Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(251,1050)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.251");
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.b (of order \(2\), degree \(1\), 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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.10 | ||
Root | \(0.721683 + 1.57454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.e.251.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.721683 | − | 1.57454i | 0.416664 | − | 0.909060i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.57454 | + | 0.721683i | 0.642803 | + | 0.294626i | ||||
\(7\) | 1.31429 | + | 2.29622i | 0.496756 | + | 0.867891i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −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 | \(0.798945\pi\) | |||||||
\(12\) | −0.721683 | + | 1.57454i | −0.208332 | + | 0.454530i | ||||
\(13\) | 4.99166i | 1.38444i | 0.721688 | + | 0.692219i | \(0.243367\pi\) | ||||
−0.721688 | + | 0.692219i | \(0.756633\pi\) | |||||||
\(14\) | −2.29622 | + | 1.31429i | −0.613691 | + | 0.351259i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.54830 | −0.860588 | −0.430294 | − | 0.902689i | \(-0.641590\pi\) | ||||
−0.430294 | + | 0.902689i | \(0.641590\pi\) | |||||||
\(18\) | 2.27264 | − | 1.95835i | 0.535666 | − | 0.461587i | ||||
\(19\) | 3.14908i | 0.722448i | 0.932479 | + | 0.361224i | \(0.117641\pi\) | ||||
−0.932479 | + | 0.361224i | \(0.882359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.56399 | − | 0.412258i | 0.995945 | − | 0.0899620i | ||||
\(22\) | −3.91669 | −0.835041 | ||||||||
\(23\) | − | 7.54528i | − | 1.57330i | −0.617400 | − | 0.786649i | \(-0.711814\pi\) | ||
0.617400 | − | 0.786649i | \(-0.288186\pi\) | |||||||
\(24\) | −1.57454 | − | 0.721683i | −0.321401 | − | 0.147313i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.99166 | −0.978946 | ||||||||
\(27\) | −4.99166 | + | 1.44337i | −0.960646 | + | 0.277776i | ||||
\(28\) | −1.31429 | − | 2.29622i | −0.248378 | − | 0.433945i | ||||
\(29\) | 7.54528i | 1.40112i | 0.713592 | + | 0.700561i | \(0.247067\pi\) | ||||
−0.713592 | + | 0.700561i | \(0.752933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.19323i | 0.753126i | 0.926391 | + | 0.376563i | \(0.122894\pi\) | ||||
−0.926391 | + | 0.376563i | \(0.877106\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 6.16698 | + | 2.82661i | 1.07353 | + | 0.492050i | ||||
\(34\) | − | 3.54830i | − | 0.608528i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.95835 | + | 2.27264i | 0.326391 | + | 0.378773i | ||||
\(37\) | 10.4620 | 1.71994 | 0.859968 | − | 0.510347i | \(-0.170483\pi\) | ||||
0.859968 | + | 0.510347i | \(0.170483\pi\) | |||||||
\(38\) | −3.14908 | −0.510848 | ||||||||
\(39\) | 7.85957 | + | 3.60240i | 1.25854 | + | 0.576846i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.32176 | −1.45581 | −0.727907 | − | 0.685675i | \(-0.759507\pi\) | ||||
−0.727907 | + | 0.685675i | \(0.759507\pi\) | |||||||
\(42\) | 0.412258 | + | 4.56399i | 0.0636127 | + | 0.704240i | ||||
\(43\) | 2.91669 | 0.444791 | 0.222396 | − | 0.974956i | \(-0.428612\pi\) | ||||
0.222396 | + | 0.974956i | \(0.428612\pi\) | |||||||
\(44\) | − | 3.91669i | − | 0.590464i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.54528 | 1.11249 | ||||||||
\(47\) | 8.00387 | 1.16748 | 0.583742 | − | 0.811939i | \(-0.301588\pi\) | ||||
0.583742 | + | 0.811939i | \(0.301588\pi\) | |||||||
\(48\) | 0.721683 | − | 1.57454i | 0.104166 | − | 0.227265i | ||||
\(49\) | −3.54528 | + | 6.03581i | −0.506468 | + | 0.862259i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.56075 | + | 5.58693i | −0.358576 | + | 0.782327i | ||||
\(52\) | − | 4.99166i | − | 0.692219i | ||||||
\(53\) | 0.288109i | 0.0395748i | 0.999804 | + | 0.0197874i | \(0.00629893\pi\) | ||||
−0.999804 | + | 0.0197874i | \(0.993701\pi\) | |||||||
\(54\) | −1.44337 | − | 4.99166i | −0.196417 | − | 0.679279i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.29622 | − | 1.31429i | 0.306846 | − | 0.175630i | ||||
\(57\) | 4.95835 | + | 2.27264i | 0.656749 | + | 0.301018i | ||||
\(58\) | −7.54528 | −0.990743 | ||||||||
\(59\) | 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 | \(0.0509066\pi\) | ||||
−0.987239 | + | 0.159247i | \(0.949093\pi\) | |||||||
\(62\) | −4.19323 | −0.532540 | ||||||||
\(63\) | 2.64464 | − | 7.48371i | 0.333194 | − | 0.942858i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.82661 | + | 6.16698i | −0.347932 | + | 0.759103i | ||||
\(67\) | −0.545275 | −0.0666160 | −0.0333080 | − | 0.999445i | \(-0.510604\pi\) | ||||
−0.0333080 | + | 0.999445i | \(0.510604\pi\) | |||||||
\(68\) | 3.54830 | 0.430294 | ||||||||
\(69\) | −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 | \(0.896742\pi\) | |||||||
\(72\) | −2.27264 | + | 1.95835i | −0.267833 | + | 0.230793i | ||||
\(73\) | − | 4.85479i | − | 0.568210i | −0.958793 | − | 0.284105i | \(-0.908304\pi\) | ||
0.958793 | − | 0.284105i | \(-0.0916964\pi\) | |||||||
\(74\) | 10.4620i | 1.21618i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.14908i | − | 0.361224i | ||||||
\(77\) | −8.99360 | + | 5.14768i | −1.02492 | + | 0.586632i | ||||
\(78\) | −3.60240 | + | 7.85957i | −0.407891 | + | 0.889921i | ||||
\(79\) | 0.742834 | 0.0835753 | 0.0417876 | − | 0.999127i | \(-0.486695\pi\) | ||||
0.0417876 | + | 0.999127i | \(0.486695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.32976 | + | 8.90122i | −0.147751 | + | 0.989025i | ||||
\(82\) | − | 9.32176i | − | 1.02942i | ||||||
\(83\) | −4.45557 | −0.489063 | −0.244531 | − | 0.969641i | \(-0.578634\pi\) | ||||
−0.244531 | + | 0.969641i | \(0.578634\pi\) | |||||||
\(84\) | −4.56399 | + | 0.412258i | −0.497973 | + | 0.0449810i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.91669i | 0.314515i | ||||||||
\(87\) | 11.8803 | + | 5.44530i | 1.27371 | + | 0.583797i | ||||
\(88\) | 3.91669 | 0.417521 | ||||||||
\(89\) | 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 | ||||
\(92\) | 7.54528i | 0.786649i | ||||||||
\(93\) | 6.60240 | + | 3.02618i | 0.684637 | + | 0.313801i | ||||
\(94\) | 8.00387i | 0.825536i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.57454 | + | 0.721683i | 0.160701 | + | 0.0736565i | ||||
\(97\) | − | 0.524688i | − | 0.0532740i | −0.999645 | − | 0.0266370i | \(-0.991520\pi\) | ||
0.999645 | − | 0.0266370i | \(-0.00847982\pi\) | |||||||
\(98\) | −6.03581 | − | 3.54528i | −0.609709 | − | 0.358127i | ||||
\(99\) | 8.90122 | − | 7.67024i | 0.894606 | − | 0.770888i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.00387 | −0.796415 | −0.398207 | − | 0.917295i | \(-0.630368\pi\) | ||||
−0.398207 | + | 0.917295i | \(0.630368\pi\) | |||||||
\(102\) | −5.58693 | − | 2.56075i | −0.553188 | − | 0.253552i | ||||
\(103\) | − | 6.17269i | − | 0.608213i | −0.952638 | − | 0.304106i | \(-0.901642\pi\) | ||
0.952638 | − | 0.304106i | \(-0.0983578\pi\) | |||||||
\(104\) | 4.99166 | 0.489473 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.288109 | −0.0279836 | ||||||||
\(107\) | 2.65953i | 0.257106i | 0.991703 | + | 0.128553i | \(0.0410332\pi\) | ||||
−0.991703 | + | 0.128553i | \(0.958967\pi\) | |||||||
\(108\) | 4.99166 | − | 1.44337i | 0.480323 | − | 0.138888i | ||||
\(109\) | 14.9239 | 1.42945 | 0.714727 | − | 0.699404i | \(-0.246551\pi\) | ||||
0.714727 | + | 0.699404i | \(0.246551\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.55023 | − | 16.4728i | 0.716636 | − | 1.56353i | ||||
\(112\) | 1.31429 | + | 2.29622i | 0.124189 | + | 0.216973i | ||||
\(113\) | − | 11.8024i | − | 1.11028i | −0.831757 | − | 0.555140i | \(-0.812665\pi\) | ||
0.831757 | − | 0.555140i | \(-0.187335\pi\) | |||||||
\(114\) | −2.27264 | + | 4.95835i | −0.212852 | + | 0.464392i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.54528i | − | 0.700561i | ||||||
\(117\) | 11.3442 | − | 9.77540i | 1.04878 | − | 0.903736i | ||||
\(118\) | 5.89894i | 0.543041i | ||||||||
\(119\) | −4.66349 | − | 8.14768i | −0.427502 | − | 0.746896i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.34047 | −0.394589 | ||||||||
\(122\) | −2.48752 | −0.225209 | ||||||||
\(123\) | −6.72736 | + | 14.6775i | −0.606586 | + | 1.32342i | ||||
\(124\) | − | 4.19323i | − | 0.376563i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.48371 | + | 2.64464i | 0.666702 | + | 0.235604i | ||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 2.10493 | − | 4.59244i | 0.185329 | − | 0.404342i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.6846 | −1.28300 | −0.641500 | − | 0.767123i | \(-0.721688\pi\) | ||||
−0.641500 | + | 0.767123i | \(0.721688\pi\) | |||||||
\(132\) | −6.16698 | − | 2.82661i | −0.536767 | − | 0.246025i | ||||
\(133\) | −7.23098 | + | 4.13881i | −0.627006 | + | 0.358880i | ||||
\(134\) | − | 0.545275i | − | 0.0471046i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.54830i | 0.304264i | ||||||||
\(137\) | − | 18.3787i | − | 1.57019i | −0.619372 | − | 0.785097i | \(-0.712613\pi\) | ||
0.619372 | − | 0.785097i | \(-0.287387\pi\) | |||||||
\(138\) | 5.44530 | − | 11.8803i | 0.463535 | − | 1.01132i | ||||
\(139\) | 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 | ||||
\(142\) | −5.37142 | −0.450759 | ||||||||
\(143\) | −19.5508 | −1.63492 | ||||||||
\(144\) | −1.95835 | − | 2.27264i | −0.163195 | − | 0.189386i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.85479 | 0.401785 | ||||||||
\(147\) | 6.94505 | + | 9.93812i | 0.572818 | + | 0.819682i | ||||
\(148\) | −10.4620 | −0.859968 | ||||||||
\(149\) | − | 5.65953i | − | 0.463646i | −0.972758 | − | 0.231823i | \(-0.925531\pi\) | ||
0.972758 | − | 0.231823i | \(-0.0744691\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.62858 | −0.213911 | −0.106956 | − | 0.994264i | \(-0.534110\pi\) | ||||
−0.106956 | + | 0.994264i | \(0.534110\pi\) | |||||||
\(152\) | 3.14908 | 0.255424 | ||||||||
\(153\) | 6.94879 | + | 8.06399i | 0.561776 | + | 0.651935i | ||||
\(154\) | −5.14768 | − | 8.99360i | −0.414811 | − | 0.724725i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.85957 | − | 3.60240i | −0.629269 | − | 0.288423i | ||||
\(157\) | 24.2853i | 1.93818i | 0.246704 | + | 0.969091i | \(0.420652\pi\) | ||||
−0.246704 | + | 0.969091i | \(0.579348\pi\) | |||||||
\(158\) | 0.742834i | 0.0590967i | ||||||||
\(159\) | 0.453638 | + | 0.207923i | 0.0359758 | + | 0.0164894i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.3256 | − | 9.91669i | 1.36545 | − | 0.781545i | ||||
\(162\) | −8.90122 | − | 1.32976i | −0.699346 | − | 0.104476i | ||||
\(163\) | −13.4620 | −1.05442 | −0.527211 | − | 0.849734i | \(-0.676762\pi\) | ||||
−0.527211 | + | 0.849734i | \(0.676762\pi\) | |||||||
\(164\) | 9.32176 | 0.727907 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 4.45557i | − | 0.345819i | ||||||
\(167\) | −21.7812 | −1.68548 | −0.842740 | − | 0.538321i | \(-0.819059\pi\) | ||||
−0.842740 | + | 0.538321i | \(0.819059\pi\) | |||||||
\(168\) | −0.412258 | − | 4.56399i | −0.0318064 | − | 0.352120i | ||||
\(169\) | −11.9167 | −0.916669 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.15671 | − | 6.16698i | 0.547287 | − | 0.471601i | ||||
\(172\) | −2.91669 | −0.222396 | ||||||||
\(173\) | 0.907276 | 0.0689789 | 0.0344895 | − | 0.999405i | \(-0.489019\pi\) | ||||
0.0344895 | + | 0.999405i | \(0.489019\pi\) | |||||||
\(174\) | −5.44530 | + | 11.8803i | −0.412807 | + | 0.900645i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.91669i | 0.295232i | ||||||||
\(177\) | 4.25717 | − | 9.28811i | 0.319988 | − | 0.698137i | ||||
\(178\) | 12.3340i | 0.924470i | ||||||||
\(179\) | − | 2.08331i | − | 0.155714i | −0.996965 | − | 0.0778569i | \(-0.975192\pi\) | ||
0.996965 | − | 0.0778569i | \(-0.0248077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.6679i | − | 1.83355i | −0.399400 | − | 0.916777i | \(-0.630782\pi\) | ||
0.399400 | − | 0.916777i | \(-0.369218\pi\) | |||||||
\(182\) | −6.56050 | − | 11.4620i | −0.486297 | − | 0.849618i | ||||
\(183\) | 3.91669 | + | 1.79520i | 0.289530 | + | 0.132705i | ||||
\(184\) | −7.54528 | −0.556245 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.02618 | + | 6.60240i | −0.221891 | + | 0.484111i | ||||
\(187\) | − | 13.8976i | − | 1.01629i | ||||||
\(188\) | −8.00387 | −0.583742 | ||||||||
\(189\) | −9.87479 | − | 9.56496i | −0.718285 | − | 0.695749i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.0072i | − | 1.15824i | −0.815241 | − | 0.579122i | \(-0.803396\pi\) | ||
0.815241 | − | 0.579122i | \(-0.196604\pi\) | |||||||
\(192\) | −0.721683 | + | 1.57454i | −0.0520830 | + | 0.113633i | ||||
\(193\) | 26.4310 | 1.90255 | 0.951273 | − | 0.308349i | \(-0.0997764\pi\) | ||||
0.951273 | + | 0.308349i | \(0.0997764\pi\) | |||||||
\(194\) | 0.524688 | 0.0376704 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.54528 | − | 6.03581i | 0.253234 | − | 0.431129i | ||||
\(197\) | − | 17.2644i | − | 1.23004i | −0.788512 | − | 0.615019i | \(-0.789148\pi\) | ||
0.788512 | − | 0.615019i | \(-0.210852\pi\) | |||||||
\(198\) | 7.67024 | + | 8.90122i | 0.545100 | + | 0.632582i | ||||
\(199\) | − | 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 | ||||
\(202\) | − | 8.00387i | − | 0.563150i | ||||||
\(203\) | −17.3256 | + | 9.91669i | −1.21602 | + | 0.696015i | ||||
\(204\) | 2.56075 | − | 5.58693i | 0.179288 | − | 0.391163i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.17269 | 0.430071 | ||||||||
\(207\) | −17.1477 | + | 14.7763i | −1.19185 | + | 1.02702i | ||||
\(208\) | 4.99166i | 0.346110i | ||||||||
\(209\) | −12.3340 | −0.853158 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.88575 | −0.474035 | −0.237017 | − | 0.971505i | \(-0.576170\pi\) | ||||
−0.237017 | + | 0.971505i | \(0.576170\pi\) | |||||||
\(212\) | − | 0.288109i | − | 0.0197874i | ||||||
\(213\) | 8.45750 | + | 3.87646i | 0.579499 | + | 0.265611i | ||||
\(214\) | −2.65953 | −0.181801 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.44337 | + | 4.99166i | 0.0982087 | + | 0.339640i | ||||
\(217\) | −9.62858 | + | 5.51112i | −0.653631 | + | 0.374119i | ||||
\(218\) | 14.9239i | 1.01078i | ||||||||
\(219\) | −7.64405 | − | 3.50362i | −0.516537 | − | 0.236753i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 17.7119i | − | 1.19143i | ||||||
\(222\) | 16.4728 | + | 7.55023i | 1.10558 | + | 0.506738i | ||||
\(223\) | − | 2.90336i | − | 0.194424i | −0.995264 | − | 0.0972118i | \(-0.969008\pi\) | ||
0.995264 | − | 0.0972118i | \(-0.0309924\pi\) | |||||||
\(224\) | −2.29622 | + | 1.31429i | −0.153423 | + | 0.0878148i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8024 | 0.785087 | ||||||||
\(227\) | 21.6557 | 1.43734 | 0.718671 | − | 0.695351i | \(-0.244751\pi\) | ||||
0.718671 | + | 0.695351i | \(0.244751\pi\) | |||||||
\(228\) | −4.95835 | − | 2.27264i | −0.328374 | − | 0.150509i | ||||
\(229\) | − | 16.9378i | − | 1.11928i | −0.828735 | − | 0.559641i | \(-0.810939\pi\) | ||
0.828735 | − | 0.559641i | \(-0.189061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.61469 | + | 17.8758i | 0.106239 | + | 1.17614i | ||||
\(232\) | 7.54528 | 0.495372 | ||||||||
\(233\) | − | 5.42378i | − | 0.355324i | −0.984092 | − | 0.177662i | \(-0.943147\pi\) | ||
0.984092 | − | 0.177662i | \(-0.0568533\pi\) | |||||||
\(234\) | 9.77540 | + | 11.3442i | 0.639038 | + | 0.741596i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.89894 | −0.383988 | ||||||||
\(237\) | 0.536091 | − | 1.16962i | 0.0348228 | − | 0.0759750i | ||||
\(238\) | 8.14768 | − | 4.66349i | 0.528135 | − | 0.302289i | ||||
\(239\) | 13.2572i | 0.857535i | 0.903415 | + | 0.428767i | \(0.141052\pi\) | ||||
−0.903415 | + | 0.428767i | \(0.858948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5233i | 1.19319i | 0.802543 | + | 0.596595i | \(0.203480\pi\) | ||||
−0.802543 | + | 0.596595i | \(0.796520\pi\) | |||||||
\(242\) | − | 4.34047i | − | 0.279016i | ||||||
\(243\) | 13.0557 | + | 8.51763i | 0.837520 | + | 0.546406i | ||||
\(244\) | − | 2.48752i | − | 0.159247i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −14.6775 | − | 6.72736i | −0.935802 | − | 0.428921i | ||||
\(247\) | −15.7191 | −1.00018 | ||||||||
\(248\) | 4.19323 | 0.266270 | ||||||||
\(249\) | −3.21551 | + | 7.01547i | −0.203775 | + | 0.444587i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5355 | 1.35931 | 0.679654 | − | 0.733533i | \(-0.262130\pi\) | ||||
0.679654 | + | 0.733533i | \(0.262130\pi\) | |||||||
\(252\) | −2.64464 | + | 7.48371i | −0.166597 | + | 0.471429i | ||||
\(253\) | 29.5525 | 1.85795 | ||||||||
\(254\) | − | 2.00000i | − | 0.125491i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.8900 | 1.98924 | 0.994622 | − | 0.103575i | \(-0.0330281\pi\) | ||||
0.994622 | + | 0.103575i | \(0.0330281\pi\) | |||||||
\(258\) | 4.59244 | + | 2.10493i | 0.285913 | + | 0.131047i | ||||
\(259\) | 13.7501 | + | 24.0230i | 0.854388 | + | 1.49272i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1477 | − | 14.7763i | 1.06141 | − | 0.914627i | ||||
\(262\) | − | 14.6846i | − | 0.907218i | ||||||
\(263\) | 14.1739i | 0.873998i | 0.899462 | + | 0.436999i | \(0.143959\pi\) | ||||
−0.899462 | + | 0.436999i | \(0.856041\pi\) | |||||||
\(264\) | 2.82661 | − | 6.16698i | 0.173966 | − | 0.379552i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.13881 | − | 7.23098i | −0.253767 | − | 0.443360i | ||||
\(267\) | 8.90122 | − | 19.4203i | 0.544746 | − | 1.18850i | ||||
\(268\) | 0.545275 | 0.0333080 | ||||||||
\(269\) | −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 | \(0.0927529\pi\) | ||||
−0.957845 | + | 0.287286i | \(0.907247\pi\) | |||||||
\(272\) | −3.54830 | −0.215147 | ||||||||
\(273\) | 2.05785 | + | 22.7819i | 0.124547 | + | 1.37882i | ||||
\(274\) | 18.3787 | 1.11030 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.8803 | + | 5.44530i | 0.715112 | + | 0.327769i | ||||
\(277\) | 11.2048 | 0.673231 | 0.336616 | − | 0.941642i | \(-0.390718\pi\) | ||||
0.336616 | + | 0.941642i | \(0.390718\pi\) | |||||||
\(278\) | −12.6077 | −0.756160 | ||||||||
\(279\) | 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 | \(0.972342\pi\) | |||||||
\(282\) | 12.6024 | + | 5.77626i | 0.750462 | + | 0.343971i | ||||
\(283\) | − | 24.4056i | − | 1.45076i | −0.688348 | − | 0.725381i | \(-0.741664\pi\) | ||
0.688348 | − | 0.725381i | \(-0.258336\pi\) | |||||||
\(284\) | − | 5.37142i | − | 0.318735i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 19.5508i | − | 1.15606i | ||||||
\(287\) | −12.2515 | − | 21.4048i | −0.723184 | − | 1.26349i | ||||
\(288\) | 2.27264 | − | 1.95835i | 0.133916 | − | 0.115397i | ||||
\(289\) | −4.40960 | −0.259388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.826142 | − | 0.378659i | −0.0484293 | − | 0.0221974i | ||||
\(292\) | 4.85479i | 0.284105i | ||||||||
\(293\) | −17.0799 | −0.997819 | −0.498910 | − | 0.866654i | \(-0.666266\pi\) | ||||
−0.498910 | + | 0.866654i | \(0.666266\pi\) | |||||||
\(294\) | −9.93812 | + | 6.94505i | −0.579603 | + | 0.405044i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 10.4620i | − | 0.608089i | ||||||
\(297\) | −5.65322 | − | 19.5508i | −0.328033 | − | 1.13445i | ||||
\(298\) | 5.65953 | 0.327847 | ||||||||
\(299\) | 37.6635 | 2.17813 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.83338 | + | 6.69737i | 0.220953 | + | 0.386030i | ||||
\(302\) | − | 2.62858i | − | 0.151258i | ||||||
\(303\) | −5.77626 | + | 12.6024i | −0.331837 | + | 0.723989i | ||||
\(304\) | 3.14908i | 0.180612i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.06399 | + | 6.94879i | −0.460988 | + | 0.397236i | ||||
\(307\) | 11.8093i | 0.673991i | 0.941506 | + | 0.336996i | \(0.109411\pi\) | ||||
−0.941506 | + | 0.336996i | \(0.890589\pi\) | |||||||
\(308\) | 8.99360 | − | 5.14768i | 0.512458 | − | 0.293316i | ||||
\(309\) | −9.71913 | − | 4.45472i | −0.552902 | − | 0.253420i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.88673 | −0.163692 | −0.0818458 | − | 0.996645i | \(-0.526082\pi\) | ||||
−0.0818458 | + | 0.996645i | \(0.526082\pi\) | |||||||
\(312\) | 3.60240 | − | 7.85957i | 0.203946 | − | 0.444960i | ||||
\(313\) | 4.20986i | 0.237955i | 0.992897 | + | 0.118978i | \(0.0379617\pi\) | ||||
−0.992897 | + | 0.118978i | \(0.962038\pi\) | |||||||
\(314\) | −24.2853 | −1.37050 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.742834 | −0.0417876 | ||||||||
\(317\) | 23.2644i | 1.30666i | 0.757074 | + | 0.653330i | \(0.226628\pi\) | ||||
−0.757074 | + | 0.653330i | \(0.773372\pi\) | |||||||
\(318\) | −0.207923 | + | 0.453638i | −0.0116598 | + | 0.0254388i | ||||
\(319\) | −29.5525 | −1.65462 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.18753 | + | 1.91934i | 0.233725 | + | 0.107127i | ||||
\(322\) | 9.91669 | + | 17.3256i | 0.552636 | + | 0.965520i | ||||
\(323\) | − | 11.1739i | − | 0.621730i | ||||||
\(324\) | 1.32976 | − | 8.90122i | 0.0738757 | − | 0.494512i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 13.4620i | − | 0.745589i | ||||||
\(327\) | 10.7704 | − | 23.4983i | 0.595602 | − | 1.29946i | ||||
\(328\) | 9.32176i | 0.514708i | ||||||||
\(329\) | 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 | \(0.746709\pi\) | |||||||
\(332\) | 4.45557 | 0.244531 | ||||||||
\(333\) | −20.4881 | − | 23.7763i | −1.12274 | − | 1.30293i | ||||
\(334\) | − | 21.7812i | − | 1.19181i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.56399 | − | 0.412258i | 0.248986 | − | 0.0224905i | ||||
\(337\) | −7.68095 | −0.418408 | −0.209204 | − | 0.977872i | \(-0.567087\pi\) | ||||
−0.209204 | + | 0.977872i | \(0.567087\pi\) | |||||||
\(338\) | − | 11.9167i | − | 0.648183i | ||||||
\(339\) | −18.5834 | − | 8.51763i | −1.00931 | − | 0.462614i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4236 | −0.889387 | ||||||||
\(342\) | 6.16698 | + | 7.15671i | 0.333472 | + | 0.386991i | ||||
\(343\) | −18.5191 | − | 0.207923i | −0.999937 | − | 0.0112268i | ||||
\(344\) | − | 2.91669i | − | 0.157257i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.907276i | 0.0487755i | ||||||||
\(347\) | 8.26441i | 0.443657i | 0.975086 | + | 0.221828i | \(0.0712025\pi\) | ||||
−0.975086 | + | 0.221828i | \(0.928798\pi\) | |||||||
\(348\) | −11.8803 | − | 5.44530i | −0.636853 | − | 0.291899i | ||||
\(349\) | − | 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 | ||||
\(352\) | −3.91669 | −0.208760 | ||||||||
\(353\) | 18.8945 | 1.00565 | 0.502826 | − | 0.864388i | \(-0.332294\pi\) | ||||
0.502826 | + | 0.864388i | \(0.332294\pi\) | |||||||
\(354\) | 9.28811 | + | 4.25717i | 0.493657 | + | 0.226266i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.3340 | −0.653699 | ||||||||
\(357\) | −16.1944 | + | 1.46281i | −0.857098 | + | 0.0774202i | ||||
\(358\) | 2.08331 | 0.110106 | ||||||||
\(359\) | 1.49291i | 0.0787927i | 0.999224 | + | 0.0393964i | \(0.0125435\pi\) | ||||
−0.999224 | + | 0.0393964i | \(0.987457\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.08331 | 0.478069 | ||||||||
\(362\) | 24.6679 | 1.29652 | ||||||||
\(363\) | −3.13245 | + | 6.83425i | −0.164411 | + | 0.358705i | ||||
\(364\) | 11.4620 | − | 6.56050i | 0.600770 | − | 0.343864i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.79520 | + | 3.91669i | −0.0938366 | + | 0.204729i | ||||
\(367\) | − | 16.9544i | − | 0.885015i | −0.896765 | − | 0.442507i | \(-0.854089\pi\) | ||
0.896765 | − | 0.442507i | \(-0.145911\pi\) | |||||||
\(368\) | − | 7.54528i | − | 0.393325i | ||||||
\(369\) | 18.2552 | + | 21.1850i | 0.950330 | + | 1.10285i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.661561 | + | 0.378659i | −0.0343466 | + | 0.0196590i | ||||
\(372\) | −6.60240 | − | 3.02618i | −0.342319 | − | 0.156900i | ||||
\(373\) | 22.8097 | 1.18104 | 0.590520 | − | 0.807023i | \(-0.298923\pi\) | ||||
0.590520 | + | 0.807023i | \(0.298923\pi\) | |||||||
\(374\) | 13.8976 | 0.718627 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 8.00387i | − | 0.412768i | ||||||
\(377\) | −37.6635 | −1.93977 | ||||||||
\(378\) | 9.56496 | − | 9.87479i | 0.491969 | − | 0.507904i | ||||
\(379\) | 0.371417 | 0.0190784 | 0.00953920 | − | 0.999955i | \(-0.496964\pi\) | ||||
0.00953920 | + | 0.999955i | \(0.496964\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.44337 | + | 3.14908i | −0.0739459 | + | 0.161332i | ||||
\(382\) | 16.0072 | 0.819002 | ||||||||
\(383\) | 32.8367 | 1.67788 | 0.838939 | − | 0.544226i | \(-0.183177\pi\) | ||||
0.838939 | + | 0.544226i | \(0.183177\pi\) | |||||||
\(384\) | −1.57454 | − | 0.721683i | −0.0803504 | − | 0.0368283i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.4310i | 1.34530i | ||||||||
\(387\) | −5.71189 | − | 6.62858i | −0.290352 | − | 0.336950i | ||||
\(388\) | 0.524688i | 0.0266370i | ||||||||
\(389\) | − | 24.1287i | − | 1.22338i | −0.791099 | − | 0.611688i | \(-0.790491\pi\) | ||
0.791099 | − | 0.611688i | \(-0.209509\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.7729i | 1.35396i | ||||||||
\(392\) | 6.03581 | + | 3.54528i | 0.304855 | + | 0.179063i | ||||
\(393\) | −10.5976 | + | 23.1215i | −0.534580 | + | 1.16632i | ||||
\(394\) | 17.2644 | 0.869768 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.90122 | + | 7.67024i | −0.447303 | + | 0.385444i | ||||
\(397\) | − | 7.35371i | − | 0.369072i | −0.982826 | − | 0.184536i | \(-0.940922\pi\) | ||
0.982826 | − | 0.184536i | \(-0.0590782\pi\) | |||||||
\(398\) | 10.8906 | 0.545896 | ||||||||
\(399\) | 1.29823 | + | 14.3724i | 0.0649929 | + | 0.719519i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1215i | 0.855007i | 0.904014 | + | 0.427503i | \(0.140607\pi\) | ||||
−0.904014 | + | 0.427503i | \(0.859393\pi\) | |||||||
\(402\) | −0.858557 | − | 0.393516i | −0.0428209 | − | 0.0196268i | ||||
\(403\) | −20.9312 | −1.04266 | ||||||||
\(404\) | 8.00387 | 0.398207 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.91669 | − | 17.3256i | −0.492157 | − | 0.859857i | ||||
\(407\) | 40.9763i | 2.03112i | ||||||||
\(408\) | 5.58693 | + | 2.56075i | 0.276594 | + | 0.126776i | ||||
\(409\) | − | 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 | ||||
\(412\) | 6.17269i | 0.304106i | ||||||||
\(413\) | 7.75293 | + | 13.5453i | 0.381497 | + | 0.666519i | ||||
\(414\) | −14.7763 | − | 17.1477i | −0.726213 | − | 0.842762i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.99166 | −0.244736 | ||||||||
\(417\) | 19.8513 | + | 9.09878i | 0.972124 | + | 0.445569i | ||||
\(418\) | − | 12.3340i | − | 0.603274i | ||||||
\(419\) | −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 | \(0.143726\pi\) | |||||||
\(422\) | − | 6.88575i | − | 0.335193i | ||||||
\(423\) | −15.6743 | − | 18.1899i | −0.762112 | − | 0.884423i | ||||
\(424\) | 0.288109 | 0.0139918 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.87646 | + | 8.45750i | −0.187815 | + | 0.409767i | ||||
\(427\) | −5.71189 | + | 3.26932i | −0.276418 | + | 0.158214i | ||||
\(428\) | − | 2.65953i | − | 0.128553i | ||||||
\(429\) | −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 | \(-0.0386633\pi\) | |||||||
\(432\) | −4.99166 | + | 1.44337i | −0.240161 | + | 0.0694440i | ||||
\(433\) | 3.04024i | 0.146104i | 0.997328 | + | 0.0730522i | \(0.0232740\pi\) | ||||
−0.997328 | + | 0.0730522i | \(0.976726\pi\) | |||||||
\(434\) | −5.51112 | − | 9.62858i | −0.264542 | − | 0.462187i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.9239 | −0.714727 | ||||||||
\(437\) | 23.7607 | 1.13663 | ||||||||
\(438\) | 3.50362 | − | 7.64405i | 0.167409 | − | 0.365247i | ||||
\(439\) | 19.8184i | 0.945879i | 0.881095 | + | 0.472940i | \(0.156807\pi\) | ||||
−0.881095 | + | 0.472940i | \(0.843193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.6601 | − | 3.76308i | 0.983814 | − | 0.179194i | ||||
\(442\) | 17.7119 | 0.842469 | ||||||||
\(443\) | 10.5976i | 0.503509i | 0.967791 | + | 0.251755i | \(0.0810076\pi\) | ||||
−0.967791 | + | 0.251755i | \(0.918992\pi\) | |||||||
\(444\) | −7.55023 | + | 16.4728i | −0.358318 | + | 0.781763i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.90336 | 0.137478 | ||||||||
\(447\) | −8.91114 | − | 4.08439i | −0.421483 | − | 0.193185i | ||||
\(448\) | −1.31429 | − | 2.29622i | −0.0620944 | − | 0.108486i | ||||
\(449\) | 6.19756i | 0.292481i | 0.989249 | + | 0.146240i | \(0.0467173\pi\) | ||||
−0.989249 | + | 0.146240i | \(0.953283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.5105i | − | 1.71921i | ||||||
\(452\) | 11.8024i | 0.555140i | ||||||||
\(453\) | −1.89701 | + | 4.13881i | −0.0891291 | + | 0.194458i | ||||
\(454\) | 21.6557i | 1.01635i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.27264 | − | 4.95835i | 0.106426 | − | 0.232196i | ||||
\(457\) | −19.7573 | −0.924208 | −0.462104 | − | 0.886826i | \(-0.652905\pi\) | ||||
−0.462104 | + | 0.886826i | \(0.652905\pi\) | |||||||
\(458\) | 16.9378 | 0.791452 | ||||||||
\(459\) | 17.7119 | − | 5.12149i | 0.826720 | − | 0.239051i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.8983 | 1.25278 | 0.626390 | − | 0.779510i | \(-0.284532\pi\) | ||||
0.626390 | + | 0.779510i | \(0.284532\pi\) | |||||||
\(462\) | −17.8758 | + | 1.61469i | −0.831656 | + | 0.0751220i | ||||
\(463\) | −38.7573 | −1.80121 | −0.900603 | − | 0.434643i | \(-0.856874\pi\) | ||||
−0.900603 | + | 0.434643i | \(0.856874\pi\) | |||||||
\(464\) | 7.54528i | 0.350281i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.42378 | 0.251252 | ||||||||
\(467\) | −18.5181 | −0.856913 | −0.428457 | − | 0.903562i | \(-0.640943\pi\) | ||||
−0.428457 | + | 0.903562i | \(0.640943\pi\) | |||||||
\(468\) | −11.3442 | + | 9.77540i | −0.524388 | + | 0.451868i | ||||
\(469\) | −0.716650 | − | 1.25207i | −0.0330918 | − | 0.0578154i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.2382 | + | 17.5263i | 1.76192 | + | 0.807571i | ||||
\(472\) | − | 5.89894i | − | 0.271521i | ||||||
\(473\) | 11.4238i | 0.525266i | ||||||||
\(474\) | 1.16962 | + | 0.536091i | 0.0537224 | + | 0.0246235i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.66349 | + | 8.14768i | 0.213751 | + | 0.373448i | ||||
\(477\) | 0.654766 | − | 0.564216i | 0.0299797 | − | 0.0258337i | ||||
\(478\) | −13.2572 | −0.606369 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | −18.5233 | −0.843712 | ||||||||
\(483\) | −3.11060 | − | 34.4366i | −0.141537 | − | 1.56692i | ||||
\(484\) | 4.34047 | 0.197294 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.51763 | + | 13.0557i | −0.386367 | + | 0.592216i | ||||
\(487\) | −26.2430 | −1.18918 | −0.594592 | − | 0.804028i | \(-0.702686\pi\) | ||||
−0.594592 | + | 0.804028i | \(0.702686\pi\) | |||||||
\(488\) | 2.48752 | 0.112605 | ||||||||
\(489\) | −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 | \(0.763305\pi\) | |||||||
\(492\) | 6.72736 | − | 14.6775i | 0.303293 | − | 0.661712i | ||||
\(493\) | − | 26.7729i | − | 1.20579i | ||||||
\(494\) | − | 15.7191i | − | 0.707237i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.19323i | 0.188281i | ||||||||
\(497\) | −12.3340 | + | 7.05961i | −0.553254 | + | 0.316667i | ||||
\(498\) | −7.01547 | − | 3.21551i | −0.314371 | − | 0.144091i | ||||
\(499\) | 41.6740 | 1.86558 | 0.932792 | − | 0.360414i | \(-0.117365\pi\) | ||||
0.932792 | + | 0.360414i | \(0.117365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.7191 | + | 34.2954i | −0.702279 | + | 1.53220i | ||||
\(502\) | 21.5355i | 0.961176i | ||||||||
\(503\) | 0.415846 | 0.0185417 | 0.00927084 | − | 0.999957i | \(-0.497049\pi\) | ||||
0.00927084 | + | 0.999957i | \(0.497049\pi\) | |||||||
\(504\) | −7.48371 | − | 2.64464i | −0.333351 | − | 0.117802i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 29.5525i | 1.31377i | ||||||||
\(507\) | −8.60008 | + | 18.7633i | −0.381943 | + | 0.833307i | ||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | −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 | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.54528 | − | 15.7191i | −0.200679 | − | 0.694017i | ||||
\(514\) | 31.8900i | 1.40661i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.10493 | + | 4.59244i | −0.0926643 | + | 0.202171i | ||||
\(517\) | 31.3487i | 1.37871i | ||||||||
\(518\) | −24.0230 | + | 13.7501i | −1.05551 | + | 0.604144i | ||||
\(519\) | 0.654766 | − | 1.42854i | 0.0287411 | − | 0.0627060i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.47611 | 0.108481 | 0.0542403 | − | 0.998528i | \(-0.482726\pi\) | ||||
0.0542403 | + | 0.998528i | \(0.482726\pi\) | |||||||
\(522\) | 14.7763 | + | 17.1477i | 0.646739 | + | 0.750533i | ||||
\(523\) | 12.0602i | 0.527357i | 0.964611 | + | 0.263678i | \(0.0849357\pi\) | ||||
−0.964611 | + | 0.263678i | \(0.915064\pi\) | |||||||
\(524\) | 14.6846 | 0.641500 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.1739 | −0.618010 | ||||||||
\(527\) | − | 14.8788i | − | 0.648131i | ||||||
\(528\) | 6.16698 | + | 2.82661i | 0.268384 | + | 0.123012i | ||||
\(529\) | −33.9312 | −1.47527 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.5522 | − | 13.4061i | −0.501321 | − | 0.581777i | ||||
\(532\) | 7.23098 | − | 4.13881i | 0.313503 | − | 0.179440i | ||||
\(533\) | − | 46.5311i | − | 2.01549i | ||||||
\(534\) | 19.4203 | + | 8.90122i | 0.840399 | + | 0.385193i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.545275i | 0.0235523i | ||||||||
\(537\) | −3.28025 | − | 1.50349i | −0.141553 | − | 0.0648803i | ||||
\(538\) | − | 6.68074i | − | 0.288027i | ||||||
\(539\) | −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 | \(0.464737\pi\) | |||||||
\(542\) | −9.45864 | −0.406283 | ||||||||
\(543\) | −38.8406 | − | 17.8024i | −1.66681 | − | 0.763976i | ||||
\(544\) | − | 3.54830i | − | 0.152132i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −22.7819 | + | 2.05785i | −0.974976 | + | 0.0880679i | ||||
\(547\) | −3.11425 | −0.133156 | −0.0665779 | − | 0.997781i | \(-0.521208\pi\) | ||||
−0.0665779 | + | 0.997781i | \(0.521208\pi\) | |||||||
\(548\) | 18.3787i | 0.785097i | ||||||||
\(549\) | 5.65322 | − | 4.87142i | 0.241274 | − | 0.207907i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.7607 | −1.01224 | ||||||||
\(552\) | −5.44530 | + | 11.8803i | −0.231767 | + | 0.505660i | ||||
\(553\) | 0.976300 | + | 1.70571i | 0.0415165 | + | 0.0725342i | ||||
\(554\) | 11.2048i | 0.476046i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 12.6077i | − | 0.534686i | ||||||
\(557\) | − | 1.93812i | − | 0.0821206i | −0.999157 | − | 0.0410603i | \(-0.986926\pi\) | ||
0.999157 | − | 0.0410603i | \(-0.0130736\pi\) | |||||||
\(558\) | 8.21179 | + | 9.52969i | 0.347633 | + | 0.403424i | ||||
\(559\) | 14.5591i | 0.615786i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.8823 | − | 10.0297i | −0.923871 | − | 0.423452i | ||||
\(562\) | −2.90945 | −0.122728 | ||||||||
\(563\) | 25.8656 | 1.09010 | 0.545052 | − | 0.838402i | \(-0.316510\pi\) | ||||
0.545052 | + | 0.838402i | \(0.316510\pi\) | |||||||
\(564\) | −5.77626 | + | 12.6024i | −0.243224 | + | 0.530657i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.4056 | 1.02584 | ||||||||
\(567\) | −22.1869 | + | 8.64537i | −0.931761 | + | 0.363071i | ||||
\(568\) | 5.37142 | 0.225380 | ||||||||
\(569\) | 30.3787i | 1.27354i | 0.771054 | + | 0.636770i | \(0.219730\pi\) | ||||
−0.771054 | + | 0.636770i | \(0.780270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.56898 | 0.191206 | 0.0956028 | − | 0.995420i | \(-0.469522\pi\) | ||||
0.0956028 | + | 0.995420i | \(0.469522\pi\) | |||||||
\(572\) | 19.5508 | 0.817460 | ||||||||
\(573\) | −25.2040 | − | 11.5522i | −1.05291 | − | 0.482598i | ||||
\(574\) | 21.4048 | − | 12.2515i | 0.893421 | − | 0.511368i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.95835 | + | 2.27264i | 0.0815977 | + | 0.0946932i | ||||
\(577\) | 23.7493i | 0.988694i | 0.869265 | + | 0.494347i | \(0.164593\pi\) | ||||
−0.869265 | + | 0.494347i | \(0.835407\pi\) | |||||||
\(578\) | − | 4.40960i | − | 0.183415i | ||||||
\(579\) | 19.0748 | − | 41.6167i | 0.792723 | − | 1.72953i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.85592 | − | 10.2310i | −0.242945 | − | 0.424453i | ||||
\(582\) | 0.378659 | − | 0.826142i | 0.0156959 | − | 0.0342447i | ||||
\(583\) | −1.12843 | −0.0467349 | ||||||||
\(584\) | −4.85479 | −0.200893 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 17.0799i | − | 0.705565i | ||||||
\(587\) | 28.8726 | 1.19170 | 0.595849 | − | 0.803096i | \(-0.296816\pi\) | ||||
0.595849 | + | 0.803096i | \(0.296816\pi\) | |||||||
\(588\) | −6.94505 | − | 9.93812i | −0.286409 | − | 0.409841i | ||||
\(589\) | −13.2048 | −0.544094 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.1835 | − | 12.4594i | −1.11818 | − | 0.512513i | ||||
\(592\) | 10.4620 | 0.429984 | ||||||||
\(593\) | −4.74595 | −0.194893 | −0.0974463 | − | 0.995241i | \(-0.531067\pi\) | ||||
−0.0974463 | + | 0.995241i | \(0.531067\pi\) | |||||||
\(594\) | 19.5508 | − | 5.65322i | 0.802179 | − | 0.231955i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.65953i | 0.231823i | ||||||||
\(597\) | −17.1477 | − | 7.85957i | −0.701808 | − | 0.321671i | ||||
\(598\) | 37.6635i | 1.54017i | ||||||||
\(599\) | − | 3.19756i | − | 0.130649i | −0.997864 | − | 0.0653243i | \(-0.979192\pi\) | ||
0.997864 | − | 0.0653243i | \(-0.0208082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.16962i | 0.0477098i | 0.999715 | + | 0.0238549i | \(0.00759397\pi\) | ||||
−0.999715 | + | 0.0238549i | \(0.992406\pi\) | |||||||
\(602\) | −6.69737 | + | 3.83338i | −0.272965 | + | 0.156237i | ||||
\(603\) | 1.06784 | + | 1.23921i | 0.0434857 | + | 0.0504646i | ||||
\(604\) | 2.62858 | 0.106956 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.6024 | − | 5.77626i | −0.511938 | − | 0.234644i | ||||
\(607\) | − | 42.5463i | − | 1.72690i | −0.504434 | − | 0.863450i | \(-0.668299\pi\) | ||
0.504434 | − | 0.863450i | \(-0.331701\pi\) | |||||||
\(608\) | −3.14908 | −0.127712 | ||||||||
\(609\) | 3.11060 | + | 34.4366i | 0.126048 | + | 1.39544i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.9526i | 1.61631i | ||||||||
\(612\) | −6.94879 | − | 8.06399i | −0.280888 | − | 0.325967i | ||||
\(613\) | 11.1524 | 0.450443 | 0.225221 | − | 0.974308i | \(-0.427689\pi\) | ||||
0.225221 | + | 0.974308i | \(0.427689\pi\) | |||||||
\(614\) | −11.8093 | −0.476584 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.14768 | + | 8.99360i | 0.207406 | + | 0.362362i | ||||
\(617\) | 42.1811i | 1.69815i | 0.528275 | + | 0.849074i | \(0.322839\pi\) | ||||
−0.528275 | + | 0.849074i | \(0.677161\pi\) | |||||||
\(618\) | 4.45472 | − | 9.71913i | 0.179195 | − | 0.390961i | ||||
\(619\) | − | 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 | ||||
\(622\) | − | 2.88673i | − | 0.115747i | ||||||
\(623\) | 16.2104 | + | 28.3215i | 0.649457 | + | 1.13468i | ||||
\(624\) | 7.85957 | + | 3.60240i | 0.314634 | + | 0.144211i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.20986 | −0.168260 | ||||||||
\(627\) | −8.90122 | + | 19.4203i | −0.355481 | + | 0.775573i | ||||
\(628\) | − | 24.2853i | − | 0.969091i | ||||||
\(629\) | −37.1221 | −1.48016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.46197 | 0.177628 | 0.0888140 | − | 0.996048i | \(-0.471692\pi\) | ||||
0.0888140 | + | 0.996048i | \(0.471692\pi\) | |||||||
\(632\) | − | 0.742834i | − | 0.0295483i | ||||||
\(633\) | −4.96933 | + | 10.8419i | −0.197513 | + | 0.430926i | ||||
\(634\) | −23.2644 | −0.923948 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.453638 | − | 0.207923i | −0.0179879 | − | 0.00824469i | ||||
\(637\) | −30.1287 | − | 17.6968i | −1.19374 | − | 0.701173i | ||||
\(638\) | − | 29.5525i | − | 1.17000i | ||||||
\(639\) | 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 | \(-0.0182996\pi\) | |||||||
\(642\) | −1.91934 | + | 4.18753i | −0.0757501 | + | 0.165268i | ||||
\(643\) | − | 31.7645i | − | 1.25267i | −0.779554 | − | 0.626335i | \(-0.784554\pi\) | ||
0.779554 | − | 0.626335i | \(-0.215446\pi\) | |||||||
\(644\) | −17.3256 | + | 9.91669i | −0.682725 | + | 0.390772i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.1739 | 0.439630 | ||||||||
\(647\) | −23.3448 | −0.917779 | −0.458890 | − | 0.888493i | \(-0.651753\pi\) | ||||
−0.458890 | + | 0.888493i | \(0.651753\pi\) | |||||||
\(648\) | 8.90122 | + | 1.32976i | 0.349673 | + | 0.0522380i | ||||
\(649\) | 23.1043i | 0.906924i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.72869 | + | 19.1379i | 0.0677527 | + | 0.750072i | ||||
\(652\) | 13.4620 | 0.527211 | ||||||||
\(653\) | − | 2.28087i | − | 0.0892572i | −0.999004 | − | 0.0446286i | \(-0.985790\pi\) | ||
0.999004 | − | 0.0446286i | \(-0.0142104\pi\) | |||||||
\(654\) | 23.4983 | + | 10.7704i | 0.918857 | + | 0.421154i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.32176 | −0.363954 | ||||||||
\(657\) | −11.0332 | + | 9.50736i | −0.430445 | + | 0.370917i | ||||
\(658\) | −18.3787 | + | 10.5194i | −0.716475 | + | 0.410089i | ||||
\(659\) | − | 2.08331i | − | 0.0811542i | −0.999176 | − | 0.0405771i | \(-0.987080\pi\) | ||
0.999176 | − | 0.0405771i | \(-0.0129196\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.34150i | 0.168865i | 0.996429 | + | 0.0844325i | \(0.0269077\pi\) | ||||
−0.996429 | + | 0.0844325i | \(0.973092\pi\) | |||||||
\(662\) | − | 25.4620i | − | 0.989607i | ||||||
\(663\) | −27.8881 | − | 12.7824i | −1.08308 | − | 0.496426i | ||||
\(664\) | 4.45557i | 0.172910i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23.7763 | − | 20.4881i | 0.921311 | − | 0.793900i | ||||
\(667\) | 56.9312 | 2.20438 | ||||||||
\(668\) | 21.7812 | 0.842740 | ||||||||
\(669\) | −4.57146 | − | 2.09531i | −0.176743 | − | 0.0810093i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.74284 | −0.376118 | ||||||||
\(672\) | 0.412258 | + | 4.56399i | 0.0159032 | + | 0.176060i | ||||
\(673\) | −2.00724 | −0.0773735 | −0.0386867 | − | 0.999251i | \(-0.512317\pi\) | ||||
−0.0386867 | + | 0.999251i | \(0.512317\pi\) | |||||||
\(674\) | − | 7.68095i | − | 0.295859i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.9167 | 0.458334 | ||||||||
\(677\) | 27.5547 | 1.05901 | 0.529506 | − | 0.848306i | \(-0.322377\pi\) | ||||
0.529506 | + | 0.848306i | \(0.322377\pi\) | |||||||
\(678\) | 8.51763 | − | 18.5834i | 0.327117 | − | 0.713691i | ||||
\(679\) | 1.20480 | − | 0.689593i | 0.0462360 | − | 0.0264642i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6286 | − | 34.0978i | 0.598889 | − | 1.30663i | ||||
\(682\) | − | 16.4236i | − | 0.628891i | ||||||
\(683\) | − | 5.75008i | − | 0.220021i | −0.993930 | − | 0.110010i | \(-0.964912\pi\) | ||
0.993930 | − | 0.110010i | \(-0.0350884\pi\) | |||||||
\(684\) | −7.15671 | + | 6.16698i | −0.273644 | + | 0.235801i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.207923 | − | 18.5191i | 0.00793854 | − | 0.707062i | ||||
\(687\) | −26.6693 | − | 12.2237i | −1.01750 | − | 0.466365i | ||||
\(688\) | 2.91669 | 0.111198 | ||||||||
\(689\) | −1.43814 | −0.0547888 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 23.6404i | − | 0.899324i | −0.893199 | − | 0.449662i | \(-0.851544\pi\) | ||
0.893199 | − | 0.449662i | \(-0.148456\pi\) | |||||||
\(692\) | −0.907276 | −0.0344895 | ||||||||
\(693\) | 29.3114 | + | 10.3583i | 1.11345 | + | 0.393478i | ||||
\(694\) | −8.26441 | −0.313713 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.44530 | − | 11.8803i | 0.206404 | − | 0.450323i | ||||
\(697\) | 33.0764 | 1.25286 | ||||||||
\(698\) | 24.6846 | 0.934325 | ||||||||
\(699\) | −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 | \(0.656403\pi\) | |||||||
\(702\) | 24.9167 | − | 7.20480i | 0.940420 | − | 0.271928i | ||||
\(703\) | 32.9455i | 1.24256i | ||||||||
\(704\) | − | 3.91669i | − | 0.147616i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.8945i | 0.711103i | ||||||||
\(707\) | −10.5194 | − | 18.3787i | −0.395623 | − | 0.691201i | ||||
\(708\) | −4.25717 | + | 9.28811i | −0.159994 | + | 0.349068i | ||||
\(709\) | 17.8334 | 0.669747 | 0.334873 | − | 0.942263i | \(-0.391306\pi\) | ||||
0.334873 | + | 0.942263i | \(0.391306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.45472 | − | 1.68819i | −0.0545564 | − | 0.0633121i | ||||
\(712\) | − | 12.3340i | − | 0.462235i | ||||||
\(713\) | 31.6391 | 1.18489 | ||||||||
\(714\) | −1.46281 | − | 16.1944i | −0.0547443 | − | 0.606060i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.08331i | 0.0778569i | ||||||||
\(717\) | 20.8739 | + | 9.56748i | 0.779551 | + | 0.357304i | ||||
\(718\) | −1.49291 | −0.0557149 | ||||||||
\(719\) | −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 | ||||
\(722\) | 9.08331i | 0.338046i | ||||||||
\(723\) | 29.1656 | + | 13.3679i | 1.08468 | + | 0.497159i | ||||
\(724\) | 24.6679i | 0.916777i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.83425 | − | 3.13245i | −0.253643 | − | 0.116256i | ||||
\(727\) | 8.92777i | 0.331113i | 0.986200 | + | 0.165556i | \(0.0529420\pi\) | ||||
−0.986200 | + | 0.165556i | \(0.947058\pi\) | |||||||
\(728\) | 6.56050 | + | 11.4620i | 0.243148 | + | 0.424809i | ||||
\(729\) | 22.8334 | − | 14.4096i | 0.845681 | − | 0.533689i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.3493 | −0.382782 | ||||||||
\(732\) | −3.91669 | − | 1.79520i | −0.144765 | − | 0.0663525i | ||||
\(733\) | − | 24.7934i | − | 0.915765i | −0.889013 | − | 0.457883i | \(-0.848608\pi\) | ||
0.889013 | − | 0.457883i | \(-0.151392\pi\) | |||||||
\(734\) | 16.9544 | 0.625800 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.54528 | 0.278123 | ||||||||
\(737\) | − | 2.13567i | − | 0.0786686i | ||||||
\(738\) | −21.1850 | + | 18.2552i | −0.779830 | + | 0.671985i | ||||
\(739\) | 5.32629 | 0.195931 | 0.0979654 | − | 0.995190i | \(-0.468767\pi\) | ||||
0.0979654 | + | 0.995190i | \(0.468767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.3442 | + | 24.7504i | −0.416741 | + | 0.909228i | ||||
\(742\) | −0.378659 | − | 0.661561i | −0.0139010 | − | 0.0242867i | ||||
\(743\) | 45.7409i | 1.67807i | 0.544078 | + | 0.839035i | \(0.316880\pi\) | ||||
−0.544078 | + | 0.839035i | \(0.683120\pi\) | |||||||
\(744\) | 3.02618 | − | 6.60240i | 0.110945 | − | 0.242056i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.8097i | 0.835122i | ||||||||
\(747\) | 8.72555 | + | 10.1259i | 0.319251 | + | 0.370487i | ||||
\(748\) | 13.8976i | 0.508146i | ||||||||
\(749\) | −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 | \(0.630751\pi\) | |||||||
\(752\) | 8.00387 | 0.291871 | ||||||||
\(753\) | 15.5418 | − | 33.9085i | 0.566375 | − | 1.23569i | ||||
\(754\) | − | 37.6635i | − | 1.37162i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.87479 | + | 9.56496i | 0.359143 | + | 0.347874i | ||||
\(757\) | 14.0524 | 0.510742 | 0.255371 | − | 0.966843i | \(-0.417802\pi\) | ||||
0.255371 | + | 0.966843i | \(0.417802\pi\) | |||||||
\(758\) | 0.371417i | 0.0134905i | ||||||||
\(759\) | 21.3276 | − | 46.5316i | 0.774142 | − | 1.68899i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.6210 | 1.79876 | 0.899380 | − | 0.437167i | \(-0.144018\pi\) | ||||
0.899380 | + | 0.437167i | \(0.144018\pi\) | |||||||
\(762\) | −3.14908 | − | 1.44337i | −0.114079 | − | 0.0522877i | ||||
\(763\) | 19.6144 | + | 34.2687i | 0.710089 | + | 1.24061i | ||||
\(764\) | 16.0072i | 0.579122i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.8367i | 1.18644i | ||||||||
\(767\) | 29.4455i | 1.06322i | ||||||||
\(768\) | 0.721683 | − | 1.57454i | 0.0260415 | − | 0.0568163i | ||||
\(769\) | − | 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 | ||||
\(772\) | −26.4310 | −0.951273 | ||||||||
\(773\) | −29.9500 | −1.07723 | −0.538613 | − | 0.842553i | \(-0.681051\pi\) | ||||
−0.538613 | + | 0.842553i | \(0.681051\pi\) | |||||||
\(774\) | 6.62858 | − | 5.71189i | 0.238260 | − | 0.205310i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.524688 | −0.0188352 | ||||||||
\(777\) | 47.7484 | − | 4.31302i | 1.71296 | − | 0.154729i | ||||
\(778\) | 24.1287 | 0.865057 | ||||||||
\(779\) | − | 29.3550i | − | 1.05175i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.0382 | −0.752805 | ||||||||
\(782\) | −26.7729 | −0.957396 | ||||||||
\(783\) | −10.8906 | − | 37.6635i | −0.389198 | − | 1.34598i | ||||
\(784\) | −3.54528 | + | 6.03581i | −0.126617 | + | 0.215565i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.1215 | − | 10.5976i | −0.824716 | − | 0.378005i | ||||
\(787\) | − | 1.01612i | − | 0.0362207i | −0.999836 | − | 0.0181103i | \(-0.994235\pi\) | ||
0.999836 | − | 0.0181103i | \(-0.00576502\pi\) | |||||||
\(788\) | 17.2644i | 0.615019i | ||||||||
\(789\) | 22.3173 | + | 10.2290i | 0.794517 | + | 0.364163i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.1010 | − | 15.5119i | 0.963602 | − | 0.551538i | ||||
\(792\) | −7.67024 | − | 8.90122i | −0.272550 | − | 0.316291i | ||||
\(793\) | −12.4168 | −0.440935 | ||||||||
\(794\) | 7.35371 | 0.260973 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.8906i | 0.386007i | ||||||||
\(797\) | 40.4247 | 1.43192 | 0.715959 | − | 0.698143i | \(-0.245990\pi\) | ||||
0.715959 | + | 0.698143i | \(0.245990\pi\) | |||||||
\(798\) | −14.3724 | + | 1.29823i | −0.508777 | + | 0.0459569i | ||||
\(799\) | −28.4001 | −1.00472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.1542 | − | 28.0306i | −0.853446 | − | 0.990414i | ||||
\(802\) | −17.1215 | −0.604581 | ||||||||
\(803\) | 19.0147 | 0.671015 | ||||||||
\(804\) | 0.393516 | − | 0.858557i | 0.0138782 | − | 0.0302790i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 20.9312i | − | 0.737269i | ||||||
\(807\) | −4.82138 | + | 10.5191i | −0.169721 | + | 0.370290i | ||||
\(808\) | 8.00387i | 0.281575i | ||||||||
\(809\) | − | 23.0287i | − | 0.809645i | −0.914395 | − | 0.404822i | \(-0.867333\pi\) | ||
0.914395 | − | 0.404822i | \(-0.132667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.9272i | 1.05089i | 0.850829 | + | 0.525443i | \(0.176100\pi\) | ||||
−0.850829 | + | 0.525443i | \(0.823900\pi\) | |||||||
\(812\) | 17.3256 | − | 9.91669i | 0.608010 | − | 0.348008i | ||||
\(813\) | 14.8930 | + | 6.82614i | 0.522320 | + | 0.239403i | ||||
\(814\) | −40.9763 | −1.43622 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.56075 | + | 5.58693i | −0.0896440 | + | 0.195582i | ||||
\(817\) | 9.18489i | 0.321339i | ||||||||
\(818\) | 23.2246 | 0.812028 | ||||||||
\(819\) | 37.3561 | + | 13.2012i | 1.30533 | + | 0.461286i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.9763i | − | 0.383076i | −0.981485 | − | 0.191538i | \(-0.938653\pi\) | ||
0.981485 | − | 0.191538i | \(-0.0613474\pi\) | |||||||
\(822\) | 13.2636 | − | 28.9379i | 0.462620 | − | 1.00933i | ||||
\(823\) | 28.6286 | 0.997930 | 0.498965 | − | 0.866622i | \(-0.333714\pi\) | ||||
0.498965 | + | 0.866622i | \(0.333714\pi\) | |||||||
\(824\) | −6.17269 | −0.215036 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.5453 | + | 7.75293i | −0.471300 | + | 0.269759i | ||||
\(827\) | 1.97858i | 0.0688018i | 0.999408 | + | 0.0344009i | \(0.0109523\pi\) | ||||
−0.999408 | + | 0.0344009i | \(0.989048\pi\) | |||||||
\(828\) | 17.1477 | − | 14.7763i | 0.595923 | − | 0.513510i | ||||
\(829\) | − | 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 | ||||
\(832\) | − | 4.99166i | − | 0.173055i | ||||||
\(833\) | 12.5797 | − | 21.4168i | 0.435860 | − | 0.742050i | ||||
\(834\) | −9.09878 | + | 19.8513i | −0.315065 | + | 0.687396i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.3340 | 0.426579 | ||||||||
\(837\) | −6.05237 | − | 20.9312i | −0.209200 | − | 0.723487i | ||||
\(838\) | − | 11.5522i | − | 0.399063i | ||||||
\(839\) | 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 | ||||||||
\(842\) | 36.9239i | 1.27248i | ||||||||
\(843\) | 4.58104 | + | 2.09970i | 0.157779 | + | 0.0723176i | ||||
\(844\) | 6.88575 | 0.237017 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.1899 | − | 15.6743i | 0.625381 | − | 0.538895i | ||||
\(847\) | −5.70465 | − | 9.96670i | −0.196014 | − | 0.342460i | ||||
\(848\) | 0.288109i | 0.00989369i | ||||||||
\(849\) | −38.4276 | − | 17.6131i | −1.31883 | − | 0.604480i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 78.9384i | − | 2.70597i | ||||||
\(852\) | −8.45750 | − | 3.87646i | −0.289749 | − | 0.132805i | ||||
\(853\) | 11.6724i | 0.399656i | 0.979831 | + | 0.199828i | \(0.0640383\pi\) | ||||
−0.979831 | + | 0.199828i | \(0.935962\pi\) | |||||||
\(854\) | −3.26932 | − | 5.71189i | −0.111874 | − | 0.195457i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.65953 | 0.0909007 | ||||||||
\(857\) | 3.91425 | 0.133708 | 0.0668542 | − | 0.997763i | \(-0.478704\pi\) | ||||
0.0668542 | + | 0.997763i | \(0.478704\pi\) | |||||||
\(858\) | −30.7835 | − | 14.1095i | −1.05093 | − | 0.481690i | ||||
\(859\) | 43.3229i | 1.47816i | 0.673619 | + | 0.739079i | \(0.264739\pi\) | ||||
−0.673619 | + | 0.739079i | \(0.735261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.5445 | + | 3.84297i | −1.44991 | + | 0.130968i | ||||
\(862\) | 5.03094 | 0.171355 | ||||||||
\(863\) | − | 33.8479i | − | 1.15219i | −0.817381 | − | 0.576097i | \(-0.804575\pi\) | ||
0.817381 | − | 0.576097i | \(-0.195425\pi\) | |||||||
\(864\) | −1.44337 | − | 4.99166i | −0.0491043 | − | 0.169820i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.04024 | −0.103311 | ||||||||
\(867\) | −3.18234 | + | 6.94309i | −0.108078 | + | 0.235800i | ||||
\(868\) | 9.62858 | − | 5.51112i | 0.326815 | − | 0.187060i | ||||
\(869\) | 2.90945i | 0.0986963i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.72183i | − | 0.0922257i | ||||||
\(872\) | − | 14.9239i | − | 0.505388i | ||||||
\(873\) | −1.19243 | + | 1.02752i | −0.0403575 | + | 0.0347763i | ||||
\(874\) | 23.7607i | 0.803716i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.64405 | + | 3.50362i | 0.258269 | + | 0.118376i | ||||
\(877\) | −15.4383 | −0.521313 | −0.260657 | − | 0.965432i | \(-0.583939\pi\) | ||||
−0.260657 | + | 0.965432i | \(0.583939\pi\) | |||||||
\(878\) | −19.8184 | −0.668838 | ||||||||
\(879\) | −12.3263 | + | 26.8930i | −0.415756 | + | 0.907078i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.64800 | 0.190286 | 0.0951429 | − | 0.995464i | \(-0.469669\pi\) | ||||
0.0951429 | + | 0.995464i | \(0.469669\pi\) | |||||||
\(882\) | 3.76308 | + | 20.6601i | 0.126710 | + | 0.695661i | ||||
\(883\) | −7.05237 | −0.237331 | −0.118666 | − | 0.992934i | \(-0.537862\pi\) | ||||
−0.118666 | + | 0.992934i | \(0.537862\pi\) | |||||||
\(884\) | 17.7119i | 0.595715i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.5976 | −0.356035 | ||||||||
\(887\) | 21.9461 | 0.736878 | 0.368439 | − | 0.929652i | \(-0.379892\pi\) | ||||
0.368439 | + | 0.929652i | \(0.379892\pi\) | |||||||
\(888\) | −16.4728 | − | 7.55023i | −0.552790 | − | 0.253369i | ||||
\(889\) | −2.62858 | − | 4.59244i | −0.0881599 | − | 0.154026i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.8633 | − | 5.20827i | −1.16797 | − | 0.174484i | ||||
\(892\) | 2.90336i | 0.0972118i | ||||||||
\(893\) | 25.2048i | 0.843446i | ||||||||
\(894\) | 4.08439 | − | 8.91114i | 0.136602 | − | 0.298033i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.29622 | − | 1.31429i | 0.0767114 | − | 0.0439074i | ||||
\(897\) | 27.1811 | − | 59.3026i | 0.907551 | − | 1.98006i | ||||
\(898\) | −6.19756 | −0.206815 | ||||||||
\(899\) | −31.6391 | −1.05522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.02229i | − | 0.0340576i | ||||||
\(902\) | 36.5105 | 1.21567 | ||||||||
\(903\) | 13.3118 | − | 1.20243i | 0.442988 | − | 0.0400143i | ||||
\(904\) | −11.8024 | −0.392543 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.13881 | − | 1.89701i | −0.137503 | − | 0.0630238i | ||||
\(907\) | 51.7787 | 1.71928 | 0.859642 | − | 0.510896i | \(-0.170686\pi\) | ||||
0.859642 | + | 0.510896i | \(0.170686\pi\) | |||||||
\(908\) | −21.6557 | −0.718671 | ||||||||
\(909\) | 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 | \(0.801416\pi\) | |||||||
\(912\) | 4.95835 | + | 2.27264i | 0.164187 | + | 0.0752545i | ||||
\(913\) | − | 17.4511i | − | 0.577547i | ||||||
\(914\) | − | 19.7573i | − | 0.653514i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.9378i | 0.559641i | ||||||||
\(917\) | −19.2999 | − | 33.7191i | −0.637338 | − | 1.11350i | ||||
\(918\) | 5.12149 | + | 17.7119i | 0.169034 | + | 0.584580i | ||||
\(919\) | −22.0145 | −0.726191 | −0.363095 | − | 0.931752i | \(-0.618280\pi\) | ||||
−0.363095 | + | 0.931752i | \(0.618280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.5942 | + | 8.52256i | 0.612699 | + | 0.280828i | ||||
\(922\) | 26.8983i | 0.885849i | ||||||||
\(923\) | −26.8123 | −0.882538 | ||||||||
\(924\) | −1.61469 | − | 17.8758i | −0.0531193 | − | 0.588069i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 38.7573i | − | 1.27364i | ||||||
\(927\) | −14.0283 | + | 12.0883i | −0.460749 | + | 0.397030i | ||||
\(928\) | −7.54528 | −0.247686 | ||||||||
\(929\) | 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 | ||||
\(932\) | 5.42378i | 0.177662i | ||||||||
\(933\) | −2.08331 | + | 4.54528i | −0.0682044 | + | 0.148806i | ||||
\(934\) | − | 18.5181i | − | 0.605929i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.77540 | − | 11.3442i | −0.319519 | − | 0.370798i | ||||
\(937\) | − | 37.3845i | − | 1.22130i | −0.791901 | − | 0.610649i | \(-0.790909\pi\) | ||
0.791901 | − | 0.610649i | \(-0.209091\pi\) | |||||||
\(938\) | 1.25207 | − | 0.716650i | 0.0408816 | − | 0.0233995i | ||||
\(939\) | 6.62858 | + | 3.03818i | 0.216316 | + | 0.0991474i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.1598 | 1.11358 | 0.556789 | − | 0.830654i | \(-0.312033\pi\) | ||||
0.556789 | + | 0.830654i | \(0.312033\pi\) | |||||||
\(942\) | −17.5263 | + | 38.2382i | −0.571039 | + | 1.24587i | ||||
\(943\) | 70.3353i | 2.29043i | ||||||||
\(944\) | 5.89894 | 0.191994 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.4238 | −0.371419 | ||||||||
\(947\) | − | 46.2430i | − | 1.50270i | −0.659907 | − | 0.751348i | \(-0.729404\pi\) | ||
0.659907 | − | 0.751348i | \(-0.270596\pi\) | |||||||
\(948\) | −0.536091 | + | 1.16962i | −0.0174114 | + | 0.0379875i | ||||
\(949\) | 24.2335 | 0.786652 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.6307 | + | 16.7895i | 1.18783 | + | 0.544438i | ||||
\(952\) | −8.14768 | + | 4.66349i | −0.264068 | + | 0.151145i | ||||
\(953\) | 25.1360i | 0.814234i | 0.913376 | + | 0.407117i | \(0.133466\pi\) | ||||
−0.913376 | + | 0.407117i | \(0.866534\pi\) | |||||||
\(954\) | 0.564216 | + | 0.654766i | 0.0182672 | + | 0.0211988i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 13.2572i | − | 0.428767i | ||||||
\(957\) | −21.3276 | + | 46.5316i | −0.689422 | + | 1.50415i | ||||
\(958\) | − | 14.4337i | − | 0.466331i | ||||||
\(959\) | 42.2015 | − | 24.1549i | 1.36276 | − | 0.780003i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.4168 | 0.432801 | ||||||||
\(962\) | −52.2226 | −1.68372 | ||||||||
\(963\) | 6.04414 | − | 5.20827i | 0.194770 | − | 0.167834i | ||||
\(964\) | − | 18.5233i | − | 0.596595i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 34.4366 | − | 3.11060i | 1.10798 | − | 0.100082i | ||||
\(967\) | −50.1287 | −1.61203 | −0.806016 | − | 0.591894i | \(-0.798380\pi\) | ||||
−0.806016 | + | 0.591894i | \(0.798380\pi\) | |||||||
\(968\) | 4.34047i | 0.139508i | ||||||||
\(969\) | −17.5937 | − | 8.06399i | −0.565190 | − | 0.259053i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.5387 | 1.62187 | 0.810933 | − | 0.585139i | \(-0.198960\pi\) | ||||
0.810933 | + | 0.585139i | \(0.198960\pi\) | |||||||
\(972\) | −13.0557 | − | 8.51763i | −0.418760 | − | 0.273203i | ||||
\(973\) | −28.9501 | + | 16.5702i | −0.928098 | + | 0.531217i | ||||
\(974\) | − | 26.2430i | − | 0.840879i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.48752i | 0.0796235i | ||||||||
\(977\) | − | 61.1360i | − | 1.95591i | −0.208808 | − | 0.977957i | \(-0.566958\pi\) | ||
0.208808 | − | 0.977957i | \(-0.433042\pi\) | |||||||
\(978\) | −21.1964 | − | 9.71528i | −0.677786 | − | 0.310660i | ||||
\(979\) | 48.3084i | 1.54394i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.2262 | − | 33.9167i | −0.933122 | − | 1.08288i | ||||
\(982\) | −30.0000 | −0.957338 | ||||||||
\(983\) | −9.32699 | −0.297485 | −0.148742 | − | 0.988876i | \(-0.547523\pi\) | ||||
−0.148742 | + | 0.988876i | \(0.547523\pi\) | |||||||
\(984\) | 14.6775 | + | 6.72736i | 0.467901 | + | 0.214460i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 26.7729 | 0.852622 | ||||||||
\(987\) | 36.5296 | − | 3.29965i | 1.16275 | − | 0.105029i | ||||
\(988\) | 15.7191 | 0.500092 | ||||||||
\(989\) | − | 22.0072i | − | 0.699790i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0527 | 1.43115 | 0.715573 | − | 0.698538i | \(-0.246166\pi\) | ||||
0.715573 | + | 0.698538i | \(0.246166\pi\) | |||||||
\(992\) | −4.19323 | −0.133135 | ||||||||
\(993\) | −18.3755 | + | 40.0909i | −0.583128 | + | 1.27224i | ||||
\(994\) | −7.05961 | − | 12.3340i | −0.223917 | − | 0.391210i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.21551 | − | 7.01547i | 0.101887 | − | 0.222294i | ||||
\(997\) | − | 14.0283i | − | 0.444280i | −0.975015 | − | 0.222140i | \(-0.928696\pi\) | ||
0.975015 | − | 0.222140i | \(-0.0713042\pi\) | |||||||
\(998\) | 41.6740i | 1.31917i | ||||||||
\(999\) | −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.b.e.251.10 | yes | 12 | |
3.2 | odd | 2 | inner | 1050.2.b.e.251.3 | yes | 12 | |
5.2 | odd | 4 | 1050.2.d.g.1049.1 | 12 | |||
5.3 | odd | 4 | 1050.2.d.h.1049.12 | 12 | |||
5.4 | even | 2 | 1050.2.b.d.251.3 | ✓ | 12 | ||
7.6 | odd | 2 | inner | 1050.2.b.e.251.9 | yes | 12 | |
15.2 | even | 4 | 1050.2.d.h.1049.2 | 12 | |||
15.8 | even | 4 | 1050.2.d.g.1049.11 | 12 | |||
15.14 | odd | 2 | 1050.2.b.d.251.10 | yes | 12 | ||
21.20 | even | 2 | inner | 1050.2.b.e.251.4 | yes | 12 | |
35.13 | even | 4 | 1050.2.d.h.1049.1 | 12 | |||
35.27 | even | 4 | 1050.2.d.g.1049.12 | 12 | |||
35.34 | odd | 2 | 1050.2.b.d.251.4 | yes | 12 | ||
105.62 | odd | 4 | 1050.2.d.h.1049.11 | 12 | |||
105.83 | odd | 4 | 1050.2.d.g.1049.2 | 12 | |||
105.104 | even | 2 | 1050.2.b.d.251.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.b.d.251.3 | ✓ | 12 | 5.4 | even | 2 | ||
1050.2.b.d.251.4 | yes | 12 | 35.34 | odd | 2 | ||
1050.2.b.d.251.9 | yes | 12 | 105.104 | even | 2 | ||
1050.2.b.d.251.10 | yes | 12 | 15.14 | odd | 2 | ||
1050.2.b.e.251.3 | yes | 12 | 3.2 | odd | 2 | inner | |
1050.2.b.e.251.4 | yes | 12 | 21.20 | even | 2 | inner | |
1050.2.b.e.251.9 | yes | 12 | 7.6 | odd | 2 | inner | |
1050.2.b.e.251.10 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.2.d.g.1049.1 | 12 | 5.2 | odd | 4 | |||
1050.2.d.g.1049.2 | 12 | 105.83 | odd | 4 | |||
1050.2.d.g.1049.11 | 12 | 15.8 | even | 4 | |||
1050.2.d.g.1049.12 | 12 | 35.27 | even | 4 | |||
1050.2.d.h.1049.1 | 12 | 35.13 | even | 4 | |||
1050.2.d.h.1049.2 | 12 | 15.2 | even | 4 | |||
1050.2.d.h.1049.11 | 12 | 105.62 | odd | 4 | |||
1050.2.d.h.1049.12 | 12 | 5.3 | odd | 4 |