Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 557.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.557 |
Dual form | 784.2.x.c.373.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | ||||
\(3\) | −1.36603 | + | 0.366025i | −0.788675 | + | 0.211325i | −0.630606 | − | 0.776103i | \(-0.717194\pi\) |
−0.158069 | + | 0.987428i | \(0.550527\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | −1.36603 | − | 0.366025i | −0.610905 | − | 0.163692i | −0.0599153 | − | 0.998203i | \(-0.519083\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | −1.73205 | − | 1.00000i | −0.547723 | − | 0.316228i | ||||
\(11\) | 0.366025 | + | 1.36603i | 0.110361 | + | 0.411872i | 0.998898 | − | 0.0469323i | \(-0.0149445\pi\) |
−0.888537 | + | 0.458804i | \(0.848278\pi\) | |||||||
\(12\) | −2.73205 | − | 0.732051i | −0.788675 | − | 0.211325i | ||||
\(13\) | 1.00000 | + | 1.00000i | 0.277350 | + | 0.277350i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | −1.36603 | + | 0.366025i | −0.321975 | + | 0.0862730i | ||||
\(19\) | −1.09808 | + | 4.09808i | −0.251916 | + | 0.940163i | 0.717864 | + | 0.696183i | \(0.245120\pi\) |
−0.969780 | + | 0.243980i | \(0.921547\pi\) | |||||||
\(20\) | −2.00000 | − | 2.00000i | −0.447214 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | −3.46410 | − | 2.00000i | −0.707107 | − | 0.408248i | ||||
\(25\) | −2.59808 | − | 1.50000i | −0.519615 | − | 0.300000i | ||||
\(26\) | 1.00000 | + | 1.73205i | 0.196116 | + | 0.339683i | ||||
\(27\) | 4.00000 | − | 4.00000i | 0.769800 | − | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 3.00000i | 0.557086 | + | 0.557086i | 0.928477 | − | 0.371391i | \(-0.121119\pi\) |
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 2.73205 | + | 0.732051i | 0.498802 | + | 0.133654i | ||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | 1.46410 | + | 5.46410i | 0.258819 | + | 0.965926i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | −2.00000 | + | 2.00000i | −0.342997 | + | 0.342997i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −4.09808 | − | 1.09808i | −0.673720 | − | 0.180523i | −0.0942898 | − | 0.995545i | \(-0.530058\pi\) |
−0.579430 | + | 0.815022i | \(0.696725\pi\) | |||||||
\(38\) | −3.00000 | + | 5.19615i | −0.486664 | + | 0.842927i | ||||
\(39\) | −1.73205 | − | 1.00000i | −0.277350 | − | 0.160128i | ||||
\(40\) | −2.00000 | − | 3.46410i | −0.316228 | − | 0.547723i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | − | 5.00000i | 0.762493 | − | 0.762493i | −0.214280 | − | 0.976772i | \(-0.568740\pi\) |
0.976772 | + | 0.214280i | \(0.0687403\pi\) | |||||||
\(44\) | −0.732051 | + | 2.73205i | −0.110361 | + | 0.411872i | ||||
\(45\) | 1.36603 | − | 0.366025i | 0.203635 | − | 0.0545638i | ||||
\(46\) | −8.19615 | + | 2.19615i | −1.20846 | + | 0.323805i | ||||
\(47\) | 4.00000 | + | 6.92820i | 0.583460 | + | 1.01058i | 0.995066 | + | 0.0992202i | \(0.0316348\pi\) |
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(48\) | −4.00000 | − | 4.00000i | −0.577350 | − | 0.577350i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00000 | − | 3.00000i | −0.424264 | − | 0.424264i | ||||
\(51\) | 0.732051 | − | 2.73205i | 0.102508 | − | 0.382564i | ||||
\(52\) | 0.732051 | + | 2.73205i | 0.101517 | + | 0.378867i | ||||
\(53\) | −1.83013 | − | 6.83013i | −0.251387 | − | 0.938190i | −0.970065 | − | 0.242846i | \(-0.921919\pi\) |
0.718677 | − | 0.695344i | \(-0.244748\pi\) | |||||||
\(54\) | 6.92820 | − | 4.00000i | 0.942809 | − | 0.544331i | ||||
\(55\) | − | 2.00000i | − | 0.269680i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 3.00000 | + | 5.19615i | 0.393919 | + | 0.682288i | ||||
\(59\) | 1.09808 | + | 4.09808i | 0.142957 | + | 0.533524i | 0.999838 | + | 0.0180090i | \(0.00573274\pi\) |
−0.856880 | + | 0.515515i | \(0.827601\pi\) | |||||||
\(60\) | 3.46410 | + | 2.00000i | 0.447214 | + | 0.258199i | ||||
\(61\) | 3.29423 | − | 12.2942i | 0.421783 | − | 1.57411i | −0.349067 | − | 0.937098i | \(-0.613501\pi\) |
0.770850 | − | 0.637017i | \(-0.219832\pi\) | |||||||
\(62\) | −8.00000 | + | 8.00000i | −1.01600 | + | 1.01600i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | −0.732051 | − | 2.73205i | −0.0901092 | − | 0.336292i | ||||
\(67\) | 6.83013 | − | 1.83013i | 0.834433 | − | 0.223586i | 0.183786 | − | 0.982966i | \(-0.441165\pi\) |
0.650647 | + | 0.759381i | \(0.274498\pi\) | |||||||
\(68\) | −3.46410 | + | 2.00000i | −0.420084 | + | 0.242536i | ||||
\(69\) | 6.00000 | − | 6.00000i | 0.722315 | − | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000i | 1.18678i | 0.804914 | + | 0.593391i | \(0.202211\pi\) | ||||
−0.804914 | + | 0.593391i | \(0.797789\pi\) | |||||||
\(72\) | −2.73205 | − | 0.732051i | −0.321975 | − | 0.0862730i | ||||
\(73\) | 3.46410 | + | 2.00000i | 0.405442 | + | 0.234082i | 0.688830 | − | 0.724923i | \(-0.258125\pi\) |
−0.283387 | + | 0.959006i | \(0.591458\pi\) | |||||||
\(74\) | −5.19615 | − | 3.00000i | −0.604040 | − | 0.348743i | ||||
\(75\) | 4.09808 | + | 1.09808i | 0.473205 | + | 0.126795i | ||||
\(76\) | −6.00000 | + | 6.00000i | −0.688247 | + | 0.688247i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.00000 | − | 2.00000i | −0.226455 | − | 0.226455i | ||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | −1.46410 | − | 5.46410i | −0.163692 | − | 0.610905i | ||||
\(81\) | −2.50000 | + | 4.33013i | −0.277778 | + | 0.481125i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00000 | + | 1.00000i | 0.109764 | + | 0.109764i | 0.759856 | − | 0.650092i | \(-0.225269\pi\) |
−0.650092 | + | 0.759856i | \(0.725269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 2.00000i | 0.216930 | − | 0.216930i | ||||
\(86\) | 8.66025 | − | 5.00000i | 0.933859 | − | 0.539164i | ||||
\(87\) | −5.19615 | − | 3.00000i | −0.557086 | − | 0.321634i | ||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | 3.46410 | − | 2.00000i | 0.367194 | − | 0.212000i | −0.305038 | − | 0.952340i | \(-0.598669\pi\) |
0.672232 | + | 0.740341i | \(0.265336\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.0000 | −1.25109 | ||||||||
\(93\) | 2.92820 | − | 10.9282i | 0.303641 | − | 1.13320i | ||||
\(94\) | 2.92820 | + | 10.9282i | 0.302021 | + | 1.12716i | ||||
\(95\) | 3.00000 | − | 5.19615i | 0.307794 | − | 0.533114i | ||||
\(96\) | −4.00000 | − | 6.92820i | −0.408248 | − | 0.707107i | ||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | − | 1.00000i | −0.100504 | − | 0.100504i | ||||
\(100\) | −3.00000 | − | 5.19615i | −0.300000 | − | 0.519615i | ||||
\(101\) | −4.02628 | − | 15.0263i | −0.400630 | − | 1.49517i | −0.811976 | − | 0.583691i | \(-0.801608\pi\) |
0.411346 | − | 0.911479i | \(-0.365059\pi\) | |||||||
\(102\) | 2.00000 | − | 3.46410i | 0.198030 | − | 0.342997i | ||||
\(103\) | 5.19615 | − | 3.00000i | 0.511992 | − | 0.295599i | −0.221660 | − | 0.975124i | \(-0.571148\pi\) |
0.733652 | + | 0.679525i | \(0.237814\pi\) | |||||||
\(104\) | 4.00000i | 0.392232i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 10.0000i | − | 0.971286i | ||||||
\(107\) | 9.56218 | + | 2.56218i | 0.924411 | + | 0.247695i | 0.689470 | − | 0.724315i | \(-0.257844\pi\) |
0.234941 | + | 0.972010i | \(0.424510\pi\) | |||||||
\(108\) | 10.9282 | − | 2.92820i | 1.05157 | − | 0.281766i | ||||
\(109\) | −4.09808 | + | 1.09808i | −0.392525 | + | 0.105177i | −0.449682 | − | 0.893189i | \(-0.648463\pi\) |
0.0571579 | + | 0.998365i | \(0.481796\pi\) | |||||||
\(110\) | 0.732051 | − | 2.73205i | 0.0697983 | − | 0.260491i | ||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 2.19615 | − | 8.19615i | 0.205689 | − | 0.767640i | ||||
\(115\) | 8.19615 | − | 2.19615i | 0.764295 | − | 0.204792i | ||||
\(116\) | 2.19615 | + | 8.19615i | 0.203908 | + | 0.760994i | ||||
\(117\) | −1.36603 | − | 0.366025i | −0.126289 | − | 0.0338391i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.00000 | + | 4.00000i | 0.365148 | + | 0.365148i | ||||
\(121\) | 7.79423 | − | 4.50000i | 0.708566 | − | 0.409091i | ||||
\(122\) | 9.00000 | − | 15.5885i | 0.814822 | − | 1.41131i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.8564 | + | 8.00000i | −1.24434 | + | 0.718421i | ||||
\(125\) | 8.00000 | + | 8.00000i | 0.715542 | + | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | −5.00000 | + | 8.66025i | −0.440225 | + | 0.762493i | ||||
\(130\) | −0.732051 | − | 2.73205i | −0.0642051 | − | 0.239617i | ||||
\(131\) | −4.02628 | + | 15.0263i | −0.351778 | + | 1.31285i | 0.532714 | + | 0.846296i | \(0.321172\pi\) |
−0.884491 | + | 0.466557i | \(0.845494\pi\) | |||||||
\(132\) | − | 4.00000i | − | 0.348155i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.0000 | 0.863868 | ||||||||
\(135\) | −6.92820 | + | 4.00000i | −0.596285 | + | 0.344265i | ||||
\(136\) | −5.46410 | + | 1.46410i | −0.468543 | + | 0.125546i | ||||
\(137\) | 6.92820 | + | 4.00000i | 0.591916 | + | 0.341743i | 0.765855 | − | 0.643013i | \(-0.222316\pi\) |
−0.173939 | + | 0.984757i | \(0.555649\pi\) | |||||||
\(138\) | 10.3923 | − | 6.00000i | 0.884652 | − | 0.510754i | ||||
\(139\) | 3.00000 | − | 3.00000i | 0.254457 | − | 0.254457i | −0.568338 | − | 0.822795i | \(-0.692414\pi\) |
0.822795 | + | 0.568338i | \(0.192414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | − | 8.00000i | −0.673722 | − | 0.673722i | ||||
\(142\) | −3.66025 | + | 13.6603i | −0.307162 | + | 1.14634i | ||||
\(143\) | −1.00000 | + | 1.73205i | −0.0836242 | + | 0.144841i | ||||
\(144\) | −3.46410 | − | 2.00000i | −0.288675 | − | 0.166667i | ||||
\(145\) | −3.00000 | − | 5.19615i | −0.249136 | − | 0.431517i | ||||
\(146\) | 4.00000 | + | 4.00000i | 0.331042 | + | 0.331042i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.00000 | − | 6.00000i | −0.493197 | − | 0.493197i | ||||
\(149\) | −9.56218 | − | 2.56218i | −0.783364 | − | 0.209902i | −0.155097 | − | 0.987899i | \(-0.549569\pi\) |
−0.628267 | + | 0.777997i | \(0.716236\pi\) | |||||||
\(150\) | 5.19615 | + | 3.00000i | 0.424264 | + | 0.244949i | ||||
\(151\) | −8.66025 | − | 5.00000i | −0.704761 | − | 0.406894i | 0.104357 | − | 0.994540i | \(-0.466722\pi\) |
−0.809118 | + | 0.587646i | \(0.800055\pi\) | |||||||
\(152\) | −10.3923 | + | 6.00000i | −0.842927 | + | 0.486664i | ||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | − | 8.00000i | 0.642575 | − | 0.642575i | ||||
\(156\) | −2.00000 | − | 3.46410i | −0.160128 | − | 0.277350i | ||||
\(157\) | 20.4904 | − | 5.49038i | 1.63531 | − | 0.438180i | 0.679862 | − | 0.733340i | \(-0.262039\pi\) |
0.955448 | + | 0.295160i | \(0.0953728\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.00000 | + | 8.66025i | 0.396526 | + | 0.686803i | ||||
\(160\) | − | 8.00000i | − | 0.632456i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.00000 | + | 5.00000i | −0.392837 | + | 0.392837i | ||||
\(163\) | −0.366025 | + | 1.36603i | −0.0286693 | + | 0.106995i | −0.978778 | − | 0.204924i | \(-0.934305\pi\) |
0.950109 | + | 0.311919i | \(0.100972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.732051 | + | 2.73205i | 0.0569901 | + | 0.212690i | ||||
\(166\) | 1.00000 | + | 1.73205i | 0.0776151 | + | 0.134433i | ||||
\(167\) | − | 2.00000i | − | 0.154765i | −0.997001 | − | 0.0773823i | \(-0.975344\pi\) | ||
0.997001 | − | 0.0773823i | \(-0.0246562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 3.46410 | − | 2.00000i | 0.265684 | − | 0.153393i | ||||
\(171\) | −1.09808 | − | 4.09808i | −0.0839720 | − | 0.313388i | ||||
\(172\) | 13.6603 | − | 3.66025i | 1.04158 | − | 0.279092i | ||||
\(173\) | 0.366025 | − | 1.36603i | 0.0278284 | − | 0.103857i | −0.950615 | − | 0.310373i | \(-0.899546\pi\) |
0.978443 | + | 0.206516i | \(0.0662126\pi\) | |||||||
\(174\) | −6.00000 | − | 6.00000i | −0.454859 | − | 0.454859i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | + | 4.00000i | −0.301511 | + | 0.301511i | ||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 5.46410 | − | 1.46410i | 0.409552 | − | 0.109739i | ||||
\(179\) | 23.2224 | − | 6.22243i | 1.73573 | − | 0.465086i | 0.754237 | − | 0.656603i | \(-0.228007\pi\) |
0.981489 | + | 0.191516i | \(0.0613405\pi\) | |||||||
\(180\) | 2.73205 | + | 0.732051i | 0.203635 | + | 0.0545638i | ||||
\(181\) | 9.00000 | − | 9.00000i | 0.668965 | − | 0.668965i | −0.288512 | − | 0.957476i | \(-0.593160\pi\) |
0.957476 | + | 0.288512i | \(0.0931604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.0000i | 1.33060i | ||||||||
\(184\) | −16.3923 | − | 4.39230i | −1.20846 | − | 0.323805i | ||||
\(185\) | 5.19615 | + | 3.00000i | 0.382029 | + | 0.220564i | ||||
\(186\) | 8.00000 | − | 13.8564i | 0.586588 | − | 1.01600i | ||||
\(187\) | −2.73205 | − | 0.732051i | −0.199787 | − | 0.0535329i | ||||
\(188\) | 16.0000i | 1.16692i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | − | 6.00000i | 0.435286 | − | 0.435286i | ||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | −2.92820 | − | 10.9282i | −0.211325 | − | 0.788675i | ||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 2.73205 | + | 0.732051i | 0.196150 | + | 0.0525582i | ||||
\(195\) | 2.00000 | + | 2.00000i | 0.143223 | + | 0.143223i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.0000 | + | 17.0000i | −1.21120 | + | 1.21120i | −0.240567 | + | 0.970632i | \(0.577334\pi\) |
−0.970632 | + | 0.240567i | \(0.922666\pi\) | |||||||
\(198\) | −1.00000 | − | 1.73205i | −0.0710669 | − | 0.123091i | ||||
\(199\) | −12.1244 | − | 7.00000i | −0.859473 | − | 0.496217i | 0.00436292 | − | 0.999990i | \(-0.498611\pi\) |
−0.863836 | + | 0.503774i | \(0.831945\pi\) | |||||||
\(200\) | −2.19615 | − | 8.19615i | −0.155291 | − | 0.579555i | ||||
\(201\) | −8.66025 | + | 5.00000i | −0.610847 | + | 0.352673i | ||||
\(202\) | − | 22.0000i | − | 1.54791i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.00000 | − | 4.00000i | 0.280056 | − | 0.280056i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.19615 | − | 2.19615i | 0.571053 | − | 0.153013i | ||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | −1.46410 | + | 5.46410i | −0.101517 | + | 0.378867i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | − | 9.00000i | −0.619586 | − | 0.619586i | 0.325840 | − | 0.945425i | \(-0.394353\pi\) |
−0.945425 | + | 0.325840i | \(0.894353\pi\) | |||||||
\(212\) | 3.66025 | − | 13.6603i | 0.251387 | − | 0.938190i | ||||
\(213\) | −3.66025 | − | 13.6603i | −0.250796 | − | 0.935985i | ||||
\(214\) | 12.1244 | + | 7.00000i | 0.828804 | + | 0.478510i | ||||
\(215\) | −8.66025 | + | 5.00000i | −0.590624 | + | 0.340997i | ||||
\(216\) | 16.0000 | 1.08866 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | −5.46410 | − | 1.46410i | −0.369230 | − | 0.0989348i | ||||
\(220\) | 2.00000 | − | 3.46410i | 0.134840 | − | 0.233550i | ||||
\(221\) | −2.73205 | + | 0.732051i | −0.183778 | + | 0.0492431i | ||||
\(222\) | 8.19615 | + | 2.19615i | 0.550090 | + | 0.147396i | ||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | −8.19615 | − | 2.19615i | −0.545200 | − | 0.146086i | ||||
\(227\) | 20.4904 | − | 5.49038i | 1.35999 | − | 0.364409i | 0.496180 | − | 0.868220i | \(-0.334736\pi\) |
0.863814 | + | 0.503810i | \(0.168069\pi\) | |||||||
\(228\) | 6.00000 | − | 10.3923i | 0.397360 | − | 0.688247i | ||||
\(229\) | 9.56218 | + | 2.56218i | 0.631886 | + | 0.169313i | 0.560526 | − | 0.828137i | \(-0.310599\pi\) |
0.0713609 | + | 0.997451i | \(0.477266\pi\) | |||||||
\(230\) | 12.0000 | 0.791257 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0000i | 0.787839i | ||||||||
\(233\) | 3.46410 | − | 2.00000i | 0.226941 | − | 0.131024i | −0.382219 | − | 0.924072i | \(-0.624840\pi\) |
0.609160 | + | 0.793047i | \(0.291507\pi\) | |||||||
\(234\) | −1.73205 | − | 1.00000i | −0.113228 | − | 0.0653720i | ||||
\(235\) | −2.92820 | − | 10.9282i | −0.191015 | − | 0.712877i | ||||
\(236\) | −2.19615 | + | 8.19615i | −0.142957 | + | 0.533524i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 4.00000 | + | 6.92820i | 0.258199 | + | 0.447214i | ||||
\(241\) | −9.00000 | + | 15.5885i | −0.579741 | + | 1.00414i | 0.415768 | + | 0.909471i | \(0.363513\pi\) |
−0.995509 | + | 0.0946700i | \(0.969820\pi\) | |||||||
\(242\) | 12.2942 | − | 3.29423i | 0.790303 | − | 0.211761i | ||||
\(243\) | −2.56218 | + | 9.56218i | −0.164364 | + | 0.613414i | ||||
\(244\) | 18.0000 | − | 18.0000i | 1.15233 | − | 1.15233i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.19615 | + | 3.00000i | −0.330623 | + | 0.190885i | ||||
\(248\) | −21.8564 | + | 5.85641i | −1.38788 | + | 0.371882i | ||||
\(249\) | −1.73205 | − | 1.00000i | −0.109764 | − | 0.0633724i | ||||
\(250\) | 8.00000 | + | 13.8564i | 0.505964 | + | 0.876356i | ||||
\(251\) | −21.0000 | + | 21.0000i | −1.32551 | + | 1.32551i | −0.416265 | + | 0.909243i | \(0.636661\pi\) |
−0.909243 | + | 0.416265i | \(0.863339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | − | 6.00000i | −0.377217 | − | 0.377217i | ||||
\(254\) | 10.9282 | + | 2.92820i | 0.685696 | + | 0.183732i | ||||
\(255\) | −2.00000 | + | 3.46410i | −0.125245 | + | 0.216930i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −11.0000 | − | 19.0526i | −0.686161 | − | 1.18847i | −0.973070 | − | 0.230508i | \(-0.925961\pi\) |
0.286909 | − | 0.957958i | \(-0.407372\pi\) | |||||||
\(258\) | −10.0000 | + | 10.0000i | −0.622573 | + | 0.622573i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.00000i | − | 0.248069i | ||||||
\(261\) | −4.09808 | − | 1.09808i | −0.253665 | − | 0.0679692i | ||||
\(262\) | −11.0000 | + | 19.0526i | −0.679582 | + | 1.17707i | ||||
\(263\) | 5.19615 | + | 3.00000i | 0.320408 | + | 0.184988i | 0.651575 | − | 0.758585i | \(-0.274109\pi\) |
−0.331166 | + | 0.943572i | \(0.607442\pi\) | |||||||
\(264\) | 1.46410 | − | 5.46410i | 0.0901092 | − | 0.336292i | ||||
\(265\) | 10.0000i | 0.614295i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.00000 | + | 4.00000i | −0.244796 | + | 0.244796i | ||||
\(268\) | 13.6603 | + | 3.66025i | 0.834433 | + | 0.223586i | ||||
\(269\) | 4.09808 | − | 1.09808i | 0.249864 | − | 0.0669509i | −0.131713 | − | 0.991288i | \(-0.542048\pi\) |
0.381577 | + | 0.924337i | \(0.375381\pi\) | |||||||
\(270\) | −10.9282 | + | 2.92820i | −0.665069 | + | 0.178205i | ||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000 | + | 8.00000i | 0.483298 | + | 0.483298i | ||||
\(275\) | 1.09808 | − | 4.09808i | 0.0662165 | − | 0.247123i | ||||
\(276\) | 16.3923 | − | 4.39230i | 0.986701 | − | 0.264386i | ||||
\(277\) | 1.09808 | + | 4.09808i | 0.0659770 | + | 0.246230i | 0.991036 | − | 0.133593i | \(-0.0426516\pi\) |
−0.925059 | + | 0.379823i | \(0.875985\pi\) | |||||||
\(278\) | 5.19615 | − | 3.00000i | 0.311645 | − | 0.179928i | ||||
\(279\) | − | 8.00000i | − | 0.478947i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000i | 1.19310i | 0.802576 | + | 0.596550i | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | −8.00000 | − | 13.8564i | −0.476393 | − | 0.825137i | ||||
\(283\) | 5.49038 | + | 20.4904i | 0.326369 | + | 1.21803i | 0.912928 | + | 0.408120i | \(0.133816\pi\) |
−0.586559 | + | 0.809907i | \(0.699518\pi\) | |||||||
\(284\) | −10.0000 | + | 17.3205i | −0.593391 | + | 1.02778i | ||||
\(285\) | −2.19615 | + | 8.19615i | −0.130089 | + | 0.485498i | ||||
\(286\) | −2.00000 | + | 2.00000i | −0.118262 | + | 0.118262i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.00000 | − | 4.00000i | −0.235702 | − | 0.235702i | ||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −2.19615 | − | 8.19615i | −0.128963 | − | 0.481295i | ||||
\(291\) | −2.73205 | + | 0.732051i | −0.160156 | + | 0.0429136i | ||||
\(292\) | 4.00000 | + | 6.92820i | 0.234082 | + | 0.405442i | ||||
\(293\) | −15.0000 | + | 15.0000i | −0.876309 | + | 0.876309i | −0.993151 | − | 0.116841i | \(-0.962723\pi\) |
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.00000i | − | 0.349334i | ||||||
\(296\) | −6.00000 | − | 10.3923i | −0.348743 | − | 0.604040i | ||||
\(297\) | 6.92820 | + | 4.00000i | 0.402015 | + | 0.232104i | ||||
\(298\) | −12.1244 | − | 7.00000i | −0.702345 | − | 0.405499i | ||||
\(299\) | −8.19615 | − | 2.19615i | −0.473996 | − | 0.127007i | ||||
\(300\) | 6.00000 | + | 6.00000i | 0.346410 | + | 0.346410i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.0000 | − | 10.0000i | −0.575435 | − | 0.575435i | ||||
\(303\) | 11.0000 | + | 19.0526i | 0.631933 | + | 1.09454i | ||||
\(304\) | −16.3923 | + | 4.39230i | −0.940163 | + | 0.251916i | ||||
\(305\) | −9.00000 | + | 15.5885i | −0.515339 | + | 0.892592i | ||||
\(306\) | 0.732051 | − | 2.73205i | 0.0418486 | − | 0.156181i | ||||
\(307\) | 5.00000 | + | 5.00000i | 0.285365 | + | 0.285365i | 0.835244 | − | 0.549879i | \(-0.185326\pi\) |
−0.549879 | + | 0.835244i | \(0.685326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | + | 6.00000i | −0.341328 | + | 0.341328i | ||||
\(310\) | 13.8564 | − | 8.00000i | 0.786991 | − | 0.454369i | ||||
\(311\) | −25.9808 | − | 15.0000i | −1.47323 | − | 0.850572i | −0.473688 | − | 0.880693i | \(-0.657077\pi\) |
−0.999546 | + | 0.0301210i | \(0.990411\pi\) | |||||||
\(312\) | −1.46410 | − | 5.46410i | −0.0828884 | − | 0.309344i | ||||
\(313\) | 13.8564 | − | 8.00000i | 0.783210 | − | 0.452187i | −0.0543564 | − | 0.998522i | \(-0.517311\pi\) |
0.837567 | + | 0.546335i | \(0.183977\pi\) | |||||||
\(314\) | 30.0000 | 1.69300 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.83013 | + | 6.83013i | −0.102790 | + | 0.383618i | −0.998085 | − | 0.0618557i | \(-0.980298\pi\) |
0.895295 | + | 0.445474i | \(0.146965\pi\) | |||||||
\(318\) | 3.66025 | + | 13.6603i | 0.205257 | + | 0.766029i | ||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 2.92820 | − | 10.9282i | 0.163692 | − | 0.610905i | ||||
\(321\) | −14.0000 | −0.781404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | − | 6.00000i | −0.333849 | − | 0.333849i | ||||
\(324\) | −8.66025 | + | 5.00000i | −0.481125 | + | 0.277778i | ||||
\(325\) | −1.09808 | − | 4.09808i | −0.0609103 | − | 0.227320i | ||||
\(326\) | −1.00000 | + | 1.73205i | −0.0553849 | + | 0.0959294i | ||||
\(327\) | 5.19615 | − | 3.00000i | 0.287348 | − | 0.165900i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.00000i | 0.220193i | ||||||||
\(331\) | −1.36603 | − | 0.366025i | −0.0750835 | − | 0.0201186i | 0.221082 | − | 0.975255i | \(-0.429041\pi\) |
−0.296165 | + | 0.955137i | \(0.595708\pi\) | |||||||
\(332\) | 0.732051 | + | 2.73205i | 0.0401765 | + | 0.149941i | ||||
\(333\) | 4.09808 | − | 1.09808i | 0.224573 | − | 0.0601742i | ||||
\(334\) | 0.732051 | − | 2.73205i | 0.0400560 | − | 0.149491i | ||||
\(335\) | −10.0000 | −0.546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 4.02628 | − | 15.0263i | 0.219001 | − | 0.817322i | ||||
\(339\) | 8.19615 | − | 2.19615i | 0.445154 | − | 0.119279i | ||||
\(340\) | 5.46410 | − | 1.46410i | 0.296333 | − | 0.0794021i | ||||
\(341\) | −10.9282 | − | 2.92820i | −0.591795 | − | 0.158571i | ||||
\(342\) | − | 6.00000i | − | 0.324443i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 20.0000 | 1.07833 | ||||||||
\(345\) | −10.3923 | + | 6.00000i | −0.559503 | + | 0.323029i | ||||
\(346\) | 1.00000 | − | 1.73205i | 0.0537603 | − | 0.0931156i | ||||
\(347\) | 4.75833 | + | 17.7583i | 0.255441 | + | 0.953317i | 0.967845 | + | 0.251548i | \(0.0809396\pi\) |
−0.712404 | + | 0.701769i | \(0.752394\pi\) | |||||||
\(348\) | −6.00000 | − | 10.3923i | −0.321634 | − | 0.557086i | ||||
\(349\) | −3.00000 | − | 3.00000i | −0.160586 | − | 0.160586i | 0.622240 | − | 0.782826i | \(-0.286223\pi\) |
−0.782826 | + | 0.622240i | \(0.786223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000 | 0.427008 | ||||||||
\(352\) | −6.92820 | + | 4.00000i | −0.369274 | + | 0.213201i | ||||
\(353\) | −3.00000 | + | 5.19615i | −0.159674 | + | 0.276563i | −0.934751 | − | 0.355303i | \(-0.884378\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(354\) | −2.19615 | − | 8.19615i | −0.116724 | − | 0.435621i | ||||
\(355\) | 3.66025 | − | 13.6603i | 0.194266 | − | 0.725011i | ||||
\(356\) | 8.00000 | 0.423999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 34.0000 | 1.79696 | ||||||||
\(359\) | 22.5167 | − | 13.0000i | 1.18838 | − | 0.686114i | 0.230445 | − | 0.973085i | \(-0.425982\pi\) |
0.957939 | + | 0.286972i | \(0.0926486\pi\) | |||||||
\(360\) | 3.46410 | + | 2.00000i | 0.182574 | + | 0.105409i | ||||
\(361\) | 0.866025 | + | 0.500000i | 0.0455803 | + | 0.0263158i | ||||
\(362\) | 15.5885 | − | 9.00000i | 0.819311 | − | 0.473029i | ||||
\(363\) | −9.00000 | + | 9.00000i | −0.472377 | + | 0.472377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | − | 4.00000i | −0.209370 | − | 0.209370i | ||||
\(366\) | −6.58846 | + | 24.5885i | −0.344384 | + | 1.28526i | ||||
\(367\) | 4.00000 | − | 6.92820i | 0.208798 | − | 0.361649i | −0.742538 | − | 0.669804i | \(-0.766378\pi\) |
0.951336 | + | 0.308155i | \(0.0997115\pi\) | |||||||
\(368\) | −20.7846 | − | 12.0000i | −1.08347 | − | 0.625543i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | + | 6.00000i | 0.311925 | + | 0.311925i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 16.0000 | − | 16.0000i | 0.829561 | − | 0.829561i | ||||
\(373\) | 6.83013 | + | 1.83013i | 0.353651 | + | 0.0947604i | 0.431271 | − | 0.902223i | \(-0.358065\pi\) |
−0.0776200 | + | 0.996983i | \(0.524732\pi\) | |||||||
\(374\) | −3.46410 | − | 2.00000i | −0.179124 | − | 0.103418i | ||||
\(375\) | −13.8564 | − | 8.00000i | −0.715542 | − | 0.413118i | ||||
\(376\) | −5.85641 | + | 21.8564i | −0.302021 | + | 1.12716i | ||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00000 | + | 3.00000i | −0.154100 | + | 0.154100i | −0.779946 | − | 0.625847i | \(-0.784754\pi\) |
0.625847 | + | 0.779946i | \(0.284754\pi\) | |||||||
\(380\) | 10.3923 | − | 6.00000i | 0.533114 | − | 0.307794i | ||||
\(381\) | −10.9282 | + | 2.92820i | −0.559869 | + | 0.150016i | ||||
\(382\) | 2.92820 | + | 10.9282i | 0.149820 | + | 0.559136i | ||||
\(383\) | −8.00000 | − | 13.8564i | −0.408781 | − | 0.708029i | 0.585973 | − | 0.810331i | \(-0.300713\pi\) |
−0.994753 | + | 0.102302i | \(0.967379\pi\) | |||||||
\(384\) | − | 16.0000i | − | 0.816497i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | + | 14.0000i | −0.712581 | + | 0.712581i | ||||
\(387\) | −1.83013 | + | 6.83013i | −0.0930306 | + | 0.347195i | ||||
\(388\) | 3.46410 | + | 2.00000i | 0.175863 | + | 0.101535i | ||||
\(389\) | −4.75833 | − | 17.7583i | −0.241257 | − | 0.900383i | −0.975228 | − | 0.221202i | \(-0.929002\pi\) |
0.733971 | − | 0.679181i | \(-0.237665\pi\) | |||||||
\(390\) | 2.00000 | + | 3.46410i | 0.101274 | + | 0.175412i | ||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 22.0000i | − | 1.10975i | ||||||
\(394\) | −29.4449 | + | 17.0000i | −1.48341 | + | 0.856448i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.732051 | − | 2.73205i | −0.0367869 | − | 0.137291i | ||||
\(397\) | 1.83013 | − | 6.83013i | 0.0918514 | − | 0.342794i | −0.904672 | − | 0.426109i | \(-0.859884\pi\) |
0.996523 | + | 0.0833147i | \(0.0265507\pi\) | |||||||
\(398\) | −14.0000 | − | 14.0000i | −0.701757 | − | 0.701757i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 12.0000i | − | 0.600000i | ||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | −13.6603 | + | 3.66025i | −0.681312 | + | 0.182557i | ||||
\(403\) | −10.9282 | + | 2.92820i | −0.544373 | + | 0.145864i | ||||
\(404\) | 8.05256 | − | 30.0526i | 0.400630 | − | 1.49517i | ||||
\(405\) | 5.00000 | − | 5.00000i | 0.248452 | − | 0.248452i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | 6.92820 | − | 4.00000i | 0.342997 | − | 0.198030i | ||||
\(409\) | 13.8564 | + | 8.00000i | 0.685155 | + | 0.395575i | 0.801795 | − | 0.597600i | \(-0.203879\pi\) |
−0.116639 | + | 0.993174i | \(0.537212\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.9282 | − | 2.92820i | −0.539049 | − | 0.144438i | ||||
\(412\) | 12.0000 | 0.591198 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.00000 | − | 6.00000i | 0.294884 | − | 0.294884i | ||||
\(415\) | −1.00000 | − | 1.73205i | −0.0490881 | − | 0.0850230i | ||||
\(416\) | −4.00000 | + | 6.92820i | −0.196116 | + | 0.339683i | ||||
\(417\) | −3.00000 | + | 5.19615i | −0.146911 | + | 0.254457i | ||||
\(418\) | −8.19615 | − | 2.19615i | −0.400887 | − | 0.107417i | ||||
\(419\) | −3.00000 | − | 3.00000i | −0.146560 | − | 0.146560i | 0.630020 | − | 0.776579i | \(-0.283047\pi\) |
−0.776579 | + | 0.630020i | \(0.783047\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | + | 9.00000i | −0.438633 | + | 0.438633i | −0.891552 | − | 0.452919i | \(-0.850383\pi\) |
0.452919 | + | 0.891552i | \(0.350383\pi\) | |||||||
\(422\) | −9.00000 | − | 15.5885i | −0.438113 | − | 0.758834i | ||||
\(423\) | −6.92820 | − | 4.00000i | −0.336861 | − | 0.194487i | ||||
\(424\) | 10.0000 | − | 17.3205i | 0.485643 | − | 0.841158i | ||||
\(425\) | 5.19615 | − | 3.00000i | 0.252050 | − | 0.145521i | ||||
\(426\) | − | 20.0000i | − | 0.969003i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.0000 | + | 14.0000i | 0.676716 | + | 0.676716i | ||||
\(429\) | 0.732051 | − | 2.73205i | 0.0353437 | − | 0.131905i | ||||
\(430\) | −13.6603 | + | 3.66025i | −0.658756 | + | 0.176513i | ||||
\(431\) | −16.0000 | + | 27.7128i | −0.770693 | + | 1.33488i | 0.166491 | + | 0.986043i | \(0.446756\pi\) |
−0.937184 | + | 0.348836i | \(0.886577\pi\) | |||||||
\(432\) | 21.8564 | + | 5.85641i | 1.05157 | + | 0.281766i | ||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.00000 | + | 6.00000i | 0.287678 | + | 0.287678i | ||||
\(436\) | −8.19615 | − | 2.19615i | −0.392525 | − | 0.105177i | ||||
\(437\) | −6.58846 | − | 24.5885i | −0.315169 | − | 1.17623i | ||||
\(438\) | −6.92820 | − | 4.00000i | −0.331042 | − | 0.191127i | ||||
\(439\) | 12.1244 | − | 7.00000i | 0.578664 | − | 0.334092i | −0.181938 | − | 0.983310i | \(-0.558237\pi\) |
0.760602 | + | 0.649218i | \(0.224904\pi\) | |||||||
\(440\) | 4.00000 | − | 4.00000i | 0.190693 | − | 0.190693i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | −0.190261 | ||||||||
\(443\) | 20.4904 | + | 5.49038i | 0.973527 | + | 0.260856i | 0.710316 | − | 0.703882i | \(-0.248552\pi\) |
0.263211 | + | 0.964738i | \(0.415218\pi\) | |||||||
\(444\) | 10.3923 | + | 6.00000i | 0.493197 | + | 0.284747i | ||||
\(445\) | −5.46410 | + | 1.46410i | −0.259023 | + | 0.0694051i | ||||
\(446\) | −32.7846 | − | 8.78461i | −1.55240 | − | 0.415963i | ||||
\(447\) | 14.0000 | 0.662177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 4.09808 | + | 1.09808i | 0.193185 | + | 0.0517638i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −10.3923 | − | 6.00000i | −0.488813 | − | 0.282216i | ||||
\(453\) | 13.6603 | + | 3.66025i | 0.641815 | + | 0.171974i | ||||
\(454\) | 30.0000 | 1.40797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.0000 | − | 12.0000i | 0.561951 | − | 0.561951i | ||||
\(457\) | 27.7128 | − | 16.0000i | 1.29635 | − | 0.748448i | 0.316579 | − | 0.948566i | \(-0.397466\pi\) |
0.979772 | + | 0.200118i | \(0.0641325\pi\) | |||||||
\(458\) | 12.1244 | + | 7.00000i | 0.566534 | + | 0.327089i | ||||
\(459\) | 2.92820 | + | 10.9282i | 0.136677 | + | 0.510085i | ||||
\(460\) | 16.3923 | + | 4.39230i | 0.764295 | + | 0.204792i | ||||
\(461\) | −11.0000 | − | 11.0000i | −0.512321 | − | 0.512321i | 0.402916 | − | 0.915237i | \(-0.367997\pi\) |
−0.915237 | + | 0.402916i | \(0.867997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | −4.39230 | + | 16.3923i | −0.203908 | + | 0.760994i | ||||
\(465\) | −8.00000 | + | 13.8564i | −0.370991 | + | 0.642575i | ||||
\(466\) | 5.46410 | − | 1.46410i | 0.253120 | − | 0.0678232i | ||||
\(467\) | 1.83013 | − | 6.83013i | 0.0846882 | − | 0.316061i | −0.910567 | − | 0.413362i | \(-0.864354\pi\) |
0.995255 | + | 0.0973014i | \(0.0310211\pi\) | |||||||
\(468\) | −2.00000 | − | 2.00000i | −0.0924500 | − | 0.0924500i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 16.0000i | − | 0.738025i | ||||||
\(471\) | −25.9808 | + | 15.0000i | −1.19713 | + | 0.691164i | ||||
\(472\) | −6.00000 | + | 10.3923i | −0.276172 | + | 0.478345i | ||||
\(473\) | 8.66025 | + | 5.00000i | 0.398199 | + | 0.229900i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.00000 | − | 9.00000i | 0.412948 | − | 0.412948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.00000 | + | 5.00000i | 0.228934 | + | 0.228934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0000 | + | 34.6410i | −0.913823 | + | 1.58279i | −0.105208 | + | 0.994450i | \(0.533551\pi\) |
−0.808615 | + | 0.588338i | \(0.799782\pi\) | |||||||
\(480\) | 2.92820 | + | 10.9282i | 0.133654 | + | 0.498802i | ||||
\(481\) | −3.00000 | − | 5.19615i | −0.136788 | − | 0.236924i | ||||
\(482\) | −18.0000 | + | 18.0000i | −0.819878 | + | 0.819878i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.0000 | 0.818182 | ||||||||
\(485\) | −2.73205 | − | 0.732051i | −0.124056 | − | 0.0332407i | ||||
\(486\) | −7.00000 | + | 12.1244i | −0.317526 | + | 0.549972i | ||||
\(487\) | −1.73205 | − | 1.00000i | −0.0784867 | − | 0.0453143i | 0.460243 | − | 0.887793i | \(-0.347762\pi\) |
−0.538730 | + | 0.842479i | \(0.681096\pi\) | |||||||
\(488\) | 31.1769 | − | 18.0000i | 1.41131 | − | 0.814822i | ||||
\(489\) | − | 2.00000i | − | 0.0904431i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0000 | + | 19.0000i | −0.857458 | + | 0.857458i | −0.991038 | − | 0.133580i | \(-0.957353\pi\) |
0.133580 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.19615 | + | 2.19615i | −0.369136 | + | 0.0989097i | ||||
\(494\) | −8.19615 | + | 2.19615i | −0.368762 | + | 0.0988096i | ||||
\(495\) | 1.00000 | + | 1.73205i | 0.0449467 | + | 0.0778499i | ||||
\(496\) | −32.0000 | −1.43684 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.00000 | − | 2.00000i | −0.0896221 | − | 0.0896221i | ||||
\(499\) | 8.41858 | − | 31.4186i | 0.376868 | − | 1.40649i | −0.473729 | − | 0.880671i | \(-0.657092\pi\) |
0.850597 | − | 0.525818i | \(-0.176241\pi\) | |||||||
\(500\) | 5.85641 | + | 21.8564i | 0.261906 | + | 0.977448i | ||||
\(501\) | 0.732051 | + | 2.73205i | 0.0327056 | + | 0.122059i | ||||
\(502\) | −36.3731 | + | 21.0000i | −1.62341 | + | 0.937276i | ||||
\(503\) | 6.00000i | 0.267527i | 0.991013 | + | 0.133763i | \(0.0427062\pi\) | ||||
−0.991013 | + | 0.133763i | \(0.957294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0000i | 0.978987i | ||||||||
\(506\) | −6.00000 | − | 10.3923i | −0.266733 | − | 0.461994i | ||||
\(507\) | 4.02628 | + | 15.0263i | 0.178813 | + | 0.667340i | ||||
\(508\) | 13.8564 | + | 8.00000i | 0.614779 | + | 0.354943i | ||||
\(509\) | −8.41858 | + | 31.4186i | −0.373147 | + | 1.39260i | 0.482886 | + | 0.875683i | \(0.339589\pi\) |
−0.856033 | + | 0.516921i | \(0.827078\pi\) | |||||||
\(510\) | −4.00000 | + | 4.00000i | −0.177123 | + | 0.177123i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 12.0000 | + | 20.7846i | 0.529813 | + | 0.917663i | ||||
\(514\) | −8.05256 | − | 30.0526i | −0.355183 | − | 1.32556i | ||||
\(515\) | −8.19615 | + | 2.19615i | −0.361166 | + | 0.0967740i | ||||
\(516\) | −17.3205 | + | 10.0000i | −0.762493 | + | 0.440225i | ||||
\(517\) | −8.00000 | + | 8.00000i | −0.351840 | + | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00000i | 0.0877903i | ||||||||
\(520\) | 1.46410 | − | 5.46410i | 0.0642051 | − | 0.239617i | ||||
\(521\) | −34.6410 | − | 20.0000i | −1.51765 | − | 0.876216i | −0.999785 | − | 0.0207541i | \(-0.993393\pi\) |
−0.517866 | − | 0.855462i | \(-0.673273\pi\) | |||||||
\(522\) | −5.19615 | − | 3.00000i | −0.227429 | − | 0.131306i | ||||
\(523\) | 34.1506 | + | 9.15064i | 1.49330 | + | 0.400129i | 0.910851 | − | 0.412736i | \(-0.135427\pi\) |
0.582452 | + | 0.812865i | \(0.302093\pi\) | |||||||
\(524\) | −22.0000 | + | 22.0000i | −0.961074 | + | 0.961074i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.00000 | + | 6.00000i | 0.261612 | + | 0.261612i | ||||
\(527\) | −8.00000 | − | 13.8564i | −0.348485 | − | 0.603595i | ||||
\(528\) | 4.00000 | − | 6.92820i | 0.174078 | − | 0.301511i | ||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | −3.66025 | + | 13.6603i | −0.158991 | + | 0.593364i | ||||
\(531\) | −3.00000 | − | 3.00000i | −0.130189 | − | 0.130189i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.92820 | + | 4.00000i | −0.299813 | + | 0.173097i | ||||
\(535\) | −12.1244 | − | 7.00000i | −0.524182 | − | 0.302636i | ||||
\(536\) | 17.3205 | + | 10.0000i | 0.748132 | + | 0.431934i | ||||
\(537\) | −29.4449 | + | 17.0000i | −1.27064 | + | 0.733604i | ||||
\(538\) | 6.00000 | 0.258678 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −16.0000 | −0.688530 | ||||||||
\(541\) | −3.29423 | + | 12.2942i | −0.141630 | + | 0.528570i | 0.858252 | + | 0.513228i | \(0.171550\pi\) |
−0.999882 | + | 0.0153422i | \(0.995116\pi\) | |||||||
\(542\) | −2.92820 | − | 10.9282i | −0.125777 | − | 0.469407i | ||||
\(543\) | −9.00000 | + | 15.5885i | −0.386227 | + | 0.668965i | ||||
\(544\) | −10.9282 | − | 2.92820i | −0.468543 | − | 0.125546i | ||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | − | 5.00000i | −0.213785 | − | 0.213785i | 0.592088 | − | 0.805873i | \(-0.298304\pi\) |
−0.805873 | + | 0.592088i | \(0.798304\pi\) | |||||||
\(548\) | 8.00000 | + | 13.8564i | 0.341743 | + | 0.591916i | ||||
\(549\) | 3.29423 | + | 12.2942i | 0.140594 | + | 0.524705i | ||||
\(550\) | 3.00000 | − | 5.19615i | 0.127920 | − | 0.221565i | ||||
\(551\) | −15.5885 | + | 9.00000i | −0.664091 | + | 0.383413i | ||||
\(552\) | 24.0000 | 1.02151 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.00000i | 0.254916i | ||||||||
\(555\) | −8.19615 | − | 2.19615i | −0.347907 | − | 0.0932215i | ||||
\(556\) | 8.19615 | − | 2.19615i | 0.347594 | − | 0.0931376i | ||||
\(557\) | 34.1506 | − | 9.15064i | 1.44701 | − | 0.387725i | 0.552027 | − | 0.833827i | \(-0.313855\pi\) |
0.894982 | + | 0.446102i | \(0.147188\pi\) | |||||||
\(558\) | 2.92820 | − | 10.9282i | 0.123961 | − | 0.462628i | ||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | −7.32051 | + | 27.3205i | −0.308797 | + | 1.15245i | ||||
\(563\) | 25.9545 | − | 6.95448i | 1.09385 | − | 0.293096i | 0.333593 | − | 0.942717i | \(-0.391739\pi\) |
0.760258 | + | 0.649621i | \(0.225072\pi\) | |||||||
\(564\) | −5.85641 | − | 21.8564i | −0.246599 | − | 0.920321i | ||||
\(565\) | 8.19615 | + | 2.19615i | 0.344815 | + | 0.0923928i | ||||
\(566\) | 30.0000i | 1.26099i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.0000 | + | 20.0000i | −0.839181 | + | 0.839181i | ||||
\(569\) | −20.7846 | + | 12.0000i | −0.871336 | + | 0.503066i | −0.867792 | − | 0.496928i | \(-0.834461\pi\) |
−0.00354413 | + | 0.999994i | \(0.501128\pi\) | |||||||
\(570\) | −6.00000 | + | 10.3923i | −0.251312 | + | 0.435286i | ||||
\(571\) | 0.366025 | + | 1.36603i | 0.0153177 | + | 0.0571664i | 0.973162 | − | 0.230123i | \(-0.0739127\pi\) |
−0.957844 | + | 0.287289i | \(0.907246\pi\) | |||||||
\(572\) | −3.46410 | + | 2.00000i | −0.144841 | + | 0.0836242i | ||||
\(573\) | −8.00000 | − | 8.00000i | −0.334205 | − | 0.334205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.0000 | 0.750652 | ||||||||
\(576\) | −4.00000 | − | 6.92820i | −0.166667 | − | 0.288675i | ||||
\(577\) | 9.00000 | − | 15.5885i | 0.374675 | − | 0.648956i | −0.615603 | − | 0.788056i | \(-0.711088\pi\) |
0.990278 | + | 0.139100i | \(0.0444210\pi\) | |||||||
\(578\) | 4.75833 | + | 17.7583i | 0.197920 | + | 0.738649i | ||||
\(579\) | 5.12436 | − | 19.1244i | 0.212961 | − | 0.794781i | ||||
\(580\) | − | 12.0000i | − | 0.498273i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.00000 | −0.165805 | ||||||||
\(583\) | 8.66025 | − | 5.00000i | 0.358671 | − | 0.207079i | ||||
\(584\) | 2.92820 | + | 10.9282i | 0.121170 | + | 0.452212i | ||||
\(585\) | 1.73205 | + | 1.00000i | 0.0716115 | + | 0.0413449i | ||||
\(586\) | −25.9808 | + | 15.0000i | −1.07326 | + | 0.619644i | ||||
\(587\) | 7.00000 | − | 7.00000i | 0.288921 | − | 0.288921i | −0.547733 | − | 0.836653i | \(-0.684509\pi\) |
0.836653 | + | 0.547733i | \(0.184509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | − | 24.0000i | −0.988903 | − | 0.988903i | ||||
\(590\) | 2.19615 | − | 8.19615i | 0.0904142 | − | 0.337430i | ||||
\(591\) | 17.0000 | − | 29.4449i | 0.699287 | − | 1.21120i | ||||
\(592\) | −4.39230 | − | 16.3923i | −0.180523 | − | 0.673720i | ||||
\(593\) | 17.0000 | + | 29.4449i | 0.698106 | + | 1.20916i | 0.969122 | + | 0.246581i | \(0.0793071\pi\) |
−0.271016 | + | 0.962575i | \(0.587360\pi\) | |||||||
\(594\) | 8.00000 | + | 8.00000i | 0.328244 | + | 0.328244i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14.0000 | − | 14.0000i | −0.573462 | − | 0.573462i | ||||
\(597\) | 19.1244 | + | 5.12436i | 0.782708 | + | 0.209726i | ||||
\(598\) | −10.3923 | − | 6.00000i | −0.424973 | − | 0.245358i | ||||
\(599\) | 12.1244 | + | 7.00000i | 0.495388 | + | 0.286012i | 0.726807 | − | 0.686842i | \(-0.241004\pi\) |
−0.231419 | + | 0.972854i | \(0.574337\pi\) | |||||||
\(600\) | 6.00000 | + | 10.3923i | 0.244949 | + | 0.424264i | ||||
\(601\) | 20.0000i | 0.815817i | 0.913023 | + | 0.407909i | \(0.133742\pi\) | ||||
−0.913023 | + | 0.407909i | \(0.866258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.00000 | + | 5.00000i | −0.203616 | + | 0.203616i | ||||
\(604\) | −10.0000 | − | 17.3205i | −0.406894 | − | 0.704761i | ||||
\(605\) | −12.2942 | + | 3.29423i | −0.499831 | + | 0.133929i | ||||
\(606\) | 8.05256 | + | 30.0526i | 0.327113 | + | 1.22080i | ||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | −24.0000 | −0.973329 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0000 | + | 18.0000i | −0.728799 | + | 0.728799i | ||||
\(611\) | −2.92820 | + | 10.9282i | −0.118462 | + | 0.442108i | ||||
\(612\) | 2.00000 | − | 3.46410i | 0.0808452 | − | 0.140028i | ||||
\(613\) | −9.15064 | − | 34.1506i | −0.369591 | − | 1.37933i | −0.861090 | − | 0.508453i | \(-0.830218\pi\) |
0.491499 | − | 0.870878i | \(-0.336449\pi\) | |||||||
\(614\) | 5.00000 | + | 8.66025i | 0.201784 | + | 0.349499i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(618\) | −10.3923 | + | 6.00000i | −0.418040 | + | 0.241355i | ||||
\(619\) | −6.22243 | − | 23.2224i | −0.250101 | − | 0.933388i | −0.970751 | − | 0.240089i | \(-0.922823\pi\) |
0.720650 | − | 0.693299i | \(-0.243843\pi\) | |||||||
\(620\) | 21.8564 | − | 5.85641i | 0.877774 | − | 0.235199i | ||||
\(621\) | −8.78461 | + | 32.7846i | −0.352514 | + | 1.31560i | ||||
\(622\) | −30.0000 | − | 30.0000i | −1.20289 | − | 1.20289i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 8.00000i | − | 0.320256i | ||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 21.8564 | − | 5.85641i | 0.873558 | − | 0.234069i | ||||
\(627\) | 8.19615 | − | 2.19615i | 0.327323 | − | 0.0877059i | ||||
\(628\) | 40.9808 | + | 10.9808i | 1.63531 | + | 0.438180i | ||||
\(629\) | 6.00000 | − | 6.00000i | 0.239236 | − | 0.239236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.0000i | 0.398094i | 0.979990 | + | 0.199047i | \(0.0637846\pi\) | ||||
−0.979990 | + | 0.199047i | \(0.936215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.5885 | + | 9.00000i | 0.619586 | + | 0.357718i | ||||
\(634\) | −5.00000 | + | 8.66025i | −0.198575 | + | 0.343943i | ||||
\(635\) | −10.9282 | − | 2.92820i | −0.433673 | − | 0.116202i | ||||
\(636\) | 20.0000i | 0.793052i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.00000 | + | 6.00000i | −0.237542 | + | 0.237542i | ||||
\(639\) | −5.00000 | − | 8.66025i | −0.197797 | − | 0.342594i | ||||
\(640\) | 8.00000 | − | 13.8564i | 0.316228 | − | 0.547723i | ||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | −19.1244 | − | 5.12436i | −0.754778 | − | 0.202242i | ||||
\(643\) | 21.0000 | + | 21.0000i | 0.828159 | + | 0.828159i | 0.987262 | − | 0.159103i | \(-0.0508601\pi\) |
−0.159103 | + | 0.987262i | \(0.550860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0000 | − | 10.0000i | 0.393750 | − | 0.393750i | ||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 36.3731 | + | 21.0000i | 1.42997 | + | 0.825595i | 0.997118 | − | 0.0758684i | \(-0.0241729\pi\) |
0.432855 | + | 0.901464i | \(0.357506\pi\) | |||||||
\(648\) | −13.6603 | + | 3.66025i | −0.536625 | + | 0.143788i | ||||
\(649\) | −5.19615 | + | 3.00000i | −0.203967 | + | 0.117760i | ||||
\(650\) | − | 6.00000i | − | 0.235339i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00000 | + | 2.00000i | −0.0783260 | + | 0.0783260i | ||||
\(653\) | 6.95448 | − | 25.9545i | 0.272150 | − | 1.01568i | −0.685577 | − | 0.728000i | \(-0.740450\pi\) |
0.957727 | − | 0.287678i | \(-0.0928832\pi\) | |||||||
\(654\) | 8.19615 | − | 2.19615i | 0.320495 | − | 0.0858764i | ||||
\(655\) | 11.0000 | − | 19.0526i | 0.429806 | − | 0.744445i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0000 | − | 17.0000i | −0.662226 | − | 0.662226i | 0.293678 | − | 0.955904i | \(-0.405121\pi\) |
−0.955904 | + | 0.293678i | \(0.905121\pi\) | |||||||
\(660\) | −1.46410 | + | 5.46410i | −0.0569901 | + | 0.212690i | ||||
\(661\) | 3.29423 | + | 12.2942i | 0.128131 | + | 0.478190i | 0.999932 | − | 0.0116697i | \(-0.00371465\pi\) |
−0.871801 | + | 0.489860i | \(0.837048\pi\) | |||||||
\(662\) | −1.73205 | − | 1.00000i | −0.0673181 | − | 0.0388661i | ||||
\(663\) | 3.46410 | − | 2.00000i | 0.134535 | − | 0.0776736i | ||||
\(664\) | 4.00000i | 0.155230i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | −24.5885 | − | 6.58846i | −0.952069 | − | 0.255106i | ||||
\(668\) | 2.00000 | − | 3.46410i | 0.0773823 | − | 0.134030i | ||||
\(669\) | 32.7846 | − | 8.78461i | 1.26753 | − | 0.339633i | ||||
\(670\) | −13.6603 | − | 3.66025i | −0.527742 | − | 0.141408i | ||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 24.5885 | + | 6.58846i | 0.947112 | + | 0.253778i | ||||
\(675\) | −16.3923 | + | 4.39230i | −0.630940 | + | 0.169060i | ||||
\(676\) | 11.0000 | − | 19.0526i | 0.423077 | − | 0.732791i | ||||
\(677\) | 4.09808 | + | 1.09808i | 0.157502 | + | 0.0422025i | 0.336708 | − | 0.941609i | \(-0.390686\pi\) |
−0.179206 | + | 0.983811i | \(0.557353\pi\) | |||||||
\(678\) | 12.0000 | 0.460857 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.00000 | 0.306786 | ||||||||
\(681\) | −25.9808 | + | 15.0000i | −0.995585 | + | 0.574801i | ||||
\(682\) | −13.8564 | − | 8.00000i | −0.530589 | − | 0.306336i | ||||
\(683\) | 1.83013 | + | 6.83013i | 0.0700279 | + | 0.261348i | 0.992060 | − | 0.125766i | \(-0.0401388\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(684\) | 2.19615 | − | 8.19615i | 0.0839720 | − | 0.313388i | ||||
\(685\) | −8.00000 | − | 8.00000i | −0.305664 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | 27.3205 | + | 7.32051i | 1.04158 | + | 0.279092i | ||||
\(689\) | 5.00000 | − | 8.66025i | 0.190485 | − | 0.329929i | ||||
\(690\) | −16.3923 | + | 4.39230i | −0.624044 | + | 0.167212i | ||||
\(691\) | 3.29423 | − | 12.2942i | 0.125318 | − | 0.467694i | −0.874532 | − | 0.484967i | \(-0.838832\pi\) |
0.999851 | + | 0.0172725i | \(0.00549828\pi\) | |||||||
\(692\) | 2.00000 | − | 2.00000i | 0.0760286 | − | 0.0760286i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.0000i | 0.986947i | ||||||||
\(695\) | −5.19615 | + | 3.00000i | −0.197101 | + | 0.113796i | ||||
\(696\) | −4.39230 | − | 16.3923i | −0.166490 | − | 0.621349i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −3.00000 | − | 5.19615i | −0.113552 | − | 0.196677i | ||||
\(699\) | −4.00000 | + | 4.00000i | −0.151294 | + | 0.151294i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.0000 | + | 31.0000i | 1.17085 | + | 1.17085i | 0.982006 | + | 0.188847i | \(0.0604752\pi\) |
0.188847 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(702\) | 10.9282 | + | 2.92820i | 0.412458 | + | 0.110518i | ||||
\(703\) | 9.00000 | − | 15.5885i | 0.339441 | − | 0.587930i | ||||
\(704\) | −10.9282 | + | 2.92820i | −0.411872 | + | 0.110361i | ||||
\(705\) | 8.00000 | + | 13.8564i | 0.301297 | + | 0.521862i | ||||
\(706\) | −6.00000 | + | 6.00000i | −0.225813 | + | 0.225813i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 12.0000i | − | 0.450988i | ||||||
\(709\) | −36.8827 | − | 9.88269i | −1.38516 | − | 0.371152i | −0.512166 | − | 0.858886i | \(-0.671157\pi\) |
−0.872992 | + | 0.487734i | \(0.837823\pi\) | |||||||
\(710\) | 10.0000 | − | 17.3205i | 0.375293 | − | 0.650027i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.9282 | + | 2.92820i | 0.409552 | + | 0.109739i | ||||
\(713\) | − | 48.0000i | − | 1.79761i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | − | 2.00000i | 0.0747958 | − | 0.0747958i | ||||
\(716\) | 46.4449 | + | 12.4449i | 1.73573 | + | 0.465086i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.5167 | − | 9.51666i | 1.32547 | − | 0.355159i | ||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 4.00000 | + | 4.00000i | 0.149071 | + | 0.149071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.00000 | + | 1.00000i | 0.0372161 | + | 0.0372161i | ||||
\(723\) | 6.58846 | − | 24.5885i | 0.245027 | − | 0.914455i | ||||
\(724\) | 24.5885 | − | 6.58846i | 0.913823 | − | 0.244858i | ||||
\(725\) | −3.29423 | − | 12.2942i | −0.122345 | − | 0.456596i | ||||
\(726\) | −15.5885 | + | 9.00000i | −0.578542 | + | 0.334021i | ||||
\(727\) | − | 2.00000i | − | 0.0741759i | −0.999312 | − | 0.0370879i | \(-0.988192\pi\) | ||
0.999312 | − | 0.0370879i | \(-0.0118082\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | −4.00000 | − | 6.92820i | −0.148047 | − | 0.256424i | ||||
\(731\) | 3.66025 | + | 13.6603i | 0.135379 | + | 0.505243i | ||||
\(732\) | −18.0000 | + | 31.1769i | −0.665299 | + | 1.15233i | ||||
\(733\) | 7.68653 | − | 28.6865i | 0.283909 | − | 1.05956i | −0.665725 | − | 0.746198i | \(-0.731877\pi\) |
0.949633 | − | 0.313364i | \(-0.101456\pi\) | |||||||
\(734\) | 8.00000 | − | 8.00000i | 0.295285 | − | 0.295285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0000 | − | 24.0000i | −0.884652 | − | 0.884652i | ||||
\(737\) | 5.00000 | + | 8.66025i | 0.184177 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.4186 | + | 8.41858i | −1.15575 | + | 0.309683i | −0.785268 | − | 0.619156i | \(-0.787475\pi\) |
−0.370484 | + | 0.928839i | \(0.620808\pi\) | |||||||
\(740\) | 6.00000 | + | 10.3923i | 0.220564 | + | 0.382029i | ||||
\(741\) | 6.00000 | − | 6.00000i | 0.220416 | − | 0.220416i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 46.0000i | − | 1.68758i | −0.536676 | − | 0.843788i | \(-0.680320\pi\) | ||
0.536676 | − | 0.843788i | \(-0.319680\pi\) | |||||||
\(744\) | 27.7128 | − | 16.0000i | 1.01600 | − | 0.586588i | ||||
\(745\) | 12.1244 | + | 7.00000i | 0.444202 | + | 0.256460i | ||||
\(746\) | 8.66025 | + | 5.00000i | 0.317074 | + | 0.183063i | ||||
\(747\) | −1.36603 | − | 0.366025i | −0.0499803 | − | 0.0133922i | ||||
\(748\) | −4.00000 | − | 4.00000i | −0.146254 | − | 0.146254i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16.0000 | − | 16.0000i | −0.584237 | − | 0.584237i | ||||
\(751\) | −16.0000 | − | 27.7128i | −0.583848 | − | 1.01125i | −0.995018 | − | 0.0996961i | \(-0.968213\pi\) |
0.411170 | − | 0.911559i | \(-0.365120\pi\) | |||||||
\(752\) | −16.0000 | + | 27.7128i | −0.583460 | + | 1.01058i | ||||
\(753\) | 21.0000 | − | 36.3731i | 0.765283 | − | 1.32551i | ||||
\(754\) | −2.19615 | + | 8.19615i | −0.0799792 | + | 0.298486i | ||||
\(755\) | 10.0000 | + | 10.0000i | 0.363937 | + | 0.363937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0000 | − | 23.0000i | 0.835949 | − | 0.835949i | −0.152374 | − | 0.988323i | \(-0.548692\pi\) |
0.988323 | + | 0.152374i | \(0.0486917\pi\) | |||||||
\(758\) | −5.19615 | + | 3.00000i | −0.188733 | + | 0.108965i | ||||
\(759\) | 10.3923 | + | 6.00000i | 0.377217 | + | 0.217786i | ||||
\(760\) | 16.3923 | − | 4.39230i | 0.594611 | − | 0.159326i | ||||
\(761\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(762\) | −16.0000 | −0.579619 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.0000i | 0.578860i | ||||||||
\(765\) | −0.732051 | + | 2.73205i | −0.0264674 | + | 0.0987775i | ||||
\(766\) | −5.85641 | − | 21.8564i | −0.211601 | − | 0.789704i | ||||
\(767\) | −3.00000 | + | 5.19615i | −0.108324 | + | 0.187622i | ||||
\(768\) | 5.85641 | − | 21.8564i | 0.211325 | − | 0.788675i | ||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0000 | + | 22.0000i | 0.792311 | + | 0.792311i | ||||
\(772\) | −24.2487 | + | 14.0000i | −0.872730 | + | 0.503871i | ||||
\(773\) | 1.83013 | + | 6.83013i | 0.0658251 | + | 0.245663i | 0.990997 | − | 0.133887i | \(-0.0427458\pi\) |
−0.925172 | + | 0.379549i | \(0.876079\pi\) | |||||||
\(774\) | −5.00000 | + | 8.66025i | −0.179721 | + | 0.311286i | ||||
\(775\) | 20.7846 | − | 12.0000i | 0.746605 | − | 0.431053i | ||||
\(776\) | 4.00000 | + | 4.00000i | 0.143592 | + | 0.143592i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 26.0000i | − | 0.932145i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.46410 | + | 5.46410i | 0.0524232 | + | 0.195646i | ||||
\(781\) | −13.6603 | + | 3.66025i | −0.488802 | + | 0.130974i | ||||
\(782\) | 4.39230 | − | 16.3923i | 0.157069 | − | 0.586188i | ||||
\(783\) | 24.0000 | 0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.0000 | −1.07075 | ||||||||
\(786\) | 8.05256 | − | 30.0526i | 0.287225 | − | 1.07194i | ||||
\(787\) | 20.4904 | − | 5.49038i | 0.730403 | − | 0.195711i | 0.125594 | − | 0.992082i | \(-0.459916\pi\) |
0.604809 | + | 0.796371i | \(0.293250\pi\) | |||||||
\(788\) | −46.4449 | + | 12.4449i | −1.65453 | + | 0.443330i | ||||
\(789\) | −8.19615 | − | 2.19615i | −0.291791 | − | 0.0781851i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 4.00000i | − | 0.142134i | ||||||
\(793\) | 15.5885 | − | 9.00000i | 0.553562 | − | 0.319599i | ||||
\(794\) | 5.00000 | − | 8.66025i | 0.177443 | − | 0.307341i | ||||
\(795\) | −3.66025 | − | 13.6603i | −0.129816 | − | 0.484479i | ||||
\(796\) | −14.0000 | − | 24.2487i | −0.496217 | − | 0.859473i | ||||
\(797\) | 25.0000 | + | 25.0000i | 0.885545 | + | 0.885545i | 0.994091 | − | 0.108546i | \(-0.0346195\pi\) |
−0.108546 | + | 0.994091i | \(0.534619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | 4.39230 | − | 16.3923i | 0.155291 | − | 0.579555i | ||||
\(801\) | −2.00000 | + | 3.46410i | −0.0706665 | + | 0.122398i | ||||
\(802\) | 6.58846 | + | 24.5885i | 0.232647 | + | 0.868249i | ||||
\(803\) | −1.46410 | + | 5.46410i | −0.0516670 | + | 0.192824i | ||||
\(804\) | −20.0000 | −0.705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.0000 | −0.563576 | ||||||||
\(807\) | −5.19615 | + | 3.00000i | −0.182913 | + | 0.105605i | ||||
\(808\) | 22.0000 | − | 38.1051i | 0.773957 | − | 1.34053i | ||||
\(809\) | −13.8564 | − | 8.00000i | −0.487165 | − | 0.281265i | 0.236232 | − | 0.971697i | \(-0.424087\pi\) |
−0.723398 | + | 0.690432i | \(0.757421\pi\) | |||||||
\(810\) | 8.66025 | − | 5.00000i | 0.304290 | − | 0.175682i | ||||
\(811\) | 39.0000 | − | 39.0000i | 1.36948 | − | 1.36948i | 0.508288 | − | 0.861187i | \(-0.330278\pi\) |
0.861187 | − | 0.508288i | \(-0.169722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | + | 8.00000i | 0.280572 | + | 0.280572i | ||||
\(814\) | 2.19615 | − | 8.19615i | 0.0769751 | − | 0.287275i | ||||
\(815\) | 1.00000 | − | 1.73205i | 0.0350285 | − | 0.0606711i | ||||
\(816\) | 10.9282 | − | 2.92820i | 0.382564 | − | 0.102508i | ||||
\(817\) | 15.0000 | + | 25.9808i | 0.524784 | + | 0.908952i | ||||
\(818\) | 16.0000 | + | 16.0000i | 0.559427 | + | 0.559427i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0263 | − | 4.02628i | −0.524421 | − | 0.140518i | −0.0131101 | − | 0.999914i | \(-0.504173\pi\) |
−0.511311 | + | 0.859396i | \(0.670840\pi\) | |||||||
\(822\) | −13.8564 | − | 8.00000i | −0.483298 | − | 0.279032i | ||||
\(823\) | −29.4449 | − | 17.0000i | −1.02638 | − | 0.592583i | −0.110437 | − | 0.993883i | \(-0.535225\pi\) |
−0.915947 | + | 0.401300i | \(0.868558\pi\) | |||||||
\(824\) | 16.3923 | + | 4.39230i | 0.571053 | + | 0.153013i | ||||
\(825\) | 6.00000i | 0.208893i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0000 | − | 33.0000i | 1.14752 | − | 1.14752i | 0.160484 | − | 0.987038i | \(-0.448695\pi\) |
0.987038 | − | 0.160484i | \(-0.0513055\pi\) | |||||||
\(828\) | 10.3923 | − | 6.00000i | 0.361158 | − | 0.208514i | ||||
\(829\) | 31.4186 | − | 8.41858i | 1.09121 | − | 0.292390i | 0.332031 | − | 0.943268i | \(-0.392266\pi\) |
0.759182 | + | 0.650879i | \(0.225599\pi\) | |||||||
\(830\) | −0.732051 | − | 2.73205i | −0.0254099 | − | 0.0948309i | ||||
\(831\) | −3.00000 | − | 5.19615i | −0.104069 | − | 0.180253i | ||||
\(832\) | −8.00000 | + | 8.00000i | −0.277350 | + | 0.277350i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.00000 | + | 6.00000i | −0.207763 | + | 0.207763i | ||||
\(835\) | −0.732051 | + | 2.73205i | −0.0253337 | + | 0.0945465i | ||||
\(836\) | −10.3923 | − | 6.00000i | −0.359425 | − | 0.207514i | ||||
\(837\) | 11.7128 | + | 43.7128i | 0.404854 | + | 1.51094i | ||||
\(838\) | −3.00000 | − | 5.19615i | −0.103633 | − | 0.179498i | ||||
\(839\) | 14.0000i | 0.483334i | 0.970359 | + | 0.241667i | \(0.0776941\pi\) | ||||
−0.970359 | + | 0.241667i | \(0.922306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | −15.5885 | + | 9.00000i | −0.537214 | + | 0.310160i | ||||
\(843\) | −7.32051 | − | 27.3205i | −0.252132 | − | 0.940968i | ||||
\(844\) | −6.58846 | − | 24.5885i | −0.226784 | − | 0.846370i | ||||
\(845\) | −4.02628 | + | 15.0263i | −0.138508 | + | 0.516920i | ||||
\(846\) | −8.00000 | − | 8.00000i | −0.275046 | − | 0.275046i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.0000 | − | 20.0000i | 0.686803 | − | 0.686803i | ||||
\(849\) | −15.0000 | − | 25.9808i | −0.514799 | − | 0.891657i | ||||
\(850\) | 8.19615 | − | 2.19615i | 0.281126 | − | 0.0753274i | ||||
\(851\) | 24.5885 | − | 6.58846i | 0.842881 | − | 0.225849i | ||||
\(852\) | 7.32051 | − | 27.3205i | 0.250796 | − | 0.935985i | ||||
\(853\) | 5.00000 | − | 5.00000i | 0.171197 | − | 0.171197i | −0.616308 | − | 0.787505i | \(-0.711372\pi\) |
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000i | 0.205196i | ||||||||
\(856\) | 14.0000 | + | 24.2487i | 0.478510 | + | 0.828804i | ||||
\(857\) | −6.92820 | − | 4.00000i | −0.236663 | − | 0.136637i | 0.376979 | − | 0.926222i | \(-0.376963\pi\) |
−0.613642 | + | 0.789584i | \(0.710296\pi\) | |||||||
\(858\) | 2.00000 | − | 3.46410i | 0.0682789 | − | 0.118262i | ||||
\(859\) | −4.09808 | − | 1.09808i | −0.139825 | − | 0.0374659i | 0.188228 | − | 0.982125i | \(-0.439726\pi\) |
−0.328053 | + | 0.944659i | \(0.606392\pi\) | |||||||
\(860\) | −20.0000 | −0.681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.0000 | + | 32.0000i | −1.08992 | + | 1.08992i | ||||
\(863\) | −12.0000 | − | 20.7846i | −0.408485 | − | 0.707516i | 0.586235 | − | 0.810141i | \(-0.300609\pi\) |
−0.994720 | + | 0.102624i | \(0.967276\pi\) | |||||||
\(864\) | 27.7128 | + | 16.0000i | 0.942809 | + | 0.544331i | ||||
\(865\) | −1.00000 | + | 1.73205i | −0.0340010 | + | 0.0588915i | ||||
\(866\) | −19.1244 | − | 5.12436i | −0.649872 | − | 0.174133i | ||||
\(867\) | −13.0000 | − | 13.0000i | −0.441503 | − | 0.441503i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6.00000 | + | 10.3923i | 0.203419 | + | 0.352332i | ||||
\(871\) | 8.66025 | + | 5.00000i | 0.293442 | + | 0.169419i | ||||
\(872\) | −10.3923 | − | 6.00000i | −0.351928 | − | 0.203186i | ||||
\(873\) | −1.73205 | + | 1.00000i | −0.0586210 | + | 0.0338449i | ||||
\(874\) | − | 36.0000i | − | 1.21772i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.00000 | − | 8.00000i | −0.270295 | − | 0.270295i | ||||
\(877\) | −1.83013 | + | 6.83013i | −0.0617990 | + | 0.230637i | −0.989917 | − | 0.141649i | \(-0.954759\pi\) |
0.928118 | + | 0.372286i | \(0.121426\pi\) | |||||||
\(878\) | 19.1244 | − | 5.12436i | 0.645416 | − | 0.172939i | ||||
\(879\) | 15.0000 | − | 25.9808i | 0.505937 | − | 0.876309i | ||||
\(880\) | 6.92820 | − | 4.00000i | 0.233550 | − | 0.134840i | ||||
\(881\) | −2.00000 | −0.0673817 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.0000 | − | 21.0000i | −0.706706 | − | 0.706706i | 0.259135 | − | 0.965841i | \(-0.416563\pi\) |
−0.965841 | + | 0.259135i | \(0.916563\pi\) | |||||||
\(884\) | −5.46410 | − | 1.46410i | −0.183778 | − | 0.0492431i | ||||
\(885\) | 2.19615 | + | 8.19615i | 0.0738229 | + | 0.275511i | ||||
\(886\) | 25.9808 | + | 15.0000i | 0.872841 | + | 0.503935i | ||||
\(887\) | −1.73205 | + | 1.00000i | −0.0581566 | + | 0.0335767i | −0.528796 | − | 0.848749i | \(-0.677356\pi\) |
0.470640 | + | 0.882325i | \(0.344023\pi\) | |||||||
\(888\) | 12.0000 | + | 12.0000i | 0.402694 | + | 0.402694i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.00000 | −0.268161 | ||||||||
\(891\) | −6.83013 | − | 1.83013i | −0.228818 | − | 0.0613116i | ||||
\(892\) | −41.5692 | − | 24.0000i | −1.39184 | − | 0.803579i | ||||
\(893\) | −32.7846 | + | 8.78461i | −1.09710 | + | 0.293966i | ||||
\(894\) | 19.1244 | + | 5.12436i | 0.639614 | + | 0.171384i | ||||
\(895\) | −34.0000 | −1.13649 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 40.9808 | + | 10.9808i | 1.36755 | + | 0.366433i | ||||
\(899\) | −32.7846 | + | 8.78461i | −1.09343 | + | 0.292983i | ||||
\(900\) | 5.19615 | + | 3.00000i | 0.173205 | + | 0.100000i | ||||
\(901\) | 13.6603 | + | 3.66025i | 0.455089 | + | 0.121941i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.0000 | − | 12.0000i | −0.399114 | − | 0.399114i | ||||
\(905\) | −15.5885 | + | 9.00000i | −0.518178 | + | 0.299170i | ||||
\(906\) | 17.3205 | + | 10.0000i | 0.575435 | + | 0.332228i | ||||
\(907\) | −9.88269 | − | 36.8827i | −0.328149 | − | 1.22467i | −0.911108 | − | 0.412168i | \(-0.864772\pi\) |
0.582959 | − | 0.812502i | \(-0.301895\pi\) | |||||||
\(908\) | 40.9808 | + | 10.9808i | 1.35999 | + | 0.364409i | ||||
\(909\) | 11.0000 | + | 11.0000i | 0.364847 | + | 0.364847i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00000 | −0.265052 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(912\) | 20.7846 | − | 12.0000i | 0.688247 | − | 0.397360i | ||||
\(913\) | −1.00000 | + | 1.73205i | −0.0330952 | + | 0.0573225i | ||||
\(914\) | 43.7128 | − | 11.7128i | 1.44589 | − | 0.387425i | ||||
\(915\) | 6.58846 | − | 24.5885i | 0.217808 | − | 0.812869i | ||||
\(916\) | 14.0000 | + | 14.0000i | 0.462573 | + | 0.462573i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 16.0000i | 0.528079i | ||||||||
\(919\) | 22.5167 | − | 13.0000i | 0.742756 | − | 0.428830i | −0.0803145 | − | 0.996770i | \(-0.525592\pi\) |
0.823071 | + | 0.567939i | \(0.192259\pi\) | |||||||
\(920\) | 20.7846 | + | 12.0000i | 0.685248 | + | 0.395628i | ||||
\(921\) | −8.66025 | − | 5.00000i | −0.285365 | − | 0.164756i | ||||
\(922\) | −11.0000 | − | 19.0526i | −0.362266 | − | 0.627463i | ||||
\(923\) | −10.0000 | + | 10.0000i | −0.329154 | + | 0.329154i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | + | 9.00000i | 0.295918 | + | 0.295918i | ||||
\(926\) | −21.8564 | − | 5.85641i | −0.718246 | − | 0.192453i | ||||
\(927\) | −3.00000 | + | 5.19615i | −0.0985329 | + | 0.170664i | ||||
\(928\) | −12.0000 | + | 20.7846i | −0.393919 | + | 0.682288i | ||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | −16.0000 | + | 16.0000i | −0.524661 | + | 0.524661i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.00000 | 0.262049 | ||||||||
\(933\) | 40.9808 | + | 10.9808i | 1.34165 | + | 0.359494i | ||||
\(934\) | 5.00000 | − | 8.66025i | 0.163605 | − | 0.283372i | ||||
\(935\) | 3.46410 | + | 2.00000i | 0.113288 | + | 0.0654070i | ||||
\(936\) | −2.00000 | − | 3.46410i | −0.0653720 | − | 0.113228i | ||||
\(937\) | 28.0000i | 0.914720i | 0.889282 | + | 0.457360i | \(0.151205\pi\) | ||||
−0.889282 | + | 0.457360i | \(0.848795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | + | 16.0000i | −0.522140 | + | 0.522140i | ||||
\(940\) | 5.85641 | − | 21.8564i | 0.191015 | − | 0.712877i | ||||
\(941\) | −39.6147 | + | 10.6147i | −1.29140 | + | 0.346031i | −0.838193 | − | 0.545373i | \(-0.816388\pi\) |
−0.453210 | + | 0.891404i | \(0.649721\pi\) | |||||||
\(942\) | −40.9808 | + | 10.9808i | −1.33523 | + | 0.357773i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.0000 | + | 12.0000i | −0.390567 | + | 0.390567i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0000 | + | 10.0000i | 0.325128 | + | 0.325128i | ||||
\(947\) | −1.83013 | + | 6.83013i | −0.0594711 | + | 0.221949i | −0.989265 | − | 0.146131i | \(-0.953318\pi\) |
0.929794 | + | 0.368080i | \(0.119985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.46410 | + | 5.46410i | 0.0475267 | + | 0.177372i | ||||
\(950\) | 15.5885 | − | 9.00000i | 0.505756 | − | 0.291999i | ||||
\(951\) | − | 10.0000i | − | 0.324272i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 5.00000 | + | 8.66025i | 0.161881 | + | 0.280386i | ||||
\(955\) | −2.92820 | − | 10.9282i | −0.0947544 | − | 0.353628i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.19615 | − | 8.19615i | 0.0709915 | − | 0.264944i | ||||
\(958\) | −40.0000 | + | 40.0000i | −1.29234 | + | 1.29234i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 16.0000i | 0.516398i | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | −2.19615 | − | 8.19615i | −0.0708068 | − | 0.264255i | ||||
\(963\) | −9.56218 | + | 2.56218i | −0.308137 | + | 0.0825650i | ||||
\(964\) | −31.1769 | + | 18.0000i | −1.00414 | + | 0.579741i | ||||
\(965\) | 14.0000 | − | 14.0000i | 0.450676 | − | 0.450676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000i | 0.0643157i | 0.999483 | + | 0.0321578i | \(0.0102379\pi\) | ||||
−0.999483 | + | 0.0321578i | \(0.989762\pi\) | |||||||
\(968\) | 24.5885 | + | 6.58846i | 0.790303 | + | 0.211761i | ||||
\(969\) | 10.3923 | + | 6.00000i | 0.333849 | + | 0.192748i | ||||
\(970\) | −3.46410 | − | 2.00000i | −0.111226 | − | 0.0642161i | ||||
\(971\) | −25.9545 | − | 6.95448i | −0.832919 | − | 0.223180i | −0.182932 | − | 0.983126i | \(-0.558559\pi\) |
−0.649987 | + | 0.759946i | \(0.725226\pi\) | |||||||
\(972\) | −14.0000 | + | 14.0000i | −0.449050 | + | 0.449050i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.00000 | − | 2.00000i | −0.0640841 | − | 0.0640841i | ||||
\(975\) | 3.00000 | + | 5.19615i | 0.0960769 | + | 0.166410i | ||||
\(976\) | 49.1769 | − | 13.1769i | 1.57411 | − | 0.421783i | ||||
\(977\) | 1.00000 | − | 1.73205i | 0.0319928 | − | 0.0554132i | −0.849586 | − | 0.527451i | \(-0.823148\pi\) |
0.881579 | + | 0.472037i | \(0.156481\pi\) | |||||||
\(978\) | 0.732051 | − | 2.73205i | 0.0234084 | − | 0.0873614i | ||||
\(979\) | 4.00000 | + | 4.00000i | 0.127841 | + | 0.127841i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.00000 | − | 3.00000i | 0.0957826 | − | 0.0957826i | ||||
\(982\) | −32.9090 | + | 19.0000i | −1.05017 | + | 0.606314i | ||||
\(983\) | 29.4449 | + | 17.0000i | 0.939145 | + | 0.542216i | 0.889692 | − | 0.456561i | \(-0.150919\pi\) |
0.0494530 | + | 0.998776i | \(0.484252\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.4449 | − | 17.0000i | 0.938191 | − | 0.541665i | ||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | −10.9808 | + | 40.9808i | −0.349168 | + | 1.30311i | ||||
\(990\) | 0.732051 | + | 2.73205i | 0.0232661 | + | 0.0868303i | ||||
\(991\) | −16.0000 | + | 27.7128i | −0.508257 | + | 0.880327i | 0.491698 | + | 0.870766i | \(0.336377\pi\) |
−0.999954 | + | 0.00956046i | \(0.996957\pi\) | |||||||
\(992\) | −43.7128 | − | 11.7128i | −1.38788 | − | 0.371882i | ||||
\(993\) | 2.00000 | 0.0634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0000 | + | 14.0000i | 0.443830 | + | 0.443830i | ||||
\(996\) | −2.00000 | − | 3.46410i | −0.0633724 | − | 0.109764i | ||||
\(997\) | 13.5429 | + | 50.5429i | 0.428909 | + | 1.60071i | 0.755235 | + | 0.655454i | \(0.227523\pi\) |
−0.326326 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(998\) | 23.0000 | − | 39.8372i | 0.728052 | − | 1.26102i | ||||
\(999\) | −20.7846 | + | 12.0000i | −0.657596 | + | 0.379663i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))