Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(881,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.cc (of order \(6\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.1 | ||
Root | \(-1.62181 - 0.608059i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.881 |
Dual form | 3024.2.cc.b.2897.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.94556 | + | 3.36980i | −0.870080 | + | 1.50702i | −0.00816625 | + | 0.999967i | \(0.502599\pi\) |
−0.861913 | + | 0.507056i | \(0.830734\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.343982 | − | 2.62329i | −0.130013 | − | 0.991512i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41614 | − | 1.97231i | 1.03001 | − | 0.594674i | 0.113019 | − | 0.993593i | \(-0.463948\pi\) |
0.916986 | + | 0.398919i | \(0.130615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46687 | + | 1.42425i | 0.684186 | + | 0.395015i | 0.801430 | − | 0.598088i | \(-0.204073\pi\) |
−0.117244 | + | 0.993103i | \(0.537406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.742117 | −0.179990 | −0.0899949 | − | 0.995942i | \(-0.528685\pi\) | ||||
−0.0899949 | + | 0.995942i | \(0.528685\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78474i | 0.409447i | 0.978820 | + | 0.204723i | \(0.0656295\pi\) | ||||
−0.978820 | + | 0.204723i | \(0.934370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.41535 | − | 3.12656i | −1.12918 | − | 0.651932i | −0.185451 | − | 0.982654i | \(-0.559374\pi\) |
−0.943728 | + | 0.330722i | \(0.892708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.07039 | − | 8.78217i | −1.01408 | − | 1.75643i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.50079 | − | 1.44383i | 0.464385 | − | 0.268113i | −0.249501 | − | 0.968374i | \(-0.580267\pi\) |
0.713886 | + | 0.700262i | \(0.246933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.04125 | − | 1.75587i | −0.546225 | − | 0.315363i | 0.201373 | − | 0.979515i | \(-0.435460\pi\) |
−0.747598 | + | 0.664152i | \(0.768793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.50923 | + | 3.94462i | 1.60735 | + | 0.666762i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00158 | 0.493456 | 0.246728 | − | 0.969085i | \(-0.420645\pi\) | ||||
0.246728 | + | 0.969085i | \(0.420645\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.24705 | − | 9.08816i | 0.819452 | − | 1.41933i | −0.0866345 | − | 0.996240i | \(-0.527611\pi\) |
0.906087 | − | 0.423092i | \(-0.139055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.471521 | − | 0.816699i | −0.0719063 | − | 0.124545i | 0.827830 | − | 0.560978i | \(-0.189575\pi\) |
−0.899737 | + | 0.436433i | \(0.856242\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.09263 | + | 1.89248i | 0.159376 | + | 0.276047i | 0.934644 | − | 0.355585i | \(-0.115718\pi\) |
−0.775268 | + | 0.631633i | \(0.782385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.76335 | + | 1.80473i | −0.966193 | + | 0.257819i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.3490i | 2.06965i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0105673 | − | 0.0183031i | 0.00137575 | − | 0.00238286i | −0.865337 | − | 0.501191i | \(-0.832895\pi\) |
0.866712 | + | 0.498808i | \(0.166229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.13832 | + | 1.23456i | −0.273783 | + | 0.158069i | −0.630606 | − | 0.776103i | \(-0.717193\pi\) |
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.59886 | + | 5.54191i | −1.19059 | + | 0.687389i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.72463 | − | 11.6474i | 0.821544 | − | 1.42296i | −0.0829874 | − | 0.996551i | \(-0.526446\pi\) |
0.904532 | − | 0.426406i | \(-0.140221\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.94304i | − | 0.230597i | −0.993331 | − | 0.115298i | \(-0.963218\pi\) | ||
0.993331 | − | 0.115298i | \(-0.0367824\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.85486i | 0.568218i | 0.958792 | + | 0.284109i | \(0.0916978\pi\) | ||||
−0.958792 | + | 0.284109i | \(0.908302\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.34904 | − | 8.28311i | −0.723540 | − | 0.943948i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.81806 | + | 3.14898i | 0.204548 | + | 0.354288i | 0.949989 | − | 0.312284i | \(-0.101094\pi\) |
−0.745440 | + | 0.666572i | \(0.767761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.02998 | − | 6.98012i | −0.442347 | − | 0.766168i | 0.555516 | − | 0.831506i | \(-0.312521\pi\) |
−0.997863 | + | 0.0653378i | \(0.979188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44383 | − | 2.50079i | 0.156605 | − | 0.271249i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.26646 | 0.982243 | 0.491122 | − | 0.871091i | \(-0.336587\pi\) | ||||
0.491122 | + | 0.871091i | \(0.336587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.88766 | − | 6.96124i | 0.302709 | − | 0.729736i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.01422 | − | 3.47231i | −0.617046 | − | 0.356251i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2983 | − | 9.40980i | 1.65484 | − | 0.955421i | 0.679794 | − | 0.733403i | \(-0.262069\pi\) |
0.975043 | − | 0.222018i | \(-0.0712643\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.14079 | − | 7.17206i | −0.412024 | − | 0.713647i | 0.583087 | − | 0.812410i | \(-0.301845\pi\) |
−0.995111 | + | 0.0987631i | \(0.968511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7646 | + | 8.52435i | 1.45480 | + | 0.839929i | 0.998748 | − | 0.0500247i | \(-0.0159300\pi\) |
0.456051 | + | 0.889953i | \(0.349263\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3369i | 1.38600i | 0.720936 | + | 0.693001i | \(0.243712\pi\) | ||||
−0.720936 | + | 0.693001i | \(0.756288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.2800 | 1.08042 | 0.540212 | − | 0.841529i | \(-0.318344\pi\) | ||||
0.540212 | + | 0.841529i | \(0.318344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.51501 | + | 4.91614i | 0.801024 | + | 0.462472i | 0.843829 | − | 0.536612i | \(-0.180296\pi\) |
−0.0428049 | + | 0.999083i | \(0.513629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.0718 | − | 12.1658i | 1.96495 | − | 1.13447i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.255275 | + | 1.94679i | 0.0234010 | + | 0.178462i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.28001 | − | 3.94910i | 0.207274 | − | 0.359009i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.0033 | 1.78915 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.94462 | −0.261293 | −0.130646 | − | 0.991429i | \(-0.541705\pi\) | ||||
−0.130646 | + | 0.991429i | \(0.541705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.53255 | − | 13.0468i | 0.658122 | − | 1.13990i | −0.322979 | − | 0.946406i | \(-0.604684\pi\) |
0.981101 | − | 0.193495i | \(-0.0619823\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.68189 | − | 0.613917i | 0.405972 | − | 0.0532334i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6139 | − | 7.85997i | 1.16311 | − | 0.671523i | 0.211064 | − | 0.977472i | \(-0.432307\pi\) |
0.952048 | + | 0.305950i | \(0.0989739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.86373 | − | 1.65337i | −0.242898 | − | 0.140237i | 0.373610 | − | 0.927586i | \(-0.378120\pi\) |
−0.616508 | + | 0.787349i | \(0.711453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2362 | 0.939620 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2362i | 0.933118i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.52765 | − | 5.50079i | −0.780535 | − | 0.450642i | 0.0560848 | − | 0.998426i | \(-0.482138\pi\) |
−0.836620 | + | 0.547784i | \(0.815472\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.719988 | − | 1.24706i | −0.0585918 | − | 0.101484i | 0.835242 | − | 0.549883i | \(-0.185328\pi\) |
−0.893834 | + | 0.448399i | \(0.851994\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.8339 | − | 6.83228i | 0.950518 | − | 0.548782i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3822 | + | 8.30354i | 1.14782 | + | 0.662695i | 0.948355 | − | 0.317210i | \(-0.102746\pi\) |
0.199465 | + | 0.979905i | \(0.436079\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.33909 | + | 15.2815i | −0.499591 | + | 1.20435i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3955 | 0.970887 | 0.485444 | − | 0.874268i | \(-0.338658\pi\) | ||||
0.485444 | + | 0.874268i | \(0.338658\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.86087 | + | 10.1513i | −0.453528 | + | 0.785534i | −0.998602 | − | 0.0528541i | \(-0.983168\pi\) |
0.545074 | + | 0.838388i | \(0.316502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.44304 | − | 4.23147i | −0.187926 | − | 0.325498i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.38548 | + | 14.5241i | 0.637536 | + | 1.10425i | 0.985972 | + | 0.166913i | \(0.0533798\pi\) |
−0.348435 | + | 0.937333i | \(0.613287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.2941 | + | 16.3220i | −1.60968 | + | 1.23383i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.77532i | − | 0.431668i | −0.976430 | − | 0.215834i | \(-0.930753\pi\) | ||
0.976430 | − | 0.215834i | \(-0.0692470\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.53310i | 0.411272i | 0.978629 | + | 0.205636i | \(0.0659263\pi\) | ||||
−0.978629 | + | 0.205636i | \(0.934074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.83974 | + | 10.1147i | −0.429346 | + | 0.743649i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.53518 | + | 1.46368i | −0.185390 | + | 0.107035i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.38124 | + | 3.10686i | −0.389373 | + | 0.224805i | −0.681888 | − | 0.731456i | \(-0.738841\pi\) |
0.292515 | + | 0.956261i | \(0.405508\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.90271 | − | 6.75970i | 0.280923 | − | 0.486574i | −0.690689 | − | 0.723152i | \(-0.742693\pi\) |
0.971612 | + | 0.236578i | \(0.0760260\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.7737i | − | 0.910092i | −0.890468 | − | 0.455046i | \(-0.849623\pi\) | ||
0.890468 | − | 0.455046i | \(-0.150377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.81201i | − | 0.128450i | −0.997935 | − | 0.0642250i | \(-0.979542\pi\) | ||
0.997935 | − | 0.0642250i | \(-0.0204575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.64782 | − | 6.06365i | −0.326213 | − | 0.425585i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.4169 | + | 35.3631i | 1.42598 | + | 2.46986i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.52006 | + | 6.09692i | 0.243487 | + | 0.421732i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.88766 | − | 3.26953i | 0.129952 | − | 0.225083i | −0.793706 | − | 0.608302i | \(-0.791851\pi\) |
0.923658 | + | 0.383218i | \(0.125184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.66949 | 0.250257 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.56002 | + | 8.58209i | −0.241670 | + | 0.582590i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.83070 | − | 1.05696i | −0.123146 | − | 0.0710987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0662 | + | 6.38910i | −0.741051 | + | 0.427846i | −0.822451 | − | 0.568836i | \(-0.807394\pi\) |
0.0814006 | + | 0.996681i | \(0.474061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.99110 | − | 17.3051i | −0.663133 | − | 1.14858i | −0.979788 | − | 0.200039i | \(-0.935893\pi\) |
0.316655 | − | 0.948541i | \(-0.397440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.77402 | + | 5.06568i | 0.579804 | + | 0.334750i | 0.761055 | − | 0.648687i | \(-0.224682\pi\) |
−0.181252 | + | 0.983437i | \(0.558015\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.31007i | − | 0.478898i | −0.970909 | − | 0.239449i | \(-0.923033\pi\) | ||
0.970909 | − | 0.239449i | \(-0.0769669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.50307 | −0.554679 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.28317 | + | 4.20494i | 0.471109 | + | 0.271995i | 0.716704 | − | 0.697378i | \(-0.245650\pi\) |
−0.245595 | + | 0.969373i | \(0.578983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.75277 | + | 4.47607i | −0.499400 | + | 0.288329i | −0.728466 | − | 0.685082i | \(-0.759766\pi\) |
0.229066 | + | 0.973411i | \(0.426433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.07690 | − | 26.3024i | 0.452127 | − | 1.68040i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.54191 | + | 4.40271i | −0.161738 | + | 0.280138i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.6432 | 0.798033 | 0.399017 | − | 0.916944i | \(-0.369352\pi\) | ||||
0.399017 | + | 0.916944i | \(0.369352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.6661 | −1.55075 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.15329 | − | 14.1219i | 0.508588 | − | 0.880900i | −0.491362 | − | 0.870955i | \(-0.663501\pi\) |
0.999951 | − | 0.00994523i | \(-0.00316572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.03249 | − | 7.87402i | −0.0641557 | − | 0.489268i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5434 | − | 11.8608i | 1.26676 | − | 0.731366i | 0.292389 | − | 0.956300i | \(-0.405550\pi\) |
0.974374 | + | 0.224934i | \(0.0722166\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.28288 | −0.444045 | −0.222022 | − | 0.975042i | \(-0.571266\pi\) | ||||
−0.222022 | + | 0.975042i | \(0.571266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.6879i | − | 1.37819i | −0.724669 | − | 0.689097i | \(-0.758007\pi\) | ||
0.724669 | − | 0.689097i | \(-0.241993\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −34.6423 | − | 20.0007i | −2.08901 | − | 1.20609i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0838 | − | 20.9298i | −0.726046 | − | 1.25755i | −0.958542 | − | 0.284951i | \(-0.908023\pi\) |
0.232496 | − | 0.972597i | \(-0.425311\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.11229 | − | 2.37423i | 0.245319 | − | 0.141635i | −0.372300 | − | 0.928112i | \(-0.621431\pi\) |
0.617619 | + | 0.786478i | \(0.288097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.4484 | + | 14.6926i | 1.51275 | + | 0.873387i | 0.999889 | + | 0.0149153i | \(0.00474785\pi\) |
0.512861 | + | 0.858471i | \(0.328585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.6458 | − | 10.6384i | −1.51382 | − | 0.627965i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4493 | −0.967604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.31206 | + | 5.73666i | −0.193493 | + | 0.335139i | −0.946405 | − | 0.322981i | \(-0.895315\pi\) |
0.752913 | + | 0.658121i | \(0.228648\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0411186 | + | 0.0712195i | 0.00239402 | + | 0.00414656i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.90597 | − | 15.4256i | −0.515046 | − | 0.892085i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.98025 | + | 1.51787i | −0.114140 | + | 0.0874885i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.60761i | − | 0.550130i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.7242i | 1.23987i | 0.784655 | + | 0.619933i | \(0.212840\pi\) | ||||
−0.784655 | + | 0.619933i | \(0.787160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.14900 | − | 5.45422i | 0.178563 | − | 0.309281i | −0.762825 | − | 0.646605i | \(-0.776188\pi\) |
0.941389 | + | 0.337324i | \(0.109522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.2423 | + | 11.1095i | −1.08764 | + | 0.627948i | −0.932946 | − | 0.360015i | \(-0.882771\pi\) |
−0.154691 | + | 0.987963i | \(0.549438\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5632 | + | 7.83070i | −0.761784 | + | 0.439816i | −0.829936 | − | 0.557859i | \(-0.811623\pi\) |
0.0681519 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.69536 | − | 9.86466i | 0.318879 | − | 0.552315i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.32448i | − | 0.0736963i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 28.8859i | − | 1.60230i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.58870 | − | 3.51726i | 0.252983 | − | 0.193913i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.636129 | + | 1.10181i | 0.0349648 | + | 0.0605608i | 0.882978 | − | 0.469414i | \(-0.155535\pi\) |
−0.848013 | + | 0.529975i | \(0.822201\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.1663 | + | 45.3214i | 1.42962 | + | 2.47617i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.78001 | + | 6.54717i | −0.205910 | + | 0.356647i | −0.950422 | − | 0.310962i | \(-0.899349\pi\) |
0.744512 | + | 0.667609i | \(0.232682\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.8525 | −0.750153 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.06081 | + | 17.1215i | 0.381248 | + | 0.924473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.1470 | + | 11.0545i | 1.02787 | + | 0.593439i | 0.916373 | − | 0.400326i | \(-0.131103\pi\) |
0.111494 | + | 0.993765i | \(0.464436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7682 | + | 7.37173i | −0.683467 | + | 0.394600i | −0.801160 | − | 0.598450i | \(-0.795783\pi\) |
0.117693 | + | 0.993050i | \(0.462450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.63881 | − | 14.9629i | −0.459798 | − | 0.796393i | 0.539152 | − | 0.842208i | \(-0.318745\pi\) |
−0.998950 | + | 0.0458154i | \(0.985411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.54767 | + | 3.78030i | 0.347514 | + | 0.200638i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.9129i | 0.575963i | 0.957636 | + | 0.287982i | \(0.0929842\pi\) | ||||
−0.957636 | + | 0.287982i | \(0.907016\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8147 | 0.832353 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3599 | − | 9.44541i | −0.856318 | − | 0.494395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.9407 | + | 17.8636i | −1.61509 | + | 0.932472i | −0.626923 | + | 0.779081i | \(0.715686\pi\) |
−0.988166 | + | 0.153391i | \(0.950981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0300 | − | 27.7648i | 0.830003 | − | 1.43761i | −0.0680328 | − | 0.997683i | \(-0.521672\pi\) |
0.898035 | − | 0.439923i | \(-0.144994\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.22549 | 0.423634 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.8891 | −1.79214 | −0.896068 | − | 0.443918i | \(-0.853588\pi\) | ||||
−0.896068 | + | 0.443918i | \(0.853588\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.76711 | + | 15.1851i | −0.447978 | + | 0.775921i | −0.998254 | − | 0.0590616i | \(-0.981189\pi\) |
0.550276 | + | 0.834983i | \(0.314523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 40.2649 | − | 5.27976i | 2.05209 | − | 0.269082i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.60060 | − | 3.81086i | 0.334664 | − | 0.193218i | −0.323246 | − | 0.946315i | \(-0.604774\pi\) |
0.657910 | + | 0.753097i | \(0.271441\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.01882 | + | 2.32027i | 0.203241 | + | 0.117341i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.1486 | −0.711893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 37.6469i | − | 1.88944i | −0.327873 | − | 0.944722i | \(-0.606332\pi\) | ||
0.327873 | − | 0.944722i | \(-0.393668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.5689 | − | 10.7207i | −0.927284 | − | 0.535368i | −0.0413326 | − | 0.999145i | \(-0.513160\pi\) |
−0.885952 | + | 0.463778i | \(0.846494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00158 | − | 8.66299i | −0.249146 | − | 0.431534i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2538 | − | 5.92004i | 0.508262 | − | 0.293445i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.6086 | − | 14.7851i | −1.26627 | − | 0.731079i | −0.291986 | − | 0.956423i | \(-0.594316\pi\) |
−0.974279 | + | 0.225344i | \(0.927649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.0516494 | − | 0.0214252i | −0.00254150 | − | 0.00105427i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.3622 | 1.53951 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.56481 | − | 6.17443i | 0.174152 | − | 0.301641i | −0.765715 | − | 0.643180i | \(-0.777615\pi\) |
0.939868 | + | 0.341539i | \(0.110948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31007 | − | 4.00115i | −0.112586 | − | 0.195004i | 0.804226 | − | 0.594323i | \(-0.202580\pi\) |
−0.916812 | + | 0.399319i | \(0.869247\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.76282 | + | 6.51739i | 0.182524 | + | 0.316140i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.97415 | + | 5.18477i | 0.192323 | + | 0.250908i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.00771i | − | 0.193045i | −0.995331 | − | 0.0965223i | \(-0.969228\pi\) | ||
0.995331 | − | 0.0965223i | \(-0.0307719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.4125i | 1.41348i | 0.707475 | + | 0.706738i | \(0.249834\pi\) | ||||
−0.707475 | + | 0.706738i | \(0.750166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.58008 | − | 9.66498i | 0.266931 | − | 0.462339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.5130 | + | 10.6885i | −0.883575 | + | 0.510133i | −0.871836 | − | 0.489799i | \(-0.837070\pi\) |
−0.0117398 | + | 0.999931i | \(0.503737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.05227 | − | 2.91693i | 0.240041 | − | 0.138587i | −0.375155 | − | 0.926962i | \(-0.622410\pi\) |
0.615195 | + | 0.788375i | \(0.289077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0284 | + | 31.2262i | −0.854630 | + | 1.48026i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5823i | 1.06573i | 0.846202 | + | 0.532863i | \(0.178884\pi\) | ||||
−0.846202 | + | 0.532863i | \(0.821116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 41.3953i | − | 1.94923i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.8399 | + | 23.2743i | 0.836347 | + | 1.09112i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9311 | − | 34.5218i | −0.932340 | − | 1.61486i | −0.779310 | − | 0.626638i | \(-0.784430\pi\) |
−0.153029 | − | 0.988222i | \(-0.548903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.68254 | − | 6.37834i | −0.171513 | − | 0.297069i | 0.767436 | − | 0.641125i | \(-0.221532\pi\) |
−0.938949 | + | 0.344056i | \(0.888199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3457 | − | 24.8475i | 0.666702 | − | 1.15476i | −0.312119 | − | 0.950043i | \(-0.601039\pi\) |
0.978821 | − | 0.204718i | \(-0.0656278\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.6704 | 0.632590 | 0.316295 | − | 0.948661i | \(-0.397561\pi\) | ||||
0.316295 | + | 0.948661i | \(0.397561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.8677 | − | 13.6342i | −1.51769 | − | 0.629569i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.22157 | − | 1.85997i | −0.148128 | − | 0.0855216i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.6739 | − | 9.04931i | 0.719166 | − | 0.415211i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.20537 | − | 9.01596i | −0.237839 | − | 0.411950i | 0.722255 | − | 0.691627i | \(-0.243106\pi\) |
−0.960094 | + | 0.279677i | \(0.909773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.40449 | + | 4.27499i | 0.337616 | + | 0.194923i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 73.2292i | 3.32517i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.33850 | −0.105968 | −0.0529838 | − | 0.998595i | \(-0.516873\pi\) | ||||
−0.0529838 | + | 0.998595i | \(0.516873\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.3448 | − | 16.9422i | −1.32431 | − | 0.764591i | −0.339898 | − | 0.940462i | \(-0.610392\pi\) |
−0.984413 | + | 0.175871i | \(0.943726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.85588 | + | 1.07149i | −0.0835845 | + | 0.0482575i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.09717 | + | 0.668371i | −0.228639 | + | 0.0299805i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.30223 | + | 14.3799i | −0.371659 | + | 0.643732i | −0.989821 | − | 0.142319i | \(-0.954544\pi\) |
0.618162 | + | 0.786051i | \(0.287877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.3661 | 1.57690 | 0.788449 | − | 0.615100i | \(-0.210885\pi\) | ||||
0.788449 | + | 0.615100i | \(0.210885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.2246 | 1.43398 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5291 | + | 32.0933i | −0.821287 | + | 1.42251i | 0.0834371 | + | 0.996513i | \(0.473410\pi\) |
−0.904724 | + | 0.425998i | \(0.859923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7357 | − | 1.66998i | 0.563396 | − | 0.0738757i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −57.4507 | + | 33.1692i | −2.53158 | + | 1.46161i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.46513 | + | 4.30999i | 0.328316 | + | 0.189553i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.78309 | 0.0781187 | 0.0390594 | − | 0.999237i | \(-0.487564\pi\) | ||||
0.0390594 | + | 0.999237i | \(0.487564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.0538i | − | 1.05180i | −0.850546 | − | 0.525901i | \(-0.823728\pi\) | ||
0.850546 | − | 0.525901i | \(-0.176272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.25696 | + | 1.30306i | 0.0983149 | + | 0.0567621i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.05069 | + | 13.9442i | 0.350030 | + | 0.606270i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.8876 | − | 14.9462i | 1.12132 | − | 0.647392i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −48.3126 | − | 27.8933i | −2.08874 | − | 1.20593i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.5451 | + | 19.5046i | −0.841866 | + | 0.840124i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0032 | 1.28994 | 0.644968 | − | 0.764209i | \(-0.276871\pi\) | ||||
0.644968 | + | 0.764209i | \(0.276871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.9458 | + | 38.0113i | −0.940056 | + | 1.62822i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7816 | + | 18.6743i | 0.460987 | + | 0.798454i | 0.999010 | − | 0.0444765i | \(-0.0141620\pi\) |
−0.538023 | + | 0.842930i | \(0.680829\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.57686 | + | 4.46325i | 0.109778 | + | 0.190141i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.63532 | − | 5.85251i | 0.324687 | − | 0.248874i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.9477i | 1.56552i | 0.622321 | + | 0.782762i | \(0.286190\pi\) | ||||
−0.622321 | + | 0.782762i | \(0.713810\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.68625i | − | 0.113616i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.58422 | + | 13.1363i | −0.319637 | + | 0.553627i | −0.980412 | − | 0.196957i | \(-0.936894\pi\) |
0.660776 | + | 0.750584i | \(0.270228\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.1329 | + | 19.1293i | −1.39391 | + | 0.804774i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.8084 | − | 18.3646i | 1.33348 | − | 0.769885i | 0.347648 | − | 0.937625i | \(-0.386980\pi\) |
0.985831 | + | 0.167740i | \(0.0536470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.61387 | − | 9.72351i | 0.234933 | − | 0.406916i | −0.724320 | − | 0.689464i | \(-0.757846\pi\) |
0.959253 | + | 0.282548i | \(0.0911795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 63.4114i | 2.64444i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 36.5515i | − | 1.52166i | −0.648952 | − | 0.760829i | \(-0.724792\pi\) | ||
0.648952 | − | 0.760829i | \(-0.275208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.9247 | + | 12.9729i | −0.702154 | + | 0.538205i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.99738 | − | 8.65571i | −0.206264 | − | 0.357259i | 0.744271 | − | 0.667878i | \(-0.232797\pi\) |
−0.950535 | + | 0.310619i | \(0.899464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.13376 | − | 5.42784i | 0.129124 | − | 0.223650i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.78223 | 0.319578 | 0.159789 | − | 0.987151i | \(-0.448919\pi\) | ||||
0.159789 | + | 0.987151i | \(0.448919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.05696 | − | 2.92737i | −0.289307 | − | 0.120010i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.6614 | + | 12.5062i | 0.885061 | + | 0.510990i | 0.872324 | − | 0.488929i | \(-0.162612\pi\) |
0.0127373 | + | 0.999919i | \(0.495945\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.9925 | + | 15.0068i | −1.06026 | + | 0.612139i | −0.925503 | − | 0.378740i | \(-0.876357\pi\) |
−0.134753 | + | 0.990879i | \(0.543024\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.87179 | + | 15.3664i | 0.360689 | + | 0.624732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.96882 | + | 2.29140i | 0.161089 | + | 0.0930050i | 0.578378 | − | 0.815769i | \(-0.303686\pi\) |
−0.417288 | + | 0.908774i | \(0.637019\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.22468i | 0.251823i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.5522 | 1.23399 | 0.616996 | − | 0.786966i | \(-0.288349\pi\) | ||||
0.616996 | + | 0.786966i | \(0.288349\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.2484 | + | 16.3092i | 1.13724 | + | 0.656585i | 0.945745 | − | 0.324909i | \(-0.105334\pi\) |
0.191493 | + | 0.981494i | \(0.438667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.3244 | + | 10.0023i | −0.696327 | + | 0.402024i | −0.805978 | − | 0.591946i | \(-0.798360\pi\) |
0.109651 | + | 0.993970i | \(0.465027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.18749 | − | 24.3087i | −0.127704 | − | 0.973906i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.5657 | + | 23.4965i | −0.542628 | + | 0.939859i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.22752 | −0.0888171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.09634 | −0.242692 | −0.121346 | − | 0.992610i | \(-0.538721\pi\) | ||||
−0.121346 | + | 0.992610i | \(0.538721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.72893 | − | 9.92279i | 0.227345 | − | 0.393774i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.2547 | − | 5.18065i | −0.762898 | − | 0.205265i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.9612 | + | 16.7207i | −1.14390 | + | 0.660429i | −0.947393 | − | 0.320074i | \(-0.896292\pi\) |
−0.196504 | + | 0.980503i | \(0.562959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.6022 | − | 9.58527i | −0.654726 | − | 0.378006i | 0.135539 | − | 0.990772i | \(-0.456724\pi\) |
−0.790264 | + | 0.612766i | \(0.790057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.6049 | −1.75360 | −0.876800 | − | 0.480854i | \(-0.840327\pi\) | ||||
−0.876800 | + | 0.480854i | \(0.840327\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.0833680i | − | 0.00327248i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.564755 | + | 0.326061i | 0.0221006 | + | 0.0127598i | 0.511010 | − | 0.859575i | \(-0.329272\pi\) |
−0.488909 | + | 0.872335i | \(0.662605\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.3100 | + | 50.7664i | 1.14524 | + | 1.98361i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.2738 | − | 15.1692i | 1.02348 | − | 0.590908i | 0.108372 | − | 0.994110i | \(-0.465436\pi\) |
0.915111 | + | 0.403202i | \(0.132103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1004 | − | 6.40881i | −0.431755 | − | 0.249274i | 0.268339 | − | 0.963325i | \(-0.413525\pi\) |
−0.700094 | + | 0.714051i | \(0.746859\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.04011 | + | 16.9715i | −0.273004 | + | 0.658126i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0569 | −0.699165 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.86986 | + | 8.43484i | −0.187999 | + | 0.325623i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.2246 | + | 19.4416i | 0.432678 | + | 0.749420i | 0.997103 | − | 0.0760644i | \(-0.0242355\pi\) |
−0.564425 | + | 0.825484i | \(0.690902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5903 | − | 44.3237i | −0.983516 | − | 1.70350i | −0.648353 | − | 0.761340i | \(-0.724542\pi\) |
−0.335163 | − | 0.942160i | \(-0.608791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.2910 | − | 39.5183i | −1.16246 | − | 1.51657i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 14.5616i | − | 0.557184i | −0.960410 | − | 0.278592i | \(-0.910132\pi\) | ||
0.960410 | − | 0.278592i | \(-0.0898677\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 61.1681i | 2.33711i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.1757 | − | 12.2258i | 0.805560 | − | 0.465090i | −0.0398517 | − | 0.999206i | \(-0.512689\pi\) |
0.845412 | + | 0.534115i | \(0.179355\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.1431 | − | 6.43347i | 0.422682 | − | 0.244035i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.89393 | + | 6.74448i | −0.147493 | + | 0.255465i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.21697i | 0.0837337i | 0.999123 | + | 0.0418669i | \(0.0133305\pi\) | ||||
−0.999123 | + | 0.0418669i | \(0.986669\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.35703i | 0.202044i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.3901 | + | 13.3296i | −0.654021 | + | 0.501310i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1962 | + | 21.1244i | 0.458036 | + | 0.793342i | 0.998857 | − | 0.0477959i | \(-0.0152197\pi\) |
−0.540821 | + | 0.841138i | \(0.681886\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.9796 | + | 19.0173i | 0.411190 | + | 0.712203i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.8607 | + | 37.8639i | −0.817544 | + | 1.41603i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.22752 | −0.0830725 | −0.0415363 | − | 0.999137i | \(-0.513225\pi\) | ||||
−0.0415363 | + | 0.999137i | \(0.513225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2831 | − | 41.6641i | 0.643657 | − | 1.55165i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.3599 | − | 14.6416i | −0.941844 | − | 0.543774i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4880 | + | 6.05523i | −0.388977 | + | 0.224576i | −0.681717 | − | 0.731616i | \(-0.738766\pi\) |
0.292740 | + | 0.956192i | \(0.405433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.349924 | + | 0.606086i | 0.0129424 | + | 0.0224169i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.5673 | + | 7.83306i | 0.501118 | + | 0.289321i | 0.729175 | − | 0.684327i | \(-0.239904\pi\) |
−0.228057 | + | 0.973648i | \(0.573237\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 53.0522i | − | 1.95420i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.10454 | 0.298130 | 0.149065 | − | 0.988827i | \(-0.452374\pi\) | ||||
0.149065 | + | 0.988827i | \(0.452374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5429 | − | 6.08697i | −0.386783 | − | 0.223309i | 0.293982 | − | 0.955811i | \(-0.405019\pi\) |
−0.680765 | + | 0.732502i | \(0.738353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.0732 | − | 21.4042i | 1.35826 | − | 0.784189i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.6100 | − | 4.93164i | 1.37424 | − | 0.180198i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3062 | − | 29.9752i | 0.631511 | − | 1.09381i | −0.355732 | − | 0.934588i | \(-0.615768\pi\) |
0.987243 | − | 0.159221i | \(-0.0508983\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.60311 | 0.203918 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.0553 | −1.41949 | −0.709744 | − | 0.704459i | \(-0.751190\pi\) | ||||
−0.709744 | + | 0.704459i | \(0.751190\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.11262 | + | 8.85532i | −0.185332 | + | 0.321005i | −0.943688 | − | 0.330835i | \(-0.892670\pi\) |
0.758356 | + | 0.651840i | \(0.226003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.88010 | − | 29.5907i | −0.140469 | − | 1.07125i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.0521363 | − | 0.0301009i | 0.00188253 | − | 0.00108688i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.6746 | − | 15.4006i | −0.961910 | − | 0.555359i | −0.0651494 | − | 0.997876i | \(-0.520752\pi\) |
−0.896760 | + | 0.442517i | \(0.854086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.7833 | 1.28704 | 0.643518 | − | 0.765431i | \(-0.277474\pi\) | ||||
0.643518 | + | 0.765431i | \(0.277474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.6117i | 1.27921i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.2200 | + | 9.36461i | 0.581141 | + | 0.335522i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.83228 | − | 6.63771i | −0.137130 | − | 0.237516i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −55.9626 | + | 32.3100i | −1.99739 | + | 1.15319i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.2859 | − | 7.67064i | −0.473592 | − | 0.273429i | 0.244150 | − | 0.969737i | \(-0.421491\pi\) |
−0.717742 | + | 0.696309i | \(0.754824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.96748 | − | 24.0284i | 0.354403 | − | 0.854353i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.03326 | −0.249758 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5200 | − | 30.3455i | 0.620590 | − | 1.07489i | −0.368786 | − | 0.929514i | \(-0.620226\pi\) |
0.989376 | − | 0.145379i | \(-0.0464402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.810856 | − | 1.40444i | −0.0286860 | − | 0.0496857i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.57529 | + | 16.5849i | 0.337905 | + | 0.585268i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.1627 | − | 51.0926i | −1.38031 | − | 1.80078i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.2925i | − | 0.959553i | −0.877391 | − | 0.479777i | \(-0.840718\pi\) | ||
0.877391 | − | 0.479777i | \(-0.159282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7628i | 0.974883i | 0.873156 | + | 0.487442i | \(0.162070\pi\) | ||||
−0.873156 | + | 0.487442i | \(0.837930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.1161 | + | 41.7703i | −0.844749 | + | 1.46315i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.45759 | − | 0.841542i | 0.0509947 | − | 0.0294418i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4968 | − | 22.2262i | 1.34355 | − | 0.775698i | 0.356223 | − | 0.934401i | \(-0.384064\pi\) |
0.987326 | + | 0.158703i | \(0.0507311\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.5577 | + | 44.2672i | −0.890884 | + | 1.54306i | −0.0520663 | + | 0.998644i | \(0.516581\pi\) |
−0.838818 | + | 0.544413i | \(0.816753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.5414i | − | 0.505653i | −0.967512 | − | 0.252826i | \(-0.918640\pi\) | ||
0.967512 | − | 0.252826i | \(-0.0813601\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.9681i | 0.971373i | 0.874133 | + | 0.485686i | \(0.161430\pi\) | ||||
−0.874133 | + | 0.485686i | \(0.838570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.01920 | − | 1.33932i | 0.173905 | − | 0.0464047i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.8053 | − | 39.5000i | −0.789211 | − | 1.36695i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.499354 | − | 0.864906i | −0.0172396 | − | 0.0298599i | 0.857277 | − | 0.514856i | \(-0.172154\pi\) |
−0.874517 | + | 0.484996i | \(0.838821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.3307 | + | 17.8933i | −0.356231 | + | 0.617011i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.0123 | 0.654044 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.1439 | − | 4.62273i | −0.382910 | − | 0.158839i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.2546 | − | 9.38460i | −0.557200 | − | 0.321700i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.48739 | − | 4.90020i | 0.290603 | − | 0.167780i | −0.347611 | − | 0.937639i | \(-0.613007\pi\) |
0.638214 | + | 0.769859i | \(0.279674\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.85002 | − | 6.66842i | −0.131514 | − | 0.227789i | 0.792746 | − | 0.609552i | \(-0.208651\pi\) |
−0.924260 | + | 0.381763i | \(0.875317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4022 | + | 9.46979i | 0.559634 | + | 0.323105i | 0.752999 | − | 0.658022i | \(-0.228607\pi\) |
−0.193364 | + | 0.981127i | \(0.561940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4540i | 0.594141i | 0.954856 | + | 0.297070i | \(0.0960096\pi\) | ||||
−0.954856 | + | 0.297070i | \(0.903990\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −65.2578 | −2.21883 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.4215 | + | 7.17157i | 0.421371 | + | 0.243279i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.1776 | − | 19.1551i | 1.12418 | − | 0.649045i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.88078 | − | 52.4746i | −0.232613 | − | 1.77397i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.196152 | + | 0.339746i | −0.00662360 | + | 0.0114724i | −0.869318 | − | 0.494253i | \(-0.835442\pi\) |
0.862695 | + | 0.505725i | \(0.168775\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.0259 | −1.24744 | −0.623718 | − | 0.781650i | \(-0.714378\pi\) | ||||
−0.623718 | + | 0.781650i | \(0.714378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.9586 | 1.00819 | 0.504094 | − | 0.863649i | \(-0.331826\pi\) | ||||
0.504094 | + | 0.863649i | \(0.331826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4930 | + | 25.1026i | −0.486626 | + | 0.842861i | −0.999882 | − | 0.0153745i | \(-0.995106\pi\) |
0.513256 | + | 0.858236i | \(0.328439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.01290 | + | 7.72461i | 0.0339714 | + | 0.259075i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.37759 | + | 1.95005i | −0.113027 | + | 0.0652560i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.4617 | + | 11.2362i | 0.650533 | + | 0.375586i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.1407 | −0.338211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.6455 | − | 10.7650i | −0.619796 | − | 0.357839i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.94773 | − | 3.37357i | −0.0646733 | − | 0.112017i | 0.831876 | − | 0.554962i | \(-0.187267\pi\) |
−0.896549 | + | 0.442945i | \(0.853934\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.32768 | − | 0.766538i | 0.0439881 | − | 0.0253966i | −0.477845 | − | 0.878444i | \(-0.658582\pi\) |
0.521833 | + | 0.853048i | \(0.325248\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.5339 | − | 15.8967i | −0.911240 | − | 0.526105i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.8166 | − | 15.2723i | −1.21579 | − | 0.504334i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.2531 | −0.931984 | −0.465992 | − | 0.884789i | \(-0.654302\pi\) | ||||
−0.465992 | + | 0.884789i | \(0.654302\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.76737 | − | 4.79323i | 0.0910892 | − | 0.157771i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.2192 | − | 26.3603i | −0.500403 | − | 0.866723i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.64363 | − | 2.84685i | −0.0539257 | − | 0.0934021i | 0.837802 | − | 0.545974i | \(-0.183840\pi\) |
−0.891728 | + | 0.452571i | \(0.850507\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.22097 | − | 12.0708i | −0.105563 | − | 0.395605i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 11.3907i | − | 0.372517i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.5084i | 1.16001i | 0.814613 | + | 0.580005i | \(0.196949\pi\) | ||||
−0.814613 | + | 0.580005i | \(0.803051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.24941 | + | 10.8243i | −0.203725 | + | 0.352862i | −0.949726 | − | 0.313083i | \(-0.898638\pi\) |
0.746001 | + | 0.665945i | \(0.231972\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.8293 | + | 32.8104i | −1.85062 | + | 1.06845i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.2769 | − | 18.0577i | 1.01636 | − | 0.586796i | 0.103313 | − | 0.994649i | \(-0.467056\pi\) |
0.913048 | + | 0.407852i | \(0.133722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.91452 | + | 11.9763i | −0.224455 | + | 0.388767i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 45.2925i | − | 1.46717i | −0.679599 | − | 0.733584i | \(-0.737846\pi\) | ||
0.679599 | − | 0.733584i | \(-0.262154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 24.1783i | − | 0.782392i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.3019 | − | 33.0095i | −0.817042 | − | 1.06593i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.33386 | − | 16.1667i | −0.301092 | − | 0.521507i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.1859 | + | 26.3028i | 0.488851 | + | 0.846716i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.0000 | + | 20.7845i | −0.385893 | + | 0.668385i | −0.991893 | − | 0.127079i | \(-0.959440\pi\) |
0.606000 | + | 0.795465i | \(0.292773\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.3626 | −1.07066 | −0.535328 | − | 0.844644i | \(-0.679812\pi\) | ||||
−0.535328 | + | 0.844644i | \(0.679812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.35222 | + | 8.08113i | −0.107467 | + | 0.259069i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.8846 | + | 17.2539i | 0.956091 | + | 0.552000i | 0.894968 | − | 0.446131i | \(-0.147198\pi\) |
0.0611236 | + | 0.998130i | \(0.480532\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.6555 | − | 18.2763i | 1.01172 | − | 0.584114i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.20651 | − | 2.08973i | −0.0384817 | − | 0.0666522i | 0.846143 | − | 0.532956i | \(-0.178919\pi\) |
−0.884625 | + | 0.466304i | \(0.845585\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.0450 | + | 24.8521i | 1.37153 | + | 0.791852i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.89695i | 0.187512i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.5982 | −1.54377 | −0.771887 | − | 0.635760i | \(-0.780687\pi\) | ||||
−0.771887 | + | 0.635760i | \(0.780687\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.10612 | + | 3.52537i | 0.193577 | + | 0.111762i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.8449 | − | 22.4271i | 1.23023 | − | 0.710274i | 0.263152 | − | 0.964754i | \(-0.415238\pi\) |
0.967078 | + | 0.254481i | \(0.0819045\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))