Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(204,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("287.204");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.c (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: | \(2.29170653801\) |
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: | \( x^{12} + 18x^{10} + 113x^{8} + 290x^{6} + 258x^{4} + 49x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 204.2 | ||
Root | \(-2.72816i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.204 |
Dual form | 287.2.c.b.204.1 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.72816 | −1.92910 | −0.964550 | − | 0.263902i | \(-0.914990\pi\) | ||||
−0.964550 | + | 0.263902i | \(0.914990\pi\) | |||||||
\(3\) | 1.72816i | 0.997753i | 0.866673 | + | 0.498876i | \(0.166254\pi\) | ||||
−0.866673 | + | 0.498876i | \(0.833746\pi\) | |||||||
\(4\) | 5.44285 | 2.72142 | ||||||||
\(5\) | −1.58817 | −0.710252 | −0.355126 | − | 0.934818i | \(-0.615562\pi\) | ||||
−0.355126 | + | 0.934818i | \(0.615562\pi\) | |||||||
\(6\) | − | 4.71469i | − | 1.92476i | ||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −9.39263 | −3.32080 | ||||||||
\(9\) | 0.0134697 | 0.00448990 | ||||||||
\(10\) | 4.33279 | 1.37015 | ||||||||
\(11\) | 6.33279i | 1.90941i | 0.297559 | + | 0.954703i | \(0.403827\pi\) | ||||
−0.297559 | + | 0.954703i | \(0.596173\pi\) | |||||||
\(12\) | 9.40610i | 2.71531i | ||||||||
\(13\) | − | 2.36161i | − | 0.654993i | −0.944852 | − | 0.327496i | \(-0.893795\pi\) | ||
0.944852 | − | 0.327496i | \(-0.106205\pi\) | |||||||
\(14\) | − | 2.72816i | − | 0.729131i | ||||||
\(15\) | − | 2.74461i | − | 0.708656i | ||||||
\(16\) | 14.7389 | 3.68472 | ||||||||
\(17\) | − | 3.29792i | − | 0.799864i | −0.916545 | − | 0.399932i | \(-0.869034\pi\) | ||
0.916545 | − | 0.399932i | \(-0.130966\pi\) | |||||||
\(18\) | −0.0367475 | −0.00866146 | ||||||||
\(19\) | 3.34626i | 0.767684i | 0.923399 | + | 0.383842i | \(0.125399\pi\) | ||||
−0.923399 | + | 0.383842i | \(0.874601\pi\) | |||||||
\(20\) | −8.64418 | −1.93290 | ||||||||
\(21\) | −1.72816 | −0.377115 | ||||||||
\(22\) | − | 17.2768i | − | 3.68343i | ||||||
\(23\) | −2.17141 | −0.452770 | −0.226385 | − | 0.974038i | \(-0.572691\pi\) | ||||
−0.226385 | + | 0.974038i | \(0.572691\pi\) | |||||||
\(24\) | − | 16.2319i | − | 3.31333i | ||||||
\(25\) | −2.47771 | −0.495542 | ||||||||
\(26\) | 6.44285i | 1.26355i | ||||||||
\(27\) | 5.20775i | 1.00223i | ||||||||
\(28\) | 5.44285i | 1.02860i | ||||||||
\(29\) | 1.97861i | 0.367418i | 0.982981 | + | 0.183709i | \(0.0588104\pi\) | ||||
−0.982981 | + | 0.183709i | \(0.941190\pi\) | |||||||
\(30\) | 7.48774i | 1.36707i | ||||||||
\(31\) | −7.04449 | −1.26523 | −0.632614 | − | 0.774467i | \(-0.718018\pi\) | ||||
−0.632614 | + | 0.774467i | \(0.718018\pi\) | |||||||
\(32\) | −21.4247 | −3.78740 | ||||||||
\(33\) | −10.9441 | −1.90512 | ||||||||
\(34\) | 8.99726i | 1.54302i | ||||||||
\(35\) | − | 1.58817i | − | 0.268450i | ||||||
\(36\) | 0.0733135 | 0.0122189 | ||||||||
\(37\) | −6.69440 | −1.10055 | −0.550276 | − | 0.834983i | \(-0.685477\pi\) | ||||
−0.550276 | + | 0.834983i | \(0.685477\pi\) | |||||||
\(38\) | − | 9.12911i | − | 1.48094i | ||||||
\(39\) | 4.08124 | 0.653521 | ||||||||
\(40\) | 14.9171 | 2.35860 | ||||||||
\(41\) | 1.38002 | − | 6.25264i | 0.215523 | − | 0.976499i | ||||
\(42\) | 4.71469 | 0.727492 | ||||||||
\(43\) | −6.85467 | −1.04533 | −0.522664 | − | 0.852539i | \(-0.675062\pi\) | ||||
−0.522664 | + | 0.852539i | \(0.675062\pi\) | |||||||
\(44\) | 34.4684i | 5.19630i | ||||||||
\(45\) | −0.0213922 | −0.00318896 | ||||||||
\(46\) | 5.92394 | 0.873438 | ||||||||
\(47\) | − | 4.19130i | − | 0.611364i | −0.952134 | − | 0.305682i | \(-0.901116\pi\) | ||
0.952134 | − | 0.305682i | \(-0.0988844\pi\) | |||||||
\(48\) | 25.4711i | 3.67644i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 6.75958 | 0.955949 | ||||||||
\(51\) | 5.69933 | 0.798066 | ||||||||
\(52\) | − | 12.8539i | − | 1.78251i | ||||||
\(53\) | 3.14492i | 0.431988i | 0.976395 | + | 0.215994i | \(0.0692992\pi\) | ||||
−0.976395 | + | 0.215994i | \(0.930701\pi\) | |||||||
\(54\) | − | 14.2076i | − | 1.93341i | ||||||
\(55\) | − | 10.0576i | − | 1.35616i | ||||||
\(56\) | − | 9.39263i | − | 1.25514i | ||||||
\(57\) | −5.78286 | −0.765958 | ||||||||
\(58\) | − | 5.39795i | − | 0.708786i | ||||||
\(59\) | −7.58817 | −0.987896 | −0.493948 | − | 0.869491i | \(-0.664447\pi\) | ||||
−0.493948 | + | 0.869491i | \(0.664447\pi\) | |||||||
\(60\) | − | 14.9385i | − | 1.92855i | ||||||
\(61\) | 14.2054 | 1.81882 | 0.909408 | − | 0.415905i | \(-0.136535\pi\) | ||||
0.909408 | + | 0.415905i | \(0.136535\pi\) | |||||||
\(62\) | 19.2185 | 2.44075 | ||||||||
\(63\) | 0.0134697i | 0.00169702i | ||||||||
\(64\) | 28.9723 | 3.62154 | ||||||||
\(65\) | 3.75064i | 0.465210i | ||||||||
\(66\) | 29.8571 | 3.67516 | ||||||||
\(67\) | 14.0207i | 1.71291i | 0.516225 | + | 0.856453i | \(0.327337\pi\) | ||||
−0.516225 | + | 0.856453i | \(0.672663\pi\) | |||||||
\(68\) | − | 17.9501i | − | 2.17677i | ||||||
\(69\) | − | 3.75254i | − | 0.451752i | ||||||
\(70\) | 4.33279i | 0.517867i | ||||||||
\(71\) | − | 1.84675i | − | 0.219169i | −0.993977 | − | 0.109585i | \(-0.965048\pi\) | ||
0.993977 | − | 0.109585i | \(-0.0349520\pi\) | |||||||
\(72\) | −0.126516 | −0.0149100 | ||||||||
\(73\) | 6.52220 | 0.763365 | 0.381683 | − | 0.924293i | \(-0.375345\pi\) | ||||
0.381683 | + | 0.924293i | \(0.375345\pi\) | |||||||
\(74\) | 18.2634 | 2.12307 | ||||||||
\(75\) | − | 4.28187i | − | 0.494428i | ||||||
\(76\) | 18.2132i | 2.08919i | ||||||||
\(77\) | −6.33279 | −0.721688 | ||||||||
\(78\) | −11.1343 | −1.26071 | ||||||||
\(79\) | 6.15260i | 0.692221i | 0.938194 | + | 0.346111i | \(0.112498\pi\) | ||||
−0.938194 | + | 0.346111i | \(0.887502\pi\) | |||||||
\(80\) | −23.4079 | −2.61708 | ||||||||
\(81\) | −8.95941 | −0.995490 | ||||||||
\(82\) | −3.76491 | + | 17.0582i | −0.415764 | + | 1.88376i | ||||
\(83\) | 10.7760 | 1.18282 | 0.591412 | − | 0.806370i | \(-0.298571\pi\) | ||||
0.591412 | + | 0.806370i | \(0.298571\pi\) | |||||||
\(84\) | −9.40610 | −1.02629 | ||||||||
\(85\) | 5.23767i | 0.568105i | ||||||||
\(86\) | 18.7006 | 2.01654 | ||||||||
\(87\) | −3.41935 | −0.366592 | ||||||||
\(88\) | − | 59.4815i | − | 6.34075i | ||||||
\(89\) | 10.2497i | 1.08646i | 0.839583 | + | 0.543231i | \(0.182799\pi\) | ||||
−0.839583 | + | 0.543231i | \(0.817201\pi\) | |||||||
\(90\) | 0.0583613 | 0.00615182 | ||||||||
\(91\) | 2.36161 | 0.247564 | ||||||||
\(92\) | −11.8186 | −1.23218 | ||||||||
\(93\) | − | 12.1740i | − | 1.26238i | ||||||
\(94\) | 11.4345i | 1.17938i | ||||||||
\(95\) | − | 5.31443i | − | 0.545249i | ||||||
\(96\) | − | 37.0254i | − | 3.77888i | ||||||
\(97\) | 9.34775i | 0.949120i | 0.880223 | + | 0.474560i | \(0.157393\pi\) | ||||
−0.880223 | + | 0.474560i | \(0.842607\pi\) | |||||||
\(98\) | 2.72816 | 0.275586 | ||||||||
\(99\) | 0.0853007i | 0.00857305i | ||||||||
\(100\) | −13.4858 | −1.34858 | ||||||||
\(101\) | − | 6.38598i | − | 0.635429i | −0.948186 | − | 0.317714i | \(-0.897085\pi\) | ||
0.948186 | − | 0.317714i | \(-0.102915\pi\) | |||||||
\(102\) | −15.5487 | −1.53955 | ||||||||
\(103\) | 10.3206 | 1.01692 | 0.508460 | − | 0.861085i | \(-0.330215\pi\) | ||||
0.508460 | + | 0.861085i | \(0.330215\pi\) | |||||||
\(104\) | 22.1817i | 2.17510i | ||||||||
\(105\) | 2.74461 | 0.267847 | ||||||||
\(106\) | − | 8.57985i | − | 0.833348i | ||||||
\(107\) | −0.924553 | −0.0893799 | −0.0446900 | − | 0.999001i | \(-0.514230\pi\) | ||||
−0.0446900 | + | 0.999001i | \(0.514230\pi\) | |||||||
\(108\) | 28.3450i | 2.72750i | ||||||||
\(109\) | − | 5.30372i | − | 0.508004i | −0.967204 | − | 0.254002i | \(-0.918253\pi\) | ||
0.967204 | − | 0.254002i | \(-0.0817470\pi\) | |||||||
\(110\) | 27.4386i | 2.61617i | ||||||||
\(111\) | − | 11.5690i | − | 1.09808i | ||||||
\(112\) | 14.7389i | 1.39269i | ||||||||
\(113\) | 4.49971 | 0.423297 | 0.211649 | − | 0.977346i | \(-0.432117\pi\) | ||||
0.211649 | + | 0.977346i | \(0.432117\pi\) | |||||||
\(114\) | 15.7766 | 1.47761 | ||||||||
\(115\) | 3.44857 | 0.321581 | ||||||||
\(116\) | 10.7693i | 0.999901i | ||||||||
\(117\) | − | 0.0318102i | − | 0.00294085i | ||||||
\(118\) | 20.7017 | 1.90575 | ||||||||
\(119\) | 3.29792 | 0.302320 | ||||||||
\(120\) | 25.7791i | 2.35330i | ||||||||
\(121\) | −29.1042 | −2.64583 | ||||||||
\(122\) | −38.7546 | −3.50868 | ||||||||
\(123\) | 10.8056 | + | 2.38489i | 0.974304 | + | 0.215038i | ||||
\(124\) | −38.3421 | −3.44322 | ||||||||
\(125\) | 11.8759 | 1.06221 | ||||||||
\(126\) | − | 0.0367475i | − | 0.00327373i | ||||||
\(127\) | 5.13749 | 0.455879 | 0.227939 | − | 0.973675i | \(-0.426801\pi\) | ||||
0.227939 | + | 0.973675i | \(0.426801\pi\) | |||||||
\(128\) | −36.1916 | −3.19892 | ||||||||
\(129\) | − | 11.8460i | − | 1.04298i | ||||||
\(130\) | − | 10.2324i | − | 0.897437i | ||||||
\(131\) | 10.2845 | 0.898557 | 0.449278 | − | 0.893392i | \(-0.351681\pi\) | ||||
0.449278 | + | 0.893392i | \(0.351681\pi\) | |||||||
\(132\) | −59.5668 | −5.18462 | ||||||||
\(133\) | −3.34626 | −0.290157 | ||||||||
\(134\) | − | 38.2508i | − | 3.30437i | ||||||
\(135\) | − | 8.27081i | − | 0.711838i | ||||||
\(136\) | 30.9762i | 2.65618i | ||||||||
\(137\) | 20.4701i | 1.74888i | 0.485135 | + | 0.874439i | \(0.338770\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661230\pi\) | |||||||
\(138\) | 10.2375i | 0.871475i | ||||||||
\(139\) | −11.9165 | −1.01074 | −0.505371 | − | 0.862902i | \(-0.668644\pi\) | ||||
−0.505371 | + | 0.862902i | \(0.668644\pi\) | |||||||
\(140\) | − | 8.64418i | − | 0.730566i | ||||||
\(141\) | 7.24322 | 0.609989 | ||||||||
\(142\) | 5.03823i | 0.422799i | ||||||||
\(143\) | 14.9556 | 1.25065 | ||||||||
\(144\) | 0.198528 | 0.0165440 | ||||||||
\(145\) | − | 3.14237i | − | 0.260960i | ||||||
\(146\) | −17.7936 | −1.47261 | ||||||||
\(147\) | − | 1.72816i | − | 0.142536i | ||||||
\(148\) | −36.4366 | −2.99507 | ||||||||
\(149\) | − | 3.94015i | − | 0.322790i | −0.986890 | − | 0.161395i | \(-0.948401\pi\) | ||
0.986890 | − | 0.161395i | \(-0.0515993\pi\) | |||||||
\(150\) | 11.6816i | 0.953800i | ||||||||
\(151\) | 9.16632i | 0.745944i | 0.927843 | + | 0.372972i | \(0.121661\pi\) | ||||
−0.927843 | + | 0.372972i | \(0.878339\pi\) | |||||||
\(152\) | − | 31.4301i | − | 2.54932i | ||||||
\(153\) | − | 0.0444221i | − | 0.00359131i | ||||||
\(154\) | 17.2768 | 1.39221 | ||||||||
\(155\) | 11.1879 | 0.898631 | ||||||||
\(156\) | 22.2135 | 1.77851 | ||||||||
\(157\) | 21.9129i | 1.74884i | 0.485172 | + | 0.874419i | \(0.338757\pi\) | ||||
−0.485172 | + | 0.874419i | \(0.661243\pi\) | |||||||
\(158\) | − | 16.7853i | − | 1.33536i | ||||||
\(159\) | −5.43492 | −0.431018 | ||||||||
\(160\) | 34.0262 | 2.69001 | ||||||||
\(161\) | − | 2.17141i | − | 0.171131i | ||||||
\(162\) | 24.4427 | 1.92040 | ||||||||
\(163\) | 15.6921 | 1.22910 | 0.614548 | − | 0.788879i | \(-0.289338\pi\) | ||||
0.614548 | + | 0.788879i | \(0.289338\pi\) | |||||||
\(164\) | 7.51122 | − | 34.0322i | 0.586528 | − | 2.65747i | ||||
\(165\) | 17.3810 | 1.35311 | ||||||||
\(166\) | −29.3987 | −2.28178 | ||||||||
\(167\) | − | 8.82477i | − | 0.682881i | −0.939903 | − | 0.341441i | \(-0.889085\pi\) | ||
0.939903 | − | 0.341441i | \(-0.110915\pi\) | |||||||
\(168\) | 16.2319 | 1.25232 | ||||||||
\(169\) | 7.42280 | 0.570984 | ||||||||
\(170\) | − | 14.2892i | − | 1.09593i | ||||||
\(171\) | 0.0450731i | 0.00344682i | ||||||||
\(172\) | −37.3089 | −2.84478 | ||||||||
\(173\) | −4.49306 | −0.341601 | −0.170800 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170800 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(174\) | 9.32852 | 0.707193 | ||||||||
\(175\) | − | 2.47771i | − | 0.187297i | ||||||
\(176\) | 93.3382i | 7.03563i | ||||||||
\(177\) | − | 13.1136i | − | 0.985676i | ||||||
\(178\) | − | 27.9627i | − | 2.09589i | ||||||
\(179\) | 5.96309i | 0.445702i | 0.974852 | + | 0.222851i | \(0.0715364\pi\) | ||||
−0.974852 | + | 0.222851i | \(0.928464\pi\) | |||||||
\(180\) | −0.116435 | −0.00867852 | ||||||||
\(181\) | − | 21.3416i | − | 1.58631i | −0.609023 | − | 0.793153i | \(-0.708438\pi\) | ||
0.609023 | − | 0.793153i | \(-0.291562\pi\) | |||||||
\(182\) | −6.44285 | −0.477576 | ||||||||
\(183\) | 24.5492i | 1.81473i | ||||||||
\(184\) | 20.3952 | 1.50356 | ||||||||
\(185\) | 10.6319 | 0.781670 | ||||||||
\(186\) | 33.2126i | 2.43526i | ||||||||
\(187\) | 20.8850 | 1.52727 | ||||||||
\(188\) | − | 22.8126i | − | 1.66378i | ||||||
\(189\) | −5.20775 | −0.378808 | ||||||||
\(190\) | 14.4986i | 1.05184i | ||||||||
\(191\) | 1.04897i | 0.0759009i | 0.999280 | + | 0.0379504i | \(0.0120829\pi\) | ||||
−0.999280 | + | 0.0379504i | \(0.987917\pi\) | |||||||
\(192\) | 50.0688i | 3.61340i | ||||||||
\(193\) | − | 10.6726i | − | 0.768230i | −0.923285 | − | 0.384115i | \(-0.874507\pi\) | ||
0.923285 | − | 0.384115i | \(-0.125493\pi\) | |||||||
\(194\) | − | 25.5021i | − | 1.83095i | ||||||
\(195\) | −6.48171 | −0.464165 | ||||||||
\(196\) | −5.44285 | −0.388775 | ||||||||
\(197\) | −4.36309 | −0.310857 | −0.155429 | − | 0.987847i | \(-0.549676\pi\) | ||||
−0.155429 | + | 0.987847i | \(0.549676\pi\) | |||||||
\(198\) | − | 0.232714i | − | 0.0165383i | ||||||
\(199\) | − | 14.7840i | − | 1.04801i | −0.851715 | − | 0.524006i | \(-0.824437\pi\) | ||
0.851715 | − | 0.524006i | \(-0.175563\pi\) | |||||||
\(200\) | 23.2722 | 1.64559 | ||||||||
\(201\) | −24.2301 | −1.70906 | ||||||||
\(202\) | 17.4220i | 1.22581i | ||||||||
\(203\) | −1.97861 | −0.138871 | ||||||||
\(204\) | 31.0206 | 2.17188 | ||||||||
\(205\) | −2.19171 | + | 9.93028i | −0.153075 | + | 0.693561i | ||||
\(206\) | −28.1563 | −1.96174 | ||||||||
\(207\) | −0.0292482 | −0.00203289 | ||||||||
\(208\) | − | 34.8075i | − | 2.41347i | ||||||
\(209\) | −21.1911 | −1.46582 | ||||||||
\(210\) | −7.48774 | −0.516703 | ||||||||
\(211\) | − | 16.9879i | − | 1.16950i | −0.811215 | − | 0.584748i | \(-0.801193\pi\) | ||
0.811215 | − | 0.584748i | \(-0.198807\pi\) | |||||||
\(212\) | 17.1173i | 1.17562i | ||||||||
\(213\) | 3.19148 | 0.218677 | ||||||||
\(214\) | 2.52233 | 0.172423 | ||||||||
\(215\) | 10.8864 | 0.742447 | ||||||||
\(216\) | − | 48.9145i | − | 3.32821i | ||||||
\(217\) | − | 7.04449i | − | 0.478211i | ||||||
\(218\) | 14.4694i | 0.979990i | ||||||||
\(219\) | 11.2714i | 0.761650i | ||||||||
\(220\) | − | 54.7417i | − | 3.69069i | ||||||
\(221\) | −7.78841 | −0.523905 | ||||||||
\(222\) | 31.5620i | 2.11830i | ||||||||
\(223\) | −10.8872 | −0.729060 | −0.364530 | − | 0.931192i | \(-0.618770\pi\) | ||||
−0.364530 | + | 0.931192i | \(0.618770\pi\) | |||||||
\(224\) | − | 21.4247i | − | 1.43150i | ||||||
\(225\) | −0.0333740 | −0.00222493 | ||||||||
\(226\) | −12.2759 | −0.816582 | ||||||||
\(227\) | − | 9.19154i | − | 0.610064i | −0.952342 | − | 0.305032i | \(-0.901333\pi\) | ||
0.952342 | − | 0.305032i | \(-0.0986671\pi\) | |||||||
\(228\) | −31.4752 | −2.08450 | ||||||||
\(229\) | 16.1981i | 1.07040i | 0.844725 | + | 0.535201i | \(0.179764\pi\) | ||||
−0.844725 | + | 0.535201i | \(0.820236\pi\) | |||||||
\(230\) | −9.40824 | −0.620361 | ||||||||
\(231\) | − | 10.9441i | − | 0.720066i | ||||||
\(232\) | − | 18.5843i | − | 1.22012i | ||||||
\(233\) | 20.6673i | 1.35396i | 0.736000 | + | 0.676981i | \(0.236712\pi\) | ||||
−0.736000 | + | 0.676981i | \(0.763288\pi\) | |||||||
\(234\) | 0.0867832i | 0.00567320i | ||||||||
\(235\) | 6.65650i | 0.434222i | ||||||||
\(236\) | −41.3013 | −2.68848 | ||||||||
\(237\) | −10.6327 | −0.690666 | ||||||||
\(238\) | −8.99726 | −0.583206 | ||||||||
\(239\) | 9.88334i | 0.639300i | 0.947536 | + | 0.319650i | \(0.103565\pi\) | ||||
−0.947536 | + | 0.319650i | \(0.896435\pi\) | |||||||
\(240\) | − | 40.4525i | − | 2.61120i | ||||||
\(241\) | −6.78526 | −0.437077 | −0.218538 | − | 0.975828i | \(-0.570129\pi\) | ||||
−0.218538 | + | 0.975828i | \(0.570129\pi\) | |||||||
\(242\) | 79.4008 | 5.10408 | ||||||||
\(243\) | 0.139980i | 0.00897973i | ||||||||
\(244\) | 77.3179 | 4.94977 | ||||||||
\(245\) | 1.58817 | 0.101465 | ||||||||
\(246\) | −29.4793 | − | 6.50635i | −1.87953 | − | 0.414830i | ||||
\(247\) | 7.90255 | 0.502827 | ||||||||
\(248\) | 66.1663 | 4.20156 | ||||||||
\(249\) | 18.6227i | 1.18017i | ||||||||
\(250\) | −32.3993 | −2.04911 | ||||||||
\(251\) | 24.1079 | 1.52168 | 0.760840 | − | 0.648940i | \(-0.224787\pi\) | ||||
0.760840 | + | 0.648940i | \(0.224787\pi\) | |||||||
\(252\) | 0.0733135i | 0.00461832i | ||||||||
\(253\) | − | 13.7511i | − | 0.864522i | ||||||
\(254\) | −14.0159 | −0.879435 | ||||||||
\(255\) | −9.05152 | −0.566828 | ||||||||
\(256\) | 40.7917 | 2.54948 | ||||||||
\(257\) | 3.52723i | 0.220022i | 0.993930 | + | 0.110011i | \(0.0350887\pi\) | ||||
−0.993930 | + | 0.110011i | \(0.964911\pi\) | |||||||
\(258\) | 32.3177i | 2.01201i | ||||||||
\(259\) | − | 6.69440i | − | 0.415970i | ||||||
\(260\) | 20.4142i | 1.26603i | ||||||||
\(261\) | 0.0266513i | 0.00164967i | ||||||||
\(262\) | −28.0576 | −1.73341 | ||||||||
\(263\) | 14.5722i | 0.898558i | 0.893392 | + | 0.449279i | \(0.148319\pi\) | ||||
−0.893392 | + | 0.449279i | \(0.851681\pi\) | |||||||
\(264\) | 102.793 | 6.32650 | ||||||||
\(265\) | − | 4.99468i | − | 0.306821i | ||||||
\(266\) | 9.12911 | 0.559742 | ||||||||
\(267\) | −17.7130 | −1.08402 | ||||||||
\(268\) | 76.3127i | 4.66154i | ||||||||
\(269\) | 2.97762 | 0.181548 | 0.0907742 | − | 0.995872i | \(-0.471066\pi\) | ||||
0.0907742 | + | 0.995872i | \(0.471066\pi\) | |||||||
\(270\) | 22.5641i | 1.37321i | ||||||||
\(271\) | 1.44928 | 0.0880376 | 0.0440188 | − | 0.999031i | \(-0.485984\pi\) | ||||
0.0440188 | + | 0.999031i | \(0.485984\pi\) | |||||||
\(272\) | − | 48.6077i | − | 2.94728i | ||||||
\(273\) | 4.08124i | 0.247008i | ||||||||
\(274\) | − | 55.8457i | − | 3.37376i | ||||||
\(275\) | − | 15.6908i | − | 0.946191i | ||||||
\(276\) | − | 20.4245i | − | 1.22941i | ||||||
\(277\) | 13.5089 | 0.811669 | 0.405834 | − | 0.913947i | \(-0.366981\pi\) | ||||
0.405834 | + | 0.913947i | \(0.366981\pi\) | |||||||
\(278\) | 32.5100 | 1.94982 | ||||||||
\(279\) | −0.0948872 | −0.00568075 | ||||||||
\(280\) | 14.9171i | 0.891468i | ||||||||
\(281\) | 6.61575i | 0.394663i | 0.980337 | + | 0.197331i | \(0.0632275\pi\) | ||||
−0.980337 | + | 0.197331i | \(0.936773\pi\) | |||||||
\(282\) | −19.7607 | −1.17673 | ||||||||
\(283\) | 8.21936 | 0.488590 | 0.244295 | − | 0.969701i | \(-0.421443\pi\) | ||||
0.244295 | + | 0.969701i | \(0.421443\pi\) | |||||||
\(284\) | − | 10.0516i | − | 0.596452i | ||||||
\(285\) | 9.18418 | 0.544024 | ||||||||
\(286\) | −40.8012 | −2.41262 | ||||||||
\(287\) | 6.25264 | + | 1.38002i | 0.369082 | + | 0.0814599i | ||||
\(288\) | −0.288585 | −0.0170050 | ||||||||
\(289\) | 6.12370 | 0.360218 | ||||||||
\(290\) | 8.57288i | 0.503417i | ||||||||
\(291\) | −16.1544 | −0.946987 | ||||||||
\(292\) | 35.4993 | 2.07744 | ||||||||
\(293\) | 25.7737i | 1.50572i | 0.658182 | + | 0.752859i | \(0.271326\pi\) | ||||
−0.658182 | + | 0.752859i | \(0.728674\pi\) | |||||||
\(294\) | 4.71469i | 0.274966i | ||||||||
\(295\) | 12.0513 | 0.701655 | ||||||||
\(296\) | 62.8780 | 3.65471 | ||||||||
\(297\) | −32.9796 | −1.91367 | ||||||||
\(298\) | 10.7494i | 0.622693i | ||||||||
\(299\) | 5.12802i | 0.296561i | ||||||||
\(300\) | − | 23.3056i | − | 1.34555i | ||||||
\(301\) | − | 6.85467i | − | 0.395097i | ||||||
\(302\) | − | 25.0072i | − | 1.43900i | ||||||
\(303\) | 11.0360 | 0.634001 | ||||||||
\(304\) | 49.3201i | 2.82870i | ||||||||
\(305\) | −22.5606 | −1.29182 | ||||||||
\(306\) | 0.121190i | 0.00692799i | ||||||||
\(307\) | −30.6173 | −1.74742 | −0.873711 | − | 0.486446i | \(-0.838293\pi\) | ||||
−0.873711 | + | 0.486446i | \(0.838293\pi\) | |||||||
\(308\) | −34.4684 | −1.96402 | ||||||||
\(309\) | 17.8357i | 1.01464i | ||||||||
\(310\) | −30.5223 | −1.73355 | ||||||||
\(311\) | 16.1116i | 0.913605i | 0.889568 | + | 0.456802i | \(0.151005\pi\) | ||||
−0.889568 | + | 0.456802i | \(0.848995\pi\) | |||||||
\(312\) | −38.3335 | −2.17021 | ||||||||
\(313\) | − | 4.23750i | − | 0.239517i | −0.992803 | − | 0.119759i | \(-0.961788\pi\) | ||
0.992803 | − | 0.119759i | \(-0.0382121\pi\) | |||||||
\(314\) | − | 59.7818i | − | 3.37368i | ||||||
\(315\) | − | 0.0213922i | − | 0.00120531i | ||||||
\(316\) | 33.4876i | 1.88383i | ||||||||
\(317\) | − | 7.39882i | − | 0.415559i | −0.978176 | − | 0.207780i | \(-0.933376\pi\) | ||
0.978176 | − | 0.207780i | \(-0.0666237\pi\) | |||||||
\(318\) | 14.8273 | 0.831475 | ||||||||
\(319\) | −12.5301 | −0.701551 | ||||||||
\(320\) | −46.0131 | −2.57221 | ||||||||
\(321\) | − | 1.59777i | − | 0.0891790i | ||||||
\(322\) | 5.92394i | 0.330128i | ||||||||
\(323\) | 11.0357 | 0.614042 | ||||||||
\(324\) | −48.7647 | −2.70915 | ||||||||
\(325\) | 5.85138i | 0.324576i | ||||||||
\(326\) | −42.8104 | −2.37105 | ||||||||
\(327\) | 9.16566 | 0.506862 | ||||||||
\(328\) | −12.9620 | + | 58.7288i | −0.715706 | + | 3.24275i | ||||
\(329\) | 4.19130 | 0.231074 | ||||||||
\(330\) | −47.4182 | −2.61029 | ||||||||
\(331\) | − | 4.76900i | − | 0.262128i | −0.991374 | − | 0.131064i | \(-0.958161\pi\) | ||
0.991374 | − | 0.131064i | \(-0.0418393\pi\) | |||||||
\(332\) | 58.6523 | 3.21896 | ||||||||
\(333\) | −0.0901715 | −0.00494137 | ||||||||
\(334\) | 24.0754i | 1.31735i | ||||||||
\(335\) | − | 22.2674i | − | 1.21660i | ||||||
\(336\) | −25.4711 | −1.38956 | ||||||||
\(337\) | −8.17118 | −0.445113 | −0.222556 | − | 0.974920i | \(-0.571440\pi\) | ||||
−0.222556 | + | 0.974920i | \(0.571440\pi\) | |||||||
\(338\) | −20.2506 | −1.10149 | ||||||||
\(339\) | 7.77621i | 0.422346i | ||||||||
\(340\) | 28.5078i | 1.54605i | ||||||||
\(341\) | − | 44.6112i | − | 2.41583i | ||||||
\(342\) | − | 0.122966i | − | 0.00664926i | ||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 64.3834 | 3.47132 | ||||||||
\(345\) | 5.95967i | 0.320858i | ||||||||
\(346\) | 12.2578 | 0.658982 | ||||||||
\(347\) | − | 2.85656i | − | 0.153348i | −0.997056 | − | 0.0766742i | \(-0.975570\pi\) | ||
0.997056 | − | 0.0766742i | \(-0.0244301\pi\) | |||||||
\(348\) | −18.6110 | −0.997653 | ||||||||
\(349\) | −2.88634 | −0.154502 | −0.0772512 | − | 0.997012i | \(-0.524614\pi\) | ||||
−0.0772512 | + | 0.997012i | \(0.524614\pi\) | |||||||
\(350\) | 6.75958i | 0.361315i | ||||||||
\(351\) | 12.2987 | 0.656455 | ||||||||
\(352\) | − | 135.678i | − | 7.23168i | ||||||
\(353\) | −7.30891 | −0.389014 | −0.194507 | − | 0.980901i | \(-0.562311\pi\) | ||||
−0.194507 | + | 0.980901i | \(0.562311\pi\) | |||||||
\(354\) | 35.7759i | 1.90147i | ||||||||
\(355\) | 2.93296i | 0.155665i | ||||||||
\(356\) | 55.7873i | 2.95672i | ||||||||
\(357\) | 5.69933i | 0.301641i | ||||||||
\(358\) | − | 16.2683i | − | 0.859804i | ||||||
\(359\) | 33.3194 | 1.75853 | 0.879265 | − | 0.476334i | \(-0.158035\pi\) | ||||
0.879265 | + | 0.476334i | \(0.158035\pi\) | |||||||
\(360\) | 0.200929 | 0.0105899 | ||||||||
\(361\) | 7.80258 | 0.410662 | ||||||||
\(362\) | 58.2231i | 3.06014i | ||||||||
\(363\) | − | 50.2966i | − | 2.63989i | ||||||
\(364\) | 12.8539 | 0.673727 | ||||||||
\(365\) | −10.3584 | −0.542182 | ||||||||
\(366\) | − | 66.9741i | − | 3.50079i | ||||||
\(367\) | −27.0498 | −1.41199 | −0.705994 | − | 0.708218i | \(-0.749499\pi\) | ||||
−0.705994 | + | 0.708218i | \(0.749499\pi\) | |||||||
\(368\) | −32.0041 | −1.66833 | ||||||||
\(369\) | 0.0185884 | − | 0.0842213i | 0.000967675 | − | 0.00438438i | ||||
\(370\) | −29.0054 | −1.50792 | ||||||||
\(371\) | −3.14492 | −0.163276 | ||||||||
\(372\) | − | 66.2612i | − | 3.43548i | ||||||
\(373\) | 23.6784 | 1.22602 | 0.613010 | − | 0.790075i | \(-0.289958\pi\) | ||||
0.613010 | + | 0.790075i | \(0.289958\pi\) | |||||||
\(374\) | −56.9777 | −2.94625 | ||||||||
\(375\) | 20.5234i | 1.05982i | ||||||||
\(376\) | 39.3673i | 2.03021i | ||||||||
\(377\) | 4.67270 | 0.240656 | ||||||||
\(378\) | 14.2076 | 0.730759 | ||||||||
\(379\) | −0.144696 | −0.00743253 | −0.00371627 | − | 0.999993i | \(-0.501183\pi\) | ||||
−0.00371627 | + | 0.999993i | \(0.501183\pi\) | |||||||
\(380\) | − | 28.9256i | − | 1.48385i | ||||||
\(381\) | 8.87840i | 0.454854i | ||||||||
\(382\) | − | 2.86176i | − | 0.146420i | ||||||
\(383\) | − | 24.5984i | − | 1.25692i | −0.777841 | − | 0.628461i | \(-0.783685\pi\) | ||
0.777841 | − | 0.628461i | \(-0.216315\pi\) | |||||||
\(384\) | − | 62.5448i | − | 3.19173i | ||||||
\(385\) | 10.0576 | 0.512580 | ||||||||
\(386\) | 29.1165i | 1.48199i | ||||||||
\(387\) | −0.0923304 | −0.00469342 | ||||||||
\(388\) | 50.8784i | 2.58296i | ||||||||
\(389\) | 12.4897 | 0.633253 | 0.316626 | − | 0.948550i | \(-0.397450\pi\) | ||||
0.316626 | + | 0.948550i | \(0.397450\pi\) | |||||||
\(390\) | 17.6831 | 0.895420 | ||||||||
\(391\) | 7.16114i | 0.362154i | ||||||||
\(392\) | 9.39263 | 0.474399 | ||||||||
\(393\) | 17.7732i | 0.896537i | ||||||||
\(394\) | 11.9032 | 0.599675 | ||||||||
\(395\) | − | 9.77139i | − | 0.491652i | ||||||
\(396\) | 0.464279i | 0.0233309i | ||||||||
\(397\) | 3.02007i | 0.151573i | 0.997124 | + | 0.0757865i | \(0.0241467\pi\) | ||||
−0.997124 | + | 0.0757865i | \(0.975853\pi\) | |||||||
\(398\) | 40.3332i | 2.02172i | ||||||||
\(399\) | − | 5.78286i | − | 0.289505i | ||||||
\(400\) | −36.5187 | −1.82593 | ||||||||
\(401\) | −4.21447 | −0.210460 | −0.105230 | − | 0.994448i | \(-0.533558\pi\) | ||||
−0.105230 | + | 0.994448i | \(0.533558\pi\) | |||||||
\(402\) | 66.1034 | 3.29694 | ||||||||
\(403\) | 16.6363i | 0.828715i | ||||||||
\(404\) | − | 34.7579i | − | 1.72927i | ||||||
\(405\) | 14.2291 | 0.707049 | ||||||||
\(406\) | 5.39795 | 0.267896 | ||||||||
\(407\) | − | 42.3942i | − | 2.10140i | ||||||
\(408\) | −53.5317 | −2.65022 | ||||||||
\(409\) | 2.29691 | 0.113575 | 0.0567875 | − | 0.998386i | \(-0.481914\pi\) | ||||
0.0567875 | + | 0.998386i | \(0.481914\pi\) | |||||||
\(410\) | 5.97932 | − | 27.0914i | 0.295298 | − | 1.33795i | ||||
\(411\) | −35.3756 | −1.74495 | ||||||||
\(412\) | 56.1735 | 2.76747 | ||||||||
\(413\) | − | 7.58817i | − | 0.373390i | ||||||
\(414\) | 0.0797938 | 0.00392165 | ||||||||
\(415\) | −17.1142 | −0.840103 | ||||||||
\(416\) | 50.5969i | 2.48072i | ||||||||
\(417\) | − | 20.5936i | − | 1.00847i | ||||||
\(418\) | 57.8127 | 2.82771 | ||||||||
\(419\) | −26.3559 | −1.28757 | −0.643784 | − | 0.765207i | \(-0.722636\pi\) | ||||
−0.643784 | + | 0.765207i | \(0.722636\pi\) | |||||||
\(420\) | 14.9385 | 0.728925 | ||||||||
\(421\) | 34.8204i | 1.69704i | 0.529163 | + | 0.848520i | \(0.322506\pi\) | ||||
−0.529163 | + | 0.848520i | \(0.677494\pi\) | |||||||
\(422\) | 46.3457i | 2.25607i | ||||||||
\(423\) | − | 0.0564555i | − | 0.00274496i | ||||||
\(424\) | − | 29.5391i | − | 1.43455i | ||||||
\(425\) | 8.17129i | 0.396366i | ||||||||
\(426\) | −8.70686 | −0.421849 | ||||||||
\(427\) | 14.2054i | 0.687448i | ||||||||
\(428\) | −5.03220 | −0.243241 | ||||||||
\(429\) | 25.8456i | 1.24784i | ||||||||
\(430\) | −29.6998 | −1.43225 | ||||||||
\(431\) | −19.3419 | −0.931668 | −0.465834 | − | 0.884872i | \(-0.654246\pi\) | ||||
−0.465834 | + | 0.884872i | \(0.654246\pi\) | |||||||
\(432\) | 76.7565i | 3.69295i | ||||||||
\(433\) | 26.3927 | 1.26835 | 0.634176 | − | 0.773189i | \(-0.281339\pi\) | ||||
0.634176 | + | 0.773189i | \(0.281339\pi\) | |||||||
\(434\) | 19.2185i | 0.922516i | ||||||||
\(435\) | 5.43051 | 0.260373 | ||||||||
\(436\) | − | 28.8673i | − | 1.38249i | ||||||
\(437\) | − | 7.26608i | − | 0.347584i | ||||||
\(438\) | − | 30.7501i | − | 1.46930i | ||||||
\(439\) | − | 25.8188i | − | 1.23226i | −0.787643 | − | 0.616132i | \(-0.788699\pi\) | ||
0.787643 | − | 0.616132i | \(-0.211301\pi\) | |||||||
\(440\) | 94.4669i | 4.50353i | ||||||||
\(441\) | −0.0134697 | −0.000641414 | ||||||||
\(442\) | 21.2480 | 1.01066 | ||||||||
\(443\) | 16.8943 | 0.802671 | 0.401335 | − | 0.915931i | \(-0.368546\pi\) | ||||
0.401335 | + | 0.915931i | \(0.368546\pi\) | |||||||
\(444\) | − | 62.9681i | − | 2.98834i | ||||||
\(445\) | − | 16.2782i | − | 0.771662i | ||||||
\(446\) | 29.7020 | 1.40643 | ||||||||
\(447\) | 6.80920 | 0.322064 | ||||||||
\(448\) | 28.9723i | 1.36881i | ||||||||
\(449\) | −0.826112 | −0.0389866 | −0.0194933 | − | 0.999810i | \(-0.506205\pi\) | ||||
−0.0194933 | + | 0.999810i | \(0.506205\pi\) | |||||||
\(450\) | 0.0910495 | 0.00429212 | ||||||||
\(451\) | 39.5967 | + | 8.73935i | 1.86453 | + | 0.411520i | ||||
\(452\) | 24.4912 | 1.15197 | ||||||||
\(453\) | −15.8408 | −0.744268 | ||||||||
\(454\) | 25.0760i | 1.17687i | ||||||||
\(455\) | −3.75064 | −0.175833 | ||||||||
\(456\) | 54.3162 | 2.54359 | ||||||||
\(457\) | − | 32.8865i | − | 1.53836i | −0.639030 | − | 0.769182i | \(-0.720664\pi\) | ||
0.639030 | − | 0.769182i | \(-0.279336\pi\) | |||||||
\(458\) | − | 44.1910i | − | 2.06491i | ||||||
\(459\) | 17.1748 | 0.801650 | ||||||||
\(460\) | 18.7700 | 0.875157 | ||||||||
\(461\) | −3.69324 | −0.172012 | −0.0860058 | − | 0.996295i | \(-0.527410\pi\) | ||||
−0.0860058 | + | 0.996295i | \(0.527410\pi\) | |||||||
\(462\) | 29.8571i | 1.38908i | ||||||||
\(463\) | − | 25.9484i | − | 1.20592i | −0.797770 | − | 0.602962i | \(-0.793987\pi\) | ||
0.797770 | − | 0.602962i | \(-0.206013\pi\) | |||||||
\(464\) | 29.1625i | 1.35383i | ||||||||
\(465\) | 19.3344i | 0.896611i | ||||||||
\(466\) | − | 56.3838i | − | 2.61193i | ||||||
\(467\) | −11.9439 | −0.552697 | −0.276349 | − | 0.961057i | \(-0.589124\pi\) | ||||
−0.276349 | + | 0.961057i | \(0.589124\pi\) | |||||||
\(468\) | − | 0.173138i | − | 0.00800331i | ||||||
\(469\) | −14.0207 | −0.647418 | ||||||||
\(470\) | − | 18.1600i | − | 0.837658i | ||||||
\(471\) | −37.8689 | −1.74491 | ||||||||
\(472\) | 71.2729 | 3.28060 | ||||||||
\(473\) | − | 43.4092i | − | 1.99596i | ||||||
\(474\) | 29.0076 | 1.33236 | ||||||||
\(475\) | − | 8.29104i | − | 0.380419i | ||||||
\(476\) | 17.9501 | 0.822741 | ||||||||
\(477\) | 0.0423612i | 0.00193959i | ||||||||
\(478\) | − | 26.9633i | − | 1.23327i | ||||||
\(479\) | − | 9.64918i | − | 0.440882i | −0.975400 | − | 0.220441i | \(-0.929250\pi\) | ||
0.975400 | − | 0.220441i | \(-0.0707497\pi\) | |||||||
\(480\) | 58.8026i | 2.68396i | ||||||||
\(481\) | 15.8096i | 0.720854i | ||||||||
\(482\) | 18.5113 | 0.843165 | ||||||||
\(483\) | 3.75254 | 0.170746 | ||||||||
\(484\) | −158.410 | −7.20043 | ||||||||
\(485\) | − | 14.8458i | − | 0.674115i | ||||||
\(486\) | − | 0.381888i | − | 0.0173228i | ||||||
\(487\) | 27.8889 | 1.26377 | 0.631884 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631884 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(488\) | −133.426 | −6.03992 | ||||||||
\(489\) | 27.1184i | 1.22633i | ||||||||
\(490\) | −4.33279 | −0.195735 | ||||||||
\(491\) | 22.4897 | 1.01495 | 0.507474 | − | 0.861667i | \(-0.330579\pi\) | ||||
0.507474 | + | 0.861667i | \(0.330579\pi\) | |||||||
\(492\) | 58.8130 | + | 12.9806i | 2.65149 | + | 0.585210i | ||||
\(493\) | 6.52530 | 0.293885 | ||||||||
\(494\) | −21.5594 | −0.970004 | ||||||||
\(495\) | − | 0.135472i | − | 0.00608903i | ||||||
\(496\) | −103.828 | −4.66201 | ||||||||
\(497\) | 1.84675 | 0.0828381 | ||||||||
\(498\) | − | 50.8056i | − | 2.27666i | ||||||
\(499\) | 14.0838i | 0.630479i | 0.949012 | + | 0.315239i | \(0.102085\pi\) | ||||
−0.949012 | + | 0.315239i | \(0.897915\pi\) | |||||||
\(500\) | 64.6386 | 2.89073 | ||||||||
\(501\) | 15.2506 | 0.681346 | ||||||||
\(502\) | −65.7703 | −2.93547 | ||||||||
\(503\) | 35.4759i | 1.58179i | 0.611951 | + | 0.790896i | \(0.290385\pi\) | ||||
−0.611951 | + | 0.790896i | \(0.709615\pi\) | |||||||
\(504\) | − | 0.126516i | − | 0.00563547i | ||||||
\(505\) | 10.1420i | 0.451315i | ||||||||
\(506\) | 37.5151i | 1.66775i | ||||||||
\(507\) | 12.8278i | 0.569701i | ||||||||
\(508\) | 27.9626 | 1.24064 | ||||||||
\(509\) | 17.5946i | 0.779866i | 0.920843 | + | 0.389933i | \(0.127502\pi\) | ||||
−0.920843 | + | 0.389933i | \(0.872498\pi\) | |||||||
\(510\) | 24.6940 | 1.09347 | ||||||||
\(511\) | 6.52220i | 0.288525i | ||||||||
\(512\) | −38.9031 | −1.71929 | ||||||||
\(513\) | −17.4265 | −0.769397 | ||||||||
\(514\) | − | 9.62284i | − | 0.424445i | ||||||
\(515\) | −16.3909 | −0.722270 | ||||||||
\(516\) | − | 64.4757i | − | 2.83839i | ||||||
\(517\) | 26.5426 | 1.16734 | ||||||||
\(518\) | 18.2634i | 0.802446i | ||||||||
\(519\) | − | 7.76471i | − | 0.340833i | ||||||
\(520\) | − | 35.2284i | − | 1.54487i | ||||||
\(521\) | − | 1.16311i | − | 0.0509567i | −0.999675 | − | 0.0254783i | \(-0.991889\pi\) | ||
0.999675 | − | 0.0254783i | \(-0.00811088\pi\) | |||||||
\(522\) | − | 0.0727089i | − | 0.00318238i | ||||||
\(523\) | −11.6390 | −0.508937 | −0.254468 | − | 0.967081i | \(-0.581900\pi\) | ||||
−0.254468 | + | 0.967081i | \(0.581900\pi\) | |||||||
\(524\) | 55.9767 | 2.44535 | ||||||||
\(525\) | 4.28187 | 0.186876 | ||||||||
\(526\) | − | 39.7552i | − | 1.73341i | ||||||
\(527\) | 23.2322i | 1.01201i | ||||||||
\(528\) | −161.303 | −7.01982 | ||||||||
\(529\) | −18.2850 | −0.795000 | ||||||||
\(530\) | 13.6263i | 0.591888i | ||||||||
\(531\) | −0.102210 | −0.00443556 | ||||||||
\(532\) | −18.2132 | −0.789640 | ||||||||
\(533\) | −14.7663 | − | 3.25906i | −0.639600 | − | 0.141166i | ||||
\(534\) | 48.3239 | 2.09118 | ||||||||
\(535\) | 1.46835 | 0.0634823 | ||||||||
\(536\) | − | 131.692i | − | 5.68821i | ||||||
\(537\) | −10.3052 | −0.444701 | ||||||||
\(538\) | −8.12340 | −0.350225 | ||||||||
\(539\) | − | 6.33279i | − | 0.272772i | ||||||
\(540\) | − | 45.0167i | − | 1.93721i | ||||||
\(541\) | 25.9764 | 1.11681 | 0.558406 | − | 0.829568i | \(-0.311413\pi\) | ||||
0.558406 | + | 0.829568i | \(0.311413\pi\) | |||||||
\(542\) | −3.95387 | −0.169833 | ||||||||
\(543\) | 36.8816 | 1.58274 | ||||||||
\(544\) | 70.6572i | 3.02940i | ||||||||
\(545\) | 8.42322i | 0.360811i | ||||||||
\(546\) | − | 11.1343i | − | 0.476502i | ||||||
\(547\) | 40.6869i | 1.73964i | 0.493365 | + | 0.869822i | \(0.335767\pi\) | ||||
−0.493365 | + | 0.869822i | \(0.664233\pi\) | |||||||
\(548\) | 111.416i | 4.75944i | ||||||||
\(549\) | 0.191343 | 0.00816631 | ||||||||
\(550\) | 42.8070i | 1.82530i | ||||||||
\(551\) | −6.62093 | −0.282061 | ||||||||
\(552\) | 35.2462i | 1.50018i | ||||||||
\(553\) | −6.15260 | −0.261635 | ||||||||
\(554\) | −36.8543 | −1.56579 | ||||||||
\(555\) | 18.3735i | 0.779913i | ||||||||
\(556\) | −64.8595 | −2.75066 | ||||||||
\(557\) | − | 27.9485i | − | 1.18422i | −0.805858 | − | 0.592108i | \(-0.798296\pi\) | ||
0.805858 | − | 0.592108i | \(-0.201704\pi\) | |||||||
\(558\) | 0.258867 | 0.0109587 | ||||||||
\(559\) | 16.1881i | 0.684682i | ||||||||
\(560\) | − | 23.4079i | − | 0.989164i | ||||||
\(561\) | 36.0927i | 1.52383i | ||||||||
\(562\) | − | 18.0488i | − | 0.761343i | ||||||
\(563\) | − | 0.912204i | − | 0.0384448i | −0.999815 | − | 0.0192224i | \(-0.993881\pi\) | ||
0.999815 | − | 0.0192224i | \(-0.00611906\pi\) | |||||||
\(564\) | 39.4238 | 1.66004 | ||||||||
\(565\) | −7.14632 | −0.300648 | ||||||||
\(566\) | −22.4237 | −0.942539 | ||||||||
\(567\) | − | 8.95941i | − | 0.376260i | ||||||
\(568\) | 17.3459i | 0.727816i | ||||||||
\(569\) | −21.4934 | −0.901049 | −0.450524 | − | 0.892764i | \(-0.648763\pi\) | ||||
−0.450524 | + | 0.892764i | \(0.648763\pi\) | |||||||
\(570\) | −25.0559 | −1.04948 | ||||||||
\(571\) | 41.2697i | 1.72708i | 0.504277 | + | 0.863542i | \(0.331759\pi\) | ||||
−0.504277 | + | 0.863542i | \(0.668241\pi\) | |||||||
\(572\) | 81.4009 | 3.40354 | ||||||||
\(573\) | −1.81279 | −0.0757303 | ||||||||
\(574\) | −17.0582 | − | 3.76491i | −0.711996 | − | 0.157144i | ||||
\(575\) | 5.38011 | 0.224366 | ||||||||
\(576\) | 0.390249 | 0.0162604 | ||||||||
\(577\) | 22.6298i | 0.942089i | 0.882109 | + | 0.471045i | \(0.156123\pi\) | ||||
−0.882109 | + | 0.471045i | \(0.843877\pi\) | |||||||
\(578\) | −16.7064 | −0.694896 | ||||||||
\(579\) | 18.4439 | 0.766504 | ||||||||
\(580\) | − | 17.1034i | − | 0.710182i | ||||||
\(581\) | 10.7760i | 0.447065i | ||||||||
\(582\) | 44.0717 | 1.82683 | ||||||||
\(583\) | −19.9161 | −0.824841 | ||||||||
\(584\) | −61.2606 | −2.53498 | ||||||||
\(585\) | 0.0505201i | 0.00208875i | ||||||||
\(586\) | − | 70.3148i | − | 2.90468i | ||||||
\(587\) | − | 0.556658i | − | 0.0229758i | −0.999934 | − | 0.0114879i | \(-0.996343\pi\) | ||
0.999934 | − | 0.0114879i | \(-0.00365678\pi\) | |||||||
\(588\) | − | 9.40610i | − | 0.387901i | ||||||
\(589\) | − | 23.5727i | − | 0.971294i | ||||||
\(590\) | −32.8779 | −1.35356 | ||||||||
\(591\) | − | 7.54011i | − | 0.310159i | ||||||
\(592\) | −98.6679 | −4.05523 | ||||||||
\(593\) | − | 4.65161i | − | 0.191019i | −0.995429 | − | 0.0955094i | \(-0.969552\pi\) | ||
0.995429 | − | 0.0955094i | \(-0.0304480\pi\) | |||||||
\(594\) | 89.9735 | 3.69166 | ||||||||
\(595\) | −5.23767 | −0.214724 | ||||||||
\(596\) | − | 21.4456i | − | 0.878447i | ||||||
\(597\) | 25.5491 | 1.04566 | ||||||||
\(598\) | − | 13.9900i | − | 0.572096i | ||||||
\(599\) | −6.12297 | −0.250178 | −0.125089 | − | 0.992146i | \(-0.539922\pi\) | ||||
−0.125089 | + | 0.992146i | \(0.539922\pi\) | |||||||
\(600\) | 40.2180i | 1.64189i | ||||||||
\(601\) | − | 32.2061i | − | 1.31371i | −0.754016 | − | 0.656857i | \(-0.771886\pi\) | ||
0.754016 | − | 0.656857i | \(-0.228114\pi\) | |||||||
\(602\) | 18.7006i | 0.762181i | ||||||||
\(603\) | 0.188855i | 0.00769078i | ||||||||
\(604\) | 49.8908i | 2.03003i | ||||||||
\(605\) | 46.2224 | 1.87921 | ||||||||
\(606\) | −30.1079 | −1.22305 | ||||||||
\(607\) | −36.7385 | −1.49117 | −0.745586 | − | 0.666410i | \(-0.767830\pi\) | ||||
−0.745586 | + | 0.666410i | \(0.767830\pi\) | |||||||
\(608\) | − | 71.6927i | − | 2.90752i | ||||||
\(609\) | − | 3.41935i | − | 0.138559i | ||||||
\(610\) | 61.5490 | 2.49205 | ||||||||
\(611\) | −9.89821 | −0.400439 | ||||||||
\(612\) | − | 0.241782i | − | 0.00977347i | ||||||
\(613\) | 17.6423 | 0.712564 | 0.356282 | − | 0.934378i | \(-0.384044\pi\) | ||||
0.356282 | + | 0.934378i | \(0.384044\pi\) | |||||||
\(614\) | 83.5288 | 3.37095 | ||||||||
\(615\) | −17.1611 | − | 3.78761i | −0.692002 | − | 0.152731i | ||||
\(616\) | 59.4815 | 2.39658 | ||||||||
\(617\) | −8.87689 | −0.357370 | −0.178685 | − | 0.983906i | \(-0.557184\pi\) | ||||
−0.178685 | + | 0.983906i | \(0.557184\pi\) | |||||||
\(618\) | − | 48.6585i | − | 1.95733i | ||||||
\(619\) | 9.61795 | 0.386578 | 0.193289 | − | 0.981142i | \(-0.438084\pi\) | ||||
0.193289 | + | 0.981142i | \(0.438084\pi\) | |||||||
\(620\) | 60.8938 | 2.44555 | ||||||||
\(621\) | − | 11.3082i | − | 0.453781i | ||||||
\(622\) | − | 43.9550i | − | 1.76243i | ||||||
\(623\) | −10.2497 | −0.410644 | ||||||||
\(624\) | 60.1529 | 2.40804 | ||||||||
\(625\) | −6.47242 | −0.258897 | ||||||||
\(626\) | 11.5606i | 0.462053i | ||||||||
\(627\) | − | 36.6216i | − | 1.46253i | ||||||
\(628\) | 119.268i | 4.75933i | ||||||||
\(629\) | 22.0776i | 0.880292i | ||||||||
\(630\) | 0.0583613i | 0.00232517i | ||||||||
\(631\) | 13.1951 | 0.525290 | 0.262645 | − | 0.964893i | \(-0.415405\pi\) | ||||
0.262645 | + | 0.964893i | \(0.415405\pi\) | |||||||
\(632\) | − | 57.7891i | − | 2.29873i | ||||||
\(633\) | 29.3578 | 1.16687 | ||||||||
\(634\) | 20.1852i | 0.801655i | ||||||||
\(635\) | −8.15922 | −0.323789 | ||||||||
\(636\) | −29.5815 | −1.17298 | ||||||||
\(637\) | 2.36161i | 0.0935704i | ||||||||
\(638\) | 34.1841 | 1.35336 | ||||||||
\(639\) | − | 0.0248752i | − | 0.000984048i | ||||||
\(640\) | 57.4785 | 2.27204 | ||||||||
\(641\) | − | 21.9177i | − | 0.865698i | −0.901466 | − | 0.432849i | \(-0.857508\pi\) | ||
0.901466 | − | 0.432849i | \(-0.142492\pi\) | |||||||
\(642\) | 4.35898i | 0.172035i | ||||||||
\(643\) | − | 23.0816i | − | 0.910251i | −0.890427 | − | 0.455125i | \(-0.849594\pi\) | ||
0.890427 | − | 0.455125i | \(-0.150406\pi\) | |||||||
\(644\) | − | 11.8186i | − | 0.465720i | ||||||
\(645\) | 18.8134i | 0.740778i | ||||||||
\(646\) | −30.1071 | −1.18455 | ||||||||
\(647\) | −1.06211 | −0.0417558 | −0.0208779 | − | 0.999782i | \(-0.506646\pi\) | ||||
−0.0208779 | + | 0.999782i | \(0.506646\pi\) | |||||||
\(648\) | 84.1524 | 3.30582 | ||||||||
\(649\) | − | 48.0543i | − | 1.88630i | ||||||
\(650\) | − | 15.9635i | − | 0.626140i | ||||||
\(651\) | 12.1740 | 0.477136 | ||||||||
\(652\) | 85.4094 | 3.34489 | ||||||||
\(653\) | 5.96470i | 0.233417i | 0.993166 | + | 0.116708i | \(0.0372343\pi\) | ||||
−0.993166 | + | 0.116708i | \(0.962766\pi\) | |||||||
\(654\) | −25.0054 | −0.977788 | ||||||||
\(655\) | −16.3335 | −0.638202 | ||||||||
\(656\) | 20.3399 | − | 92.1570i | 0.794140 | − | 3.59813i | ||||
\(657\) | 0.0878521 | 0.00342744 | ||||||||
\(658\) | −11.4345 | −0.445764 | ||||||||
\(659\) | 30.3564i | 1.18252i | 0.806482 | + | 0.591259i | \(0.201369\pi\) | ||||
−0.806482 | + | 0.591259i | \(0.798631\pi\) | |||||||
\(660\) | 94.6024 | 3.68239 | ||||||||
\(661\) | −22.2278 | −0.864561 | −0.432281 | − | 0.901739i | \(-0.642291\pi\) | ||||
−0.432281 | + | 0.901739i | \(0.642291\pi\) | |||||||
\(662\) | 13.0106i | 0.505671i | ||||||||
\(663\) | − | 13.4596i | − | 0.522728i | ||||||
\(664\) | −101.215 | −3.92792 | ||||||||
\(665\) | 5.31443 | 0.206085 | ||||||||
\(666\) | 0.246002 | 0.00953239 | ||||||||
\(667\) | − | 4.29636i | − | 0.166356i | ||||||
\(668\) | − | 48.0319i | − | 1.85841i | ||||||
\(669\) | − | 18.8148i | − | 0.727421i | ||||||
\(670\) | 60.7489i | 2.34693i | ||||||||
\(671\) | 89.9598i | 3.47286i | ||||||||
\(672\) | 37.0254 | 1.42828 | ||||||||
\(673\) | 2.72867i | 0.105183i | 0.998616 | + | 0.0525913i | \(0.0167481\pi\) | ||||
−0.998616 | + | 0.0525913i | \(0.983252\pi\) | |||||||
\(674\) | 22.2923 | 0.858666 | ||||||||
\(675\) | − | 12.9033i | − | 0.496648i | ||||||
\(676\) | 40.4011 | 1.55389 | ||||||||
\(677\) | 44.7433 | 1.71962 | 0.859812 | − | 0.510611i | \(-0.170581\pi\) | ||||
0.859812 | + | 0.510611i | \(0.170581\pi\) | |||||||
\(678\) | − | 21.2147i | − | 0.814747i | ||||||
\(679\) | −9.34775 | −0.358734 | ||||||||
\(680\) | − | 49.1955i | − | 1.88656i | ||||||
\(681\) | 15.8844 | 0.608693 | ||||||||
\(682\) | 121.706i | 4.66038i | ||||||||
\(683\) | − | 10.6927i | − | 0.409143i | −0.978852 | − | 0.204572i | \(-0.934420\pi\) | ||
0.978852 | − | 0.204572i | \(-0.0655802\pi\) | |||||||
\(684\) | 0.245326i | 0.00938027i | ||||||||
\(685\) | − | 32.5100i | − | 1.24214i | ||||||
\(686\) | 2.72816i | 0.104162i | ||||||||
\(687\) | −27.9929 | −1.06800 | ||||||||
\(688\) | −101.030 | −3.85174 | ||||||||
\(689\) | 7.42708 | 0.282949 | ||||||||
\(690\) | − | 16.2589i | − | 0.618967i | ||||||
\(691\) | 30.0511i | 1.14320i | 0.820533 | + | 0.571599i | \(0.193677\pi\) | ||||
−0.820533 | + | 0.571599i | \(0.806323\pi\) | |||||||
\(692\) | −24.4550 | −0.929641 | ||||||||
\(693\) | −0.0853007 | −0.00324031 | ||||||||
\(694\) | 7.79316i | 0.295824i | ||||||||
\(695\) | 18.9254 | 0.717882 | ||||||||
\(696\) | 32.1167 | 1.21738 | ||||||||
\(697\) | −20.6207 | − | 4.55119i | −0.781066 | − | 0.172389i | ||||
\(698\) | 7.87440 | 0.298051 | ||||||||
\(699\) | −35.7164 | −1.35092 | ||||||||
\(700\) | − | 13.4858i | − | 0.509715i | ||||||
\(701\) | −42.2827 | −1.59699 | −0.798497 | − | 0.601999i | \(-0.794371\pi\) | ||||
−0.798497 | + | 0.601999i | \(0.794371\pi\) | |||||||
\(702\) | −33.5527 | −1.26637 | ||||||||
\(703\) | − | 22.4012i | − | 0.844876i | ||||||
\(704\) | 183.476i | 6.91499i | ||||||||
\(705\) | −11.5035 | −0.433246 | ||||||||
\(706\) | 19.9399 | 0.750447 | ||||||||
\(707\) | 6.38598 | 0.240170 | ||||||||
\(708\) | − | 71.3751i | − | 2.68244i | ||||||
\(709\) | − | 46.1118i | − | 1.73177i | −0.500247 | − | 0.865883i | \(-0.666757\pi\) | ||
0.500247 | − | 0.865883i | \(-0.333243\pi\) | |||||||
\(710\) | − | 8.00158i | − | 0.300294i | ||||||
\(711\) | 0.0828737i | 0.00310801i | ||||||||
\(712\) | − | 96.2712i | − | 3.60792i | ||||||
\(713\) | 15.2965 | 0.572857 | ||||||||
\(714\) | − | 15.5487i | − | 0.581895i | ||||||
\(715\) | −23.7520 | −0.888275 | ||||||||
\(716\) | 32.4562i | 1.21294i | ||||||||
\(717\) | −17.0800 | −0.637863 | ||||||||
\(718\) | −90.9005 | −3.39238 | ||||||||
\(719\) | 11.9585i | 0.445976i | 0.974821 | + | 0.222988i | \(0.0715811\pi\) | ||||
−0.974821 | + | 0.222988i | \(0.928419\pi\) | |||||||
\(720\) | −0.315297 | −0.0117504 | ||||||||
\(721\) | 10.3206i | 0.384360i | ||||||||
\(722\) | −21.2867 | −0.792208 | ||||||||
\(723\) | − | 11.7260i | − | 0.436095i | ||||||
\(724\) | − | 116.159i | − | 4.31701i | ||||||
\(725\) | − | 4.90241i | − | 0.182071i | ||||||
\(726\) | 137.217i | 5.09260i | ||||||||
\(727\) | − | 21.6176i | − | 0.801753i | −0.916132 | − | 0.400877i | \(-0.868706\pi\) | ||
0.916132 | − | 0.400877i | \(-0.131294\pi\) | |||||||
\(728\) | −22.1817 | −0.822110 | ||||||||
\(729\) | −27.1201 | −1.00445 | ||||||||
\(730\) | 28.2593 | 1.04592 | ||||||||
\(731\) | 22.6062i | 0.836120i | ||||||||
\(732\) | 133.618i | 4.93865i | ||||||||
\(733\) | 33.4999 | 1.23735 | 0.618673 | − | 0.785649i | \(-0.287671\pi\) | ||||
0.618673 | + | 0.785649i | \(0.287671\pi\) | |||||||
\(734\) | 73.7961 | 2.72386 | ||||||||
\(735\) | 2.74461i | 0.101237i | ||||||||
\(736\) | 46.5219 | 1.71482 | ||||||||
\(737\) | −88.7903 | −3.27063 | ||||||||
\(738\) | −0.0507122 | + | 0.229769i | −0.00186674 | + | 0.00845791i | ||||
\(739\) | 1.23982 | 0.0456073 | 0.0228037 | − | 0.999740i | \(-0.492741\pi\) | ||||
0.0228037 | + | 0.999740i | \(0.492741\pi\) | |||||||
\(740\) | 57.8676 | 2.12725 | ||||||||
\(741\) | 13.6569i | 0.501697i | ||||||||
\(742\) | 8.57985 | 0.314976 | ||||||||
\(743\) | 12.6353 | 0.463542 | 0.231771 | − | 0.972770i | \(-0.425548\pi\) | ||||
0.231771 | + | 0.972770i | \(0.425548\pi\) | |||||||
\(744\) | 114.346i | 4.19212i | ||||||||
\(745\) | 6.25764i | 0.229262i | ||||||||
\(746\) | −64.5984 | −2.36512 | ||||||||
\(747\) | 0.145150 | 0.00531076 | ||||||||
\(748\) | 113.674 | 4.15634 | ||||||||
\(749\) | − | 0.924553i | − | 0.0337824i | ||||||
\(750\) | − | 55.9911i | − | 2.04451i | ||||||
\(751\) | − | 35.1470i | − | 1.28253i | −0.767318 | − | 0.641267i | \(-0.778409\pi\) | ||
0.767318 | − | 0.641267i | \(-0.221591\pi\) | |||||||
\(752\) | − | 61.7750i | − | 2.25270i | ||||||
\(753\) | 41.6623i | 1.51826i | ||||||||
\(754\) | −12.7479 | −0.464250 | ||||||||
\(755\) | − | 14.5577i | − | 0.529809i | ||||||
\(756\) | −28.3450 | −1.03090 | ||||||||
\(757\) | 36.7182i | 1.33455i | 0.744813 | + | 0.667273i | \(0.232539\pi\) | ||||
−0.744813 | + | 0.667273i | \(0.767461\pi\) | |||||||
\(758\) | 0.394753 | 0.0143381 | ||||||||
\(759\) | 23.7640 | 0.862579 | ||||||||
\(760\) | 49.9165i | 1.81066i | ||||||||
\(761\) | −22.2613 | −0.806973 | −0.403486 | − | 0.914986i | \(-0.632202\pi\) | ||||
−0.403486 | + | 0.914986i | \(0.632202\pi\) | |||||||
\(762\) | − | 24.2217i | − | 0.877458i | ||||||
\(763\) | 5.30372 | 0.192008 | ||||||||
\(764\) | 5.70939i | 0.206558i | ||||||||
\(765\) | 0.0705499i | 0.00255074i | ||||||||
\(766\) | 67.1084i | 2.42473i | ||||||||
\(767\) | 17.9203i | 0.647065i | ||||||||
\(768\) | 70.4946i | 2.54375i | ||||||||
\(769\) | 30.1091 | 1.08576 | 0.542882 | − | 0.839809i | \(-0.317333\pi\) | ||||
0.542882 | + | 0.839809i | \(0.317333\pi\) | |||||||
\(770\) | −27.4386 | −0.988819 | ||||||||
\(771\) | −6.09561 | −0.219528 | ||||||||
\(772\) | − | 58.0893i | − | 2.09068i | ||||||
\(773\) | − | 34.6738i | − | 1.24713i | −0.781771 | − | 0.623566i | \(-0.785683\pi\) | ||
0.781771 | − | 0.623566i | \(-0.214317\pi\) | |||||||
\(774\) | 0.251892 | 0.00905407 | ||||||||
\(775\) | 17.4542 | 0.626973 | ||||||||
\(776\) | − | 87.8000i | − | 3.15184i | ||||||
\(777\) | 11.5690 | 0.415035 | ||||||||
\(778\) | −34.0739 | −1.22161 | ||||||||
\(779\) | 20.9229 | + | 4.61789i | 0.749642 | + | 0.165453i | ||||
\(780\) | −35.2789 | −1.26319 | ||||||||
\(781\) | 11.6951 | 0.418483 | ||||||||
\(782\) | − | 19.5367i | − | 0.698631i | ||||||
\(783\) | −10.3041 | −0.368238 | ||||||||
\(784\) | −14.7389 | −0.526389 | ||||||||
\(785\) | − | 34.8014i | − | 1.24212i | ||||||
\(786\) | − | 48.4880i | − | 1.72951i | ||||||
\(787\) | −22.1393 | −0.789182 | −0.394591 | − | 0.918857i | \(-0.629114\pi\) | ||||
−0.394591 | + | 0.918857i | \(0.629114\pi\) | |||||||
\(788\) | −23.7476 | −0.845975 | ||||||||
\(789\) | −25.1830 | −0.896538 | ||||||||
\(790\) | 26.6579i | 0.948445i | ||||||||
\(791\) | 4.49971i | 0.159991i | ||||||||
\(792\) | − | 0.801198i | − | 0.0284693i | ||||||
\(793\) | − | 33.5476i | − | 1.19131i | ||||||
\(794\) | − | 8.23923i | − | 0.292399i | ||||||
\(795\) | 8.63160 | 0.306131 | ||||||||
\(796\) | − | 80.4672i | − | 2.85208i | ||||||
\(797\) | −15.9924 | −0.566481 | −0.283241 | − | 0.959049i | \(-0.591410\pi\) | ||||
−0.283241 | + | 0.959049i | \(0.591410\pi\) | |||||||
\(798\) | 15.7766i | 0.558484i | ||||||||
\(799\) | −13.8226 | −0.489008 | ||||||||
\(800\) | 53.0843 | 1.87681 | ||||||||
\(801\) | 0.138060i | 0.00487811i | ||||||||
\(802\) | 11.4977 | 0.405999 | ||||||||
\(803\) | 41.3037i | 1.45757i | ||||||||
\(804\) | −131.880 | −4.65107 | ||||||||
\(805\) | 3.44857i | 0.121546i | ||||||||
\(806\) | − | 45.3866i | − | 1.59867i | ||||||
\(807\) | 5.14579i | 0.181140i | ||||||||
\(808\) | 59.9812i | 2.11013i | ||||||||
\(809\) | 16.6457i | 0.585233i | 0.956230 | + | 0.292616i | \(0.0945259\pi\) | ||||
−0.956230 | + | 0.292616i | \(0.905474\pi\) | |||||||
\(810\) | −38.8192 | −1.36397 | ||||||||
\(811\) | 28.3191 | 0.994419 | 0.497210 | − | 0.867630i | \(-0.334358\pi\) | ||||
0.497210 | + | 0.867630i | \(0.334358\pi\) | |||||||
\(812\) | −10.7693 | −0.377927 | ||||||||
\(813\) | 2.50459i | 0.0878397i | ||||||||
\(814\) | 115.658i | 4.05381i | ||||||||
\(815\) | −24.9217 | −0.872969 | ||||||||
\(816\) | 84.0018 | 2.94065 | ||||||||
\(817\) | − | 22.9375i | − | 0.802481i | ||||||
\(818\) | −6.26634 | −0.219097 | ||||||||
\(819\) | 0.0318102 | 0.00111154 | ||||||||
\(820\) | −11.9291 | + | 54.0490i | −0.416583 | + | 1.88747i | ||||
\(821\) | −28.3525 | −0.989509 | −0.494755 | − | 0.869033i | \(-0.664742\pi\) | ||||
−0.494755 | + | 0.869033i | \(0.664742\pi\) | |||||||
\(822\) | 96.5101 | 3.36618 | ||||||||
\(823\) | − | 14.0767i | − | 0.490681i | −0.969437 | − | 0.245341i | \(-0.921100\pi\) | ||
0.969437 | − | 0.245341i | \(-0.0788998\pi\) | |||||||
\(824\) | −96.9377 | −3.37699 | ||||||||
\(825\) | 27.1162 | 0.944064 | ||||||||
\(826\) | 20.7017i | 0.720305i | ||||||||
\(827\) | − | 6.68674i | − | 0.232521i | −0.993219 | − | 0.116260i | \(-0.962909\pi\) | ||
0.993219 | − | 0.116260i | \(-0.0370907\pi\) | |||||||
\(828\) | −0.159194 | −0.00553236 | ||||||||
\(829\) | 16.4614 | 0.571729 | 0.285865 | − | 0.958270i | \(-0.407719\pi\) | ||||
0.285865 | + | 0.958270i | \(0.407719\pi\) | |||||||
\(830\) | 46.6902 | 1.62064 | ||||||||
\(831\) | 23.3454i | 0.809845i | ||||||||
\(832\) | − | 68.4214i | − | 2.37208i | ||||||
\(833\) | 3.29792i | 0.114266i | ||||||||
\(834\) | 56.1825i | 1.94544i | ||||||||
\(835\) | 14.0153i | 0.485018i | ||||||||
\(836\) | −115.340 | −3.98912 | ||||||||
\(837\) | − | 36.6859i | − | 1.26805i | ||||||
\(838\) | 71.9029 | 2.48385 | ||||||||
\(839\) | − | 14.2042i | − | 0.490384i | −0.969475 | − | 0.245192i | \(-0.921149\pi\) | ||
0.969475 | − | 0.245192i | \(-0.0788510\pi\) | |||||||
\(840\) | −25.7791 | −0.889465 | ||||||||
\(841\) | 25.0851 | 0.865004 | ||||||||
\(842\) | − | 94.9954i | − | 3.27376i | ||||||
\(843\) | −11.4331 | −0.393776 | ||||||||
\(844\) | − | 92.4625i | − | 3.18269i | ||||||
\(845\) | −11.7887 | −0.405543 | ||||||||
\(846\) | 0.154020i | 0.00529530i | ||||||||
\(847\) | − | 29.1042i | − | 1.00003i | ||||||
\(848\) | 46.3527i | 1.59176i | ||||||||
\(849\) | 14.2043i | 0.487492i | ||||||||
\(850\) | − | 22.2926i | − | 0.764629i | ||||||
\(851\) | 14.5363 | 0.498297 | ||||||||
\(852\) | 17.3707 | 0.595111 | ||||||||
\(853\) | 20.2084 | 0.691921 | 0.345961 | − | 0.938249i | \(-0.387553\pi\) | ||||
0.345961 | + | 0.938249i | \(0.387553\pi\) | |||||||
\(854\) | − | 38.7546i | − | 1.32616i | ||||||
\(855\) | − | 0.0715838i | − | 0.00244811i | ||||||
\(856\) | 8.68398 | 0.296812 | ||||||||
\(857\) | −37.1260 | −1.26820 | −0.634100 | − | 0.773251i | \(-0.718629\pi\) | ||||
−0.634100 | + | 0.773251i | \(0.718629\pi\) | |||||||
\(858\) | − | 70.5109i | − | 2.40720i | ||||||
\(859\) | −42.1440 | −1.43794 | −0.718968 | − | 0.695043i | \(-0.755385\pi\) | ||||
−0.718968 | + | 0.695043i | \(0.755385\pi\) | |||||||
\(860\) | 59.2530 | 2.02051 | ||||||||
\(861\) | −2.38489 | + | 10.8056i | −0.0812768 | + | 0.368252i | ||||
\(862\) | 52.7679 | 1.79728 | ||||||||
\(863\) | −14.1793 | −0.482669 | −0.241334 | − | 0.970442i | \(-0.577585\pi\) | ||||
−0.241334 | + | 0.970442i | \(0.577585\pi\) | |||||||
\(864\) | − | 111.575i | − | 3.79585i | ||||||
\(865\) | 7.13575 | 0.242623 | ||||||||
\(866\) | −72.0034 | −2.44678 | ||||||||
\(867\) | 10.5827i | 0.359408i | ||||||||
\(868\) | − | 38.3421i | − | 1.30141i | ||||||
\(869\) | −38.9631 | −1.32173 | ||||||||
\(870\) | −14.8153 | −0.502286 | ||||||||
\(871\) | 33.1115 | 1.12194 | ||||||||
\(872\) | 49.8159i | 1.68698i | ||||||||
\(873\) | 0.125911i | 0.00426146i | ||||||||
\(874\) | 19.8230i | 0.670524i | ||||||||
\(875\) | 11.8759i | 0.401478i | ||||||||
\(876\) | 61.3484i | 2.07277i | ||||||||
\(877\) | 35.0845 | 1.18472 | 0.592360 | − | 0.805674i | \(-0.298196\pi\) | ||||
0.592360 | + | 0.805674i | \(0.298196\pi\) | |||||||
\(878\) | 70.4377i | 2.37716i | ||||||||
\(879\) | −44.5411 | −1.50233 | ||||||||
\(880\) | − | 148.237i | − | 4.99707i | ||||||
\(881\) | 45.4290 | 1.53054 | 0.765271 | − | 0.643708i | \(-0.222605\pi\) | ||||
0.765271 | + | 0.643708i | \(0.222605\pi\) | |||||||
\(882\) | 0.0367475 | 0.00123735 | ||||||||
\(883\) | 41.0997i | 1.38311i | 0.722322 | + | 0.691557i | \(0.243075\pi\) | ||||
−0.722322 | + | 0.691557i | \(0.756925\pi\) | |||||||
\(884\) | −42.3911 | −1.42577 | ||||||||
\(885\) | 20.8266i | 0.700078i | ||||||||
\(886\) | −46.0902 | −1.54843 | ||||||||
\(887\) | − | 11.4933i | − | 0.385908i | −0.981208 | − | 0.192954i | \(-0.938193\pi\) | ||
0.981208 | − | 0.192954i | \(-0.0618069\pi\) | |||||||
\(888\) | 108.663i | 3.64649i | ||||||||
\(889\) | 5.13749i | 0.172306i | ||||||||
\(890\) | 44.4096i | 1.48861i | ||||||||
\(891\) | − | 56.7380i | − | 1.90080i | ||||||
\(892\) | −59.2573 | −1.98408 | ||||||||
\(893\) | 14.0251 | 0.469334 | ||||||||
\(894\) | −18.5766 | −0.621294 | ||||||||
\(895\) | − | 9.47042i | − | 0.316561i | ||||||
\(896\) | − | 36.1916i | − | 1.20908i | ||||||
\(897\) | −8.86203 | −0.295894 | ||||||||
\(898\) | 2.25376 | 0.0752091 | ||||||||
\(899\) | − | 13.9383i | − | 0.464868i | ||||||
\(900\) | −0.181650 | −0.00605498 | ||||||||
\(901\) | 10.3717 | 0.345532 | ||||||||
\(902\) | −108.026 | − | 23.8423i | −3.59687 | − | 0.793863i | ||||
\(903\) | 11.8460 | 0.394209 | ||||||||
\(904\) | −42.2641 | −1.40568 | ||||||||
\(905\) | 33.8941i | 1.12668i | ||||||||
\(906\) | 43.2163 | 1.43577 | ||||||||
\(907\) | 2.28582 | 0.0758995 | 0.0379497 | − | 0.999280i | \(-0.487917\pi\) | ||||
0.0379497 | + | 0.999280i | \(0.487917\pi\) | |||||||
\(908\) | − | 50.0281i | − | 1.66024i | ||||||
\(909\) | − | 0.0860173i | − | 0.00285301i | ||||||
\(910\) | 10.2324 | 0.339199 | ||||||||
\(911\) | −13.0710 | −0.433063 | −0.216532 | − | 0.976276i | \(-0.569474\pi\) | ||||
−0.216532 | + | 0.976276i | \(0.569474\pi\) | |||||||
\(912\) | −85.2329 | −2.82234 | ||||||||
\(913\) | 68.2423i | 2.25849i | ||||||||
\(914\) | 89.7195i | 2.96766i | ||||||||
\(915\) | − | 38.9884i | − | 1.28892i | ||||||
\(916\) | 88.1639i | 2.91302i | ||||||||
\(917\) | 10.2845i | 0.339623i | ||||||||
\(918\) | −46.8555 | −1.54646 | ||||||||
\(919\) | 10.5657i | 0.348530i | 0.984699 | + | 0.174265i | \(0.0557549\pi\) | ||||
−0.984699 | + | 0.174265i | \(0.944245\pi\) | |||||||
\(920\) | −32.3911 | −1.06790 | ||||||||
\(921\) | − | 52.9115i | − | 1.74349i | ||||||
\(922\) | 10.0758 | 0.331827 | ||||||||
\(923\) | −4.36131 | −0.143554 | ||||||||
\(924\) | − | 59.5668i | − | 1.95960i | ||||||
\(925\) | 16.5868 | 0.545369 | ||||||||
\(926\) | 70.7913i | 2.32634i | ||||||||
\(927\) | 0.139016 | 0.00456587 | ||||||||
\(928\) | − | 42.3912i | − | 1.39156i | ||||||
\(929\) | − | 14.8268i | − | 0.486452i | −0.969970 | − | 0.243226i | \(-0.921794\pi\) | ||
0.969970 | − | 0.243226i | \(-0.0782056\pi\) | |||||||
\(930\) | − | 52.7473i | − | 1.72965i | ||||||
\(931\) | − | 3.34626i | − | 0.109669i | ||||||
\(932\) | 112.489i | 3.68471i | ||||||||
\(933\) | −27.8434 | −0.911552 | ||||||||
\(934\) | 32.5848 | 1.06621 | ||||||||
\(935\) | −33.1690 | −1.08474 | ||||||||
\(936\) | 0.298781i | 0.00976597i | ||||||||
\(937\) | 21.1237i | 0.690081i | 0.938588 | + | 0.345041i | \(0.112135\pi\) | ||||
−0.938588 | + | 0.345041i | \(0.887865\pi\) | |||||||
\(938\) | 38.2508 | 1.24893 | ||||||||
\(939\) | 7.32306 | 0.238979 | ||||||||
\(940\) | 36.2303i | 1.18170i | ||||||||
\(941\) | −25.2099 | −0.821820 | −0.410910 | − | 0.911676i | \(-0.634789\pi\) | ||||
−0.410910 | + | 0.911676i | \(0.634789\pi\) | |||||||
\(942\) | 103.312 | 3.36610 | ||||||||
\(943\) | −2.99658 | + | 13.5770i | −0.0975821 | + | 0.442129i | ||||
\(944\) | −111.841 | −3.64012 | ||||||||
\(945\) | 8.27081 | 0.269049 | ||||||||
\(946\) | 118.427i | 3.85040i | ||||||||
\(947\) | −16.8971 | −0.549083 | −0.274542 | − | 0.961575i | \(-0.588526\pi\) | ||||
−0.274542 | + | 0.961575i | \(0.588526\pi\) | |||||||
\(948\) | −57.8719 | −1.87959 | ||||||||
\(949\) | − | 15.4029i | − | 0.499999i | ||||||
\(950\) | 22.6193i | 0.733866i | ||||||||
\(951\) | 12.7863 | 0.414625 | ||||||||
\(952\) | −30.9762 | −1.00394 | ||||||||
\(953\) | 37.4437 | 1.21292 | 0.606460 | − | 0.795114i | \(-0.292589\pi\) | ||||
0.606460 | + | 0.795114i | \(0.292589\pi\) | |||||||
\(954\) | − | 0.115568i | − | 0.00374165i | ||||||
\(955\) | − | 1.66595i | − | 0.0539088i | ||||||
\(956\) | 53.7935i | 1.73981i | ||||||||
\(957\) | − | 21.6540i | − | 0.699974i | ||||||
\(958\) | 26.3245i | 0.850505i | ||||||||
\(959\) | −20.4701 | −0.661014 | ||||||||
\(960\) | − | 79.5178i | − | 2.56643i | ||||||
\(961\) | 18.6248 | 0.600801 | ||||||||
\(962\) | − | 43.1310i | − | 1.39060i | ||||||
\(963\) | −0.0124535 | −0.000401307 | ||||||||
\(964\) | −36.9311 | −1.18947 | ||||||||
\(965\) | 16.9499i | 0.545637i | ||||||||
\(966\) | −10.2375 | −0.329386 | ||||||||
\(967\) | 25.2099i | 0.810695i | 0.914163 | + | 0.405347i | \(0.132849\pi\) | ||||
−0.914163 | + | 0.405347i | \(0.867151\pi\) | |||||||
\(968\) | 273.365 | 8.78627 | ||||||||
\(969\) | 19.0714i | 0.612662i | ||||||||
\(970\) | 40.5018i | 1.30043i | ||||||||
\(971\) | 46.8483i | 1.50343i | 0.659487 | + | 0.751716i | \(0.270774\pi\) | ||||
−0.659487 | + | 0.751716i | \(0.729226\pi\) | |||||||
\(972\) | 0.761891i | 0.0244377i | ||||||||
\(973\) | − | 11.9165i | − | 0.382025i | ||||||
\(974\) | −76.0854 | −2.43793 | ||||||||
\(975\) | −10.1121 | −0.323847 | ||||||||
\(976\) | 209.372 | 6.70183 | ||||||||
\(977\) | − | 17.0743i | − | 0.546256i | −0.961978 | − | 0.273128i | \(-0.911942\pi\) | ||
0.961978 | − | 0.273128i | \(-0.0880582\pi\) | |||||||
\(978\) | − | 73.9832i | − | 2.36572i | ||||||
\(979\) | −64.9089 | −2.07450 | ||||||||
\(980\) | 8.64418 | 0.276128 | ||||||||
\(981\) | − | 0.0714395i | − | 0.00228089i | ||||||
\(982\) | −61.3555 | −1.95793 | ||||||||
\(983\) | −11.6164 | −0.370507 | −0.185253 | − | 0.982691i | \(-0.559311\pi\) | ||||
−0.185253 | + | 0.982691i | \(0.559311\pi\) | |||||||
\(984\) | −101.493 | − | 22.4004i | −3.23547 | − | 0.714098i | ||||
\(985\) | 6.92934 | 0.220787 | ||||||||
\(986\) | −17.8020 | −0.566933 | ||||||||
\(987\) | 7.24322i | 0.230554i | ||||||||
\(988\) | 43.0124 | 1.36841 | ||||||||
\(989\) | 14.8843 | 0.473293 | ||||||||
\(990\) | 0.369590i | 0.0117463i | ||||||||
\(991\) | − | 15.3988i | − | 0.489160i | −0.969629 | − | 0.244580i | \(-0.921350\pi\) | ||
0.969629 | − | 0.244580i | \(-0.0786500\pi\) | |||||||
\(992\) | 150.926 | 4.79192 | ||||||||
\(993\) | 8.24159 | 0.261539 | ||||||||
\(994\) | −5.03823 | −0.159803 | ||||||||
\(995\) | 23.4796i | 0.744353i | ||||||||
\(996\) | 101.360i | 3.21173i | ||||||||
\(997\) | − | 2.32934i | − | 0.0737708i | −0.999320 | − | 0.0368854i | \(-0.988256\pi\) | ||
0.999320 | − | 0.0368854i | \(-0.0117437\pi\) | |||||||
\(998\) | − | 38.4229i | − | 1.21626i | ||||||
\(999\) | − | 34.8628i | − | 1.10301i |
(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 | 287.2.c.b.204.2 | yes | 12 | |
41.40 | even | 2 | inner | 287.2.c.b.204.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.c.b.204.1 | ✓ | 12 | 41.40 | even | 2 | inner | |
287.2.c.b.204.2 | yes | 12 | 1.1 | even | 1 | trivial |