||||||
\(317\) | −5.23558 | − | 9.06829i | −0.294060 | − | 0.509326i | 0.680706 | − | 0.732557i | \(-0.261673\pi\) |
−0.974766 | + | 0.223231i | \(0.928340\pi\) | |||||||
\(318\) | 0.874485 | − | 0.720978i | 0.0490387 | − | 0.0404304i | ||||
\(319\) | 12.6821 | − | 21.9660i | 0.710059 | − | 1.22986i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.40841 | + | 20.3586i | 0.190239 | + | 1.13631i | ||||
\(322\) | −2.41679 | − | 4.18601i | −0.134683 | − | 0.233277i | ||||
\(323\) | −12.4896 | −0.694942 | ||||||||
\(324\) | −2.09970 | − | 14.9083i | −0.116650 | − | 0.828238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.09555 | − | 8.82575i | −0.282216 | − | 0.488813i | ||||
\(327\) | 4.76244 | + | 28.4464i | 0.263364 | + | 1.57309i | ||||
\(328\) | 1.54533 | − | 2.67659i | 0.0853267 | − | 0.147790i | ||||
\(329\) | −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 | \(0.985875\pi\) | |||||||
\(332\) | −7.16641 | −0.393308 | ||||||||
\(333\) | −5.15322 | + | 1.77525i | −0.282395 | + | 0.0972829i | ||||
\(334\) | 8.06558 | 0.441329 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.96721 | − | 1.85675i | −0.270984 | − | 0.101294i | ||||
\(337\) | −13.5905 | + | 23.5394i | −0.740320 | + | 1.28227i | 0.212030 | + | 0.977263i | \(0.431993\pi\) |
−0.952350 | + | 0.305008i | \(0.901341\pi\) | |||||||
\(338\) | 2.52686 | − | 4.37665i | 0.137443 | − | 0.238058i | ||||
\(339\) | −32.6481 | − | 12.2039i | −1.77320 | − | 0.662825i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.6050 | 1.00752 | ||||||||
\(342\) | −6.05239 | − | 5.25970i | −0.327276 | − | 0.284412i | ||||
\(343\) | 17.0801 | 0.922239 | ||||||||
\(344\) | 0.494917 | + | 0.857221i | 0.0266841 | + | 0.0462182i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.24877 | + | 2.16293i | −0.0671343 | + | 0.116280i | ||||
\(347\) | −11.7829 | + | 20.4086i | −0.632539 | + | 1.09559i | 0.354492 | + | 0.935059i | \(0.384654\pi\) |
−0.987031 | + | 0.160530i | \(0.948680\pi\) | |||||||
\(348\) | −4.54005 | − | 27.1180i | −0.243372 | − | 1.45368i | ||||
\(349\) | 5.35601 | + | 9.27689i | 0.286701 | + | 0.496580i | 0.973020 | − | 0.230720i | \(-0.0741081\pi\) |
−0.686319 | + | 0.727300i | \(0.740775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.2725 | + | 0.630233i | 1.29557 | + | 0.0336393i | ||||
\(352\) | −14.5081 | −0.773285 | ||||||||
\(353\) | 13.6336 | + | 23.6141i | 0.725644 | + | 1.25685i | 0.958708 | + | 0.284392i | \(0.0917916\pi\) |
−0.233064 | + | 0.972461i | \(0.574875\pi\) | |||||||
\(354\) | −0.187143 | − | 1.11781i | −0.00994652 | − | 0.0594112i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.50924 | + | 4.34612i | −0.132989 | + | 0.230344i | ||||
\(357\) | −5.10083 | + | 4.20543i | −0.269965 | + | 0.222575i | ||||
\(358\) | −4.33641 | − | 7.51089i | −0.229186 | − | 0.396963i | ||||
\(359\) | −10.6807 | −0.563707 | −0.281854 | − | 0.959457i | \(-0.590949\pi\) | ||||
−0.281854 | + | 0.959457i | \(0.590949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.83528 | 0.149225 | ||||||||
\(362\) | 0.915664 | + | 1.58598i | 0.0481262 | + | 0.0833571i | ||||
\(363\) | −6.25603 | − | 2.33851i | −0.328356 | − | 0.122740i | ||||
\(364\) | 5.58123 | − | 9.66697i | 0.292536 | − | 0.506687i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.34678 | + | 0.877227i | 0.122668 | + | 0.0458534i | ||||
\(367\) | −4.23558 | − | 7.33624i | −0.221096 | − | 0.382949i | 0.734045 | − | 0.679100i | \(-0.237630\pi\) |
−0.955141 | + | 0.296152i | \(0.904297\pi\) | |||||||
\(368\) | 12.6873 | 0.661373 | ||||||||
\(369\) | −0.841495 | + | 4.33252i | −0.0438065 | + | 0.225542i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.816810 | + | 1.41476i | 0.0424067 | + | 0.0734505i | ||||
\(372\) | 15.5614 | − | 12.8298i | 0.806822 | − | 0.665193i | ||||
\(373\) | 5.06163 | − | 8.76700i | 0.262081 | − | 0.453938i | −0.704714 | − | 0.709492i | \(-0.748925\pi\) |
0.966795 | + | 0.255554i | \(0.0822579\pi\) | |||||||
\(374\) | −2.04316 | + | 3.53885i | −0.105649 | + | 0.182990i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.30757 | + | 12.6571i | 0.376859 | + | 0.652740i | ||||
\(377\) | 44.3434 | 2.28380 | ||||||||
\(378\) | −4.24284 | − | 0.110165i | −0.218228 | − | 0.00566626i | ||||
\(379\) | 11.9216 | 0.612371 | 0.306186 | − | 0.951972i | \(-0.400947\pi\) | ||||
0.306186 | + | 0.951972i | \(0.400947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.625515 | + | 3.73624i | 0.0320461 | + | 0.191414i | ||||
\(382\) | −0.811528 | + | 1.40561i | −0.0415214 | + | 0.0719171i | ||||
\(383\) | 4.90841 | − | 8.50161i | 0.250808 | − | 0.434412i | −0.712941 | − | 0.701224i | \(-0.752637\pi\) |
0.963748 | + | 0.266813i | \(0.0859705\pi\) | |||||||
\(384\) | −15.4126 | + | 12.7070i | −0.786519 | + | 0.648453i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.7467 | −0.546993 | ||||||||
\(387\) | −1.06691 | − | 0.927175i | −0.0542341 | − | 0.0471309i | ||||
\(388\) | 13.1070 | 0.665409 | ||||||||
\(389\) | −4.61007 | − | 7.98487i | −0.233740 | − | 0.404849i | 0.725166 | − | 0.688574i | \(-0.241763\pi\) |
−0.958906 | + | 0.283725i | \(0.908430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.90841 | − | 13.6978i | 0.399945 | − | 0.692725i | ||||
\(392\) | 5.21090 | − | 9.02554i | 0.263190 | − | 0.455858i | ||||
\(393\) | −9.73445 | − | 3.63875i | −0.491038 | − | 0.183550i | ||||
\(394\) | −1.66887 | − | 2.89057i | −0.0840765 | − | 0.145625i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.6821 | − | 4.36887i | 0.637297 | − | 0.219544i | ||||
\(397\) | 22.9793 | 1.15330 | 0.576648 | − | 0.816993i | \(-0.304360\pi\) | ||||
0.576648 | + | 0.816993i | \(0.304360\pi\) | |||||||
\(398\) | 3.73973 | + | 6.47741i | 0.187456 | + | 0.324683i | ||||
\(399\) | 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 | \(0.0775602\pi\) | |||||||
\(402\) | 1.07812 | + | 6.43969i | 0.0537718 | + | 0.321183i | ||||
\(403\) | 16.2633 | + | 28.1688i | 0.810132 | + | 1.40319i | ||||
\(404\) | 7.02864 | 0.349688 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.75123 | −0.384687 | ||||||||
\(407\) | −2.42801 | − | 4.20543i | −0.120352 | − | 0.208455i | ||||
\(408\) | 1.60591 | + | 9.59222i | 0.0795046 | + | 0.474886i | ||||
\(409\) | 8.81681 | − | 15.2712i | 0.435963 | − | 0.755110i | −0.561411 | − | 0.827537i | \(-0.689741\pi\) |
0.997374 | + | 0.0724270i | \(0.0230744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.6336 | + | 11.2404i | −0.672497 | + | 0.554447i | ||||
\(412\) | 1.51960 | + | 2.63203i | 0.0748654 | + | 0.129671i | ||||
\(413\) | 1.63362 | 0.0803852 | ||||||||
\(414\) | 9.60083 | − | 3.30741i | 0.471855 | − | 0.162550i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.6821 | − | 21.9660i | −0.621789 | − | 1.07697i | ||||
\(417\) | 12.9793 | + | 4.85166i | 0.635597 | + | 0.237587i | ||||
\(418\) | 3.57199 | − | 6.18687i | 0.174712 | − | 0.302610i | ||||
\(419\) | −18.5173 | + | 32.0730i | −0.904631 | + | 1.56687i | −0.0832199 | + | 0.996531i | \(0.526520\pi\) |
−0.821411 | + | 0.570336i | \(0.806813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.52884 | − | 4.38007i | −0.123248 | − | 0.213472i | 0.797799 | − | 0.602924i | \(-0.205998\pi\) |
−0.921047 | + | 0.389452i | \(0.872664\pi\) | |||||||
\(422\) | −4.79608 | −0.233469 | ||||||||
\(423\) | −15.7532 | − | 13.6900i | −0.765947 | − | 0.665630i | ||||
\(424\) | 2.40332 | 0.116716 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.84150 | + | 8.11392i | −0.476822 | + | 0.393121i | ||||
\(427\) | −1.80560 | + | 3.12739i | −0.0873790 | + | 0.151345i | ||||
\(428\) | −9.96806 | + | 17.2652i | −0.481824 | + | 0.834544i | ||||
\(429\) | 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 | \(0.540203\pi\) | |||||||
\(432\) | 5.81879 | − | 9.50011i | 0.279957 | − | 0.457074i | ||||
\(433\) | −34.3434 | −1.65044 | −0.825219 | − | 0.564813i | \(-0.808948\pi\) | ||||
−0.825219 | + | 0.564813i | \(0.808948\pi\) | |||||||
\(434\) | −2.84283 | − | 4.92392i | −0.136460 | − | 0.236356i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.9280 | + | 24.1240i | −0.667031 | + | 1.15533i | ||||
\(437\) | −13.8260 | + | 23.9474i | −0.661389 | + | 1.14556i | ||||
\(438\) | 1.30871 | − | 1.07898i | 0.0625324 | − | 0.0515554i | ||||
\(439\) | 9.77365 | + | 16.9285i | 0.466471 | + | 0.807952i | 0.999267 | − | 0.0382924i | \(-0.0121918\pi\) |
−0.532796 | + | 0.846244i | \(0.678859\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.83754 | + | 14.6094i | −0.135121 | + | 0.695685i | ||||
\(442\) | −7.14399 | −0.339805 | ||||||||
\(443\) | 5.25208 | + | 9.09686i | 0.249534 | + | 0.432205i | 0.963396 | − | 0.268081i | \(-0.0863893\pi\) |
−0.713863 | + | 0.700286i | \(0.753056\pi\) | |||||||
\(444\) | −4.93083 | − | 1.84315i | −0.234007 | − | 0.0874719i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.62156 | + | 4.54068i | −0.124135 | + | 0.215007i | ||||
\(447\) | −32.5717 | − | 12.1753i | −1.54059 | − | 0.575873i | ||||
\(448\) | −0.844801 | − | 1.46324i | −0.0399131 | − | 0.0691315i | ||||
\(449\) | 22.8560 | 1.07864 | 0.539321 | − | 0.842100i | \(-0.318681\pi\) | ||||
0.539321 | + | 0.842100i | \(0.318681\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.93216 | −0.185158 | ||||||||
\(452\) | −16.8313 | − | 29.1527i | −0.791679 | − | 1.37123i | ||||
\(453\) | −4.06163 | + | 3.34865i | −0.190832 | + | 0.157333i | ||||
\(454\) | 0.764419 | − | 1.32401i | 0.0358759 | − | 0.0621390i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.80757 | − | 16.7698i | −0.131477 | − | 0.785319i | ||||
\(457\) | −7.01319 | − | 12.1472i | −0.328063 | − | 0.568222i | 0.654064 | − | 0.756439i | \(-0.273063\pi\) |
−0.982127 | + | 0.188217i | \(0.939729\pi\) | |||||||
\(458\) | −1.45704 | −0.0680832 | ||||||||
\(459\) | −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 | \(0.643641\pi\) | |||||||
\(462\) | −0.624385 | − | 3.72949i | −0.0290490 | − | 0.173512i | ||||
\(463\) | −16.9700 | + | 29.3930i | −0.788664 | + | 1.36601i | 0.138121 | + | 0.990415i | \(0.455894\pi\) |
−0.926785 | + | 0.375591i | \(0.877440\pi\) | |||||||
\(464\) | 10.1728 | − | 17.6198i | 0.472261 | − | 0.817981i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.77894 | + | 3.08121i | 0.0824077 | + | 0.142734i | ||||
\(467\) | 27.3720 | 1.26663 | 0.633313 | − | 0.773896i | \(-0.281695\pi\) | ||||
0.633313 | + | 0.773896i | \(0.281695\pi\) | |||||||
\(468\) | 17.7005 | + | 15.3823i | 0.818207 | + | 0.711045i | ||||
\(469\) | −9.41123 | −0.434570 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.327176 | − | 0.122299i | −0.0150755 | − | 0.00563523i | ||||
\(472\) | 1.20166 | − | 2.08134i | 0.0553109 | − | 0.0958013i | ||||
\(473\) | 0.629668 | − | 1.09062i | 0.0289521 | − | 0.0501466i | ||||
\(474\) | 0.267241 | + | 0.0998949i | 0.0122748 | + | 0.00458832i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.38485 | −0.292649 | ||||||||
\(477\) | −3.24482 | + | 1.11781i | −0.148570 | + | 0.0511812i | ||||
\(478\) | −4.64645 | −0.212524 | ||||||||
\(479\) | −2.61515 | − | 4.52957i | −0.119489 | − | 0.206961i | 0.800076 | − | 0.599898i | \(-0.204792\pi\) |
−0.919565 | + | 0.392937i | \(0.871459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.24482 | − | 7.35224i | 0.193547 | − | 0.335233i | ||||
\(482\) | −7.54005 | + | 13.0597i | −0.343440 | + | 0.594855i | ||||
\(483\) | 2.41679 | + | 14.4357i | 0.109968 | + | 0.656846i | ||||
\(484\) | −3.22522 | − | 5.58624i | −0.146601 | − | 0.253920i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.92668 | − | 8.70585i | 0.0873958 | − | 0.394905i | ||||
\(487\) | 24.0185 | 1.08838 | 0.544190 | − | 0.838962i | \(-0.316837\pi\) | ||||
0.544190 | + | 0.838962i | \(0.316837\pi\) | |||||||
\(488\) | 2.65633 | + | 4.60090i | 0.120246 | + | 0.208273i | ||||
\(489\) | 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 | \(0.274880\pi\) | |||||||
\(492\) | −3.28890 | + | 2.71157i | −0.148275 | + | 0.122247i | ||||
\(493\) | −12.6821 | − | 21.9660i | −0.571171 | − | 0.989298i | ||||
\(494\) | 12.4896 | 0.561935 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.9239 | 0.670101 | ||||||||
\(497\) | −9.19243 | − | 15.9217i | −0.412337 | − | 0.714188i | ||||
\(498\) | −3.97560 | − | 1.48608i | −0.178151 | − | 0.0665929i | ||||
\(499\) | −12.4280 | + | 21.5259i | −0.556354 | + | 0.963633i | 0.441443 | + | 0.897289i | \(0.354467\pi\) |
−0.997797 | + | 0.0663440i | \(0.978867\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.8773 | − | 8.55155i | −1.02208 | − | 0.382055i | ||||
\(502\) | −0.157175 | − | 0.272235i | −0.00701506 | − | 0.0121504i | ||||
\(503\) | −38.9154 | −1.73515 | −0.867576 | − | 0.497305i | \(-0.834323\pi\) | ||||
−0.867576 | + | 0.497305i | \(0.834323\pi\) | |||||||
\(504\) | −6.79326 | − | 5.90353i | −0.302596 | − | 0.262964i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.52355 | + | 7.83503i | 0.201097 | + | 0.348309i | ||||
\(507\) | −11.8076 | + | 9.73487i | −0.524393 | + | 0.432341i | ||||
\(508\) | −1.82935 | + | 3.16853i | −0.0811644 | + | 0.140581i | ||||
\(509\) | −1.01037 | + | 1.75001i | −0.0447837 | + | 0.0775676i | −0.887548 | − | 0.460715i | \(-0.847593\pi\) |
0.842765 | + | 0.538282i | \(0.180927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.22239 | + | 2.11725i | 0.0540755 | + | 0.0936615i | ||||
\(512\) | −20.6459 | −0.912428 | ||||||||
\(513\) | 11.5905 | + | 21.3357i | 0.511732 | + | 0.941996i | ||||
\(514\) | −10.2959 | −0.454132 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.225415 | − | 1.34642i | −0.00992333 | − | 0.0592726i | ||||
\(517\) | 9.29721 | − | 16.1032i | 0.408891 | − | 0.708220i | ||||
\(518\) | −0.741995 | + | 1.28517i | −0.0326014 | + | 0.0564672i | ||||
\(519\) | 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 | \(0.668308\pi\) | |||||||
\(522\) | 3.10478 | − | 15.9853i | 0.135893 | − | 0.699657i | ||||
\(523\) | 41.1170 | 1.79792 | 0.898961 | − | 0.438028i | \(-0.144323\pi\) | ||||
0.898961 | + | 0.438028i | \(0.144323\pi\) | |||||||
\(524\) | −5.01847 | − | 8.69225i | −0.219233 | − | 0.379723i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.40199 | + | 5.89242i | −0.148334 | + | 0.256922i | ||||
\(527\) | 9.30249 | − | 16.1124i | 0.405223 | − | 0.701867i | ||||
\(528\) | 9.29721 | + | 3.47530i | 0.404609 | + | 0.151243i | ||||
\(529\) | −6.00924 | − | 10.4083i | −0.261271 | − | 0.452535i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.654353 | + | 3.36900i | −0.0283965 | + | 0.146202i | ||||
\(532\) | 11.1625 | 0.483954 | ||||||||
\(533\) | −3.43724 | − | 5.95348i | −0.148883 | − | 0.257874i | ||||
\(534\) | −2.29326 | + | 1.89070i | −0.0992389 | + | 0.0818185i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.92272 | + | 11.9905i | −0.299016 | + | 0.517911i | ||||
\(537\) | 4.33641 | + | 25.9017i | 0.187130 | + | 1.11774i | ||||
\(538\) | 8.17198 | + | 14.1543i | 0.352319 | + | 0.610234i | ||||
\(539\) | −13.2593 | −0.571120 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.20957 | 0.223977 | 0.111988 | − | 0.993710i | \(-0.464278\pi\) | ||||
0.111988 | + | 0.993710i | \(0.464278\pi\) | |||||||
\(542\) | −6.68206 | − | 11.5737i | −0.287019 | − | 0.497132i | ||||
\(543\) | −0.915664 | − | 5.46932i | −0.0392949 | − | 0.234711i | ||||
\(544\) | −7.25405 | + | 12.5644i | −0.311015 | + | 0.538694i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.10083 | − | 4.20543i | 0.218295 | − | 0.179976i | ||||
\(547\) | 20.0204 | + | 34.6764i | 0.856013 | + | 1.48266i | 0.875702 | + | 0.482851i | \(0.160399\pi\) |
−0.0196900 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(548\) | −17.0656 | −0.729005 | ||||||||
\(549\) | −5.72635 | − | 4.97636i | −0.244394 | − | 0.212386i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.1717 | + | 38.4025i | 0.944546 | + | 1.63600i | ||||
\(552\) | 20.1697 | + | 7.53946i | 0.858480 | + | 0.320901i | ||||
\(553\) | −0.205614 | + | 0.356133i | −0.00874359 | + | 0.0151443i | ||||
\(554\) | 4.31173 | − | 7.46813i | 0.183188 | − | 0.317290i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.69129 | + | 11.5897i | 0.283774 | + | 0.491511i | ||||
\(557\) | 14.4033 | 0.610288 | 0.305144 | − | 0.952306i | \(-0.401295\pi\) | ||||
0.305144 | + | 0.952306i | \(0.401295\pi\) | |||||||
\(558\) | 11.2933 | − | 3.89044i | 0.478082 | − | 0.164695i | ||||
\(559\) | 2.20166 | 0.0931203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.54731 | − | 7.87137i | 0.403088 | − | 0.332330i | ||||
\(562\) | 1.90248 | − | 3.29518i | 0.0802511 | − | 0.138999i | ||||
\(563\) | 14.6840 | − | 25.4335i | 0.618858 | − | 1.07189i | −0.370836 | − | 0.928698i | \(-0.620929\pi\) |
0.989694 | − | 0.143196i | \(-0.0457378\pi\) | |||||||
\(564\) | −3.32831 | − | 19.8802i | −0.140147 | − | 0.837107i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.3849 | 0.646674 | ||||||||
\(567\) | 11.9176 | + | 4.81096i | 0.500494 | + | 0.202041i | ||||
\(568\) | −27.0471 | −1.13487 | ||||||||
\(569\) | −23.4033 | − | 40.5357i | −0.981118 | − | 1.69935i | −0.658056 | − | 0.752969i | \(-0.728621\pi\) |
−0.323062 | − | 0.946378i | \(-0.604712\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −10.4465 | + | 18.0938i | −0.436789 | + | 0.756541i | ||||
\(573\) | 3.79213 | − | 3.12646i | 0.158418 | − | 0.130610i | ||||
\(574\) | 0.600830 | + | 1.04067i | 0.0250782 | + | 0.0434367i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.35601 | − | 1.15612i | 0.139834 | − | 0.0481717i | ||||
\(577\) | −28.2386 | −1.17559 | −0.587794 | − | 0.809010i | \(-0.700004\pi\) | ||||
−0.587794 | + | 0.809010i | \(0.700004\pi\) | |||||||
\(578\) | −2.81879 | − | 4.88228i | −0.117246 | − | 0.203076i | ||||
\(579\) | 30.4821 | + | 11.3942i | 1.26679 | + | 0.473528i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.05880 | − | 5.29801i | 0.126901 | − | 0.219798i | ||||
\(582\) | 7.27119 | + | 2.71798i | 0.301401 | + | 0.112664i | ||||
\(583\) | −1.52884 | − | 2.64802i | −0.0633180 | − | 0.109670i | ||||
\(584\) | 3.59668 | 0.148832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.08405 | 0.292639 | ||||||||
\(587\) | 9.04118 | + | 15.6598i | 0.373169 | + | 0.646348i | 0.990051 | − | 0.140707i | \(-0.0449377\pi\) |
−0.616882 | + | 0.787056i | \(0.711604\pi\) | |||||||
\(588\) | −11.0903 | + | 9.14348i | −0.457355 | + | 0.377071i | ||||
\(589\) | −16.2633 | + | 28.1688i | −0.670117 | + | 1.16068i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.66887 | + | 9.96827i | 0.0686482 | + | 0.410040i | ||||
\(592\) | −1.94761 | − | 3.37336i | −0.0800462 | − | 0.138644i | ||||
\(593\) | 7.73840 | 0.317778 | 0.158889 | − | 0.987296i | \(-0.449209\pi\) | ||||
0.158889 | + | 0.987296i | \(0.449209\pi\) | |||||||
\(594\) | 7.94139 | + | 0.206197i | 0.325839 | + | 0.00846037i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.7919 | − | 29.0845i | −0.687824 | − | 1.19135i | ||||
\(597\) | −3.73973 | − | 22.3377i | −0.153057 | − | 0.914220i | ||||
\(598\) | −7.90841 | + | 13.6978i | −0.323399 | + | 0.560143i | ||||
\(599\) | 13.9608 | − | 24.1808i | 0.570423 | − | 0.988001i | −0.426100 | − | 0.904676i | \(-0.640113\pi\) |
0.996522 | − | 0.0833249i | \(-0.0265539\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2201 | − | 33.2902i | −0.784006 | − | 1.35794i | −0.929591 | − | 0.368592i | \(-0.879840\pi\) |
0.145586 | − | 0.989346i | \(-0.453493\pi\) | |||||||
\(602\) | −0.384851 | −0.0156853 | ||||||||
\(603\) | 3.76970 | − | 19.4087i | 0.153514 | − | 0.790383i | ||||
\(604\) | −5.08405 | −0.206867 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.89917 | + | 1.45751i | 0.158393 | + | 0.0592074i | ||||
\(607\) | −0.319917 | + | 0.554113i | −0.0129850 | + | 0.0224907i | −0.872445 | − | 0.488712i | \(-0.837467\pi\) |
0.859460 | + | 0.511203i | \(0.170800\pi\) | |||||||
\(608\) | 12.6821 | − | 21.9660i | 0.514325 | − | 0.890838i | ||||
\(609\) | 21.9857 | + | 8.21826i | 0.890905 | + | 0.333021i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.5081 | 1.31514 | ||||||||
\(612\) | 2.55748 | − | 13.1674i | 0.103380 | − | 0.532261i | ||||
\(613\) | −42.7467 | −1.72652 | −0.863262 | − | 0.504757i | \(-0.831582\pi\) | ||||
−0.863262 | + | 0.504757i | \(0.831582\pi\) | |||||||
\(614\) | 0.713157 | + | 1.23522i | 0.0287807 | + | 0.0498496i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00924 | − | 6.94420i | 0.161537 | − | 0.279790i | ||||
\(617\) | 10.5513 | − | 18.2753i | 0.424778 | − | 0.735737i | −0.571622 | − | 0.820517i | \(-0.693686\pi\) |
0.996400 | + | 0.0847805i | \(0.0270189\pi\) | |||||||
\(618\) | 0.297209 | + | 1.77525i | 0.0119555 | + | 0.0714109i | ||||
\(619\) | 6.82605 | + | 11.8231i | 0.274362 | + | 0.475209i | 0.969974 | − | 0.243209i | \(-0.0782000\pi\) |
−0.695612 | + | 0.718418i | \(0.744867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.7386 | − | 0.798123i | −1.23350 | − | 0.0320276i | ||||
\(622\) | 13.8538 | 0.555485 | ||||||||
\(623\) | −2.14201 | − | 3.71007i | −0.0858178 | − | 0.148641i | ||||
\(624\) | 2.86525 | + | 17.1143i | 0.114702 | + | 0.685121i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.0339 | − | 17.3793i | 0.401036 | − | 0.694615i | ||||
\(627\) | −16.6913 | + | 13.7613i | −0.666586 | + | 0.549574i | ||||
\(628\) | −0.168672 | − | 0.292148i | −0.00673073 | − | 0.0116580i | ||||
\(629\) | −4.85601 | −0.193622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2593 | 1.32403 | 0.662017 | − | 0.749489i | \(-0.269701\pi\) | ||||
0.662017 | + | 0.749489i | \(0.269701\pi\) | |||||||
\(632\) | 0.302491 | + | 0.523930i | 0.0120325 | + | 0.0208408i | ||||
\(633\) | 13.6037 | + | 5.08506i | 0.540697 | + | 0.202113i | ||||
\(634\) | 2.99472 | − | 5.18700i | 0.118935 | − | 0.206002i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.10478 | − | 1.16057i | −0.123113 | − | 0.0460196i | ||||
\(637\) | −11.5905 | − | 20.0753i | −0.459231 | − | 0.795411i | ||||
\(638\) | 14.5081 | 0.574381 | ||||||||
\(639\) | 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 | \(-0.340404\pi\) | |||||||
\(642\) | −9.11007 | + | 7.51089i | −0.359546 | + | 0.296431i | ||||
\(643\) | 10.2913 | − | 17.8250i | 0.405848 | − | 0.702950i | −0.588571 | − | 0.808445i | \(-0.700309\pi\) |
0.994420 | + | 0.105495i | \(0.0336427\pi\) | |||||||
\(644\) | −7.06804 | + | 12.2422i | −0.278520 | + | 0.482410i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.57199 | − | 6.18687i | −0.140538 | − | 0.243419i | ||||
\(647\) | −23.2527 | −0.914159 | −0.457079 | − | 0.889426i | \(-0.651104\pi\) | ||||
−0.457079 | + | 0.889426i | \(0.651104\pi\) | |||||||
\(648\) | 14.8959 | − | 11.6450i | 0.585165 | − | 0.457458i | ||||
\(649\) | −3.05767 | −0.120024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.84283 | + | 16.9804i | 0.111419 | + | 0.665513i | ||||
\(652\) | −14.9022 | + | 25.8114i | −0.583615 | + | 1.01085i | ||||
\(653\) | 9.37957 | − | 16.2459i | 0.367051 | − | 0.635751i | −0.622052 | − | 0.782976i | \(-0.713701\pi\) |
0.989103 | + | 0.147225i | \(0.0470342\pi\) | |||||||
\(654\) | −12.7292 | + | 10.4947i | −0.497750 | + | 0.410375i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.15415 | −0.123149 | ||||||||
\(657\) | −4.85601 | + | 1.67286i | −0.189451 | + | 0.0652645i | ||||
\(658\) | −5.68242 | −0.221524 | ||||||||
\(659\) | 0.140034 | + | 0.242545i | 0.00545494 | + | 0.00944823i | 0.868740 | − | 0.495268i | \(-0.164930\pi\) |
−0.863285 | + | 0.504717i | \(0.831597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8930 | − | 34.4556i | 0.773746 | − | 1.34017i | −0.161750 | − | 0.986832i | \(-0.551714\pi\) |
0.935496 | − | 0.353336i | \(-0.114953\pi\) | |||||||
\(662\) | 4.79834 | − | 8.31097i | 0.186493 | − | 0.323015i | ||||
\(663\) | 20.2633 | + | 7.57443i | 0.786961 | + | 0.294167i | ||||
\(664\) | −4.50000 | − | 7.79423i | −0.174634 | − | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.35319 | − | 2.04499i | −0.0911843 | − | 0.0792417i | ||||
\(667\) | −56.1562 | −2.17438 | ||||||||
\(668\) | −11.7941 | − | 20.4280i | −0.456327 | − | 0.790382i | ||||
\(669\) | 12.2501 | − | 10.0997i | 0.473616 | − | 0.390478i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.37957 | − | 5.85358i | 0.130467 | − | 0.225975i | ||||
\(672\) | −2.21683 | − | 13.2412i | −0.0855159 | − | 0.510792i | ||||
\(673\) | 16.7644 | + | 29.0368i | 0.646221 | + | 1.11929i | 0.984018 | + | 0.178068i | \(0.0569848\pi\) |
−0.337797 | + | 0.941219i | \(0.609682\pi\) | |||||||
\(674\) | −15.5473 | −0.598860 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.7799 | −0.568456 | ||||||||
\(677\) | 13.7437 | + | 23.8048i | 0.528213 | + | 0.914891i | 0.999459 | + | 0.0328897i | \(0.0104710\pi\) |
−0.471246 | + | 0.882002i | \(0.656196\pi\) | |||||||
\(678\) | −3.29193 | − | 19.6629i | −0.126426 | − | 0.755148i | ||||
\(679\) | −5.59442 | + | 9.68981i | −0.214694 | + | 0.371861i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.57199 | + | 2.94497i | −0.136879 | + | 0.112851i | ||||
\(682\) | 5.32096 | + | 9.21618i | 0.203750 | + | 0.352906i | ||||
\(683\) | 34.5865 | 1.32342 | 0.661708 | − | 0.749762i | \(-0.269832\pi\) | ||||
0.661708 | + | 0.749762i | \(0.269832\pi\) | |||||||
\(684\) | −4.47116 | + | 23.0202i | −0.170959 | + | 0.880201i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.88485 | + | 8.46081i | 0.186504 | + | 0.323035i | ||||
\(687\) | 4.13277 | + | 1.54483i | 0.157675 | + | 0.0589391i | ||||
\(688\) | 0.505083 | − | 0.874830i | 0.0192561 | − | 0.0333526i | ||||
\(689\) | 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 | \(-0.448760\pi\) | |||||||
\(692\) | 7.30418 | 0.277663 | ||||||||
\(693\) | −2.18319 | + | 11.2404i | −0.0829325 | + | 0.426987i | ||||
\(694\) | −13.4795 | −0.511674 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 26.6429 | − | 21.9660i | 1.00989 | − | 0.832618i | ||||
\(697\) | −1.96608 | + | 3.40535i | −0.0744706 | + | 0.128987i | ||||
\(698\) | −3.06360 | + | 5.30632i | −0.115959 | + | 0.200847i | ||||
\(699\) | −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 | \(0.619857\pi\) | |||||||
\(702\) | 6.62967 | + | 12.2039i | 0.250221 | + | 0.460606i | ||||
\(703\) | 8.48963 | 0.320193 | ||||||||
\(704\) | 1.58123 | + | 2.73877i | 0.0595948 | + | 0.103221i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.79834 | + | 13.5071i | −0.293494 | + | 0.508347i | ||||
\(707\) | −3.00000 | + | 5.19615i | −0.112827 | + | 0.195421i | ||||
\(708\) | −2.55748 | + | 2.10854i | −0.0961158 | + | 0.0792436i | ||||
\(709\) | −7.54316 | − | 13.0651i | −0.283289 | − | 0.490671i | 0.688904 | − | 0.724853i | \(-0.258092\pi\) |
−0.972193 | + | 0.234182i | \(0.924759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.652092 | − | 0.566686i | −0.0244553 | − | 0.0212524i | ||||
\(712\) | −6.30249 | −0.236196 | ||||||||
\(713\) | −20.5957 | − | 35.6729i | −0.771317 | − | 1.33596i | ||||
\(714\) | −3.54203 | − | 1.32401i | −0.132557 | − | 0.0495499i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.6821 | + | 21.9660i | −0.473951 | + | 0.820907i | ||||
\(717\) | 13.1792 | + | 4.92641i | 0.492188 | + | 0.183980i | ||||
\(718\) | −3.05465 | − | 5.29081i | −0.113999 | − | 0.197451i | ||||
\(719\) | −3.43196 | −0.127990 | −0.0639952 | − | 0.997950i | \(-0.520384\pi\) | ||||
−0.0639952 | + | 0.997950i | \(0.520384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.59442 | −0.0966211 | ||||||||
\(722\) | 0.810881 | + | 1.40449i | 0.0301779 | + | 0.0522696i | ||||
\(723\) | 35.2333 | − | 29.0485i | 1.31034 | − | 1.08032i | ||||
\(724\) | 2.67791 | − | 4.63827i | 0.0995236 | − | 0.172380i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.630798 | − | 3.76780i | −0.0234111 | − | 0.139836i | ||||
\(727\) | −17.8857 | − | 30.9789i | −0.663344 | − | 1.14895i | −0.979732 | − | 0.200315i | \(-0.935803\pi\) |
0.316388 | − | 0.948630i | \(-0.397530\pi\) | |||||||
\(728\) | 14.0185 | 0.519559 | ||||||||
\(729\) | −14.6952 | + | 22.6506i | −0.544268 | + | 0.838911i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.629668 | − | 1.09062i | −0.0232891 | − | 0.0403379i | ||||
\(732\) | −1.20985 | − | 7.22652i | −0.0447174 | − | 0.267100i | ||||
\(733\) | −11.0000 | + | 19.0526i | −0.406294 | + | 0.703722i | −0.994471 | − | 0.105010i | \(-0.966513\pi\) |
0.588177 | + | 0.808732i | \(0.299846\pi\) | |||||||
\(734\) | 2.42272 | − | 4.19628i | 0.0894244 | − | 0.154888i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0605 | + | 27.8176i | 0.591998 | + | 1.02537i | ||||
\(737\) | 17.6151 | 0.648862 | ||||||||
\(738\) | −2.38683 | + | 0.822244i | −0.0878603 | + | 0.0302672i | ||||
\(739\) | 6.08631 | 0.223889 | 0.111944 | − | 0.993714i | \(-0.464292\pi\) | ||||
0.111944 | + | 0.993714i | \(0.464292\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.4257 | − | 13.2422i | −1.30140 | − | 0.486463i | ||||
\(742\) | −0.467210 | + | 0.809231i | −0.0171518 | + | 0.0297078i | ||||
\(743\) | −12.7509 | + | 22.0853i | −0.467787 | + | 0.810231i | −0.999322 | − | 0.0368054i | \(-0.988282\pi\) |
0.531536 | + | 0.847036i | \(0.321615\pi\) | |||||||
\(744\) | 23.7252 | + | 8.86850i | 0.869809 | + | 0.325135i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.79043 | 0.212003 | ||||||||
\(747\) | 9.70081 | + | 8.43028i | 0.354934 | + | 0.308448i | ||||
\(748\) | 11.9506 | 0.436958 | ||||||||
\(749\) | −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 | \(0.0577342\pi\) | |||||||
\(752\) | 7.45769 | − | 12.9171i | 0.271954 | − | 0.471038i | ||||
\(753\) | 0.157175 | + | 0.938816i | 0.00572777 | + | 0.0342124i | ||||
\(754\) | 12.6821 | + | 21.9660i | 0.461853 | + | 0.799953i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.92518 | + | 10.9071i | 0.215497 | + | 0.396687i | ||||
\(757\) | 41.8986 | 1.52283 | 0.761415 | − | 0.648264i | \(-0.224505\pi\) | ||||
0.761415 | + | 0.648264i | \(0.224505\pi\) | |||||||
\(758\) | 3.40954 | + | 5.90549i | 0.123840 | + | 0.214497i | ||||
\(759\) | −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 | \(0.120515\pi\) | |||||||
\(762\) | −1.67189 | + | 1.37841i | −0.0605663 | + | 0.0499345i | ||||
\(763\) | −11.8896 | − | 20.5935i | −0.430434 | − | 0.745534i | ||||
\(764\) | 4.74671 | 0.171730 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.61515 | 0.202884 | ||||||||
\(767\) | −2.67282 | − | 4.62947i | −0.0965101 | − | 0.167160i | ||||
\(768\) | −6.86327 | − | 2.56550i | −0.247657 | − | 0.0925744i | ||||
\(769\) | −3.01432 | + | 5.22095i | −0.108699 | + | 0.188272i | −0.915244 | − | 0.402901i | \(-0.868002\pi\) |
0.806544 | + | 0.591174i | \(0.201335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.2034 | + | 10.9162i | 1.05173 | + | 0.393139i | ||||
\(772\) | 15.7147 | + | 27.2186i | 0.565583 | + | 0.979618i | ||||
\(773\) | −44.4033 | −1.59708 | −0.798538 | − | 0.601944i | \(-0.794393\pi\) | ||||
−0.798538 | + | 0.601944i | \(0.794393\pi\) | |||||||
\(774\) | 0.154153 | − | 0.793674i | 0.00554093 | − | 0.0285280i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.23030 | + | 14.2553i | 0.295451 | + | 0.511735i | ||||
\(777\) | 3.46721 | − | 2.85858i | 0.124385 | − | 0.102551i | ||||
\(778\) | 2.63693 | − | 4.56729i | 0.0945384 | − | 0.163745i | ||||
\(779\) | 3.43724 | − | 5.95348i | 0.123152 | − | 0.213305i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.2056 | + | 29.8010i | 0.615665 | + | 1.06636i | ||||
\(782\) | 9.04711 | 0.323524 | ||||||||
\(783\) | −25.7549 | + | 42.0490i | −0.920405 | + | 1.50271i | ||||
\(784\) | −10.6359 | −0.379853 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.981529 | − | 5.86273i | −0.0350100 | − | 0.209117i | ||||
\(787\) | 8.41877 | − | 14.5817i | 0.300097 | − | 0.519783i | −0.676061 | − | 0.736846i | \(-0.736314\pi\) |
0.976158 | + | 0.217063i | \(0.0696477\pi\) | |||||||
\(788\) | −4.88070 | + | 8.45362i | −0.173868 | + | 0.301148i | ||||
\(789\) | 15.8969 | − | 13.1064i | 0.565945 | − | 0.466599i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.7361 | 1.02174 | ||||||||
\(792\) | 12.7150 | + | 11.0497i | 0.451810 | + | 0.392635i | ||||
\(793\) | 11.8168 | 0.419627 | ||||||||
\(794\) | 6.57199 | + | 11.3830i | 0.233231 | + | 0.403968i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.9370 | − | 18.9435i | 0.387653 | − | 0.671435i | ||||
\(797\) | −16.6860 | + | 28.9010i | −0.591049 | + | 1.02373i | 0.403043 | + | 0.915181i | \(0.367953\pi\) |
−0.994091 | + | 0.108545i | \(0.965381\pi\) | |||||||
\(798\) | 6.19243 | + | 2.31473i | 0.219209 | + | 0.0819407i | ||||
\(799\) | −9.29721 | − | 16.1032i | −0.328912 | − | 0.569692i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.50924 | − | 2.93137i | 0.300659 | − | 0.103575i | ||||
\(802\) | 6.32944 | 0.223500 | ||||||||
\(803\) | −2.28797 | − | 3.96289i | −0.0807408 | − | 0.139847i | ||||
\(804\) | 14.7335 | − | 12.1472i | 0.519611 | − | 0.428399i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.30249 | + | 16.1124i | −0.327666 | + | 0.567535i | ||||
\(807\) | −8.17198 | − | 48.8117i | −0.287667 | − | 1.71825i | ||||
\(808\) | 4.41349 | + | 7.64439i | 0.155266 | + | 0.268929i | ||||
\(809\) | 29.1809 | 1.02595 | 0.512973 | − | 0.858404i | \(-0.328544\pi\) | ||||
0.512973 | + | 0.858404i | \(0.328544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5552 | −0.546217 | −0.273109 | − | 0.961983i | \(-0.588052\pi\) | ||||
−0.273109 | + | 0.961983i | \(0.588052\pi\) | |||||||
\(812\) | 11.3344 | + | 19.6318i | 0.397761 | + | 0.688942i | ||||
\(813\) | 6.68206 | + | 39.9124i | 0.234350 | + | 1.39979i | ||||
\(814\) | 1.38880 | − | 2.40548i | 0.0486775 | − | 0.0843120i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.65831 | − | 6.31397i | 0.268094 | − | 0.221033i | ||||
\(817\) | 1.10083 | + | 1.90669i | 0.0385132 | + | 0.0667068i | ||||
\(818\) | 10.0863 | 0.352660 | ||||||||
\(819\) | −18.9269 | + | 6.52016i | −0.661359 | + | 0.227833i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.8588 | + | 20.5401i | 0.413876 | + | 0.716855i | 0.995310 | − | 0.0967393i | \(-0.0308413\pi\) |
−0.581434 | + | 0.813594i | \(0.697508\pi\) | |||||||
\(822\) | −9.46721 | − | 3.53885i | −0.330207 | − | 0.123432i | ||||
\(823\) | 9.68404 | − | 16.7732i | 0.337564 | − | 0.584678i | −0.646410 | − | 0.762990i | \(-0.723730\pi\) |
0.983974 | + | 0.178312i | \(0.0570636\pi\) | |||||||
\(824\) | −1.90841 | + | 3.30545i | −0.0664824 | + | 0.115151i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.467210 | + | 0.809231i | 0.0162563 | + | 0.0281568i | ||||
\(827\) | −52.2241 | −1.81601 | −0.908005 | − | 0.418960i | \(-0.862395\pi\) | ||||
−0.908005 | + | 0.418960i | \(0.862395\pi\) | |||||||
\(828\) | −22.4159 | − | 19.4800i | −0.779005 | − | 0.676977i | ||||
\(829\) | −26.6442 | −0.925391 | −0.462695 | − | 0.886517i | \(-0.653118\pi\) | ||||
−0.462695 | + | 0.886517i | \(0.653118\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.1479 | + | 16.6112i | −0.698924 | + | 0.576235i | ||||
\(832\) | −2.76442 | + | 4.78811i | −0.0958390 | + | 0.165998i | ||||
\(833\) | −6.62967 | + | 11.4829i | −0.229704 | + | 0.397860i | ||||
\(834\) | 1.30871 | + | 7.81698i | 0.0453168 | + | 0.270680i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.8930 | −0.722598 | ||||||||
\(837\) | −36.1572 | − | 0.938816i | −1.24977 | − | 0.0324502i | ||||
\(838\) | −21.1836 | −0.731775 | ||||||||
\(839\) | 12.5196 | + | 21.6846i | 0.432225 | + | 0.748635i | 0.997065 | − | 0.0765655i | \(-0.0243954\pi\) |
−0.564840 | + | 0.825201i | \(0.691062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.5266 | + | 52.8736i | −1.05264 | + | 1.82323i | ||||
\(842\) | 1.44648 | − | 2.50537i | 0.0498489 | − | 0.0863409i | ||||
\(843\) | −8.88993 | + | 7.32940i | −0.306186 | + | 0.252438i | ||||
\(844\) | 7.01319 | + | 12.1472i | 0.241404 | + | 0.418124i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.27611 | − | 11.7188i | 0.0782544 | − | 0.402901i | ||||
\(847\) | 5.50641 | 0.189203 | ||||||||
\(848\) | −1.22635 | − | 2.12409i | −0.0421129 | − | 0.0729417i | ||||
\(849\) | −43.6378 | − | 16.3118i | −1.49764 | − | 0.559821i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.37562 | + | 9.31084i | −0.184274 | + | 0.319171i | ||||
\(852\) | 34.9414 | + | 13.0611i | 1.19707 | + | 0.447467i | ||||
\(853\) | −5.43724 | − | 9.41758i | −0.186168 | − | 0.322452i | 0.757802 | − | 0.652485i | \(-0.226273\pi\) |
−0.943969 | + | 0.330033i | \(0.892940\pi\) | |||||||
\(854\) | −2.06558 | −0.0706827 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.0369 | −0.855745 | ||||||||
\(857\) | −9.29721 | − | 16.1032i | −0.317587 | − | 0.550076i | 0.662397 | − | 0.749153i | \(-0.269539\pi\) |
−0.979984 | + | 0.199077i | \(0.936206\pi\) | |||||||
\(858\) | −9.54731 | + | 7.87137i | −0.325940 | + | 0.268724i | ||||
\(859\) | 2.33246 | − | 4.03994i | 0.0795825 | − | 0.137841i | −0.823487 | − | 0.567335i | \(-0.807975\pi\) |
0.903070 | + | 0.429494i | \(0.141308\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.600830 | − | 3.58880i | −0.0204762 | − | 0.122306i | ||||
\(862\) | −1.49585 | − | 2.59088i | −0.0509488 | − | 0.0882459i | ||||
\(863\) | 28.0594 | 0.955152 | 0.477576 | − | 0.878590i | \(-0.341516\pi\) | ||||
0.477576 | + | 0.878590i | \(0.341516\pi\) | |||||||
\(864\) | 28.1952 | + | 0.732086i | 0.959222 | + | 0.0249061i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.82209 | − | 17.0124i | −0.333768 | − | 0.578104i | ||||
\(867\) | 2.81879 | + | 16.8368i | 0.0957310 | + | 0.571807i | ||||
\(868\) | −8.31399 | + | 14.4002i | −0.282195 | + | 0.488776i | ||||
\(869\) | 0.384851 | − | 0.666581i | 0.0130552 | − | 0.0226122i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3980 | + | 26.6702i | 0.521743 | + | 0.903685i | ||||
\(872\) | −34.9832 | −1.18468 | ||||||||
\(873\) | −17.7424 | − | 15.4186i | −0.600488 | − | 0.521841i | ||||
\(874\) | −15.8168 | −0.535012 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.64645 | − | 1.73685i | −0.156989 | − | 0.0586826i | ||||
\(877\) | 17.3342 | − | 30.0236i | 0.585333 | − | 1.01383i | −0.409501 | − | 0.912310i | \(-0.634297\pi\) |
0.994834 | − | 0.101516i | \(-0.0323694\pi\) | |||||||
\(878\) | −5.59046 | + | 9.68297i | −0.188669 | + | 0.326784i | ||||
\(879\) | −20.0933 | − | 7.51089i | −0.677730 | − | 0.253336i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.29854 | −0.178512 | −0.0892561 | − | 0.996009i | \(-0.528449\pi\) | ||||
−0.0892561 | + | 0.996009i | \(0.528449\pi\) | |||||||
\(882\) | −8.04844 | + | 2.77263i | −0.271005 | + | 0.0933592i | ||||
\(883\) | 10.3025 | 0.346706 | 0.173353 | − | 0.984860i | \(-0.444540\pi\) | ||||
0.173353 | + | 0.984860i | \(0.444540\pi\) | |||||||
\(884\) | 10.4465 | + | 18.0938i | 0.351353 | + | 0.608561i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.00415 | + | 5.20334i | −0.100926 | + | 0.174810i | ||||
\(887\) | 20.7252 | − | 35.8971i | 0.695885 | − | 1.20531i | −0.273997 | − | 0.961731i | \(-0.588346\pi\) |
0.969882 | − | 0.243577i | \(-0.0783208\pi\) | |||||||
\(888\) | −1.09159 | − | 6.52016i | −0.0366315 | − | 0.218802i | ||||
\(889\) | −1.56163 | − | 2.70482i | −0.0523753 | − | 0.0907167i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.3064 | − | 9.00475i | −0.747294 | − | 0.301670i | ||||
\(892\) | 15.3338 | 0.513413 | ||||||||
\(893\) | 16.2541 | + | 28.1528i | 0.543921 | + | 0.942099i | ||||
\(894\) | −3.28422 | − | 19.6168i | −0.109841 | − | 0.656086i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.23445 | − | 14.2625i | 0.275094 | − | 0.476476i | ||||
\(897\) | 36.9546 | − | 30.4676i | 1.23388 | − | 1.01728i | ||||
\(898\) | 6.53674 | + | 11.3220i | 0.218134 | + | 0.377819i | ||||
\(899\) | −66.0554 | −2.20307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.05767 | −0.101866 | ||||||||
\(902\) | −1.12458 | − | 1.94784i | −0.0374446 | − | 0.0648559i | ||||
\(903\) | 1.09159 | + | 0.408039i | 0.0363260 | + | 0.0135787i | ||||
\(904\) | 21.1378 | − | 36.6117i | 0.703032 | − | 1.21769i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.82040 | − | 1.05427i | −0.0937015 | − | 0.0350257i | ||||
\(907\) | −8.39606 | − | 14.5424i | −0.278787 | − | 0.482873i | 0.692297 | − | 0.721613i | \(-0.256599\pi\) |
−0.971083 | + | 0.238740i | \(0.923266\pi\) | |||||||
\(908\) | −4.47116 | −0.148381 | ||||||||
\(909\) | −9.51432 | − | 8.26821i | −0.315570 | − | 0.274239i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.6768 | − | 32.3491i | −0.618789 | − | 1.07177i | −0.989707 | − | 0.143109i | \(-0.954290\pi\) |
0.370918 | − | 0.928666i | \(-0.379043\pi\) | |||||||
\(912\) | −13.3888 | + | 11.0385i | −0.443348 | + | 0.365522i | ||||
\(913\) | −5.72522 | + | 9.91636i | −0.189477 | + | 0.328184i | ||||
\(914\) | 4.01150 | − | 6.94812i | 0.132689 | − | 0.229823i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.13060 | + | 3.69031i | 0.0703970 | + | 0.121931i | ||||
\(917\) | 8.56804 | 0.282942 | ||||||||
\(918\) | 4.14927 | − | 6.77435i | 0.136946 | − | 0.223587i | ||||
\(919\) | 37.1316 | 1.22486 | 0.612429 | − | 0.790526i | \(-0.290193\pi\) | ||||
0.612429 | + | 0.790526i | \(0.290193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.713157 | − | 4.25973i | −0.0234993 | − | 0.140363i | ||||
\(922\) | −6.89324 | + | 11.9394i | −0.227017 | + | 0.393205i | ||||
\(923\) | −30.0801 | + | 52.1003i | −0.990098 | + | 1.71490i | ||||
\(924\) | −8.53279 | + | 7.03494i | −0.280708 | + | 0.231433i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19.4135 | −0.637967 | ||||||||
\(927\) | 1.03920 | − | 5.35044i | 0.0341319 | − | 0.175732i | ||||
\(928\) | 51.5098 | 1.69089 | ||||||||
\(929\) | 23.9977 | + | 41.5653i | 0.787340 | + | 1.36371i | 0.927591 | + | 0.373597i | \(0.121876\pi\) |
−0.140251 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.5905 | − | 20.0753i | 0.379862 | − | 0.657941i | ||||
\(932\) | 5.20259 | − | 9.01115i | 0.170417 | − | 0.295170i | ||||
\(933\) | −39.2949 | − | 14.6885i | −1.28646 | − | 0.480879i | ||||
\(934\) | 7.82831 | + | 13.5590i | 0.256150 | + | 0.443665i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.61515 | + | 28.9102i | −0.183537 | + | 0.944958i | ||||
\(937\) | −22.0079 | −0.718967 | −0.359483 | − | 0.933151i | \(-0.617047\pi\) | ||||
−0.359483 | + | 0.933151i | \(0.617047\pi\) | |||||||
\(938\) | −2.69158 | − | 4.66195i | −0.0878832 | − | 0.152218i | ||||
\(939\) | −46.8867 | + | 38.6562i | −1.53009 | + | 1.26150i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.2921 | + | 35.1470i | −0.661504 | + | 1.14576i | 0.318716 | + | 0.947850i | \(0.396748\pi\) |
−0.980220 | + | 0.197909i | \(0.936585\pi\) | |||||||
\(942\) | −0.0329893 | − | 0.197047i | −0.00107485 | − | 0.00642015i | ||||
\(943\) | 4.35291 | + | 7.53946i | 0.141750 | + | 0.245518i | ||||
\(944\) | −2.45269 | −0.0798283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.720331 | 0.0234200 | ||||||||
\(947\) | 15.1160 | + | 26.1817i | 0.491204 | + | 0.850790i | 0.999949 | − | 0.0101273i | \(-0.00322368\pi\) |
−0.508745 | + | 0.860917i | \(0.669890\pi\) | |||||||
\(948\) | −0.137773 | − | 0.822925i | −0.00447465 | − | 0.0267273i | ||||
\(949\) | 4.00000 | − | 6.92820i | 0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.9938 | + | 11.5373i | −0.453780 | + | 0.374123i | ||||
\(952\) | −4.00924 | − | 6.94420i | −0.129940 | − | 0.225063i | ||||
\(953\) | −2.50811 | −0.0812455 | −0.0406227 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406227 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(954\) | −1.48173 | − | 1.28766i | −0.0479727 | − | 0.0416896i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.79439 | + | 11.7682i | 0.219746 | + | 0.380612i | ||||
\(957\) | −41.1510 | − | 15.3823i | −1.33022 | − | 0.497238i | ||||
\(958\) | 1.49585 | − | 2.59088i | 0.0483286 | − | 0.0837077i | ||||
\(959\) | 7.28402 | − | 12.6163i | 0.235213 | − | 0.407401i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.72635 | − | 15.1145i | −0.281495 | − | 0.487564i | ||||
\(962\) | 4.85601 | 0.156564 | ||||||||
\(963\) | 33.8033 | − | 11.6450i | 1.08930 | − | 0.375255i | ||||
\(964\) | 44.1025 | 1.42045 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.45967 | + | 5.32574i | −0.207836 | + | 0.171353i | ||||
\(967\) | −10.8765 | + | 18.8386i | −0.349763 | + | 0.605808i | −0.986207 | − | 0.165515i | \(-0.947071\pi\) |
0.636444 | + | 0.771323i | \(0.280405\pi\) | |||||||
\(968\) | 4.05042 | − | 7.01552i | 0.130185 | − | 0.225488i | ||||
\(969\) | 3.57199 | + | 21.3357i | 0.114749 | + | 0.685403i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.7512 | 0.730122 | 0.365061 | − | 0.930984i | \(-0.381048\pi\) | ||||
0.365061 | + | 0.930984i | \(0.381048\pi\) | |||||||
\(972\) | −24.8669 | + | 7.85058i | −0.797608 | + | 0.251808i | ||||
\(973\) | −11.4241 | −0.366238 | ||||||||
\(974\) | 6.86920 | + | 11.8978i | 0.220103 | + | 0.381230i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.71090 | − | 4.69541i | 0.0867737 | − | 0.150296i | ||||
\(977\) | 19.6389 | − | 34.0156i | 0.628304 | − | 1.08825i | −0.359588 | − | 0.933111i | \(-0.617083\pi\) |
0.987892 | − | 0.155143i | \(-0.0495840\pi\) | |||||||
\(978\) | −13.6195 | + | 11.2287i | −0.435504 | + | 0.359055i | ||||
\(979\) | 4.00924 | + | 6.94420i | 0.128136 | + | 0.221938i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.2322 | − | 16.2711i | 1.50801 | − | 0.519497i | ||||
\(982\) | −8.45269 | −0.269736 | ||||||||
\(983\) | 16.8949 | + | 29.2629i | 0.538865 | + | 0.933341i | 0.998966 | + | 0.0454743i | \(0.0144799\pi\) |
−0.460101 | + | 0.887867i | \(0.652187\pi\) | |||||||
\(984\) | −5.01432 | − | 1.87436i | −0.159851 | − | 0.0597523i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.25405 | − | 12.5644i | 0.231016 | − | 0.400132i | ||||
\(987\) | 16.1177 | + | 6.02480i | 0.513032 | + | 0.191772i | ||||
\(988\) | −18.2633 | − | 31.6329i | −0.581033 | − | 1.00638i | ||||
\(989\) | −2.78817 | −0.0886587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7983 | −0.755979 | −0.377990 | − | 0.925810i | \(-0.623384\pi\) | ||||
−0.377990 | + | 0.925810i | \(0.623384\pi\) | |||||||
\(992\) | 18.8916 | + | 32.7213i | 0.599810 | + | 1.03890i | ||||
\(993\) | −22.4218 | + | 18.4859i | −0.711534 | + | 0.586631i | ||||
\(994\) | 5.25801 | − | 9.10713i | 0.166774 | − | 0.288861i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.04957 | + | 12.2422i | 0.0649431 | + | 0.387909i | ||||
\(997\) | 25.8392 | + | 44.7549i | 0.818337 | + | 1.41740i | 0.906907 | + | 0.421331i | \(0.138437\pi\) |
−0.0885702 | + | 0.996070i | \(0.528230\pi\) | |||||||
\(998\) | −14.2175 | −0.450046 | ||||||||
\(999\) | 4.50641 | + | 8.29541i | 0.142577 | + | 0.262455i |
(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 | 225.2.e.b.76.2 | 6 | ||
3.2 | odd | 2 | 675.2.e.b.226.2 | 6 | |||
5.2 | odd | 4 | 225.2.k.b.49.3 | 12 | |||
5.3 | odd | 4 | 225.2.k.b.49.4 | 12 | |||
5.4 | even | 2 | 45.2.e.b.31.2 | yes | 6 | ||
9.2 | odd | 6 | 675.2.e.b.451.2 | 6 | |||
9.4 | even | 3 | 2025.2.a.n.1.2 | 3 | |||
9.5 | odd | 6 | 2025.2.a.o.1.2 | 3 | |||
9.7 | even | 3 | inner | 225.2.e.b.151.2 | 6 | ||
15.2 | even | 4 | 675.2.k.b.199.4 | 12 | |||
15.8 | even | 4 | 675.2.k.b.199.3 | 12 | |||
15.14 | odd | 2 | 135.2.e.b.91.2 | 6 | |||
20.19 | odd | 2 | 720.2.q.i.481.2 | 6 | |||
45.2 | even | 12 | 675.2.k.b.424.3 | 12 | |||
45.4 | even | 6 | 405.2.a.j.1.2 | 3 | |||
45.7 | odd | 12 | 225.2.k.b.124.4 | 12 | |||
45.13 | odd | 12 | 2025.2.b.l.649.4 | 6 | |||
45.14 | odd | 6 | 405.2.a.i.1.2 | 3 | |||
45.22 | odd | 12 | 2025.2.b.l.649.3 | 6 | |||
45.23 | even | 12 | 2025.2.b.m.649.3 | 6 | |||
45.29 | odd | 6 | 135.2.e.b.46.2 | 6 | |||
45.32 | even | 12 | 2025.2.b.m.649.4 | 6 | |||
45.34 | even | 6 | 45.2.e.b.16.2 | ✓ | 6 | ||
45.38 | even | 12 | 675.2.k.b.424.4 | 12 | |||
45.43 | odd | 12 | 225.2.k.b.124.3 | 12 | |||
60.59 | even | 2 | 2160.2.q.k.1441.2 | 6 | |||
180.59 | even | 6 | 6480.2.a.bs.1.2 | 3 | |||
180.79 | odd | 6 | 720.2.q.i.241.2 | 6 | |||
180.119 | even | 6 | 2160.2.q.k.721.2 | 6 | |||
180.139 | odd | 6 | 6480.2.a.bv.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.2 | ✓ | 6 | 45.34 | even | 6 | ||
45.2.e.b.31.2 | yes | 6 | 5.4 | even | 2 | ||
135.2.e.b.46.2 | 6 | 45.29 | odd | 6 | |||
135.2.e.b.91.2 | 6 | 15.14 | odd | 2 | |||
225.2.e.b.76.2 | 6 | 1.1 | even | 1 | trivial | ||
225.2.e.b.151.2 | 6 | 9.7 | even | 3 | inner | ||
225.2.k.b.49.3 | 12 | 5.2 | odd | 4 | |||
225.2.k.b.49.4 | 12 | 5.3 | odd | 4 | |||
225.2.k.b.124.3 | 12 | 45.43 | odd | 12 | |||
225.2.k.b.124.4 | 12 | 45.7 | odd | 12 | |||
405.2.a.i.1.2 | 3 | 45.14 | odd | 6 | |||
405.2.a.j.1.2 | 3 | 45.4 | even | 6 | |||
675.2.e.b.226.2 | 6 | 3.2 | odd | 2 | |||
675.2.e.b.451.2 | 6 | 9.2 | odd | 6 | |||
675.2.k.b.199.3 | 12 | 15.8 | even | 4 | |||
675.2.k.b.199.4 | 12 | 15.2 | even | 4 | |||
675.2.k.b.424.3 | 12 | 45.2 | even | 12 | |||
675.2.k.b.424.4 | 12 | 45.38 | even | 12 | |||
720.2.q.i.241.2 | 6 | 180.79 | odd | 6 | |||
720.2.q.i.481.2 | 6 | 20.19 | odd | 2 | |||
2025.2.a.n.1.2 | 3 | 9.4 | even | 3 | |||
2025.2.a.o.1.2 | 3 | 9.5 | odd | 6 | |||
2025.2.b.l.649.3 | 6 | 45.22 | odd | 12 | |||
2025.2.b.l.649.4 | 6 | 45.13 | odd | 12 | |||
2025.2.b.m.649.3 | 6 | 45.23 | even | 12 | |||
2025.2.b.m.649.4 | 6 | 45.32 | even | 12 | |||
2160.2.q.k.721.2 | 6 | 180.119 | even | 6 | |||
2160.2.q.k.1441.2 | 6 | 60.59 | even | 2 | |||
6480.2.a.bs.1.2 | 3 | 180.59 | even | 6 | |||
6480.2.a.bv.1.2 | 3 | 180.139 | odd | 6 |