Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(442,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.442");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.f (of order \(3\), degree \(2\), 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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 442.2 | ||
Root | \(0.500000 + 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.442 |
Dual form | 1323.2.f.c.883.2 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.119562 | − | 0.207087i | −0.0845428 | − | 0.146433i | 0.820653 | − | 0.571426i | \(-0.193610\pi\) |
−0.905196 | + | 0.424994i | \(0.860276\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.971410 | − | 1.68253i | 0.485705 | − | 0.841266i | ||||
\(5\) | −0.590972 | + | 1.02359i | −0.264291 | + | 0.457765i | −0.967378 | − | 0.253339i | \(-0.918471\pi\) |
0.703087 | + | 0.711104i | \(0.251804\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.942820 | −0.333337 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.282630 | 0.0893755 | ||||||||
\(11\) | −1.85185 | − | 3.20750i | −0.558353 | − | 0.967096i | −0.997634 | − | 0.0687465i | \(-0.978100\pi\) |
0.439281 | − | 0.898350i | \(-0.355233\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.83009 | − | 3.16982i | −0.457524 | − | 0.792454i | ||||
\(17\) | −6.94282 | −1.68388 | −0.841941 | − | 0.539570i | \(-0.818587\pi\) | ||||
−0.841941 | + | 0.539570i | \(0.818587\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94282 | −0.445713 | −0.222857 | − | 0.974851i | \(-0.571538\pi\) | ||||
−0.222857 | + | 0.974851i | \(0.571538\pi\) | |||||||
\(20\) | 1.14815 | + | 1.98866i | 0.256735 | + | 0.444677i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.442820 | + | 0.766987i | −0.0944096 | + | 0.163522i | ||||
\(23\) | −2.80150 | + | 4.85235i | −0.584154 | + | 1.01178i | 0.410826 | + | 0.911714i | \(0.365240\pi\) |
−0.994980 | + | 0.100071i | \(0.968093\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.80150 | + | 3.12030i | 0.360301 | + | 0.624060i | ||||
\(26\) | −0.239123 | −0.0468959 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.119562 | + | 0.207087i | 0.0222020 | + | 0.0384551i | 0.876913 | − | 0.480649i | \(-0.159599\pi\) |
−0.854711 | + | 0.519104i | \(0.826266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.830095 | − | 1.43777i | 0.149089 | − | 0.258231i | −0.781802 | − | 0.623527i | \(-0.785699\pi\) |
0.930891 | + | 0.365297i | \(0.119032\pi\) | |||||||
\(32\) | −1.38044 | + | 2.39099i | −0.244029 | + | 0.422671i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.830095 | + | 1.43777i | 0.142360 | + | 0.246575i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.54583 | −1.56932 | −0.784662 | − | 0.619923i | \(-0.787164\pi\) | ||||
−0.784662 | + | 0.619923i | \(0.787164\pi\) | |||||||
\(38\) | 0.232287 | + | 0.402332i | 0.0376819 | + | 0.0652669i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.557180 | − | 0.965064i | 0.0880979 | − | 0.152590i | ||||
\(41\) | 5.09097 | − | 8.81782i | 0.795076 | − | 1.37711i | −0.127715 | − | 0.991811i | \(-0.540764\pi\) |
0.922791 | − | 0.385301i | \(-0.125903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.11273 | − | 1.92730i | −0.169689 | − | 0.293910i | 0.768622 | − | 0.639704i | \(-0.220943\pi\) |
−0.938311 | + | 0.345794i | \(0.887610\pi\) | |||||||
\(44\) | −7.19562 | −1.08478 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.33981 | 0.197544 | ||||||||
\(47\) | −2.91423 | − | 5.04759i | −0.425084 | − | 0.736267i | 0.571344 | − | 0.820711i | \(-0.306422\pi\) |
−0.996428 | + | 0.0844432i | \(0.973089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.430782 | − | 0.746136i | 0.0609217 | − | 0.105520i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.971410 | − | 1.68253i | −0.134710 | − | 0.233325i | ||||
\(53\) | 11.6030 | 1.59380 | 0.796898 | − | 0.604114i | \(-0.206473\pi\) | ||||
0.796898 | + | 0.604114i | \(0.206473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.37756 | 0.590270 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.0285900 | − | 0.0495193i | 0.00375405 | − | 0.00650220i | ||||
\(59\) | −1.30150 | + | 2.25427i | −0.169442 | + | 0.293481i | −0.938224 | − | 0.346029i | \(-0.887530\pi\) |
0.768782 | + | 0.639511i | \(0.220863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.80150 | − | 6.58440i | −0.486733 | − | 0.843046i | 0.513151 | − | 0.858298i | \(-0.328478\pi\) |
−0.999884 | + | 0.0152524i | \(0.995145\pi\) | |||||||
\(62\) | −0.396990 | −0.0504178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.66019 | −0.832524 | ||||||||
\(65\) | 0.590972 | + | 1.02359i | 0.0733010 | + | 0.126961i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.75404 | + | 3.03809i | −0.214290 | + | 0.371161i | −0.953053 | − | 0.302804i | \(-0.902077\pi\) |
0.738763 | + | 0.673966i | \(0.235410\pi\) | |||||||
\(68\) | −6.74433 | + | 11.6815i | −0.817870 | + | 1.41659i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.60301 | −1.02099 | −0.510495 | − | 0.859881i | \(-0.670538\pi\) | ||||
−0.510495 | + | 0.859881i | \(0.670538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.1488 | −1.77304 | −0.886519 | − | 0.462693i | \(-0.846883\pi\) | ||||
−0.886519 | + | 0.462693i | \(0.846883\pi\) | |||||||
\(74\) | 1.14132 | + | 1.97682i | 0.132675 | + | 0.229800i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.88727 | + | 3.26886i | −0.216485 | + | 0.374963i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.68878 | − | 6.38915i | −0.415020 | − | 0.718836i | 0.580410 | − | 0.814324i | \(-0.302892\pi\) |
−0.995431 | + | 0.0954881i | \(0.969559\pi\) | |||||||
\(80\) | 4.32614 | 0.483677 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.43474 | −0.268872 | ||||||||
\(83\) | 3.47141 | + | 6.01266i | 0.381037 | + | 0.659975i | 0.991211 | − | 0.132292i | \(-0.0422338\pi\) |
−0.610174 | + | 0.792267i | \(0.708900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.10301 | − | 7.10662i | 0.445034 | − | 0.770821i | ||||
\(86\) | −0.266078 | + | 0.460861i | −0.0286920 | + | 0.0496960i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.74596 | + | 3.02409i | 0.186120 | + | 0.322369i | ||||
\(89\) | 2.74720 | 0.291203 | 0.145602 | − | 0.989343i | \(-0.453488\pi\) | ||||
0.145602 | + | 0.989343i | \(0.453488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.44282 | + | 9.42724i | 0.567453 | + | 0.982858i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.696860 | + | 1.20700i | −0.0718756 | + | 0.124492i | ||||
\(95\) | 1.14815 | − | 1.98866i | 0.117798 | − | 0.204032i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.58414 | + | 6.20790i | 0.363914 | + | 0.630317i | 0.988601 | − | 0.150558i | \(-0.0481069\pi\) |
−0.624687 | + | 0.780875i | \(0.714774\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.00000 | 0.700000 | ||||||||
\(101\) | 6.39248 | + | 11.0721i | 0.636075 | + | 1.10171i | 0.986286 | + | 0.165044i | \(0.0527765\pi\) |
−0.350211 | + | 0.936671i | \(0.613890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19850 | + | 3.80791i | −0.216624 | + | 0.375204i | −0.953774 | − | 0.300526i | \(-0.902838\pi\) |
0.737150 | + | 0.675730i | \(0.236171\pi\) | |||||||
\(104\) | −0.471410 | + | 0.816506i | −0.0462256 | + | 0.0800650i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.38727 | − | 2.40283i | −0.134744 | − | 0.233384i | ||||
\(107\) | −13.7278 | −1.32711 | −0.663557 | − | 0.748126i | \(-0.730954\pi\) | ||||
−0.663557 | + | 0.748126i | \(0.730954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.26320 | 0.120993 | 0.0604963 | − | 0.998168i | \(-0.480732\pi\) | ||||
0.0604963 | + | 0.998168i | \(0.480732\pi\) | |||||||
\(110\) | −0.523388 | − | 0.906535i | −0.0499031 | − | 0.0864347i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.08126 | − | 10.5330i | 0.572076 | − | 0.990866i | −0.424276 | − | 0.905533i | \(-0.639471\pi\) |
0.996353 | − | 0.0853326i | \(-0.0271953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.31122 | − | 5.73520i | −0.308773 | − | 0.534810i | ||||
\(116\) | 0.464574 | 0.0431346 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.622440 | 0.0573003 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.35868 | + | 2.35331i | −0.123517 | + | 0.213937i | ||||
\(122\) | −0.909028 | + | 1.57448i | −0.0822996 | + | 0.142547i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.61273 | − | 2.79332i | −0.144827 | − | 0.250848i | ||||
\(125\) | −10.1683 | −0.909478 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.33981 | 0.118889 | 0.0594445 | − | 0.998232i | \(-0.481067\pi\) | ||||
0.0594445 | + | 0.998232i | \(0.481067\pi\) | |||||||
\(128\) | 3.55718 | + | 6.16122i | 0.314413 | + | 0.544580i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.141315 | − | 0.244765i | 0.0123942 | − | 0.0214673i | ||||
\(131\) | 2.48345 | − | 4.30146i | 0.216980 | − | 0.375820i | −0.736903 | − | 0.675998i | \(-0.763713\pi\) |
0.953883 | + | 0.300178i | \(0.0970461\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.838864 | 0.0724668 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.54583 | 0.561300 | ||||||||
\(137\) | −2.16991 | − | 3.75839i | −0.185387 | − | 0.321101i | 0.758320 | − | 0.651883i | \(-0.226021\pi\) |
−0.943707 | + | 0.330782i | \(0.892687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.97141 | − | 3.41458i | 0.167213 | − | 0.289621i | −0.770226 | − | 0.637771i | \(-0.779857\pi\) |
0.937439 | + | 0.348150i | \(0.113190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.02859 | + | 1.78157i | 0.0863174 | + | 0.149506i | ||||
\(143\) | −3.70370 | −0.309719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.282630 | −0.0234712 | ||||||||
\(146\) | 1.81122 | + | 3.13713i | 0.149898 | + | 0.259630i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.27292 | + | 16.0612i | −0.762229 | + | 1.32022i | ||||
\(149\) | 5.55555 | − | 9.62249i | 0.455128 | − | 0.788305i | −0.543568 | − | 0.839365i | \(-0.682927\pi\) |
0.998696 | + | 0.0510606i | \(0.0162602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.96169 | − | 12.0580i | −0.566535 | − | 0.981267i | −0.996905 | − | 0.0786145i | \(-0.974950\pi\) |
0.430370 | − | 0.902652i | \(-0.358383\pi\) | |||||||
\(152\) | 1.83173 | 0.148573 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.981125 | + | 1.69936i | 0.0788059 | + | 0.136496i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0285900 | − | 0.0495193i | 0.00228173 | − | 0.00395207i | −0.864882 | − | 0.501975i | \(-0.832607\pi\) |
0.867164 | + | 0.498023i | \(0.165940\pi\) | |||||||
\(158\) | −0.882073 | + | 1.52780i | −0.0701740 | + | 0.121545i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.63160 | − | 2.82601i | −0.128989 | − | 0.223416i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.50808 | −0.118122 | −0.0590610 | − | 0.998254i | \(-0.518811\pi\) | ||||
−0.0590610 | + | 0.998254i | \(0.518811\pi\) | |||||||
\(164\) | −9.89084 | − | 17.1314i | −0.772345 | − | 1.33774i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.830095 | − | 1.43777i | 0.0644279 | − | 0.111592i | ||||
\(167\) | 7.34213 | − | 12.7169i | 0.568151 | − | 0.984067i | −0.428598 | − | 0.903496i | \(-0.640992\pi\) |
0.996749 | − | 0.0805714i | \(-0.0256745\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | −1.96225 | −0.150498 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.32365 | −0.329675 | ||||||||
\(173\) | −0.126398 | − | 0.218928i | −0.00960987 | − | 0.0166448i | 0.861180 | − | 0.508299i | \(-0.169726\pi\) |
−0.870790 | + | 0.491655i | \(0.836392\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.77812 | + | 11.7400i | −0.510920 | + | 0.884939i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.328460 | − | 0.568910i | −0.0246191 | − | 0.0426416i | ||||
\(179\) | −14.1923 | −1.06079 | −0.530393 | − | 0.847752i | \(-0.677956\pi\) | ||||
−0.530393 | + | 0.847752i | \(0.677956\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.43147 | 0.106400 | 0.0532002 | − | 0.998584i | \(-0.483058\pi\) | ||||
0.0532002 | + | 0.998584i | \(0.483058\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.64132 | − | 4.57489i | 0.194720 | − | 0.337266i | ||||
\(185\) | 5.64132 | − | 9.77104i | 0.414758 | − | 0.718381i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.8571 | + | 22.2691i | 0.940201 | + | 1.62848i | ||||
\(188\) | −11.3236 | −0.825862 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.549100 | −0.0398359 | ||||||||
\(191\) | 7.53379 | + | 13.0489i | 0.545126 | + | 0.944186i | 0.998599 | + | 0.0529159i | \(0.0168515\pi\) |
−0.453473 | + | 0.891270i | \(0.649815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.92395 | − | 6.79647i | 0.282452 | − | 0.489221i | −0.689536 | − | 0.724251i | \(-0.742186\pi\) |
0.971988 | + | 0.235030i | \(0.0755190\pi\) | |||||||
\(194\) | 0.857050 | − | 1.48445i | 0.0615326 | − | 0.106578i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.69002 | −0.476644 | −0.238322 | − | 0.971186i | \(-0.576597\pi\) | ||||
−0.238322 | + | 0.971186i | \(0.576597\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9396 | 1.41348 | 0.706739 | − | 0.707475i | \(-0.250166\pi\) | ||||
0.706739 | + | 0.707475i | \(0.250166\pi\) | |||||||
\(200\) | −1.69850 | − | 2.94188i | −0.120102 | − | 0.208022i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.52859 | − | 2.64760i | 0.107551 | − | 0.186284i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.01724 | + | 10.4222i | 0.420262 | + | 0.727916i | ||||
\(206\) | 1.05142 | 0.0732561 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.66019 | −0.253789 | ||||||||
\(209\) | 3.59781 | + | 6.23159i | 0.248866 | + | 0.431048i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.04583 | − | 15.6678i | 0.622741 | − | 1.07862i | −0.366233 | − | 0.930523i | \(-0.619353\pi\) |
0.988973 | − | 0.148095i | \(-0.0473141\pi\) | |||||||
\(212\) | 11.2713 | − | 19.5224i | 0.774115 | − | 1.34081i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.64132 | + | 2.84284i | 0.112198 | + | 0.194333i | ||||
\(215\) | 2.63036 | 0.179389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.151030 | − | 0.261592i | −0.0102291 | − | 0.0177172i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.25241 | − | 7.36538i | 0.286697 | − | 0.496574i | ||||
\(221\) | −3.47141 | + | 6.01266i | −0.233512 | + | 0.404455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3285 | − | 19.6215i | −0.758610 | − | 1.31395i | −0.943560 | − | 0.331203i | \(-0.892546\pi\) |
0.184950 | − | 0.982748i | \(-0.440788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.90834 | −0.193460 | ||||||||
\(227\) | 2.64132 | + | 4.57489i | 0.175310 | + | 0.303646i | 0.940269 | − | 0.340433i | \(-0.110574\pi\) |
−0.764958 | + | 0.644080i | \(0.777240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.66827 | − | 16.7459i | 0.638897 | − | 1.10660i | −0.346778 | − | 0.937947i | \(-0.612724\pi\) |
0.985675 | − | 0.168655i | \(-0.0539425\pi\) | |||||||
\(230\) | −0.791790 | + | 1.37142i | −0.0522091 | + | 0.0904288i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.112725 | − | 0.195246i | −0.00740077 | − | 0.0128185i | ||||
\(233\) | 16.9806 | 1.11243 | 0.556217 | − | 0.831037i | \(-0.312252\pi\) | ||||
0.556217 | + | 0.831037i | \(0.312252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.88891 | 0.449383 | ||||||||
\(236\) | 2.52859 | + | 4.37965i | 0.164597 | + | 0.285091i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.44282 | − | 14.6234i | 0.546121 | − | 0.945909i | −0.452415 | − | 0.891808i | \(-0.649437\pi\) |
0.998535 | − | 0.0541011i | \(-0.0172293\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5728 | + | 23.5088i | 0.874300 | + | 1.51433i | 0.857507 | + | 0.514473i | \(0.172012\pi\) |
0.0167933 | + | 0.999859i | \(0.494654\pi\) | |||||||
\(242\) | 0.649786 | 0.0417699 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.7713 | −0.945634 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.971410 | + | 1.68253i | −0.0618093 | + | 0.107057i | ||||
\(248\) | −0.782630 | + | 1.35556i | −0.0496971 | + | 0.0860778i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.21574 | + | 2.10571i | 0.0768898 | + | 0.133177i | ||||
\(251\) | −19.0780 | −1.20419 | −0.602096 | − | 0.798424i | \(-0.705668\pi\) | ||||
−0.602096 | + | 0.798424i | \(0.705668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7518 | 1.30466 | ||||||||
\(254\) | −0.160190 | − | 0.277457i | −0.0100512 | − | 0.0174092i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.80959 | + | 10.0625i | −0.363099 | + | 0.628906i | ||||
\(257\) | 7.42107 | − | 12.8537i | 0.462913 | − | 0.801790i | −0.536191 | − | 0.844097i | \(-0.680137\pi\) |
0.999105 | + | 0.0423070i | \(0.0134707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.29630 | 0.142411 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.18770 | −0.0733764 | ||||||||
\(263\) | −3.87072 | − | 6.70429i | −0.238679 | − | 0.413404i | 0.721656 | − | 0.692251i | \(-0.243381\pi\) |
−0.960335 | + | 0.278847i | \(0.910048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.85705 | + | 11.8768i | −0.421225 | + | 0.729584i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.40778 | + | 5.90246i | 0.208164 | + | 0.360550i | ||||
\(269\) | −1.51135 | −0.0921486 | −0.0460743 | − | 0.998938i | \(-0.514671\pi\) | ||||
−0.0460743 | + | 0.998938i | \(0.514671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9806 | 1.33522 | 0.667612 | − | 0.744509i | \(-0.267316\pi\) | ||||
0.667612 | + | 0.744509i | \(0.267316\pi\) | |||||||
\(272\) | 12.7060 | + | 22.0075i | 0.770416 | + | 1.33440i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.518875 | + | 0.898718i | −0.0313464 | + | 0.0542935i | ||||
\(275\) | 6.67223 | − | 11.5566i | 0.402350 | − | 0.696892i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.41423 | + | 9.37772i | 0.325310 | + | 0.563453i | 0.981575 | − | 0.191077i | \(-0.0611982\pi\) |
−0.656265 | + | 0.754530i | \(0.727865\pi\) | |||||||
\(278\) | −0.942820 | −0.0565466 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.43831 | − | 14.6156i | −0.503387 | − | 0.871892i | −0.999992 | − | 0.00391559i | \(-0.998754\pi\) |
0.496605 | − | 0.867977i | \(-0.334580\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.65856 | + | 13.2650i | −0.455254 | + | 0.788523i | −0.998703 | − | 0.0509194i | \(-0.983785\pi\) |
0.543449 | + | 0.839442i | \(0.317118\pi\) | |||||||
\(284\) | −8.35705 | + | 14.4748i | −0.495900 | + | 0.858923i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.442820 | + | 0.766987i | 0.0261845 | + | 0.0453529i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.2028 | 1.83546 | ||||||||
\(290\) | 0.0337917 | + | 0.0585290i | 0.00198432 | + | 0.00343694i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.7157 | + | 25.4884i | −0.861173 | + | 1.49160i | ||||
\(293\) | 4.68482 | − | 8.11435i | 0.273690 | − | 0.474045i | −0.696114 | − | 0.717932i | \(-0.745089\pi\) |
0.969804 | + | 0.243886i | \(0.0784224\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.53831 | − | 2.66442i | −0.0895636 | − | 0.155129i | ||||
\(296\) | 9.00000 | 0.523114 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.65692 | −0.153911 | ||||||||
\(299\) | 2.80150 | + | 4.85235i | 0.162015 | + | 0.280619i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.66470 | + | 2.88335i | −0.0957929 | + | 0.165918i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.55555 | + | 6.15838i | 0.203925 | + | 0.353208i | ||||
\(305\) | 8.98633 | 0.514556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.71410 | −0.154902 | −0.0774509 | − | 0.996996i | \(-0.524678\pi\) | ||||
−0.0774509 | + | 0.996996i | \(0.524678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.234610 | − | 0.406356i | 0.0133249 | − | 0.0230795i | ||||
\(311\) | 6.99028 | − | 12.1075i | 0.396383 | − | 0.686555i | −0.596894 | − | 0.802320i | \(-0.703599\pi\) |
0.993277 | + | 0.115765i | \(0.0369320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.52696 | − | 16.5012i | −0.538495 | − | 0.932701i | −0.998985 | − | 0.0450364i | \(-0.985660\pi\) |
0.460490 | − | 0.887665i | \(-0.347674\pi\) | |||||||
\(314\) | −0.0136731 | −0.000771615 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.3333 | −0.806309 | ||||||||
\(317\) | −2.00972 | − | 3.48093i | −0.112877 | − | 0.195508i | 0.804052 | − | 0.594559i | \(-0.202673\pi\) |
−0.916929 | + | 0.399050i | \(0.869340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.442820 | − | 0.766987i | 0.0247932 | − | 0.0429430i | ||||
\(320\) | 3.93598 | − | 6.81732i | 0.220028 | − | 0.381100i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.4887 | 0.750529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.60301 | 0.199859 | ||||||||
\(326\) | 0.180309 | + | 0.312304i | 0.00998637 | + | 0.0172969i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.79987 | + | 8.31362i | −0.265028 | + | 0.459043i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.18878 | + | 10.7193i | 0.340166 | + | 0.589185i | 0.984463 | − | 0.175590i | \(-0.0561834\pi\) |
−0.644297 | + | 0.764775i | \(0.722850\pi\) | |||||||
\(332\) | 13.4887 | 0.740286 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.51135 | −0.192133 | ||||||||
\(335\) | −2.07318 | − | 3.59085i | −0.113270 | − | 0.196189i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.12997 | + | 10.6174i | −0.333920 | + | 0.578367i | −0.983277 | − | 0.182117i | \(-0.941705\pi\) |
0.649356 | + | 0.760484i | \(0.275038\pi\) | |||||||
\(338\) | 1.43474 | − | 2.48504i | 0.0780395 | − | 0.135168i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.97141 | − | 13.8069i | −0.432310 | − | 0.748784i | ||||
\(341\) | −6.14884 | −0.332978 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.04910 | + | 1.81709i | 0.0565637 | + | 0.0979711i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0302247 | + | 0.0523508i | −0.00162489 | + | 0.00281440i | ||||
\(347\) | 3.32489 | − | 5.75888i | 0.178490 | − | 0.309153i | −0.762874 | − | 0.646547i | \(-0.776212\pi\) |
0.941363 | + | 0.337394i | \(0.109546\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.71737 | + | 9.90278i | 0.306044 | + | 0.530083i | 0.977493 | − | 0.210967i | \(-0.0676613\pi\) |
−0.671449 | + | 0.741050i | \(0.734328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.2255 | 0.545018 | ||||||||
\(353\) | 11.0978 | + | 19.2220i | 0.590677 | + | 1.02308i | 0.994141 | + | 0.108087i | \(0.0344725\pi\) |
−0.403465 | + | 0.914995i | \(0.632194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.08414 | − | 8.80598i | 0.269838 | − | 0.467373i | ||||
\(356\) | 2.66866 | − | 4.62226i | 0.141439 | − | 0.244979i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.69686 | + | 2.93905i | 0.0896819 | + | 0.155334i | ||||
\(359\) | 7.55623 | 0.398803 | 0.199401 | − | 0.979918i | \(-0.436100\pi\) | ||||
0.199401 | + | 0.979918i | \(0.436100\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2255 | −0.801339 | ||||||||
\(362\) | −0.171149 | − | 0.296439i | −0.00899539 | − | 0.0155805i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.95254 | − | 15.5062i | 0.468597 | − | 0.811634i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.26157 | − | 16.0415i | −0.483450 | − | 0.837360i | 0.516370 | − | 0.856366i | \(-0.327283\pi\) |
−0.999819 | + | 0.0190063i | \(0.993950\pi\) | |||||||
\(368\) | 20.5081 | 1.06906 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.69794 | −0.140259 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.83009 | + | 13.5621i | −0.405427 | + | 0.702220i | −0.994371 | − | 0.105954i | \(-0.966210\pi\) |
0.588944 | + | 0.808174i | \(0.299544\pi\) | |||||||
\(374\) | 3.07442 | − | 5.32505i | 0.158974 | − | 0.275352i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.74759 | + | 4.75897i | 0.141696 | + | 0.245425i | ||||
\(377\) | 0.239123 | 0.0123155 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.03775 | 0.207405 | 0.103703 | − | 0.994608i | \(-0.466931\pi\) | ||||
0.103703 | + | 0.994608i | \(0.466931\pi\) | |||||||
\(380\) | −2.23065 | − | 3.86360i | −0.114430 | − | 0.198199i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.80150 | − | 3.12030i | 0.0921730 | − | 0.159648i | ||||
\(383\) | −0.112725 | + | 0.195246i | −0.00575998 | + | 0.00997659i | −0.868891 | − | 0.495003i | \(-0.835167\pi\) |
0.863131 | + | 0.504980i | \(0.168500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.87661 | −0.0955171 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.9267 | 0.707019 | ||||||||
\(389\) | 12.6316 | + | 21.8786i | 0.640448 | + | 1.10929i | 0.985333 | + | 0.170643i | \(0.0545844\pi\) |
−0.344885 | + | 0.938645i | \(0.612082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4503 | − | 33.6890i | 0.983646 | − | 1.70373i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.799870 | + | 1.38542i | 0.0402969 | + | 0.0697962i | ||||
\(395\) | 8.71986 | 0.438744 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3009 | 1.01888 | 0.509438 | − | 0.860508i | \(-0.329853\pi\) | ||||
0.509438 | + | 0.860508i | \(0.329853\pi\) | |||||||
\(398\) | −2.38401 | − | 4.12922i | −0.119499 | − | 0.206979i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.59385 | − | 11.4209i | 0.329693 | − | 0.571044i | ||||
\(401\) | −7.61273 | + | 13.1856i | −0.380161 | + | 0.658459i | −0.991085 | − | 0.133231i | \(-0.957465\pi\) |
0.610924 | + | 0.791689i | \(0.290798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.830095 | − | 1.43777i | −0.0413500 | − | 0.0716203i | ||||
\(404\) | 24.8389 | 1.23578 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.6774 | + | 30.6182i | 0.876238 | + | 1.51769i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.828460 | − | 1.43494i | 0.0409647 | − | 0.0709530i | −0.844816 | − | 0.535057i | \(-0.820290\pi\) |
0.885781 | + | 0.464104i | \(0.153624\pi\) | |||||||
\(410\) | 1.43886 | − | 2.49218i | 0.0710603 | − | 0.123080i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.27128 | + | 7.39807i | 0.210431 | + | 0.364477i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.20602 | −0.402818 | ||||||||
\(416\) | 1.38044 | + | 2.39099i | 0.0676816 | + | 0.117228i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.860320 | − | 1.49012i | 0.0420796 | − | 0.0728840i | ||||
\(419\) | −16.6871 | + | 28.9030i | −0.815220 | + | 1.41200i | 0.0939492 | + | 0.995577i | \(0.470051\pi\) |
−0.909170 | + | 0.416426i | \(0.863282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.12025 | − | 15.7967i | −0.444494 | − | 0.769886i | 0.553523 | − | 0.832834i | \(-0.313283\pi\) |
−0.998017 | + | 0.0629481i | \(0.979950\pi\) | |||||||
\(422\) | −4.32614 | −0.210593 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.9396 | −0.531272 | ||||||||
\(425\) | −12.5075 | − | 21.6637i | −0.606704 | − | 1.05084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −13.3353 | + | 23.0974i | −0.644586 | + | 1.11646i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.314490 | − | 0.544712i | −0.0151660 | − | 0.0262684i | ||||
\(431\) | −29.2826 | −1.41049 | −0.705247 | − | 0.708961i | \(-0.749164\pi\) | ||||
−0.705247 | + | 0.708961i | \(0.749164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2449 | 0.588451 | 0.294226 | − | 0.955736i | \(-0.404938\pi\) | ||||
0.294226 | + | 0.955736i | \(0.404938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.22708 | − | 2.12537i | 0.0587667 | − | 0.101787i | ||||
\(437\) | 5.44282 | − | 9.42724i | 0.260365 | − | 0.450966i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.41586 | − | 4.18440i | −0.115303 | − | 0.199711i | 0.802598 | − | 0.596520i | \(-0.203451\pi\) |
−0.917901 | + | 0.396810i | \(0.870117\pi\) | |||||||
\(440\) | −4.12725 | −0.196759 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.66019 | 0.0789672 | ||||||||
\(443\) | 0.622440 | + | 1.07810i | 0.0295730 | + | 0.0512220i | 0.880433 | − | 0.474170i | \(-0.157252\pi\) |
−0.850860 | + | 0.525392i | \(0.823919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.62352 | + | 2.81202i | −0.0769622 | + | 0.133302i | ||||
\(446\) | −2.70890 | + | 4.69195i | −0.128270 | + | 0.222170i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.82846 | −0.416641 | −0.208320 | − | 0.978061i | \(-0.566800\pi\) | ||||
−0.208320 | + | 0.978061i | \(0.566800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7108 | −1.77573 | ||||||||
\(452\) | −11.8148 | − | 20.4638i | −0.555721 | − | 0.962537i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.631600 | − | 1.09396i | 0.0296425 | − | 0.0513422i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.25404 | + | 9.10026i | 0.245774 | + | 0.425692i | 0.962349 | − | 0.271817i | \(-0.0876247\pi\) |
−0.716575 | + | 0.697510i | \(0.754291\pi\) | |||||||
\(458\) | −4.62382 | −0.216057 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.8662 | −0.599890 | ||||||||
\(461\) | −11.2758 | − | 19.5302i | −0.525166 | − | 0.909614i | −0.999570 | − | 0.0293073i | \(-0.990670\pi\) |
0.474404 | − | 0.880307i | \(-0.342663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.19850 | + | 9.00406i | −0.241595 | + | 0.418454i | −0.961169 | − | 0.275962i | \(-0.911004\pi\) |
0.719574 | + | 0.694416i | \(0.244337\pi\) | |||||||
\(464\) | 0.437618 | − | 0.757977i | 0.0203159 | − | 0.0351882i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.03022 | − | 3.51645i | −0.0940483 | − | 0.162897i | ||||
\(467\) | 13.3171 | 0.616242 | 0.308121 | − | 0.951347i | \(-0.400300\pi\) | ||||
0.308121 | + | 0.951347i | \(0.400300\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.823649 | − | 1.42660i | −0.0379921 | − | 0.0658043i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.22708 | − | 2.12537i | 0.0564812 | − | 0.0978282i | ||||
\(473\) | −4.12120 | + | 7.13812i | −0.189493 | + | 0.328211i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | − | 6.06218i | −0.160591 | − | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.03775 | −0.184682 | ||||||||
\(479\) | −7.26771 | − | 12.5880i | −0.332070 | − | 0.575163i | 0.650847 | − | 0.759209i | \(-0.274414\pi\) |
−0.982918 | + | 0.184046i | \(0.941080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.77292 | + | 8.26693i | −0.217626 | + | 0.376940i | ||||
\(482\) | 3.24557 | − | 5.62149i | 0.147832 | − | 0.256052i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.63968 | + | 4.57206i | 0.119985 | + | 0.207821i | ||||
\(485\) | −8.47249 | −0.384716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0539 | 0.591529 | 0.295765 | − | 0.955261i | \(-0.404426\pi\) | ||||
0.295765 | + | 0.955261i | \(0.404426\pi\) | |||||||
\(488\) | 3.58414 | + | 6.20790i | 0.162246 | + | 0.281019i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.67223 | − | 16.7528i | 0.436502 | − | 0.756043i | −0.560915 | − | 0.827873i | \(-0.689551\pi\) |
0.997417 | + | 0.0718303i | \(0.0228840\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.830095 | − | 1.43777i | −0.0373856 | − | 0.0647538i | ||||
\(494\) | 0.464574 | 0.0209022 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.07661 | −0.272848 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.1111 | − | 31.3693i | 0.810764 | − | 1.40428i | −0.101566 | − | 0.994829i | \(-0.532385\pi\) |
0.912330 | − | 0.409455i | \(-0.134281\pi\) | |||||||
\(500\) | −9.87756 | + | 17.1084i | −0.441738 | + | 0.765112i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.28100 | + | 3.95080i | 0.101806 | + | 0.176333i | ||||
\(503\) | 15.6764 | 0.698974 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.1111 | −0.672435 | ||||||||
\(506\) | −2.48113 | − | 4.29743i | −0.110299 | − | 0.191044i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.30150 | − | 2.25427i | 0.0577449 | − | 0.100017i | ||||
\(509\) | −17.1517 | + | 29.7076i | −0.760237 | + | 1.31677i | 0.182492 | + | 0.983207i | \(0.441584\pi\) |
−0.942729 | + | 0.333561i | \(0.891750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 17.0071 | 0.751616 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.54910 | −0.156544 | ||||||||
\(515\) | −2.59850 | − | 4.50073i | −0.114503 | − | 0.198326i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.7934 | + | 18.6948i | −0.474694 | + | 0.822195i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.557180 | − | 0.965064i | −0.0244340 | − | 0.0423209i | ||||
\(521\) | −10.2449 | −0.448836 | −0.224418 | − | 0.974493i | \(-0.572048\pi\) | ||||
−0.224418 | + | 0.974493i | \(0.572048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6030 | −1.33818 | −0.669088 | − | 0.743183i | \(-0.733315\pi\) | ||||
−0.669088 | + | 0.743183i | \(0.733315\pi\) | |||||||
\(524\) | −4.82489 | − | 8.35696i | −0.210776 | − | 0.365075i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.925580 | + | 1.60315i | −0.0403572 | + | 0.0699007i | ||||
\(527\) | −5.76320 | + | 9.98215i | −0.251049 | + | 0.434829i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.19686 | − | 7.26918i | −0.182472 | − | 0.316051i | ||||
\(530\) | 3.27936 | 0.142446 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.09097 | − | 8.81782i | −0.220514 | − | 0.381942i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.11273 | − | 14.0517i | 0.350744 | − | 0.607506i | ||||
\(536\) | 1.65374 | − | 2.86437i | 0.0714309 | − | 0.123722i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.180699 | + | 0.312981i | 0.00779051 | + | 0.0134936i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0917 | −1.12177 | −0.560884 | − | 0.827894i | \(-0.689539\pi\) | ||||
−0.560884 | + | 0.827894i | \(0.689539\pi\) | |||||||
\(542\) | −2.62803 | − | 4.55189i | −0.112884 | − | 0.195520i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.58414 | − | 16.6002i | 0.410916 | − | 0.711728i | ||||
\(545\) | −0.746515 | + | 1.29300i | −0.0319772 | + | 0.0553861i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.46169 | + | 9.45993i | 0.233525 | + | 0.404478i | 0.958843 | − | 0.283937i | \(-0.0916405\pi\) |
−0.725318 | + | 0.688414i | \(0.758307\pi\) | |||||||
\(548\) | −8.43147 | −0.360175 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.19097 | −0.136063 | ||||||||
\(551\) | −0.232287 | − | 0.402332i | −0.00989575 | − | 0.0171399i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.29467 | − | 2.24243i | 0.0550052 | − | 0.0952718i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.83009 | − | 6.63392i | −0.162432 | − | 0.281341i | ||||
\(557\) | 13.9442 | 0.590835 | 0.295417 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295417 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.22545 | −0.0941265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.01780 | + | 3.49492i | −0.0851156 | + | 0.147424i | ||||
\(563\) | −15.1287 | + | 26.2037i | −0.637600 | + | 1.10435i | 0.348358 | + | 0.937361i | \(0.386739\pi\) |
−0.985958 | + | 0.166993i | \(0.946594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.18770 | + | 12.4495i | 0.302389 | + | 0.523753i | ||||
\(566\) | 3.66268 | 0.153954 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.11109 | 0.340334 | ||||||||
\(569\) | −10.5676 | − | 18.3036i | −0.443016 | − | 0.767326i | 0.554896 | − | 0.831920i | \(-0.312758\pi\) |
−0.997912 | + | 0.0645936i | \(0.979425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.3932 | − | 28.3938i | 0.686033 | − | 1.18824i | −0.287078 | − | 0.957907i | \(-0.592684\pi\) |
0.973111 | − | 0.230336i | \(-0.0739826\pi\) | |||||||
\(572\) | −3.59781 | + | 6.23159i | −0.150432 | + | 0.260556i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.1877 | −0.841885 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3743 | 0.723301 | 0.361651 | − | 0.932314i | \(-0.382213\pi\) | ||||
0.361651 | + | 0.932314i | \(0.382213\pi\) | |||||||
\(578\) | −3.73065 | − | 6.46168i | −0.155175 | − | 0.268770i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.274550 | + | 0.475534i | −0.0114001 | + | 0.0197455i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.4870 | − | 37.2166i | −0.889901 | − | 1.54135i | ||||
\(584\) | 14.2826 | 0.591019 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.24050 | −0.0925542 | ||||||||
\(587\) | −8.48796 | − | 14.7016i | −0.350336 | − | 0.606799i | 0.635973 | − | 0.771712i | \(-0.280599\pi\) |
−0.986308 | + | 0.164913i | \(0.947266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.61273 | + | 2.79332i | −0.0664512 | + | 0.115097i | ||||
\(590\) | −0.367845 | + | 0.637125i | −0.0151439 | + | 0.0262300i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.4698 | + | 30.2585i | 0.718003 | + | 1.24362i | ||||
\(593\) | −13.0733 | −0.536858 | −0.268429 | − | 0.963300i | \(-0.586504\pi\) | ||||
−0.268429 | + | 0.963300i | \(0.586504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.7934 | − | 18.6948i | −0.442116 | − | 0.765767i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.669905 | − | 1.16031i | 0.0273945 | − | 0.0474486i | ||||
\(599\) | 14.6030 | − | 25.2932i | 0.596663 | − | 1.03345i | −0.396647 | − | 0.917971i | \(-0.629826\pi\) |
0.993310 | − | 0.115479i | \(-0.0368403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.89536 | + | 6.74695i | 0.158895 | + | 0.275214i | 0.934470 | − | 0.356041i | \(-0.115874\pi\) |
−0.775576 | + | 0.631255i | \(0.782540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.0506 | −1.10067 | ||||||||
\(605\) | −1.60589 | − | 2.78148i | −0.0652887 | − | 0.113083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.82038 | + | 17.0094i | −0.398597 | + | 0.690390i | −0.993553 | − | 0.113368i | \(-0.963836\pi\) |
0.594956 | + | 0.803758i | \(0.297169\pi\) | |||||||
\(608\) | 2.68194 | − | 4.64526i | 0.108767 | − | 0.188390i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.07442 | − | 1.86095i | −0.0435020 | − | 0.0753477i | ||||
\(611\) | −5.82846 | −0.235794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5653 | 0.951792 | 0.475896 | − | 0.879502i | \(-0.342124\pi\) | ||||
0.475896 | + | 0.879502i | \(0.342124\pi\) | |||||||
\(614\) | 0.324502 | + | 0.562054i | 0.0130958 | + | 0.0226827i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.33009 | + | 9.23200i | −0.214582 | + | 0.371666i | −0.953143 | − | 0.302520i | \(-0.902172\pi\) |
0.738562 | + | 0.674186i | \(0.235505\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.00752 | − | 15.6015i | −0.362043 | − | 0.627077i | 0.626254 | − | 0.779619i | \(-0.284587\pi\) |
−0.988297 | + | 0.152542i | \(0.951254\pi\) | |||||||
\(620\) | 3.81230 | 0.153106 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.34308 | −0.134045 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.99837 | + | 5.19332i | −0.119935 | + | 0.207733i | ||||
\(626\) | −2.27812 | + | 3.94581i | −0.0910519 | + | 0.157706i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0555452 | − | 0.0962071i | −0.00221649 | − | 0.00383908i | ||||
\(629\) | 66.2750 | 2.64256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4703 | 0.496436 | 0.248218 | − | 0.968704i | \(-0.420155\pi\) | ||||
0.248218 | + | 0.968704i | \(0.420155\pi\) | |||||||
\(632\) | 3.47786 | + | 6.02382i | 0.138342 | + | 0.239615i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.480570 | + | 0.832371i | −0.0190859 | + | 0.0330577i | ||||
\(635\) | −0.791790 | + | 1.37142i | −0.0314212 | + | 0.0544232i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.211777 | −0.00838434 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.40877 | −0.332386 | ||||||||
\(641\) | 9.57279 | + | 16.5806i | 0.378102 | + | 0.654892i | 0.990786 | − | 0.135436i | \(-0.0432434\pi\) |
−0.612684 | + | 0.790328i | \(0.709910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.24433 | − | 5.61934i | 0.127944 | − | 0.221605i | −0.794936 | − | 0.606693i | \(-0.792496\pi\) |
0.922880 | + | 0.385088i | \(0.125829\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.61273 | − | 2.79332i | −0.0634518 | − | 0.109902i | ||||
\(647\) | −48.0988 | −1.89096 | −0.945479 | − | 0.325682i | \(-0.894406\pi\) | ||||
−0.945479 | + | 0.325682i | \(0.894406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.64076 | 0.378433 | ||||||||
\(650\) | −0.430782 | − | 0.746136i | −0.0168967 | − | 0.0292659i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.46496 | + | 2.53739i | −0.0573724 | + | 0.0993720i | ||||
\(653\) | −21.6202 | + | 37.4474i | −0.846066 | + | 1.46543i | 0.0386267 | + | 0.999254i | \(0.487702\pi\) |
−0.884692 | + | 0.466175i | \(0.845632\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.93530 | + | 5.08408i | 0.114691 | + | 0.198651i | ||||
\(656\) | −37.2678 | −1.45506 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.25404 | − | 2.17206i | −0.0488505 | − | 0.0846115i | 0.840566 | − | 0.541709i | \(-0.182222\pi\) |
−0.889417 | + | 0.457097i | \(0.848889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.1677 | + | 36.6636i | −0.823329 | + | 1.42605i | 0.0798613 | + | 0.996806i | \(0.474552\pi\) |
−0.903190 | + | 0.429241i | \(0.858781\pi\) | |||||||
\(662\) | 1.47988 | − | 2.56323i | 0.0575172 | − | 0.0996227i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.27292 | − | 5.66886i | −0.127014 | − | 0.219994i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.33981 | −0.0518777 | ||||||||
\(668\) | −14.2644 | − | 24.7067i | −0.551908 | − | 0.955933i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.495745 | + | 0.858655i | −0.0191523 | + | 0.0331727i | ||||
\(671\) | −14.0796 | + | 24.3866i | −0.543538 | + | 0.941435i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.70765 | − | 11.6180i | −0.258561 | − | 0.447841i | 0.707296 | − | 0.706918i | \(-0.249915\pi\) |
−0.965857 | + | 0.259077i | \(0.916582\pi\) | |||||||
\(674\) | 2.93163 | 0.112922 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.3138 | 0.896686 | ||||||||
\(677\) | −0.981125 | − | 1.69936i | −0.0377077 | − | 0.0653117i | 0.846556 | − | 0.532300i | \(-0.178672\pi\) |
−0.884263 | + | 0.466989i | \(0.845339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.86840 | + | 6.70027i | −0.148346 | + | 0.256943i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.735165 | + | 1.27334i | 0.0281509 | + | 0.0487589i | ||||
\(683\) | −27.1672 | −1.03952 | −0.519761 | − | 0.854312i | \(-0.673979\pi\) | ||||
−0.519761 | + | 0.854312i | \(0.673979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.12941 | 0.195985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.07279 | + | 7.05427i | −0.155273 | + | 0.268942i | ||||
\(689\) | 5.80150 | − | 10.0485i | 0.221020 | − | 0.382817i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1586 | − | 43.5759i | −0.957077 | − | 1.65771i | −0.729543 | − | 0.683935i | \(-0.760267\pi\) |
−0.227534 | − | 0.973770i | \(-0.573066\pi\) | |||||||
\(692\) | −0.491138 | −0.0186703 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.59012 | −0.0603601 | ||||||||
\(695\) | 2.33009 | + | 4.03584i | 0.0883855 | + | 0.153088i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.3457 | + | 61.2205i | −1.33881 | + | 2.31889i | ||||
\(698\) | 1.36716 | − | 2.36798i | 0.0517476 | − | 0.0896295i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.1672 | −1.70594 | −0.852970 | − | 0.521960i | \(-0.825201\pi\) | ||||
−0.852970 | + | 0.521960i | \(0.825201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5458 | 0.699469 | ||||||||
\(704\) | 12.3337 | + | 21.3625i | 0.464842 | + | 0.805131i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.65374 | − | 4.59642i | 0.0998750 | − | 0.172989i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.8090 | − | 34.3102i | −0.743944 | − | 1.28855i | −0.950687 | − | 0.310153i | \(-0.899620\pi\) |
0.206743 | − | 0.978395i | \(-0.433714\pi\) | |||||||
\(710\) | −2.43147 | −0.0912514 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.59012 | −0.0970688 | ||||||||
\(713\) | 4.65103 | + | 8.05582i | 0.174182 | + | 0.301693i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.18878 | − | 3.79108i | 0.0818557 | − | 0.141778i | ||||
\(716\) | −13.7866 | + | 23.8791i | −0.515229 | + | 0.892403i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.903436 | − | 1.56480i | −0.0337159 | − | 0.0583977i | ||||
\(719\) | −22.0377 | −0.821869 | −0.410935 | − | 0.911665i | \(-0.634798\pi\) | ||||
−0.410935 | + | 0.911665i | \(0.634798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.82038 | + | 3.15299i | 0.0677475 | + | 0.117342i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.39054 | − | 2.40849i | 0.0516792 | − | 0.0895110i | ||||
\(725\) | −0.430782 | + | 0.746136i | −0.0159988 | + | 0.0277108i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0555 | + | 24.3449i | 0.521291 | + | 0.902903i | 0.999693 | + | 0.0247621i | \(0.00788284\pi\) |
−0.478402 | + | 0.878141i | \(0.658784\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.28152 | −0.158466 | ||||||||
\(731\) | 7.72545 | + | 13.3809i | 0.285736 | + | 0.494909i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.93474 | − | 10.2793i | 0.219205 | − | 0.379674i | −0.735360 | − | 0.677676i | \(-0.762987\pi\) |
0.954565 | + | 0.298003i | \(0.0963204\pi\) | |||||||
\(734\) | −2.21466 | + | 3.83590i | −0.0817444 | + | 0.141586i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.73461 | − | 13.3967i | −0.285102 | − | 0.493810i | ||||
\(737\) | 12.9929 | 0.478598 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.1844 | −0.448212 | −0.224106 | − | 0.974565i | \(-0.571946\pi\) | ||||
−0.224106 | + | 0.974565i | \(0.571946\pi\) | |||||||
\(740\) | −10.9601 | − | 18.9834i | −0.402900 | − | 0.697843i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2427 | + | 38.5255i | −0.816005 | + | 1.41336i | 0.0925987 | + | 0.995704i | \(0.470483\pi\) |
−0.908604 | + | 0.417659i | \(0.862851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.56634 | + | 11.3732i | 0.240572 | + | 0.416683i | ||||
\(746\) | 3.74472 | 0.137104 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 49.9579 | 1.82664 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.4029 | + | 37.0709i | −0.781002 | + | 1.35274i | 0.150356 | + | 0.988632i | \(0.451958\pi\) |
−0.931358 | + | 0.364104i | \(0.881375\pi\) | |||||||
\(752\) | −10.6666 | + | 18.4752i | −0.388972 | + | 0.673720i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0285900 | − | 0.0495193i | −0.00104119 | − | 0.00180339i | ||||
\(755\) | 16.4567 | 0.598919 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4919 | −0.817483 | −0.408741 | − | 0.912650i | \(-0.634032\pi\) | ||||
−0.408741 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(758\) | −0.482760 | − | 0.836165i | −0.0175346 | − | 0.0303709i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.08250 | + | 1.87495i | −0.0392664 | + | 0.0680114i | ||||
\(761\) | 7.16827 | − | 12.4158i | 0.259850 | − | 0.450073i | −0.706352 | − | 0.707861i | \(-0.749660\pi\) |
0.966201 | + | 0.257788i | \(0.0829937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 29.2736 | 1.05908 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.0539104 | 0.00194786 | ||||||||
\(767\) | 1.30150 | + | 2.25427i | 0.0469946 | + | 0.0813971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.6105 | + | 27.0382i | −0.562930 | + | 0.975024i | 0.434309 | + | 0.900764i | \(0.356993\pi\) |
−0.997239 | + | 0.0742597i | \(0.976341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.62352 | − | 13.2043i | −0.274376 | − | 0.475234i | ||||
\(773\) | 4.38005 | 0.157539 | 0.0787697 | − | 0.996893i | \(-0.474901\pi\) | ||||
0.0787697 | + | 0.996893i | \(0.474901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.98168 | 0.214868 | ||||||||
\(776\) | −3.37919 | − | 5.85294i | −0.121306 | − | 0.210108i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.02051 | − | 5.23168i | 0.108291 | − | 0.187565i | ||||
\(779\) | −9.89084 | + | 17.1314i | −0.354376 | + | 0.613798i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.9315 | + | 27.5941i | 0.570073 | + | 0.987395i | ||||
\(782\) | −9.30206 | −0.332641 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0337917 | + | 0.0585290i | 0.00120608 | + | 0.00208899i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8107 | − | 23.9208i | 0.492297 | − | 0.852683i | −0.507664 | − | 0.861555i | \(-0.669491\pi\) |
0.999961 | + | 0.00887191i | \(0.00282405\pi\) | |||||||
\(788\) | −6.49876 | + | 11.2562i | −0.231509 | + | 0.400985i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.04256 | − | 1.80577i | −0.0370926 | − | 0.0642463i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.60301 | −0.269991 | ||||||||
\(794\) | −2.42721 | − | 4.20406i | −0.0861386 | − | 0.149196i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.3695 | − | 33.5489i | 0.686533 | − | 1.18911i | ||||
\(797\) | 1.48181 | − | 2.56658i | 0.0524885 | − | 0.0909128i | −0.838587 | − | 0.544767i | \(-0.816618\pi\) |
0.891076 | + | 0.453854i | \(0.149951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.2330 | + | 35.0445i | 0.715791 | + | 1.23979i | ||||
\(800\) | −9.94747 | −0.351696 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.64076 | 0.128560 | ||||||||
\(803\) | 28.0534 | + | 48.5898i | 0.989981 | + | 1.71470i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.198495 | + | 0.343803i | −0.00699169 | + | 0.0121100i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.02696 | − | 10.4390i | −0.212028 | − | 0.367242i | ||||
\(809\) | 24.7896 | 0.871556 | 0.435778 | − | 0.900054i | \(-0.356473\pi\) | ||||
0.435778 | + | 0.900054i | \(0.356473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.24377 | −0.289478 | −0.144739 | − | 0.989470i | \(-0.546234\pi\) | ||||
−0.144739 | + | 0.989470i | \(0.546234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.22708 | − | 7.32153i | 0.148159 | − | 0.256619i | ||||
\(815\) | 0.891233 | − | 1.54366i | 0.0312185 | − | 0.0540721i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.16182 | + | 3.74439i | 0.0756327 | + | 0.131000i | ||||
\(818\) | −0.396208 | −0.0138531 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.3808 | 0.816494 | ||||||||
\(821\) | −14.4497 | − | 25.0275i | −0.504296 | − | 0.873467i | −0.999988 | − | 0.00496829i | \(-0.998419\pi\) |
0.495691 | − | 0.868499i | \(-0.334915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.0000 | − | 31.1769i | 0.627441 | − | 1.08676i | −0.360623 | − | 0.932712i | \(-0.617436\pi\) |
0.988063 | − | 0.154047i | \(-0.0492308\pi\) | |||||||
\(824\) | 2.07279 | − | 3.59017i | 0.0722089 | − | 0.125069i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.7108 | 1.76339 | 0.881694 | − | 0.471821i | \(-0.156403\pi\) | ||||
0.881694 | + | 0.471821i | \(0.156403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.8123 | −0.514452 | −0.257226 | − | 0.966351i | \(-0.582809\pi\) | ||||
−0.257226 | + | 0.966351i | \(0.582809\pi\) | |||||||
\(830\) | 0.981125 | + | 1.69936i | 0.0340554 | + | 0.0589856i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.33009 | + | 5.76789i | −0.115450 | + | 0.199966i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.67799 | + | 15.0307i | 0.300314 | + | 0.520159i | ||||
\(836\) | 13.9798 | 0.483501 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.98057 | 0.275684 | ||||||||
\(839\) | −16.8606 | − | 29.2034i | −0.582093 | − | 1.00821i | −0.995231 | − | 0.0975464i | \(-0.968901\pi\) |
0.413138 | − | 0.910669i | \(-0.364433\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4714 | − | 25.0652i | 0.499014 | − | 0.864318i | ||||
\(842\) | −2.18086 | + | 3.77737i | −0.0751575 | + | 0.130177i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.5744 | − | 30.4398i | −0.604936 | − | 1.04778i | ||||
\(845\) | −14.1833 | −0.487921 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −21.2346 | − | 36.7794i | −0.729199 | − | 1.26301i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.99084 | + | 5.18029i | −0.102585 | + | 0.177682i | ||||
\(851\) | 26.7427 | − | 46.3197i | 0.916728 | − | 1.58782i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.89480 | + | 10.2101i | 0.201834 | + | 0.349587i | 0.949119 | − | 0.314916i | \(-0.101976\pi\) |
−0.747285 | + | 0.664503i | \(0.768643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.9428 | 0.442376 | ||||||||
\(857\) | 15.6631 | + | 27.1292i | 0.535040 | + | 0.926717i | 0.999161 | + | 0.0409451i | \(0.0130369\pi\) |
−0.464121 | + | 0.885772i | \(0.653630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.1947 | + | 43.6384i | −0.859631 | + | 1.48892i | 0.0126501 | + | 0.999920i | \(0.495973\pi\) |
−0.872281 | + | 0.489005i | \(0.837360\pi\) | |||||||
\(860\) | 2.55515 | − | 4.42566i | 0.0871300 | − | 0.150914i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.50108 | + | 6.06405i | 0.119247 | + | 0.206542i | ||||
\(863\) | −1.13268 | −0.0385568 | −0.0192784 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192784 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.298791 | 0.0101592 | ||||||||
\(866\) | −1.46402 | − | 2.53575i | −0.0497494 | − | 0.0861684i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.6621 | + | 23.6635i | −0.463456 | + | 0.802729i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.75404 | + | 3.03809i | 0.0594334 | + | 0.102942i | ||||
\(872\) | −1.19097 | −0.0403313 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.60301 | −0.0880481 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.6969 | − | 23.7237i | 0.462510 | − | 0.801091i | −0.536575 | − | 0.843853i | \(-0.680282\pi\) |
0.999085 | + | 0.0427615i | \(0.0136156\pi\) | |||||||
\(878\) | −0.577690 | + | 1.00059i | −0.0194961 | + | 0.0337682i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.01135 | − | 13.8761i | −0.270063 | − | 0.467762i | ||||
\(881\) | 1.20929 | 0.0407420 | 0.0203710 | − | 0.999792i | \(-0.493515\pi\) | ||||
0.0203710 | + | 0.999792i | \(0.493515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.0884 | −1.71926 | −0.859631 | − | 0.510916i | \(-0.829306\pi\) | ||||
−0.859631 | + | 0.510916i | \(0.829306\pi\) | |||||||
\(884\) | 6.74433 | + | 11.6815i | 0.226836 | + | 0.392892i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.148840 | − | 0.257798i | 0.00500038 | − | 0.00866091i | ||||
\(887\) | 20.7878 | − | 36.0056i | 0.697987 | − | 1.20895i | −0.271176 | − | 0.962530i | \(-0.587413\pi\) |
0.969163 | − | 0.246419i | \(-0.0792541\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.776443 | 0.0260264 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −44.0183 | −1.47384 | ||||||||
\(893\) | 5.66182 | + | 9.80657i | 0.189466 | + | 0.328164i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.38727 | − | 14.5272i | 0.280356 | − | 0.485590i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.05555 | + | 1.82826i | 0.0352240 | + | 0.0610098i | ||||
\(899\) | 0.396990 | 0.0132404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −80.5576 | −2.68376 | ||||||||
\(902\) | 4.50877 | + | 7.80942i | 0.150126 | + | 0.260025i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.73353 | + | 9.93077i | −0.190694 | + | 0.330292i | ||||
\(905\) | −0.845958 | + | 1.46524i | −0.0281206 | + | 0.0487063i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.7255 | − | 30.7014i | −0.588564 | − | 1.01942i | −0.994421 | − | 0.105486i | \(-0.966360\pi\) |
0.405857 | − | 0.913937i | \(-0.366973\pi\) | |||||||
\(908\) | 10.2632 | 0.340596 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3554 | − | 17.9361i | −0.343090 | − | 0.594250i | 0.641915 | − | 0.766776i | \(-0.278140\pi\) |
−0.985005 | + | 0.172526i | \(0.944807\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.8571 | − | 22.2691i | 0.425506 | − | 0.736998i | ||||
\(914\) | 1.25636 | − | 2.17609i | 0.0415568 | − | 0.0719785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.7837 | − | 32.5343i | −0.620631 | − | 1.07496i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.3926 | 0.474768 | 0.237384 | − | 0.971416i | \(-0.423710\pi\) | ||||
0.237384 | + | 0.971416i | \(0.423710\pi\) | |||||||
\(920\) | 3.12188 | + | 5.40726i | 0.102925 | + | 0.178272i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.69630 | + | 4.67014i | −0.0887981 | + | 0.153803i | ||||
\(923\) | −4.30150 | + | 7.45043i | −0.141586 | + | 0.245234i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1969 | − | 29.7858i | −0.565429 | − | 0.979352i | ||||
\(926\) | 2.48616 | 0.0817004 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.660190 | −0.0216718 | ||||||||
\(929\) | 20.8714 | + | 36.1503i | 0.684769 | + | 1.18605i | 0.973509 | + | 0.228647i | \(0.0734302\pi\) |
−0.288741 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.4951 | − | 28.5703i | 0.540315 | − | 0.935853i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.59222 | − | 2.75780i | −0.0520989 | − | 0.0902379i | ||||
\(935\) | −30.3926 | −0.993945 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.17154 | −0.103610 | −0.0518048 | − | 0.998657i | \(-0.516497\pi\) | ||||
−0.0518048 | + | 0.998657i | \(0.516497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.69196 | − | 11.5908i | 0.218268 | − | 0.378050i | ||||
\(941\) | 1.61040 | − | 2.78930i | 0.0524976 | − | 0.0909285i | −0.838582 | − | 0.544775i | \(-0.816615\pi\) |
0.891080 | + | 0.453846i | \(0.149948\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.5248 | + | 49.4063i | 0.928894 | + | 1.60889i | ||||
\(944\) | 9.52751 | 0.310094 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.97095 | 0.0640810 | ||||||||
\(947\) | −22.6735 | − | 39.2716i | −0.736789 | − | 1.27616i | −0.953934 | − | 0.300016i | \(-0.903008\pi\) |
0.217145 | − | 0.976139i | \(-0.430325\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.57442 | + | 13.1193i | −0.245876 | + | 0.425870i | ||||
\(950\) | −0.836931 | + | 1.44961i | −0.0271536 | + | 0.0470315i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.2703 | 1.75799 | 0.878994 | − | 0.476832i | \(-0.158215\pi\) | ||||
0.878994 | + | 0.476832i | \(0.158215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8090 | −0.576287 | ||||||||
\(956\) | −16.4029 | − | 28.4106i | −0.530507 | − | 0.918865i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.73788 | + | 3.01010i | −0.0561483 | + | 0.0972518i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1219 | + | 24.4598i | 0.455545 | + | 0.789027i | ||||
\(962\) | 2.28263 | 0.0735950 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 52.7390 | 1.69861 | ||||||||
\(965\) | 4.63788 | + | 8.03305i | 0.149299 | + | 0.258593i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8295 | + | 22.2214i | −0.412570 | + | 0.714593i | −0.995170 | − | 0.0981667i | \(-0.968702\pi\) |
0.582600 | + | 0.812759i | \(0.302036\pi\) | |||||||
\(968\) | 1.28100 | − | 2.21875i | 0.0411728 | − | 0.0713133i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.01298 | + | 1.75454i | 0.0325250 | + | 0.0563349i | ||||
\(971\) | −21.0183 | −0.674510 | −0.337255 | − | 0.941413i | \(-0.609498\pi\) | ||||
−0.337255 | + | 0.941413i | \(0.609498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.56075 | − | 2.70329i | −0.0500096 | − | 0.0866191i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.9142 | + | 24.1002i | −0.445384 | + | 0.771427i | ||||
\(977\) | −1.04910 | + | 1.81709i | −0.0335637 | + | 0.0581340i | −0.882319 | − | 0.470651i | \(-0.844019\pi\) |
0.848756 | + | 0.528785i | \(0.177352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.08740 | − | 8.81164i | −0.162594 | − | 0.281621i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.62571 | −0.147612 | ||||||||
\(983\) | −21.4962 | − | 37.2325i | −0.685622 | − | 1.18753i | −0.973241 | − | 0.229787i | \(-0.926197\pi\) |
0.287620 | − | 0.957745i | \(-0.407136\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.95361 | − | 6.84786i | 0.125973 | − | 0.218191i | ||||
\(986\) | −0.198495 | + | 0.343803i | −0.00632137 | + | 0.0109489i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.88727 | + | 3.26886i | 0.0600422 | + | 0.103996i | ||||
\(989\) | 12.4692 | 0.396498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.2632 | −0.548384 | −0.274192 | − | 0.961675i | \(-0.588410\pi\) | ||||
−0.274192 | + | 0.961675i | \(0.588410\pi\) | |||||||
\(992\) | 2.29179 | + | 3.96950i | 0.0727644 | + | 0.126032i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.7837 | + | 20.4100i | −0.373569 | + | 0.647040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.4509 | − | 33.6899i | −0.616016 | − | 1.06697i | −0.990205 | − | 0.139619i | \(-0.955412\pi\) |
0.374189 | − | 0.927352i | \(-0.377921\pi\) | |||||||
\(998\) | −8.66157 | −0.274177 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))