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: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
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 | \(-0.173648 - 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.667 |
Dual form | 1323.2.g.e.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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.673648 | + | 1.16679i | 0.476341 | + | 0.825047i | 0.999633 | − | 0.0271067i | \(-0.00862938\pi\) |
−0.523291 | + | 0.852154i | \(0.675296\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0923963 | − | 0.160035i | 0.0461981 | − | 0.0800175i | ||||
\(5\) | 2.53209 | 1.13238 | 0.566192 | − | 0.824273i | \(-0.308416\pi\) | ||||
0.566192 | + | 0.824273i | \(0.308416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.94356 | 1.04071 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.70574 | + | 2.95442i | 0.539401 | + | 0.934271i | ||||
\(11\) | −0.467911 | −0.141081 | −0.0705403 | − | 0.997509i | \(-0.522472\pi\) | ||||
−0.0705403 | + | 0.997509i | \(0.522472\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.91147 | + | 5.04282i | 0.807498 | + | 1.39863i | 0.914592 | + | 0.404378i | \(0.132512\pi\) |
−0.107094 | + | 0.994249i | \(0.534155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.79813 | + | 3.11446i | 0.449533 | + | 0.778615i | ||||
\(17\) | −1.93969 | − | 3.35965i | −0.470445 | − | 0.814834i | 0.528984 | − | 0.848632i | \(-0.322573\pi\) |
−0.999429 | + | 0.0337978i | \(0.989240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.09240 | + | 1.89209i | −0.250613 | + | 0.434074i | −0.963695 | − | 0.267007i | \(-0.913965\pi\) |
0.713082 | + | 0.701081i | \(0.247299\pi\) | |||||||
\(20\) | 0.233956 | − | 0.405223i | 0.0523141 | − | 0.0906106i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.315207 | − | 0.545955i | −0.0672025 | − | 0.116398i | ||||
\(23\) | 0.106067 | 0.0221165 | 0.0110582 | − | 0.999939i | \(-0.496480\pi\) | ||||
0.0110582 | + | 0.999939i | \(0.496480\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.41147 | 0.282295 | ||||||||
\(26\) | −3.92262 | + | 6.79417i | −0.769289 | + | 1.33245i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.39053 | − | 7.60462i | 0.815301 | − | 1.41214i | −0.0938108 | − | 0.995590i | \(-0.529905\pi\) |
0.909112 | − | 0.416552i | \(-0.136762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.84002 | + | 6.65111i | −0.689688 | + | 1.19458i | 0.282250 | + | 0.959341i | \(0.408919\pi\) |
−0.971939 | + | 0.235235i | \(0.924414\pi\) | |||||||
\(32\) | 0.520945 | − | 0.902302i | 0.0920909 | − | 0.159506i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.61334 | − | 4.52644i | 0.448184 | − | 0.776278i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.84002 | − | 6.65111i | 0.631296 | − | 1.09344i | −0.355991 | − | 0.934489i | \(-0.615857\pi\) |
0.987287 | − | 0.158947i | \(-0.0508099\pi\) | |||||||
\(38\) | −2.94356 | −0.477509 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.45336 | 1.17848 | ||||||||
\(41\) | 1.11334 | + | 1.92836i | 0.173875 | + | 0.301160i | 0.939771 | − | 0.341804i | \(-0.111038\pi\) |
−0.765897 | + | 0.642964i | \(0.777705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.613341 | + | 1.06234i | −0.0935336 | + | 0.162005i | −0.908996 | − | 0.416806i | \(-0.863150\pi\) |
0.815462 | + | 0.578811i | \(0.196483\pi\) | |||||||
\(44\) | −0.0432332 | + | 0.0748822i | −0.00651766 | + | 0.0112889i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0714517 | + | 0.123758i | 0.0105350 | + | 0.0182471i | ||||
\(47\) | 2.66637 | + | 4.61830i | 0.388931 | + | 0.673648i | 0.992306 | − | 0.123810i | \(-0.0395112\pi\) |
−0.603375 | + | 0.797457i | \(0.706178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.950837 | + | 1.64690i | 0.134469 | + | 0.232907i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.07604 | 0.149220 | ||||||||
\(53\) | −0.358441 | − | 0.620838i | −0.0492356 | − | 0.0852786i | 0.840357 | − | 0.542033i | \(-0.182345\pi\) |
−0.889593 | + | 0.456754i | \(0.849012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18479 | −0.159757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.8307 | 1.55345 | ||||||||
\(59\) | −0.368241 | + | 0.637812i | −0.0479409 | + | 0.0830360i | −0.889000 | − | 0.457907i | \(-0.848599\pi\) |
0.841059 | + | 0.540943i | \(0.181933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.479055 | + | 0.829748i | 0.0613368 | + | 0.106238i | 0.895063 | − | 0.445939i | \(-0.147130\pi\) |
−0.833726 | + | 0.552178i | \(0.813797\pi\) | |||||||
\(62\) | −10.3473 | −1.31411 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.59627 | 1.07453 | ||||||||
\(65\) | 7.37211 | + | 12.7689i | 0.914398 | + | 1.58378i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.81908 | − | 8.34689i | 0.588744 | − | 1.01973i | −0.405653 | − | 0.914027i | \(-0.632956\pi\) |
0.994397 | − | 0.105708i | \(-0.0337107\pi\) | |||||||
\(68\) | −0.716881 | −0.0869346 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2344 | −1.57064 | −0.785318 | − | 0.619092i | \(-0.787501\pi\) | ||||
−0.785318 | + | 0.619092i | \(0.787501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.13429 | − | 8.89284i | −0.600923 | − | 1.04083i | −0.992682 | − | 0.120761i | \(-0.961467\pi\) |
0.391759 | − | 0.920068i | \(-0.371867\pi\) | |||||||
\(74\) | 10.3473 | 1.20285 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.201867 | + | 0.349643i | 0.0231557 | + | 0.0401068i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.31908 | + | 10.9450i | 0.710952 | + | 1.23140i | 0.964500 | + | 0.264082i | \(0.0850689\pi\) |
−0.253548 | + | 0.967323i | \(0.581598\pi\) | |||||||
\(80\) | 4.55303 | + | 7.88609i | 0.509045 | + | 0.881691i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.50000 | + | 2.59808i | −0.165647 | + | 0.286910i | ||||
\(83\) | 1.36571 | − | 2.36549i | 0.149907 | − | 0.259646i | −0.781286 | − | 0.624173i | \(-0.785436\pi\) |
0.931193 | + | 0.364527i | \(0.118769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.91147 | − | 8.50692i | −0.532724 | − | 0.922705i | ||||
\(86\) | −1.65270 | −0.178216 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.37733 | −0.146823 | ||||||||
\(89\) | 4.05690 | − | 7.02676i | 0.430031 | − | 0.744835i | −0.566845 | − | 0.823825i | \(-0.691836\pi\) |
0.996875 | + | 0.0789894i | \(0.0251693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.00980018 | − | 0.0169744i | 0.00102174 | − | 0.00176970i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.59240 | + | 6.22221i | −0.370527 | + | 0.641772i | ||||
\(95\) | −2.76604 | + | 4.79093i | −0.283790 | + | 0.491539i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.80200 | + | 11.7814i | −0.690639 | + | 1.19622i | 0.280990 | + | 0.959711i | \(0.409337\pi\) |
−0.971629 | + | 0.236511i | \(0.923996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.130415 | − | 0.225885i | 0.0130415 | − | 0.0225885i | ||||
\(101\) | −9.57398 | −0.952646 | −0.476323 | − | 0.879270i | \(-0.658031\pi\) | ||||
−0.476323 | + | 0.879270i | \(0.658031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.04189 | −0.299726 | −0.149863 | − | 0.988707i | \(-0.547883\pi\) | ||||
−0.149863 | + | 0.988707i | \(0.547883\pi\) | |||||||
\(104\) | 8.57011 | + | 14.8439i | 0.840368 | + | 1.45556i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.482926 | − | 0.836452i | 0.0469059 | − | 0.0812434i | ||||
\(107\) | −3.25877 | + | 5.64436i | −0.315037 | + | 0.545660i | −0.979445 | − | 0.201709i | \(-0.935350\pi\) |
0.664408 | + | 0.747370i | \(0.268684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.31908 | − | 9.21291i | −0.509475 | − | 0.882437i | −0.999940 | − | 0.0109759i | \(-0.996506\pi\) |
0.490465 | − | 0.871461i | \(-0.336827\pi\) | |||||||
\(110\) | −0.798133 | − | 1.38241i | −0.0760990 | − | 0.131807i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.58853 | + | 4.48346i | 0.243508 | + | 0.421768i | 0.961711 | − | 0.274065i | \(-0.0883684\pi\) |
−0.718203 | + | 0.695834i | \(0.755035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.268571 | 0.0250443 | ||||||||
\(116\) | −0.811337 | − | 1.40528i | −0.0753308 | − | 0.130477i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.992259 | −0.0913449 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7811 | −0.980096 | ||||||||
\(122\) | −0.645430 | + | 1.11792i | −0.0584345 | + | 0.101211i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.709607 | + | 1.22908i | 0.0637246 | + | 0.110374i | ||||
\(125\) | −9.08647 | −0.812718 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.88207 | −0.788157 | −0.394078 | − | 0.919077i | \(-0.628936\pi\) | ||||
−0.394078 | + | 0.919077i | \(0.628936\pi\) | |||||||
\(128\) | 4.74897 | + | 8.22546i | 0.419754 | + | 0.727035i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.93242 | + | 17.2035i | −0.871131 | + | 1.50884i | ||||
\(131\) | 11.3628 | 0.992771 | 0.496385 | − | 0.868102i | \(-0.334660\pi\) | ||||
0.496385 | + | 0.868102i | \(0.334660\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.9855 | 1.12177 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.70961 | − | 9.88933i | −0.489595 | − | 0.848003i | ||||
\(137\) | 5.72462 | 0.489087 | 0.244544 | − | 0.969638i | \(-0.421362\pi\) | ||||
0.244544 | + | 0.969638i | \(0.421362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.461981 | − | 0.800175i | −0.0391847 | − | 0.0678700i | 0.845768 | − | 0.533551i | \(-0.179143\pi\) |
−0.884953 | + | 0.465681i | \(0.845809\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.91534 | − | 15.4418i | −0.748159 | − | 1.29585i | ||||
\(143\) | −1.36231 | − | 2.35959i | −0.113922 | − | 0.197319i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.1172 | − | 19.2556i | 0.923234 | − | 1.59909i | ||||
\(146\) | 6.91740 | − | 11.9813i | 0.572488 | − | 0.991579i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.709607 | − | 1.22908i | −0.0583294 | − | 0.101029i | ||||
\(149\) | −8.72462 | −0.714749 | −0.357374 | − | 0.933961i | \(-0.616328\pi\) | ||||
−0.357374 | + | 0.933961i | \(0.616328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4270 | 1.49956 | 0.749782 | − | 0.661685i | \(-0.230158\pi\) | ||||
0.749782 | + | 0.661685i | \(0.230158\pi\) | |||||||
\(152\) | −3.21554 | + | 5.56947i | −0.260815 | + | 0.451744i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.72328 | + | 16.8412i | −0.780992 | + | 1.35272i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.46198 | − | 4.26428i | 0.196488 | − | 0.340326i | −0.750900 | − | 0.660416i | \(-0.770380\pi\) |
0.947387 | + | 0.320090i | \(0.103713\pi\) | |||||||
\(158\) | −8.51367 | + | 14.7461i | −0.677311 | + | 1.17314i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.31908 | − | 2.28471i | 0.104282 | − | 0.180622i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.81908 | + | 6.61484i | −0.299133 | + | 0.518114i | −0.975938 | − | 0.218049i | \(-0.930031\pi\) |
0.676805 | + | 0.736163i | \(0.263364\pi\) | |||||||
\(164\) | 0.411474 | 0.0321307 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.68004 | 0.285627 | ||||||||
\(167\) | 2.82770 | + | 4.89771i | 0.218814 | + | 0.378996i | 0.954446 | − | 0.298385i | \(-0.0964480\pi\) |
−0.735632 | + | 0.677382i | \(0.763115\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4534 | + | 18.1058i | −0.804105 | + | 1.39275i | ||||
\(170\) | 6.61721 | − | 11.4613i | 0.507517 | − | 0.879045i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.113341 | + | 0.196312i | 0.00864215 | + | 0.0149687i | ||||
\(173\) | −10.5346 | − | 18.2465i | −0.800932 | − | 1.38725i | −0.919003 | − | 0.394250i | \(-0.871005\pi\) |
0.118071 | − | 0.993005i | \(-0.462329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.841367 | − | 1.45729i | −0.0634204 | − | 0.109847i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.9317 | 0.819366 | ||||||||
\(179\) | −2.56031 | − | 4.43458i | −0.191366 | − | 0.331456i | 0.754337 | − | 0.656487i | \(-0.227959\pi\) |
−0.945703 | + | 0.325031i | \(0.894625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.319955 | 0.0237821 | 0.0118910 | − | 0.999929i | \(-0.496215\pi\) | ||||
0.0118910 | + | 0.999929i | \(0.496215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.312214 | 0.0230168 | ||||||||
\(185\) | 9.72328 | − | 16.8412i | 0.714870 | − | 1.23819i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.907604 | + | 1.57202i | 0.0663706 | + | 0.114957i | ||||
\(188\) | 0.985452 | 0.0718715 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.45336 | −0.540724 | ||||||||
\(191\) | −7.78359 | − | 13.4816i | −0.563200 | − | 0.975492i | −0.997215 | − | 0.0745858i | \(-0.976237\pi\) |
0.434014 | − | 0.900906i | \(-0.357097\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.02094 | + | 5.23243i | −0.217452 | + | 0.376639i | −0.954028 | − | 0.299716i | \(-0.903108\pi\) |
0.736576 | + | 0.676355i | \(0.236441\pi\) | |||||||
\(194\) | −18.3286 | −1.31592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.2344 | −1.79788 | −0.898939 | − | 0.438074i | \(-0.855661\pi\) | ||||
−0.898939 | + | 0.438074i | \(0.855661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.52094 | + | 2.63435i | 0.107817 | + | 0.186744i | 0.914886 | − | 0.403713i | \(-0.132281\pi\) |
−0.807069 | + | 0.590458i | \(0.798947\pi\) | |||||||
\(200\) | 4.15476 | 0.293786 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.44949 | − | 11.1708i | −0.453785 | − | 0.785978i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.81908 | + | 4.88279i | 0.196893 | + | 0.341029i | ||||
\(206\) | −2.04916 | − | 3.54925i | −0.142772 | − | 0.247288i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.4704 | + | 18.1353i | −0.725994 | + | 1.25746i | ||||
\(209\) | 0.511144 | − | 0.885328i | 0.0353566 | − | 0.0612394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.72668 | + | 4.72275i | 0.187713 | + | 0.325128i | 0.944487 | − | 0.328548i | \(-0.106559\pi\) |
−0.756775 | + | 0.653676i | \(0.773226\pi\) | |||||||
\(212\) | −0.132474 | −0.00909837 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.78106 | −0.600261 | ||||||||
\(215\) | −1.55303 | + | 2.68993i | −0.105916 | + | 0.183452i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.16637 | − | 12.4125i | 0.485368 | − | 0.840682i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.109470 | + | 0.189608i | −0.00738049 | + | 0.0127834i | ||||
\(221\) | 11.2947 | − | 19.5630i | 0.759766 | − | 1.31595i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.09627 | − | 12.2911i | 0.475201 | − | 0.823073i | −0.524395 | − | 0.851475i | \(-0.675709\pi\) |
0.999597 | + | 0.0284023i | \(0.00904195\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.48751 | + | 6.04055i | −0.231986 | + | 0.401811i | ||||
\(227\) | −2.89393 | −0.192077 | −0.0960385 | − | 0.995378i | \(-0.530617\pi\) | ||||
−0.0960385 | + | 0.995378i | \(0.530617\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.16756 | −0.605809 | −0.302905 | − | 0.953021i | \(-0.597956\pi\) | ||||
−0.302905 | + | 0.953021i | \(0.597956\pi\) | |||||||
\(230\) | 0.180922 | + | 0.313366i | 0.0119297 | + | 0.0206628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.9238 | − | 22.3847i | 0.848489 | − | 1.46963i | ||||
\(233\) | 6.63563 | − | 11.4932i | 0.434715 | − | 0.752948i | −0.562558 | − | 0.826758i | \(-0.690183\pi\) |
0.997272 | + | 0.0738103i | \(0.0235159\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.75150 | + | 11.6939i | 0.440419 | + | 0.762828i | ||||
\(236\) | 0.0680482 | + | 0.117863i | 0.00442956 | + | 0.00767222i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.76857 | + | 8.25941i | 0.308453 | + | 0.534257i | 0.978024 | − | 0.208491i | \(-0.0668553\pi\) |
−0.669571 | + | 0.742748i | \(0.733522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.95811 | 0.577043 | 0.288521 | − | 0.957473i | \(-0.406836\pi\) | ||||
0.288521 | + | 0.957473i | \(0.406836\pi\) | |||||||
\(242\) | −7.26264 | − | 12.5793i | −0.466860 | − | 0.808626i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.177052 | 0.0113346 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.7219 | −0.809477 | ||||||||
\(248\) | −11.3033 | + | 19.5780i | −0.717763 | + | 1.24320i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.12108 | − | 10.6020i | −0.387131 | − | 0.670531i | ||||
\(251\) | −24.9982 | −1.57788 | −0.788938 | − | 0.614473i | \(-0.789369\pi\) | ||||
−0.788938 | + | 0.614473i | \(0.789369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0496299 | −0.00312020 | ||||||||
\(254\) | −5.98339 | − | 10.3635i | −0.375431 | − | 0.650266i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.19800 | − | 3.80704i | 0.137375 | − | 0.237940i | ||||
\(257\) | 10.8520 | 0.676932 | 0.338466 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338466 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.72462 | 0.168974 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.65451 | + | 13.2580i | 0.472897 | + | 0.819082i | ||||
\(263\) | −26.0874 | −1.60862 | −0.804309 | − | 0.594211i | \(-0.797464\pi\) | ||||
−0.804309 | + | 0.594211i | \(0.797464\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.907604 | − | 1.57202i | −0.0557537 | − | 0.0965682i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.890530 | − | 1.54244i | −0.0543978 | − | 0.0942197i | ||||
\(269\) | 3.81655 | + | 6.61046i | 0.232699 | + | 0.403047i | 0.958602 | − | 0.284751i | \(-0.0919109\pi\) |
−0.725902 | + | 0.687798i | \(0.758578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.70187 | − | 2.94772i | 0.103381 | − | 0.179061i | −0.809695 | − | 0.586852i | \(-0.800367\pi\) |
0.913076 | + | 0.407790i | \(0.133701\pi\) | |||||||
\(272\) | 6.97565 | − | 12.0822i | 0.422961 | − | 0.732590i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.85638 | + | 6.67945i | 0.232973 | + | 0.403520i | ||||
\(275\) | −0.660444 | −0.0398263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.72193 | −0.343798 | −0.171899 | − | 0.985115i | \(-0.554990\pi\) | ||||
−0.171899 | + | 0.985115i | \(0.554990\pi\) | |||||||
\(278\) | 0.622426 | − | 1.07807i | 0.0373306 | − | 0.0646585i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1887 | − | 24.5755i | 0.846425 | − | 1.46605i | −0.0379535 | − | 0.999280i | \(-0.512084\pi\) |
0.884378 | − | 0.466771i | \(-0.154583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.28564 | − | 3.95885i | 0.135867 | − | 0.235329i | −0.790061 | − | 0.613028i | \(-0.789951\pi\) |
0.925929 | + | 0.377699i | \(0.123285\pi\) | |||||||
\(284\) | −1.22281 | + | 2.11797i | −0.0725605 | + | 0.125678i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.83544 | − | 3.17907i | 0.108532 | − | 0.187982i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.975185 | − | 1.68907i | 0.0573638 | − | 0.0993571i | ||||
\(290\) | 29.9564 | 1.75910 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.89756 | −0.111046 | ||||||||
\(293\) | −2.16385 | − | 3.74789i | −0.126413 | − | 0.218954i | 0.795871 | − | 0.605466i | \(-0.207013\pi\) |
−0.922285 | + | 0.386512i | \(0.873680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.932419 | + | 1.61500i | −0.0542875 | + | 0.0940287i | ||||
\(296\) | 11.3033 | − | 19.5780i | 0.656994 | − | 1.13795i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.87733 | − | 10.1798i | −0.340464 | − | 0.589702i | ||||
\(299\) | 0.308811 | + | 0.534876i | 0.0178590 | + | 0.0309327i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.4133 | + | 21.5004i | 0.714304 | + | 1.23721i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.85710 | −0.450635 | ||||||||
\(305\) | 1.21301 | + | 2.10100i | 0.0694568 | + | 0.120303i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3773 | −0.706411 | −0.353206 | − | 0.935546i | \(-0.614908\pi\) | ||||
−0.353206 | + | 0.935546i | \(0.614908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −26.2003 | −1.48808 | ||||||||
\(311\) | 10.9927 | − | 19.0400i | 0.623340 | − | 1.07966i | −0.365519 | − | 0.930804i | \(-0.619108\pi\) |
0.988859 | − | 0.148853i | \(-0.0475582\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.94491 | − | 12.0289i | −0.392549 | − | 0.679915i | 0.600236 | − | 0.799823i | \(-0.295073\pi\) |
−0.992785 | + | 0.119908i | \(0.961740\pi\) | |||||||
\(314\) | 6.63404 | 0.374380 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.33544 | 0.131379 | ||||||||
\(317\) | −3.09105 | − | 5.35386i | −0.173611 | − | 0.300703i | 0.766069 | − | 0.642759i | \(-0.222210\pi\) |
−0.939680 | + | 0.342056i | \(0.888877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.05438 | + | 3.55829i | −0.115023 | + | 0.199226i | ||||
\(320\) | 21.7665 | 1.21678 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.47565 | 0.471598 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.10947 | + | 7.11781i | 0.227952 | + | 0.394825i | ||||
\(326\) | −10.2909 | −0.569958 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.27719 | + | 5.67626i | 0.180952 | + | 0.313419i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.36571 | − | 9.29369i | −0.294926 | − | 0.510827i | 0.680041 | − | 0.733174i | \(-0.261962\pi\) |
−0.974968 | + | 0.222346i | \(0.928628\pi\) | |||||||
\(332\) | −0.252374 | − | 0.437124i | −0.0138508 | − | 0.0239903i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.80974 | + | 6.59867i | −0.208460 | + | 0.361063i | ||||
\(335\) | 12.2023 | − | 21.1351i | 0.666685 | − | 1.15473i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.29726 | + | 16.1033i | 0.506454 | + | 0.877204i | 0.999972 | + | 0.00746831i | \(0.00237726\pi\) |
−0.493518 | + | 0.869735i | \(0.664289\pi\) | |||||||
\(338\) | −28.1676 | −1.53211 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.81521 | −0.0984434 | ||||||||
\(341\) | 1.79679 | − | 3.11213i | 0.0973016 | − | 0.168531i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.80541 | + | 3.12706i | −0.0973410 | + | 0.168600i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.1932 | − | 24.5834i | 0.763034 | − | 1.32161i | ||||
\(347\) | −10.2062 | + | 17.6777i | −0.547898 | + | 0.948987i | 0.450521 | + | 0.892766i | \(0.351238\pi\) |
−0.998418 | + | 0.0562207i | \(0.982095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.78106 | + | 3.08489i | −0.0953379 | + | 0.165130i | −0.909750 | − | 0.415157i | \(-0.863726\pi\) |
0.814412 | + | 0.580288i | \(0.197060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.243756 | + | 0.422197i | −0.0129922 | + | 0.0225032i | ||||
\(353\) | 10.0223 | 0.533433 | 0.266716 | − | 0.963775i | \(-0.414061\pi\) | ||||
0.266716 | + | 0.963775i | \(0.414061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.5107 | −1.77857 | ||||||||
\(356\) | −0.749686 | − | 1.29849i | −0.0397333 | − | 0.0688200i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.44949 | − | 5.97470i | 0.182311 | − | 0.315773i | ||||
\(359\) | 4.74035 | − | 8.21053i | 0.250186 | − | 0.433335i | −0.713391 | − | 0.700766i | \(-0.752841\pi\) |
0.963577 | + | 0.267431i | \(0.0861748\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.11334 | + | 12.3207i | 0.374386 | + | 0.648456i | ||||
\(362\) | 0.215537 | + | 0.373321i | 0.0113284 | + | 0.0196213i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0005 | − | 22.5175i | −0.680476 | − | 1.17862i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.1334 | −0.842157 | −0.421079 | − | 0.907024i | \(-0.638348\pi\) | ||||
−0.421079 | + | 0.907024i | \(0.638348\pi\) | |||||||
\(368\) | 0.190722 | + | 0.330341i | 0.00994209 | + | 0.0172202i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.2003 | 1.36209 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0496 | 0.727462 | 0.363731 | − | 0.931504i | \(-0.381503\pi\) | ||||
0.363731 | + | 0.931504i | \(0.381503\pi\) | |||||||
\(374\) | −1.22281 | + | 2.11797i | −0.0632301 | + | 0.109518i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.84864 | + | 13.5942i | 0.404763 | + | 0.701070i | ||||
\(377\) | 51.1317 | 2.63341 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0574 | 0.824812 | 0.412406 | − | 0.911000i | \(-0.364689\pi\) | ||||
0.412406 | + | 0.911000i | \(0.364689\pi\) | |||||||
\(380\) | 0.511144 | + | 0.885328i | 0.0262212 | + | 0.0454164i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.4868 | − | 18.1637i | 0.536551 | − | 0.929334i | ||||
\(383\) | −32.0205 | −1.63617 | −0.818086 | − | 0.575095i | \(-0.804965\pi\) | ||||
−0.818086 | + | 0.575095i | \(0.804965\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.14022 | −0.414326 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.25696 | + | 2.17712i | 0.0638124 | + | 0.110526i | ||||
\(389\) | 30.0428 | 1.52323 | 0.761616 | − | 0.648029i | \(-0.224406\pi\) | ||||
0.761616 | + | 0.648029i | \(0.224406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.205737 | − | 0.356347i | −0.0104046 | − | 0.0180212i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.9991 | − | 29.4433i | −0.856403 | − | 1.48333i | ||||
\(395\) | 16.0005 | + | 27.7136i | 0.805071 | + | 1.39442i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.15998 | + | 10.6694i | −0.309160 | + | 0.535482i | −0.978179 | − | 0.207764i | \(-0.933381\pi\) |
0.669019 | + | 0.743246i | \(0.266715\pi\) | |||||||
\(398\) | −2.04916 | + | 3.54925i | −0.102715 | + | 0.177908i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.53802 | + | 4.39598i | 0.126901 | + | 0.219799i | ||||
\(401\) | −20.9760 | −1.04749 | −0.523745 | − | 0.851875i | \(-0.675465\pi\) | ||||
−0.523745 | + | 0.851875i | \(0.675465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44.7205 | −2.22769 | ||||||||
\(404\) | −0.884600 | + | 1.53217i | −0.0440105 | + | 0.0762284i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.79679 | + | 3.11213i | −0.0890635 | + | 0.154263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.8307 | − | 22.2234i | 0.634437 | − | 1.09888i | −0.352197 | − | 0.935926i | \(-0.614565\pi\) |
0.986634 | − | 0.162951i | \(-0.0521012\pi\) | |||||||
\(410\) | −3.79813 | + | 6.57856i | −0.187576 | + | 0.324892i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.281059 | + | 0.486809i | −0.0138468 | + | 0.0239833i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.45811 | − | 5.98962i | 0.169752 | − | 0.294019i | ||||
\(416\) | 6.06687 | 0.297453 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.37733 | 0.0673672 | ||||||||
\(419\) | 0.739885 | + | 1.28152i | 0.0361458 | + | 0.0626063i | 0.883532 | − | 0.468370i | \(-0.155159\pi\) |
−0.847387 | + | 0.530976i | \(0.821825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55350 | + | 11.3510i | −0.319398 | + | 0.553214i | −0.980363 | − | 0.197203i | \(-0.936814\pi\) |
0.660965 | + | 0.750417i | \(0.270147\pi\) | |||||||
\(422\) | −3.67365 | + | 6.36295i | −0.178830 | + | 0.309743i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.05509 | − | 1.82747i | −0.0512398 | − | 0.0887500i | ||||
\(425\) | −2.73783 | − | 4.74205i | −0.132804 | − | 0.230023i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.602196 | + | 1.04303i | 0.0291083 | + | 0.0504170i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.18479 | −0.201809 | ||||||||
\(431\) | 8.86349 | + | 15.3520i | 0.426939 | + | 0.739481i | 0.996599 | − | 0.0823997i | \(-0.0262584\pi\) |
−0.569660 | + | 0.821881i | \(0.692925\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.83843 | 0.280577 | 0.140289 | − | 0.990111i | \(-0.455197\pi\) | ||||
0.140289 | + | 0.990111i | \(0.455197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.96585 | −0.0941472 | ||||||||
\(437\) | −0.115867 | + | 0.200688i | −0.00554267 | + | 0.00960019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.9277 | + | 25.8555i | 0.712459 | + | 1.23401i | 0.963931 | + | 0.266151i | \(0.0857518\pi\) |
−0.251473 | + | 0.967864i | \(0.580915\pi\) | |||||||
\(440\) | −3.48751 | −0.166261 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.4347 | 1.44763 | ||||||||
\(443\) | 5.33275 | + | 9.23659i | 0.253367 | + | 0.438844i | 0.964451 | − | 0.264263i | \(-0.0851288\pi\) |
−0.711084 | + | 0.703107i | \(0.751795\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2724 | − | 17.7924i | 0.486960 | − | 0.843440i | ||||
\(446\) | 19.1215 | 0.905432 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.55438 | −0.167741 | −0.0838707 | − | 0.996477i | \(-0.526728\pi\) | ||||
−0.0838707 | + | 0.996477i | \(0.526728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.520945 | − | 0.902302i | −0.0245303 | − | 0.0424878i | ||||
\(452\) | 0.956680 | 0.0449985 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.94949 | − | 3.37662i | −0.0914942 | − | 0.158473i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.51161 | − | 4.35024i | −0.117488 | − | 0.203496i | 0.801283 | − | 0.598285i | \(-0.204151\pi\) |
−0.918772 | + | 0.394789i | \(0.870818\pi\) | |||||||
\(458\) | −6.17571 | − | 10.6966i | −0.288572 | − | 0.499821i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.0248149 | − | 0.0429807i | 0.00115700 | − | 0.00200399i | ||||
\(461\) | −9.23055 | + | 15.9878i | −0.429910 | + | 0.744625i | −0.996865 | − | 0.0791233i | \(-0.974788\pi\) |
0.566955 | + | 0.823749i | \(0.308121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.11721 | + | 12.3274i | 0.330765 | + | 0.572902i | 0.982662 | − | 0.185406i | \(-0.0593600\pi\) |
−0.651897 | + | 0.758307i | \(0.726027\pi\) | |||||||
\(464\) | 31.5790 | 1.46602 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.8803 | 0.828290 | ||||||||
\(467\) | 1.68433 | − | 2.91734i | 0.0779413 | − | 0.134998i | −0.824420 | − | 0.565978i | \(-0.808499\pi\) |
0.902362 | + | 0.430980i | \(0.141832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.09627 | + | 15.7552i | −0.419579 | + | 0.726733i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.08394 | + | 1.87744i | −0.0498924 | + | 0.0864162i | ||||
\(473\) | 0.286989 | − | 0.497079i | 0.0131958 | − | 0.0228557i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.54189 | + | 2.67063i | −0.0707467 | + | 0.122537i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.42468 | + | 11.1279i | −0.293858 | + | 0.508977i | ||||
\(479\) | −36.7665 | −1.67990 | −0.839952 | − | 0.542660i | \(-0.817417\pi\) | ||||
−0.839952 | + | 0.542660i | \(0.817417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.7205 | 2.03908 | ||||||||
\(482\) | 6.03462 | + | 10.4523i | 0.274869 | + | 0.476087i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.996130 | + | 1.72535i | −0.0452786 | + | 0.0784249i | ||||
\(485\) | −17.2233 | + | 29.8316i | −0.782069 | + | 1.35458i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7087 | + | 32.4045i | 0.847773 | + | 1.46839i | 0.883191 | + | 0.469014i | \(0.155391\pi\) |
−0.0354172 | + | 0.999373i | \(0.511276\pi\) | |||||||
\(488\) | 1.41013 | + | 2.44242i | 0.0638336 | + | 0.110563i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3353 | − | 23.0974i | −0.601813 | − | 1.04237i | −0.992547 | − | 0.121866i | \(-0.961112\pi\) |
0.390734 | − | 0.920504i | \(-0.372221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.0651 | −1.53422 | ||||||||
\(494\) | −8.57011 | − | 14.8439i | −0.385587 | − | 0.667857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −27.6195 | −1.24015 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.7452 | 1.51064 | 0.755320 | − | 0.655356i | \(-0.227481\pi\) | ||||
0.755320 | + | 0.655356i | \(0.227481\pi\) | |||||||
\(500\) | −0.839556 | + | 1.45415i | −0.0375461 | + | 0.0650317i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.8400 | − | 29.1678i | −0.751607 | − | 1.30182i | ||||
\(503\) | −32.0401 | −1.42860 | −0.714299 | − | 0.699840i | \(-0.753255\pi\) | ||||
−0.714299 | + | 0.699840i | \(0.753255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.2422 | −1.07876 | ||||||||
\(506\) | −0.0334331 | − | 0.0579078i | −0.00148628 | − | 0.00257431i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.820670 | + | 1.42144i | −0.0364114 | + | 0.0630663i | ||||
\(509\) | −7.93851 | −0.351868 | −0.175934 | − | 0.984402i | \(-0.556295\pi\) | ||||
−0.175934 | + | 0.984402i | \(0.556295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.9186 | 1.10126 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.31046 | + | 12.6621i | 0.322451 | + | 0.558501i | ||||
\(515\) | −7.70233 | −0.339405 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.24763 | − | 2.16095i | −0.0548705 | − | 0.0950386i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.7003 | + | 37.5860i | 0.951620 | + | 1.64825i | ||||
\(521\) | 7.33750 | + | 12.7089i | 0.321462 | + | 0.556788i | 0.980790 | − | 0.195067i | \(-0.0624926\pi\) |
−0.659328 | + | 0.751855i | \(0.729159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.1716 | − | 24.5459i | 0.619680 | − | 1.07332i | −0.369864 | − | 0.929086i | \(-0.620596\pi\) |
0.989544 | − | 0.144232i | \(-0.0460711\pi\) | |||||||
\(524\) | 1.04988 | − | 1.81844i | 0.0458641 | − | 0.0794390i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.5737 | − | 30.4386i | −0.766251 | − | 1.32719i | ||||
\(527\) | 29.7939 | 1.29784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9887 | −0.999511 | ||||||||
\(530\) | 1.22281 | − | 2.11797i | 0.0531155 | − | 0.0919988i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.48293 | + | 11.2288i | −0.280807 | + | 0.486371i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.25150 | + | 14.2920i | −0.356743 | + | 0.617898i | ||||
\(536\) | 14.1853 | − | 24.5696i | 0.612710 | − | 1.06124i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.14203 | + | 8.90625i | −0.221688 | + | 0.383976i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.64290 | + | 9.77380i | −0.242607 | + | 0.420208i | −0.961456 | − | 0.274958i | \(-0.911336\pi\) |
0.718849 | + | 0.695166i | \(0.244669\pi\) | |||||||
\(542\) | 4.58584 | 0.196979 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.04189 | −0.173295 | ||||||||
\(545\) | −13.4684 | − | 23.3279i | −0.576922 | − | 0.999258i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6202 | − | 25.3229i | 0.625115 | − | 1.08273i | −0.363404 | − | 0.931632i | \(-0.618385\pi\) |
0.988519 | − | 0.151099i | \(-0.0482812\pi\) | |||||||
\(548\) | 0.528934 | − | 0.916140i | 0.0225949 | − | 0.0391356i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.444907 | − | 0.770602i | −0.0189709 | − | 0.0328586i | ||||
\(551\) | 9.59240 | + | 16.6145i | 0.408650 | + | 0.707802i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.85457 | − | 6.67631i | −0.163765 | − | 0.283649i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.170741 | −0.00724105 | ||||||||
\(557\) | −0.387841 | − | 0.671761i | −0.0164334 | − | 0.0284634i | 0.857692 | − | 0.514164i | \(-0.171898\pi\) |
−0.874125 | + | 0.485701i | \(0.838564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.14290 | −0.302113 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 38.2327 | 1.61275 | ||||||||
\(563\) | −12.4761 | + | 21.6093i | −0.525806 | + | 0.910722i | 0.473742 | + | 0.880663i | \(0.342903\pi\) |
−0.999548 | + | 0.0300588i | \(0.990431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.55438 | + | 11.3525i | 0.275745 | + | 0.477604i | ||||
\(566\) | 6.15888 | 0.258877 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −38.9564 | −1.63457 | ||||||||
\(569\) | −12.4017 | − | 21.4803i | −0.519905 | − | 0.900502i | −0.999732 | − | 0.0231391i | \(-0.992634\pi\) |
0.479827 | − | 0.877363i | \(-0.340699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.39827 | + | 7.61803i | −0.184062 | + | 0.318805i | −0.943260 | − | 0.332055i | \(-0.892258\pi\) |
0.759198 | + | 0.650860i | \(0.225591\pi\) | |||||||
\(572\) | −0.503490 | −0.0210520 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.149711 | 0.00624336 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.43717 | − | 11.1495i | −0.267983 | − | 0.464160i | 0.700358 | − | 0.713792i | \(-0.253024\pi\) |
−0.968341 | + | 0.249632i | \(0.919690\pi\) | |||||||
\(578\) | 2.62773 | 0.109299 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.05438 | − | 3.55829i | −0.0853034 | − | 0.147750i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.167718 | + | 0.290497i | 0.00694619 | + | 0.0120311i | ||||
\(584\) | −15.1131 | − | 26.1766i | −0.625384 | − | 1.08320i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.91534 | − | 5.04952i | 0.120432 | − | 0.208594i | ||||
\(587\) | −22.4315 | + | 38.8526i | −0.925849 | + | 1.60362i | −0.135658 | + | 0.990756i | \(0.543315\pi\) |
−0.790190 | + | 0.612861i | \(0.790018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.38965 | − | 14.5313i | −0.345690 | − | 0.598752i | ||||
\(590\) | −2.51249 | −0.103438 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.6195 | 1.13515 | ||||||||
\(593\) | −1.88026 | + | 3.25671i | −0.0772131 | + | 0.133737i | −0.902047 | − | 0.431639i | \(-0.857936\pi\) |
0.824833 | + | 0.565376i | \(0.191269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.806123 | + | 1.39625i | −0.0330201 | + | 0.0571924i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.416060 | + | 0.720637i | −0.0170139 | + | 0.0294690i | ||||
\(599\) | −1.84524 | + | 3.19604i | −0.0753943 | + | 0.130587i | −0.901258 | − | 0.433283i | \(-0.857355\pi\) |
0.825863 | + | 0.563870i | \(0.190688\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9285 | + | 18.9288i | −0.445785 | + | 0.772122i | −0.998107 | − | 0.0615091i | \(-0.980409\pi\) |
0.552322 | + | 0.833631i | \(0.313742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.70258 | − | 2.94896i | 0.0692771 | − | 0.119991i | ||||
\(605\) | −27.2986 | −1.10985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.3946 | −0.990145 | −0.495072 | − | 0.868852i | \(-0.664858\pi\) | ||||
−0.495072 | + | 0.868852i | \(0.664858\pi\) | |||||||
\(608\) | 1.13816 | + | 1.97134i | 0.0461583 | + | 0.0799485i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.63429 | + | 2.83067i | −0.0661703 | + | 0.114610i | ||||
\(611\) | −15.5262 | + | 26.8921i | −0.628121 | + | 1.08794i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0107 | − | 36.3917i | −0.848616 | − | 1.46985i | −0.882444 | − | 0.470418i | \(-0.844103\pi\) |
0.0338284 | − | 0.999428i | \(-0.489230\pi\) | |||||||
\(614\) | −8.33796 | − | 14.4418i | −0.336493 | − | 0.582823i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2049 | + | 40.1920i | 0.934192 | + | 1.61807i | 0.776068 | + | 0.630650i | \(0.217212\pi\) |
0.158125 | + | 0.987419i | \(0.449455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.2094 | 1.09364 | 0.546820 | − | 0.837250i | \(-0.315838\pi\) | ||||
0.546820 | + | 0.837250i | \(0.315838\pi\) | |||||||
\(620\) | 1.79679 | + | 3.11213i | 0.0721608 | + | 0.124986i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.6209 | 1.18769 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0651 | −1.20260 | ||||||||
\(626\) | 9.35685 | − | 16.2065i | 0.373975 | − | 0.647743i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.454956 | − | 0.788006i | −0.0181547 | − | 0.0314449i | ||||
\(629\) | −29.7939 | −1.18796 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6023 | −1.17845 | −0.589224 | − | 0.807970i | \(-0.700566\pi\) | ||||
−0.589224 | + | 0.807970i | \(0.700566\pi\) | |||||||
\(632\) | 18.6006 | + | 32.2172i | 0.739892 | + | 1.28153i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.16456 | − | 7.21324i | 0.165396 | − | 0.286474i | ||||
\(635\) | −22.4902 | −0.892496 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.53571 | −0.219161 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.0248 | + | 20.8276i | 0.475323 | + | 0.823283i | ||||
\(641\) | 0.279000 | 0.0110198 | 0.00550991 | − | 0.999985i | \(-0.498246\pi\) | ||||
0.00550991 | + | 0.999985i | \(0.498246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.12196 | − | 15.7997i | −0.359735 | − | 0.623079i | 0.628181 | − | 0.778067i | \(-0.283800\pi\) |
−0.987916 | + | 0.154988i | \(0.950466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.70961 | + | 9.88933i | 0.224642 | + | 0.389090i | ||||
\(647\) | −11.2285 | − | 19.4483i | −0.441438 | − | 0.764592i | 0.556359 | − | 0.830942i | \(-0.312198\pi\) |
−0.997796 | + | 0.0663498i | \(0.978865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.172304 | − | 0.298439i | 0.00676352 | − | 0.0117148i | ||||
\(650\) | −5.53667 | + | 9.58980i | −0.217166 | + | 0.376143i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.705737 | + | 1.22237i | 0.0276388 | + | 0.0478718i | ||||
\(653\) | 50.5313 | 1.97744 | 0.988721 | − | 0.149771i | \(-0.0478538\pi\) | ||||
0.988721 | + | 0.149771i | \(0.0478538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.7716 | 1.12420 | ||||||||
\(656\) | −4.00387 | + | 6.93491i | −0.156325 | + | 0.270763i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.33631 | + | 2.31456i | −0.0520554 | + | 0.0901626i | −0.890879 | − | 0.454241i | \(-0.849911\pi\) |
0.838824 | + | 0.544403i | \(0.183244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.3050 | + | 29.9731i | −0.673086 | + | 1.16582i | 0.303938 | + | 0.952692i | \(0.401698\pi\) |
−0.977024 | + | 0.213128i | \(0.931635\pi\) | |||||||
\(662\) | 7.22921 | − | 12.5214i | 0.280971 | − | 0.486656i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.02007 | − | 6.96296i | 0.156009 | − | 0.270215i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.465690 | − | 0.806598i | 0.0180316 | − | 0.0312316i | ||||
\(668\) | 1.04507 | 0.0404351 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32.8803 | 1.27028 | ||||||||
\(671\) | −0.224155 | − | 0.388249i | −0.00865342 | − | 0.0149882i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.25624 | + | 14.3002i | −0.318255 | + | 0.551234i | −0.980124 | − | 0.198386i | \(-0.936430\pi\) |
0.661869 | + | 0.749619i | \(0.269763\pi\) | |||||||
\(674\) | −12.5262 | + | 21.6959i | −0.482490 | + | 0.835697i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.93170 | + | 3.34581i | 0.0742963 | + | 0.128685i | ||||
\(677\) | 21.8790 | + | 37.8955i | 0.840877 | + | 1.45644i | 0.889154 | + | 0.457608i | \(0.151294\pi\) |
−0.0482766 | + | 0.998834i | \(0.515373\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.4572 | − | 25.0407i | −0.554410 | − | 0.960266i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.84161 | 0.185395 | ||||||||
\(683\) | 14.1206 | + | 24.4576i | 0.540310 | + | 0.935845i | 0.998886 | + | 0.0471895i | \(0.0150265\pi\) |
−0.458576 | + | 0.888655i | \(0.651640\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.4953 | 0.553835 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.41147 | −0.168186 | ||||||||
\(689\) | 2.08718 | − | 3.61510i | 0.0795153 | − | 0.137725i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5326 | − | 25.1711i | −0.552844 | − | 0.957555i | −0.998068 | − | 0.0621351i | \(-0.980209\pi\) |
0.445223 | − | 0.895420i | \(-0.353124\pi\) | |||||||
\(692\) | −3.89344 | −0.148006 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.5016 | −1.04395 | ||||||||
\(695\) | −1.16978 | − | 2.02611i | −0.0443722 | − | 0.0768549i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.31908 | − | 7.48086i | 0.163597 | − | 0.283358i | ||||
\(698\) | −4.79923 | −0.181654 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.10876 | 0.0418771 | 0.0209386 | − | 0.999781i | \(-0.493335\pi\) | ||||
0.0209386 | + | 0.999781i | \(0.493335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.38965 | + | 14.5313i | 0.316422 | + | 0.548059i | ||||
\(704\) | −4.02229 | −0.151596 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.75150 | + | 11.6939i | 0.254096 | + | 0.440107i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.23442 | + | 15.9945i | 0.346806 | + | 0.600686i | 0.985680 | − | 0.168626i | \(-0.0539329\pi\) |
−0.638874 | + | 0.769311i | \(0.720600\pi\) | |||||||
\(710\) | −22.5744 | − | 39.1001i | −0.847204 | − | 1.46740i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.9418 | − | 20.6837i | 0.447536 | − | 0.775155i | ||||
\(713\) | −0.407299 | + | 0.705463i | −0.0152535 | + | 0.0264198i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.44949 | − | 5.97470i | −0.129004 | − | 0.223441i | ||||
\(716\) | −0.946251 | −0.0353631 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.7733 | 0.476696 | ||||||||
\(719\) | 16.8885 | − | 29.2517i | 0.629834 | − | 1.09090i | −0.357751 | − | 0.933817i | \(-0.616456\pi\) |
0.987585 | − | 0.157087i | \(-0.0502103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.58378 | + | 16.5996i | −0.356671 | + | 0.617773i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.0295627 | − | 0.0512040i | 0.00109869 | − | 0.00190298i | ||||
\(725\) | 6.19712 | − | 10.7337i | 0.230155 | − | 0.398641i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.40214 | − | 14.5529i | 0.311618 | − | 0.539738i | −0.667095 | − | 0.744973i | \(-0.732462\pi\) |
0.978713 | + | 0.205234i | \(0.0657957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 17.5155 | − | 30.3377i | 0.648277 | − | 1.12285i | ||||
\(731\) | 4.75877 | 0.176009 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.6364 | 0.503672 | 0.251836 | − | 0.967770i | \(-0.418966\pi\) | ||||
0.251836 | + | 0.967770i | \(0.418966\pi\) | |||||||
\(734\) | −10.8682 | − | 18.8243i | −0.401154 | − | 0.694819i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0552549 | − | 0.0957044i | 0.00203672 | − | 0.00352771i | ||||
\(737\) | −2.25490 | + | 3.90560i | −0.0830603 | + | 0.143865i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0209 | + | 27.7491i | 0.589340 | + | 1.02077i | 0.994319 | + | 0.106441i | \(0.0339455\pi\) |
−0.404979 | + | 0.914326i | \(0.632721\pi\) | |||||||
\(740\) | −1.79679 | − | 3.11213i | −0.0660513 | − | 0.114404i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8764 | + | 29.2309i | 0.619137 | + | 1.07238i | 0.989644 | + | 0.143547i | \(0.0458507\pi\) |
−0.370507 | + | 0.928830i | \(0.620816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.0915 | −0.809371 | ||||||||
\(746\) | 9.46451 | + | 16.3930i | 0.346520 | + | 0.600191i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.335437 | 0.0122648 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.1165 | 0.953004 | 0.476502 | − | 0.879173i | \(-0.341904\pi\) | ||||
0.476502 | + | 0.879173i | \(0.341904\pi\) | |||||||
\(752\) | −9.58899 | + | 16.6086i | −0.349675 | + | 0.605654i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.4447 | + | 59.6600i | 1.25440 | + | 2.17269i | ||||
\(755\) | 46.6587 | 1.69808 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.6536 | 1.29585 | 0.647927 | − | 0.761703i | \(-0.275636\pi\) | ||||
0.647927 | + | 0.761703i | \(0.275636\pi\) | |||||||
\(758\) | 10.8170 | + | 18.7356i | 0.392892 | + | 0.680509i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.14203 | + | 14.1024i | −0.295342 | + | 0.511548i | ||||
\(761\) | 40.7648 | 1.47772 | 0.738861 | − | 0.673858i | \(-0.235364\pi\) | ||||
0.738861 | + | 0.673858i | \(0.235364\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.87670 | −0.104075 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.5706 | − | 37.3613i | −0.779377 | − | 1.34992i | ||||
\(767\) | −4.28850 | −0.154849 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.7135 | + | 34.1447i | 0.710886 | + | 1.23129i | 0.964525 | + | 0.263992i | \(0.0850392\pi\) |
−0.253639 | + | 0.967299i | \(0.581627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.558248 | + | 0.966914i | 0.0200918 | + | 0.0348000i | ||||
\(773\) | −12.4513 | − | 21.5663i | −0.447842 | − | 0.775686i | 0.550403 | − | 0.834899i | \(-0.314474\pi\) |
−0.998245 | + | 0.0592135i | \(0.981141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.42009 | + | 9.38788i | −0.194695 | + | 0.337222i | ||||
\(776\) | −20.0221 | + | 34.6793i | −0.718752 | + | 1.24492i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.2383 | + | 35.0538i | 0.725578 | + | 1.25674i | ||||
\(779\) | −4.86484 | −0.174301 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.19253 | 0.221586 | ||||||||
\(782\) | 0.277189 | − | 0.480105i | 0.00991225 | − | 0.0171685i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.23396 | − | 10.7975i | 0.222499 | − | 0.385380i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3525 | + | 26.5913i | −0.547258 | + | 0.947879i | 0.451203 | + | 0.892421i | \(0.350995\pi\) |
−0.998461 | + | 0.0554572i | \(0.982338\pi\) | |||||||
\(788\) | −2.33157 | + | 4.03839i | −0.0830586 | + | 0.143862i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.5574 | + | 37.3385i | −0.766977 | + | 1.32844i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.78952 | + | 4.83158i | −0.0990586 | + | 0.171575i | ||||
\(794\) | −16.5986 | −0.589063 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.562118 | 0.0199238 | ||||||||
\(797\) | 5.50686 | + | 9.53817i | 0.195063 | + | 0.337859i | 0.946921 | − | 0.321466i | \(-0.104175\pi\) |
−0.751858 | + | 0.659325i | \(0.770842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.3439 | − | 17.9161i | 0.365941 | − | 0.633828i | ||||
\(800\) | 0.735300 | − | 1.27358i | 0.0259968 | − | 0.0450277i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.1304 | − | 24.4746i | −0.498962 | − | 0.864228i | ||||
\(803\) | 2.40239 | + | 4.16106i | 0.0847785 | + | 0.146841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.1259 | − | 52.1796i | −1.06114 | − | 1.83795i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.1816 | −0.991425 | ||||||||
\(809\) | 8.49407 | + | 14.7122i | 0.298636 | + | 0.517252i | 0.975824 | − | 0.218558i | \(-0.0701352\pi\) |
−0.677188 | + | 0.735810i | \(0.736802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.9796 | −1.33364 | −0.666822 | − | 0.745217i | \(-0.732346\pi\) | ||||
−0.666822 | + | 0.745217i | \(0.732346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.84161 | −0.169699 | ||||||||
\(815\) | −9.67024 | + | 16.7494i | −0.338734 | + | 0.586704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.34002 | − | 2.32099i | −0.0468814 | − | 0.0812011i | ||||
\(818\) | 34.5735 | 1.20883 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.04189 | 0.0363843 | ||||||||
\(821\) | 4.13934 | + | 7.16954i | 0.144464 | + | 0.250219i | 0.929173 | − | 0.369646i | \(-0.120521\pi\) |
−0.784709 | + | 0.619864i | \(0.787188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2763 | + | 47.2440i | −0.950792 | + | 1.64682i | −0.207077 | + | 0.978325i | \(0.566395\pi\) |
−0.743716 | + | 0.668496i | \(0.766938\pi\) | |||||||
\(824\) | −8.95399 | −0.311927 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8708 | 1.10826 | 0.554129 | − | 0.832431i | \(-0.313052\pi\) | ||||
0.554129 | + | 0.832431i | \(0.313052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.176174 | − | 0.305143i | −0.00611879 | − | 0.0105981i | 0.862950 | − | 0.505290i | \(-0.168614\pi\) |
−0.869069 | + | 0.494692i | \(0.835281\pi\) | |||||||
\(830\) | 9.31820 | 0.323439 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.0278 | + | 43.3494i | 0.867683 | + | 1.50287i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.15998 | + | 12.4014i | 0.247781 | + | 0.429170i | ||||
\(836\) | −0.0944557 | − | 0.163602i | −0.00326682 | − | 0.00565829i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.996845 | + | 1.72659i | −0.0344354 | + | 0.0596439i | ||||
\(839\) | −12.5077 | + | 21.6640i | −0.431815 | + | 0.747926i | −0.997030 | − | 0.0770182i | \(-0.975460\pi\) |
0.565215 | + | 0.824944i | \(0.308793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0535 | − | 41.6619i | −0.829431 | − | 1.43662i | ||||
\(842\) | −17.6590 | −0.608570 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.00774 | 0.0346879 | ||||||||
\(845\) | −26.4688 | + | 45.8454i | −0.910556 | + | 1.57713i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.28905 | − | 2.23270i | 0.0442661 | − | 0.0766711i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.68866 | − | 6.38895i | 0.126520 | − | 0.219139i | ||||
\(851\) | 0.407299 | − | 0.705463i | 0.0139620 | − | 0.0241829i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.5954 | − | 33.9402i | 0.670933 | − | 1.16209i | −0.306706 | − | 0.951804i | \(-0.599227\pi\) |
0.977640 | − | 0.210286i | \(-0.0674397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.59240 | + | 16.6145i | −0.327861 | + | 0.567873i | ||||
\(857\) | 16.4074 | 0.560465 | 0.280232 | − | 0.959932i | \(-0.409589\pi\) | ||||
0.280232 | + | 0.959932i | \(0.409589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.8324 | 0.915511 | 0.457756 | − | 0.889078i | \(-0.348653\pi\) | ||||
0.457756 | + | 0.889078i | \(0.348653\pi\) | |||||||
\(860\) | 0.286989 | + | 0.497079i | 0.00978624 | + | 0.0169503i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.9418 | + | 20.6837i | −0.406738 | + | 0.704490i | ||||
\(863\) | 7.25284 | − | 12.5623i | 0.246890 | − | 0.427625i | −0.715772 | − | 0.698334i | \(-0.753925\pi\) |
0.962661 | + | 0.270709i | \(0.0872582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.6746 | − | 46.2017i | −0.906963 | − | 1.57091i | ||||
\(866\) | 3.93305 | + | 6.81224i | 0.133650 | + | 0.231489i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.95677 | − | 5.12127i | −0.100301 | − | 0.173727i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.1225 | 1.90164 | ||||||||
\(872\) | −15.6570 | − | 27.1188i | −0.530214 | − | 0.918358i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.312214 | −0.0105608 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9145 | 0.638696 | 0.319348 | − | 0.947637i | \(-0.396536\pi\) | ||||
0.319348 | + | 0.947637i | \(0.396536\pi\) | |||||||
\(878\) | −20.1120 | + | 34.8350i | −0.678747 | + | 1.17562i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.13041 | − | 3.68999i | −0.0718163 | − | 0.124389i | ||||
\(881\) | 53.8976 | 1.81585 | 0.907927 | − | 0.419128i | \(-0.137664\pi\) | ||||
0.907927 | + | 0.419128i | \(0.137664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.4252 | 1.46137 | 0.730687 | − | 0.682712i | \(-0.239200\pi\) | ||||
0.730687 | + | 0.682712i | \(0.239200\pi\) | |||||||
\(884\) | −2.08718 | − | 3.61510i | −0.0701995 | − | 0.121589i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.18479 | + | 12.4444i | −0.241378 | + | 0.418079i | ||||
\(887\) | −38.9600 | −1.30815 | −0.654074 | − | 0.756431i | \(-0.726942\pi\) | ||||
−0.654074 | + | 0.756431i | \(0.726942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27.6800 | 0.927837 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.31134 | − | 2.27130i | −0.0439068 | − | 0.0760488i | ||||
\(893\) | −11.6509 | −0.389884 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.48293 | − | 11.2288i | −0.216700 | − | 0.375336i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.39440 | − | 4.14722i | −0.0799022 | − | 0.138395i | ||||
\(899\) | 33.7195 | + | 58.4038i | 1.12461 | + | 1.94788i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.39053 | + | 2.40847i | −0.0463253 | + | 0.0802377i | ||||
\(902\) | 0.701867 | − | 1.21567i | 0.0233696 | − | 0.0404773i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.61949 | + | 13.1973i | 0.253420 | + | 0.438937i | ||||
\(905\) | 0.810155 | 0.0269305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.5276 | 1.14647 | 0.573236 | − | 0.819390i | \(-0.305688\pi\) | ||||
0.573236 | + | 0.819390i | \(0.305688\pi\) | |||||||
\(908\) | −0.267389 | + | 0.463131i | −0.00887360 | + | 0.0153695i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2631 | − | 40.2929i | 0.770741 | − | 1.33496i | −0.166416 | − | 0.986056i | \(-0.553220\pi\) |
0.937157 | − | 0.348907i | \(-0.113447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.639033 | + | 1.10684i | −0.0211489 | + | 0.0366310i | ||||
\(914\) | 3.38388 | − | 5.86106i | 0.111929 | − | 0.193867i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.847048 | + | 1.46713i | −0.0279873 | + | 0.0484753i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.97818 | − | 8.62246i | 0.164215 | − | 0.284429i | −0.772161 | − | 0.635427i | \(-0.780824\pi\) |
0.936376 | + | 0.350998i | \(0.114158\pi\) | |||||||
\(920\) | 0.790555 | 0.0260638 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.8726 | −0.819135 | ||||||||
\(923\) | −38.5317 | − | 66.7388i | −1.26829 | − | 2.19674i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.42009 | − | 9.38788i | 0.178212 | − | 0.308671i | ||||
\(926\) | −9.58899 | + | 16.6086i | −0.315114 | + | 0.545793i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.57444 | − | 7.92317i | −0.150164 | − | 0.260091i | ||||
\(929\) | −4.52300 | − | 7.83407i | −0.148395 | − | 0.257028i | 0.782239 | − | 0.622978i | \(-0.214077\pi\) |
−0.930634 | + | 0.365950i | \(0.880744\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.22621 | − | 2.12387i | −0.0401660 | − | 0.0695696i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.53857 | 0.148507 | ||||||||
\(935\) | 2.29813 | + | 3.98048i | 0.0751570 | + | 0.130176i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.3928 | 0.796878 | 0.398439 | − | 0.917195i | \(-0.369552\pi\) | ||||
0.398439 | + | 0.917195i | \(0.369552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.49525 | 0.0813862 | ||||||||
\(941\) | 29.7690 | − | 51.5615i | 0.970443 | − | 1.68086i | 0.276223 | − | 0.961094i | \(-0.410917\pi\) |
0.694220 | − | 0.719763i | \(-0.255749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.118089 | + | 0.204535i | 0.00384549 | + | 0.00666059i | ||||
\(944\) | −2.64858 | −0.0862041 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.773318 | 0.0251428 | ||||||||
\(947\) | 4.32429 | + | 7.48989i | 0.140521 | + | 0.243389i | 0.927693 | − | 0.373344i | \(-0.121789\pi\) |
−0.787172 | + | 0.616733i | \(0.788456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8967 | − | 51.7826i | 0.970487 | − | 1.68093i | ||||
\(950\) | −4.15476 | −0.134798 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.78249 | −0.122527 | −0.0612634 | − | 0.998122i | \(-0.519513\pi\) | ||||
−0.0612634 | + | 0.998122i | \(0.519513\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.7087 | − | 34.1365i | −0.637760 | − | 1.10463i | ||||
\(956\) | 1.76239 | 0.0569998 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.7677 | − | 42.8989i | −0.800208 | − | 1.38600i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9915 | − | 24.2341i | −0.451340 | − | 0.781744i | ||||
\(962\) | 30.1259 | + | 52.1796i | 0.971298 | + | 1.68234i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.827696 | − | 1.43361i | 0.0266583 | − | 0.0461735i | ||||
\(965\) | −7.64930 | + | 13.2490i | −0.246240 | + | 0.426500i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.4745 | + | 28.5346i | 0.529783 | + | 0.917611i | 0.999396 | + | 0.0347392i | \(0.0110601\pi\) |
−0.469613 | + | 0.882872i | \(0.655607\pi\) | |||||||
\(968\) | −31.7347 | −1.01999 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −46.4097 | −1.49013 | ||||||||
\(971\) | 27.7285 | − | 48.0272i | 0.889850 | − | 1.54126i | 0.0497974 | − | 0.998759i | \(-0.484142\pi\) |
0.840052 | − | 0.542506i | \(-0.182524\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −25.2062 | + | 43.6584i | −0.807659 | + | 1.39891i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.72281 | + | 2.98400i | −0.0551458 | + | 0.0955154i | ||||
\(977\) | 28.2743 | − | 48.9724i | 0.904573 | − | 1.56677i | 0.0830847 | − | 0.996542i | \(-0.473523\pi\) |
0.821489 | − | 0.570225i | \(-0.193144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.89827 | + | 3.28790i | −0.0606690 | + | 0.105082i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.9666 | − | 31.1190i | 0.573336 | − | 0.993047i | ||||
\(983\) | 28.9973 | 0.924871 | 0.462435 | − | 0.886653i | \(-0.346976\pi\) | ||||
0.462435 | + | 0.886653i | \(0.346976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.8958 | −2.03589 | ||||||||
\(986\) | −22.9479 | − | 39.7469i | −0.730810 | − | 1.26580i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.17546 | + | 2.03596i | −0.0373963 | + | 0.0647724i | ||||
\(989\) | −0.0650551 | + | 0.112679i | −0.00206863 | + | 0.00358298i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.40461 | − | 5.89696i | −0.108151 | − | 0.187323i | 0.806870 | − | 0.590729i | \(-0.201160\pi\) |
−0.915021 | + | 0.403406i | \(0.867826\pi\) | |||||||
\(992\) | 4.00088 | + | 6.92972i | 0.127028 | + | 0.220019i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.85117 | + | 6.67042i | 0.122090 | + | 0.211466i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.9377 | 1.23317 | 0.616585 | − | 0.787289i | \(-0.288516\pi\) | ||||
0.616585 | + | 0.787289i | \(0.288516\pi\) | |||||||
\(998\) | 22.7324 | + | 39.3736i | 0.719580 | + | 1.24635i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))