Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(1049,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.d (of order \(2\), degree \(1\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 4x^{8} - 30x^{6} + 36x^{4} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.1 | ||
Root | \(-0.721683 + 1.57454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.1049 |
Dual form | 1050.2.d.h.1049.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.57454 | − | 0.721683i | −0.909060 | − | 0.416664i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.57454 | − | 0.721683i | −0.642803 | − | 0.294626i | ||||
\(7\) | −2.29622 | − | 1.31429i | −0.867891 | − | 0.496756i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.95835 | + | 2.27264i | 0.652782 | + | 0.757546i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.91669i | 1.18093i | 0.807064 | + | 0.590464i | \(0.201055\pi\) | ||||
−0.807064 | + | 0.590464i | \(0.798945\pi\) | |||||||
\(12\) | −1.57454 | − | 0.721683i | −0.454530 | − | 0.208332i | ||||
\(13\) | 4.99166 | 1.38444 | 0.692219 | − | 0.721688i | \(-0.256633\pi\) | ||||
0.692219 | + | 0.721688i | \(0.256633\pi\) | |||||||
\(14\) | −2.29622 | − | 1.31429i | −0.613691 | − | 0.351259i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.54830i | − | 0.860588i | −0.902689 | − | 0.430294i | \(-0.858410\pi\) | ||
0.902689 | − | 0.430294i | \(-0.141590\pi\) | |||||||
\(18\) | 1.95835 | + | 2.27264i | 0.461587 | + | 0.535666i | ||||
\(19\) | 3.14908i | 0.722448i | 0.932479 | + | 0.361224i | \(0.117641\pi\) | ||||
−0.932479 | + | 0.361224i | \(0.882359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.66699 | + | 3.72655i | 0.581985 | + | 0.813200i | ||||
\(22\) | 3.91669i | 0.835041i | ||||||||
\(23\) | 7.54528 | 1.57330 | 0.786649 | − | 0.617400i | \(-0.211814\pi\) | ||||
0.786649 | + | 0.617400i | \(0.211814\pi\) | |||||||
\(24\) | −1.57454 | − | 0.721683i | −0.321401 | − | 0.147313i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.99166 | 0.978946 | ||||||||
\(27\) | −1.44337 | − | 4.99166i | −0.277776 | − | 0.960646i | ||||
\(28\) | −2.29622 | − | 1.31429i | −0.433945 | − | 0.248378i | ||||
\(29\) | − | 7.54528i | − | 1.40112i | −0.713592 | − | 0.700561i | \(-0.752933\pi\) | ||
0.713592 | − | 0.700561i | \(-0.247067\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.19323i | − | 0.753126i | −0.926391 | − | 0.376563i | \(-0.877106\pi\) | ||
0.926391 | − | 0.376563i | \(-0.122894\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.82661 | − | 6.16698i | 0.492050 | − | 1.07353i | ||||
\(34\) | − | 3.54830i | − | 0.608528i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.95835 | + | 2.27264i | 0.326391 | + | 0.378773i | ||||
\(37\) | − | 10.4620i | − | 1.71994i | −0.510347 | − | 0.859968i | \(-0.670483\pi\) | ||
0.510347 | − | 0.859968i | \(-0.329517\pi\) | |||||||
\(38\) | 3.14908i | 0.510848i | ||||||||
\(39\) | −7.85957 | − | 3.60240i | −1.25854 | − | 0.576846i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.32176 | 1.45581 | 0.727907 | − | 0.685675i | \(-0.240493\pi\) | ||||
0.727907 | + | 0.685675i | \(0.240493\pi\) | |||||||
\(42\) | 2.66699 | + | 3.72655i | 0.411525 | + | 0.575019i | ||||
\(43\) | 2.91669i | 0.444791i | 0.974956 | + | 0.222396i | \(0.0713877\pi\) | ||||
−0.974956 | + | 0.222396i | \(0.928612\pi\) | |||||||
\(44\) | 3.91669i | 0.590464i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.54528 | 1.11249 | ||||||||
\(47\) | 8.00387i | 1.16748i | 0.811939 | + | 0.583742i | \(0.198412\pi\) | ||||
−0.811939 | + | 0.583742i | \(0.801588\pi\) | |||||||
\(48\) | −1.57454 | − | 0.721683i | −0.227265 | − | 0.104166i | ||||
\(49\) | 3.54528 | + | 6.03581i | 0.506468 | + | 0.862259i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.56075 | + | 5.58693i | −0.358576 | + | 0.782327i | ||||
\(52\) | 4.99166 | 0.692219 | ||||||||
\(53\) | −0.288109 | −0.0395748 | −0.0197874 | − | 0.999804i | \(-0.506299\pi\) | ||||
−0.0197874 | + | 0.999804i | \(0.506299\pi\) | |||||||
\(54\) | −1.44337 | − | 4.99166i | −0.196417 | − | 0.679279i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.29622 | − | 1.31429i | −0.306846 | − | 0.175630i | ||||
\(57\) | 2.27264 | − | 4.95835i | 0.301018 | − | 0.656749i | ||||
\(58\) | − | 7.54528i | − | 0.990743i | ||||||
\(59\) | 5.89894 | 0.767976 | 0.383988 | − | 0.923338i | \(-0.374550\pi\) | ||||
0.383988 | + | 0.923338i | \(0.374550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.48752i | − | 0.318494i | −0.987239 | − | 0.159247i | \(-0.949093\pi\) | ||
0.987239 | − | 0.159247i | \(-0.0509066\pi\) | |||||||
\(62\) | − | 4.19323i | − | 0.532540i | ||||||
\(63\) | −1.50989 | − | 7.79232i | −0.190228 | − | 0.981740i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.82661 | − | 6.16698i | 0.347932 | − | 0.759103i | ||||
\(67\) | 0.545275i | 0.0666160i | 0.999445 | + | 0.0333080i | \(0.0106042\pi\) | ||||
−0.999445 | + | 0.0333080i | \(0.989396\pi\) | |||||||
\(68\) | − | 3.54830i | − | 0.430294i | ||||||
\(69\) | −11.8803 | − | 5.44530i | −1.43022 | − | 0.655537i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.37142i | 0.637470i | 0.947844 | + | 0.318735i | \(0.103258\pi\) | ||||
−0.947844 | + | 0.318735i | \(0.896742\pi\) | |||||||
\(72\) | 1.95835 | + | 2.27264i | 0.230793 | + | 0.267833i | ||||
\(73\) | −4.85479 | −0.568210 | −0.284105 | − | 0.958793i | \(-0.591696\pi\) | ||||
−0.284105 | + | 0.958793i | \(0.591696\pi\) | |||||||
\(74\) | − | 10.4620i | − | 1.21618i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.14908i | 0.361224i | ||||||||
\(77\) | 5.14768 | − | 8.99360i | 0.586632 | − | 1.02492i | ||||
\(78\) | −7.85957 | − | 3.60240i | −0.889921 | − | 0.407891i | ||||
\(79\) | −0.742834 | −0.0835753 | −0.0417876 | − | 0.999127i | \(-0.513305\pi\) | ||||
−0.0417876 | + | 0.999127i | \(0.513305\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.32976 | + | 8.90122i | −0.147751 | + | 0.989025i | ||||
\(82\) | 9.32176 | 1.02942 | ||||||||
\(83\) | 4.45557i | 0.489063i | 0.969641 | + | 0.244531i | \(0.0786341\pi\) | ||||
−0.969641 | + | 0.244531i | \(0.921366\pi\) | |||||||
\(84\) | 2.66699 | + | 3.72655i | 0.290992 | + | 0.406600i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.91669i | 0.314515i | ||||||||
\(87\) | −5.44530 | + | 11.8803i | −0.583797 | + | 1.27371i | ||||
\(88\) | 3.91669i | 0.417521i | ||||||||
\(89\) | 12.3340 | 1.30740 | 0.653699 | − | 0.756755i | \(-0.273216\pi\) | ||||
0.653699 | + | 0.756755i | \(0.273216\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.4620 | − | 6.56050i | −1.20154 | − | 0.687727i | ||||
\(92\) | 7.54528 | 0.786649 | ||||||||
\(93\) | −3.02618 | + | 6.60240i | −0.313801 | + | 0.684637i | ||||
\(94\) | 8.00387i | 0.825536i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.57454 | − | 0.721683i | −0.160701 | − | 0.0736565i | ||||
\(97\) | 0.524688 | 0.0532740 | 0.0266370 | − | 0.999645i | \(-0.491520\pi\) | ||||
0.0266370 | + | 0.999645i | \(0.491520\pi\) | |||||||
\(98\) | 3.54528 | + | 6.03581i | 0.358127 | + | 0.609709i | ||||
\(99\) | −8.90122 | + | 7.67024i | −0.894606 | + | 0.770888i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00387 | 0.796415 | 0.398207 | − | 0.917295i | \(-0.369632\pi\) | ||||
0.398207 | + | 0.917295i | \(0.369632\pi\) | |||||||
\(102\) | −2.56075 | + | 5.58693i | −0.253552 | + | 0.553188i | ||||
\(103\) | −6.17269 | −0.608213 | −0.304106 | − | 0.952638i | \(-0.598358\pi\) | ||||
−0.304106 | + | 0.952638i | \(0.598358\pi\) | |||||||
\(104\) | 4.99166 | 0.489473 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.288109 | −0.0279836 | ||||||||
\(107\) | 2.65953 | 0.257106 | 0.128553 | − | 0.991703i | \(-0.458967\pi\) | ||||
0.128553 | + | 0.991703i | \(0.458967\pi\) | |||||||
\(108\) | −1.44337 | − | 4.99166i | −0.138888 | − | 0.480323i | ||||
\(109\) | −14.9239 | −1.42945 | −0.714727 | − | 0.699404i | \(-0.753449\pi\) | ||||
−0.714727 | + | 0.699404i | \(0.753449\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.55023 | + | 16.4728i | −0.716636 | + | 1.56353i | ||||
\(112\) | −2.29622 | − | 1.31429i | −0.216973 | − | 0.124189i | ||||
\(113\) | 11.8024 | 1.11028 | 0.555140 | − | 0.831757i | \(-0.312665\pi\) | ||||
0.555140 | + | 0.831757i | \(0.312665\pi\) | |||||||
\(114\) | 2.27264 | − | 4.95835i | 0.212852 | − | 0.464392i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.54528i | − | 0.700561i | ||||||
\(117\) | 9.77540 | + | 11.3442i | 0.903736 | + | 1.04878i | ||||
\(118\) | 5.89894 | 0.543041 | ||||||||
\(119\) | −4.66349 | + | 8.14768i | −0.427502 | + | 0.746896i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.34047 | −0.394589 | ||||||||
\(122\) | − | 2.48752i | − | 0.225209i | ||||||
\(123\) | −14.6775 | − | 6.72736i | −1.32342 | − | 0.606586i | ||||
\(124\) | − | 4.19323i | − | 0.376563i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.50989 | − | 7.79232i | −0.134512 | − | 0.694195i | ||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.10493 | − | 4.59244i | 0.185329 | − | 0.404342i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6846 | 1.28300 | 0.641500 | − | 0.767123i | \(-0.278312\pi\) | ||||
0.641500 | + | 0.767123i | \(0.278312\pi\) | |||||||
\(132\) | 2.82661 | − | 6.16698i | 0.246025 | − | 0.536767i | ||||
\(133\) | 4.13881 | − | 7.23098i | 0.358880 | − | 0.627006i | ||||
\(134\) | 0.545275i | 0.0471046i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.54830i | − | 0.304264i | ||||||
\(137\) | −18.3787 | −1.57019 | −0.785097 | − | 0.619372i | \(-0.787387\pi\) | ||||
−0.785097 | + | 0.619372i | \(0.787387\pi\) | |||||||
\(138\) | −11.8803 | − | 5.44530i | −1.01132 | − | 0.463535i | ||||
\(139\) | 12.6077i | 1.06937i | 0.845051 | + | 0.534686i | \(0.179570\pi\) | ||||
−0.845051 | + | 0.534686i | \(0.820430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.77626 | − | 12.6024i | 0.486449 | − | 1.06131i | ||||
\(142\) | 5.37142i | 0.450759i | ||||||||
\(143\) | 19.5508i | 1.63492i | ||||||||
\(144\) | 1.95835 | + | 2.27264i | 0.163195 | + | 0.189386i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.85479 | −0.401785 | ||||||||
\(147\) | −1.22623 | − | 12.0622i | −0.101138 | − | 0.994872i | ||||
\(148\) | − | 10.4620i | − | 0.859968i | ||||||
\(149\) | 5.65953i | 0.463646i | 0.972758 | + | 0.231823i | \(0.0744691\pi\) | ||||
−0.972758 | + | 0.231823i | \(0.925531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.62858 | −0.213911 | −0.106956 | − | 0.994264i | \(-0.534110\pi\) | ||||
−0.106956 | + | 0.994264i | \(0.534110\pi\) | |||||||
\(152\) | 3.14908i | 0.255424i | ||||||||
\(153\) | 8.06399 | − | 6.94879i | 0.651935 | − | 0.561776i | ||||
\(154\) | 5.14768 | − | 8.99360i | 0.414811 | − | 0.724725i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.85957 | − | 3.60240i | −0.629269 | − | 0.288423i | ||||
\(157\) | −24.2853 | −1.93818 | −0.969091 | − | 0.246704i | \(-0.920652\pi\) | ||||
−0.969091 | + | 0.246704i | \(0.920652\pi\) | |||||||
\(158\) | −0.742834 | −0.0590967 | ||||||||
\(159\) | 0.453638 | + | 0.207923i | 0.0359758 | + | 0.0164894i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.3256 | − | 9.91669i | −1.36545 | − | 0.781545i | ||||
\(162\) | −1.32976 | + | 8.90122i | −0.104476 | + | 0.699346i | ||||
\(163\) | − | 13.4620i | − | 1.05442i | −0.849734 | − | 0.527211i | \(-0.823238\pi\) | ||
0.849734 | − | 0.527211i | \(-0.176762\pi\) | |||||||
\(164\) | 9.32176 | 0.727907 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.45557i | 0.345819i | ||||||||
\(167\) | − | 21.7812i | − | 1.68548i | −0.538321 | − | 0.842740i | \(-0.680941\pi\) | ||
0.538321 | − | 0.842740i | \(-0.319059\pi\) | |||||||
\(168\) | 2.66699 | + | 3.72655i | 0.205763 | + | 0.287510i | ||||
\(169\) | 11.9167 | 0.916669 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.15671 | + | 6.16698i | −0.547287 | + | 0.471601i | ||||
\(172\) | 2.91669i | 0.222396i | ||||||||
\(173\) | − | 0.907276i | − | 0.0689789i | −0.999405 | − | 0.0344895i | \(-0.989019\pi\) | ||
0.999405 | − | 0.0344895i | \(-0.0109805\pi\) | |||||||
\(174\) | −5.44530 | + | 11.8803i | −0.412807 | + | 0.900645i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.91669i | 0.295232i | ||||||||
\(177\) | −9.28811 | − | 4.25717i | −0.698137 | − | 0.319988i | ||||
\(178\) | 12.3340 | 0.924470 | ||||||||
\(179\) | 2.08331i | 0.155714i | 0.996965 | + | 0.0778569i | \(0.0248077\pi\) | ||||
−0.996965 | + | 0.0778569i | \(0.975192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6679i | 1.83355i | 0.399400 | + | 0.916777i | \(0.369218\pi\) | ||||
−0.399400 | + | 0.916777i | \(0.630782\pi\) | |||||||
\(182\) | −11.4620 | − | 6.56050i | −0.849618 | − | 0.486297i | ||||
\(183\) | −1.79520 | + | 3.91669i | −0.132705 | + | 0.289530i | ||||
\(184\) | 7.54528 | 0.556245 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.02618 | + | 6.60240i | −0.221891 | + | 0.484111i | ||||
\(187\) | 13.8976 | 1.01629 | ||||||||
\(188\) | 8.00387i | 0.583742i | ||||||||
\(189\) | −3.24621 | + | 13.3590i | −0.236127 | + | 0.971722i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.0072i | − | 1.15824i | −0.815241 | − | 0.579122i | \(-0.803396\pi\) | ||
0.815241 | − | 0.579122i | \(-0.196604\pi\) | |||||||
\(192\) | −1.57454 | − | 0.721683i | −0.113633 | − | 0.0520830i | ||||
\(193\) | 26.4310i | 1.90255i | 0.308349 | + | 0.951273i | \(0.400224\pi\) | ||||
−0.308349 | + | 0.951273i | \(0.599776\pi\) | |||||||
\(194\) | 0.524688 | 0.0376704 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.54528 | + | 6.03581i | 0.253234 | + | 0.431129i | ||||
\(197\) | −17.2644 | −1.23004 | −0.615019 | − | 0.788512i | \(-0.710852\pi\) | ||||
−0.615019 | + | 0.788512i | \(0.710852\pi\) | |||||||
\(198\) | −8.90122 | + | 7.67024i | −0.632582 | + | 0.545100i | ||||
\(199\) | − | 10.8906i | − | 0.772014i | −0.922496 | − | 0.386007i | \(-0.873854\pi\) | ||
0.922496 | − | 0.386007i | \(-0.126146\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.393516 | − | 0.858557i | 0.0277565 | − | 0.0605579i | ||||
\(202\) | 8.00387 | 0.563150 | ||||||||
\(203\) | −9.91669 | + | 17.3256i | −0.696015 | + | 1.21602i | ||||
\(204\) | −2.56075 | + | 5.58693i | −0.179288 | + | 0.391163i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.17269 | −0.430071 | ||||||||
\(207\) | 14.7763 | + | 17.1477i | 1.02702 | + | 1.19185i | ||||
\(208\) | 4.99166 | 0.346110 | ||||||||
\(209\) | −12.3340 | −0.853158 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.88575 | −0.474035 | −0.237017 | − | 0.971505i | \(-0.576170\pi\) | ||||
−0.237017 | + | 0.971505i | \(0.576170\pi\) | |||||||
\(212\) | −0.288109 | −0.0197874 | ||||||||
\(213\) | 3.87646 | − | 8.45750i | 0.265611 | − | 0.579499i | ||||
\(214\) | 2.65953 | 0.181801 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.44337 | − | 4.99166i | −0.0982087 | − | 0.339640i | ||||
\(217\) | −5.51112 | + | 9.62858i | −0.374119 | + | 0.653631i | ||||
\(218\) | −14.9239 | −1.01078 | ||||||||
\(219\) | 7.64405 | + | 3.50362i | 0.516537 | + | 0.236753i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 17.7119i | − | 1.19143i | ||||||
\(222\) | −7.55023 | + | 16.4728i | −0.506738 | + | 1.10558i | ||||
\(223\) | −2.90336 | −0.194424 | −0.0972118 | − | 0.995264i | \(-0.530992\pi\) | ||||
−0.0972118 | + | 0.995264i | \(0.530992\pi\) | |||||||
\(224\) | −2.29622 | − | 1.31429i | −0.153423 | − | 0.0878148i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8024 | 0.785087 | ||||||||
\(227\) | 21.6557i | 1.43734i | 0.695351 | + | 0.718671i | \(0.255249\pi\) | ||||
−0.695351 | + | 0.718671i | \(0.744751\pi\) | |||||||
\(228\) | 2.27264 | − | 4.95835i | 0.150509 | − | 0.328374i | ||||
\(229\) | − | 16.9378i | − | 1.11928i | −0.828735 | − | 0.559641i | \(-0.810939\pi\) | ||
0.828735 | − | 0.559641i | \(-0.189061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.5957 | + | 10.4458i | −0.960329 | + | 0.687282i | ||||
\(232\) | − | 7.54528i | − | 0.495372i | ||||||
\(233\) | 5.42378 | 0.355324 | 0.177662 | − | 0.984092i | \(-0.443147\pi\) | ||||
0.177662 | + | 0.984092i | \(0.443147\pi\) | |||||||
\(234\) | 9.77540 | + | 11.3442i | 0.639038 | + | 0.741596i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.89894 | 0.383988 | ||||||||
\(237\) | 1.16962 | + | 0.536091i | 0.0759750 | + | 0.0348228i | ||||
\(238\) | −4.66349 | + | 8.14768i | −0.302289 | + | 0.528135i | ||||
\(239\) | − | 13.2572i | − | 0.857535i | −0.903415 | − | 0.428767i | \(-0.858948\pi\) | ||
0.903415 | − | 0.428767i | \(-0.141052\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.5233i | − | 1.19319i | −0.802543 | − | 0.596595i | \(-0.796520\pi\) | ||
0.802543 | − | 0.596595i | \(-0.203480\pi\) | |||||||
\(242\) | −4.34047 | −0.279016 | ||||||||
\(243\) | 8.51763 | − | 13.0557i | 0.546406 | − | 0.837520i | ||||
\(244\) | − | 2.48752i | − | 0.159247i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −14.6775 | − | 6.72736i | −0.935802 | − | 0.428921i | ||||
\(247\) | 15.7191i | 1.00018i | ||||||||
\(248\) | − | 4.19323i | − | 0.266270i | ||||||
\(249\) | 3.21551 | − | 7.01547i | 0.203775 | − | 0.444587i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.5355 | −1.35931 | −0.679654 | − | 0.733533i | \(-0.737870\pi\) | ||||
−0.679654 | + | 0.733533i | \(0.737870\pi\) | |||||||
\(252\) | −1.50989 | − | 7.79232i | −0.0951141 | − | 0.490870i | ||||
\(253\) | 29.5525i | 1.85795i | ||||||||
\(254\) | 2.00000i | 0.125491i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.8900i | 1.98924i | 0.103575 | + | 0.994622i | \(0.466972\pi\) | ||||
−0.103575 | + | 0.994622i | \(0.533028\pi\) | |||||||
\(258\) | 2.10493 | − | 4.59244i | 0.131047 | − | 0.285913i | ||||
\(259\) | −13.7501 | + | 24.0230i | −0.854388 | + | 1.49272i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1477 | − | 14.7763i | 1.06141 | − | 0.914627i | ||||
\(262\) | 14.6846 | 0.907218 | ||||||||
\(263\) | −14.1739 | −0.873998 | −0.436999 | − | 0.899462i | \(-0.643959\pi\) | ||||
−0.436999 | + | 0.899462i | \(0.643959\pi\) | |||||||
\(264\) | 2.82661 | − | 6.16698i | 0.173966 | − | 0.379552i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.13881 | − | 7.23098i | 0.253767 | − | 0.443360i | ||||
\(267\) | −19.4203 | − | 8.90122i | −1.18850 | − | 0.544746i | ||||
\(268\) | 0.545275i | 0.0333080i | ||||||||
\(269\) | −6.68074 | −0.407332 | −0.203666 | − | 0.979040i | \(-0.565286\pi\) | ||||
−0.203666 | + | 0.979040i | \(0.565286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.45864i | − | 0.574571i | −0.957845 | − | 0.287286i | \(-0.907247\pi\) | ||
0.957845 | − | 0.287286i | \(-0.0927529\pi\) | |||||||
\(272\) | − | 3.54830i | − | 0.215147i | ||||||
\(273\) | 13.3127 | + | 18.6017i | 0.805722 | + | 1.12582i | ||||
\(274\) | −18.3787 | −1.11030 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.8803 | − | 5.44530i | −0.715112 | − | 0.327769i | ||||
\(277\) | − | 11.2048i | − | 0.673231i | −0.941642 | − | 0.336616i | \(-0.890718\pi\) | ||
0.941642 | − | 0.336616i | \(-0.109282\pi\) | |||||||
\(278\) | 12.6077i | 0.756160i | ||||||||
\(279\) | 9.52969 | − | 8.21179i | 0.570527 | − | 0.491627i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.90945i | 0.173563i | 0.996227 | + | 0.0867816i | \(0.0276582\pi\) | ||||
−0.996227 | + | 0.0867816i | \(0.972342\pi\) | |||||||
\(282\) | 5.77626 | − | 12.6024i | 0.343971 | − | 0.750462i | ||||
\(283\) | −24.4056 | −1.45076 | −0.725381 | − | 0.688348i | \(-0.758336\pi\) | ||||
−0.725381 | + | 0.688348i | \(0.758336\pi\) | |||||||
\(284\) | 5.37142i | 0.318735i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.5508i | 1.15606i | ||||||||
\(287\) | −21.4048 | − | 12.2515i | −1.26349 | − | 0.723184i | ||||
\(288\) | 1.95835 | + | 2.27264i | 0.115397 | + | 0.133916i | ||||
\(289\) | 4.40960 | 0.259388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.826142 | − | 0.378659i | −0.0484293 | − | 0.0221974i | ||||
\(292\) | −4.85479 | −0.284105 | ||||||||
\(293\) | 17.0799i | 0.997819i | 0.866654 | + | 0.498910i | \(0.166266\pi\) | ||||
−0.866654 | + | 0.498910i | \(0.833734\pi\) | |||||||
\(294\) | −1.22623 | − | 12.0622i | −0.0715151 | − | 0.703481i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 10.4620i | − | 0.608089i | ||||||
\(297\) | 19.5508 | − | 5.65322i | 1.13445 | − | 0.328033i | ||||
\(298\) | 5.65953i | 0.327847i | ||||||||
\(299\) | 37.6635 | 2.17813 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.83338 | − | 6.69737i | 0.220953 | − | 0.386030i | ||||
\(302\) | −2.62858 | −0.151258 | ||||||||
\(303\) | −12.6024 | − | 5.77626i | −0.723989 | − | 0.331837i | ||||
\(304\) | 3.14908i | 0.180612i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.06399 | − | 6.94879i | 0.460988 | − | 0.397236i | ||||
\(307\) | −11.8093 | −0.673991 | −0.336996 | − | 0.941506i | \(-0.609411\pi\) | ||||
−0.336996 | + | 0.941506i | \(0.609411\pi\) | |||||||
\(308\) | 5.14768 | − | 8.99360i | 0.293316 | − | 0.512458i | ||||
\(309\) | 9.71913 | + | 4.45472i | 0.552902 | + | 0.253420i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.88673 | 0.163692 | 0.0818458 | − | 0.996645i | \(-0.473918\pi\) | ||||
0.0818458 | + | 0.996645i | \(0.473918\pi\) | |||||||
\(312\) | −7.85957 | − | 3.60240i | −0.444960 | − | 0.203946i | ||||
\(313\) | 4.20986 | 0.237955 | 0.118978 | − | 0.992897i | \(-0.462038\pi\) | ||||
0.118978 | + | 0.992897i | \(0.462038\pi\) | |||||||
\(314\) | −24.2853 | −1.37050 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.742834 | −0.0417876 | ||||||||
\(317\) | 23.2644 | 1.30666 | 0.653330 | − | 0.757074i | \(-0.273372\pi\) | ||||
0.653330 | + | 0.757074i | \(0.273372\pi\) | |||||||
\(318\) | 0.453638 | + | 0.207923i | 0.0254388 | + | 0.0116598i | ||||
\(319\) | 29.5525 | 1.65462 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.18753 | − | 1.91934i | −0.233725 | − | 0.107127i | ||||
\(322\) | −17.3256 | − | 9.91669i | −0.965520 | − | 0.552636i | ||||
\(323\) | 11.1739 | 0.621730 | ||||||||
\(324\) | −1.32976 | + | 8.90122i | −0.0738757 | + | 0.494512i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 13.4620i | − | 0.745589i | ||||||
\(327\) | 23.4983 | + | 10.7704i | 1.29946 | + | 0.595602i | ||||
\(328\) | 9.32176 | 0.514708 | ||||||||
\(329\) | 10.5194 | − | 18.3787i | 0.579954 | − | 1.01325i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.4620 | −1.39952 | −0.699758 | − | 0.714380i | \(-0.746709\pi\) | ||||
−0.699758 | + | 0.714380i | \(0.746709\pi\) | |||||||
\(332\) | 4.45557i | 0.244531i | ||||||||
\(333\) | 23.7763 | − | 20.4881i | 1.30293 | − | 1.12274i | ||||
\(334\) | − | 21.7812i | − | 1.19181i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.66699 | + | 3.72655i | 0.145496 | + | 0.203300i | ||||
\(337\) | 7.68095i | 0.418408i | 0.977872 | + | 0.209204i | \(0.0670873\pi\) | ||||
−0.977872 | + | 0.209204i | \(0.932913\pi\) | |||||||
\(338\) | 11.9167 | 0.648183 | ||||||||
\(339\) | −18.5834 | − | 8.51763i | −1.00931 | − | 0.462614i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.4236 | 0.889387 | ||||||||
\(342\) | −7.15671 | + | 6.16698i | −0.386991 | + | 0.333472i | ||||
\(343\) | −0.207923 | − | 18.5191i | −0.0112268 | − | 0.999937i | ||||
\(344\) | 2.91669i | 0.157257i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 0.907276i | − | 0.0487755i | ||||||
\(347\) | 8.26441 | 0.443657 | 0.221828 | − | 0.975086i | \(-0.428798\pi\) | ||||
0.221828 | + | 0.975086i | \(0.428798\pi\) | |||||||
\(348\) | −5.44530 | + | 11.8803i | −0.291899 | + | 0.636853i | ||||
\(349\) | − | 24.6846i | − | 1.32133i | −0.750679 | − | 0.660667i | \(-0.770273\pi\) | ||
0.750679 | − | 0.660667i | \(-0.229727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.20480 | − | 24.9167i | −0.384564 | − | 1.32995i | ||||
\(352\) | 3.91669i | 0.208760i | ||||||||
\(353\) | − | 18.8945i | − | 1.00565i | −0.864388 | − | 0.502826i | \(-0.832294\pi\) | ||
0.864388 | − | 0.502826i | \(-0.167706\pi\) | |||||||
\(354\) | −9.28811 | − | 4.25717i | −0.493657 | − | 0.226266i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.3340 | 0.653699 | ||||||||
\(357\) | 13.2229 | − | 9.46326i | 0.699830 | − | 0.500849i | ||||
\(358\) | 2.08331i | 0.110106i | ||||||||
\(359\) | − | 1.49291i | − | 0.0787927i | −0.999224 | − | 0.0393964i | \(-0.987457\pi\) | ||
0.999224 | − | 0.0393964i | \(-0.0125435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.08331 | 0.478069 | ||||||||
\(362\) | 24.6679i | 1.29652i | ||||||||
\(363\) | 6.83425 | + | 3.13245i | 0.358705 | + | 0.164411i | ||||
\(364\) | −11.4620 | − | 6.56050i | −0.600770 | − | 0.343864i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.79520 | + | 3.91669i | −0.0938366 | + | 0.204729i | ||||
\(367\) | 16.9544 | 0.885015 | 0.442507 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442507 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(368\) | 7.54528 | 0.393325 | ||||||||
\(369\) | 18.2552 | + | 21.1850i | 0.950330 | + | 1.10285i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.661561 | + | 0.378659i | 0.0343466 | + | 0.0196590i | ||||
\(372\) | −3.02618 | + | 6.60240i | −0.156900 | + | 0.342319i | ||||
\(373\) | 22.8097i | 1.18104i | 0.807023 | + | 0.590520i | \(0.201077\pi\) | ||||
−0.807023 | + | 0.590520i | \(0.798923\pi\) | |||||||
\(374\) | 13.8976 | 0.718627 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00387i | 0.412768i | ||||||||
\(377\) | − | 37.6635i | − | 1.93977i | ||||||
\(378\) | −3.24621 | + | 13.3590i | −0.166967 | + | 0.687111i | ||||
\(379\) | −0.371417 | −0.0190784 | −0.00953920 | − | 0.999955i | \(-0.503036\pi\) | ||||
−0.00953920 | + | 0.999955i | \(0.503036\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.44337 | − | 3.14908i | 0.0739459 | − | 0.161332i | ||||
\(382\) | − | 16.0072i | − | 0.819002i | ||||||
\(383\) | − | 32.8367i | − | 1.67788i | −0.544226 | − | 0.838939i | \(-0.683177\pi\) | ||
0.544226 | − | 0.838939i | \(-0.316823\pi\) | |||||||
\(384\) | −1.57454 | − | 0.721683i | −0.0803504 | − | 0.0368283i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.4310i | 1.34530i | ||||||||
\(387\) | −6.62858 | + | 5.71189i | −0.336950 | + | 0.290352i | ||||
\(388\) | 0.524688 | 0.0266370 | ||||||||
\(389\) | 24.1287i | 1.22338i | 0.791099 | + | 0.611688i | \(0.209509\pi\) | ||||
−0.791099 | + | 0.611688i | \(0.790491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 26.7729i | − | 1.35396i | ||||||
\(392\) | 3.54528 | + | 6.03581i | 0.179063 | + | 0.304855i | ||||
\(393\) | −23.1215 | − | 10.5976i | −1.16632 | − | 0.534580i | ||||
\(394\) | −17.2644 | −0.869768 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.90122 | + | 7.67024i | −0.447303 | + | 0.385444i | ||||
\(397\) | 7.35371 | 0.369072 | 0.184536 | − | 0.982826i | \(-0.440922\pi\) | ||||
0.184536 | + | 0.982826i | \(0.440922\pi\) | |||||||
\(398\) | − | 10.8906i | − | 0.545896i | ||||||
\(399\) | −11.7352 | + | 8.39856i | −0.587495 | + | 0.420454i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1215i | 0.855007i | 0.904014 | + | 0.427503i | \(0.140607\pi\) | ||||
−0.904014 | + | 0.427503i | \(0.859393\pi\) | |||||||
\(402\) | 0.393516 | − | 0.858557i | 0.0196268 | − | 0.0428209i | ||||
\(403\) | − | 20.9312i | − | 1.04266i | ||||||
\(404\) | 8.00387 | 0.398207 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.91669 | + | 17.3256i | −0.492157 | + | 0.859857i | ||||
\(407\) | 40.9763 | 2.03112 | ||||||||
\(408\) | −2.56075 | + | 5.58693i | −0.126776 | + | 0.276594i | ||||
\(409\) | − | 23.2246i | − | 1.14838i | −0.818722 | − | 0.574191i | \(-0.805317\pi\) | ||
0.818722 | − | 0.574191i | \(-0.194683\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.9379 | + | 13.2636i | 1.42740 | + | 0.654244i | ||||
\(412\) | −6.17269 | −0.304106 | ||||||||
\(413\) | −13.5453 | − | 7.75293i | −0.666519 | − | 0.381497i | ||||
\(414\) | 14.7763 | + | 17.1477i | 0.726213 | + | 0.842762i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.99166 | 0.244736 | ||||||||
\(417\) | 9.09878 | − | 19.8513i | 0.445569 | − | 0.972124i | ||||
\(418\) | −12.3340 | −0.603274 | ||||||||
\(419\) | −11.5522 | −0.564360 | −0.282180 | − | 0.959361i | \(-0.591058\pi\) | ||||
−0.282180 | + | 0.959361i | \(0.591058\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.9239 | 1.79956 | 0.899781 | − | 0.436341i | \(-0.143726\pi\) | ||||
0.899781 | + | 0.436341i | \(0.143726\pi\) | |||||||
\(422\) | −6.88575 | −0.335193 | ||||||||
\(423\) | −18.1899 | + | 15.6743i | −0.884423 | + | 0.762112i | ||||
\(424\) | −0.288109 | −0.0139918 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.87646 | − | 8.45750i | 0.187815 | − | 0.409767i | ||||
\(427\) | −3.26932 | + | 5.71189i | −0.158214 | + | 0.276418i | ||||
\(428\) | 2.65953 | 0.128553 | ||||||||
\(429\) | 14.1095 | − | 30.7835i | 0.681213 | − | 1.48624i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.03094i | − | 0.242332i | −0.992632 | − | 0.121166i | \(-0.961337\pi\) | ||
0.992632 | − | 0.121166i | \(-0.0386633\pi\) | |||||||
\(432\) | −1.44337 | − | 4.99166i | −0.0694440 | − | 0.240161i | ||||
\(433\) | 3.04024 | 0.146104 | 0.0730522 | − | 0.997328i | \(-0.476726\pi\) | ||||
0.0730522 | + | 0.997328i | \(0.476726\pi\) | |||||||
\(434\) | −5.51112 | + | 9.62858i | −0.264542 | + | 0.462187i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.9239 | −0.714727 | ||||||||
\(437\) | 23.7607i | 1.13663i | ||||||||
\(438\) | 7.64405 | + | 3.50362i | 0.365247 | + | 0.167409i | ||||
\(439\) | 19.8184i | 0.945879i | 0.881095 | + | 0.472940i | \(0.156807\pi\) | ||||
−0.881095 | + | 0.472940i | \(0.843193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.77434 | + | 19.8773i | −0.322588 | + | 0.946540i | ||||
\(442\) | − | 17.7119i | − | 0.842469i | ||||||
\(443\) | −10.5976 | −0.503509 | −0.251755 | − | 0.967791i | \(-0.581008\pi\) | ||||
−0.251755 | + | 0.967791i | \(0.581008\pi\) | |||||||
\(444\) | −7.55023 | + | 16.4728i | −0.358318 | + | 0.781763i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.90336 | −0.137478 | ||||||||
\(447\) | 4.08439 | − | 8.91114i | 0.193185 | − | 0.421483i | ||||
\(448\) | −2.29622 | − | 1.31429i | −0.108486 | − | 0.0620944i | ||||
\(449\) | − | 6.19756i | − | 0.292481i | −0.989249 | − | 0.146240i | \(-0.953283\pi\) | ||
0.989249 | − | 0.146240i | \(-0.0467173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.5105i | 1.71921i | ||||||||
\(452\) | 11.8024 | 0.555140 | ||||||||
\(453\) | 4.13881 | + | 1.89701i | 0.194458 | + | 0.0891291i | ||||
\(454\) | 21.6557i | 1.01635i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.27264 | − | 4.95835i | 0.106426 | − | 0.232196i | ||||
\(457\) | 19.7573i | 0.924208i | 0.886826 | + | 0.462104i | \(0.152905\pi\) | ||||
−0.886826 | + | 0.462104i | \(0.847095\pi\) | |||||||
\(458\) | − | 16.9378i | − | 0.791452i | ||||||
\(459\) | −17.7119 | + | 5.12149i | −0.826720 | + | 0.239051i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.8983 | −1.25278 | −0.626390 | − | 0.779510i | \(-0.715468\pi\) | ||||
−0.626390 | + | 0.779510i | \(0.715468\pi\) | |||||||
\(462\) | −14.5957 | + | 10.4458i | −0.679055 | + | 0.485981i | ||||
\(463\) | − | 38.7573i | − | 1.80121i | −0.434643 | − | 0.900603i | \(-0.643126\pi\) | ||
0.434643 | − | 0.900603i | \(-0.356874\pi\) | |||||||
\(464\) | − | 7.54528i | − | 0.350281i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.42378 | 0.251252 | ||||||||
\(467\) | − | 18.5181i | − | 0.856913i | −0.903562 | − | 0.428457i | \(-0.859057\pi\) | ||
0.903562 | − | 0.428457i | \(-0.140943\pi\) | |||||||
\(468\) | 9.77540 | + | 11.3442i | 0.451868 | + | 0.524388i | ||||
\(469\) | 0.716650 | − | 1.25207i | 0.0330918 | − | 0.0578154i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.2382 | + | 17.5263i | 1.76192 | + | 0.807571i | ||||
\(472\) | 5.89894 | 0.271521 | ||||||||
\(473\) | −11.4238 | −0.525266 | ||||||||
\(474\) | 1.16962 | + | 0.536091i | 0.0537224 | + | 0.0246235i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.66349 | + | 8.14768i | −0.213751 | + | 0.373448i | ||||
\(477\) | −0.564216 | − | 0.654766i | −0.0258337 | − | 0.0299797i | ||||
\(478\) | − | 13.2572i | − | 0.606369i | ||||||
\(479\) | −14.4337 | −0.659491 | −0.329746 | − | 0.944070i | \(-0.606963\pi\) | ||||
−0.329746 | + | 0.944070i | \(0.606963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 52.2226i | − | 2.38115i | ||||||
\(482\) | − | 18.5233i | − | 0.843712i | ||||||
\(483\) | 20.1232 | + | 28.1178i | 0.915636 | + | 1.27941i | ||||
\(484\) | −4.34047 | −0.197294 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.51763 | − | 13.0557i | 0.386367 | − | 0.592216i | ||||
\(487\) | 26.2430i | 1.18918i | 0.804028 | + | 0.594592i | \(0.202686\pi\) | ||||
−0.804028 | + | 0.594592i | \(0.797314\pi\) | |||||||
\(488\) | − | 2.48752i | − | 0.112605i | ||||||
\(489\) | −9.71528 | + | 21.1964i | −0.439340 | + | 0.958534i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0000i | 1.35388i | 0.736038 | + | 0.676941i | \(0.236695\pi\) | ||||
−0.736038 | + | 0.676941i | \(0.763305\pi\) | |||||||
\(492\) | −14.6775 | − | 6.72736i | −0.661712 | − | 0.303293i | ||||
\(493\) | −26.7729 | −1.20579 | ||||||||
\(494\) | 15.7191i | 0.707237i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.19323i | − | 0.188281i | ||||||
\(497\) | 7.05961 | − | 12.3340i | 0.316667 | − | 0.553254i | ||||
\(498\) | 3.21551 | − | 7.01547i | 0.144091 | − | 0.314371i | ||||
\(499\) | −41.6740 | −1.86558 | −0.932792 | − | 0.360414i | \(-0.882635\pi\) | ||||
−0.932792 | + | 0.360414i | \(0.882635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.7191 | + | 34.2954i | −0.702279 | + | 1.53220i | ||||
\(502\) | −21.5355 | −0.961176 | ||||||||
\(503\) | − | 0.415846i | − | 0.0185417i | −0.999957 | − | 0.00927084i | \(-0.997049\pi\) | ||
0.999957 | − | 0.00927084i | \(-0.00295104\pi\) | |||||||
\(504\) | −1.50989 | − | 7.79232i | −0.0672558 | − | 0.347097i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 29.5525i | 1.31377i | ||||||||
\(507\) | −18.7633 | − | 8.60008i | −0.833307 | − | 0.381943i | ||||
\(508\) | 2.00000i | 0.0887357i | ||||||||
\(509\) | −11.3064 | −0.501149 | −0.250575 | − | 0.968097i | \(-0.580620\pi\) | ||||
−0.250575 | + | 0.968097i | \(0.580620\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1477 | + | 6.38061i | 0.493144 | + | 0.282261i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.7191 | − | 4.54528i | 0.694017 | − | 0.200679i | ||||
\(514\) | 31.8900i | 1.40661i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.10493 | − | 4.59244i | 0.0926643 | − | 0.202171i | ||||
\(517\) | −31.3487 | −1.37871 | ||||||||
\(518\) | −13.7501 | + | 24.0230i | −0.604144 | + | 1.05551i | ||||
\(519\) | −0.654766 | + | 1.42854i | −0.0287411 | + | 0.0627060i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.47611 | −0.108481 | −0.0542403 | − | 0.998528i | \(-0.517274\pi\) | ||||
−0.0542403 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(522\) | 17.1477 | − | 14.7763i | 0.750533 | − | 0.646739i | ||||
\(523\) | 12.0602 | 0.527357 | 0.263678 | − | 0.964611i | \(-0.415064\pi\) | ||||
0.263678 | + | 0.964611i | \(0.415064\pi\) | |||||||
\(524\) | 14.6846 | 0.641500 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.1739 | −0.618010 | ||||||||
\(527\) | −14.8788 | −0.648131 | ||||||||
\(528\) | 2.82661 | − | 6.16698i | 0.123012 | − | 0.268384i | ||||
\(529\) | 33.9312 | 1.47527 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.5522 | + | 13.4061i | 0.501321 | + | 0.581777i | ||||
\(532\) | 4.13881 | − | 7.23098i | 0.179440 | − | 0.313503i | ||||
\(533\) | 46.5311 | 2.01549 | ||||||||
\(534\) | −19.4203 | − | 8.90122i | −0.840399 | − | 0.385193i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.545275i | 0.0235523i | ||||||||
\(537\) | 1.50349 | − | 3.28025i | 0.0648803 | − | 0.141553i | ||||
\(538\) | −6.68074 | −0.288027 | ||||||||
\(539\) | −23.6404 | + | 13.8857i | −1.01826 | + | 0.598102i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.14292 | 0.221111 | 0.110556 | − | 0.993870i | \(-0.464737\pi\) | ||||
0.110556 | + | 0.993870i | \(0.464737\pi\) | |||||||
\(542\) | − | 9.45864i | − | 0.406283i | ||||||
\(543\) | 17.8024 | − | 38.8406i | 0.763976 | − | 1.66681i | ||||
\(544\) | − | 3.54830i | − | 0.152132i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.3127 | + | 18.6017i | 0.569731 | + | 0.796078i | ||||
\(547\) | 3.11425i | 0.133156i | 0.997781 | + | 0.0665779i | \(0.0212081\pi\) | ||||
−0.997781 | + | 0.0665779i | \(0.978792\pi\) | |||||||
\(548\) | −18.3787 | −0.785097 | ||||||||
\(549\) | 5.65322 | − | 4.87142i | 0.241274 | − | 0.207907i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.7607 | 1.01224 | ||||||||
\(552\) | −11.8803 | − | 5.44530i | −0.505660 | − | 0.231767i | ||||
\(553\) | 1.70571 | + | 0.976300i | 0.0725342 | + | 0.0415165i | ||||
\(554\) | − | 11.2048i | − | 0.476046i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.6077i | 0.534686i | ||||||||
\(557\) | −1.93812 | −0.0821206 | −0.0410603 | − | 0.999157i | \(-0.513074\pi\) | ||||
−0.0410603 | + | 0.999157i | \(0.513074\pi\) | |||||||
\(558\) | 9.52969 | − | 8.21179i | 0.403424 | − | 0.347633i | ||||
\(559\) | 14.5591i | 0.615786i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.8823 | − | 10.0297i | −0.923871 | − | 0.423452i | ||||
\(562\) | 2.90945i | 0.122728i | ||||||||
\(563\) | − | 25.8656i | − | 1.09010i | −0.838402 | − | 0.545052i | \(-0.816510\pi\) | ||
0.838402 | − | 0.545052i | \(-0.183490\pi\) | |||||||
\(564\) | 5.77626 | − | 12.6024i | 0.243224 | − | 0.530657i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.4056 | −1.02584 | ||||||||
\(567\) | 14.7522 | − | 18.6915i | 0.619535 | − | 0.784969i | ||||
\(568\) | 5.37142i | 0.225380i | ||||||||
\(569\) | − | 30.3787i | − | 1.27354i | −0.771054 | − | 0.636770i | \(-0.780270\pi\) | ||
0.771054 | − | 0.636770i | \(-0.219730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.56898 | 0.191206 | 0.0956028 | − | 0.995420i | \(-0.469522\pi\) | ||||
0.0956028 | + | 0.995420i | \(0.469522\pi\) | |||||||
\(572\) | 19.5508i | 0.817460i | ||||||||
\(573\) | −11.5522 | + | 25.2040i | −0.482598 | + | 1.05291i | ||||
\(574\) | −21.4048 | − | 12.2515i | −0.893421 | − | 0.511368i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.95835 | + | 2.27264i | 0.0815977 | + | 0.0946932i | ||||
\(577\) | −23.7493 | −0.988694 | −0.494347 | − | 0.869265i | \(-0.664593\pi\) | ||||
−0.494347 | + | 0.869265i | \(0.664593\pi\) | |||||||
\(578\) | 4.40960 | 0.183415 | ||||||||
\(579\) | 19.0748 | − | 41.6167i | 0.792723 | − | 1.72953i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.85592 | − | 10.2310i | 0.242945 | − | 0.424453i | ||||
\(582\) | −0.826142 | − | 0.378659i | −0.0342447 | − | 0.0156959i | ||||
\(583\) | − | 1.12843i | − | 0.0467349i | ||||||
\(584\) | −4.85479 | −0.200893 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.0799i | 0.705565i | ||||||||
\(587\) | 28.8726i | 1.19170i | 0.803096 | + | 0.595849i | \(0.203184\pi\) | ||||
−0.803096 | + | 0.595849i | \(0.796816\pi\) | |||||||
\(588\) | −1.22623 | − | 12.0622i | −0.0505688 | − | 0.497436i | ||||
\(589\) | 13.2048 | 0.544094 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.1835 | + | 12.4594i | 1.11818 | + | 0.512513i | ||||
\(592\) | − | 10.4620i | − | 0.429984i | ||||||
\(593\) | 4.74595i | 0.194893i | 0.995241 | + | 0.0974463i | \(0.0310674\pi\) | ||||
−0.995241 | + | 0.0974463i | \(0.968933\pi\) | |||||||
\(594\) | 19.5508 | − | 5.65322i | 0.802179 | − | 0.231955i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.65953i | 0.231823i | ||||||||
\(597\) | −7.85957 | + | 17.1477i | −0.321671 | + | 0.701808i | ||||
\(598\) | 37.6635 | 1.54017 | ||||||||
\(599\) | 3.19756i | 0.130649i | 0.997864 | + | 0.0653243i | \(0.0208082\pi\) | ||||
−0.997864 | + | 0.0653243i | \(0.979192\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.16962i | − | 0.0477098i | −0.999715 | − | 0.0238549i | \(-0.992406\pi\) | ||
0.999715 | − | 0.0238549i | \(-0.00759397\pi\) | |||||||
\(602\) | 3.83338 | − | 6.69737i | 0.156237 | − | 0.272965i | ||||
\(603\) | −1.23921 | + | 1.06784i | −0.0504646 | + | 0.0434857i | ||||
\(604\) | −2.62858 | −0.106956 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.6024 | − | 5.77626i | −0.511938 | − | 0.234644i | ||||
\(607\) | 42.5463 | 1.72690 | 0.863450 | − | 0.504434i | \(-0.168299\pi\) | ||||
0.863450 | + | 0.504434i | \(0.168299\pi\) | |||||||
\(608\) | 3.14908i | 0.127712i | ||||||||
\(609\) | 28.1178 | − | 20.1232i | 1.13939 | − | 0.815432i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.9526i | 1.61631i | ||||||||
\(612\) | 8.06399 | − | 6.94879i | 0.325967 | − | 0.280888i | ||||
\(613\) | 11.1524i | 0.450443i | 0.974308 | + | 0.225221i | \(0.0723105\pi\) | ||||
−0.974308 | + | 0.225221i | \(0.927689\pi\) | |||||||
\(614\) | −11.8093 | −0.476584 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.14768 | − | 8.99360i | 0.207406 | − | 0.362362i | ||||
\(617\) | 42.1811 | 1.69815 | 0.849074 | − | 0.528275i | \(-0.177161\pi\) | ||||
0.849074 | + | 0.528275i | \(0.177161\pi\) | |||||||
\(618\) | 9.71913 | + | 4.45472i | 0.390961 | + | 0.179195i | ||||
\(619\) | − | 11.0327i | − | 0.443442i | −0.975110 | − | 0.221721i | \(-0.928833\pi\) | ||
0.975110 | − | 0.221721i | \(-0.0711674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.8906 | − | 37.6635i | −0.437025 | − | 1.51138i | ||||
\(622\) | 2.88673 | 0.115747 | ||||||||
\(623\) | −28.3215 | − | 16.2104i | −1.13468 | − | 0.649457i | ||||
\(624\) | −7.85957 | − | 3.60240i | −0.314634 | − | 0.144211i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.20986 | 0.168260 | ||||||||
\(627\) | 19.4203 | + | 8.90122i | 0.775573 | + | 0.355481i | ||||
\(628\) | −24.2853 | −0.969091 | ||||||||
\(629\) | −37.1221 | −1.48016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.46197 | 0.177628 | 0.0888140 | − | 0.996048i | \(-0.471692\pi\) | ||||
0.0888140 | + | 0.996048i | \(0.471692\pi\) | |||||||
\(632\) | −0.742834 | −0.0295483 | ||||||||
\(633\) | 10.8419 | + | 4.96933i | 0.430926 | + | 0.197513i | ||||
\(634\) | 23.2644 | 0.923948 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.453638 | + | 0.207923i | 0.0179879 | + | 0.00824469i | ||||
\(637\) | 17.6968 | + | 30.1287i | 0.701173 | + | 1.19374i | ||||
\(638\) | 29.5525 | 1.17000 | ||||||||
\(639\) | −12.2073 | + | 10.5191i | −0.482913 | + | 0.416129i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.90945i | − | 0.114916i | −0.998348 | − | 0.0574582i | \(-0.981700\pi\) | ||
0.998348 | − | 0.0574582i | \(-0.0182996\pi\) | |||||||
\(642\) | −4.18753 | − | 1.91934i | −0.165268 | − | 0.0757501i | ||||
\(643\) | −31.7645 | −1.25267 | −0.626335 | − | 0.779554i | \(-0.715446\pi\) | ||||
−0.626335 | + | 0.779554i | \(0.715446\pi\) | |||||||
\(644\) | −17.3256 | − | 9.91669i | −0.682725 | − | 0.390772i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.1739 | 0.439630 | ||||||||
\(647\) | − | 23.3448i | − | 0.917779i | −0.888493 | − | 0.458890i | \(-0.848247\pi\) | ||
0.888493 | − | 0.458890i | \(-0.151753\pi\) | |||||||
\(648\) | −1.32976 | + | 8.90122i | −0.0522380 | + | 0.349673i | ||||
\(649\) | 23.1043i | 0.906924i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.6263 | − | 11.1833i | 0.612442 | − | 0.438308i | ||||
\(652\) | − | 13.4620i | − | 0.527211i | ||||||
\(653\) | 2.28087 | 0.0892572 | 0.0446286 | − | 0.999004i | \(-0.485790\pi\) | ||||
0.0446286 | + | 0.999004i | \(0.485790\pi\) | |||||||
\(654\) | 23.4983 | + | 10.7704i | 0.918857 | + | 0.421154i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.32176 | 0.363954 | ||||||||
\(657\) | −9.50736 | − | 11.0332i | −0.370917 | − | 0.430445i | ||||
\(658\) | 10.5194 | − | 18.3787i | 0.410089 | − | 0.716475i | ||||
\(659\) | 2.08331i | 0.0811542i | 0.999176 | + | 0.0405771i | \(0.0129196\pi\) | ||||
−0.999176 | + | 0.0405771i | \(0.987080\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.34150i | − | 0.168865i | −0.996429 | − | 0.0844325i | \(-0.973092\pi\) | ||
0.996429 | − | 0.0844325i | \(-0.0269077\pi\) | |||||||
\(662\) | −25.4620 | −0.989607 | ||||||||
\(663\) | −12.7824 | + | 27.8881i | −0.496426 | + | 1.08308i | ||||
\(664\) | 4.45557i | 0.172910i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23.7763 | − | 20.4881i | 0.921311 | − | 0.793900i | ||||
\(667\) | − | 56.9312i | − | 2.20438i | ||||||
\(668\) | − | 21.7812i | − | 0.842740i | ||||||
\(669\) | 4.57146 | + | 2.09531i | 0.176743 | + | 0.0810093i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.74284 | 0.376118 | ||||||||
\(672\) | 2.66699 | + | 3.72655i | 0.102881 | + | 0.143755i | ||||
\(673\) | − | 2.00724i | − | 0.0773735i | −0.999251 | − | 0.0386867i | \(-0.987683\pi\) | ||
0.999251 | − | 0.0386867i | \(-0.0123174\pi\) | |||||||
\(674\) | 7.68095i | 0.295859i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.9167 | 0.458334 | ||||||||
\(677\) | 27.5547i | 1.05901i | 0.848306 | + | 0.529506i | \(0.177623\pi\) | ||||
−0.848306 | + | 0.529506i | \(0.822377\pi\) | |||||||
\(678\) | −18.5834 | − | 8.51763i | −0.713691 | − | 0.327117i | ||||
\(679\) | −1.20480 | − | 0.689593i | −0.0462360 | − | 0.0264642i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6286 | − | 34.0978i | 0.598889 | − | 1.30663i | ||||
\(682\) | 16.4236 | 0.628891 | ||||||||
\(683\) | 5.75008 | 0.220021 | 0.110010 | − | 0.993930i | \(-0.464912\pi\) | ||||
0.110010 | + | 0.993930i | \(0.464912\pi\) | |||||||
\(684\) | −7.15671 | + | 6.16698i | −0.273644 | + | 0.235801i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.207923 | − | 18.5191i | −0.00793854 | − | 0.707062i | ||||
\(687\) | −12.2237 | + | 26.6693i | −0.466365 | + | 1.01750i | ||||
\(688\) | 2.91669i | 0.111198i | ||||||||
\(689\) | −1.43814 | −0.0547888 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.6404i | 0.899324i | 0.893199 | + | 0.449662i | \(0.148456\pi\) | ||||
−0.893199 | + | 0.449662i | \(0.851544\pi\) | |||||||
\(692\) | − | 0.907276i | − | 0.0344895i | ||||||
\(693\) | 30.5201 | − | 5.91377i | 1.15936 | − | 0.224646i | ||||
\(694\) | 8.26441 | 0.313713 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.44530 | + | 11.8803i | −0.206404 | + | 0.450323i | ||||
\(697\) | − | 33.0764i | − | 1.25286i | ||||||
\(698\) | − | 24.6846i | − | 0.934325i | ||||||
\(699\) | −8.53996 | − | 3.91425i | −0.323011 | − | 0.148051i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.6882i | 1.76339i | 0.471821 | + | 0.881694i | \(0.343597\pi\) | ||||
−0.471821 | + | 0.881694i | \(0.656403\pi\) | |||||||
\(702\) | −7.20480 | − | 24.9167i | −0.271928 | − | 0.940420i | ||||
\(703\) | 32.9455 | 1.24256 | ||||||||
\(704\) | 3.91669i | 0.147616i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.8945i | − | 0.711103i | ||||||
\(707\) | −18.3787 | − | 10.5194i | −0.691201 | − | 0.395623i | ||||
\(708\) | −9.28811 | − | 4.25717i | −0.349068 | − | 0.159994i | ||||
\(709\) | −17.8334 | −0.669747 | −0.334873 | − | 0.942263i | \(-0.608694\pi\) | ||||
−0.334873 | + | 0.942263i | \(0.608694\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.45472 | − | 1.68819i | −0.0545564 | − | 0.0633121i | ||||
\(712\) | 12.3340 | 0.462235 | ||||||||
\(713\) | − | 31.6391i | − | 1.18489i | ||||||
\(714\) | 13.2229 | − | 9.46326i | 0.494854 | − | 0.354154i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.08331i | 0.0778569i | ||||||||
\(717\) | −9.56748 | + | 20.8739i | −0.357304 | + | 0.779551i | ||||
\(718\) | − | 1.49291i | − | 0.0557149i | ||||||
\(719\) | −18.4786 | −0.689136 | −0.344568 | − | 0.938761i | \(-0.611975\pi\) | ||||
−0.344568 | + | 0.938761i | \(0.611975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.1739 | + | 8.11271i | 0.527862 | + | 0.302133i | ||||
\(722\) | 9.08331 | 0.338046 | ||||||||
\(723\) | −13.3679 | + | 29.1656i | −0.497159 | + | 1.08468i | ||||
\(724\) | 24.6679i | 0.916777i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.83425 | + | 3.13245i | 0.253643 | + | 0.116256i | ||||
\(727\) | −8.92777 | −0.331113 | −0.165556 | − | 0.986200i | \(-0.552942\pi\) | ||||
−0.165556 | + | 0.986200i | \(0.552942\pi\) | |||||||
\(728\) | −11.4620 | − | 6.56050i | −0.424809 | − | 0.243148i | ||||
\(729\) | −22.8334 | + | 14.4096i | −0.845681 | + | 0.533689i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.3493 | 0.382782 | ||||||||
\(732\) | −1.79520 | + | 3.91669i | −0.0663525 | + | 0.144765i | ||||
\(733\) | −24.7934 | −0.915765 | −0.457883 | − | 0.889013i | \(-0.651392\pi\) | ||||
−0.457883 | + | 0.889013i | \(0.651392\pi\) | |||||||
\(734\) | 16.9544 | 0.625800 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.54528 | 0.278123 | ||||||||
\(737\) | −2.13567 | −0.0786686 | ||||||||
\(738\) | 18.2552 | + | 21.1850i | 0.671985 | + | 0.779830i | ||||
\(739\) | −5.32629 | −0.195931 | −0.0979654 | − | 0.995190i | \(-0.531233\pi\) | ||||
−0.0979654 | + | 0.995190i | \(0.531233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.3442 | − | 24.7504i | 0.416741 | − | 0.909228i | ||||
\(742\) | 0.661561 | + | 0.378659i | 0.0242867 | + | 0.0139010i | ||||
\(743\) | −45.7409 | −1.67807 | −0.839035 | − | 0.544078i | \(-0.816880\pi\) | ||||
−0.839035 | + | 0.544078i | \(0.816880\pi\) | |||||||
\(744\) | −3.02618 | + | 6.60240i | −0.110945 | + | 0.242056i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.8097i | 0.835122i | ||||||||
\(747\) | −10.1259 | + | 8.72555i | −0.370487 | + | 0.319251i | ||||
\(748\) | 13.8976 | 0.508146 | ||||||||
\(749\) | −6.10686 | − | 3.49539i | −0.223140 | − | 0.127719i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.8857 | −0.798622 | −0.399311 | − | 0.916815i | \(-0.630751\pi\) | ||||
−0.399311 | + | 0.916815i | \(0.630751\pi\) | |||||||
\(752\) | 8.00387i | 0.291871i | ||||||||
\(753\) | 33.9085 | + | 15.5418i | 1.23569 | + | 0.566375i | ||||
\(754\) | − | 37.6635i | − | 1.37162i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.24621 | + | 13.3590i | −0.118063 | + | 0.485861i | ||||
\(757\) | − | 14.0524i | − | 0.510742i | −0.966843 | − | 0.255371i | \(-0.917802\pi\) | ||
0.966843 | − | 0.255371i | \(-0.0821976\pi\) | |||||||
\(758\) | −0.371417 | −0.0134905 | ||||||||
\(759\) | 21.3276 | − | 46.5316i | 0.774142 | − | 1.68899i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.6210 | −1.79876 | −0.899380 | − | 0.437167i | \(-0.855982\pi\) | ||||
−0.899380 | + | 0.437167i | \(0.855982\pi\) | |||||||
\(762\) | 1.44337 | − | 3.14908i | 0.0522877 | − | 0.114079i | ||||
\(763\) | 34.2687 | + | 19.6144i | 1.24061 | + | 0.710089i | ||||
\(764\) | − | 16.0072i | − | 0.579122i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 32.8367i | − | 1.18644i | ||||||
\(767\) | 29.4455 | 1.06322 | ||||||||
\(768\) | −1.57454 | − | 0.721683i | −0.0568163 | − | 0.0260415i | ||||
\(769\) | − | 12.9903i | − | 0.468442i | −0.972183 | − | 0.234221i | \(-0.924746\pi\) | ||
0.972183 | − | 0.234221i | \(-0.0752540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.0145 | − | 50.2120i | 0.828846 | − | 1.80834i | ||||
\(772\) | 26.4310i | 0.951273i | ||||||||
\(773\) | 29.9500i | 1.07723i | 0.842553 | + | 0.538613i | \(0.181051\pi\) | ||||
−0.842553 | + | 0.538613i | \(0.818949\pi\) | |||||||
\(774\) | −6.62858 | + | 5.71189i | −0.238260 | + | 0.205310i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.524688 | 0.0188352 | ||||||||
\(777\) | 38.9870 | − | 27.9020i | 1.39865 | − | 1.00098i | ||||
\(778\) | 24.1287i | 0.865057i | ||||||||
\(779\) | 29.3550i | 1.05175i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.0382 | −0.752805 | ||||||||
\(782\) | − | 26.7729i | − | 0.957396i | ||||||
\(783\) | −37.6635 | + | 10.8906i | −1.34598 | + | 0.389198i | ||||
\(784\) | 3.54528 | + | 6.03581i | 0.126617 | + | 0.215565i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.1215 | − | 10.5976i | −0.824716 | − | 0.378005i | ||||
\(787\) | 1.01612 | 0.0362207 | 0.0181103 | − | 0.999836i | \(-0.494235\pi\) | ||||
0.0181103 | + | 0.999836i | \(0.494235\pi\) | |||||||
\(788\) | −17.2644 | −0.615019 | ||||||||
\(789\) | 22.3173 | + | 10.2290i | 0.794517 | + | 0.364163i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.1010 | − | 15.5119i | −0.963602 | − | 0.551538i | ||||
\(792\) | −8.90122 | + | 7.67024i | −0.316291 | + | 0.272550i | ||||
\(793\) | − | 12.4168i | − | 0.440935i | ||||||
\(794\) | 7.35371 | 0.260973 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 10.8906i | − | 0.386007i | ||||||
\(797\) | 40.4247i | 1.43192i | 0.698143 | + | 0.715959i | \(0.254010\pi\) | ||||
−0.698143 | + | 0.715959i | \(0.745990\pi\) | |||||||
\(798\) | −11.7352 | + | 8.39856i | −0.415421 | + | 0.297306i | ||||
\(799\) | 28.4001 | 1.00472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.1542 | + | 28.0306i | 0.853446 | + | 0.990414i | ||||
\(802\) | 17.1215i | 0.604581i | ||||||||
\(803\) | − | 19.0147i | − | 0.671015i | ||||||
\(804\) | 0.393516 | − | 0.858557i | 0.0138782 | − | 0.0302790i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 20.9312i | − | 0.737269i | ||||||
\(807\) | 10.5191 | + | 4.82138i | 0.370290 | + | 0.169721i | ||||
\(808\) | 8.00387 | 0.281575 | ||||||||
\(809\) | 23.0287i | 0.809645i | 0.914395 | + | 0.404822i | \(0.132667\pi\) | ||||
−0.914395 | + | 0.404822i | \(0.867333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.9272i | − | 1.05089i | −0.850829 | − | 0.525443i | \(-0.823900\pi\) | ||
0.850829 | − | 0.525443i | \(-0.176100\pi\) | |||||||
\(812\) | −9.91669 | + | 17.3256i | −0.348008 | + | 0.608010i | ||||
\(813\) | −6.82614 | + | 14.8930i | −0.239403 | + | 0.522320i | ||||
\(814\) | 40.9763 | 1.43622 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.56075 | + | 5.58693i | −0.0896440 | + | 0.195582i | ||||
\(817\) | −9.18489 | −0.321339 | ||||||||
\(818\) | − | 23.2246i | − | 0.812028i | ||||||
\(819\) | −7.53686 | − | 38.8966i | −0.263359 | − | 1.35916i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.9763i | − | 0.383076i | −0.981485 | − | 0.191538i | \(-0.938653\pi\) | ||
0.981485 | − | 0.191538i | \(-0.0613474\pi\) | |||||||
\(822\) | 28.9379 | + | 13.2636i | 1.00933 | + | 0.462620i | ||||
\(823\) | 28.6286i | 0.997930i | 0.866622 | + | 0.498965i | \(0.166286\pi\) | ||||
−0.866622 | + | 0.498965i | \(0.833714\pi\) | |||||||
\(824\) | −6.17269 | −0.215036 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.5453 | − | 7.75293i | −0.471300 | − | 0.269759i | ||||
\(827\) | 1.97858 | 0.0688018 | 0.0344009 | − | 0.999408i | \(-0.489048\pi\) | ||||
0.0344009 | + | 0.999408i | \(0.489048\pi\) | |||||||
\(828\) | 14.7763 | + | 17.1477i | 0.513510 | + | 0.595923i | ||||
\(829\) | − | 39.7518i | − | 1.38064i | −0.723506 | − | 0.690318i | \(-0.757471\pi\) | ||
0.723506 | − | 0.690318i | \(-0.242529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.08632 | + | 17.6424i | −0.280511 | + | 0.612008i | ||||
\(832\) | 4.99166 | 0.173055 | ||||||||
\(833\) | 21.4168 | − | 12.5797i | 0.742050 | − | 0.435860i | ||||
\(834\) | 9.09878 | − | 19.8513i | 0.315065 | − | 0.687396i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.3340 | −0.426579 | ||||||||
\(837\) | −20.9312 | + | 6.05237i | −0.723487 | + | 0.209200i | ||||
\(838\) | −11.5522 | −0.399063 | ||||||||
\(839\) | 19.5508 | 0.674969 | 0.337484 | − | 0.941331i | \(-0.390424\pi\) | ||||
0.337484 | + | 0.941331i | \(0.390424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9312 | −0.963144 | ||||||||
\(842\) | 36.9239 | 1.27248 | ||||||||
\(843\) | 2.09970 | − | 4.58104i | 0.0723176 | − | 0.157779i | ||||
\(844\) | −6.88575 | −0.237017 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.1899 | + | 15.6743i | −0.625381 | + | 0.538895i | ||||
\(847\) | 9.96670 | + | 5.70465i | 0.342460 | + | 0.196014i | ||||
\(848\) | −0.288109 | −0.00989369 | ||||||||
\(849\) | 38.4276 | + | 17.6131i | 1.31883 | + | 0.604480i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 78.9384i | − | 2.70597i | ||||||
\(852\) | 3.87646 | − | 8.45750i | 0.132805 | − | 0.289749i | ||||
\(853\) | 11.6724 | 0.399656 | 0.199828 | − | 0.979831i | \(-0.435962\pi\) | ||||
0.199828 | + | 0.979831i | \(0.435962\pi\) | |||||||
\(854\) | −3.26932 | + | 5.71189i | −0.111874 | + | 0.195457i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.65953 | 0.0909007 | ||||||||
\(857\) | 3.91425i | 0.133708i | 0.997763 | + | 0.0668542i | \(0.0212962\pi\) | ||||
−0.997763 | + | 0.0668542i | \(0.978704\pi\) | |||||||
\(858\) | 14.1095 | − | 30.7835i | 0.481690 | − | 1.05093i | ||||
\(859\) | 43.3229i | 1.47816i | 0.673619 | + | 0.739079i | \(0.264739\pi\) | ||||
−0.673619 | + | 0.739079i | \(0.735261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.8610 | + | 34.7380i | 0.847262 | + | 1.18387i | ||||
\(862\) | − | 5.03094i | − | 0.171355i | ||||||
\(863\) | 33.8479 | 1.15219 | 0.576097 | − | 0.817381i | \(-0.304575\pi\) | ||||
0.576097 | + | 0.817381i | \(0.304575\pi\) | |||||||
\(864\) | −1.44337 | − | 4.99166i | −0.0491043 | − | 0.169820i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.04024 | 0.103311 | ||||||||
\(867\) | −6.94309 | − | 3.18234i | −0.235800 | − | 0.108078i | ||||
\(868\) | −5.51112 | + | 9.62858i | −0.187060 | + | 0.326815i | ||||
\(869\) | − | 2.90945i | − | 0.0986963i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.72183i | 0.0922257i | ||||||||
\(872\) | −14.9239 | −0.505388 | ||||||||
\(873\) | 1.02752 | + | 1.19243i | 0.0347763 | + | 0.0403575i | ||||
\(874\) | 23.7607i | 0.803716i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.64405 | + | 3.50362i | 0.258269 | + | 0.118376i | ||||
\(877\) | 15.4383i | 0.521313i | 0.965432 | + | 0.260657i | \(0.0839390\pi\) | ||||
−0.965432 | + | 0.260657i | \(0.916061\pi\) | |||||||
\(878\) | 19.8184i | 0.668838i | ||||||||
\(879\) | 12.3263 | − | 26.8930i | 0.415756 | − | 0.907078i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.64800 | −0.190286 | −0.0951429 | − | 0.995464i | \(-0.530331\pi\) | ||||
−0.0951429 | + | 0.995464i | \(0.530331\pi\) | |||||||
\(882\) | −6.77434 | + | 19.8773i | −0.228104 | + | 0.669305i | ||||
\(883\) | − | 7.05237i | − | 0.237331i | −0.992934 | − | 0.118666i | \(-0.962138\pi\) | ||
0.992934 | − | 0.118666i | \(-0.0378616\pi\) | |||||||
\(884\) | − | 17.7119i | − | 0.595715i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.5976 | −0.356035 | ||||||||
\(887\) | 21.9461i | 0.736878i | 0.929652 | + | 0.368439i | \(0.120108\pi\) | ||||
−0.929652 | + | 0.368439i | \(0.879892\pi\) | |||||||
\(888\) | −7.55023 | + | 16.4728i | −0.253369 | + | 0.552790i | ||||
\(889\) | 2.62858 | − | 4.59244i | 0.0881599 | − | 0.154026i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.8633 | − | 5.20827i | −1.16797 | − | 0.174484i | ||||
\(892\) | −2.90336 | −0.0972118 | ||||||||
\(893\) | −25.2048 | −0.843446 | ||||||||
\(894\) | 4.08439 | − | 8.91114i | 0.136602 | − | 0.298033i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.29622 | − | 1.31429i | −0.0767114 | − | 0.0439074i | ||||
\(897\) | −59.3026 | − | 27.1811i | −1.98006 | − | 0.907551i | ||||
\(898\) | − | 6.19756i | − | 0.206815i | ||||||
\(899\) | −31.6391 | −1.05522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.02229i | 0.0340576i | ||||||||
\(902\) | 36.5105i | 1.21567i | ||||||||
\(903\) | −10.8692 | + | 7.77879i | −0.361704 | + | 0.258862i | ||||
\(904\) | 11.8024 | 0.392543 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.13881 | + | 1.89701i | 0.137503 | + | 0.0630238i | ||||
\(907\) | − | 51.7787i | − | 1.71928i | −0.510896 | − | 0.859642i | \(-0.670686\pi\) | ||
0.510896 | − | 0.859642i | \(-0.329314\pi\) | |||||||
\(908\) | 21.6557i | 0.718671i | ||||||||
\(909\) | 15.6743 | + | 18.1899i | 0.519885 | + | 0.603321i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.2644i | 1.16836i | 0.811623 | + | 0.584181i | \(0.198584\pi\) | ||||
−0.811623 | + | 0.584181i | \(0.801416\pi\) | |||||||
\(912\) | 2.27264 | − | 4.95835i | 0.0752545 | − | 0.164187i | ||||
\(913\) | −17.4511 | −0.577547 | ||||||||
\(914\) | 19.7573i | 0.653514i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 16.9378i | − | 0.559641i | ||||||
\(917\) | −33.7191 | − | 19.2999i | −1.11350 | − | 0.637338i | ||||
\(918\) | −17.7119 | + | 5.12149i | −0.584580 | + | 0.169034i | ||||
\(919\) | 22.0145 | 0.726191 | 0.363095 | − | 0.931752i | \(-0.381720\pi\) | ||||
0.363095 | + | 0.931752i | \(0.381720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.5942 | + | 8.52256i | 0.612699 | + | 0.280828i | ||||
\(922\) | −26.8983 | −0.885849 | ||||||||
\(923\) | 26.8123i | 0.882538i | ||||||||
\(924\) | −14.5957 | + | 10.4458i | −0.480165 | + | 0.343641i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 38.7573i | − | 1.27364i | ||||||
\(927\) | −12.0883 | − | 14.0283i | −0.397030 | − | 0.460749i | ||||
\(928\) | − | 7.54528i | − | 0.247686i | ||||||
\(929\) | 21.4048 | 0.702268 | 0.351134 | − | 0.936325i | \(-0.385796\pi\) | ||||
0.351134 | + | 0.936325i | \(0.385796\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.0072 | + | 11.1643i | −0.622937 | + | 0.365897i | ||||
\(932\) | 5.42378 | 0.177662 | ||||||||
\(933\) | −4.54528 | − | 2.08331i | −0.148806 | − | 0.0682044i | ||||
\(934\) | − | 18.5181i | − | 0.605929i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.77540 | + | 11.3442i | 0.319519 | + | 0.370798i | ||||
\(937\) | 37.3845 | 1.22130 | 0.610649 | − | 0.791901i | \(-0.290909\pi\) | ||||
0.610649 | + | 0.791901i | \(0.290909\pi\) | |||||||
\(938\) | 0.716650 | − | 1.25207i | 0.0233995 | − | 0.0408816i | ||||
\(939\) | −6.62858 | − | 3.03818i | −0.216316 | − | 0.0991474i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.1598 | −1.11358 | −0.556789 | − | 0.830654i | \(-0.687967\pi\) | ||||
−0.556789 | + | 0.830654i | \(0.687967\pi\) | |||||||
\(942\) | 38.2382 | + | 17.5263i | 1.24587 | + | 0.571039i | ||||
\(943\) | 70.3353 | 2.29043 | ||||||||
\(944\) | 5.89894 | 0.191994 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.4238 | −0.371419 | ||||||||
\(947\) | −46.2430 | −1.50270 | −0.751348 | − | 0.659907i | \(-0.770596\pi\) | ||||
−0.751348 | + | 0.659907i | \(0.770596\pi\) | |||||||
\(948\) | 1.16962 | + | 0.536091i | 0.0379875 | + | 0.0174114i | ||||
\(949\) | −24.2335 | −0.786652 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.6307 | − | 16.7895i | −1.18783 | − | 0.544438i | ||||
\(952\) | −4.66349 | + | 8.14768i | −0.151145 | + | 0.264068i | ||||
\(953\) | −25.1360 | −0.814234 | −0.407117 | − | 0.913376i | \(-0.633466\pi\) | ||||
−0.407117 | + | 0.913376i | \(0.633466\pi\) | |||||||
\(954\) | −0.564216 | − | 0.654766i | −0.0182672 | − | 0.0211988i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 13.2572i | − | 0.428767i | ||||||
\(957\) | −46.5316 | − | 21.3276i | −1.50415 | − | 0.689422i | ||||
\(958\) | −14.4337 | −0.466331 | ||||||||
\(959\) | 42.2015 | + | 24.1549i | 1.36276 | + | 0.780003i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.4168 | 0.432801 | ||||||||
\(962\) | − | 52.2226i | − | 1.68372i | ||||||
\(963\) | 5.20827 | + | 6.04414i | 0.167834 | + | 0.194770i | ||||
\(964\) | − | 18.5233i | − | 0.596595i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 20.1232 | + | 28.1178i | 0.647452 | + | 0.904677i | ||||
\(967\) | 50.1287i | 1.61203i | 0.591894 | + | 0.806016i | \(0.298380\pi\) | ||||
−0.591894 | + | 0.806016i | \(0.701620\pi\) | |||||||
\(968\) | −4.34047 | −0.139508 | ||||||||
\(969\) | −17.5937 | − | 8.06399i | −0.565190 | − | 0.259053i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.5387 | −1.62187 | −0.810933 | − | 0.585139i | \(-0.801040\pi\) | ||||
−0.810933 | + | 0.585139i | \(0.801040\pi\) | |||||||
\(972\) | 8.51763 | − | 13.0557i | 0.273203 | − | 0.418760i | ||||
\(973\) | 16.5702 | − | 28.9501i | 0.531217 | − | 0.928098i | ||||
\(974\) | 26.2430i | 0.840879i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 2.48752i | − | 0.0796235i | ||||||
\(977\) | −61.1360 | −1.95591 | −0.977957 | − | 0.208808i | \(-0.933042\pi\) | ||||
−0.977957 | + | 0.208808i | \(0.933042\pi\) | |||||||
\(978\) | −9.71528 | + | 21.1964i | −0.310660 | + | 0.677786i | ||||
\(979\) | 48.3084i | 1.54394i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.2262 | − | 33.9167i | −0.933122 | − | 1.08288i | ||||
\(982\) | 30.0000i | 0.957338i | ||||||||
\(983\) | 9.32699i | 0.297485i | 0.988876 | + | 0.148742i | \(0.0475225\pi\) | ||||
−0.988876 | + | 0.148742i | \(0.952477\pi\) | |||||||
\(984\) | −14.6775 | − | 6.72736i | −0.467901 | − | 0.214460i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −26.7729 | −0.852622 | ||||||||
\(987\) | −29.8268 | + | 21.3462i | −0.949398 | + | 0.679458i | ||||
\(988\) | 15.7191i | 0.500092i | ||||||||
\(989\) | 22.0072i | 0.699790i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0527 | 1.43115 | 0.715573 | − | 0.698538i | \(-0.246166\pi\) | ||||
0.715573 | + | 0.698538i | \(0.246166\pi\) | |||||||
\(992\) | − | 4.19323i | − | 0.133135i | ||||||
\(993\) | 40.0909 | + | 18.3755i | 1.27224 | + | 0.583128i | ||||
\(994\) | 7.05961 | − | 12.3340i | 0.223917 | − | 0.391210i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.21551 | − | 7.01547i | 0.101887 | − | 0.222294i | ||||
\(997\) | 14.0283 | 0.444280 | 0.222140 | − | 0.975015i | \(-0.428696\pi\) | ||||
0.222140 | + | 0.975015i | \(0.428696\pi\) | |||||||
\(998\) | −41.6740 | −1.31917 | ||||||||
\(999\) | −52.2226 | + | 15.1005i | −1.65225 | + | 0.477757i |
(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 | 1050.2.d.h.1049.1 | 12 | ||
3.2 | odd | 2 | 1050.2.d.g.1049.2 | 12 | |||
5.2 | odd | 4 | 1050.2.b.e.251.9 | yes | 12 | ||
5.3 | odd | 4 | 1050.2.b.d.251.4 | yes | 12 | ||
5.4 | even | 2 | 1050.2.d.g.1049.12 | 12 | |||
7.6 | odd | 2 | inner | 1050.2.d.h.1049.12 | 12 | ||
15.2 | even | 4 | 1050.2.b.e.251.4 | yes | 12 | ||
15.8 | even | 4 | 1050.2.b.d.251.9 | yes | 12 | ||
15.14 | odd | 2 | inner | 1050.2.d.h.1049.11 | 12 | ||
21.20 | even | 2 | 1050.2.d.g.1049.11 | 12 | |||
35.13 | even | 4 | 1050.2.b.d.251.3 | ✓ | 12 | ||
35.27 | even | 4 | 1050.2.b.e.251.10 | yes | 12 | ||
35.34 | odd | 2 | 1050.2.d.g.1049.1 | 12 | |||
105.62 | odd | 4 | 1050.2.b.e.251.3 | yes | 12 | ||
105.83 | odd | 4 | 1050.2.b.d.251.10 | yes | 12 | ||
105.104 | even | 2 | inner | 1050.2.d.h.1049.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.b.d.251.3 | ✓ | 12 | 35.13 | even | 4 | ||
1050.2.b.d.251.4 | yes | 12 | 5.3 | odd | 4 | ||
1050.2.b.d.251.9 | yes | 12 | 15.8 | even | 4 | ||
1050.2.b.d.251.10 | yes | 12 | 105.83 | odd | 4 | ||
1050.2.b.e.251.3 | yes | 12 | 105.62 | odd | 4 | ||
1050.2.b.e.251.4 | yes | 12 | 15.2 | even | 4 | ||
1050.2.b.e.251.9 | yes | 12 | 5.2 | odd | 4 | ||
1050.2.b.e.251.10 | yes | 12 | 35.27 | even | 4 | ||
1050.2.d.g.1049.1 | 12 | 35.34 | odd | 2 | |||
1050.2.d.g.1049.2 | 12 | 3.2 | odd | 2 | |||
1050.2.d.g.1049.11 | 12 | 21.20 | even | 2 | |||
1050.2.d.g.1049.12 | 12 | 5.4 | even | 2 | |||
1050.2.d.h.1049.1 | 12 | 1.1 | even | 1 | trivial | ||
1050.2.d.h.1049.2 | 12 | 105.104 | even | 2 | inner | ||
1050.2.d.h.1049.11 | 12 | 15.14 | odd | 2 | inner | ||
1050.2.d.h.1049.12 | 12 | 7.6 | odd | 2 | inner |