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 | 1049.12 | ||
Root | \(0.721683 - 1.57454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.1049 |
Dual form | 1050.2.d.h.1049.11 |
$q$-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 | \(-0.743367\pi\) | ||||
−0.692219 | + | 0.721688i | \(0.743367\pi\) | |||||||
\(14\) | 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 | \(0.141590\pi\) | ||||
−0.902689 | + | 0.430294i | \(0.858410\pi\) | |||||||
\(18\) | 1.95835 | + | 2.27264i | 0.461587 | + | 0.535666i | ||||
\(19\) | − | 3.14908i | − | 0.722448i | −0.932479 | − | 0.361224i | \(-0.882359\pi\) | ||
0.932479 | − | 0.361224i | \(-0.117641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.56399 | − | 0.412258i | 0.995945 | − | 0.0899620i | ||||
\(22\) | 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 | \(0.122894\pi\) | ||||
−0.926391 | + | 0.376563i | \(0.877106\pi\) | |||||||
\(32\) | 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 | \(-0.759507\pi\) | ||||
−0.727907 | + | 0.685675i | \(0.759507\pi\) | |||||||
\(42\) | 4.56399 | − | 0.412258i | 0.704240 | − | 0.0636127i | ||||
\(43\) | 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 | \(-0.801588\pi\) | ||
0.811939 | − | 0.583742i | \(-0.198412\pi\) | |||||||
\(48\) | 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 | \(-0.625450\pi\) | ||||
−0.383988 | + | 0.923338i | \(0.625450\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.48752i | 0.318494i | 0.987239 | + | 0.159247i | \(0.0509066\pi\) | ||||
−0.987239 | + | 0.159247i | \(0.949093\pi\) | |||||||
\(62\) | 4.19323i | 0.532540i | ||||||||
\(63\) | 7.48371 | + | 2.64464i | 0.942858 | + | 0.333194i | ||||
\(64\) | 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 | \(-0.408304\pi\) | ||||
0.284105 | + | 0.958793i | \(0.408304\pi\) | |||||||
\(74\) | − | 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 | \(-0.921366\pi\) | ||
0.969641 | − | 0.244531i | \(-0.0786341\pi\) | |||||||
\(84\) | 4.56399 | − | 0.412258i | 0.497973 | − | 0.0449810i | ||||
\(85\) | 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 | \(-0.726784\pi\) | ||||
−0.653699 | + | 0.756755i | \(0.726784\pi\) | |||||||
\(90\) | 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 | \(-0.508480\pi\) | ||||
−0.0266370 | + | 0.999645i | \(0.508480\pi\) | |||||||
\(98\) | 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 | \(-0.630368\pi\) | ||||
−0.398207 | + | 0.917295i | \(0.630368\pi\) | |||||||
\(102\) | −2.56075 | + | 5.58693i | −0.253552 | + | 0.553188i | ||||
\(103\) | 6.17269 | 0.608213 | 0.304106 | − | 0.952638i | \(-0.401642\pi\) | ||||
0.304106 | + | 0.952638i | \(0.401642\pi\) | |||||||
\(104\) | −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 | ||||||||
\(126\) | 7.48371 | + | 2.64464i | 0.666702 | + | 0.235604i | ||||
\(127\) | 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 | \(-0.721688\pi\) | ||||
−0.641500 | + | 0.767123i | \(0.721688\pi\) | |||||||
\(132\) | −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 | \(-0.820430\pi\) | ||
0.845051 | − | 0.534686i | \(-0.179570\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 9.93812 | − | 6.94505i | 0.819682 | − | 0.572818i | ||||
\(148\) | − | 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 | \(-0.0793476\pi\) | ||||
0.969091 | + | 0.246704i | \(0.0793476\pi\) | |||||||
\(158\) | −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 | \(0.319059\pi\) | ||||
−0.538321 | + | 0.842740i | \(0.680941\pi\) | |||||||
\(168\) | 4.56399 | − | 0.412258i | 0.352120 | − | 0.0318064i | ||||
\(169\) | 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 | \(0.0109805\pi\) | ||||
−0.999405 | + | 0.0344895i | \(0.989019\pi\) | |||||||
\(174\) | 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 | \(-0.630782\pi\) | ||
0.399400 | − | 0.916777i | \(-0.369218\pi\) | |||||||
\(182\) | −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 | ||||||
\(189\) | 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 | \(-0.196604\pi\) | |||||||
\(192\) | 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 | \(0.126146\pi\) | ||||
−0.922496 | + | 0.386007i | \(0.873854\pi\) | |||||||
\(200\) | 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 | \(-0.469008\pi\) | ||||
0.0972118 | + | 0.995264i | \(0.469008\pi\) | |||||||
\(224\) | 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 | \(-0.744751\pi\) | ||
0.695351 | − | 0.718671i | \(-0.255249\pi\) | |||||||
\(228\) | 2.27264 | − | 4.95835i | 0.150509 | − | 0.328374i | ||||
\(229\) | 16.9378i | 1.11928i | 0.828735 | + | 0.559641i | \(0.189061\pi\) | ||||
−0.828735 | + | 0.559641i | \(0.810939\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.61469 | + | 17.8758i | 0.106239 | + | 1.17614i | ||||
\(232\) | − | 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 | \(0.203480\pi\) | ||||
−0.802543 | + | 0.596595i | \(0.796520\pi\) | |||||||
\(242\) | −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 | \(-0.262130\pi\) | ||||
0.679654 | + | 0.733533i | \(0.262130\pi\) | |||||||
\(252\) | 7.48371 | + | 2.64464i | 0.471429 | + | 0.166597i | ||||
\(253\) | 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 | \(-0.533028\pi\) | ||
0.103575 | − | 0.994622i | \(-0.466972\pi\) | |||||||
\(258\) | −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 | \(-0.434714\pi\) | ||||
0.203666 | + | 0.979040i | \(0.434714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.45864i | 0.574571i | 0.957845 | + | 0.287286i | \(0.0927529\pi\) | ||||
−0.957845 | + | 0.287286i | \(0.907247\pi\) | |||||||
\(272\) | 3.54830i | 0.215147i | ||||||||
\(273\) | −22.7819 | + | 2.05785i | −1.37882 | + | 0.124547i | ||||
\(274\) | −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 | \(-0.241664\pi\) | ||||
0.725381 | + | 0.688348i | \(0.241664\pi\) | |||||||
\(284\) | 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 | \(-0.833734\pi\) | ||
0.866654 | − | 0.498910i | \(-0.166266\pi\) | |||||||
\(294\) | 9.93812 | − | 6.94505i | 0.579603 | − | 0.405044i | ||||
\(295\) | 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 | \(-0.390589\pi\) | ||||
0.336996 | + | 0.941506i | \(0.390589\pi\) | |||||||
\(308\) | 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 | \(-0.526082\pi\) | ||||
−0.0818458 | + | 0.996645i | \(0.526082\pi\) | |||||||
\(312\) | −7.85957 | − | 3.60240i | −0.444960 | − | 0.203946i | ||||
\(313\) | −4.20986 | −0.237955 | −0.118978 | − | 0.992897i | \(-0.537962\pi\) | ||||
−0.118978 | + | 0.992897i | \(0.537962\pi\) | |||||||
\(314\) | 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 | ||||||||
\(336\) | 4.56399 | − | 0.412258i | 0.248986 | − | 0.0224905i | ||||
\(337\) | 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 | \(0.229727\pi\) | ||||
−0.750679 | + | 0.660667i | \(0.770273\pi\) | |||||||
\(350\) | 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 | \(0.167706\pi\) | ||||
−0.864388 | + | 0.502826i | \(0.832294\pi\) | |||||||
\(354\) | −9.28811 | − | 4.25717i | −0.493657 | − | 0.226266i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.3340 | −0.653699 | ||||||||
\(357\) | 1.46281 | + | 16.1944i | 0.0774202 | + | 0.857098i | ||||
\(358\) | 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 | \(-0.645911\pi\) | ||||
−0.442507 | + | 0.896765i | \(0.645911\pi\) | |||||||
\(368\) | 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 | ||||||||
\(378\) | 9.87479 | + | 9.56496i | 0.507904 | + | 0.491969i | ||||
\(379\) | −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 | \(0.316823\pi\) | ||||
−0.544226 | + | 0.838939i | \(0.683177\pi\) | |||||||
\(384\) | 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 | \(-0.559078\pi\) | ||||
−0.184536 | + | 0.982826i | \(0.559078\pi\) | |||||||
\(398\) | 10.8906i | 0.545896i | ||||||||
\(399\) | −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 | \(0.859393\pi\) | |||||||
\(402\) | −0.393516 | + | 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 | \(0.194683\pi\) | ||||
−0.818722 | + | 0.574191i | \(0.805317\pi\) | |||||||
\(410\) | 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 | \(-0.408942\pi\) | ||||
0.282180 | + | 0.959361i | \(0.408942\pi\) | |||||||
\(420\) | 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 | \(-0.523274\pi\) | ||||
−0.0730522 | + | 0.997328i | \(0.523274\pi\) | |||||||
\(434\) | 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 | \(-0.843193\pi\) | ||
0.881095 | − | 0.472940i | \(-0.156807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.6601 | − | 3.76308i | 0.983814 | − | 0.179194i | ||||
\(442\) | − | 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 | \(-0.284532\pi\) | ||||
0.626390 | + | 0.779510i | \(0.284532\pi\) | |||||||
\(462\) | 1.61469 | + | 17.8758i | 0.0751220 | + | 0.831656i | ||||
\(463\) | − | 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 | \(0.140943\pi\) | ||||
−0.903562 | + | 0.428457i | \(0.859057\pi\) | |||||||
\(468\) | −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 | \(-0.393037\pi\) | ||||
0.329746 | + | 0.944070i | \(0.393037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.2226i | 2.38115i | ||||||||
\(482\) | 18.5233i | 0.843712i | ||||||||
\(483\) | 34.4366 | − | 3.11060i | 1.56692 | − | 0.141537i | ||||
\(484\) | −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 | \(0.00295104\pi\) | ||||
−0.999957 | + | 0.00927084i | \(0.997049\pi\) | |||||||
\(504\) | 7.48371 | + | 2.64464i | 0.333351 | + | 0.117802i | ||||
\(505\) | 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 | \(-0.419380\pi\) | ||||
0.250575 | + | 0.968097i | \(0.419380\pi\) | |||||||
\(510\) | 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 | \(-0.482726\pi\) | ||||
0.0542403 | + | 0.998528i | \(0.482726\pi\) | |||||||
\(522\) | 17.1477 | − | 14.7763i | 0.750533 | − | 0.646739i | ||||
\(523\) | −12.0602 | −0.527357 | −0.263678 | − | 0.964611i | \(-0.584936\pi\) | ||||
−0.263678 | + | 0.964611i | \(0.584936\pi\) | |||||||
\(524\) | −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 | ||||||||
\(546\) | −22.7819 | + | 2.05785i | −0.974976 | + | 0.0880679i | ||||
\(547\) | 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 | \(0.183490\pi\) | ||||
−0.838402 | + | 0.545052i | \(0.816510\pi\) | |||||||
\(564\) | 5.77626 | − | 12.6024i | 0.243224 | − | 0.530657i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.4056 | 1.02584 | ||||||||
\(567\) | 8.64537 | + | 22.1869i | 0.363071 | + | 0.931761i | ||||
\(568\) | 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 | \(-0.335407\pi\) | ||||
0.494347 | + | 0.869265i | \(0.335407\pi\) | |||||||
\(578\) | 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 | \(-0.796816\pi\) | ||
0.803096 | − | 0.595849i | \(-0.203184\pi\) | |||||||
\(588\) | 9.93812 | − | 6.94505i | 0.409841 | − | 0.286409i | ||||
\(589\) | 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 | \(-0.968933\pi\) | ||
0.995241 | − | 0.0974463i | \(-0.0310674\pi\) | |||||||
\(594\) | −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 | \(0.00759397\pi\) | ||||
−0.999715 | + | 0.0238549i | \(0.992406\pi\) | |||||||
\(602\) | 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 | \(-0.831701\pi\) | ||||
−0.863450 | + | 0.504434i | \(0.831701\pi\) | |||||||
\(608\) | − | 3.14908i | − | 0.127712i | ||||||
\(609\) | −3.11060 | − | 34.4366i | −0.126048 | − | 1.39544i | ||||
\(610\) | 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 | \(0.0711674\pi\) | ||||
−0.975110 | + | 0.221721i | \(0.928833\pi\) | |||||||
\(620\) | 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 | \(-0.284554\pi\) | ||||
0.626335 | + | 0.779554i | \(0.284554\pi\) | |||||||
\(644\) | 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 | \(0.151753\pi\) | ||||
−0.888493 | + | 0.458890i | \(0.848247\pi\) | |||||||
\(648\) | −1.32976 | + | 8.90122i | −0.0522380 | + | 0.349673i | ||||
\(649\) | − | 23.1043i | − | 0.906924i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.72869 | + | 19.1379i | 0.0677527 | + | 0.750072i | ||||
\(652\) | − | 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 | \(0.0269077\pi\) | ||||
−0.996429 | + | 0.0844325i | \(0.973092\pi\) | |||||||
\(662\) | −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 | ||||||||
\(672\) | 4.56399 | − | 0.412258i | 0.176060 | − | 0.0159032i | ||||
\(673\) | − | 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 | \(-0.822377\pi\) | ||
0.848306 | − | 0.529506i | \(-0.177623\pi\) | |||||||
\(678\) | 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 | \(-0.851544\pi\) | ||
0.893199 | − | 0.449662i | \(-0.148456\pi\) | |||||||
\(692\) | 0.907276i | 0.0344895i | ||||||||
\(693\) | −10.3583 | + | 29.3114i | −0.393478 | + | 1.11345i | ||||
\(694\) | 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 | ||||||||
\(714\) | 1.46281 | + | 16.1944i | 0.0547443 | + | 0.606060i | ||||
\(715\) | 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 | \(-0.388025\pi\) | ||||
0.344568 | + | 0.938761i | \(0.388025\pi\) | |||||||
\(720\) | 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 | \(-0.447058\pi\) | ||||
0.165556 | + | 0.986200i | \(0.447058\pi\) | |||||||
\(728\) | −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 | \(-0.348608\pi\) | ||||
0.457883 | + | 0.889013i | \(0.348608\pi\) | |||||||
\(734\) | −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 | ||||||||
\(756\) | 9.87479 | + | 9.56496i | 0.359143 | + | 0.347874i | ||||
\(757\) | − | 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 | \(-0.144018\pi\) | ||||
0.899380 | + | 0.437167i | \(0.144018\pi\) | |||||||
\(762\) | −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 | \(0.0752540\pi\) | ||||
−0.972183 | + | 0.234221i | \(0.924746\pi\) | |||||||
\(770\) | 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 | \(-0.818949\pi\) | ||
0.842553 | − | 0.538613i | \(-0.181051\pi\) | |||||||
\(774\) | −6.62858 | + | 5.71189i | −0.238260 | + | 0.205310i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.524688 | −0.0188352 | ||||||||
\(777\) | −4.31302 | − | 47.7484i | −0.154729 | − | 1.71296i | ||||
\(778\) | 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 | \(-0.505765\pi\) | ||||
−0.0181103 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(788\) | −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 | \(-0.745990\pi\) | ||
0.698143 | − | 0.715959i | \(-0.254010\pi\) | |||||||
\(798\) | −1.29823 | − | 14.3724i | −0.0459569 | − | 0.508777i | ||||
\(799\) | 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 | \(0.176100\pi\) | ||||
−0.850829 | + | 0.525443i | \(0.823900\pi\) | |||||||
\(812\) | −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 | ||||||||
\(819\) | −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 | \(-0.0613474\pi\) | |||||||
\(822\) | −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 | \(0.242529\pi\) | ||||
−0.723506 | + | 0.690318i | \(0.757471\pi\) | |||||||
\(830\) | 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 | \(-0.609576\pi\) | ||||
−0.337484 | + | 0.941331i | \(0.609576\pi\) | |||||||
\(840\) | 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 | \(-0.564038\pi\) | ||||
−0.199828 | + | 0.979831i | \(0.564038\pi\) | |||||||
\(854\) | 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 | \(-0.978704\pi\) | ||
0.997763 | − | 0.0668542i | \(-0.0212962\pi\) | |||||||
\(858\) | 14.1095 | − | 30.7835i | 0.481690 | − | 1.05093i | ||||
\(859\) | − | 43.3229i | − | 1.47816i | −0.673619 | − | 0.739079i | \(-0.735261\pi\) | ||
0.673619 | − | 0.739079i | \(-0.264739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.5445 | + | 3.84297i | −1.44991 | + | 0.130968i | ||||
\(862\) | − | 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 | \(-0.469669\pi\) | ||||
0.0951429 | + | 0.995464i | \(0.469669\pi\) | |||||||
\(882\) | 20.6601 | − | 3.76308i | 0.695661 | − | 0.126710i | ||||
\(883\) | − | 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 | \(-0.879892\pi\) | ||
0.929652 | − | 0.368439i | \(-0.120108\pi\) | |||||||
\(888\) | 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 | ||||||
\(903\) | 1.20243 | + | 13.3118i | 0.0400143 | + | 0.442988i | ||||
\(904\) | 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 | ||||||
\(924\) | 1.61469 | + | 17.8758i | 0.0531193 | + | 0.588069i | ||||
\(925\) | 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 | \(-0.614204\pi\) | ||||
−0.351134 | + | 0.936325i | \(0.614204\pi\) | |||||||
\(930\) | 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 | \(-0.709091\pi\) | ||||
−0.610649 | + | 0.791901i | \(0.709091\pi\) | |||||||
\(938\) | 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 | \(-0.312033\pi\) | ||||
0.556789 | + | 0.830654i | \(0.312033\pi\) | |||||||
\(942\) | 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 | ||||||||
\(966\) | 34.4366 | − | 3.11060i | 1.10798 | − | 0.100082i | ||||
\(967\) | 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 | \(-0.198960\pi\) | ||||
0.810933 | + | 0.585139i | \(0.198960\pi\) | |||||||
\(972\) | −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 | \(-0.952477\pi\) | ||
0.988876 | − | 0.148742i | \(-0.0475225\pi\) | |||||||
\(984\) | −14.6775 | − | 6.72736i | −0.467901 | − | 0.214460i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 26.7729 | 0.852622 | ||||||||
\(987\) | −3.29965 | − | 36.5296i | −0.105029 | − | 1.16275i | ||||
\(988\) | 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 | \(-0.571304\pi\) | ||||
−0.222140 | + | 0.975015i | \(0.571304\pi\) | |||||||
\(998\) | −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.1049.12 | 12 | ||
3.2 | odd | 2 | 1050.2.d.g.1049.11 | 12 | |||
5.2 | odd | 4 | 1050.2.b.e.251.10 | yes | 12 | ||
5.3 | odd | 4 | 1050.2.b.d.251.3 | ✓ | 12 | ||
5.4 | even | 2 | 1050.2.d.g.1049.1 | 12 | |||
7.6 | odd | 2 | inner | 1050.2.d.h.1049.1 | 12 | ||
15.2 | even | 4 | 1050.2.b.e.251.3 | yes | 12 | ||
15.8 | even | 4 | 1050.2.b.d.251.10 | yes | 12 | ||
15.14 | odd | 2 | inner | 1050.2.d.h.1049.2 | 12 | ||
21.20 | even | 2 | 1050.2.d.g.1049.2 | 12 | |||
35.13 | even | 4 | 1050.2.b.d.251.4 | yes | 12 | ||
35.27 | even | 4 | 1050.2.b.e.251.9 | yes | 12 | ||
35.34 | odd | 2 | 1050.2.d.g.1049.12 | 12 | |||
105.62 | odd | 4 | 1050.2.b.e.251.4 | yes | 12 | ||
105.83 | odd | 4 | 1050.2.b.d.251.9 | yes | 12 | ||
105.104 | even | 2 | inner | 1050.2.d.h.1049.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.b.d.251.3 | ✓ | 12 | 5.3 | odd | 4 | ||
1050.2.b.d.251.4 | yes | 12 | 35.13 | even | 4 | ||
1050.2.b.d.251.9 | yes | 12 | 105.83 | odd | 4 | ||
1050.2.b.d.251.10 | yes | 12 | 15.8 | even | 4 | ||
1050.2.b.e.251.3 | yes | 12 | 15.2 | even | 4 | ||
1050.2.b.e.251.4 | yes | 12 | 105.62 | odd | 4 | ||
1050.2.b.e.251.9 | yes | 12 | 35.27 | even | 4 | ||
1050.2.b.e.251.10 | yes | 12 | 5.2 | odd | 4 | ||
1050.2.d.g.1049.1 | 12 | 5.4 | even | 2 | |||
1050.2.d.g.1049.2 | 12 | 21.20 | even | 2 | |||
1050.2.d.g.1049.11 | 12 | 3.2 | odd | 2 | |||
1050.2.d.g.1049.12 | 12 | 35.34 | odd | 2 | |||
1050.2.d.h.1049.1 | 12 | 7.6 | odd | 2 | inner | ||
1050.2.d.h.1049.2 | 12 | 15.14 | odd | 2 | inner | ||
1050.2.d.h.1049.11 | 12 | 105.104 | even | 2 | inner | ||
1050.2.d.h.1049.12 | 12 | 1.1 | even | 1 | trivial |