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 | 204.1 | ||
Root | \(2.72816i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.204 |
Dual form | 287.2.c.b.204.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | \(-0.833746\pi\) | ||
0.866673 | − | 0.498876i | \(-0.166254\pi\) | |||||||
\(4\) | 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 | \(-0.596173\pi\) | ||
0.297559 | − | 0.954703i | \(-0.403827\pi\) | |||||||
\(12\) | − | 9.40610i | − | 2.71531i | ||||||
\(13\) | 2.36161i | 0.654993i | 0.944852 | + | 0.327496i | \(0.106205\pi\) | ||||
−0.944852 | + | 0.327496i | \(0.893795\pi\) | |||||||
\(14\) | 2.72816i | 0.729131i | ||||||||
\(15\) | 2.74461i | 0.708656i | ||||||||
\(16\) | 14.7389 | 3.68472 | ||||||||
\(17\) | 3.29792i | 0.799864i | 0.916545 | + | 0.399932i | \(0.130966\pi\) | ||||
−0.916545 | + | 0.399932i | \(0.869034\pi\) | |||||||
\(18\) | −0.0367475 | −0.00866146 | ||||||||
\(19\) | − | 3.34626i | − | 0.767684i | −0.923399 | − | 0.383842i | \(-0.874601\pi\) | ||
0.923399 | − | 0.383842i | \(-0.125399\pi\) | |||||||
\(20\) | −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 | \(-0.941190\pi\) | ||
0.982981 | − | 0.183709i | \(-0.0588104\pi\) | |||||||
\(30\) | − | 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 | \(0.0988844\pi\) | ||||
−0.952134 | + | 0.305682i | \(0.901116\pi\) | |||||||
\(48\) | − | 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 | \(-0.930701\pi\) | ||
0.976395 | − | 0.215994i | \(-0.0692992\pi\) | |||||||
\(54\) | 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 | \(-0.672663\pi\) | ||
0.516225 | − | 0.856453i | \(-0.327337\pi\) | |||||||
\(68\) | 17.9501i | 2.17677i | ||||||||
\(69\) | 3.75254i | 0.451752i | ||||||||
\(70\) | − | 4.33279i | − | 0.517867i | ||||||
\(71\) | 1.84675i | 0.219169i | 0.993977 | + | 0.109585i | \(0.0349520\pi\) | ||||
−0.993977 | + | 0.109585i | \(0.965048\pi\) | |||||||
\(72\) | −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 | \(-0.887502\pi\) | ||
0.938194 | − | 0.346111i | \(-0.112498\pi\) | |||||||
\(80\) | −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 | \(-0.817201\pi\) | ||
0.839583 | − | 0.543231i | \(-0.182799\pi\) | |||||||
\(90\) | 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 | \(-0.842607\pi\) | ||
0.880223 | − | 0.474560i | \(-0.157393\pi\) | |||||||
\(98\) | 2.72816 | 0.275586 | ||||||||
\(99\) | − | 0.0853007i | − | 0.00857305i | ||||||
\(100\) | −13.4858 | −1.34858 | ||||||||
\(101\) | 6.38598i | 0.635429i | 0.948186 | + | 0.317714i | \(0.102915\pi\) | ||||
−0.948186 | + | 0.317714i | \(0.897085\pi\) | |||||||
\(102\) | −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 | \(0.0817470\pi\) | ||||
−0.967204 | + | 0.254002i | \(0.918253\pi\) | |||||||
\(110\) | − | 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 | \(-0.661230\pi\) | ||
0.485135 | − | 0.874439i | \(-0.338770\pi\) | |||||||
\(138\) | − | 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 | \(0.0515993\pi\) | ||||
−0.986890 | + | 0.161395i | \(0.948401\pi\) | |||||||
\(150\) | − | 11.6816i | − | 0.953800i | ||||||
\(151\) | − | 9.16632i | − | 0.745944i | −0.927843 | − | 0.372972i | \(-0.878339\pi\) | ||
0.927843 | − | 0.372972i | \(-0.121661\pi\) | |||||||
\(152\) | 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 | \(-0.661243\pi\) | ||
0.485172 | − | 0.874419i | \(-0.338757\pi\) | |||||||
\(158\) | 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 | \(0.110915\pi\) | ||||
−0.939903 | + | 0.341441i | \(0.889085\pi\) | |||||||
\(168\) | 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 | \(-0.928464\pi\) | ||
0.974852 | − | 0.222851i | \(-0.0715364\pi\) | |||||||
\(180\) | −0.116435 | −0.00867852 | ||||||||
\(181\) | 21.3416i | 1.58631i | 0.609023 | + | 0.793153i | \(0.291562\pi\) | ||||
−0.609023 | + | 0.793153i | \(0.708438\pi\) | |||||||
\(182\) | −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 | \(-0.987917\pi\) | ||
0.999280 | − | 0.0379504i | \(-0.0120829\pi\) | |||||||
\(192\) | − | 50.0688i | − | 3.61340i | ||||||
\(193\) | 10.6726i | 0.768230i | 0.923285 | + | 0.384115i | \(0.125493\pi\) | ||||
−0.923285 | + | 0.384115i | \(0.874507\pi\) | |||||||
\(194\) | 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 | \(0.175563\pi\) | ||||
−0.851715 | + | 0.524006i | \(0.824437\pi\) | |||||||
\(200\) | 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 | \(0.198807\pi\) | ||||
−0.811215 | + | 0.584748i | \(0.801193\pi\) | |||||||
\(212\) | − | 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 | \(0.0986671\pi\) | ||||
−0.952342 | + | 0.305032i | \(0.901333\pi\) | |||||||
\(228\) | −31.4752 | −2.08450 | ||||||||
\(229\) | − | 16.1981i | − | 1.07040i | −0.844725 | − | 0.535201i | \(-0.820236\pi\) | ||
0.844725 | − | 0.535201i | \(-0.179764\pi\) | |||||||
\(230\) | −9.40824 | −0.620361 | ||||||||
\(231\) | 10.9441i | 0.720066i | ||||||||
\(232\) | 18.5843i | 1.22012i | ||||||||
\(233\) | − | 20.6673i | − | 1.35396i | −0.736000 | − | 0.676981i | \(-0.763288\pi\) | ||
0.736000 | − | 0.676981i | \(-0.236712\pi\) | |||||||
\(234\) | − | 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 | \(-0.896435\pi\) | ||
0.947536 | − | 0.319650i | \(-0.103565\pi\) | |||||||
\(240\) | 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 | \(-0.964911\pi\) | ||
0.993930 | − | 0.110011i | \(-0.0350887\pi\) | |||||||
\(258\) | − | 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 | \(-0.851681\pi\) | ||
0.893392 | − | 0.449279i | \(-0.148319\pi\) | |||||||
\(264\) | 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 | \(-0.936773\pi\) | ||
0.980337 | − | 0.197331i | \(-0.0632275\pi\) | |||||||
\(282\) | −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 | \(-0.728674\pi\) | ||
0.658182 | − | 0.752859i | \(-0.271326\pi\) | |||||||
\(294\) | − | 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 | \(-0.848995\pi\) | ||
0.889568 | − | 0.456802i | \(-0.151005\pi\) | |||||||
\(312\) | −38.3335 | −2.17021 | ||||||||
\(313\) | 4.23750i | 0.239517i | 0.992803 | + | 0.119759i | \(0.0382121\pi\) | ||||
−0.992803 | + | 0.119759i | \(0.961788\pi\) | |||||||
\(314\) | 59.7818i | 3.37368i | ||||||||
\(315\) | 0.0213922i | 0.00120531i | ||||||||
\(316\) | − | 33.4876i | − | 1.88383i | ||||||
\(317\) | 7.39882i | 0.415559i | 0.978176 | + | 0.207780i | \(0.0666237\pi\) | ||||
−0.978176 | + | 0.207780i | \(0.933376\pi\) | |||||||
\(318\) | 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 | \(0.0418393\pi\) | ||||
−0.991374 | + | 0.131064i | \(0.958161\pi\) | |||||||
\(332\) | 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 | \(0.0244301\pi\) | ||||
−0.997056 | + | 0.0766742i | \(0.975570\pi\) | |||||||
\(348\) | −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 | \(0.216315\pi\) | ||||
−0.777841 | + | 0.628461i | \(0.783685\pi\) | |||||||
\(384\) | 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 | \(-0.975853\pi\) | ||
0.997124 | − | 0.0757865i | \(-0.0241467\pi\) | |||||||
\(398\) | − | 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 | \(-0.677494\pi\) | ||
0.529163 | − | 0.848520i | \(-0.322506\pi\) | |||||||
\(422\) | − | 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 | \(0.211301\pi\) | ||||
−0.787643 | + | 0.616132i | \(0.788699\pi\) | |||||||
\(440\) | − | 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 | \(0.279336\pi\) | ||||
−0.639030 | + | 0.769182i | \(0.720664\pi\) | |||||||
\(458\) | 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 | \(0.206013\pi\) | ||||
−0.797770 | + | 0.602962i | \(0.793987\pi\) | |||||||
\(464\) | − | 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 | \(0.0707497\pi\) | ||||
−0.975400 | + | 0.220441i | \(0.929250\pi\) | |||||||
\(480\) | − | 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 | \(-0.897915\pi\) | ||
0.949012 | − | 0.315239i | \(-0.102085\pi\) | |||||||
\(500\) | 64.6386 | 2.89073 | ||||||||
\(501\) | 15.2506 | 0.681346 | ||||||||
\(502\) | −65.7703 | −2.93547 | ||||||||
\(503\) | − | 35.4759i | − | 1.58179i | −0.611951 | − | 0.790896i | \(-0.709615\pi\) | ||
0.611951 | − | 0.790896i | \(-0.290385\pi\) | |||||||
\(504\) | 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 | \(-0.872498\pi\) | ||
0.920843 | − | 0.389933i | \(-0.127502\pi\) | |||||||
\(510\) | 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 | \(0.00811088\pi\) | ||||
−0.999675 | + | 0.0254783i | \(0.991889\pi\) | |||||||
\(522\) | 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 | \(-0.664233\pi\) | ||
0.493365 | − | 0.869822i | \(-0.335767\pi\) | |||||||
\(548\) | − | 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 | \(0.201704\pi\) | ||||
−0.805858 | + | 0.592108i | \(0.798296\pi\) | |||||||
\(558\) | 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 | \(0.00611906\pi\) | ||||
−0.999815 | + | 0.0192224i | \(0.993881\pi\) | |||||||
\(564\) | 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 | \(-0.668241\pi\) | ||
0.504277 | − | 0.863542i | \(-0.331759\pi\) | |||||||
\(572\) | 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 | \(-0.843877\pi\) | ||
0.882109 | − | 0.471045i | \(-0.156123\pi\) | |||||||
\(578\) | −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 | \(0.00365678\pi\) | ||||
−0.999934 | + | 0.0114879i | \(0.996343\pi\) | |||||||
\(588\) | 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 | \(0.0304480\pi\) | ||||
−0.995429 | + | 0.0955094i | \(0.969552\pi\) | |||||||
\(594\) | 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 | \(0.228114\pi\) | ||||
−0.754016 | + | 0.656857i | \(0.771886\pi\) | |||||||
\(602\) | − | 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 | \(0.142492\pi\) | ||||
−0.901466 | + | 0.432849i | \(0.857508\pi\) | |||||||
\(642\) | − | 4.35898i | − | 0.172035i | ||||||
\(643\) | 23.0816i | 0.910251i | 0.890427 | + | 0.455125i | \(0.150406\pi\) | ||||
−0.890427 | + | 0.455125i | \(0.849594\pi\) | |||||||
\(644\) | 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 | \(-0.962766\pi\) | ||
0.993166 | − | 0.116708i | \(-0.0372343\pi\) | |||||||
\(654\) | −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 | \(-0.798631\pi\) | ||
0.806482 | − | 0.591259i | \(-0.201369\pi\) | |||||||
\(660\) | 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 | \(-0.983252\pi\) | ||
0.998616 | − | 0.0525913i | \(-0.0167481\pi\) | |||||||
\(674\) | 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 | \(0.0655802\pi\) | ||||
−0.978852 | + | 0.204572i | \(0.934420\pi\) | |||||||
\(684\) | − | 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 | \(-0.806323\pi\) | ||
0.820533 | − | 0.571599i | \(-0.193677\pi\) | |||||||
\(692\) | −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 | \(0.333243\pi\) | ||||
−0.500247 | + | 0.865883i | \(0.666757\pi\) | |||||||
\(710\) | 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 | \(-0.928419\pi\) | ||
0.974821 | − | 0.222988i | \(-0.0715811\pi\) | |||||||
\(720\) | −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 | \(0.131294\pi\) | ||||
−0.916132 | + | 0.400877i | \(0.868706\pi\) | |||||||
\(728\) | −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 | \(0.221591\pi\) | ||||
−0.767318 | + | 0.641267i | \(0.778409\pi\) | |||||||
\(752\) | 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 | \(-0.767461\pi\) | ||
0.744813 | − | 0.667273i | \(-0.232539\pi\) | |||||||
\(758\) | 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 | \(0.214317\pi\) | ||||
−0.781771 | + | 0.623566i | \(0.785683\pi\) | |||||||
\(774\) | 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 | \(-0.905474\pi\) | ||
0.956230 | − | 0.292616i | \(-0.0945259\pi\) | |||||||
\(810\) | −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 | \(0.0788998\pi\) | ||||
−0.969437 | + | 0.245341i | \(0.921100\pi\) | |||||||
\(824\) | −96.9377 | −3.37699 | ||||||||
\(825\) | 27.1162 | 0.944064 | ||||||||
\(826\) | − | 20.7017i | − | 0.720305i | ||||||
\(827\) | 6.68674i | 0.232521i | 0.993219 | + | 0.116260i | \(0.0370907\pi\) | ||||
−0.993219 | + | 0.116260i | \(0.962909\pi\) | |||||||
\(828\) | −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 | \(0.0788510\pi\) | ||||
−0.969475 | + | 0.245192i | \(0.921149\pi\) | |||||||
\(840\) | −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 | \(-0.756925\pi\) | ||
0.722322 | − | 0.691557i | \(-0.243075\pi\) | |||||||
\(884\) | −42.3911 | −1.42577 | ||||||||
\(885\) | − | 20.8266i | − | 0.700078i | ||||||
\(886\) | −46.0902 | −1.54843 | ||||||||
\(887\) | 11.4933i | 0.385908i | 0.981208 | + | 0.192954i | \(0.0618069\pi\) | ||||
−0.981208 | + | 0.192954i | \(0.938193\pi\) | |||||||
\(888\) | − | 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 | \(-0.944245\pi\) | ||
0.984699 | − | 0.174265i | \(-0.0557549\pi\) | |||||||
\(920\) | −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 | \(0.0782056\pi\) | ||||
−0.969970 | + | 0.243226i | \(0.921794\pi\) | |||||||
\(930\) | 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 | \(-0.887865\pi\) | ||
0.938588 | − | 0.345041i | \(-0.112135\pi\) | |||||||
\(938\) | 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 | \(-0.867151\pi\) | ||
0.914163 | − | 0.405347i | \(-0.132849\pi\) | |||||||
\(968\) | 273.365 | 8.78627 | ||||||||
\(969\) | − | 19.0714i | − | 0.612662i | ||||||
\(970\) | − | 40.5018i | − | 1.30043i | ||||||
\(971\) | − | 46.8483i | − | 1.50343i | −0.659487 | − | 0.751716i | \(-0.729226\pi\) | ||
0.659487 | − | 0.751716i | \(-0.270774\pi\) | |||||||
\(972\) | − | 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 | \(0.0880582\pi\) | ||||
−0.961978 | + | 0.273128i | \(0.911942\pi\) | |||||||
\(978\) | 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 | \(0.0786500\pi\) | ||||
−0.969629 | + | 0.244580i | \(0.921350\pi\) | |||||||
\(992\) | 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 | \(0.0117437\pi\) | ||||
−0.999320 | + | 0.0368854i | \(0.988256\pi\) | |||||||
\(998\) | 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.204.1 | ✓ | 12 | |
41.40 | even | 2 | inner | 287.2.c.b.204.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.c.b.204.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
287.2.c.b.204.2 | yes | 12 | 41.40 | even | 2 | inner |