Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,2,Mod(46,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.e (of order \(3\), 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: | \(1.07798042729\) |
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: | \( 3 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 91.2 | ||
Root | \(-1.62241 - 0.606458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.91 |
Dual form | 135.2.e.b.46.2 |
$q$-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 \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(82\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0.836412 | − | 1.44871i | 0.418206 | − | 0.724354i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.714003 | − | 1.23669i | −0.269868 | − | 0.467425i | 0.698960 | − | 0.715161i | \(-0.253647\pi\) |
−0.968828 | + | 0.247736i | \(0.920313\pi\) | |||||||
\(8\) | 2.10083 | 0.742756 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.571993 | 0.180880 | ||||||||
\(11\) | 1.33641 | + | 2.31473i | 0.402943 | + | 0.697918i | 0.994080 | − | 0.108653i | \(-0.0346538\pi\) |
−0.591136 | + | 0.806572i | \(0.701321\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.33641 | + | 4.04678i | −0.648004 | + | 1.12238i | 0.335595 | + | 0.942006i | \(0.391063\pi\) |
−0.983599 | + | 0.180370i | \(0.942271\pi\) | |||||||
\(14\) | 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 | \(0.605071\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.67282 | 1.07202 | 0.536010 | − | 0.844212i | \(-0.319931\pi\) | ||||
0.536010 | + | 0.844212i | \(0.319931\pi\) | |||||||
\(20\) | −0.836412 | − | 1.44871i | −0.187027 | − | 0.323941i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −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 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −2.67282 | −0.524184 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.38880 | −0.451441 | ||||||||
\(29\) | −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 | \(0.951726\pi\) | |||||||
\(32\) | 2.71400 | − | 4.70079i | 0.479773 | − | 0.830990i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.764419 | − | 1.32401i | −0.131097 | − | 0.227066i | ||||
\(35\) | −1.42801 | −0.241377 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.81681 | −0.298682 | −0.149341 | − | 0.988786i | \(-0.547715\pi\) | ||||
−0.149341 | + | 0.988786i | \(0.547715\pi\) | |||||||
\(38\) | 1.33641 | + | 2.31473i | 0.216795 | + | 0.375499i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.05042 | − | 1.81937i | 0.166085 | − | 0.287668i | ||||
\(41\) | −0.735581 | + | 1.27406i | −0.114879 | + | 0.198975i | −0.917731 | − | 0.397202i | \(-0.869981\pi\) |
0.802853 | + | 0.596177i | \(0.203315\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.235581 | − | 0.408039i | −0.0359258 | − | 0.0622254i | 0.847503 | − | 0.530790i | \(-0.178105\pi\) |
−0.883429 | + | 0.468565i | \(0.844771\pi\) | |||||||
\(44\) | 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 | \(0.663947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.48040 | − | 4.29618i | 0.354343 | − | 0.613739i | ||||
\(50\) | 0.285997 | − | 0.495361i | 0.0404460 | − | 0.0700546i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.90841 | + | 6.76956i | 0.541998 | + | 0.938769i | ||||
\(53\) | 1.14399 | 0.157139 | 0.0785693 | − | 0.996909i | \(-0.474965\pi\) | ||||
0.0785693 | + | 0.996909i | \(0.474965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.67282 | 0.360403 | ||||||||
\(56\) | −1.50000 | − | 2.59808i | −0.200446 | − | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.71400 | − | 4.70079i | 0.356366 | − | 0.617244i | ||||
\(59\) | −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 | \(0.781574\pi\) | |||||||
\(62\) | −3.98153 | −0.505655 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.18319 | −0.147899 | ||||||||
\(65\) | 2.33641 | + | 4.04678i | 0.289796 | + | 0.501942i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.29523 | − | 5.70751i | 0.402577 | − | 0.697283i | −0.591459 | − | 0.806335i | \(-0.701448\pi\) |
0.994036 | + | 0.109051i | \(0.0347813\pi\) | |||||||
\(68\) | −2.23558 | + | 3.87214i | −0.271104 | + | 0.469566i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.408405 | − | 0.707378i | −0.0488137 | − | 0.0845479i | ||||
\(71\) | 12.8745 | 1.52792 | 0.763960 | − | 0.645263i | \(-0.223252\pi\) | ||||
0.763960 | + | 0.645263i | \(0.223252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.71203 | −0.200378 | −0.100189 | − | 0.994968i | \(-0.531945\pi\) | ||||
−0.100189 | + | 0.994968i | \(0.531945\pi\) | |||||||
\(74\) | −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 | 0 | ||||||||
\(79\) | 0.143987 | + | 0.249392i | 0.0161998 | + | 0.0280588i | 0.874012 | − | 0.485905i | \(-0.161510\pi\) |
−0.857812 | + | 0.513964i | \(0.828177\pi\) | |||||||
\(80\) | −2.14399 | −0.239705 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −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 | 0 | ||||||||
\(85\) | −1.33641 | + | 2.31473i | −0.144954 | + | 0.251068i | ||||
\(86\) | 0.134751 | − | 0.233396i | 0.0145306 | − | 0.0251677i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.80757 | + | 4.86286i | 0.299288 | + | 0.518383i | ||||
\(89\) | 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 | ||||||||
\(92\) | 4.94958 | + | 8.57293i | 0.516030 | + | 0.893790i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.98963 | + | 3.44615i | −0.205215 | + | 0.355443i | ||||
\(95\) | 2.33641 | − | 4.04678i | 0.239711 | − | 0.415191i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.91764 | − | 6.78555i | −0.397776 | − | 0.688968i | 0.595675 | − | 0.803225i | \(-0.296885\pi\) |
−0.993451 | + | 0.114257i | \(0.963551\pi\) | |||||||
\(98\) | 2.83754 | 0.286635 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.67282 | −0.167282 | ||||||||
\(101\) | −2.10083 | − | 3.63875i | −0.209040 | − | 0.362069i | 0.742372 | − | 0.669988i | \(-0.233701\pi\) |
−0.951413 | + | 0.307919i | \(0.900367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.908405 | − | 1.57340i | 0.0895078 | − | 0.155032i | −0.817795 | − | 0.575509i | \(-0.804804\pi\) |
0.907303 | + | 0.420477i | \(0.138137\pi\) | |||||||
\(104\) | −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 | \(0.695411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6521 | −1.59498 | −0.797491 | − | 0.603331i | \(-0.793840\pi\) | ||||
−0.797491 | + | 0.603331i | \(0.793840\pi\) | |||||||
\(110\) | 0.764419 | + | 1.32401i | 0.0728845 | + | 0.126240i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −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 | \(-0.228760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.95882 | + | 5.12483i | 0.275911 | + | 0.477893i | ||||
\(116\) | −15.8745 | −1.47391 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.82209 | + | 10.0842i | 0.522839 | + | 0.905584i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.18714 | 0.194078 | 0.0970388 | − | 0.995281i | \(-0.469063\pi\) | ||||
0.0970388 | + | 0.995281i | \(0.469063\pi\) | |||||||
\(128\) | −5.76640 | − | 9.98769i | −0.509682 | − | 0.882795i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.33641 | + | 2.31473i | −0.117211 | + | 0.203016i | ||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −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 | 0 | ||||||||
\(139\) | −4.00000 | + | 6.92820i | −0.339276 | + | 0.587643i | −0.984297 | − | 0.176522i | \(-0.943515\pi\) |
0.645021 | + | 0.764165i | \(0.276849\pi\) | |||||||
\(140\) | −1.19440 | + | 2.06876i | −0.100945 | + | 0.174843i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.68206 | + | 6.37751i | 0.308992 | + | 0.535189i | ||||
\(143\) | −12.4896 | −1.04444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.48963 | −0.788071 | ||||||||
\(146\) | −0.489634 | − | 0.848071i | −0.0405224 | − | 0.0701868i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.51960 | + | 2.63203i | −0.124910 | + | 0.216351i | ||||
\(149\) | −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 | \(0.872798\pi\) | |||||||
\(152\) | 9.81681 | 0.796248 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.18319 | 0.175926 | ||||||||
\(155\) | 3.48040 | + | 6.02823i | 0.279552 | + | 0.484199i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.100830 | + | 0.174643i | −0.00804714 | + | 0.0139381i | −0.870021 | − | 0.493015i | \(-0.835895\pi\) |
0.861974 | + | 0.506953i | \(0.169228\pi\) | |||||||
\(158\) | −0.0823593 | + | 0.142651i | −0.00655216 | + | 0.0113487i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.71400 | − | 4.70079i | −0.214561 | − | 0.371630i | ||||
\(161\) | 8.45043 | 0.665987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8168 | 1.39552 | 0.697760 | − | 0.716331i | \(-0.254180\pi\) | ||||
0.697760 | + | 0.716331i | \(0.254180\pi\) | |||||||
\(164\) | 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 | \(-0.0170230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.41764 | − | 7.65158i | −0.339819 | − | 0.588583i | ||||
\(170\) | −1.52884 | −0.117256 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.788172 | −0.0600976 | ||||||||
\(173\) | 2.18319 | + | 3.78140i | 0.165985 | + | 0.287494i | 0.937005 | − | 0.349317i | \(-0.113586\pi\) |
−0.771020 | + | 0.636811i | \(0.780253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.714003 | + | 1.23669i | −0.0539736 | + | 0.0934850i | ||||
\(176\) | 2.86525 | − | 4.96276i | 0.215976 | − | 0.374082i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.857990 | + | 1.48608i | 0.0643091 | + | 0.111387i | ||||
\(179\) | 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 | \(0.462035\pi\) | |||||||
\(182\) | 1.90841 | + | 3.30545i | 0.141460 | + | 0.245017i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.21598 | + | 10.7664i | −0.458248 | + | 0.793709i | ||||
\(185\) | −0.908405 | + | 1.57340i | −0.0667873 | + | 0.115679i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.57199 | − | 6.18687i | −0.261210 | − | 0.452429i | ||||
\(188\) | 11.6376 | 0.848757 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.67282 | 0.193907 | ||||||||
\(191\) | −1.41877 | − | 2.45738i | −0.102659 | − | 0.177810i | 0.810121 | − | 0.586263i | \(-0.199402\pi\) |
−0.912779 | + | 0.408453i | \(0.866068\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.39409 | − | 16.2710i | 0.676201 | − | 1.17121i | −0.299915 | − | 0.953966i | \(-0.596958\pi\) |
0.976116 | − | 0.217249i | \(-0.0697083\pi\) | |||||||
\(194\) | 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 | 0 | ||||||||
\(199\) | 13.0761 | 0.926943 | 0.463472 | − | 0.886112i | \(-0.346604\pi\) | ||||
0.463472 | + | 0.886112i | \(0.346604\pi\) | |||||||
\(200\) | −1.05042 | − | 1.81937i | −0.0742756 | − | 0.128649i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.20166 | − | 2.08134i | 0.0845486 | − | 0.146442i | ||||
\(203\) | −6.77563 | + | 11.7357i | −0.475556 | + | 0.823687i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.735581 | + | 1.27406i | 0.0513752 | + | 0.0889845i | ||||
\(206\) | 1.03920 | 0.0724047 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.40841 | − | 5.90353i | −0.232994 | − | 0.403557i | ||||
\(215\) | −0.471163 | −0.0321330 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.94006 | 0.674776 | ||||||||
\(218\) | −4.76244 | − | 8.24879i | −0.322553 | − | 0.558679i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.23558 | − | 3.87214i | 0.150723 | − | 0.261060i | ||||
\(221\) | 6.24482 | − | 10.8163i | 0.420072 | − | 0.727586i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.58321 | − | 7.93834i | −0.306914 | − | 0.531591i | 0.670772 | − | 0.741664i | \(-0.265963\pi\) |
−0.977686 | + | 0.210073i | \(0.932630\pi\) | |||||||
\(224\) | −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 | \(0.861605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.27365 | + | 2.20603i | −0.0841654 | + | 0.145779i | −0.905035 | − | 0.425336i | \(-0.860156\pi\) |
0.820870 | + | 0.571115i | \(0.193489\pi\) | |||||||
\(230\) | −1.69243 | + | 2.93137i | −0.111595 | + | 0.193289i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.96806 | − | 17.2652i | −0.654435 | − | 1.13351i | ||||
\(233\) | 6.22013 | 0.407494 | 0.203747 | − | 0.979024i | \(-0.434688\pi\) | ||||
0.203747 | + | 0.979024i | \(0.434688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.95684 | 0.453814 | ||||||||
\(236\) | 0.956844 | + | 1.65730i | 0.0622852 | + | 0.107881i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.09159 | + | 1.89070i | −0.0707576 | + | 0.122556i | ||||
\(239\) | 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 | \(0.510460\pi\) | |||||||
\(242\) | 2.20561 | 0.141782 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.23030 | 0.270817 | ||||||||
\(245\) | −2.48040 | − | 4.29618i | −0.158467 | − | 0.274473i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9176 | + | 18.9099i | −0.694673 | + | 1.20321i | ||||
\(248\) | −7.31173 | + | 12.6643i | −0.464295 | + | 0.804183i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.285997 | − | 0.495361i | −0.0180880 | − | 0.0313294i | ||||
\(251\) | 0.549569 | 0.0346885 | 0.0173443 | − | 0.999850i | \(-0.494479\pi\) | ||||
0.0173443 | + | 0.999850i | \(0.494479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | 0 | ||||||||
\(259\) | 1.29721 | + | 2.24683i | 0.0806046 | + | 0.139611i | ||||
\(260\) | 7.81681 | 0.484778 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.43196 | −0.212027 | ||||||||
\(263\) | 5.94761 | + | 10.3016i | 0.366745 | + | 0.635221i | 0.989055 | − | 0.147550i | \(-0.0471387\pi\) |
−0.622309 | + | 0.782771i | \(0.713805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.571993 | − | 0.990721i | 0.0351373 | − | 0.0608595i | ||||
\(266\) | 1.90841 | − | 3.30545i | 0.117012 | − | 0.202670i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.51234 | − | 9.54766i | −0.336720 | − | 0.583216i | ||||
\(269\) | −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 | \(0.751140\pi\) | |||||||
\(272\) | 2.86525 | + | 4.96276i | 0.173731 | + | 0.300911i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.91764 | − | 5.05350i | 0.176261 | − | 0.305293i | ||||
\(275\) | 1.33641 | − | 2.31473i | 0.0805887 | − | 0.139584i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.53807 | + | 13.0563i | 0.452919 | + | 0.784479i | 0.998566 | − | 0.0535366i | \(-0.0170494\pi\) |
−0.545647 | + | 0.838015i | \(0.683716\pi\) | |||||||
\(278\) | −4.57595 | −0.274447 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | −0.179284 | ||||||||
\(281\) | 3.32605 | + | 5.76088i | 0.198415 | + | 0.343665i | 0.948015 | − | 0.318226i | \(-0.103087\pi\) |
−0.749599 | + | 0.661892i | \(0.769754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.4485 | + | 23.2934i | −0.799428 | + | 1.38465i | 0.120562 | + | 0.992706i | \(0.461530\pi\) |
−0.919989 | + | 0.391943i | \(0.871803\pi\) | |||||||
\(284\) | 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 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.85601 | −0.579765 | ||||||||
\(290\) | −2.71400 | − | 4.70079i | −0.159372 | − | 0.276040i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −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 | 0 | ||||||||
\(295\) | 0.571993 | + | 0.990721i | 0.0333027 | + | 0.0576820i | ||||
\(296\) | −3.81681 | −0.221848 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −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 | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.00924 | − | 8.67625i | −0.287299 | − | 0.497617i | ||||
\(305\) | 2.52884 | 0.144801 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.49359 | −0.142317 | −0.0711583 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711583 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(308\) | −3.19243 | − | 5.52944i | −0.181905 | − | 0.315069i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.99076 | + | 3.44811i | −0.113068 | + | 0.195839i | ||||
\(311\) | −12.1101 | + | 20.9752i | −0.686699 | + | 1.18940i | 0.286201 | + | 0.958170i | \(0.407608\pi\) |
−0.972900 | + | 0.231228i | \(0.925726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5420 | + | 30.3837i | 0.991534 | + | 1.71739i | 0.608219 | + | 0.793770i | \(0.291884\pi\) |
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(314\) | −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 | 0 | ||||||||
\(319\) | 12.6821 | − | 21.9660i | 0.710059 | − | 1.22986i | ||||
\(320\) | −0.591595 | + | 1.02467i | −0.0330712 | + | 0.0572809i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.41679 | + | 4.18601i | 0.134683 | + | 0.233277i | ||||
\(323\) | −12.4896 | −0.694942 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.67282 | 0.259202 | ||||||||
\(326\) | 5.09555 | + | 8.82575i | 0.282216 | + | 0.488813i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.06558 | 0.441329 | ||||||||
\(335\) | −3.29523 | − | 5.70751i | −0.180038 | − | 0.311835i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5905 | − | 23.5394i | 0.740320 | − | 1.28227i | −0.212030 | − | 0.977263i | \(-0.568007\pi\) |
0.952350 | − | 0.305008i | \(-0.0986592\pi\) | |||||||
\(338\) | 2.52686 | − | 4.37665i | 0.137443 | − | 0.238058i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.23558 | + | 3.87214i | 0.121241 | + | 0.209996i | ||||
\(341\) | −18.6050 | −1.00752 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −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 | \(0.948680\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.35601 | + | 9.27689i | 0.286701 | + | 0.496580i | 0.973020 | − | 0.230720i | \(-0.0741081\pi\) |
−0.686319 | + | 0.727300i | \(0.740775\pi\) | |||||||
\(350\) | −0.816810 | −0.0436603 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 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 | 0 | ||||||||
\(355\) | 6.43724 | − | 11.1496i | 0.341653 | − | 0.591761i | ||||
\(356\) | 2.50924 | − | 4.34612i | 0.132989 | − | 0.230344i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.33641 | + | 7.51089i | 0.229186 | + | 0.396963i | ||||
\(359\) | 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 | ||||||||
\(362\) | 0.915664 | + | 1.58598i | 0.0481262 | + | 0.0833571i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.58123 | − | 9.66697i | 0.292536 | − | 0.506687i | ||||
\(365\) | −0.856013 | + | 1.48266i | −0.0448058 | + | 0.0776059i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.23558 | + | 7.33624i | 0.221096 | + | 0.382949i | 0.955141 | − | 0.296152i | \(-0.0957034\pi\) |
−0.734045 | + | 0.679100i | \(0.762370\pi\) | |||||||
\(368\) | 12.6873 | 0.661373 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.03920 | −0.0540256 | ||||||||
\(371\) | −0.816810 | − | 1.41476i | −0.0424067 | − | 0.0734505i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.06163 | + | 8.76700i | −0.262081 | + | 0.453938i | −0.966795 | − | 0.255554i | \(-0.917742\pi\) |
0.704714 | + | 0.709492i | \(0.251075\pi\) | |||||||
\(374\) | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.9216 | 0.612371 | 0.306186 | − | 0.951972i | \(-0.400947\pi\) | ||||
0.306186 | + | 0.951972i | \(0.400947\pi\) | |||||||
\(380\) | −3.90841 | − | 6.76956i | −0.200497 | − | 0.347271i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | \(0.0859705\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.90841 | − | 3.30545i | −0.0972613 | − | 0.168462i | ||||
\(386\) | 10.7467 | 0.546993 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.1070 | −0.665409 | ||||||||
\(389\) | 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 | ||||
\(392\) | 5.21090 | − | 9.02554i | 0.263190 | − | 0.455858i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.66887 | − | 2.89057i | −0.0840765 | − | 0.145625i | ||||
\(395\) | 0.287973 | 0.0144895 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9793 | −1.15330 | −0.576648 | − | 0.816993i | \(-0.695640\pi\) | ||||
−0.576648 | + | 0.816993i | \(0.695640\pi\) | |||||||
\(398\) | 3.73973 | + | 6.47741i | 0.187456 | + | 0.324683i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.07199 | + | 1.85675i | −0.0535997 | + | 0.0928373i | ||||
\(401\) | −5.53279 | + | 9.58307i | −0.276294 | + | 0.478556i | −0.970461 | − | 0.241259i | \(-0.922440\pi\) |
0.694167 | + | 0.719814i | \(0.255773\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −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 | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.81681 | − | 15.2712i | 0.435963 | − | 0.755110i | −0.561411 | − | 0.827537i | \(-0.689741\pi\) |
0.997374 | + | 0.0724270i | \(0.0230744\pi\) | |||||||
\(410\) | −0.420748 | + | 0.728756i | −0.0207792 | + | 0.0359907i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.51960 | − | 2.63203i | −0.0748654 | − | 0.129671i | ||||
\(413\) | 1.63362 | 0.0803852 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.28402 | −0.210294 | ||||||||
\(416\) | 12.6821 | + | 21.9660i | 0.621789 | + | 1.07697i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.57199 | + | 6.18687i | −0.174712 | + | 0.302610i | ||||
\(419\) | 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 | \(0.872664\pi\) | |||||||
\(422\) | −4.79608 | −0.233469 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.40332 | 0.116716 | ||||||||
\(425\) | 1.33641 | + | 2.31473i | 0.0648255 | + | 0.112281i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.80560 | − | 3.12739i | 0.0873790 | − | 0.151345i | ||||
\(428\) | −9.96806 | + | 17.2652i | −0.481824 | + | 0.834544i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.134751 | − | 0.233396i | −0.00649827 | − | 0.0112553i | ||||
\(431\) | 5.23030 | 0.251935 | 0.125967 | − | 0.992034i | \(-0.459797\pi\) | ||||
0.125967 | + | 0.992034i | \(0.459797\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.3434 | 1.65044 | 0.825219 | − | 0.564813i | \(-0.191052\pi\) | ||||
0.825219 | + | 0.564813i | \(0.191052\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.77365 | + | 16.9285i | 0.466471 | + | 0.807952i | 0.999267 | − | 0.0382924i | \(-0.0121918\pi\) |
−0.532796 | + | 0.846244i | \(0.678859\pi\) | |||||||
\(440\) | 5.61515 | 0.267692 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.14399 | 0.339805 | ||||||||
\(443\) | 5.25208 | + | 9.09686i | 0.249534 | + | 0.432205i | 0.963396 | − | 0.268081i | \(-0.0863893\pi\) |
−0.713863 | + | 0.700286i | \(0.753056\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.50000 | − | 2.59808i | 0.0711068 | − | 0.123161i | ||||
\(446\) | 2.62156 | − | 4.54068i | 0.124135 | − | 0.215007i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.844801 | + | 1.46324i | 0.0399131 | + | 0.0691315i | ||||
\(449\) | −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 | ||||||||
\(452\) | −16.8313 | − | 29.1527i | −0.791679 | − | 1.37123i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.764419 | − | 1.32401i | 0.0358759 | − | 0.0621390i | ||||
\(455\) | 3.33641 | − | 5.77883i | 0.156413 | − | 0.270916i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.01319 | + | 12.1472i | 0.328063 | + | 0.568222i | 0.982127 | − | 0.188217i | \(-0.0602708\pi\) |
−0.654064 | + | 0.756439i | \(0.726937\pi\) | |||||||
\(458\) | −1.45704 | −0.0680832 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.89917 | 0.461551 | ||||||||
\(461\) | −12.0513 | − | 20.8734i | −0.561283 | − | 0.972171i | −0.997385 | − | 0.0722736i | \(-0.976975\pi\) |
0.436102 | − | 0.899897i | \(-0.356359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9700 | − | 29.3930i | 0.788664 | − | 1.36601i | −0.138121 | − | 0.990415i | \(-0.544106\pi\) |
0.926785 | − | 0.375591i | \(-0.122560\pi\) | |||||||
\(464\) | −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 | \(0.281695\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.41123 | −0.434570 | ||||||||
\(470\) | 1.98963 | + | 3.44615i | 0.0917750 | + | 0.158959i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.20166 | + | 2.08134i | −0.0553109 | + | 0.0958013i | ||||
\(473\) | 0.629668 | − | 1.09062i | 0.0289521 | − | 0.0501466i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.33641 | − | 4.04678i | −0.107202 | − | 0.185679i | ||||
\(476\) | 6.38485 | 0.292649 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.64645 | 0.212524 | ||||||||
\(479\) | 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 | ||||
\(482\) | −7.54005 | + | 13.0597i | −0.343440 | + | 0.594855i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.22522 | − | 5.58624i | −0.146601 | − | 0.253920i | ||||
\(485\) | −7.83528 | −0.355782 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0185 | −1.08838 | −0.544190 | − | 0.838962i | \(-0.683163\pi\) | ||||
−0.544190 | + | 0.838962i | \(0.683163\pi\) | |||||||
\(488\) | 2.65633 | + | 4.60090i | 0.120246 | + | 0.208273i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.41877 | − | 2.45738i | 0.0640935 | − | 0.111013i | ||||
\(491\) | 7.38880 | − | 12.7978i | 0.333452 | − | 0.577556i | −0.649734 | − | 0.760161i | \(-0.725120\pi\) |
0.983186 | + | 0.182606i | \(0.0584531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 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 | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4280 | + | 21.5259i | −0.556354 | + | 0.963633i | 0.441443 | + | 0.897289i | \(0.354467\pi\) |
−0.997797 | + | 0.0663440i | \(0.978867\pi\) | |||||||
\(500\) | −0.836412 | + | 1.44871i | −0.0374055 | + | 0.0647882i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.157175 | + | 0.272235i | 0.00701506 | + | 0.0121504i | ||||
\(503\) | −38.9154 | −1.73515 | −0.867576 | − | 0.497305i | \(-0.834323\pi\) | ||||
−0.867576 | + | 0.497305i | \(0.834323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.20166 | −0.186971 | ||||||||
\(506\) | −4.52355 | − | 7.83503i | −0.201097 | − | 0.348309i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.82935 | − | 3.16853i | 0.0811644 | − | 0.140581i | ||||
\(509\) | 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 | ||||
\(512\) | −20.6459 | −0.912428 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.2959 | −0.454132 | ||||||||
\(515\) | −0.908405 | − | 1.57340i | −0.0400291 | − | 0.0693325i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.29721 | + | 16.1032i | −0.408891 | + | 0.708220i | ||||
\(518\) | −0.741995 | + | 1.28517i | −0.0326014 | + | 0.0564672i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.90841 | + | 8.50161i | 0.215248 | + | 0.372820i | ||||
\(521\) | 23.0290 | 1.00892 | 0.504460 | − | 0.863435i | \(-0.331692\pi\) | ||||
0.504460 | + | 0.863435i | \(0.331692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.1170 | −1.79792 | −0.898961 | − | 0.438028i | \(-0.855677\pi\) | ||||
−0.898961 | + | 0.438028i | \(0.855677\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.00924 | − | 10.4083i | −0.261271 | − | 0.452535i | ||||
\(530\) | 0.654353 | 0.0284233 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.1625 | −0.483954 | ||||||||
\(533\) | −3.43724 | − | 5.95348i | −0.148883 | − | 0.257874i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.95882 | + | 10.3210i | −0.257622 | + | 0.446215i | ||||
\(536\) | 6.92272 | − | 11.9905i | 0.299016 | − | 0.517911i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −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 | 0 | ||||||||
\(544\) | −7.25405 | + | 12.5644i | −0.311015 | + | 0.538694i | ||||
\(545\) | −8.32605 | + | 14.4211i | −0.356649 | + | 0.617734i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0204 | − | 34.6764i | −0.856013 | − | 1.48266i | −0.875702 | − | 0.482851i | \(-0.839601\pi\) |
0.0196900 | − | 0.999806i | \(-0.493732\pi\) | |||||||
\(548\) | −17.0656 | −0.729005 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.52884 | 0.0651898 | ||||||||
\(551\) | −22.1717 | − | 38.4025i | −0.944546 | − | 1.63600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.401295\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.20166 | 0.0931203 | ||||||||
\(560\) | 1.53081 | + | 2.65145i | 0.0646887 | + | 0.112044i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −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 | \(-0.0457378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0616 | − | 17.4272i | −0.423296 | − | 0.733170i | ||||
\(566\) | −15.3849 | −0.646674 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.0471 | 1.13487 | ||||||||
\(569\) | 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 | \(0.304106\pi\) | |||||||
\(572\) | −10.4465 | + | 18.0938i | −0.436789 | + | 0.756541i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.600830 | + | 1.04067i | 0.0250782 | + | 0.0434367i | ||||
\(575\) | 5.91764 | 0.246783 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2386 | 1.17559 | 0.587794 | − | 0.809010i | \(-0.299996\pi\) | ||||
0.587794 | + | 0.809010i | \(0.299996\pi\) | |||||||
\(578\) | −2.81879 | − | 4.88228i | −0.117246 | − | 0.203076i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.93724 | + | 13.7477i | −0.329576 | + | 0.570842i | ||||
\(581\) | −3.05880 | + | 5.29801i | −0.126901 | + | 0.219798i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(0.711604\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.2633 | + | 28.1688i | −0.670117 | + | 1.16068i | ||||
\(590\) | −0.327176 | + | 0.566686i | −0.0134696 | + | 0.0233301i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.94761 | + | 3.37336i | 0.0800462 | + | 0.138644i | ||||
\(593\) | 7.73840 | 0.317778 | 0.158889 | − | 0.987296i | \(-0.449209\pi\) | ||||
0.158889 | + | 0.987296i | \(0.449209\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.81681 | 0.156474 | ||||||||
\(596\) | 16.7919 | + | 29.0845i | 0.687824 | + | 1.19135i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.90841 | − | 13.6978i | 0.323399 | − | 0.560143i | ||||
\(599\) | −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 | \(-0.453493\pi\) | |||||||
\(602\) | −0.384851 | −0.0156853 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.08405 | −0.206867 | ||||||||
\(605\) | −1.92801 | − | 3.33941i | −0.0783846 | − | 0.135766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.319917 | − | 0.554113i | 0.0129850 | − | 0.0224907i | −0.859460 | − | 0.511203i | \(-0.829200\pi\) |
0.872445 | + | 0.488712i | \(0.162533\pi\) | |||||||
\(608\) | 12.6821 | − | 21.9660i | 0.514325 | − | 0.890838i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.723239 | + | 1.25269i | 0.0292831 | + | 0.0507198i | ||||
\(611\) | −32.5081 | −1.31514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.7467 | 1.72652 | 0.863262 | − | 0.504757i | \(-0.168418\pi\) | ||||
0.863262 | + | 0.504757i | \(0.168418\pi\) | |||||||
\(614\) | −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 | 0 | ||||||||
\(619\) | 6.82605 | + | 11.8231i | 0.274362 | + | 0.475209i | 0.969974 | − | 0.243209i | \(-0.0782000\pi\) |
−0.695612 | + | 0.718418i | \(0.744867\pi\) | |||||||
\(620\) | 11.6442 | 0.467642 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.8538 | −0.555485 | ||||||||
\(623\) | −2.14201 | − | 3.71007i | −0.0858178 | − | 0.148641i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −10.0339 | + | 17.3793i | −0.401036 | + | 0.694615i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.99472 | − | 5.18700i | 0.118935 | − | 0.206002i | ||||
\(635\) | 1.09357 | − | 1.89412i | 0.0433971 | − | 0.0751659i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.5905 | + | 20.0753i | 0.459231 | + | 0.795411i | ||||
\(638\) | 14.5081 | 0.574381 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.5328 | −0.455874 | ||||||||
\(641\) | 13.1429 | + | 22.7641i | 0.519112 | + | 0.899128i | 0.999753 | + | 0.0222106i | \(0.00707044\pi\) |
−0.480642 | + | 0.876917i | \(0.659596\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.2913 | + | 17.8250i | −0.405848 | + | 0.702950i | −0.994420 | − | 0.105495i | \(-0.966357\pi\) |
0.588571 | + | 0.808445i | \(0.299691\pi\) | |||||||
\(644\) | 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 | \(0.651104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.05767 | −0.120024 | ||||||||
\(650\) | 1.33641 | + | 2.31473i | 0.0524184 | + | 0.0907913i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 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 | \(0.0470342\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.00000 | + | 5.19615i | 0.117220 | + | 0.203030i | ||||
\(656\) | 3.15415 | 0.123149 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.68242 | 0.221524 | ||||||||
\(659\) | −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 | \(-0.114953\pi\) | |||||||
\(662\) | 4.79834 | − | 8.31097i | 0.186493 | − | 0.323015i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.50000 | − | 7.79423i | −0.174634 | − | 0.302475i | ||||
\(665\) | −6.67282 | −0.258761 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.1562 | 2.17438 | ||||||||
\(668\) | −11.7941 | − | 20.4280i | −0.456327 | − | 0.790382i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.88485 | − | 3.26466i | 0.0728181 | − | 0.126125i | ||||
\(671\) | −3.37957 | + | 5.85358i | −0.130467 | + | 0.225975i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7644 | − | 29.0368i | −0.646221 | − | 1.11929i | −0.984018 | − | 0.178068i | \(-0.943015\pi\) |
0.337797 | − | 0.941219i | \(-0.390318\pi\) | |||||||
\(674\) | 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 | \(0.656196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.59442 | + | 9.68981i | −0.214694 | + | 0.371861i | ||||
\(680\) | −2.80757 | + | 4.86286i | −0.107666 | + | 0.186482i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.32096 | − | 9.21618i | −0.203750 | − | 0.352906i | ||||
\(683\) | 34.5865 | 1.32342 | 0.661708 | − | 0.749762i | \(-0.269832\pi\) | ||||
0.661708 | + | 0.749762i | \(0.269832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2017 | −0.389785 | ||||||||
\(686\) | −4.88485 | − | 8.46081i | −0.186504 | − | 0.323035i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.4795 | −0.511674 | ||||||||
\(695\) | 4.00000 | + | 6.92820i | 0.151729 | + | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.96608 | − | 3.40535i | 0.0744706 | − | 0.128987i | ||||
\(698\) | −3.06360 | + | 5.30632i | −0.115959 | + | 0.200847i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.19440 | + | 2.06876i | 0.0451441 | + | 0.0781919i | ||||
\(701\) | 19.4712 | 0.735416 | 0.367708 | − | 0.929941i | \(-0.380143\pi\) | ||||
0.367708 | + | 0.929941i | \(0.380143\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −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 | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.54316 | − | 13.0651i | −0.283289 | − | 0.490671i | 0.688904 | − | 0.724853i | \(-0.258092\pi\) |
−0.972193 | + | 0.234182i | \(0.924759\pi\) | |||||||
\(710\) | 7.36412 | 0.276370 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.30249 | 0.236196 | ||||||||
\(713\) | −20.5957 | − | 35.6729i | −0.771317 | − | 1.33596i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24482 | + | 10.8163i | −0.233543 | + | 0.404508i | ||||
\(716\) | 12.6821 | − | 21.9660i | 0.473951 | − | 0.820907i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.05465 | + | 5.29081i | 0.113999 | + | 0.197451i | ||||
\(719\) | 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 | ||||||||
\(722\) | 0.810881 | + | 1.40449i | 0.0301779 | + | 0.0522696i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.67791 | − | 4.63827i | 0.0995236 | − | 0.172380i | ||||
\(725\) | −4.74482 | + | 8.21826i | −0.176218 | + | 0.305219i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.8857 | + | 30.9789i | 0.663344 | + | 1.14895i | 0.979732 | + | 0.200315i | \(0.0641966\pi\) |
−0.316388 | + | 0.948630i | \(0.602470\pi\) | |||||||
\(728\) | 14.0185 | 0.519559 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.979268 | −0.0362443 | ||||||||
\(731\) | 0.629668 | + | 1.09062i | 0.0232891 | + | 0.0403379i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | − | 19.0526i | 0.406294 | − | 0.703722i | −0.588177 | − | 0.808732i | \(-0.700154\pi\) |
0.994471 | + | 0.105010i | \(0.0334875\pi\) | |||||||
\(734\) | −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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.08631 | 0.223889 | 0.111944 | − | 0.993714i | \(-0.464292\pi\) | ||||
0.111944 | + | 0.993714i | \(0.464292\pi\) | |||||||
\(740\) | 1.51960 | + | 2.63203i | 0.0558617 | + | 0.0967552i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | \(0.321615\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0381 | + | 17.3865i | 0.367767 | + | 0.636990i | ||||
\(746\) | −5.79043 | −0.212003 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −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 | 0 | ||||||||
\(754\) | 12.6821 | + | 21.9660i | 0.461853 | + | 0.799953i | ||||
\(755\) | −3.03920 | −0.110608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.8986 | −1.52283 | −0.761415 | − | 0.648264i | \(-0.775495\pi\) | ||||
−0.761415 | + | 0.648264i | \(0.775495\pi\) | |||||||
\(758\) | 3.40954 | + | 5.90549i | 0.123840 | + | 0.214497i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.90841 | − | 8.50161i | 0.178047 | − | 0.308386i | ||||
\(761\) | −3.98568 | + | 6.90340i | −0.144481 | + | 0.250248i | −0.929179 | − | 0.369630i | \(-0.879485\pi\) |
0.784698 | + | 0.619878i | \(0.212818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 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 | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.01432 | + | 5.22095i | −0.108699 | + | 0.188272i | −0.915244 | − | 0.402901i | \(-0.868002\pi\) |
0.806544 | + | 0.591174i | \(0.201335\pi\) | |||||||
\(770\) | 1.09159 | − | 1.89070i | 0.0393383 | − | 0.0681360i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −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 | 0 | ||||||||
\(775\) | 6.96080 | 0.250039 | ||||||||
\(776\) | −8.23030 | − | 14.2553i | −0.295451 | − | 0.511735i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.6359 | −0.379853 | ||||||||
\(785\) | 0.100830 | + | 0.174643i | 0.00359879 | + | 0.00623329i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.41877 | + | 14.5817i | −0.300097 | + | 0.519783i | −0.976158 | − | 0.217063i | \(-0.930352\pi\) |
0.676061 | + | 0.736846i | \(0.263686\pi\) | |||||||
\(788\) | −4.88070 | + | 8.45362i | −0.173868 | + | 0.301148i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.0823593 | + | 0.142651i | 0.00293021 | + | 0.00507528i | ||||
\(791\) | −28.7361 | −1.02174 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −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 | \(0.965381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.29721 | − | 16.1032i | −0.328912 | − | 0.569692i | ||||
\(800\) | −5.42801 | −0.191909 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.32944 | −0.223500 | ||||||||
\(803\) | −2.28797 | − | 3.96289i | −0.0807408 | − | 0.139847i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.22522 | − | 7.31829i | 0.148919 | − | 0.257936i | ||||
\(806\) | 9.30249 | − | 16.1124i | 0.327666 | − | 0.567535i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.41349 | − | 7.64439i | −0.155266 | − | 0.268929i | ||||
\(809\) | −29.1809 | −1.02595 | −0.512973 | − | 0.858404i | \(-0.671456\pi\) | ||||
−0.512973 | + | 0.858404i | \(0.671456\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.38880 | − | 2.40548i | 0.0486775 | − | 0.0843120i | ||||
\(815\) | 8.90841 | − | 15.4298i | 0.312048 | − | 0.540483i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.10083 | − | 1.90669i | −0.0385132 | − | 0.0667068i | ||||
\(818\) | 10.0863 | 0.352660 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.46100 | 0.0859417 | ||||||||
\(821\) | −11.8588 | − | 20.5401i | −0.413876 | − | 0.716855i | 0.581434 | − | 0.813594i | \(-0.302492\pi\) |
−0.995310 | + | 0.0967393i | \(0.969159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.68404 | + | 16.7732i | −0.337564 | + | 0.584678i | −0.983974 | − | 0.178312i | \(-0.942936\pi\) |
0.646410 | + | 0.762990i | \(0.276270\pi\) | |||||||
\(824\) | 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 | \(0.862395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.6442 | −0.925391 | −0.462695 | − | 0.886517i | \(-0.653118\pi\) | ||||
−0.462695 | + | 0.886517i | \(0.653118\pi\) | |||||||
\(830\) | −1.22522 | − | 2.12214i | −0.0425278 | − | 0.0736604i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.76442 | − | 4.78811i | 0.0958390 | − | 0.165998i | ||||
\(833\) | −6.62967 | + | 11.4829i | −0.229704 | + | 0.397860i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.05042 | − | 12.2117i | −0.243990 | − | 0.422603i | ||||
\(836\) | 20.8930 | 0.722598 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.1836 | 0.731775 | ||||||||
\(839\) | −12.5196 | − | 21.6846i | −0.432225 | − | 0.748635i | 0.564840 | − | 0.825201i | \(-0.308938\pi\) |
−0.997065 | + | 0.0765655i | \(0.975605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.5266 | + | 52.8736i | −1.05264 | + | 1.82323i | ||||
\(842\) | 1.44648 | − | 2.50537i | 0.0498489 | − | 0.0863409i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.01319 | + | 12.1472i | 0.241404 | + | 0.418124i | ||||
\(845\) | −8.83528 | −0.303943 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.50641 | −0.189203 | ||||||||
\(848\) | −1.22635 | − | 2.12409i | −0.0421129 | − | 0.0729417i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.764419 | + | 1.32401i | −0.0262193 | + | 0.0454132i | ||||
\(851\) | 5.37562 | − | 9.31084i | 0.184274 | − | 0.319171i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.43724 | + | 9.41758i | 0.186168 | + | 0.322452i | 0.943969 | − | 0.330033i | \(-0.107060\pi\) |
−0.757802 | + | 0.652485i | \(0.773727\pi\) | |||||||
\(854\) | 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 | \(0.936206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.33246 | − | 4.03994i | 0.0795825 | − | 0.137841i | −0.823487 | − | 0.567335i | \(-0.807975\pi\) |
0.903070 | + | 0.429494i | \(0.141308\pi\) | |||||||
\(860\) | −0.394086 | + | 0.682577i | −0.0134382 | + | 0.0232757i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.49585 | + | 2.59088i | 0.0509488 | + | 0.0882459i | ||||
\(863\) | 28.0594 | 0.955152 | 0.477576 | − | 0.878590i | \(-0.341516\pi\) | ||||
0.477576 | + | 0.878590i | \(0.341516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.36638 | 0.148461 | ||||||||
\(866\) | 9.82209 | + | 17.0124i | 0.333768 | + | 0.578104i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.8168 | −0.535012 | ||||||||
\(875\) | 0.714003 | + | 1.23669i | 0.0241377 | + | 0.0418078i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.3342 | + | 30.0236i | −0.585333 | + | 1.01383i | 0.409501 | + | 0.912310i | \(0.365703\pi\) |
−0.994834 | + | 0.101516i | \(0.967631\pi\) | |||||||
\(878\) | −5.59046 | + | 9.68297i | −0.188669 | + | 0.326784i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.86525 | − | 4.96276i | −0.0965875 | − | 0.167294i | ||||
\(881\) | 5.29854 | 0.178512 | 0.0892561 | − | 0.996009i | \(-0.471551\pi\) | ||||
0.0892561 | + | 0.996009i | \(0.471551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.3025 | −0.346706 | −0.173353 | − | 0.984860i | \(-0.555460\pi\) | ||||
−0.173353 | + | 0.984860i | \(0.555460\pi\) | |||||||
\(884\) | −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 | \(-0.0783208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.56163 | − | 2.70482i | −0.0523753 | − | 0.0907167i | ||||
\(890\) | 1.71598 | 0.0575198 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.3338 | −0.513413 | ||||||||
\(893\) | 16.2541 | + | 28.1528i | 0.543921 | + | 0.942099i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.58123 | − | 13.1311i | 0.253413 | − | 0.438923i | ||||
\(896\) | −8.23445 | + | 14.2625i | −0.275094 | + | 0.476476i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.1378 | − | 36.6117i | 0.703032 | − | 1.21769i | ||||
\(905\) | 1.60083 | − | 2.77272i | 0.0532134 | − | 0.0921683i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.39606 | + | 14.5424i | 0.278787 | + | 0.482873i | 0.971083 | − | 0.238740i | \(-0.0767344\pi\) |
−0.692297 | + | 0.721613i | \(0.743401\pi\) | |||||||
\(908\) | −4.47116 | −0.148381 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.81681 | 0.126526 | ||||||||
\(911\) | 18.6768 | + | 32.3491i | 0.618789 | + | 1.07177i | 0.989707 | + | 0.143109i | \(0.0457098\pi\) |
−0.370918 | + | 0.928666i | \(0.620957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 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 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.1316 | 1.22486 | 0.612429 | − | 0.790526i | \(-0.290193\pi\) | ||||
0.612429 | + | 0.790526i | \(0.290193\pi\) | |||||||
\(920\) | 6.21598 | + | 10.7664i | 0.204935 | + | 0.354957i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.89324 | − | 11.9394i | 0.227017 | − | 0.393205i | ||||
\(923\) | −30.0801 | + | 52.1003i | −0.990098 | + | 1.71490i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.908405 | + | 1.57340i | 0.0298682 | + | 0.0517332i | ||||
\(926\) | 19.4135 | 0.637967 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −51.5098 | −1.69089 | ||||||||
\(929\) | −23.9977 | − | 41.5653i | −0.787340 | − | 1.36371i | −0.927591 | − | 0.373597i | \(-0.878124\pi\) |
0.140251 | − | 0.990116i | \(-0.455209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.5905 | − | 20.0753i | 0.379862 | − | 0.657941i | ||||
\(932\) | 5.20259 | − | 9.01115i | 0.170417 | − | 0.295170i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.82831 | + | 13.5590i | 0.256150 | + | 0.443665i | ||||
\(935\) | −7.14399 | −0.233633 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0079 | 0.718967 | 0.359483 | − | 0.933151i | \(-0.382953\pi\) | ||||
0.359483 | + | 0.933151i | \(0.382953\pi\) | |||||||
\(938\) | −2.69158 | − | 4.66195i | −0.0878832 | − | 0.152218i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.81879 | − | 10.0784i | 0.189788 | − | 0.328722i | ||||
\(941\) | 20.2921 | − | 35.1470i | 0.661504 | − | 1.14576i | −0.318716 | − | 0.947850i | \(-0.603252\pi\) |
0.980220 | − | 0.197909i | \(-0.0634150\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | 0 | ||||||||
\(949\) | 4.00000 | − | 6.92820i | 0.129845 | − | 0.224899i | ||||
\(950\) | 1.33641 | − | 2.31473i | 0.0433589 | − | 0.0750999i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.00924 | + | 6.94420i | 0.129940 | + | 0.225063i | ||||
\(953\) | −2.50811 | −0.0812455 | −0.0406227 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406227 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.83754 | −0.0918207 | ||||||||
\(956\) | −6.79439 | − | 11.7682i | −0.219746 | − | 0.380612i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 44.1025 | 1.42045 | ||||||||
\(965\) | −9.39409 | − | 16.2710i | −0.302406 | − | 0.523783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.8765 | − | 18.8386i | 0.349763 | − | 0.605808i | −0.636444 | − | 0.771323i | \(-0.719595\pi\) |
0.986207 | + | 0.165515i | \(0.0529286\pi\) | |||||||
\(968\) | 4.05042 | − | 7.01552i | 0.130185 | − | 0.225488i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.24086 | − | 3.88129i | −0.0719498 | − | 0.124621i | ||||
\(971\) | −22.7512 | −0.730122 | −0.365061 | − | 0.930984i | \(-0.618952\pi\) | ||||
−0.365061 | + | 0.930984i | \(0.618952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | \(-0.0495840\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00924 | + | 6.94420i | 0.128136 | + | 0.221938i | ||||
\(980\) | −8.29854 | −0.265087 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.45269 | 0.269736 | ||||||||
\(983\) | 16.8949 | + | 29.2629i | 0.538865 | + | 0.933341i | 0.998966 | + | 0.0454743i | \(0.0144799\pi\) |
−0.460101 | + | 0.887867i | \(0.652187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.91764 | + | 5.05350i | −0.0929638 | + | 0.161018i | ||||
\(986\) | −7.25405 | + | 12.5644i | −0.231016 | + | 0.400132i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.25801 | − | 9.10713i | 0.166774 | − | 0.288861i | ||||
\(995\) | 6.53807 | − | 11.3243i | 0.207271 | − | 0.359004i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.8392 | − | 44.7549i | −0.818337 | − | 1.41740i | −0.906907 | − | 0.421331i | \(-0.861563\pi\) |
0.0885702 | − | 0.996070i | \(-0.471770\pi\) | |||||||
\(998\) | −14.2175 | −0.450046 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 135.2.e.b.91.2 | 6 | ||
3.2 | odd | 2 | 45.2.e.b.31.2 | yes | 6 | ||
4.3 | odd | 2 | 2160.2.q.k.1441.2 | 6 | |||
5.2 | odd | 4 | 675.2.k.b.199.3 | 12 | |||
5.3 | odd | 4 | 675.2.k.b.199.4 | 12 | |||
5.4 | even | 2 | 675.2.e.b.226.2 | 6 | |||
9.2 | odd | 6 | 45.2.e.b.16.2 | ✓ | 6 | ||
9.4 | even | 3 | 405.2.a.i.1.2 | 3 | |||
9.5 | odd | 6 | 405.2.a.j.1.2 | 3 | |||
9.7 | even | 3 | inner | 135.2.e.b.46.2 | 6 | ||
12.11 | even | 2 | 720.2.q.i.481.2 | 6 | |||
15.2 | even | 4 | 225.2.k.b.49.4 | 12 | |||
15.8 | even | 4 | 225.2.k.b.49.3 | 12 | |||
15.14 | odd | 2 | 225.2.e.b.76.2 | 6 | |||
36.7 | odd | 6 | 2160.2.q.k.721.2 | 6 | |||
36.11 | even | 6 | 720.2.q.i.241.2 | 6 | |||
36.23 | even | 6 | 6480.2.a.bv.1.2 | 3 | |||
36.31 | odd | 6 | 6480.2.a.bs.1.2 | 3 | |||
45.2 | even | 12 | 225.2.k.b.124.3 | 12 | |||
45.4 | even | 6 | 2025.2.a.o.1.2 | 3 | |||
45.7 | odd | 12 | 675.2.k.b.424.4 | 12 | |||
45.13 | odd | 12 | 2025.2.b.m.649.4 | 6 | |||
45.14 | odd | 6 | 2025.2.a.n.1.2 | 3 | |||
45.22 | odd | 12 | 2025.2.b.m.649.3 | 6 | |||
45.23 | even | 12 | 2025.2.b.l.649.3 | 6 | |||
45.29 | odd | 6 | 225.2.e.b.151.2 | 6 | |||
45.32 | even | 12 | 2025.2.b.l.649.4 | 6 | |||
45.34 | even | 6 | 675.2.e.b.451.2 | 6 | |||
45.38 | even | 12 | 225.2.k.b.124.4 | 12 | |||
45.43 | odd | 12 | 675.2.k.b.424.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.2 | ✓ | 6 | 9.2 | odd | 6 | ||
45.2.e.b.31.2 | yes | 6 | 3.2 | odd | 2 | ||
135.2.e.b.46.2 | 6 | 9.7 | even | 3 | inner | ||
135.2.e.b.91.2 | 6 | 1.1 | even | 1 | trivial | ||
225.2.e.b.76.2 | 6 | 15.14 | odd | 2 | |||
225.2.e.b.151.2 | 6 | 45.29 | odd | 6 | |||
225.2.k.b.49.3 | 12 | 15.8 | even | 4 | |||
225.2.k.b.49.4 | 12 | 15.2 | even | 4 | |||
225.2.k.b.124.3 | 12 | 45.2 | even | 12 | |||
225.2.k.b.124.4 | 12 | 45.38 | even | 12 | |||
405.2.a.i.1.2 | 3 | 9.4 | even | 3 | |||
405.2.a.j.1.2 | 3 | 9.5 | odd | 6 | |||
675.2.e.b.226.2 | 6 | 5.4 | even | 2 | |||
675.2.e.b.451.2 | 6 | 45.34 | even | 6 | |||
675.2.k.b.199.3 | 12 | 5.2 | odd | 4 | |||
675.2.k.b.199.4 | 12 | 5.3 | odd | 4 | |||
675.2.k.b.424.3 | 12 | 45.43 | odd | 12 | |||
675.2.k.b.424.4 | 12 | 45.7 | odd | 12 | |||
720.2.q.i.241.2 | 6 | 36.11 | even | 6 | |||
720.2.q.i.481.2 | 6 | 12.11 | even | 2 | |||
2025.2.a.n.1.2 | 3 | 45.14 | odd | 6 | |||
2025.2.a.o.1.2 | 3 | 45.4 | even | 6 | |||
2025.2.b.l.649.3 | 6 | 45.23 | even | 12 | |||
2025.2.b.l.649.4 | 6 | 45.32 | even | 12 | |||
2025.2.b.m.649.3 | 6 | 45.22 | odd | 12 | |||
2025.2.b.m.649.4 | 6 | 45.13 | odd | 12 | |||
2160.2.q.k.721.2 | 6 | 36.7 | odd | 6 | |||
2160.2.q.k.1441.2 | 6 | 4.3 | odd | 2 | |||
6480.2.a.bs.1.2 | 3 | 36.31 | odd | 6 | |||
6480.2.a.bv.1.2 | 3 | 36.23 | even | 6 |