Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(274,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.274");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.274 |
Dual form | 975.2.c.h.274.1 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421i | 1.70711i | 0.521005 | + | 0.853553i | \(0.325557\pi\) | ||||
−0.521005 | + | 0.853553i | \(0.674443\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.41421 | −0.985599 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | − 4.41421i | − 1.56066i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | − 3.82843i | − 1.10517i | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | −6.82843 | −1.82497 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 3.65685i | 0.886917i | 0.896295 | + | 0.443459i | \(0.146249\pi\) | ||||
−0.896295 | + | 0.443459i | \(0.853751\pi\) | |||||||
\(18\) | − 2.41421i | − 0.569036i | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | − 4.82843i | − 1.02942i | ||||||||
\(23\) | − 4.00000i | − 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 4.41421 | 0.901048 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.41421 | 0.473466 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 10.8284i | − 2.04638i | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.82843 | −1.22642 | −0.613211 | − | 0.789919i | \(-0.710122\pi\) | ||||
−0.613211 | + | 0.789919i | \(0.710122\pi\) | |||||||
\(32\) | − 1.58579i | − 0.280330i | ||||||||
\(33\) | − 2.00000i | − 0.348155i | ||||||||
\(34\) | −8.82843 | −1.51406 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | − 3.65685i | − 0.601183i | −0.953753 | − | 0.300592i | \(-0.902816\pi\) | ||||
0.953753 | − | 0.300592i | \(-0.0971841\pi\) | |||||||
\(38\) | − 6.82843i | − 1.10772i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8284 | 1.69112 | 0.845558 | − | 0.533883i | \(-0.179268\pi\) | ||||
0.845558 | + | 0.533883i | \(0.179268\pi\) | |||||||
\(42\) | − 6.82843i | − 1.05365i | ||||||||
\(43\) | 9.65685i | 1.47266i | 0.676625 | + | 0.736328i | \(0.263442\pi\) | ||||
−0.676625 | + | 0.736328i | \(0.736558\pi\) | |||||||
\(44\) | 7.65685 | 1.15431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.65685 | 1.42383 | ||||||||
\(47\) | 0.343146i | 0.0500530i | 0.999687 | + | 0.0250265i | \(0.00796701\pi\) | ||||
−0.999687 | + | 0.0250265i | \(0.992033\pi\) | |||||||
\(48\) | 3.00000i | 0.433013i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.65685 | −0.512062 | ||||||||
\(52\) | 3.82843i | 0.530907i | ||||||||
\(53\) | − 2.00000i | − 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 2.41421 | 0.328533 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.4853 | 1.66842 | ||||||||
\(57\) | − 2.82843i | − 0.374634i | ||||||||
\(58\) | − 4.82843i | − 0.634004i | ||||||||
\(59\) | 3.65685 | 0.476082 | 0.238041 | − | 0.971255i | \(-0.423495\pi\) | ||||
0.238041 | + | 0.971255i | \(0.423495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.31371 | −1.19250 | −0.596249 | − | 0.802799i | \(-0.703343\pi\) | ||||
−0.596249 | + | 0.802799i | \(0.703343\pi\) | |||||||
\(62\) | − 16.4853i | − 2.09363i | ||||||||
\(63\) | − 2.82843i | − 0.356348i | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.82843 | 0.594338 | ||||||||
\(67\) | − 1.17157i | − 0.143130i | −0.997436 | − | 0.0715652i | \(-0.977201\pi\) | ||||
0.997436 | − | 0.0715652i | \(-0.0227994\pi\) | |||||||
\(68\) | − 14.0000i | − 1.69775i | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 4.41421i | 0.520220i | ||||||||
\(73\) | 11.6569i | 1.36433i | 0.731198 | + | 0.682166i | \(0.238962\pi\) | ||||
−0.731198 | + | 0.682166i | \(0.761038\pi\) | |||||||
\(74\) | 8.82843 | 1.02628 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.8284 | 1.24211 | ||||||||
\(77\) | − 5.65685i | − 0.644658i | ||||||||
\(78\) | 2.41421i | 0.273356i | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 26.1421i | 2.88692i | ||||||||
\(83\) | − 7.65685i | − 0.840449i | −0.907420 | − | 0.420224i | \(-0.861951\pi\) | ||||
0.907420 | − | 0.420224i | \(-0.138049\pi\) | |||||||
\(84\) | 10.8284 | 1.18148 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −23.3137 | −2.51398 | ||||||||
\(87\) | − 2.00000i | − 0.214423i | ||||||||
\(88\) | 8.82843i | 0.941113i | ||||||||
\(89\) | −9.17157 | −0.972185 | −0.486092 | − | 0.873907i | \(-0.661578\pi\) | ||||
−0.486092 | + | 0.873907i | \(0.661578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82843 | 0.296500 | ||||||||
\(92\) | 15.3137i | 1.59656i | ||||||||
\(93\) | − 6.82843i | − 0.708075i | ||||||||
\(94\) | −0.828427 | −0.0854457 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.58579 | 0.161849 | ||||||||
\(97\) | 7.65685i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(98\) | − 2.41421i | − 0.243872i | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.65685 | −0.363871 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(102\) | − 8.82843i | − 0.874145i | ||||||||
\(103\) | 13.6569i | 1.34565i | 0.739802 | + | 0.672825i | \(0.234919\pi\) | ||||
−0.739802 | + | 0.672825i | \(0.765081\pi\) | |||||||
\(104\) | −4.41421 | −0.432849 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.82843 | 0.468978 | ||||||||
\(107\) | − 11.3137i | − 1.09374i | −0.837218 | − | 0.546869i | \(-0.815820\pi\) | ||||
0.837218 | − | 0.546869i | \(-0.184180\pi\) | |||||||
\(108\) | 3.82843i | 0.368391i | ||||||||
\(109\) | 17.3137 | 1.65835 | 0.829176 | − | 0.558987i | \(-0.188810\pi\) | ||||
0.829176 | + | 0.558987i | \(0.188810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.65685 | 0.347093 | ||||||||
\(112\) | 8.48528i | 0.801784i | ||||||||
\(113\) | 17.3137i | 1.62874i | 0.580348 | + | 0.814368i | \(0.302916\pi\) | ||||
−0.580348 | + | 0.814368i | \(0.697084\pi\) | |||||||
\(114\) | 6.82843 | 0.639541 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.65685 | 0.710921 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 8.82843i | 0.812723i | ||||||||
\(119\) | −10.3431 | −0.948155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − 22.4853i | − 2.03572i | ||||||||
\(123\) | 10.8284i | 0.976366i | ||||||||
\(124\) | 26.1421 | 2.34763 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.82843 | 0.608325 | ||||||||
\(127\) | 5.65685i | 0.501965i | 0.967992 | + | 0.250982i | \(0.0807536\pi\) | ||||
−0.967992 | + | 0.250982i | \(0.919246\pi\) | |||||||
\(128\) | 20.5563i | 1.81694i | ||||||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 7.65685i | 0.666444i | ||||||||
\(133\) | − 8.00000i | − 0.693688i | ||||||||
\(134\) | 2.82843 | 0.244339 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.1421 | 1.38418 | ||||||||
\(137\) | 5.17157i | 0.441837i | 0.975292 | + | 0.220919i | \(0.0709055\pi\) | ||||
−0.975292 | + | 0.220919i | \(0.929094\pi\) | |||||||
\(138\) | 9.65685i | 0.822046i | ||||||||
\(139\) | −15.3137 | −1.29889 | −0.649446 | − | 0.760408i | \(-0.724999\pi\) | ||||
−0.649446 | + | 0.760408i | \(0.724999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.343146 | −0.0288981 | ||||||||
\(142\) | 4.82843i | 0.405193i | ||||||||
\(143\) | 2.00000i | 0.167248i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −28.1421 | −2.32906 | ||||||||
\(147\) | − 1.00000i | − 0.0824786i | ||||||||
\(148\) | 14.0000i | 1.15079i | ||||||||
\(149\) | 14.8284 | 1.21479 | 0.607396 | − | 0.794399i | \(-0.292214\pi\) | ||||
0.607396 | + | 0.794399i | \(0.292214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.4853 | −1.66707 | −0.833534 | − | 0.552468i | \(-0.813686\pi\) | ||||
−0.833534 | + | 0.552468i | \(0.813686\pi\) | |||||||
\(152\) | 12.4853i | 1.01269i | ||||||||
\(153\) | − 3.65685i | − 0.295639i | ||||||||
\(154\) | 13.6569 | 1.10050 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.82843 | −0.306519 | ||||||||
\(157\) | 10.0000i | 0.798087i | 0.916932 | + | 0.399043i | \(0.130658\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(158\) | − 27.3137i | − 2.17296i | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137 | 0.891645 | ||||||||
\(162\) | 2.41421i | 0.189679i | ||||||||
\(163\) | 13.1716i | 1.03168i | 0.856686 | + | 0.515839i | \(0.172520\pi\) | ||||
−0.856686 | + | 0.515839i | \(0.827480\pi\) | |||||||
\(164\) | −41.4558 | −3.23716 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.4853 | 1.43474 | ||||||||
\(167\) | − 7.65685i | − 0.592505i | −0.955110 | − | 0.296253i | \(-0.904263\pi\) | ||||
0.955110 | − | 0.296253i | \(-0.0957370\pi\) | |||||||
\(168\) | 12.4853i | 0.963260i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | − 36.9706i | − 2.81898i | ||||||||
\(173\) | − 0.343146i | − 0.0260889i | −0.999915 | − | 0.0130444i | \(-0.995848\pi\) | ||||
0.999915 | − | 0.0130444i | \(-0.00415229\pi\) | |||||||
\(174\) | 4.82843 | 0.366042 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 3.65685i | 0.274866i | ||||||||
\(178\) | − 22.1421i | − 1.65962i | ||||||||
\(179\) | 0.686292 | 0.0512958 | 0.0256479 | − | 0.999671i | \(-0.491835\pi\) | ||||
0.0256479 | + | 0.999671i | \(0.491835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 6.82843i | 0.506157i | ||||||||
\(183\) | − 9.31371i | − 0.688489i | ||||||||
\(184\) | −17.6569 | −1.30168 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.4853 | 1.20876 | ||||||||
\(187\) | − 7.31371i | − 0.534831i | ||||||||
\(188\) | − 1.31371i | − 0.0958120i | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.3137 | −1.39749 | −0.698745 | − | 0.715370i | \(-0.746258\pi\) | ||||
−0.698745 | + | 0.715370i | \(0.746258\pi\) | |||||||
\(192\) | 9.82843i | 0.709306i | ||||||||
\(193\) | − 17.3137i | − 1.24627i | −0.782115 | − | 0.623134i | \(-0.785859\pi\) | ||||
0.782115 | − | 0.623134i | \(-0.214141\pi\) | |||||||
\(194\) | −18.4853 | −1.32717 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 16.4853i | 1.17453i | 0.809396 | + | 0.587264i | \(0.199795\pi\) | ||||
−0.809396 | + | 0.587264i | \(0.800205\pi\) | |||||||
\(198\) | 4.82843i | 0.343141i | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.17157 | 0.0826364 | ||||||||
\(202\) | − 8.82843i | − 0.621166i | ||||||||
\(203\) | − 5.65685i | − 0.397033i | ||||||||
\(204\) | 14.0000 | 0.980196 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −32.9706 | −2.29717 | ||||||||
\(207\) | 4.00000i | 0.278019i | ||||||||
\(208\) | − 3.00000i | − 0.208013i | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 7.65685i | 0.525875i | ||||||||
\(213\) | 2.00000i | 0.137038i | ||||||||
\(214\) | 27.3137 | 1.86713 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.41421 | −0.300349 | ||||||||
\(217\) | − 19.3137i | − 1.31110i | ||||||||
\(218\) | 41.7990i | 2.83098i | ||||||||
\(219\) | −11.6569 | −0.787697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.65685 | 0.245987 | ||||||||
\(222\) | 8.82843i | 0.592525i | ||||||||
\(223\) | 4.48528i | 0.300357i | 0.988659 | + | 0.150178i | \(0.0479848\pi\) | ||||
−0.988659 | + | 0.150178i | \(0.952015\pi\) | |||||||
\(224\) | 4.48528 | 0.299685 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −41.7990 | −2.78043 | ||||||||
\(227\) | − 5.31371i | − 0.352683i | −0.984329 | − | 0.176342i | \(-0.943574\pi\) | ||||
0.984329 | − | 0.176342i | \(-0.0564263\pi\) | |||||||
\(228\) | 10.8284i | 0.717130i | ||||||||
\(229\) | −21.3137 | −1.40845 | −0.704225 | − | 0.709977i | \(-0.748705\pi\) | ||||
−0.704225 | + | 0.709977i | \(0.748705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.65685 | 0.372194 | ||||||||
\(232\) | 8.82843i | 0.579615i | ||||||||
\(233\) | − 26.9706i | − 1.76690i | −0.468525 | − | 0.883450i | \(-0.655214\pi\) | ||||
0.468525 | − | 0.883450i | \(-0.344786\pi\) | |||||||
\(234\) | −2.41421 | −0.157822 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.0000 | −0.911322 | ||||||||
\(237\) | − 11.3137i | − 0.734904i | ||||||||
\(238\) | − 24.9706i | − 1.61860i | ||||||||
\(239\) | −2.00000 | −0.129369 | −0.0646846 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646846 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6569 | 0.750884 | 0.375442 | − | 0.926846i | \(-0.377491\pi\) | ||||
0.375442 | + | 0.926846i | \(0.377491\pi\) | |||||||
\(242\) | − 16.8995i | − 1.08634i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 35.6569 | 2.28270 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.1421 | −1.66676 | ||||||||
\(247\) | 2.82843i | 0.179969i | ||||||||
\(248\) | 30.1421i | 1.91403i | ||||||||
\(249\) | 7.65685 | 0.485233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 10.8284i | 0.682127i | ||||||||
\(253\) | 8.00000i | 0.502956i | ||||||||
\(254\) | −13.6569 | −0.856907 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 15.6569i | 0.976648i | 0.872662 | + | 0.488324i | \(0.162392\pi\) | ||||
−0.872662 | + | 0.488324i | \(0.837608\pi\) | |||||||
\(258\) | − 23.3137i | − 1.45145i | ||||||||
\(259\) | 10.3431 | 0.642692 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | − 19.3137i | − 1.19320i | ||||||||
\(263\) | 12.0000i | 0.739952i | 0.929041 | + | 0.369976i | \(0.120634\pi\) | ||||
−0.929041 | + | 0.369976i | \(0.879366\pi\) | |||||||
\(264\) | −8.82843 | −0.543352 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 19.3137 | 1.18420 | ||||||||
\(267\) | − 9.17157i | − 0.561291i | ||||||||
\(268\) | 4.48528i | 0.273982i | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.7990 | 0.716738 | 0.358369 | − | 0.933580i | \(-0.383333\pi\) | ||||
0.358369 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(272\) | 10.9706i | 0.665188i | ||||||||
\(273\) | 2.82843i | 0.171184i | ||||||||
\(274\) | −12.4853 | −0.754263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −15.3137 | −0.921777 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | − 36.9706i | − 2.21735i | ||||||||
\(279\) | 6.82843 | 0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8284 | 1.60045 | 0.800225 | − | 0.599700i | \(-0.204713\pi\) | ||||
0.800225 | + | 0.599700i | \(0.204713\pi\) | |||||||
\(282\) | − 0.828427i | − 0.0493321i | ||||||||
\(283\) | − 4.97056i | − 0.295469i | −0.989027 | − | 0.147735i | \(-0.952802\pi\) | ||||
0.989027 | − | 0.147735i | \(-0.0471982\pi\) | |||||||
\(284\) | −7.65685 | −0.454351 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.82843 | −0.285511 | ||||||||
\(287\) | 30.6274i | 1.80788i | ||||||||
\(288\) | 1.58579i | 0.0934434i | ||||||||
\(289\) | 3.62742 | 0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.65685 | −0.448853 | ||||||||
\(292\) | − 44.6274i | − 2.61162i | ||||||||
\(293\) | − 26.1421i | − 1.52724i | −0.645666 | − | 0.763620i | \(-0.723420\pi\) | ||||
0.645666 | − | 0.763620i | \(-0.276580\pi\) | |||||||
\(294\) | 2.41421 | 0.140800 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16.1421 | −0.938243 | ||||||||
\(297\) | 2.00000i | 0.116052i | ||||||||
\(298\) | 35.7990i | 2.07378i | ||||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.3137 | −1.57434 | ||||||||
\(302\) | − 49.4558i | − 2.84586i | ||||||||
\(303\) | − 3.65685i | − 0.210081i | ||||||||
\(304\) | −8.48528 | −0.486664 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.82843 | 0.504688 | ||||||||
\(307\) | 17.1716i | 0.980033i | 0.871713 | + | 0.490017i | \(0.163009\pi\) | ||||
−0.871713 | + | 0.490017i | \(0.836991\pi\) | |||||||
\(308\) | 21.6569i | 1.23401i | ||||||||
\(309\) | −13.6569 | −0.776911 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.6274 | 1.96354 | 0.981770 | − | 0.190071i | \(-0.0608718\pi\) | ||||
0.981770 | + | 0.190071i | \(0.0608718\pi\) | |||||||
\(312\) | − 4.41421i | − 0.249906i | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | −24.1421 | −1.36242 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 43.3137 | 2.43659 | ||||||||
\(317\) | 8.48528i | 0.476581i | 0.971194 | + | 0.238290i | \(0.0765870\pi\) | ||||
−0.971194 | + | 0.238290i | \(0.923413\pi\) | |||||||
\(318\) | 4.82843i | 0.270765i | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.3137 | 0.631470 | ||||||||
\(322\) | 27.3137i | 1.52213i | ||||||||
\(323\) | − 10.3431i | − 0.575508i | ||||||||
\(324\) | −3.82843 | −0.212690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −31.7990 | −1.76118 | ||||||||
\(327\) | 17.3137i | 0.957450i | ||||||||
\(328\) | − 47.7990i | − 2.63926i | ||||||||
\(329\) | −0.970563 | −0.0535089 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.14214 | −0.117742 | −0.0588712 | − | 0.998266i | \(-0.518750\pi\) | ||||
−0.0588712 | + | 0.998266i | \(0.518750\pi\) | |||||||
\(332\) | 29.3137i | 1.60880i | ||||||||
\(333\) | 3.65685i | 0.200394i | ||||||||
\(334\) | 18.4853 | 1.01147 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.48528 | −0.462910 | ||||||||
\(337\) | 13.3137i | 0.725244i | 0.931936 | + | 0.362622i | \(0.118118\pi\) | ||||
−0.931936 | + | 0.362622i | \(0.881882\pi\) | |||||||
\(338\) | − 2.41421i | − 0.131316i | ||||||||
\(339\) | −17.3137 | −0.940352 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.6569 | 0.739560 | ||||||||
\(342\) | 6.82843i | 0.369239i | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 42.6274 | 2.29832 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.828427 | 0.0445365 | ||||||||
\(347\) | 31.3137i | 1.68101i | 0.541805 | + | 0.840504i | \(0.317741\pi\) | ||||
−0.541805 | + | 0.840504i | \(0.682259\pi\) | |||||||
\(348\) | 7.65685i | 0.410450i | ||||||||
\(349\) | 7.65685 | 0.409862 | 0.204931 | − | 0.978776i | \(-0.434303\pi\) | ||||
0.204931 | + | 0.978776i | \(0.434303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.17157i | 0.169045i | ||||||||
\(353\) | 17.4558i | 0.929081i | 0.885552 | + | 0.464540i | \(0.153780\pi\) | ||||
−0.885552 | + | 0.464540i | \(0.846220\pi\) | |||||||
\(354\) | −8.82843 | −0.469226 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 35.1127 | 1.86097 | ||||||||
\(357\) | − 10.3431i | − 0.547417i | ||||||||
\(358\) | 1.65685i | 0.0875675i | ||||||||
\(359\) | −1.02944 | −0.0543316 | −0.0271658 | − | 0.999631i | \(-0.508648\pi\) | ||||
−0.0271658 | + | 0.999631i | \(0.508648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 33.7990i | 1.77644i | ||||||||
\(363\) | − 7.00000i | − 0.367405i | ||||||||
\(364\) | −10.8284 | −0.567564 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 22.4853 | 1.17532 | ||||||||
\(367\) | 24.0000i | 1.25279i | 0.779506 | + | 0.626395i | \(0.215470\pi\) | ||||
−0.779506 | + | 0.626395i | \(0.784530\pi\) | |||||||
\(368\) | − 12.0000i | − 0.625543i | ||||||||
\(369\) | −10.8284 | −0.563705 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.65685 | 0.293689 | ||||||||
\(372\) | 26.1421i | 1.35541i | ||||||||
\(373\) | 10.0000i | 0.517780i | 0.965907 | + | 0.258890i | \(0.0833568\pi\) | ||||
−0.965907 | + | 0.258890i | \(0.916643\pi\) | |||||||
\(374\) | 17.6569 | 0.913014 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.51472 | 0.0781156 | ||||||||
\(377\) | 2.00000i | 0.103005i | ||||||||
\(378\) | 6.82843i | 0.351216i | ||||||||
\(379\) | 16.4853 | 0.846792 | 0.423396 | − | 0.905945i | \(-0.360838\pi\) | ||||
0.423396 | + | 0.905945i | \(0.360838\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.65685 | −0.289809 | ||||||||
\(382\) | − 46.6274i | − 2.38567i | ||||||||
\(383\) | − 2.97056i | − 0.151789i | −0.997116 | − | 0.0758943i | \(-0.975819\pi\) | ||||
0.997116 | − | 0.0758943i | \(-0.0241812\pi\) | |||||||
\(384\) | −20.5563 | −1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.7990 | 2.12751 | ||||||||
\(387\) | − 9.65685i | − 0.490885i | ||||||||
\(388\) | − 29.3137i | − 1.48818i | ||||||||
\(389\) | −6.97056 | −0.353422 | −0.176711 | − | 0.984263i | \(-0.556546\pi\) | ||||
−0.176711 | + | 0.984263i | \(0.556546\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6274 | 0.739740 | ||||||||
\(392\) | 4.41421i | 0.222951i | ||||||||
\(393\) | − 8.00000i | − 0.403547i | ||||||||
\(394\) | −39.7990 | −2.00504 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.65685 | −0.384771 | ||||||||
\(397\) | 2.97056i | 0.149088i | 0.997218 | + | 0.0745441i | \(0.0237502\pi\) | ||||
−0.997218 | + | 0.0745441i | \(0.976250\pi\) | |||||||
\(398\) | − 24.9706i | − 1.25166i | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.14214 | −0.106973 | −0.0534866 | − | 0.998569i | \(-0.517033\pi\) | ||||
−0.0534866 | + | 0.998569i | \(0.517033\pi\) | |||||||
\(402\) | 2.82843i | 0.141069i | ||||||||
\(403\) | 6.82843i | 0.340148i | ||||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.6569 | 0.677778 | ||||||||
\(407\) | 7.31371i | 0.362527i | ||||||||
\(408\) | 16.1421i | 0.799155i | ||||||||
\(409\) | 1.02944 | 0.0509024 | 0.0254512 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254512 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.17157 | −0.255095 | ||||||||
\(412\) | − 52.2843i | − 2.57586i | ||||||||
\(413\) | 10.3431i | 0.508953i | ||||||||
\(414\) | −9.65685 | −0.474608 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.58579 | −0.0777496 | ||||||||
\(417\) | − 15.3137i | − 0.749916i | ||||||||
\(418\) | 13.6569i | 0.667979i | ||||||||
\(419\) | 30.6274 | 1.49625 | 0.748124 | − | 0.663559i | \(-0.230955\pi\) | ||||
0.748124 | + | 0.663559i | \(0.230955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6863 | 0.715766 | 0.357883 | − | 0.933766i | \(-0.383499\pi\) | ||||
0.357883 | + | 0.933766i | \(0.383499\pi\) | |||||||
\(422\) | − 28.9706i | − 1.41026i | ||||||||
\(423\) | − 0.343146i | − 0.0166843i | ||||||||
\(424\) | −8.82843 | −0.428746 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.82843 | −0.233938 | ||||||||
\(427\) | − 26.3431i | − 1.27483i | ||||||||
\(428\) | 43.3137i | 2.09365i | ||||||||
\(429\) | −2.00000 | −0.0965609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.6569 | 0.946837 | 0.473419 | − | 0.880838i | \(-0.343020\pi\) | ||||
0.473419 | + | 0.880838i | \(0.343020\pi\) | |||||||
\(432\) | − 3.00000i | − 0.144338i | ||||||||
\(433\) | 1.31371i | 0.0631328i | 0.999502 | + | 0.0315664i | \(0.0100496\pi\) | ||||
−0.999502 | + | 0.0315664i | \(0.989950\pi\) | |||||||
\(434\) | 46.6274 | 2.23819 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −66.2843 | −3.17444 | ||||||||
\(437\) | 11.3137i | 0.541208i | ||||||||
\(438\) | − 28.1421i | − 1.34468i | ||||||||
\(439\) | 16.9706 | 0.809961 | 0.404980 | − | 0.914325i | \(-0.367278\pi\) | ||||
0.404980 | + | 0.914325i | \(0.367278\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 8.82843i | 0.419925i | ||||||||
\(443\) | 41.9411i | 1.99268i | 0.0854611 | + | 0.996342i | \(0.472764\pi\) | ||||
−0.0854611 | + | 0.996342i | \(0.527236\pi\) | |||||||
\(444\) | −14.0000 | −0.664411 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.8284 | −0.512741 | ||||||||
\(447\) | 14.8284i | 0.701361i | ||||||||
\(448\) | 27.7990i | 1.31338i | ||||||||
\(449\) | −7.79899 | −0.368057 | −0.184029 | − | 0.982921i | \(-0.558914\pi\) | ||||
−0.184029 | + | 0.982921i | \(0.558914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.6569 | −1.01978 | ||||||||
\(452\) | − 66.2843i | − 3.11775i | ||||||||
\(453\) | − 20.4853i | − 0.962482i | ||||||||
\(454\) | 12.8284 | 0.602068 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4853 | −0.584677 | ||||||||
\(457\) | − 3.65685i | − 0.171060i | −0.996336 | − | 0.0855302i | \(-0.972742\pi\) | ||||
0.996336 | − | 0.0855302i | \(-0.0272584\pi\) | |||||||
\(458\) | − 51.4558i | − 2.40437i | ||||||||
\(459\) | 3.65685 | 0.170687 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8284 | 0.504330 | 0.252165 | − | 0.967684i | \(-0.418857\pi\) | ||||
0.252165 | + | 0.967684i | \(0.418857\pi\) | |||||||
\(462\) | 13.6569i | 0.635374i | ||||||||
\(463\) | − 7.51472i | − 0.349239i | −0.984636 | − | 0.174619i | \(-0.944131\pi\) | ||||
0.984636 | − | 0.174619i | \(-0.0558695\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 65.1127 | 3.01629 | ||||||||
\(467\) | 8.00000i | 0.370196i | 0.982720 | + | 0.185098i | \(0.0592602\pi\) | ||||
−0.982720 | + | 0.185098i | \(0.940740\pi\) | |||||||
\(468\) | − 3.82843i | − 0.176969i | ||||||||
\(469\) | 3.31371 | 0.153013 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | − 16.1421i | − 0.743002i | ||||||||
\(473\) | − 19.3137i | − 0.888045i | ||||||||
\(474\) | 27.3137 | 1.25456 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 39.5980 | 1.81497 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | − 4.82843i | − 0.220847i | ||||||||
\(479\) | −2.68629 | −0.122740 | −0.0613699 | − | 0.998115i | \(-0.519547\pi\) | ||||
−0.0613699 | + | 0.998115i | \(0.519547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.65685 | −0.166738 | ||||||||
\(482\) | 28.1421i | 1.28184i | ||||||||
\(483\) | 11.3137i | 0.514792i | ||||||||
\(484\) | 26.7990 | 1.21814 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.41421 | −0.109511 | ||||||||
\(487\) | − 31.7990i | − 1.44095i | −0.693481 | − | 0.720475i | \(-0.743924\pi\) | ||||
0.693481 | − | 0.720475i | \(-0.256076\pi\) | |||||||
\(488\) | 41.1127i | 1.86108i | ||||||||
\(489\) | −13.1716 | −0.595639 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6274 | −0.660126 | −0.330063 | − | 0.943959i | \(-0.607070\pi\) | ||||
−0.330063 | + | 0.943959i | \(0.607070\pi\) | |||||||
\(492\) | − 41.4558i | − 1.86897i | ||||||||
\(493\) | − 7.31371i | − 0.329393i | ||||||||
\(494\) | −6.82843 | −0.307225 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.4853 | −0.919816 | ||||||||
\(497\) | 5.65685i | 0.253745i | ||||||||
\(498\) | 18.4853i | 0.828345i | ||||||||
\(499\) | 2.14214 | 0.0958952 | 0.0479476 | − | 0.998850i | \(-0.484732\pi\) | ||||
0.0479476 | + | 0.998850i | \(0.484732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.65685 | 0.342083 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.3137i | 0.682805i | 0.939917 | + | 0.341402i | \(0.110902\pi\) | ||||
−0.939917 | + | 0.341402i | \(0.889098\pi\) | |||||||
\(504\) | −12.4853 | −0.556139 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.3137 | −0.858599 | ||||||||
\(507\) | − 1.00000i | − 0.0444116i | ||||||||
\(508\) | − 21.6569i | − 0.960868i | ||||||||
\(509\) | 27.7990 | 1.23217 | 0.616084 | − | 0.787680i | \(-0.288718\pi\) | ||||
0.616084 | + | 0.787680i | \(0.288718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.9706 | −1.45853 | ||||||||
\(512\) | − 31.2426i | − 1.38074i | ||||||||
\(513\) | 2.82843i | 0.124878i | ||||||||
\(514\) | −37.7990 | −1.66724 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 36.9706 | 1.62754 | ||||||||
\(517\) | − 0.686292i | − 0.0301831i | ||||||||
\(518\) | 24.9706i | 1.09714i | ||||||||
\(519\) | 0.343146 | 0.0150624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.68629 | 0.117689 | 0.0588443 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588443 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(522\) | 4.82843i | 0.211335i | ||||||||
\(523\) | 7.31371i | 0.319806i | 0.987133 | + | 0.159903i | \(0.0511182\pi\) | ||||
−0.987133 | + | 0.159903i | \(0.948882\pi\) | |||||||
\(524\) | 30.6274 | 1.33796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.9706 | −1.26318 | ||||||||
\(527\) | − 24.9706i | − 1.08773i | ||||||||
\(528\) | − 6.00000i | − 0.261116i | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.65685 | −0.158694 | ||||||||
\(532\) | 30.6274i | 1.32787i | ||||||||
\(533\) | − 10.8284i | − 0.469031i | ||||||||
\(534\) | 22.1421 | 0.958184 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.17157 | −0.223378 | ||||||||
\(537\) | 0.686292i | 0.0296157i | ||||||||
\(538\) | − 43.4558i | − 1.87351i | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 28.4853i | 1.22355i | ||||||||
\(543\) | 14.0000i | 0.600798i | ||||||||
\(544\) | 5.79899 | 0.248630 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.82843 | −0.292230 | ||||||||
\(547\) | − 0.686292i | − 0.0293437i | −0.999892 | − | 0.0146719i | \(-0.995330\pi\) | ||||
0.999892 | − | 0.0146719i | \(-0.00467036\pi\) | |||||||
\(548\) | − 19.7990i | − 0.845771i | ||||||||
\(549\) | 9.31371 | 0.397499 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.65685 | 0.240990 | ||||||||
\(552\) | − 17.6569i | − 0.751526i | ||||||||
\(553\) | − 32.0000i | − 1.36078i | ||||||||
\(554\) | −4.82843 | −0.205140 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 58.6274 | 2.48636 | ||||||||
\(557\) | − 31.7990i | − 1.34737i | −0.739020 | − | 0.673683i | \(-0.764711\pi\) | ||||
0.739020 | − | 0.673683i | \(-0.235289\pi\) | |||||||
\(558\) | 16.4853i | 0.697878i | ||||||||
\(559\) | 9.65685 | 0.408441 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.31371 | 0.308785 | ||||||||
\(562\) | 64.7696i | 2.73214i | ||||||||
\(563\) | 4.00000i | 0.168580i | 0.996441 | + | 0.0842900i | \(0.0268622\pi\) | ||||
−0.996441 | + | 0.0842900i | \(0.973138\pi\) | |||||||
\(564\) | 1.31371 | 0.0553171 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 2.82843i | 0.118783i | ||||||||
\(568\) | − 8.82843i | − 0.370433i | ||||||||
\(569\) | 9.02944 | 0.378534 | 0.189267 | − | 0.981926i | \(-0.439389\pi\) | ||||
0.189267 | + | 0.981926i | \(0.439389\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.9706 | 0.877591 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(572\) | − 7.65685i | − 0.320149i | ||||||||
\(573\) | − 19.3137i | − 0.806842i | ||||||||
\(574\) | −73.9411 | −3.08624 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | − 35.9411i | − 1.49625i | −0.663559 | − | 0.748124i | \(-0.730955\pi\) | ||||
0.663559 | − | 0.748124i | \(-0.269045\pi\) | |||||||
\(578\) | 8.75736i | 0.364258i | ||||||||
\(579\) | 17.3137 | 0.719533 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.6569 | 0.898478 | ||||||||
\(582\) | − 18.4853i | − 0.766240i | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 51.4558 | 2.12926 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 63.1127 | 2.60716 | ||||||||
\(587\) | − 22.9706i | − 0.948097i | −0.880499 | − | 0.474048i | \(-0.842792\pi\) | ||||
0.880499 | − | 0.474048i | \(-0.157208\pi\) | |||||||
\(588\) | 3.82843i | 0.157882i | ||||||||
\(589\) | 19.3137 | 0.795807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.4853 | −0.678114 | ||||||||
\(592\) | − 10.9706i | − 0.450887i | ||||||||
\(593\) | − 3.51472i | − 0.144332i | −0.997393 | − | 0.0721661i | \(-0.977009\pi\) | ||||
0.997393 | − | 0.0721661i | \(-0.0229912\pi\) | |||||||
\(594\) | −4.82843 | −0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −56.7696 | −2.32537 | ||||||||
\(597\) | − 10.3431i | − 0.423317i | ||||||||
\(598\) | − 9.65685i | − 0.394898i | ||||||||
\(599\) | 0.686292 | 0.0280411 | 0.0140206 | − | 0.999902i | \(-0.495537\pi\) | ||||
0.0140206 | + | 0.999902i | \(0.495537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.6274 | 1.82039 | 0.910195 | − | 0.414180i | \(-0.135931\pi\) | ||||
0.910195 | + | 0.414180i | \(0.135931\pi\) | |||||||
\(602\) | − 65.9411i | − 2.68756i | ||||||||
\(603\) | 1.17157i | 0.0477101i | ||||||||
\(604\) | 78.4264 | 3.19113 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.82843 | 0.358630 | ||||||||
\(607\) | 25.9411i | 1.05292i | 0.850201 | + | 0.526459i | \(0.176481\pi\) | ||||
−0.850201 | + | 0.526459i | \(0.823519\pi\) | |||||||
\(608\) | 4.48528i | 0.181902i | ||||||||
\(609\) | 5.65685 | 0.229227 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.343146 | 0.0138822 | ||||||||
\(612\) | 14.0000i | 0.565916i | ||||||||
\(613\) | − 36.3431i | − 1.46789i | −0.679211 | − | 0.733943i | \(-0.737678\pi\) | ||||
0.679211 | − | 0.733943i | \(-0.262322\pi\) | |||||||
\(614\) | −41.4558 | −1.67302 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −24.9706 | −1.00609 | ||||||||
\(617\) | 29.1716i | 1.17440i | 0.809441 | + | 0.587202i | \(0.199770\pi\) | ||||
−0.809441 | + | 0.587202i | \(0.800230\pi\) | |||||||
\(618\) | − 32.9706i | − 1.32627i | ||||||||
\(619\) | 15.7990 | 0.635015 | 0.317508 | − | 0.948256i | \(-0.397154\pi\) | ||||
0.317508 | + | 0.948256i | \(0.397154\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 83.5980i | 3.35197i | ||||||||
\(623\) | − 25.9411i | − 1.03931i | ||||||||
\(624\) | 3.00000 | 0.120096 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.4853 | −0.578948 | ||||||||
\(627\) | 5.65685i | 0.225913i | ||||||||
\(628\) | − 38.2843i | − 1.52771i | ||||||||
\(629\) | 13.3726 | 0.533200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.1127 | −0.760865 | −0.380432 | − | 0.924809i | \(-0.624225\pi\) | ||||
−0.380432 | + | 0.924809i | \(0.624225\pi\) | |||||||
\(632\) | 49.9411i | 1.98655i | ||||||||
\(633\) | − 12.0000i | − 0.476957i | ||||||||
\(634\) | −20.4853 | −0.813574 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.65685 | −0.303614 | ||||||||
\(637\) | 1.00000i | 0.0396214i | ||||||||
\(638\) | 9.65685i | 0.382319i | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.2843 | −1.03817 | −0.519083 | − | 0.854724i | \(-0.673727\pi\) | ||||
−0.519083 | + | 0.854724i | \(0.673727\pi\) | |||||||
\(642\) | 27.3137i | 1.07799i | ||||||||
\(643\) | 17.1716i | 0.677181i | 0.940934 | + | 0.338590i | \(0.109950\pi\) | ||||
−0.940934 | + | 0.338590i | \(0.890050\pi\) | |||||||
\(644\) | −43.3137 | −1.70680 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.9706 | 0.982454 | ||||||||
\(647\) | 11.3137i | 0.444788i | 0.974957 | + | 0.222394i | \(0.0713871\pi\) | ||||
−0.974957 | + | 0.222394i | \(0.928613\pi\) | |||||||
\(648\) | − 4.41421i | − 0.173407i | ||||||||
\(649\) | −7.31371 | −0.287088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.3137 | 0.756964 | ||||||||
\(652\) | − 50.4264i | − 1.97485i | ||||||||
\(653\) | − 2.68629i | − 0.105123i | −0.998618 | − | 0.0525614i | \(-0.983261\pi\) | ||||
0.998618 | − | 0.0525614i | \(-0.0167385\pi\) | |||||||
\(654\) | −41.7990 | −1.63447 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 32.4853 | 1.26834 | ||||||||
\(657\) | − 11.6569i | − 0.454777i | ||||||||
\(658\) | − 2.34315i | − 0.0913453i | ||||||||
\(659\) | 24.6863 | 0.961641 | 0.480821 | − | 0.876819i | \(-0.340339\pi\) | ||||
0.480821 | + | 0.876819i | \(0.340339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.02944 | −0.0400405 | −0.0200202 | − | 0.999800i | \(-0.506373\pi\) | ||||
−0.0200202 | + | 0.999800i | \(0.506373\pi\) | |||||||
\(662\) | − 5.17157i | − 0.200999i | ||||||||
\(663\) | 3.65685i | 0.142020i | ||||||||
\(664\) | −33.7990 | −1.31166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.82843 | −0.342095 | ||||||||
\(667\) | 8.00000i | 0.309761i | ||||||||
\(668\) | 29.3137i | 1.13418i | ||||||||
\(669\) | −4.48528 | −0.173411 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.6274 | 0.719103 | ||||||||
\(672\) | 4.48528i | 0.173023i | ||||||||
\(673\) | − 28.6274i | − 1.10351i | −0.834008 | − | 0.551753i | \(-0.813959\pi\) | ||||
0.834008 | − | 0.551753i | \(-0.186041\pi\) | |||||||
\(674\) | −32.1421 | −1.23807 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.82843 | 0.147247 | ||||||||
\(677\) | − 49.3137i | − 1.89528i | −0.319341 | − | 0.947640i | \(-0.603462\pi\) | ||||
0.319341 | − | 0.947640i | \(-0.396538\pi\) | |||||||
\(678\) | − 41.7990i | − 1.60528i | ||||||||
\(679\) | −21.6569 | −0.831114 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.31371 | 0.203622 | ||||||||
\(682\) | 32.9706i | 1.26251i | ||||||||
\(683\) | − 19.9411i | − 0.763026i | −0.924363 | − | 0.381513i | \(-0.875403\pi\) | ||||
0.924363 | − | 0.381513i | \(-0.124597\pi\) | |||||||
\(684\) | −10.8284 | −0.414035 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −40.9706 | −1.56426 | ||||||||
\(687\) | − 21.3137i | − 0.813169i | ||||||||
\(688\) | 28.9706i | 1.10449i | ||||||||
\(689\) | −2.00000 | −0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1421 | −1.29883 | −0.649414 | − | 0.760435i | \(-0.724986\pi\) | ||||
−0.649414 | + | 0.760435i | \(0.724986\pi\) | |||||||
\(692\) | 1.31371i | 0.0499397i | ||||||||
\(693\) | 5.65685i | 0.214886i | ||||||||
\(694\) | −75.5980 | −2.86966 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.82843 | −0.334641 | ||||||||
\(697\) | 39.5980i | 1.49988i | ||||||||
\(698\) | 18.4853i | 0.699678i | ||||||||
\(699\) | 26.9706 | 1.02012 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.9706 | 1.47190 | 0.735949 | − | 0.677037i | \(-0.236736\pi\) | ||||
0.735949 | + | 0.677037i | \(0.236736\pi\) | |||||||
\(702\) | − 2.41421i | − 0.0911186i | ||||||||
\(703\) | 10.3431i | 0.390099i | ||||||||
\(704\) | −19.6569 | −0.740846 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −42.1421 | −1.58604 | ||||||||
\(707\) | − 10.3431i | − 0.388994i | ||||||||
\(708\) | − 14.0000i | − 0.526152i | ||||||||
\(709\) | −40.6274 | −1.52579 | −0.762897 | − | 0.646520i | \(-0.776224\pi\) | ||||
−0.762897 | + | 0.646520i | \(0.776224\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3137 | 0.424297 | ||||||||
\(712\) | 40.4853i | 1.51725i | ||||||||
\(713\) | 27.3137i | 1.02291i | ||||||||
\(714\) | 24.9706 | 0.934500 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.62742 | −0.0981912 | ||||||||
\(717\) | − 2.00000i | − 0.0746914i | ||||||||
\(718\) | − 2.48528i | − 0.0927499i | ||||||||
\(719\) | −37.9411 | −1.41497 | −0.707483 | − | 0.706731i | \(-0.750169\pi\) | ||||
−0.707483 | + | 0.706731i | \(0.750169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.6274 | −1.43856 | ||||||||
\(722\) | − 26.5563i | − 0.988325i | ||||||||
\(723\) | 11.6569i | 0.433523i | ||||||||
\(724\) | −53.5980 | −1.99195 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.8995 | 0.627199 | ||||||||
\(727\) | 21.6569i | 0.803208i | 0.915813 | + | 0.401604i | \(0.131547\pi\) | ||||
−0.915813 | + | 0.401604i | \(0.868453\pi\) | |||||||
\(728\) | − 12.4853i | − 0.462735i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.3137 | −1.30612 | ||||||||
\(732\) | 35.6569i | 1.31792i | ||||||||
\(733\) | 8.62742i | 0.318661i | 0.987225 | + | 0.159330i | \(0.0509335\pi\) | ||||
−0.987225 | + | 0.159330i | \(0.949066\pi\) | |||||||
\(734\) | −57.9411 | −2.13865 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.34315 | −0.233811 | ||||||||
\(737\) | 2.34315i | 0.0863109i | ||||||||
\(738\) | − 26.1421i | − 0.962305i | ||||||||
\(739\) | −10.1421 | −0.373084 | −0.186542 | − | 0.982447i | \(-0.559728\pi\) | ||||
−0.186542 | + | 0.982447i | \(0.559728\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.82843 | −0.103905 | ||||||||
\(742\) | 13.6569i | 0.501359i | ||||||||
\(743\) | 2.00000i | 0.0733729i | 0.999327 | + | 0.0366864i | \(0.0116803\pi\) | ||||
−0.999327 | + | 0.0366864i | \(0.988320\pi\) | |||||||
\(744\) | −30.1421 | −1.10506 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.1421 | −0.883906 | ||||||||
\(747\) | 7.65685i | 0.280150i | ||||||||
\(748\) | 28.0000i | 1.02378i | ||||||||
\(749\) | 32.0000 | 1.16925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.9706 | 1.20311 | 0.601556 | − | 0.798830i | \(-0.294547\pi\) | ||||
0.601556 | + | 0.798830i | \(0.294547\pi\) | |||||||
\(752\) | 1.02944i | 0.0375397i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.82843 | −0.175841 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.8284 | −0.393826 | ||||||||
\(757\) | 15.9411i | 0.579390i | 0.957119 | + | 0.289695i | \(0.0935539\pi\) | ||||
−0.957119 | + | 0.289695i | \(0.906446\pi\) | |||||||
\(758\) | 39.7990i | 1.44556i | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.5147 | 0.562408 | 0.281204 | − | 0.959648i | \(-0.409266\pi\) | ||||
0.281204 | + | 0.959648i | \(0.409266\pi\) | |||||||
\(762\) | − 13.6569i | − 0.494736i | ||||||||
\(763\) | 48.9706i | 1.77285i | ||||||||
\(764\) | 73.9411 | 2.67510 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.17157 | 0.259119 | ||||||||
\(767\) | − 3.65685i | − 0.132041i | ||||||||
\(768\) | − 29.9706i | − 1.08147i | ||||||||
\(769\) | −42.0000 | −1.51456 | −0.757279 | − | 0.653091i | \(-0.773472\pi\) | ||||
−0.757279 | + | 0.653091i | \(0.773472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.6569 | −0.563868 | ||||||||
\(772\) | 66.2843i | 2.38562i | ||||||||
\(773\) | 5.85786i | 0.210693i | 0.994436 | + | 0.105346i | \(0.0335951\pi\) | ||||
−0.994436 | + | 0.105346i | \(0.966405\pi\) | |||||||
\(774\) | 23.3137 | 0.837994 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 33.7990 | 1.21331 | ||||||||
\(777\) | 10.3431i | 0.371058i | ||||||||
\(778\) | − 16.8284i | − 0.603328i | ||||||||
\(779\) | −30.6274 | −1.09734 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 35.3137i | 1.26282i | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.3137 | 0.688897 | ||||||||
\(787\) | − 32.7696i | − 1.16811i | −0.811715 | − | 0.584054i | \(-0.801466\pi\) | ||||
0.811715 | − | 0.584054i | \(-0.198534\pi\) | |||||||
\(788\) | − 63.1127i | − 2.24830i | ||||||||
\(789\) | −12.0000 | −0.427211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.9706 | −1.74119 | ||||||||
\(792\) | − 8.82843i | − 0.313704i | ||||||||
\(793\) | 9.31371i | 0.330739i | ||||||||
\(794\) | −7.17157 | −0.254510 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39.5980 | 1.40351 | ||||||||
\(797\) | − 35.6569i | − 1.26303i | −0.775363 | − | 0.631515i | \(-0.782433\pi\) | ||||
0.775363 | − | 0.631515i | \(-0.217567\pi\) | |||||||
\(798\) | 19.3137i | 0.683698i | ||||||||
\(799\) | −1.25483 | −0.0443928 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.17157 | 0.324062 | ||||||||
\(802\) | − 5.17157i | − 0.182615i | ||||||||
\(803\) | − 23.3137i | − 0.822723i | ||||||||
\(804\) | −4.48528 | −0.158184 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.4853 | −0.580669 | ||||||||
\(807\) | − 18.0000i | − 0.633630i | ||||||||
\(808\) | 16.1421i | 0.567878i | ||||||||
\(809\) | −41.3137 | −1.45251 | −0.726256 | − | 0.687424i | \(-0.758741\pi\) | ||||
−0.726256 | + | 0.687424i | \(0.758741\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.85786 | −0.0652384 | −0.0326192 | − | 0.999468i | \(-0.510385\pi\) | ||||
−0.0326192 | + | 0.999468i | \(0.510385\pi\) | |||||||
\(812\) | 21.6569i | 0.760007i | ||||||||
\(813\) | 11.7990i | 0.413809i | ||||||||
\(814\) | −17.6569 | −0.618872 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.9706 | −0.384047 | ||||||||
\(817\) | − 27.3137i | − 0.955586i | ||||||||
\(818\) | 2.48528i | 0.0868958i | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.7990 | 0.551389 | 0.275694 | − | 0.961245i | \(-0.411092\pi\) | ||||
0.275694 | + | 0.961245i | \(0.411092\pi\) | |||||||
\(822\) | − 12.4853i | − 0.435474i | ||||||||
\(823\) | 48.9706i | 1.70701i | 0.521088 | + | 0.853503i | \(0.325527\pi\) | ||||
−0.521088 | + | 0.853503i | \(0.674473\pi\) | |||||||
\(824\) | 60.2843 | 2.10010 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.9706 | −0.868837 | ||||||||
\(827\) | 26.0000i | 0.904109i | 0.891990 | + | 0.452054i | \(0.149309\pi\) | ||||
−0.891990 | + | 0.452054i | \(0.850691\pi\) | |||||||
\(828\) | − 15.3137i | − 0.532188i | ||||||||
\(829\) | −5.31371 | −0.184553 | −0.0922764 | − | 0.995733i | \(-0.529414\pi\) | ||||
−0.0922764 | + | 0.995733i | \(0.529414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | − 9.82843i | − 0.340739i | ||||||||
\(833\) | − 3.65685i | − 0.126702i | ||||||||
\(834\) | 36.9706 | 1.28019 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −21.6569 | −0.749018 | ||||||||
\(837\) | 6.82843i | 0.236025i | ||||||||
\(838\) | 73.9411i | 2.55425i | ||||||||
\(839\) | 47.2548 | 1.63142 | 0.815709 | − | 0.578462i | \(-0.196347\pi\) | ||||
0.815709 | + | 0.578462i | \(0.196347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 35.4558i | 1.22189i | ||||||||
\(843\) | 26.8284i | 0.924020i | ||||||||
\(844\) | 45.9411 | 1.58136 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.828427 | 0.0284819 | ||||||||
\(847\) | − 19.7990i | − 0.680301i | ||||||||
\(848\) | − 6.00000i | − 0.206041i | ||||||||
\(849\) | 4.97056 | 0.170589 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.6274 | −0.501421 | ||||||||
\(852\) | − 7.65685i | − 0.262320i | ||||||||
\(853\) | − 7.65685i | − 0.262166i | −0.991371 | − | 0.131083i | \(-0.958155\pi\) | ||||
0.991371 | − | 0.131083i | \(-0.0418454\pi\) | |||||||
\(854\) | 63.5980 | 2.17628 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −49.9411 | −1.70695 | ||||||||
\(857\) | − 29.5980i | − 1.01105i | −0.862813 | − | 0.505524i | \(-0.831299\pi\) | ||||
0.862813 | − | 0.505524i | \(-0.168701\pi\) | |||||||
\(858\) | − 4.82843i | − 0.164840i | ||||||||
\(859\) | 23.3137 | 0.795453 | 0.397727 | − | 0.917504i | \(-0.369799\pi\) | ||||
0.397727 | + | 0.917504i | \(0.369799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.6274 | −1.04378 | ||||||||
\(862\) | 47.4558i | 1.61635i | ||||||||
\(863\) | − 39.6569i | − 1.34994i | −0.737847 | − | 0.674968i | \(-0.764158\pi\) | ||||
0.737847 | − | 0.674968i | \(-0.235842\pi\) | |||||||
\(864\) | −1.58579 | −0.0539496 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.17157 | −0.107774 | ||||||||
\(867\) | 3.62742i | 0.123194i | ||||||||
\(868\) | 73.9411i | 2.50973i | ||||||||
\(869\) | 22.6274 | 0.767583 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.17157 | −0.0396972 | ||||||||
\(872\) | − 76.4264i | − 2.58812i | ||||||||
\(873\) | − 7.65685i | − 0.259145i | ||||||||
\(874\) | −27.3137 | −0.923900 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.6274 | 1.50782 | ||||||||
\(877\) | 14.2843i | 0.482346i | 0.970482 | + | 0.241173i | \(0.0775321\pi\) | ||||
−0.970482 | + | 0.241173i | \(0.922468\pi\) | |||||||
\(878\) | 40.9706i | 1.38269i | ||||||||
\(879\) | 26.1421 | 0.881752 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.5980 | 1.80576 | 0.902881 | − | 0.429891i | \(-0.141448\pi\) | ||||
0.902881 | + | 0.429891i | \(0.141448\pi\) | |||||||
\(882\) | 2.41421i | 0.0812908i | ||||||||
\(883\) | − 51.5980i | − 1.73641i | −0.496205 | − | 0.868205i | \(-0.665274\pi\) | ||||
0.496205 | − | 0.868205i | \(-0.334726\pi\) | |||||||
\(884\) | −14.0000 | −0.470871 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −101.255 | −3.40172 | ||||||||
\(887\) | 8.00000i | 0.268614i | 0.990940 | + | 0.134307i | \(0.0428808\pi\) | ||||
−0.990940 | + | 0.134307i | \(0.957119\pi\) | |||||||
\(888\) | − 16.1421i | − 0.541695i | ||||||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | − 17.1716i | − 0.574947i | ||||||||
\(893\) | − 0.970563i | − 0.0324786i | ||||||||
\(894\) | −35.7990 | −1.19730 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −58.1421 | −1.94239 | ||||||||
\(897\) | − 4.00000i | − 0.133556i | ||||||||
\(898\) | − 18.8284i | − 0.628313i | ||||||||
\(899\) | 13.6569 | 0.455482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.31371 | 0.243655 | ||||||||
\(902\) | − 52.2843i | − 1.74088i | ||||||||
\(903\) | − 27.3137i | − 0.908943i | ||||||||
\(904\) | 76.4264 | 2.54190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 49.4558 | 1.64306 | ||||||||
\(907\) | − 20.9706i | − 0.696316i | −0.937436 | − | 0.348158i | \(-0.886807\pi\) | ||||
0.937436 | − | 0.348158i | \(-0.113193\pi\) | |||||||
\(908\) | 20.3431i | 0.675111i | ||||||||
\(909\) | 3.65685 | 0.121290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | − 8.48528i | − 0.280976i | ||||||||
\(913\) | 15.3137i | 0.506810i | ||||||||
\(914\) | 8.82843 | 0.292018 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 81.5980 | 2.69607 | ||||||||
\(917\) | − 22.6274i | − 0.747223i | ||||||||
\(918\) | 8.82843i | 0.291382i | ||||||||
\(919\) | 19.3137 | 0.637100 | 0.318550 | − | 0.947906i | \(-0.396804\pi\) | ||||
0.318550 | + | 0.947906i | \(0.396804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.1716 | −0.565823 | ||||||||
\(922\) | 26.1421i | 0.860945i | ||||||||
\(923\) | − 2.00000i | − 0.0658308i | ||||||||
\(924\) | −21.6569 | −0.712458 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.1421 | 0.596188 | ||||||||
\(927\) | − 13.6569i | − 0.448550i | ||||||||
\(928\) | 3.17157i | 0.104112i | ||||||||
\(929\) | 27.7990 | 0.912055 | 0.456028 | − | 0.889966i | \(-0.349272\pi\) | ||||
0.456028 | + | 0.889966i | \(0.349272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | 103.255i | 3.38222i | ||||||||
\(933\) | 34.6274i | 1.13365i | ||||||||
\(934\) | −19.3137 | −0.631964 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.41421 | 0.144283 | ||||||||
\(937\) | − 1.31371i | − 0.0429170i | −0.999770 | − | 0.0214585i | \(-0.993169\pi\) | ||||
0.999770 | − | 0.0214585i | \(-0.00683097\pi\) | |||||||
\(938\) | 8.00000i | 0.261209i | ||||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.85786 | 0.190961 | 0.0954805 | − | 0.995431i | \(-0.469561\pi\) | ||||
0.0954805 | + | 0.995431i | \(0.469561\pi\) | |||||||
\(942\) | − 24.1421i | − 0.786593i | ||||||||
\(943\) | − 43.3137i | − 1.41049i | ||||||||
\(944\) | 10.9706 | 0.357061 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.6274 | 1.51599 | ||||||||
\(947\) | 54.9706i | 1.78630i | 0.449756 | + | 0.893152i | \(0.351511\pi\) | ||||
−0.449756 | + | 0.893152i | \(0.648489\pi\) | |||||||
\(948\) | 43.3137i | 1.40676i | ||||||||
\(949\) | 11.6569 | 0.378398 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.48528 | −0.275154 | ||||||||
\(952\) | 45.6569i | 1.47975i | ||||||||
\(953\) | 51.6569i | 1.67333i | 0.547715 | + | 0.836665i | \(0.315498\pi\) | ||||
−0.547715 | + | 0.836665i | \(0.684502\pi\) | |||||||
\(954\) | −4.82843 | −0.156326 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.65685 | 0.247640 | ||||||||
\(957\) | 4.00000i | 0.129302i | ||||||||
\(958\) | − 6.48528i | − 0.209530i | ||||||||
\(959\) | −14.6274 | −0.472344 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | − 8.82843i | − 0.284640i | ||||||||
\(963\) | 11.3137i | 0.364579i | ||||||||
\(964\) | −44.6274 | −1.43735 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −27.3137 | −0.878804 | ||||||||
\(967\) | 10.1421i | 0.326149i | 0.986614 | + | 0.163075i | \(0.0521411\pi\) | ||||
−0.986614 | + | 0.163075i | \(0.947859\pi\) | |||||||
\(968\) | 30.8995i | 0.993147i | ||||||||
\(969\) | 10.3431 | 0.332270 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.31371 | 0.234708 | 0.117354 | − | 0.993090i | \(-0.462559\pi\) | ||||
0.117354 | + | 0.993090i | \(0.462559\pi\) | |||||||
\(972\) | − 3.82843i | − 0.122797i | ||||||||
\(973\) | − 43.3137i | − 1.38857i | ||||||||
\(974\) | 76.7696 | 2.45986 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9411 | −0.894374 | ||||||||
\(977\) | − 13.8579i | − 0.443352i | −0.975120 | − | 0.221676i | \(-0.928847\pi\) | ||||
0.975120 | − | 0.221676i | \(-0.0711528\pi\) | |||||||
\(978\) | − 31.7990i | − 1.01682i | ||||||||
\(979\) | 18.3431 | 0.586249 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.3137 | −0.552784 | ||||||||
\(982\) | − 35.3137i | − 1.12691i | ||||||||
\(983\) | 2.68629i | 0.0856794i | 0.999082 | + | 0.0428397i | \(0.0136405\pi\) | ||||
−0.999082 | + | 0.0428397i | \(0.986360\pi\) | |||||||
\(984\) | 47.7990 | 1.52378 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.6569 | 0.562309 | ||||||||
\(987\) | − 0.970563i | − 0.0308934i | ||||||||
\(988\) | − 10.8284i | − 0.344498i | ||||||||
\(989\) | 38.6274 | 1.22828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.3137 | 0.867649 | 0.433824 | − | 0.900998i | \(-0.357164\pi\) | ||||
0.433824 | + | 0.900998i | \(0.357164\pi\) | |||||||
\(992\) | 10.8284i | 0.343803i | ||||||||
\(993\) | − 2.14214i | − 0.0679786i | ||||||||
\(994\) | −13.6569 | −0.433169 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −29.3137 | −0.928840 | ||||||||
\(997\) | − 51.2548i | − 1.62326i | −0.584174 | − | 0.811628i | \(-0.698581\pi\) | ||||
0.584174 | − | 0.811628i | \(-0.301419\pi\) | |||||||
\(998\) | 5.17157i | 0.163703i | ||||||||
\(999\) | −3.65685 | −0.115698 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))