Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (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 | 667.2 | ||
Root | \(0.500000 + 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.667 |
Dual form | 1323.2.g.c.361.2 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(5\) | −1.18194 | −0.528581 | −0.264291 | − | 0.964443i | \(-0.585138\pi\) | ||||
−0.264291 | + | 0.964443i | \(0.585138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.942820 | −0.333337 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.141315 | + | 0.244765i | 0.0446878 | + | 0.0774015i | ||||
\(11\) | 3.70370 | 1.11671 | 0.558353 | − | 0.829603i | \(-0.311433\pi\) | ||||
0.558353 | + | 0.829603i | \(0.311433\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.83009 | − | 3.16982i | −0.457524 | − | 0.792454i | ||||
\(17\) | −3.47141 | − | 6.01266i | −0.841941 | − | 1.45828i | −0.888252 | − | 0.459357i | \(-0.848080\pi\) |
0.0463112 | − | 0.998927i | \(-0.485253\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.971410 | + | 1.68253i | −0.222857 | + | 0.385999i | −0.955674 | − | 0.294426i | \(-0.904872\pi\) |
0.732818 | + | 0.680425i | \(0.238205\pi\) | |||||||
\(20\) | −1.14815 | + | 1.98866i | −0.256735 | + | 0.444677i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.442820 | − | 0.766987i | −0.0944096 | − | 0.163522i | ||||
\(23\) | 5.60301 | 1.16831 | 0.584154 | − | 0.811643i | \(-0.301426\pi\) | ||||
0.584154 | + | 0.811643i | \(0.301426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.60301 | −0.720602 | ||||||||
\(26\) | −0.119562 | + | 0.207087i | −0.0234480 | + | 0.0406131i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.119562 | − | 0.207087i | 0.0222020 | − | 0.0384551i | −0.854711 | − | 0.519104i | \(-0.826266\pi\) |
0.876913 | + | 0.480649i | \(0.159599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.830095 | + | 1.43777i | −0.149089 | + | 0.258231i | −0.930891 | − | 0.365297i | \(-0.880968\pi\) |
0.781802 | + | 0.623527i | \(0.214301\pi\) | |||||||
\(32\) | −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 | ||||||||
\(37\) | 4.77292 | − | 8.26693i | 0.784662 | − | 1.35908i | −0.144538 | − | 0.989499i | \(-0.546170\pi\) |
0.929201 | − | 0.369576i | \(-0.120497\pi\) | |||||||
\(38\) | 0.464574 | 0.0753638 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.11436 | 0.176196 | ||||||||
\(41\) | −5.09097 | − | 8.81782i | −0.795076 | − | 1.37711i | −0.922791 | − | 0.385301i | \(-0.874097\pi\) |
0.127715 | − | 0.991811i | \(-0.459236\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.11273 | + | 1.92730i | −0.169689 | + | 0.293910i | −0.938311 | − | 0.345794i | \(-0.887610\pi\) |
0.768622 | + | 0.639704i | \(0.220943\pi\) | |||||||
\(44\) | 3.59781 | − | 6.23159i | 0.542390 | − | 0.939447i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.669905 | − | 1.16031i | −0.0987721 | − | 0.171078i | ||||
\(47\) | 2.91423 | + | 5.04759i | 0.425084 | + | 0.736267i | 0.996428 | − | 0.0844432i | \(-0.0269112\pi\) |
−0.571344 | + | 0.820711i | \(0.693578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.430782 | + | 0.746136i | 0.0609217 | + | 0.105520i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.94282 | −0.269421 | ||||||||
\(53\) | −5.80150 | − | 10.0485i | −0.796898 | − | 1.38027i | −0.921627 | − | 0.388077i | \(-0.873139\pi\) |
0.124729 | − | 0.992191i | \(-0.460194\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.37756 | −0.590270 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0571799 | −0.00750809 | ||||||||
\(59\) | 1.30150 | − | 2.25427i | 0.169442 | − | 0.293481i | −0.768782 | − | 0.639511i | \(-0.779137\pi\) |
0.938224 | + | 0.346029i | \(0.112470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.80150 | + | 6.58440i | 0.486733 | + | 0.843046i | 0.999884 | − | 0.0152524i | \(-0.00485519\pi\) |
−0.513151 | + | 0.858298i | \(0.671522\pi\) | |||||||
\(62\) | 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 | \(0.235410\pi\) | |||||||
\(68\) | −13.4887 | −1.63574 | ||||||||
\(69\) | 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 | ||||||||
\(73\) | −7.57442 | − | 13.1193i | −0.886519 | − | 1.53550i | −0.843963 | − | 0.536402i | \(-0.819783\pi\) |
−0.0425559 | − | 0.999094i | \(-0.513550\pi\) | |||||||
\(74\) | −2.28263 | −0.265350 | ||||||||
\(75\) | 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 | \(0.969559\pi\) | |||||||
\(80\) | 2.16307 | + | 3.74654i | 0.241838 | + | 0.418876i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.21737 | + | 2.10855i | −0.134436 | + | 0.232850i | ||||
\(83\) | −3.47141 | + | 6.01266i | −0.381037 | + | 0.659975i | −0.991211 | − | 0.132292i | \(-0.957766\pi\) |
0.610174 | + | 0.792267i | \(0.291100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.10301 | + | 7.10662i | 0.445034 | + | 0.770821i | ||||
\(86\) | 0.532157 | 0.0573840 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.49192 | −0.372240 | ||||||||
\(89\) | 1.37360 | − | 2.37915i | 0.145602 | − | 0.252189i | −0.783996 | − | 0.620766i | \(-0.786822\pi\) |
0.929597 | + | 0.368577i | \(0.120155\pi\) | |||||||
\(90\) | 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 | \(-0.951893\pi\) |
0.624687 | + | 0.780875i | \(0.285226\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.50000 | + | 6.06218i | −0.350000 | + | 0.606218i | ||||
\(101\) | 12.7850 | 1.27215 | 0.636075 | − | 0.771627i | \(-0.280557\pi\) | ||||
0.636075 | + | 0.771627i | \(0.280557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.39699 | −0.433248 | −0.216624 | − | 0.976255i | \(-0.569505\pi\) | ||||
−0.216624 | + | 0.976255i | \(0.569505\pi\) | |||||||
\(104\) | 0.471410 | + | 0.816506i | 0.0462256 | + | 0.0800650i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.38727 | + | 2.40283i | −0.134744 | + | 0.233384i | ||||
\(107\) | 6.86389 | − | 11.8886i | 0.663557 | − | 1.14931i | −0.316117 | − | 0.948720i | \(-0.602379\pi\) |
0.979674 | − | 0.200594i | \(-0.0642873\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.631600 | − | 1.09396i | −0.0604963 | − | 0.104783i | 0.834191 | − | 0.551476i | \(-0.185935\pi\) |
−0.894687 | + | 0.446693i | \(0.852602\pi\) | |||||||
\(110\) | 0.523388 | + | 0.906535i | 0.0499031 | + | 0.0864347i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.08126 | + | 10.5330i | 0.572076 | + | 0.990866i | 0.996353 | + | 0.0853326i | \(0.0271953\pi\) |
−0.424276 | + | 0.905533i | \(0.639471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.62244 | −0.617546 | ||||||||
\(116\) | −0.232287 | − | 0.402332i | −0.0215673 | − | 0.0373556i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.622440 | −0.0573003 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.71737 | 0.247034 | ||||||||
\(122\) | 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 | ||||
\(131\) | 4.96690 | 0.433960 | 0.216980 | − | 0.976176i | \(-0.430379\pi\) | ||||
0.216980 | + | 0.976176i | \(0.430379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.838864 | 0.0724668 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.27292 | + | 5.66886i | 0.280650 | + | 0.486100i | ||||
\(137\) | 4.33981 | 0.370775 | 0.185387 | − | 0.982665i | \(-0.440646\pi\) | ||||
0.185387 | + | 0.982665i | \(0.440646\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.97141 | − | 3.41458i | −0.167213 | − | 0.289621i | 0.770226 | − | 0.637771i | \(-0.220143\pi\) |
−0.937439 | + | 0.348150i | \(0.886810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.02859 | + | 1.78157i | 0.0863174 | + | 0.149506i | ||||
\(143\) | −1.85185 | − | 3.20750i | −0.154859 | − | 0.268224i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.141315 | + | 0.244765i | −0.0117356 | + | 0.0203266i | ||||
\(146\) | −1.81122 | + | 3.13713i | −0.149898 | + | 0.259630i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.27292 | − | 16.0612i | −0.762229 | − | 1.32022i | ||||
\(149\) | −11.1111 | −0.910256 | −0.455128 | − | 0.890426i | \(-0.650406\pi\) | ||||
−0.455128 | + | 0.890426i | \(0.650406\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9234 | 1.13307 | 0.566535 | − | 0.824038i | \(-0.308284\pi\) | ||||
0.566535 | + | 0.824038i | \(0.308284\pi\) | |||||||
\(152\) | 0.915865 | − | 1.58632i | 0.0742864 | − | 0.128668i | ||||
\(153\) | 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 | −0.867164 | − | 0.498023i | \(-0.834060\pi\) |
0.864882 | + | 0.501975i | \(0.167393\pi\) | |||||||
\(158\) | −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 | ||||||||
\(163\) | 0.754040 | − | 1.30604i | 0.0590610 | − | 0.102297i | −0.834983 | − | 0.550276i | \(-0.814523\pi\) |
0.894044 | + | 0.447979i | \(0.147856\pi\) | |||||||
\(164\) | −19.7817 | −1.54469 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.66019 | 0.128856 | ||||||||
\(167\) | −7.34213 | − | 12.7169i | −0.568151 | − | 0.984067i | −0.996749 | − | 0.0805714i | \(-0.974325\pi\) |
0.428598 | − | 0.903496i | \(-0.359008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0.981125 | − | 1.69936i | 0.0752489 | − | 0.130335i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.16182 | + | 3.74439i | 0.164838 | + | 0.285507i | ||||
\(173\) | 0.126398 | + | 0.218928i | 0.00960987 | + | 0.0166448i | 0.870790 | − | 0.491655i | \(-0.163608\pi\) |
−0.861180 | + | 0.508299i | \(0.830274\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.77812 | − | 11.7400i | −0.510920 | − | 0.884939i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.656920 | −0.0492383 | ||||||||
\(179\) | 7.09617 | + | 12.2909i | 0.530393 | + | 0.918667i | 0.999371 | + | 0.0354578i | \(0.0112889\pi\) |
−0.468978 | + | 0.883210i | \(0.655378\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.43147 | −0.106400 | −0.0532002 | − | 0.998584i | \(-0.516942\pi\) | ||||
−0.0532002 | + | 0.998584i | \(0.516942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.28263 | −0.389441 | ||||||||
\(185\) | −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 | \(0.0755190\pi\) | |||||||
\(194\) | 1.71410 | 0.123065 | ||||||||
\(195\) | 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 | ||||||||
\(199\) | 9.96978 | + | 17.2682i | 0.706739 | + | 1.22411i | 0.966060 | + | 0.258316i | \(0.0831677\pi\) |
−0.259322 | + | 0.965791i | \(0.583499\pi\) | |||||||
\(200\) | 3.39699 | 0.240203 | ||||||||
\(201\) | 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 | ||||
\(206\) | 0.525711 | + | 0.910559i | 0.0366280 | + | 0.0634416i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.83009 | + | 3.16982i | −0.126894 | + | 0.219787i | ||||
\(209\) | −3.59781 | + | 6.23159i | −0.248866 | + | 0.431048i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.04583 | + | 15.6678i | 0.622741 | + | 1.07862i | 0.988973 | + | 0.148095i | \(0.0473141\pi\) |
−0.366233 | + | 0.930523i | \(0.619353\pi\) | |||||||
\(212\) | −22.5426 | −1.54823 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.28263 | −0.224396 | ||||||||
\(215\) | 1.31518 | − | 2.27796i | 0.0896944 | − | 0.155355i | ||||
\(216\) | 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 | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331203i | \(-0.107454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.45417 | − | 2.51870i | 0.0967299 | − | 0.167541i | ||||
\(227\) | 5.28263 | 0.350620 | 0.175310 | − | 0.984513i | \(-0.443907\pi\) | ||||
0.175310 | + | 0.984513i | \(0.443907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3365 | 1.27779 | 0.638897 | − | 0.769292i | \(-0.279391\pi\) | ||||
0.638897 | + | 0.769292i | \(0.279391\pi\) | |||||||
\(230\) | 0.791790 | + | 1.37142i | 0.0522091 | + | 0.0904288i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.112725 | + | 0.195246i | −0.00740077 | + | 0.0128185i | ||||
\(233\) | −8.49028 | + | 14.7056i | −0.556217 | + | 0.963396i | 0.441591 | + | 0.897217i | \(0.354414\pi\) |
−0.997808 | + | 0.0661796i | \(0.978919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.44445 | − | 5.96597i | −0.224691 | − | 0.389177i | ||||
\(236\) | −2.52859 | − | 4.37965i | −0.164597 | − | 0.285091i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.44282 | + | 14.6234i | 0.546121 | + | 0.945909i | 0.998535 | + | 0.0541011i | \(0.0172293\pi\) |
−0.452415 | + | 0.891808i | \(0.649437\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.1456 | 1.74860 | 0.874300 | − | 0.485386i | \(-0.161321\pi\) | ||||
0.874300 | + | 0.485386i | \(0.161321\pi\) | |||||||
\(242\) | −0.324893 | − | 0.562732i | −0.0208849 | − | 0.0361738i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.7713 | 0.945634 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.94282 | 0.123619 | ||||||||
\(248\) | 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 | \(-0.294332\pi\) | ||||
0.602096 | + | 0.798424i | \(0.294332\pi\) | |||||||
\(252\) | 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 | ||||
\(257\) | 14.8421 | 0.925827 | 0.462913 | − | 0.886404i | \(-0.346804\pi\) | ||||
0.462913 | + | 0.886404i | \(0.346804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.29630 | 0.142411 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.593850 | − | 1.02858i | −0.0366882 | − | 0.0635458i | ||||
\(263\) | 7.74145 | 0.477358 | 0.238679 | − | 0.971099i | \(-0.423286\pi\) | ||||
0.238679 | + | 0.971099i | \(0.423286\pi\) | |||||||
\(264\) | 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 | ||||
\(269\) | −0.755675 | − | 1.30887i | −0.0460743 | − | 0.0798031i | 0.842069 | − | 0.539371i | \(-0.181338\pi\) |
−0.888143 | + | 0.459567i | \(0.848004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9903 | − | 19.0357i | 0.667612 | − | 1.15634i | −0.310958 | − | 0.950424i | \(-0.600650\pi\) |
0.978570 | − | 0.205915i | \(-0.0660169\pi\) | |||||||
\(272\) | −12.7060 | + | 22.0075i | −0.770416 | + | 1.33440i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.518875 | − | 0.898718i | −0.0313464 | − | 0.0542935i | ||||
\(275\) | −13.3445 | −0.804701 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8285 | −0.650619 | −0.325310 | − | 0.945608i | \(-0.605469\pi\) | ||||
−0.325310 | + | 0.945608i | \(0.605469\pi\) | |||||||
\(278\) | −0.471410 | + | 0.816506i | −0.0282733 | + | 0.0489708i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.43831 | + | 14.6156i | −0.503387 | + | 0.871892i | 0.496605 | + | 0.867977i | \(0.334580\pi\) |
−0.999992 | + | 0.00391559i | \(0.998754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.65856 | − | 13.2650i | 0.455254 | − | 0.788523i | −0.543449 | − | 0.839442i | \(-0.682882\pi\) |
0.998703 | + | 0.0509194i | \(0.0162152\pi\) | |||||||
\(284\) | −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 | ||||||||
\(289\) | −15.6014 | + | 27.0224i | −0.917728 | + | 1.58955i | ||||
\(290\) | 0.0675835 | 0.00396864 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.4315 | −1.72235 | ||||||||
\(293\) | −4.68482 | − | 8.11435i | −0.273690 | − | 0.474045i | 0.696114 | − | 0.717932i | \(-0.254911\pi\) |
−0.969804 | + | 0.243886i | \(0.921578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.53831 | + | 2.66442i | −0.0895636 | + | 0.155129i | ||||
\(296\) | −4.50000 | + | 7.79423i | −0.261557 | + | 0.453030i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.32846 | + | 2.30096i | 0.0769556 | + | 0.133291i | ||||
\(299\) | −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 | ||||||||
\(304\) | 7.11109 | 0.407849 | ||||||||
\(305\) | −4.49316 | − | 7.78239i | −0.257278 | − | 0.445618i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.71410 | 0.154902 | 0.0774509 | − | 0.996996i | \(-0.475322\pi\) | ||||
0.0774509 | + | 0.996996i | \(0.475322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.469220 | −0.0266499 | ||||||||
\(311\) | −6.99028 | + | 12.1075i | −0.396383 | + | 0.686555i | −0.993277 | − | 0.115765i | \(-0.963068\pi\) |
0.596894 | + | 0.802320i | \(0.296401\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.52696 | + | 16.5012i | 0.538495 | + | 0.932701i | 0.998985 | + | 0.0450364i | \(0.0143404\pi\) |
−0.460490 | + | 0.887665i | \(0.652326\pi\) | |||||||
\(314\) | 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 | ||||
\(320\) | 7.87197 | 0.440056 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.4887 | 0.750529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.80150 | + | 3.12030i | 0.0999295 | + | 0.173083i | ||||
\(326\) | −0.360617 | −0.0199727 | ||||||||
\(327\) | 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 | \(0.722850\pi\) | |||||||
\(332\) | 6.74433 | + | 11.6815i | 0.370143 | + | 0.641106i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.75567 | + | 3.04092i | −0.0960663 | + | 0.166392i | ||||
\(335\) | 2.07318 | − | 3.59085i | 0.113270 | − | 0.196189i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.12997 | − | 10.6174i | −0.333920 | − | 0.578367i | 0.649356 | − | 0.760484i | \(-0.275038\pi\) |
−0.983277 | + | 0.182117i | \(0.941705\pi\) | |||||||
\(338\) | −2.86948 | −0.156079 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.9428 | 0.864621 | ||||||||
\(341\) | −3.07442 | + | 5.32505i | −0.166489 | + | 0.288368i | ||||
\(342\) | 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 | \(-0.932339\pi\) |
0.671449 | + | 0.741050i | \(0.265672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.11273 | + | 8.85550i | −0.272509 | + | 0.472000i | ||||
\(353\) | 22.1956 | 1.18135 | 0.590677 | − | 0.806908i | \(-0.298861\pi\) | ||||
0.590677 | + | 0.806908i | \(0.298861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.1683 | 0.539676 | ||||||||
\(356\) | −2.66866 | − | 4.62226i | −0.141439 | − | 0.244979i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.69686 | − | 2.93905i | 0.0896819 | − | 0.155334i | ||||
\(359\) | −3.77812 | + | 6.54389i | −0.199401 | + | 0.345373i | −0.948334 | − | 0.317272i | \(-0.897233\pi\) |
0.748933 | + | 0.662646i | \(0.230566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.61273 | + | 13.1856i | 0.400670 | + | 0.693980i | ||||
\(362\) | 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 | ||||||||
\(367\) | −18.5231 | −0.966900 | −0.483450 | − | 0.875372i | \(-0.660616\pi\) | ||||
−0.483450 | + | 0.875372i | \(0.660616\pi\) | |||||||
\(368\) | −10.2540 | − | 17.7605i | −0.534529 | − | 0.925831i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.69794 | 0.140259 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.6602 | 0.810854 | 0.405427 | − | 0.914127i | \(-0.367123\pi\) | ||||
0.405427 | + | 0.914127i | \(0.367123\pi\) | |||||||
\(374\) | −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 | ||||
\(383\) | −0.225450 | −0.0115200 | −0.00575998 | − | 0.999983i | \(-0.501833\pi\) | ||||
−0.00575998 | + | 0.999983i | \(0.501833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.87661 | −0.0955171 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.96333 | + | 12.0608i | 0.353510 | + | 0.612296i | ||||
\(389\) | −25.2632 | −1.28090 | −0.640448 | − | 0.768002i | \(-0.721251\pi\) | ||||
−0.640448 | + | 0.768002i | \(0.721251\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | 4.35993 | + | 7.55162i | 0.219372 | + | 0.379963i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1505 | − | 17.5811i | 0.509438 | − | 0.882372i | −0.490503 | − | 0.871440i | \(-0.663187\pi\) |
0.999940 | − | 0.0109322i | \(-0.00347991\pi\) | |||||||
\(398\) | 2.38401 | − | 4.12922i | 0.119499 | − | 0.206979i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.59385 | + | 11.4209i | 0.329693 | + | 0.571044i | ||||
\(401\) | 15.2255 | 0.760323 | 0.380161 | − | 0.924920i | \(-0.375868\pi\) | ||||
0.380161 | + | 0.924920i | \(0.375868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.66019 | 0.0826999 | ||||||||
\(404\) | 12.4194 | − | 21.5111i | 0.617890 | − | 1.07022i | ||||
\(405\) | 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 | −0.885781 | − | 0.464104i | \(-0.846376\pi\) |
0.844816 | + | 0.535057i | \(0.179710\pi\) | |||||||
\(410\) | 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 | ||||||||
\(415\) | 4.10301 | − | 7.10662i | 0.201409 | − | 0.348850i | ||||
\(416\) | 2.76088 | 0.135363 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.72064 | 0.0841592 | ||||||||
\(419\) | 16.6871 | + | 28.9030i | 0.815220 | + | 1.41200i | 0.909170 | + | 0.416426i | \(0.136718\pi\) |
−0.0939492 | + | 0.995577i | \(0.529949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.12025 | + | 15.7967i | −0.444494 | + | 0.769886i | −0.998017 | − | 0.0629481i | \(-0.979950\pi\) |
0.553523 | + | 0.832834i | \(0.313283\pi\) | |||||||
\(422\) | 2.16307 | − | 3.74654i | 0.105297 | − | 0.182379i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.46978 | + | 9.47393i | 0.265636 | + | 0.460095i | ||||
\(425\) | 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 | ||||||||
\(430\) | −0.628979 | −0.0303321 | ||||||||
\(431\) | 14.6413 | + | 25.3595i | 0.705247 | + | 1.22152i | 0.966602 | + | 0.256281i | \(0.0824974\pi\) |
−0.261355 | + | 0.965243i | \(0.584169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2449 | −0.588451 | −0.294226 | − | 0.955736i | \(-0.595062\pi\) | ||||
−0.294226 | + | 0.955736i | \(0.595062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.45417 | −0.117533 | ||||||||
\(437\) | −5.44282 | + | 9.42724i | −0.260365 | + | 0.450966i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.41586 | + | 4.18440i | 0.115303 | + | 0.199711i | 0.917901 | − | 0.396810i | \(-0.129883\pi\) |
−0.802598 | + | 0.596520i | \(0.796549\pi\) | |||||||
\(440\) | 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 | ||||
\(446\) | −5.41780 | −0.256540 | ||||||||
\(447\) | 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 | ||||||||
\(451\) | −18.8554 | − | 32.6585i | −0.887867 | − | 1.53783i | ||||
\(452\) | 23.6296 | 1.11144 | ||||||||
\(453\) | 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 | \(0.754291\pi\) | |||||||
\(458\) | −2.31191 | − | 4.00434i | −0.108028 | − | 0.187111i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.43310 | + | 11.1425i | −0.299945 | + | 0.519520i | ||||
\(461\) | 11.2758 | − | 19.5302i | 0.525166 | − | 0.909614i | −0.474404 | − | 0.880307i | \(-0.657337\pi\) |
0.999570 | − | 0.0293073i | \(-0.00933013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.19850 | − | 9.00406i | −0.241595 | − | 0.418454i | 0.719574 | − | 0.694416i | \(-0.244337\pi\) |
−0.961169 | + | 0.275962i | \(0.911004\pi\) | |||||||
\(464\) | −0.875237 | −0.0406318 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.06045 | 0.188097 | ||||||||
\(467\) | 6.65856 | − | 11.5330i | 0.308121 | − | 0.533682i | −0.669830 | − | 0.742514i | \(-0.733633\pi\) |
0.977951 | + | 0.208833i | \(0.0669664\pi\) | |||||||
\(468\) | 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 | ||||||||
\(478\) | 2.01887 | − | 3.49679i | 0.0923412 | − | 0.159940i | ||||
\(479\) | −14.5354 | −0.664141 | −0.332070 | − | 0.943255i | \(-0.607747\pi\) | ||||
−0.332070 | + | 0.943255i | \(0.607747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.54583 | −0.435252 | ||||||||
\(482\) | −3.24557 | − | 5.62149i | −0.147832 | − | 0.256052i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.63968 | − | 4.57206i | 0.119985 | − | 0.207821i | ||||
\(485\) | 4.23624 | − | 7.33739i | 0.192358 | − | 0.333174i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.52696 | − | 11.3050i | −0.295765 | − | 0.512279i | 0.679398 | − | 0.733770i | \(-0.262241\pi\) |
−0.975162 | + | 0.221491i | \(0.928908\pi\) | |||||||
\(488\) | −3.58414 | − | 6.20790i | −0.162246 | − | 0.281019i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.67223 | + | 16.7528i | 0.436502 | + | 0.756043i | 0.997417 | − | 0.0718303i | \(-0.0228840\pi\) |
−0.560915 | + | 0.827873i | \(0.689551\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.66019 | −0.0747712 | ||||||||
\(494\) | −0.232287 | − | 0.402332i | −0.0104511 | − | 0.0181018i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.07661 | 0.272848 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.2222 | −1.62153 | −0.810764 | − | 0.585374i | \(-0.800948\pi\) | ||||
−0.810764 | + | 0.585374i | \(0.800948\pi\) | |||||||
\(500\) | 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 | \(-0.613644\pi\) | ||||
−0.349487 | + | 0.936941i | \(0.613644\pi\) | |||||||
\(504\) | 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 | ||||
\(509\) | −34.3034 | −1.52047 | −0.760237 | − | 0.649646i | \(-0.774917\pi\) | ||||
−0.760237 | + | 0.649646i | \(0.774917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 17.0071 | 0.751616 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.77455 | − | 3.07361i | −0.0782720 | − | 0.135571i | ||||
\(515\) | 5.19699 | 0.229007 | ||||||||
\(516\) | 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 | ||||
\(521\) | −5.12244 | − | 8.87233i | −0.224418 | − | 0.388704i | 0.731727 | − | 0.681598i | \(-0.238715\pi\) |
−0.956145 | + | 0.292895i | \(0.905381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.3015 | + | 26.5030i | −0.669088 | + | 1.15889i | 0.309071 | + | 0.951039i | \(0.399982\pi\) |
−0.978159 | + | 0.207856i | \(0.933352\pi\) | |||||||
\(524\) | 4.82489 | − | 8.35696i | 0.210776 | − | 0.365075i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.925580 | − | 1.60315i | −0.0403572 | − | 0.0699007i | ||||
\(527\) | 11.5264 | 0.502098 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.39372 | 0.364944 | ||||||||
\(530\) | 1.63968 | − | 2.84001i | 0.0712232 | − | 0.123362i | ||||
\(531\) | 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 | ||||||||
\(541\) | 13.0458 | − | 22.5960i | 0.560884 | − | 0.971480i | −0.436536 | − | 0.899687i | \(-0.643795\pi\) |
0.997420 | − | 0.0717926i | \(-0.0228720\pi\) | |||||||
\(542\) | −5.25607 | −0.225767 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19.1683 | 0.821833 | ||||||||
\(545\) | 0.746515 | + | 1.29300i | 0.0319772 | + | 0.0553861i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.46169 | − | 9.45993i | 0.233525 | − | 0.404478i | −0.725318 | − | 0.688414i | \(-0.758307\pi\) |
0.958843 | + | 0.283937i | \(0.0916405\pi\) | |||||||
\(548\) | 4.21574 | − | 7.30187i | 0.180087 | − | 0.311920i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.59549 | + | 2.76346i | 0.0680317 | + | 0.117834i | ||||
\(551\) | 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 | ||||||||
\(556\) | −7.66019 | −0.324864 | ||||||||
\(557\) | −6.97210 | − | 12.0760i | −0.295417 | − | 0.511678i | 0.679665 | − | 0.733523i | \(-0.262125\pi\) |
−0.975082 | + | 0.221845i | \(0.928792\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.22545 | 0.0941265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.03559 | 0.170231 | ||||||||
\(563\) | 15.1287 | − | 26.2037i | 0.637600 | − | 1.10435i | −0.348358 | − | 0.937361i | \(-0.613261\pi\) |
0.985958 | − | 0.166993i | \(-0.0534059\pi\) | |||||||
\(564\) | 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 | \(-0.0739826\pi\) | |||||||
\(572\) | −7.19562 | −0.300864 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.1877 | −0.841885 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.68715 | + | 15.0466i | 0.361651 | + | 0.626397i | 0.988233 | − | 0.152958i | \(-0.0488800\pi\) |
−0.626582 | + | 0.779355i | \(0.715547\pi\) | |||||||
\(578\) | 7.46130 | 0.310349 | ||||||||
\(579\) | 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 | ||||
\(584\) | 7.14132 | + | 12.3691i | 0.295510 | + | 0.511838i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.12025 | + | 1.94033i | −0.0462771 | + | 0.0801543i | ||||
\(587\) | 8.48796 | − | 14.7016i | 0.350336 | − | 0.606799i | −0.635973 | − | 0.771712i | \(-0.719401\pi\) |
0.986308 | + | 0.164913i | \(0.0527342\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.61273 | − | 2.79332i | −0.0664512 | − | 0.115097i | ||||
\(590\) | 0.735689 | 0.0302878 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −34.9396 | −1.43601 | ||||||||
\(593\) | −6.53667 | + | 11.3218i | −0.268429 | + | 0.464932i | −0.968456 | − | 0.249184i | \(-0.919838\pi\) |
0.700027 | + | 0.714116i | \(0.253171\pi\) | |||||||
\(594\) | 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 | \(-0.884126\pi\) |
0.775576 | + | 0.631255i | \(0.217460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.5253 | − | 23.4265i | 0.550337 | − | 0.953212i | ||||
\(605\) | −3.21178 | −0.130577 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.6408 | −0.797194 | −0.398597 | − | 0.917126i | \(-0.630503\pi\) | ||||
−0.398597 | + | 0.917126i | \(0.630503\pi\) | |||||||
\(608\) | −2.68194 | − | 4.64526i | −0.108767 | − | 0.188390i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.07442 | + | 1.86095i | −0.0435020 | + | 0.0753477i | ||||
\(611\) | 2.91423 | − | 5.04759i | 0.117897 | − | 0.204204i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7826 | − | 20.4081i | −0.475896 | − | 0.824276i | 0.523723 | − | 0.851889i | \(-0.324543\pi\) |
−0.999619 | + | 0.0276128i | \(0.991209\pi\) | |||||||
\(614\) | −0.324502 | − | 0.562054i | −0.0130958 | − | 0.0226827i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.33009 | − | 9.23200i | −0.214582 | − | 0.371666i | 0.738562 | − | 0.674186i | \(-0.235505\pi\) |
−0.953143 | + | 0.302520i | \(0.902172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.0150 | −0.724086 | −0.362043 | − | 0.932161i | \(-0.617921\pi\) | ||||
−0.362043 | + | 0.932161i | \(0.617921\pi\) | |||||||
\(620\) | −1.90615 | − | 3.30155i | −0.0765528 | − | 0.132593i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.34308 | 0.134045 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.99673 | 0.239869 | ||||||||
\(626\) | 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 | ||||
\(635\) | −1.58358 | −0.0628424 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.211777 | −0.00838434 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.20439 | − | 7.28221i | −0.166193 | − | 0.287855i | ||||
\(641\) | −19.1456 | −0.756205 | −0.378102 | − | 0.925764i | \(-0.623423\pi\) | ||||
−0.378102 | + | 0.925764i | \(0.623423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.24433 | − | 5.61934i | −0.127944 | − | 0.221605i | 0.794936 | − | 0.606693i | \(-0.207504\pi\) |
−0.922880 | + | 0.385088i | \(0.874171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.61273 | − | 2.79332i | −0.0634518 | − | 0.109902i | ||||
\(647\) | −24.0494 | − | 41.6548i | −0.945479 | − | 1.63762i | −0.754789 | − | 0.655968i | \(-0.772261\pi\) |
−0.190691 | − | 0.981650i | \(-0.561073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.82038 | − | 8.34914i | 0.189216 | − | 0.327733i | ||||
\(650\) | 0.430782 | − | 0.746136i | 0.0168967 | − | 0.0292659i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.46496 | − | 2.53739i | −0.0573724 | − | 0.0993720i | ||||
\(653\) | 43.2405 | 1.69213 | 0.846066 | − | 0.533079i | \(-0.178965\pi\) | ||||
0.846066 | + | 0.533079i | \(0.178965\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.87059 | −0.229383 | ||||||||
\(656\) | −18.6339 | + | 32.2749i | −0.727532 | + | 1.26012i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.25404 | + | 2.17206i | −0.0488505 | + | 0.0846115i | −0.889417 | − | 0.457097i | \(-0.848889\pi\) |
0.840566 | + | 0.541709i | \(0.182222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1677 | − | 36.6636i | 0.823329 | − | 1.42605i | −0.0798613 | − | 0.996806i | \(-0.525448\pi\) |
0.903190 | − | 0.429241i | \(-0.141219\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | 0.669905 | − | 1.16031i | 0.0259388 | − | 0.0449274i | ||||
\(668\) | −28.5289 | −1.10382 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.991489 | −0.0383046 | ||||||||
\(671\) | 14.0796 | + | 24.3866i | 0.543538 | + | 0.941435i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.70765 | + | 11.6180i | −0.258561 | + | 0.447841i | −0.965857 | − | 0.259077i | \(-0.916582\pi\) |
0.707296 | + | 0.706918i | \(0.249915\pi\) | |||||||
\(674\) | −1.46582 | + | 2.53887i | −0.0564612 | + | 0.0977936i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.6569 | − | 20.1904i | −0.448343 | − | 0.776553i | ||||
\(677\) | 0.981125 | + | 1.69936i | 0.0377077 | + | 0.0653117i | 0.884263 | − | 0.466989i | \(-0.154661\pi\) |
−0.846556 | + | 0.532300i | \(0.821328\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.86840 | − | 6.70027i | −0.148346 | − | 0.256943i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.47033 | 0.0563019 | ||||||||
\(683\) | 13.5836 | + | 23.5275i | 0.519761 | + | 0.900253i | 0.999736 | + | 0.0229706i | \(0.00731243\pi\) |
−0.479975 | + | 0.877282i | \(0.659354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.12941 | −0.195985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.14557 | 0.310547 | ||||||||
\(689\) | −5.80150 | + | 10.0485i | −0.221020 | + | 0.382817i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.1586 | + | 43.5759i | 0.957077 | + | 1.65771i | 0.729543 | + | 0.683935i | \(0.239733\pi\) |
0.227534 | + | 0.973770i | \(0.426934\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | 2.73431 | 0.103495 | ||||||||
\(699\) | 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 | ||||||||
\(703\) | 9.27292 | + | 16.0612i | 0.349735 | + | 0.605758i | ||||
\(704\) | −24.6673 | −0.929685 | ||||||||
\(705\) | 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 | \(-0.433714\pi\) | |||||||
\(710\) | −1.21574 | − | 2.10571i | −0.0456257 | − | 0.0790261i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.29506 | + | 2.24311i | −0.0485344 | + | 0.0840640i | ||||
\(713\) | −4.65103 | + | 8.05582i | −0.174182 | + | 0.301693i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.18878 | + | 3.79108i | 0.0818557 | + | 0.141778i | ||||
\(716\) | 27.5732 | 1.03046 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.80687 | 0.0674318 | ||||||||
\(719\) | −11.0189 | + | 19.0853i | −0.410935 | + | 0.711760i | −0.994992 | − | 0.0999525i | \(-0.968131\pi\) |
0.584058 | + | 0.811712i | \(0.301464\pi\) | |||||||
\(720\) | 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 | 0.478402 | + | 0.878141i | \(0.341216\pi\) |
−0.999693 | + | 0.0247621i | \(0.992117\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.14076 | − | 3.70790i | 0.0792331 | − | 0.137236i | ||||
\(731\) | 15.4509 | 0.571472 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8695 | 0.438409 | 0.219205 | − | 0.975679i | \(-0.429654\pi\) | ||||
0.219205 | + | 0.975679i | \(0.429654\pi\) | |||||||
\(734\) | 2.21466 | + | 3.83590i | 0.0817444 | + | 0.141586i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.73461 | + | 13.3967i | −0.285102 | + | 0.493810i | ||||
\(737\) | −6.49643 | + | 11.2522i | −0.239299 | + | 0.414478i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.09222 | + | 10.5520i | 0.224106 | + | 0.388163i | 0.956051 | − | 0.293201i | \(-0.0947206\pi\) |
−0.731945 | + | 0.681364i | \(0.761387\pi\) | |||||||
\(740\) | 10.9601 | + | 18.9834i | 0.402900 | + | 0.697843i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2427 | − | 38.5255i | −0.816005 | − | 1.41336i | −0.908604 | − | 0.417659i | \(-0.862851\pi\) |
0.0925987 | − | 0.995704i | \(-0.470483\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.1327 | 0.481144 | ||||||||
\(746\) | −1.87236 | − | 3.24302i | −0.0685519 | − | 0.118735i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −49.9579 | −1.82664 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.8058 | 1.56200 | 0.781002 | − | 0.624528i | \(-0.214709\pi\) | ||||
0.781002 | + | 0.624528i | \(0.214709\pi\) | |||||||
\(752\) | 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 | ||||
\(761\) | 14.3365 | 0.519699 | 0.259850 | − | 0.965649i | \(-0.416327\pi\) | ||||
0.259850 | + | 0.965649i | \(0.416327\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 29.2736 | 1.05908 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.0269552 | + | 0.0466878i | 0.000973931 | + | 0.00168690i | ||||
\(767\) | −2.60301 | −0.0939892 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.6105 | + | 27.0382i | 0.562930 | + | 0.975024i | 0.997239 | + | 0.0742597i | \(0.0236594\pi\) |
−0.434309 | + | 0.900764i | \(0.643007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.62352 | − | 13.2043i | −0.274376 | − | 0.475234i | ||||
\(773\) | 2.19002 | + | 3.79323i | 0.0787697 | + | 0.136433i | 0.902719 | − | 0.430230i | \(-0.141567\pi\) |
−0.823950 | + | 0.566663i | \(0.808234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.99084 | − | 5.18029i | 0.107434 | − | 0.186081i | ||||
\(776\) | 3.37919 | − | 5.85294i | 0.121306 | − | 0.210108i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.02051 | + | 5.23168i | 0.108291 | + | 0.187565i | ||||
\(779\) | 19.7817 | 0.708752 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.8629 | −1.14015 | ||||||||
\(782\) | −4.65103 | + | 8.05582i | −0.166321 | + | 0.288076i | ||||
\(783\) | 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 | −0.999961 | − | 0.00887191i | \(-0.997176\pi\) |
0.507664 | + | 0.861555i | \(0.330509\pi\) | |||||||
\(788\) | −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 | ||||||||
\(793\) | 3.80150 | − | 6.58440i | 0.134995 | − | 0.233819i | ||||
\(794\) | −4.85443 | −0.172277 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 38.7390 | 1.37307 | ||||||||
\(797\) | −1.48181 | − | 2.56658i | −0.0524885 | − | 0.0909128i | 0.838587 | − | 0.544767i | \(-0.183382\pi\) |
−0.891076 | + | 0.453854i | \(0.850049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.2330 | − | 35.0445i | 0.715791 | − | 1.23979i | ||||
\(800\) | 4.97373 | − | 8.61476i | 0.175848 | − | 0.304578i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.82038 | − | 3.15299i | −0.0642798 | − | 0.111336i | ||||
\(803\) | −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 | ||||||||
\(808\) | −12.0539 | −0.424055 | ||||||||
\(809\) | −12.3948 | − | 21.4684i | −0.435778 | − | 0.754790i | 0.561581 | − | 0.827422i | \(-0.310193\pi\) |
−0.997359 | + | 0.0726323i | \(0.976860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.24377 | 0.289478 | 0.144739 | − | 0.989470i | \(-0.453766\pi\) | ||||
0.144739 | + | 0.989470i | \(0.453766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.45417 | −0.296319 | ||||||||
\(815\) | −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 | \(-0.0492308\pi\) | |||||||
\(824\) | 4.14557 | 0.144418 | ||||||||
\(825\) | 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 | ||||||||
\(829\) | −7.40615 | − | 12.8278i | −0.257226 | − | 0.445529i | 0.708272 | − | 0.705940i | \(-0.249475\pi\) |
−0.965498 | + | 0.260411i | \(0.916142\pi\) | |||||||
\(830\) | −1.96225 | −0.0681107 | ||||||||
\(831\) | 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 | ||||
\(836\) | 6.98989 | + | 12.1069i | 0.241751 | + | 0.418724i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.99028 | − | 6.91138i | 0.137842 | − | 0.238750i | ||||
\(839\) | 16.8606 | − | 29.2034i | 0.582093 | − | 1.00821i | −0.413138 | − | 0.910669i | \(-0.635567\pi\) |
0.995231 | − | 0.0975464i | \(-0.0310994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4714 | + | 25.0652i | 0.499014 | + | 0.864318i | ||||
\(842\) | 4.36173 | 0.150315 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.1488 | 1.20987 | ||||||||
\(845\) | −7.09166 | + | 12.2831i | −0.243961 | + | 0.422552i | ||||
\(846\) | 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 | \(-0.898024\pi\) |
0.747285 | + | 0.664503i | \(0.231357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.47141 | + | 11.2088i | −0.221188 | + | 0.383109i | ||||
\(857\) | 31.3261 | 1.07008 | 0.535040 | − | 0.844827i | \(-0.320296\pi\) | ||||
0.535040 | + | 0.844827i | \(0.320296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.3893 | −1.71926 | −0.859631 | − | 0.510915i | \(-0.829307\pi\) | ||||
−0.859631 | + | 0.510915i | \(0.829307\pi\) | |||||||
\(860\) | −2.55515 | − | 4.42566i | −0.0871300 | − | 0.150914i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.50108 | − | 6.06405i | 0.119247 | − | 0.206542i | ||||
\(863\) | 0.566340 | − | 0.980929i | 0.0192784 | − | 0.0333912i | −0.856225 | − | 0.516603i | \(-0.827196\pi\) |
0.875504 | + | 0.483211i | \(0.160530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.149395 | − | 0.258761i | −0.00507960 | − | 0.00879812i | ||||
\(866\) | 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 | ||||||||
\(871\) | 3.50808 | 0.118867 | ||||||||
\(872\) | 0.595485 | + | 1.03141i | 0.0201657 | + | 0.0349280i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.60301 | 0.0880481 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.3937 | −0.925020 | −0.462510 | − | 0.886614i | \(-0.653051\pi\) | ||||
−0.462510 | + | 0.886614i | \(0.653051\pi\) | |||||||
\(878\) | 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 | \(-0.506485\pi\) | ||||
−0.0203710 | + | 0.999792i | \(0.506485\pi\) | |||||||
\(882\) | 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 | ||||
\(887\) | 41.5757 | 1.39597 | 0.697987 | − | 0.716110i | \(-0.254079\pi\) | ||||
0.697987 | + | 0.716110i | \(0.254079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.776443 | 0.0260264 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.0092 | − | 38.1210i | −0.736921 | − | 1.27638i | ||||
\(893\) | −11.3236 | −0.378931 | ||||||||
\(894\) | 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 | ||||
\(899\) | 0.198495 | + | 0.343803i | 0.00662018 | + | 0.0114665i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.2788 | + | 69.7649i | −1.34188 | + | 2.32421i | ||||
\(902\) | −4.50877 | + | 7.80942i | −0.150126 | + | 0.260025i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.73353 | − | 9.93077i | −0.190694 | − | 0.330292i | ||||
\(905\) | 1.69192 | 0.0562412 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4509 | 1.17713 | 0.588564 | − | 0.808451i | \(-0.299694\pi\) | ||||
0.588564 | + | 0.808451i | \(0.299694\pi\) | |||||||
\(908\) | 5.13160 | − | 8.88819i | 0.170298 | − | 0.294965i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3554 | + | 17.9361i | −0.343090 | + | 0.594250i | −0.985005 | − | 0.172526i | \(-0.944807\pi\) |
0.641915 | + | 0.766776i | \(0.278140\pi\) | |||||||
\(912\) | 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 | ||||||||
\(919\) | −7.19630 | + | 12.4644i | −0.237384 | + | 0.411161i | −0.959963 | − | 0.280127i | \(-0.909623\pi\) |
0.722579 | + | 0.691289i | \(0.242957\pi\) | |||||||
\(920\) | 6.24377 | 0.205851 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.39261 | −0.177596 | ||||||||
\(923\) | 4.30150 | + | 7.45043i | 0.141586 | + | 0.245234i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1969 | + | 29.7858i | −0.565429 | + | 0.979352i | ||||
\(926\) | −1.24308 | + | 2.15308i | −0.0408502 | + | 0.0707546i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.330095 | + | 0.571741i | 0.0108359 | + | 0.0187683i | ||||
\(929\) | −20.8714 | − | 36.1503i | −0.684769 | − | 1.18605i | −0.973509 | − | 0.228647i | \(-0.926570\pi\) |
0.288741 | − | 0.957407i | \(-0.406763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.4951 | + | 28.5703i | 0.540315 | + | 0.935853i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.18443 | −0.104198 | ||||||||
\(935\) | 15.1963 | + | 26.3208i | 0.496972 | + | 0.860781i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.17154 | 0.103610 | 0.0518048 | − | 0.998657i | \(-0.483503\pi\) | ||||
0.0518048 | + | 0.998657i | \(0.483503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.3839 | −0.436535 | ||||||||
\(941\) | −1.61040 | + | 2.78930i | −0.0524976 | + | 0.0909285i | −0.891080 | − | 0.453846i | \(-0.850052\pi\) |
0.838582 | + | 0.544775i | \(0.183385\pi\) | |||||||
\(942\) | 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 | ||||
\(950\) | −1.67386 | −0.0543073 | ||||||||
\(951\) | 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 | ||||||||
\(955\) | −8.90451 | − | 15.4231i | −0.288143 | − | 0.499079i | ||||
\(956\) | 32.8058 | 1.06101 | ||||||||
\(957\) | 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 | ||||
\(962\) | 1.14132 | + | 1.97682i | 0.0367975 | + | 0.0637351i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.3695 | − | 45.6733i | 0.849304 | − | 1.47104i | ||||
\(965\) | −4.63788 | + | 8.03305i | −0.149299 | + | 0.258593i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8295 | − | 22.2214i | −0.412570 | − | 0.714593i | 0.582600 | − | 0.812759i | \(-0.302036\pi\) |
−0.995170 | + | 0.0981667i | \(0.968702\pi\) | |||||||
\(968\) | −2.56199 | −0.0823455 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.02597 | −0.0650500 | ||||||||
\(971\) | −10.5092 | + | 18.2024i | −0.337255 | + | 0.584143i | −0.983915 | − | 0.178635i | \(-0.942832\pi\) |
0.646660 | + | 0.762778i | \(0.276165\pi\) | |||||||
\(972\) | 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 | ||||||||
\(982\) | 2.31285 | − | 4.00598i | 0.0738062 | − | 0.127836i | ||||
\(983\) | −42.9923 | −1.37124 | −0.685622 | − | 0.727958i | \(-0.740469\pi\) | ||||
−0.685622 | + | 0.727958i | \(0.740469\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.90723 | 0.251945 | ||||||||
\(986\) | 0.198495 | + | 0.343803i | 0.00632137 | + | 0.0109489i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.88727 | − | 3.26886i | 0.0600422 | − | 0.103996i | ||||
\(989\) | −6.23461 | + | 10.7987i | −0.198249 | + | 0.343377i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.63160 | + | 14.9504i | 0.274192 | + | 0.474914i | 0.969931 | − | 0.243380i | \(-0.0782564\pi\) |
−0.695739 | + | 0.718295i | \(0.744923\pi\) | |||||||
\(992\) | −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 | ||||||||
\(997\) | −38.9018 | −1.23203 | −0.616016 | − | 0.787733i | \(-0.711254\pi\) | ||||
−0.616016 | + | 0.787733i | \(0.711254\pi\) | |||||||
\(998\) | 4.33078 | + | 7.50114i | 0.137089 | + | 0.237444i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))