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 | 2897.1 | ||
Root | \(-1.62181 + 0.608059i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2897 |
Dual form | 3024.2.cc.b.881.1 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | −0.861913 | − | 0.507056i | \(-0.830734\pi\) |
−0.00816625 | − | 0.999967i | \(-0.502599\pi\) | |||||||
\(6\) | 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 | 0.916986 | − | 0.398919i | \(-0.130615\pi\) |
0.113019 | + | 0.993593i | \(0.463948\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46687 | − | 1.42425i | 0.684186 | − | 0.395015i | −0.117244 | − | 0.993103i | \(-0.537406\pi\) |
0.801430 | + | 0.598088i | \(0.204073\pi\) | |||||||
\(14\) | 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 | \(-0.934370\pi\) | ||
0.978820 | − | 0.204723i | \(-0.0656295\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.41535 | + | 3.12656i | −1.12918 | + | 0.651932i | −0.943728 | − | 0.330722i | \(-0.892708\pi\) |
−0.185451 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(24\) | 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 | 0.713886 | − | 0.700262i | \(-0.246933\pi\) |
−0.249501 | + | 0.968374i | \(0.580267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.04125 | + | 1.75587i | −0.546225 | + | 0.315363i | −0.747598 | − | 0.664152i | \(-0.768793\pi\) |
0.201373 | + | 0.979515i | \(0.435460\pi\) | |||||||
\(32\) | 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 | 0.906087 | + | 0.423092i | \(0.139055\pi\) |
−0.0866345 | + | 0.996240i | \(0.527611\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.471521 | + | 0.816699i | −0.0719063 | + | 0.124545i | −0.899737 | − | 0.436433i | \(-0.856242\pi\) |
0.827830 | + | 0.560978i | \(0.189575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.09263 | − | 1.89248i | 0.159376 | − | 0.276047i | −0.775268 | − | 0.631633i | \(-0.782385\pi\) |
0.934644 | + | 0.355585i | \(0.115718\pi\) | |||||||
\(48\) | 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 | 0.866712 | − | 0.498808i | \(-0.166229\pi\) |
−0.865337 | + | 0.501191i | \(0.832895\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.13832 | − | 1.23456i | −0.273783 | − | 0.158069i | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.630606 | + | 0.776103i | \(0.717193\pi\) | |||||||
\(62\) | 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 | 0.904532 | + | 0.426406i | \(0.140221\pi\) |
−0.0829874 | + | 0.996551i | \(0.526446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.94304i | 0.230597i | 0.993331 | + | 0.115298i | \(0.0367824\pi\) | ||||
−0.993331 | + | 0.115298i | \(0.963218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.85486i | − | 0.568218i | −0.958792 | − | 0.284109i | \(-0.908302\pi\) | ||
0.958792 | − | 0.284109i | \(-0.0916978\pi\) | |||||||
\(74\) | 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 | −0.745440 | − | 0.666572i | \(-0.767761\pi\) |
0.949989 | + | 0.312284i | \(0.101094\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.02998 | + | 6.98012i | −0.442347 | + | 0.766168i | −0.997863 | − | 0.0653378i | \(-0.979188\pi\) |
0.555516 | + | 0.831506i | \(0.312521\pi\) | |||||||
\(84\) | 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 | 0.975043 | + | 0.222018i | \(0.0712643\pi\) |
0.679794 | + | 0.733403i | \(0.262069\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.14079 | + | 7.17206i | −0.412024 | + | 0.713647i | −0.995111 | − | 0.0987631i | \(-0.968511\pi\) |
0.583087 | + | 0.812410i | \(0.301845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7646 | − | 8.52435i | 1.45480 | − | 0.839929i | 0.456051 | − | 0.889953i | \(-0.349263\pi\) |
0.998748 | + | 0.0500247i | \(0.0159300\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.3369i | − | 1.38600i | −0.720936 | − | 0.693001i | \(-0.756288\pi\) | ||
0.720936 | − | 0.693001i | \(-0.243712\pi\) | |||||||
\(108\) | 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 | −0.0428049 | − | 0.999083i | \(-0.513629\pi\) |
0.843829 | + | 0.536612i | \(0.180296\pi\) | |||||||
\(114\) | 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 | 0.981101 | + | 0.193495i | \(0.0619823\pi\) |
−0.322979 | + | 0.946406i | \(0.604684\pi\) | |||||||
\(132\) | 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 | 0.952048 | − | 0.305950i | \(-0.0989739\pi\) |
0.211064 | + | 0.977472i | \(0.432307\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.86373 | + | 1.65337i | −0.242898 | + | 0.140237i | −0.616508 | − | 0.787349i | \(-0.711453\pi\) |
0.373610 | + | 0.927586i | \(0.378120\pi\) | |||||||
\(140\) | 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 | −0.836620 | − | 0.547784i | \(-0.815472\pi\) |
0.0560848 | + | 0.998426i | \(0.482138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.719988 | + | 1.24706i | −0.0585918 | + | 0.101484i | −0.893834 | − | 0.448399i | \(-0.851994\pi\) |
0.835242 | + | 0.549883i | \(0.185328\pi\) | |||||||
\(152\) | 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 | 0.199465 | − | 0.979905i | \(-0.436079\pi\) |
0.948355 | + | 0.317210i | \(0.102746\pi\) | |||||||
\(158\) | 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 | 0.545074 | − | 0.838388i | \(-0.316502\pi\) |
−0.998602 | + | 0.0528541i | \(0.983168\pi\) | |||||||
\(168\) | 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 | −0.348435 | − | 0.937333i | \(-0.613287\pi\) |
0.985972 | − | 0.166913i | \(-0.0533798\pi\) | |||||||
\(174\) | 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 | \(0.0692470\pi\) | ||||
−0.976430 | + | 0.215834i | \(0.930753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.53310i | − | 0.411272i | −0.978629 | − | 0.205636i | \(-0.934074\pi\) | ||
0.978629 | − | 0.205636i | \(-0.0659263\pi\) | |||||||
\(182\) | 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 | 0.292515 | − | 0.956261i | \(-0.405508\pi\) |
−0.681888 | + | 0.731456i | \(0.738841\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.90271 | + | 6.75970i | 0.280923 | + | 0.486574i | 0.971612 | − | 0.236578i | \(-0.0760260\pi\) |
−0.690689 | + | 0.723152i | \(0.742693\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.7737i | 0.910092i | 0.890468 | + | 0.455046i | \(0.150377\pi\) | ||||
−0.890468 | + | 0.455046i | \(0.849623\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.81201i | 0.128450i | 0.997935 | + | 0.0642250i | \(0.0204575\pi\) | ||||
−0.997935 | + | 0.0642250i | \(0.979542\pi\) | |||||||
\(200\) | 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 | 0.923658 | − | 0.383218i | \(-0.125184\pi\) |
−0.793706 | + | 0.608302i | \(0.791851\pi\) | |||||||
\(212\) | 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 | 0.0814006 | − | 0.996681i | \(-0.474061\pi\) |
−0.822451 | + | 0.568836i | \(0.807394\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.99110 | + | 17.3051i | −0.663133 | + | 1.14858i | 0.316655 | + | 0.948541i | \(0.397440\pi\) |
−0.979788 | + | 0.200039i | \(0.935893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.77402 | − | 5.06568i | 0.579804 | − | 0.334750i | −0.181252 | − | 0.983437i | \(-0.558015\pi\) |
0.761055 | + | 0.648687i | \(0.224682\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.31007i | 0.478898i | 0.970909 | + | 0.239449i | \(0.0769669\pi\) | ||||
−0.970909 | + | 0.239449i | \(0.923033\pi\) | |||||||
\(234\) | 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 | −0.245595 | − | 0.969373i | \(-0.578983\pi\) |
0.716704 | + | 0.697378i | \(0.245650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.75277 | − | 4.47607i | −0.499400 | − | 0.288329i | 0.229066 | − | 0.973411i | \(-0.426433\pi\) |
−0.728466 | + | 0.685082i | \(0.759766\pi\) | |||||||
\(242\) | 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 | 0.999951 | + | 0.00994523i | \(0.00316572\pi\) |
−0.491362 | + | 0.870955i | \(0.663501\pi\) | |||||||
\(258\) | 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 | 0.974374 | − | 0.224934i | \(-0.0722166\pi\) |
0.292389 | + | 0.956300i | \(0.405550\pi\) | |||||||
\(264\) | 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 | \(0.241993\pi\) | ||||
−0.724669 | + | 0.689097i | \(0.758007\pi\) | |||||||
\(272\) | 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 | 0.232496 | + | 0.972597i | \(0.425311\pi\) |
−0.958542 | + | 0.284951i | \(0.908023\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.11229 | + | 2.37423i | 0.245319 | + | 0.141635i | 0.617619 | − | 0.786478i | \(-0.288097\pi\) |
−0.372300 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.4484 | − | 14.6926i | 1.51275 | − | 0.873387i | 0.512861 | − | 0.858471i | \(-0.328585\pi\) |
0.999889 | − | 0.0149153i | \(-0.00474785\pi\) | |||||||
\(284\) | 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 | 0.752913 | − | 0.658121i | \(-0.228648\pi\) |
−0.946405 | + | 0.322981i | \(0.895315\pi\) | |||||||
\(294\) | 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 | \(-0.787160\pi\) | ||
0.784655 | − | 0.619933i | \(-0.212840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.14900 | + | 5.45422i | 0.178563 | + | 0.309281i | 0.941389 | − | 0.337324i | \(-0.109522\pi\) |
−0.762825 | + | 0.646605i | \(0.776188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.2423 | − | 11.1095i | −1.08764 | − | 0.627948i | −0.154691 | − | 0.987963i | \(-0.549438\pi\) |
−0.932946 | + | 0.360015i | \(0.882771\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5632 | − | 7.83070i | −0.761784 | − | 0.439816i | 0.0681519 | − | 0.997675i | \(-0.478290\pi\) |
−0.829936 | + | 0.557859i | \(0.811623\pi\) | |||||||
\(318\) | 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 | −0.848013 | − | 0.529975i | \(-0.822201\pi\) |
0.882978 | + | 0.469414i | \(0.155535\pi\) | |||||||
\(332\) | 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 | 0.744512 | − | 0.667609i | \(-0.232682\pi\) |
−0.950422 | + | 0.310962i | \(0.899349\pi\) | |||||||
\(338\) | 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 | 0.111494 | − | 0.993765i | \(-0.464436\pi\) |
0.916373 | + | 0.400326i | \(0.131103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7682 | − | 7.37173i | −0.683467 | − | 0.394600i | 0.117693 | − | 0.993050i | \(-0.462450\pi\) |
−0.801160 | + | 0.598450i | \(0.795783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.63881 | + | 14.9629i | −0.459798 | + | 0.796393i | −0.998950 | − | 0.0458154i | \(-0.985411\pi\) |
0.539152 | + | 0.842208i | \(0.318745\pi\) | |||||||
\(354\) | 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 | \(-0.907016\pi\) | ||
0.957636 | − | 0.287982i | \(-0.0929842\pi\) | |||||||
\(360\) | 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 | −0.988166 | − | 0.153391i | \(-0.950981\pi\) |
−0.626923 | − | 0.779081i | \(-0.715686\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0300 | + | 27.7648i | 0.830003 | + | 1.43761i | 0.898035 | + | 0.439923i | \(0.144994\pi\) |
−0.0680328 | + | 0.997683i | \(0.521672\pi\) | |||||||
\(374\) | 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 | 0.550276 | − | 0.834983i | \(-0.314523\pi\) |
−0.998254 | + | 0.0590616i | \(0.981189\pi\) | |||||||
\(384\) | 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 | 0.657910 | − | 0.753097i | \(-0.271441\pi\) |
−0.323246 | + | 0.946315i | \(0.604774\pi\) | |||||||
\(390\) | 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 | \(0.393668\pi\) | ||||
−0.327873 | + | 0.944722i | \(0.606332\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.5689 | + | 10.7207i | −0.927284 | + | 0.535368i | −0.885952 | − | 0.463778i | \(-0.846494\pi\) |
−0.0413326 | + | 0.999145i | \(0.513160\pi\) | |||||||
\(402\) | 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 | −0.974279 | − | 0.225344i | \(-0.927649\pi\) |
−0.291986 | + | 0.956423i | \(0.594316\pi\) | |||||||
\(410\) | 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 | 0.939868 | − | 0.341539i | \(-0.110948\pi\) |
−0.765715 | + | 0.643180i | \(0.777615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31007 | + | 4.00115i | −0.112586 | + | 0.195004i | −0.916812 | − | 0.399319i | \(-0.869247\pi\) |
0.804226 | + | 0.594323i | \(0.202580\pi\) | |||||||
\(422\) | 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 | \(0.0307719\pi\) | ||||
−0.995331 | + | 0.0965223i | \(0.969228\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.4125i | − | 1.41348i | −0.707475 | − | 0.706738i | \(-0.750166\pi\) | ||
0.707475 | − | 0.706738i | \(-0.249834\pi\) | |||||||
\(434\) | 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 | −0.0117398 | − | 0.999931i | \(-0.503737\pi\) |
−0.871836 | + | 0.489799i | \(0.837070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.05227 | + | 2.91693i | 0.240041 | + | 0.138587i | 0.615195 | − | 0.788375i | \(-0.289077\pi\) |
−0.375155 | + | 0.926962i | \(0.622410\pi\) | |||||||
\(444\) | 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 | \(-0.821116\pi\) | ||
0.846202 | − | 0.532863i | \(-0.178884\pi\) | |||||||
\(450\) | 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 | −0.153029 | + | 0.988222i | \(0.548903\pi\) |
−0.779310 | + | 0.626638i | \(0.784430\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.68254 | + | 6.37834i | −0.171513 | + | 0.297069i | −0.938949 | − | 0.344056i | \(-0.888199\pi\) |
0.767436 | + | 0.641125i | \(0.221532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3457 | + | 24.8475i | 0.666702 | + | 1.15476i | 0.978821 | + | 0.204718i | \(0.0656278\pi\) |
−0.312119 | + | 0.950043i | \(0.601039\pi\) | |||||||
\(464\) | 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 | −0.960094 | − | 0.279677i | \(-0.909773\pi\) |
0.722255 | + | 0.691627i | \(0.243106\pi\) | |||||||
\(480\) | 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 | −0.984413 | − | 0.175871i | \(-0.943726\pi\) |
−0.339898 | + | 0.940462i | \(0.610392\pi\) | |||||||
\(492\) | 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 | 0.618162 | − | 0.786051i | \(-0.287877\pi\) |
−0.989821 | + | 0.142319i | \(0.954544\pi\) | |||||||
\(500\) | 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 | −0.904724 | − | 0.425998i | \(-0.859923\pi\) |
0.0834371 | − | 0.996513i | \(-0.473410\pi\) | |||||||
\(510\) | 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 | \(0.176272\pi\) | ||||
−0.850546 | + | 0.525901i | \(0.823728\pi\) | |||||||
\(524\) | 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 | −0.538023 | − | 0.842930i | \(-0.680829\pi\) |
0.999010 | + | 0.0444765i | \(0.0141620\pi\) | |||||||
\(548\) | 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 | \(-0.713810\pi\) | ||
0.622321 | − | 0.782762i | \(-0.286190\pi\) | |||||||
\(558\) | 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 | 0.660776 | − | 0.750584i | \(-0.270228\pi\) |
−0.980412 | + | 0.196957i | \(0.936894\pi\) | |||||||
\(564\) | 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 | 0.985831 | − | 0.167740i | \(-0.0536470\pi\) |
0.347648 | + | 0.937625i | \(0.386980\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.61387 | + | 9.72351i | 0.234933 | + | 0.406916i | 0.959253 | − | 0.282548i | \(-0.0911795\pi\) |
−0.724320 | + | 0.689464i | \(0.757846\pi\) | |||||||
\(572\) | 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 | \(0.275208\pi\) | ||||
−0.648952 | + | 0.760829i | \(0.724792\pi\) | |||||||
\(578\) | 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 | −0.950535 | − | 0.310619i | \(-0.899464\pi\) |
0.744271 | + | 0.667878i | \(0.232797\pi\) | |||||||
\(588\) | 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 | 0.0127373 | − | 0.999919i | \(-0.495945\pi\) |
0.872324 | + | 0.488929i | \(0.162612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.9925 | − | 15.0068i | −1.06026 | − | 0.612139i | −0.134753 | − | 0.990879i | \(-0.543024\pi\) |
−0.925503 | + | 0.378740i | \(0.876357\pi\) | |||||||
\(602\) | 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 | −0.417288 | − | 0.908774i | \(-0.637019\pi\) |
0.578378 | + | 0.815769i | \(0.303686\pi\) | |||||||
\(608\) | 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 | 0.191493 | − | 0.981494i | \(-0.438667\pi\) |
0.945745 | + | 0.324909i | \(0.105334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.3244 | − | 10.0023i | −0.696327 | − | 0.402024i | 0.109651 | − | 0.993970i | \(-0.465027\pi\) |
−0.805978 | + | 0.591946i | \(0.798360\pi\) | |||||||
\(620\) | 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 | −0.196504 | − | 0.980503i | \(-0.562959\pi\) |
−0.947393 | + | 0.320074i | \(0.896292\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.6022 | + | 9.58527i | −0.654726 | + | 0.378006i | −0.790264 | − | 0.612766i | \(-0.790057\pi\) |
0.135539 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(644\) | 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 | −0.488909 | − | 0.872335i | \(-0.662605\pi\) |
0.511010 | + | 0.859575i | \(0.329272\pi\) | |||||||
\(654\) | 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 | 0.915111 | − | 0.403202i | \(-0.132103\pi\) |
0.108372 | + | 0.994110i | \(0.465436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1004 | + | 6.40881i | −0.431755 | + | 0.249274i | −0.700094 | − | 0.714051i | \(-0.746859\pi\) |
0.268339 | + | 0.963325i | \(0.413525\pi\) | |||||||
\(662\) | 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 | −0.564425 | − | 0.825484i | \(-0.690902\pi\) |
0.997103 | + | 0.0760644i | \(0.0242355\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5903 | + | 44.3237i | −0.983516 | + | 1.70350i | −0.335163 | + | 0.942160i | \(0.608791\pi\) |
−0.648353 | + | 0.761340i | \(0.724542\pi\) | |||||||
\(678\) | 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 | \(0.0898677\pi\) | ||||
−0.960410 | + | 0.278592i | \(0.910132\pi\) | |||||||
\(684\) | 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 | 0.845412 | − | 0.534115i | \(-0.179355\pi\) |
−0.0398517 | + | 0.999206i | \(0.512689\pi\) | |||||||
\(692\) | 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 | \(-0.986669\pi\) | ||
0.999123 | − | 0.0418669i | \(-0.0133305\pi\) | |||||||
\(702\) | 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 | −0.540821 | − | 0.841138i | \(-0.681886\pi\) |
0.998857 | + | 0.0477959i | \(0.0152197\pi\) | |||||||
\(710\) | 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 | 0.292740 | − | 0.956192i | \(-0.405433\pi\) |
−0.681717 | + | 0.731616i | \(0.738766\pi\) | |||||||
\(728\) | 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 | −0.228057 | − | 0.973648i | \(-0.573237\pi\) |
0.729175 | + | 0.684327i | \(0.239904\pi\) | |||||||
\(734\) | 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 | −0.680765 | − | 0.732502i | \(-0.738353\pi\) |
0.293982 | + | 0.955811i | \(0.405019\pi\) | |||||||
\(744\) | 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 | 0.987243 | + | 0.159221i | \(0.0508983\pi\) |
−0.355732 | + | 0.934588i | \(0.615768\pi\) | |||||||
\(752\) | 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 | 0.758356 | − | 0.651840i | \(-0.226003\pi\) |
−0.943688 | + | 0.330835i | \(0.892670\pi\) | |||||||
\(762\) | 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 | −0.896760 | − | 0.442517i | \(-0.854086\pi\) |
−0.0651494 | + | 0.997876i | \(0.520752\pi\) | |||||||
\(770\) | 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 | −0.717742 | − | 0.696309i | \(-0.754824\pi\) |
0.244150 | + | 0.969737i | \(0.421491\pi\) | |||||||
\(788\) | 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 | 0.989376 | + | 0.145379i | \(0.0464402\pi\) |
−0.368786 | + | 0.929514i | \(0.620226\pi\) | |||||||
\(798\) | 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 | \(0.159282\pi\) | ||||
−0.877391 | + | 0.479777i | \(0.840718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.7628i | − | 0.974883i | −0.873156 | − | 0.487442i | \(-0.837930\pi\) | ||
0.873156 | − | 0.487442i | \(-0.162070\pi\) | |||||||
\(812\) | 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 | 0.987326 | − | 0.158703i | \(-0.0507311\pi\) |
0.356223 | + | 0.934401i | \(0.384064\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.5577 | − | 44.2672i | −0.890884 | − | 1.54306i | −0.838818 | − | 0.544413i | \(-0.816753\pi\) |
−0.0520663 | − | 0.998644i | \(-0.516581\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.5414i | 0.505653i | 0.967512 | + | 0.252826i | \(0.0813601\pi\) | ||||
−0.967512 | + | 0.252826i | \(0.918640\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27.9681i | − | 0.971373i | −0.874133 | − | 0.485686i | \(-0.838570\pi\) | ||
0.874133 | − | 0.485686i | \(-0.161430\pi\) | |||||||
\(830\) | 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 | −0.874517 | − | 0.484996i | \(-0.838821\pi\) |
0.857277 | + | 0.514856i | \(0.172154\pi\) | |||||||
\(840\) | 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 | 0.638214 | − | 0.769859i | \(-0.279674\pi\) |
−0.347611 | + | 0.937639i | \(0.613007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.85002 | + | 6.66842i | −0.131514 | + | 0.227789i | −0.924260 | − | 0.381763i | \(-0.875317\pi\) |
0.792746 | + | 0.609552i | \(0.208651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4022 | − | 9.46979i | 0.559634 | − | 0.323105i | −0.193364 | − | 0.981127i | \(-0.561940\pi\) |
0.752999 | + | 0.658022i | \(0.228607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 17.4540i | − | 0.594141i | −0.954856 | − | 0.297070i | \(-0.903990\pi\) | ||
0.954856 | − | 0.297070i | \(-0.0960096\pi\) | |||||||
\(864\) | 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 | 0.862695 | − | 0.505725i | \(-0.168775\pi\) |
−0.869318 | + | 0.494253i | \(0.835442\pi\) | |||||||
\(878\) | 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 | 0.513256 | − | 0.858236i | \(-0.328439\pi\) |
−0.999882 | + | 0.0153745i | \(0.995106\pi\) | |||||||
\(888\) | 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 | −0.896549 | − | 0.442945i | \(-0.853934\pi\) |
0.831876 | + | 0.554962i | \(0.187267\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.32768 | + | 0.766538i | 0.0439881 | + | 0.0253966i | 0.521833 | − | 0.853048i | \(-0.325248\pi\) |
−0.477845 | + | 0.878444i | \(0.658582\pi\) | |||||||
\(912\) | 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 | −0.891728 | − | 0.452571i | \(-0.850507\pi\) |
0.837802 | + | 0.545974i | \(0.183840\pi\) | |||||||
\(930\) | 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 | \(-0.803051\pi\) | ||
0.814613 | − | 0.580005i | \(-0.196949\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.24941 | − | 10.8243i | −0.203725 | − | 0.352862i | 0.746001 | − | 0.665945i | \(-0.231972\pi\) |
−0.949726 | + | 0.313083i | \(0.898638\pi\) | |||||||
\(942\) | 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 | 0.913048 | − | 0.407852i | \(-0.133722\pi\) |
0.103313 | + | 0.994649i | \(0.467056\pi\) | |||||||
\(948\) | 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 | \(0.262154\pi\) | ||||
−0.679599 | + | 0.733584i | \(0.737846\pi\) | |||||||
\(954\) | 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 | 0.606000 | − | 0.795465i | \(-0.292773\pi\) |
−0.991893 | + | 0.127079i | \(0.959440\pi\) | |||||||
\(968\) | 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 | 0.0611236 | − | 0.998130i | \(-0.480532\pi\) |
0.894968 | + | 0.446131i | \(0.147198\pi\) | |||||||
\(978\) | 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 | −0.884625 | − | 0.466304i | \(-0.845585\pi\) |
0.846143 | + | 0.532956i | \(0.178919\pi\) | |||||||
\(984\) | 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 | 0.967078 | − | 0.254481i | \(-0.0819045\pi\) |
0.263152 | + | 0.964754i | \(0.415238\pi\) | |||||||
\(998\) | 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 \(a_p\))