Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (of order \(6\), degree \(2\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 571.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.571 |
Dual form | 585.2.bt.a.376.1 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | + | 1.00000i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | −3.46410 | −1.41421 | ||||||||
\(7\) | −1.73205 | + | 1.00000i | −0.654654 | + | 0.377964i | −0.790237 | − | 0.612801i | \(-0.790043\pi\) |
0.135583 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 5.19615 | − | 3.00000i | 1.56670 | − | 0.904534i | 0.570149 | − | 0.821541i | \(-0.306886\pi\) |
0.996550 | − | 0.0829925i | \(-0.0264478\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.866025 | − | 0.500000i | ||||
\(13\) | 3.23205 | − | 1.59808i | 0.896410 | − | 0.443227i | ||||
\(14\) | 2.00000 | − | 3.46410i | 0.534522 | − | 0.925820i | ||||
\(15\) | −0.866025 | − | 1.50000i | −0.223607 | − | 0.387298i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | −5.19615 | − | 3.00000i | −1.22474 | − | 0.707107i | ||||
\(19\) | 8.00000i | 1.83533i | 0.397360 | + | 0.917663i | \(0.369927\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | −1.73205 | + | 1.00000i | −0.387298 | + | 0.223607i | ||||
\(21\) | −3.46410 | −0.755929 | ||||||||
\(22\) | −6.00000 | + | 10.3923i | −1.27920 | + | 2.21565i | ||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | −0.913434 | − | 0.406986i | \(-0.866580\pi\) |
0.809177 | + | 0.587565i | \(0.199913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −4.00000 | + | 6.00000i | −0.784465 | + | 1.17670i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 3.00000 | + | 1.73205i | 0.547723 | + | 0.316228i | ||||
\(31\) | 6.92820 | + | 4.00000i | 1.24434 | + | 0.718421i | 0.969975 | − | 0.243204i | \(-0.0781984\pi\) |
0.274367 | + | 0.961625i | \(0.411532\pi\) | |||||||
\(32\) | −6.92820 | − | 4.00000i | −1.22474 | − | 0.707107i | ||||
\(33\) | 10.3923 | 1.80907 | ||||||||
\(34\) | 1.73205 | − | 1.00000i | 0.297044 | − | 0.171499i | ||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | −8.00000 | − | 13.8564i | −1.29777 | − | 2.24781i | ||||
\(39\) | 6.23205 | + | 0.401924i | 0.997927 | + | 0.0643593i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.73205 | + | 1.00000i | 0.270501 | + | 0.156174i | 0.629115 | − | 0.777312i | \(-0.283417\pi\) |
−0.358614 | + | 0.933486i | \(0.616751\pi\) | |||||||
\(42\) | 6.00000 | − | 3.46410i | 0.925820 | − | 0.534522i | ||||
\(43\) | −2.50000 | − | 4.33013i | −0.381246 | − | 0.660338i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | − | 12.0000i | − | 1.80907i | ||||||
\(45\) | − | 3.00000i | − | 0.447214i | ||||||
\(46\) | − | 2.00000i | − | 0.294884i | ||||||
\(47\) | −8.66025 | + | 5.00000i | −1.26323 | + | 0.729325i | −0.973698 | − | 0.227844i | \(-0.926832\pi\) |
−0.289530 | + | 0.957169i | \(0.593499\pi\) | |||||||
\(48\) | 6.92820i | 1.00000i | ||||||||
\(49\) | −1.50000 | + | 2.59808i | −0.214286 | + | 0.371154i | ||||
\(50\) | −1.73205 | − | 1.00000i | −0.244949 | − | 0.141421i | ||||
\(51\) | −1.50000 | − | 0.866025i | −0.210042 | − | 0.121268i | ||||
\(52\) | 0.464102 | − | 7.19615i | 0.0643593 | − | 0.997927i | ||||
\(53\) | 9.00000 | 1.23625 | 0.618123 | − | 0.786082i | \(-0.287894\pi\) | ||||
0.618123 | + | 0.786082i | \(0.287894\pi\) | |||||||
\(54\) | −5.19615 | − | 9.00000i | −0.707107 | − | 1.22474i | ||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.92820 | + | 12.0000i | −0.917663 | + | 1.58944i | ||||
\(58\) | 3.46410 | + | 2.00000i | 0.454859 | + | 0.262613i | ||||
\(59\) | 5.19615 | + | 3.00000i | 0.676481 | + | 0.390567i | 0.798528 | − | 0.601958i | \(-0.205612\pi\) |
−0.122047 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(60\) | −3.46410 | −0.447214 | ||||||||
\(61\) | 2.50000 | + | 4.33013i | 0.320092 | + | 0.554416i | 0.980507 | − | 0.196485i | \(-0.0629528\pi\) |
−0.660415 | + | 0.750901i | \(0.729619\pi\) | |||||||
\(62\) | −16.0000 | −2.03200 | ||||||||
\(63\) | −5.19615 | − | 3.00000i | −0.654654 | − | 0.377964i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −3.59808 | − | 0.232051i | −0.446286 | − | 0.0287824i | ||||
\(66\) | −18.0000 | + | 10.3923i | −2.21565 | + | 1.27920i | ||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | −1.00000 | + | 1.73205i | −0.121268 | + | 0.210042i | ||||
\(69\) | −1.50000 | + | 0.866025i | −0.180579 | + | 0.104257i | ||||
\(70\) | −3.46410 | + | 2.00000i | −0.414039 | + | 0.239046i | ||||
\(71\) | − | 10.0000i | − | 1.18678i | −0.804914 | − | 0.593391i | \(-0.797789\pi\) | ||
0.804914 | − | 0.593391i | \(-0.202211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | 1.73205i | 0.200000i | ||||||||
\(76\) | 13.8564 | + | 8.00000i | 1.58944 | + | 0.917663i | ||||
\(77\) | −6.00000 | + | 10.3923i | −0.683763 | + | 1.18431i | ||||
\(78\) | −11.1962 | + | 5.53590i | −1.26771 | + | 0.626817i | ||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | − | 4.00000i | − | 0.447214i | ||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −4.00000 | −0.441726 | ||||||||
\(83\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(84\) | −3.46410 | + | 6.00000i | −0.377964 | + | 0.654654i | ||||
\(85\) | 0.866025 | + | 0.500000i | 0.0939336 | + | 0.0542326i | ||||
\(86\) | 8.66025 | + | 5.00000i | 0.933859 | + | 0.539164i | ||||
\(87\) | − | 3.46410i | − | 0.371391i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 3.00000 | + | 5.19615i | 0.316228 | + | 0.547723i | ||||
\(91\) | −4.00000 | + | 6.00000i | −0.419314 | + | 0.628971i | ||||
\(92\) | 1.00000 | + | 1.73205i | 0.104257 | + | 0.180579i | ||||
\(93\) | 6.92820 | + | 12.0000i | 0.718421 | + | 1.24434i | ||||
\(94\) | 10.0000 | − | 17.3205i | 1.03142 | − | 1.78647i | ||||
\(95\) | 4.00000 | − | 6.92820i | 0.410391 | − | 0.710819i | ||||
\(96\) | −6.92820 | − | 12.0000i | −0.707107 | − | 1.22474i | ||||
\(97\) | 8.66025 | − | 5.00000i | 0.879316 | − | 0.507673i | 0.00888289 | − | 0.999961i | \(-0.497172\pi\) |
0.870433 | + | 0.492287i | \(0.163839\pi\) | |||||||
\(98\) | − | 6.00000i | − | 0.606092i | ||||||
\(99\) | 15.5885 | + | 9.00000i | 1.56670 | + | 0.904534i | ||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | −3.50000 | − | 6.06218i | −0.348263 | − | 0.603209i | 0.637678 | − | 0.770303i | \(-0.279895\pi\) |
−0.985941 | + | 0.167094i | \(0.946562\pi\) | |||||||
\(102\) | 3.46410 | 0.342997 | ||||||||
\(103\) | −8.00000 | + | 13.8564i | −0.788263 | + | 1.36531i | 0.138767 | + | 0.990325i | \(0.455686\pi\) |
−0.927030 | + | 0.374987i | \(0.877647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | + | 1.73205i | 0.292770 | + | 0.169031i | ||||
\(106\) | −15.5885 | + | 9.00000i | −1.51408 | + | 0.874157i | ||||
\(107\) | 17.0000 | 1.64345 | 0.821726 | − | 0.569883i | \(-0.193011\pi\) | ||||
0.821726 | + | 0.569883i | \(0.193011\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | − | 20.0000i | − | 1.91565i | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||
0.287348 | − | 0.957826i | \(-0.407226\pi\) | |||||||
\(110\) | 10.3923 | − | 6.00000i | 0.990867 | − | 0.572078i | ||||
\(111\) | 1.73205 | − | 3.00000i | 0.164399 | − | 0.284747i | ||||
\(112\) | −6.92820 | − | 4.00000i | −0.654654 | − | 0.377964i | ||||
\(113\) | −9.50000 | + | 16.4545i | −0.893685 | + | 1.54791i | −0.0582609 | + | 0.998301i | \(0.518556\pi\) |
−0.835424 | + | 0.549606i | \(0.814778\pi\) | |||||||
\(114\) | − | 27.7128i | − | 2.59554i | ||||||
\(115\) | 0.866025 | − | 0.500000i | 0.0807573 | − | 0.0466252i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | 9.00000 | + | 6.00000i | 0.832050 | + | 0.554700i | ||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 1.73205 | − | 1.00000i | 0.158777 | − | 0.0916698i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.5000 | − | 21.6506i | 1.13636 | − | 1.96824i | ||||
\(122\) | −8.66025 | − | 5.00000i | −0.784063 | − | 0.452679i | ||||
\(123\) | 1.73205 | + | 3.00000i | 0.156174 | + | 0.270501i | ||||
\(124\) | 13.8564 | − | 8.00000i | 1.24434 | − | 0.718421i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 12.0000 | 1.06904 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.66025i | − | 0.762493i | ||||||
\(130\) | 6.46410 | − | 3.19615i | 0.566939 | − | 0.280321i | ||||
\(131\) | −7.50000 | + | 12.9904i | −0.655278 | + | 1.13497i | 0.326546 | + | 0.945181i | \(0.394115\pi\) |
−0.981824 | + | 0.189794i | \(0.939218\pi\) | |||||||
\(132\) | 10.3923 | − | 18.0000i | 0.904534 | − | 1.56670i | ||||
\(133\) | −8.00000 | − | 13.8564i | −0.693688 | − | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.59808 | − | 4.50000i | 0.223607 | − | 0.387298i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.19615 | + | 3.00000i | −0.443937 | + | 0.256307i | −0.705266 | − | 0.708942i | \(-0.749173\pi\) |
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(138\) | 1.73205 | − | 3.00000i | 0.147442 | − | 0.255377i | ||||
\(139\) | 5.50000 | − | 9.52628i | 0.466504 | − | 0.808008i | −0.532764 | − | 0.846264i | \(-0.678847\pi\) |
0.999268 | + | 0.0382553i | \(0.0121800\pi\) | |||||||
\(140\) | 2.00000 | − | 3.46410i | 0.169031 | − | 0.292770i | ||||
\(141\) | −17.3205 | −1.45865 | ||||||||
\(142\) | 10.0000 | + | 17.3205i | 0.839181 | + | 1.45350i | ||||
\(143\) | 12.0000 | − | 18.0000i | 1.00349 | − | 1.50524i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.500000 | + | 0.866025i | ||||
\(145\) | 2.00000i | 0.166091i | ||||||||
\(146\) | −4.00000 | − | 6.92820i | −0.331042 | − | 0.573382i | ||||
\(147\) | −4.50000 | + | 2.59808i | −0.371154 | + | 0.214286i | ||||
\(148\) | −3.46410 | − | 2.00000i | −0.284747 | − | 0.164399i | ||||
\(149\) | 1.73205 | + | 1.00000i | 0.141895 | + | 0.0819232i | 0.569267 | − | 0.822153i | \(-0.307227\pi\) |
−0.427372 | + | 0.904076i | \(0.640560\pi\) | |||||||
\(150\) | −1.73205 | − | 3.00000i | −0.141421 | − | 0.244949i | ||||
\(151\) | −3.46410 | + | 2.00000i | −0.281905 | + | 0.162758i | −0.634285 | − | 0.773099i | \(-0.718706\pi\) |
0.352381 | + | 0.935857i | \(0.385372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50000 | − | 2.59808i | −0.121268 | − | 0.210042i | ||||
\(154\) | − | 24.0000i | − | 1.93398i | ||||||
\(155\) | −4.00000 | − | 6.92820i | −0.321288 | − | 0.556487i | ||||
\(156\) | 6.92820 | − | 10.3923i | 0.554700 | − | 0.832050i | ||||
\(157\) | 6.50000 | − | 11.2583i | 0.518756 | − | 0.898513i | −0.481006 | − | 0.876717i | \(-0.659728\pi\) |
0.999762 | − | 0.0217953i | \(-0.00693820\pi\) | |||||||
\(158\) | 1.73205 | + | 1.00000i | 0.137795 | + | 0.0795557i | ||||
\(159\) | 13.5000 | + | 7.79423i | 1.07062 | + | 0.618123i | ||||
\(160\) | 4.00000 | + | 6.92820i | 0.316228 | + | 0.547723i | ||||
\(161\) | − | 2.00000i | − | 0.157622i | ||||||
\(162\) | − | 18.0000i | − | 1.41421i | ||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 3.46410 | − | 2.00000i | 0.270501 | − | 0.156174i | ||||
\(165\) | −9.00000 | − | 5.19615i | −0.700649 | − | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.73205 | + | 1.00000i | 0.134030 | + | 0.0773823i | 0.565516 | − | 0.824737i | \(-0.308677\pi\) |
−0.431486 | + | 0.902120i | \(0.642010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.89230 | − | 10.3301i | 0.607100 | − | 0.794625i | ||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | −20.7846 | + | 12.0000i | −1.58944 | + | 0.917663i | ||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | −6.50000 | − | 11.2583i | −0.494186 | − | 0.855955i | 0.505792 | − | 0.862656i | \(-0.331200\pi\) |
−0.999978 | + | 0.00670064i | \(0.997867\pi\) | |||||||
\(174\) | 3.46410 | + | 6.00000i | 0.262613 | + | 0.454859i | ||||
\(175\) | −1.73205 | − | 1.00000i | −0.130931 | − | 0.0755929i | ||||
\(176\) | 20.7846 | + | 12.0000i | 1.56670 | + | 0.904534i | ||||
\(177\) | 5.19615 | + | 9.00000i | 0.390567 | + | 0.676481i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0000 | 1.12115 | 0.560576 | − | 0.828103i | \(-0.310580\pi\) | ||||
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(180\) | −5.19615 | − | 3.00000i | −0.387298 | − | 0.223607i | ||||
\(181\) | 21.0000 | 1.56092 | 0.780459 | − | 0.625207i | \(-0.214986\pi\) | ||||
0.780459 | + | 0.625207i | \(0.214986\pi\) | |||||||
\(182\) | 0.928203 | − | 14.3923i | 0.0688030 | − | 1.06683i | ||||
\(183\) | 8.66025i | 0.640184i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | + | 1.73205i | −0.0735215 | + | 0.127343i | ||||
\(186\) | −24.0000 | − | 13.8564i | −1.75977 | − | 1.01600i | ||||
\(187\) | −5.19615 | + | 3.00000i | −0.379980 | + | 0.219382i | ||||
\(188\) | 20.0000i | 1.45865i | ||||||||
\(189\) | −5.19615 | − | 9.00000i | −0.377964 | − | 0.654654i | ||||
\(190\) | 16.0000i | 1.16076i | ||||||||
\(191\) | −9.50000 | − | 16.4545i | −0.687396 | − | 1.19060i | −0.972677 | − | 0.232161i | \(-0.925420\pi\) |
0.285282 | − | 0.958444i | \(-0.407913\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | −3.46410 | − | 2.00000i | −0.249351 | − | 0.143963i | 0.370116 | − | 0.928986i | \(-0.379318\pi\) |
−0.619467 | + | 0.785022i | \(0.712651\pi\) | |||||||
\(194\) | −10.0000 | + | 17.3205i | −0.717958 | + | 1.24354i | ||||
\(195\) | −5.19615 | − | 3.46410i | −0.372104 | − | 0.248069i | ||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | − | 20.0000i | − | 1.42494i | −0.701702 | − | 0.712470i | \(-0.747576\pi\) | ||
0.701702 | − | 0.712470i | \(-0.252424\pi\) | |||||||
\(198\) | −36.0000 | −2.55841 | ||||||||
\(199\) | 3.00000 | 0.212664 | 0.106332 | − | 0.994331i | \(-0.466089\pi\) | ||||
0.106332 | + | 0.994331i | \(0.466089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.1244 | + | 7.00000i | 0.853067 | + | 0.492518i | ||||
\(203\) | 3.46410 | + | 2.00000i | 0.243132 | + | 0.140372i | ||||
\(204\) | −3.00000 | + | 1.73205i | −0.210042 | + | 0.121268i | ||||
\(205\) | −1.00000 | − | 1.73205i | −0.0698430 | − | 0.120972i | ||||
\(206\) | − | 32.0000i | − | 2.22955i | ||||||
\(207\) | −3.00000 | −0.208514 | ||||||||
\(208\) | 12.0000 | + | 8.00000i | 0.832050 | + | 0.554700i | ||||
\(209\) | 24.0000 | + | 41.5692i | 1.66011 | + | 2.87540i | ||||
\(210\) | −6.92820 | −0.478091 | ||||||||
\(211\) | 7.50000 | − | 12.9904i | 0.516321 | − | 0.894295i | −0.483499 | − | 0.875345i | \(-0.660634\pi\) |
0.999820 | − | 0.0189499i | \(-0.00603229\pi\) | |||||||
\(212\) | 9.00000 | − | 15.5885i | 0.618123 | − | 1.07062i | ||||
\(213\) | 8.66025 | − | 15.0000i | 0.593391 | − | 1.02778i | ||||
\(214\) | −29.4449 | + | 17.0000i | −2.01281 | + | 1.16210i | ||||
\(215\) | 5.00000i | 0.340997i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | 20.0000 | + | 34.6410i | 1.35457 | + | 2.34619i | ||||
\(219\) | −3.46410 | + | 6.00000i | −0.234082 | + | 0.405442i | ||||
\(220\) | −6.00000 | + | 10.3923i | −0.404520 | + | 0.700649i | ||||
\(221\) | −3.23205 | + | 1.59808i | −0.217411 | + | 0.107498i | ||||
\(222\) | 6.92820i | 0.464991i | ||||||||
\(223\) | 12.1244 | − | 7.00000i | 0.811907 | − | 0.468755i | −0.0357107 | − | 0.999362i | \(-0.511370\pi\) |
0.847618 | + | 0.530607i | \(0.178036\pi\) | |||||||
\(224\) | 16.0000 | 1.06904 | ||||||||
\(225\) | −1.50000 | + | 2.59808i | −0.100000 | + | 0.173205i | ||||
\(226\) | − | 38.0000i | − | 2.52772i | ||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 13.8564 | + | 24.0000i | 0.917663 | + | 1.58944i | ||||
\(229\) | −22.5167 | − | 13.0000i | −1.48794 | − | 0.859064i | −0.488037 | − | 0.872823i | \(-0.662287\pi\) |
−0.999905 | + | 0.0137585i | \(0.995620\pi\) | |||||||
\(230\) | −1.00000 | + | 1.73205i | −0.0659380 | + | 0.114208i | ||||
\(231\) | −18.0000 | + | 10.3923i | −1.18431 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.0000 | −1.24473 | −0.622366 | − | 0.782727i | \(-0.713828\pi\) | ||||
−0.622366 | + | 0.782727i | \(0.713828\pi\) | |||||||
\(234\) | −21.5885 | − | 1.39230i | −1.41128 | − | 0.0910178i | ||||
\(235\) | 10.0000 | 0.652328 | ||||||||
\(236\) | 10.3923 | − | 6.00000i | 0.676481 | − | 0.390567i | ||||
\(237\) | − | 1.73205i | − | 0.112509i | ||||||
\(238\) | −2.00000 | + | 3.46410i | −0.129641 | + | 0.224544i | ||||
\(239\) | −17.3205 | − | 10.0000i | −1.12037 | − | 0.646846i | −0.178875 | − | 0.983872i | \(-0.557246\pi\) |
−0.941495 | + | 0.337026i | \(0.890579\pi\) | |||||||
\(240\) | 3.46410 | − | 6.00000i | 0.223607 | − | 0.387298i | ||||
\(241\) | −25.9808 | + | 15.0000i | −1.67357 | + | 0.966235i | −0.707953 | + | 0.706260i | \(0.750381\pi\) |
−0.965615 | + | 0.259975i | \(0.916286\pi\) | |||||||
\(242\) | 50.0000i | 3.21412i | ||||||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 2.59808 | − | 1.50000i | 0.165985 | − | 0.0958315i | ||||
\(246\) | −6.00000 | − | 3.46410i | −0.382546 | − | 0.220863i | ||||
\(247\) | 12.7846 | + | 25.8564i | 0.813465 | + | 1.64520i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | + | 1.73205i | 0.0632456 | + | 0.109545i | ||||
\(251\) | 3.00000 | 0.189358 | 0.0946792 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | −10.3923 | + | 6.00000i | −0.654654 | + | 0.377964i | ||||
\(253\) | 6.00000i | 0.377217i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.866025 | + | 1.50000i | 0.0542326 | + | 0.0939336i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 1.50000 | − | 2.59808i | 0.0935674 | − | 0.162064i | −0.815442 | − | 0.578838i | \(-0.803506\pi\) |
0.909010 | + | 0.416775i | \(0.136840\pi\) | |||||||
\(258\) | 8.66025 | + | 15.0000i | 0.539164 | + | 0.933859i | ||||
\(259\) | 2.00000 | + | 3.46410i | 0.124274 | + | 0.215249i | ||||
\(260\) | −4.00000 | + | 6.00000i | −0.248069 | + | 0.372104i | ||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | − | 30.0000i | − | 1.85341i | ||||||
\(263\) | −4.50000 | − | 7.79423i | −0.277482 | − | 0.480613i | 0.693276 | − | 0.720672i | \(-0.256167\pi\) |
−0.970758 | + | 0.240059i | \(0.922833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.79423 | − | 4.50000i | −0.478796 | − | 0.276433i | ||||
\(266\) | 27.7128 | + | 16.0000i | 1.69918 | + | 0.981023i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 10.3923i | 0.632456i | ||||||||
\(271\) | 28.0000i | 1.70088i | 0.526073 | + | 0.850439i | \(0.323664\pi\) | ||||
−0.526073 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(272\) | −2.00000 | − | 3.46410i | −0.121268 | − | 0.210042i | ||||
\(273\) | −11.1962 | + | 5.53590i | −0.677622 | + | 0.335048i | ||||
\(274\) | 6.00000 | − | 10.3923i | 0.362473 | − | 0.627822i | ||||
\(275\) | 5.19615 | + | 3.00000i | 0.313340 | + | 0.180907i | ||||
\(276\) | 3.46410i | 0.208514i | ||||||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | 22.0000i | 1.31947i | ||||||||
\(279\) | 24.0000i | 1.43684i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 30.0000 | − | 17.3205i | 1.78647 | − | 1.03142i | ||||
\(283\) | 15.5000 | − | 26.8468i | 0.921379 | − | 1.59588i | 0.124096 | − | 0.992270i | \(-0.460397\pi\) |
0.797283 | − | 0.603606i | \(-0.206270\pi\) | |||||||
\(284\) | −17.3205 | − | 10.0000i | −1.02778 | − | 0.593391i | ||||
\(285\) | 12.0000 | − | 6.92820i | 0.710819 | − | 0.410391i | ||||
\(286\) | −2.78461 | + | 43.1769i | −0.164657 | + | 2.55310i | ||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | − | 24.0000i | − | 1.41421i | ||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −2.00000 | − | 3.46410i | −0.117444 | − | 0.203419i | ||||
\(291\) | 17.3205 | 1.01535 | ||||||||
\(292\) | 6.92820 | + | 4.00000i | 0.405442 | + | 0.234082i | ||||
\(293\) | −5.19615 | − | 3.00000i | −0.303562 | − | 0.175262i | 0.340480 | − | 0.940252i | \(-0.389411\pi\) |
−0.644042 | + | 0.764990i | \(0.722744\pi\) | |||||||
\(294\) | 5.19615 | − | 9.00000i | 0.303046 | − | 0.524891i | ||||
\(295\) | −3.00000 | − | 5.19615i | −0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.5885 | + | 27.0000i | 0.904534 | + | 1.56670i | ||||
\(298\) | −4.00000 | −0.231714 | ||||||||
\(299\) | −0.232051 | + | 3.59808i | −0.0134198 | + | 0.208082i | ||||
\(300\) | 3.00000 | + | 1.73205i | 0.173205 | + | 0.100000i | ||||
\(301\) | 8.66025 | + | 5.00000i | 0.499169 | + | 0.288195i | ||||
\(302\) | 4.00000 | − | 6.92820i | 0.230174 | − | 0.398673i | ||||
\(303\) | − | 12.1244i | − | 0.696526i | ||||||
\(304\) | −27.7128 | + | 16.0000i | −1.58944 | + | 0.917663i | ||||
\(305\) | − | 5.00000i | − | 0.286299i | ||||||
\(306\) | 5.19615 | + | 3.00000i | 0.297044 | + | 0.171499i | ||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 12.0000 | + | 20.7846i | 0.683763 | + | 1.18431i | ||||
\(309\) | −24.0000 | + | 13.8564i | −1.36531 | + | 0.788263i | ||||
\(310\) | 13.8564 | + | 8.00000i | 0.786991 | + | 0.454369i | ||||
\(311\) | 4.00000 | − | 6.92820i | 0.226819 | − | 0.392862i | −0.730044 | − | 0.683400i | \(-0.760501\pi\) |
0.956864 | + | 0.290537i | \(0.0938340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | + | 8.66025i | 0.282617 | + | 0.489506i | 0.972028 | − | 0.234863i | \(-0.0754642\pi\) |
−0.689412 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(314\) | 26.0000i | 1.46726i | ||||||||
\(315\) | 3.00000 | + | 5.19615i | 0.169031 | + | 0.292770i | ||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | −22.5167 | + | 13.0000i | −1.26466 | + | 0.730153i | −0.973973 | − | 0.226665i | \(-0.927218\pi\) |
−0.290689 | + | 0.956818i | \(0.593884\pi\) | |||||||
\(318\) | −31.1769 | −1.74831 | ||||||||
\(319\) | −10.3923 | − | 6.00000i | −0.581857 | − | 0.335936i | ||||
\(320\) | −6.92820 | − | 4.00000i | −0.387298 | − | 0.223607i | ||||
\(321\) | 25.5000 | + | 14.7224i | 1.42327 | + | 0.821726i | ||||
\(322\) | 2.00000 | + | 3.46410i | 0.111456 | + | 0.193047i | ||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | 9.00000 | + | 15.5885i | 0.500000 | + | 0.866025i | ||||
\(325\) | 3.00000 | + | 2.00000i | 0.166410 | + | 0.110940i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.3205 | − | 30.0000i | 0.957826 | − | 1.65900i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0000 | − | 17.3205i | 0.551318 | − | 0.954911i | ||||
\(330\) | 20.7846 | 1.14416 | ||||||||
\(331\) | −6.92820 | + | 4.00000i | −0.380808 | + | 0.219860i | −0.678170 | − | 0.734905i | \(-0.737227\pi\) |
0.297361 | + | 0.954765i | \(0.403893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.19615 | − | 3.00000i | 0.284747 | − | 0.164399i | ||||
\(334\) | −4.00000 | −0.218870 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.92820 | − | 12.0000i | −0.377964 | − | 0.654654i | ||||
\(337\) | −1.50000 | + | 2.59808i | −0.0817102 | + | 0.141526i | −0.903985 | − | 0.427565i | \(-0.859372\pi\) |
0.822274 | + | 0.569091i | \(0.192705\pi\) | |||||||
\(338\) | −3.33975 | + | 25.7846i | −0.181658 | + | 1.40250i | ||||
\(339\) | −28.5000 | + | 16.4545i | −1.54791 | + | 0.893685i | ||||
\(340\) | 1.73205 | − | 1.00000i | 0.0939336 | − | 0.0542326i | ||||
\(341\) | 48.0000 | 2.59935 | ||||||||
\(342\) | 24.0000 | − | 41.5692i | 1.29777 | − | 2.24781i | ||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.73205 | 0.0932505 | ||||||||
\(346\) | 22.5167 | + | 13.0000i | 1.21050 | + | 0.698884i | ||||
\(347\) | 2.50000 | − | 4.33013i | 0.134207 | − | 0.232453i | −0.791087 | − | 0.611703i | \(-0.790485\pi\) |
0.925294 | + | 0.379250i | \(0.123818\pi\) | |||||||
\(348\) | −6.00000 | − | 3.46410i | −0.321634 | − | 0.185695i | ||||
\(349\) | −1.73205 | + | 1.00000i | −0.0927146 | + | 0.0535288i | −0.545640 | − | 0.838019i | \(-0.683714\pi\) |
0.452926 | + | 0.891548i | \(0.350380\pi\) | |||||||
\(350\) | 4.00000 | 0.213809 | ||||||||
\(351\) | 8.30385 | + | 16.7942i | 0.443227 | + | 0.896410i | ||||
\(352\) | −48.0000 | −2.55841 | ||||||||
\(353\) | −5.19615 | + | 3.00000i | −0.276563 | + | 0.159674i | −0.631867 | − | 0.775077i | \(-0.717711\pi\) |
0.355303 | + | 0.934751i | \(0.384378\pi\) | |||||||
\(354\) | −18.0000 | − | 10.3923i | −0.956689 | − | 0.552345i | ||||
\(355\) | −5.00000 | + | 8.66025i | −0.265372 | + | 0.459639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.46410 | 0.183340 | ||||||||
\(358\) | −25.9808 | + | 15.0000i | −1.37313 | + | 0.792775i | ||||
\(359\) | 10.0000i | 0.527780i | 0.964553 | + | 0.263890i | \(0.0850056\pi\) | ||||
−0.964553 | + | 0.263890i | \(0.914994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −45.0000 | −2.36842 | ||||||||
\(362\) | −36.3731 | + | 21.0000i | −1.91173 | + | 1.10374i | ||||
\(363\) | 37.5000 | − | 21.6506i | 1.96824 | − | 1.13636i | ||||
\(364\) | 6.39230 | + | 12.9282i | 0.335048 | + | 0.677622i | ||||
\(365\) | 2.00000 | − | 3.46410i | 0.104685 | − | 0.181319i | ||||
\(366\) | −8.66025 | − | 15.0000i | −0.452679 | − | 0.784063i | ||||
\(367\) | −10.5000 | − | 18.1865i | −0.548096 | − | 0.949329i | −0.998405 | − | 0.0564568i | \(-0.982020\pi\) |
0.450310 | − | 0.892873i | \(-0.351314\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | 6.00000i | 0.312348i | ||||||||
\(370\) | − | 4.00000i | − | 0.207950i | ||||||
\(371\) | −15.5885 | + | 9.00000i | −0.809312 | + | 0.467257i | ||||
\(372\) | 27.7128 | 1.43684 | ||||||||
\(373\) | −9.50000 | + | 16.4545i | −0.491891 | + | 0.851981i | −0.999956 | − | 0.00933789i | \(-0.997028\pi\) |
0.508065 | + | 0.861319i | \(0.330361\pi\) | |||||||
\(374\) | 6.00000 | − | 10.3923i | 0.310253 | − | 0.537373i | ||||
\(375\) | 0.866025 | − | 1.50000i | 0.0447214 | − | 0.0774597i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | − | 4.00000i | −0.309016 | − | 0.206010i | ||||
\(378\) | 18.0000 | + | 10.3923i | 0.925820 | + | 0.534522i | ||||
\(379\) | − | 18.0000i | − | 0.924598i | −0.886724 | − | 0.462299i | \(-0.847025\pi\) | ||
0.886724 | − | 0.462299i | \(-0.152975\pi\) | |||||||
\(380\) | −8.00000 | − | 13.8564i | −0.410391 | − | 0.710819i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 32.9090 | + | 19.0000i | 1.68377 | + | 0.972125i | ||||
\(383\) | 22.5167 | + | 13.0000i | 1.15055 | + | 0.664269i | 0.949021 | − | 0.315214i | \(-0.102076\pi\) |
0.201527 | + | 0.979483i | \(0.435410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3923 | − | 6.00000i | 0.529641 | − | 0.305788i | ||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 7.50000 | − | 12.9904i | 0.381246 | − | 0.660338i | ||||
\(388\) | − | 20.0000i | − | 1.01535i | ||||||
\(389\) | 11.5000 | + | 19.9186i | 0.583073 | + | 1.00991i | 0.995113 | + | 0.0987463i | \(0.0314832\pi\) |
−0.412039 | + | 0.911166i | \(0.635183\pi\) | |||||||
\(390\) | 12.4641 | + | 0.803848i | 0.631144 | + | 0.0407044i | ||||
\(391\) | 0.500000 | − | 0.866025i | 0.0252861 | − | 0.0437968i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.5000 | + | 12.9904i | −1.13497 | + | 0.655278i | ||||
\(394\) | 20.0000 | + | 34.6410i | 1.00759 | + | 1.74519i | ||||
\(395\) | 1.00000i | 0.0503155i | ||||||||
\(396\) | 31.1769 | − | 18.0000i | 1.56670 | − | 0.904534i | ||||
\(397\) | − | 28.0000i | − | 1.40528i | −0.711546 | − | 0.702640i | \(-0.752005\pi\) | ||
0.711546 | − | 0.702640i | \(-0.247995\pi\) | |||||||
\(398\) | −5.19615 | + | 3.00000i | −0.260460 | + | 0.150376i | ||||
\(399\) | − | 27.7128i | − | 1.38738i | ||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | −27.7128 | − | 16.0000i | −1.38391 | − | 0.799002i | −0.391292 | − | 0.920267i | \(-0.627972\pi\) |
−0.992620 | + | 0.121265i | \(0.961305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.7846 | + | 1.85641i | 1.43386 | + | 0.0924742i | ||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 7.79423 | − | 4.50000i | 0.387298 | − | 0.223607i | ||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | −6.00000 | − | 10.3923i | −0.297409 | − | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 3.46410 | + | 2.00000i | 0.171080 | + | 0.0987730i | ||||
\(411\) | −10.3923 | −0.512615 | ||||||||
\(412\) | 16.0000 | + | 27.7128i | 0.788263 | + | 1.36531i | ||||
\(413\) | −12.0000 | −0.590481 | ||||||||
\(414\) | 5.19615 | − | 3.00000i | 0.255377 | − | 0.147442i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −28.7846 | − | 1.85641i | −1.41128 | − | 0.0910178i | ||||
\(417\) | 16.5000 | − | 9.52628i | 0.808008 | − | 0.466504i | ||||
\(418\) | −83.1384 | − | 48.0000i | −4.06643 | − | 2.34776i | ||||
\(419\) | −7.50000 | + | 12.9904i | −0.366399 | + | 0.634622i | −0.989000 | − | 0.147918i | \(-0.952743\pi\) |
0.622601 | + | 0.782540i | \(0.286076\pi\) | |||||||
\(420\) | 6.00000 | − | 3.46410i | 0.292770 | − | 0.169031i | ||||
\(421\) | 6.92820 | − | 4.00000i | 0.337660 | − | 0.194948i | −0.321577 | − | 0.946883i | \(-0.604213\pi\) |
0.659237 | + | 0.751935i | \(0.270879\pi\) | |||||||
\(422\) | 30.0000i | 1.46038i | ||||||||
\(423\) | −25.9808 | − | 15.0000i | −1.26323 | − | 0.729325i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.500000 | − | 0.866025i | −0.0242536 | − | 0.0420084i | ||||
\(426\) | 34.6410i | 1.67836i | ||||||||
\(427\) | −8.66025 | − | 5.00000i | −0.419099 | − | 0.241967i | ||||
\(428\) | 17.0000 | − | 29.4449i | 0.821726 | − | 1.42327i | ||||
\(429\) | 33.5885 | − | 16.6077i | 1.62167 | − | 0.801827i | ||||
\(430\) | −5.00000 | − | 8.66025i | −0.241121 | − | 0.417635i | ||||
\(431\) | − | 24.0000i | − | 1.15604i | −0.816023 | − | 0.578020i | \(-0.803826\pi\) | ||
0.816023 | − | 0.578020i | \(-0.196174\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.866025 | + | 0.500000i | ||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 27.7128 | − | 16.0000i | 1.33026 | − | 0.768025i | ||||
\(435\) | −1.73205 | + | 3.00000i | −0.0830455 | + | 0.143839i | ||||
\(436\) | −34.6410 | − | 20.0000i | −1.65900 | − | 0.957826i | ||||
\(437\) | −6.92820 | − | 4.00000i | −0.331421 | − | 0.191346i | ||||
\(438\) | − | 13.8564i | − | 0.662085i | ||||||
\(439\) | −12.5000 | − | 21.6506i | −0.596592 | − | 1.03333i | −0.993320 | − | 0.115392i | \(-0.963188\pi\) |
0.396728 | − | 0.917936i | \(-0.370146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 4.00000 | − | 6.00000i | 0.190261 | − | 0.285391i | ||||
\(443\) | −10.5000 | − | 18.1865i | −0.498870 | − | 0.864068i | 0.501129 | − | 0.865373i | \(-0.332918\pi\) |
−0.999999 | + | 0.00130426i | \(0.999585\pi\) | |||||||
\(444\) | −3.46410 | − | 6.00000i | −0.164399 | − | 0.284747i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | + | 24.2487i | −0.662919 | + | 1.14821i | ||||
\(447\) | 1.73205 | + | 3.00000i | 0.0819232 | + | 0.141895i | ||||
\(448\) | −13.8564 | + | 8.00000i | −0.654654 | + | 0.377964i | ||||
\(449\) | 36.0000i | 1.69895i | 0.527633 | + | 0.849473i | \(0.323080\pi\) | ||||
−0.527633 | + | 0.849473i | \(0.676920\pi\) | |||||||
\(450\) | − | 6.00000i | − | 0.282843i | ||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 19.0000 | + | 32.9090i | 0.893685 | + | 1.54791i | ||||
\(453\) | −6.92820 | −0.325515 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.46410 | − | 3.19615i | 0.303042 | − | 0.149838i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.92820 | − | 4.00000i | 0.324088 | − | 0.187112i | −0.329125 | − | 0.944286i | \(-0.606754\pi\) |
0.653213 | + | 0.757174i | \(0.273421\pi\) | |||||||
\(458\) | 52.0000 | 2.42980 | ||||||||
\(459\) | − | 5.19615i | − | 0.242536i | ||||||
\(460\) | − | 2.00000i | − | 0.0932505i | ||||||
\(461\) | 1.73205 | − | 1.00000i | 0.0806696 | − | 0.0465746i | −0.459123 | − | 0.888373i | \(-0.651836\pi\) |
0.539792 | + | 0.841798i | \(0.318503\pi\) | |||||||
\(462\) | 20.7846 | − | 36.0000i | 0.966988 | − | 1.67487i | ||||
\(463\) | 19.0526 | + | 11.0000i | 0.885448 | + | 0.511213i | 0.872451 | − | 0.488702i | \(-0.162530\pi\) |
0.0129968 | + | 0.999916i | \(0.495863\pi\) | |||||||
\(464\) | 4.00000 | − | 6.92820i | 0.185695 | − | 0.321634i | ||||
\(465\) | − | 13.8564i | − | 0.642575i | ||||||
\(466\) | 32.9090 | − | 19.0000i | 1.52448 | − | 0.880158i | ||||
\(467\) | −21.0000 | −0.971764 | −0.485882 | − | 0.874024i | \(-0.661502\pi\) | ||||
−0.485882 | + | 0.874024i | \(0.661502\pi\) | |||||||
\(468\) | 19.3923 | − | 9.58846i | 0.896410 | − | 0.443227i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.3205 | + | 10.0000i | −0.798935 | + | 0.461266i | ||||
\(471\) | 19.5000 | − | 11.2583i | 0.898513 | − | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.9808 | − | 15.0000i | −1.19460 | − | 0.689701i | ||||
\(474\) | 1.73205 | + | 3.00000i | 0.0795557 | + | 0.137795i | ||||
\(475\) | −6.92820 | + | 4.00000i | −0.317888 | + | 0.183533i | ||||
\(476\) | − | 4.00000i | − | 0.183340i | ||||||
\(477\) | 13.5000 | + | 23.3827i | 0.618123 | + | 1.07062i | ||||
\(478\) | 40.0000 | 1.82956 | ||||||||
\(479\) | 15.5885 | − | 9.00000i | 0.712255 | − | 0.411220i | −0.0996406 | − | 0.995023i | \(-0.531769\pi\) |
0.811895 | + | 0.583803i | \(0.198436\pi\) | |||||||
\(480\) | 13.8564i | 0.632456i | ||||||||
\(481\) | −3.19615 | − | 6.46410i | −0.145732 | − | 0.294738i | ||||
\(482\) | 30.0000 | − | 51.9615i | 1.36646 | − | 2.36678i | ||||
\(483\) | 1.73205 | − | 3.00000i | 0.0788110 | − | 0.136505i | ||||
\(484\) | −25.0000 | − | 43.3013i | −1.13636 | − | 1.96824i | ||||
\(485\) | −10.0000 | −0.454077 | ||||||||
\(486\) | 15.5885 | − | 27.0000i | 0.707107 | − | 1.22474i | ||||
\(487\) | 24.0000i | 1.08754i | 0.839233 | + | 0.543772i | \(0.183004\pi\) | ||||
−0.839233 | + | 0.543772i | \(0.816996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.00000 | + | 5.19615i | −0.135526 | + | 0.234738i | ||||
\(491\) | 8.00000 | − | 13.8564i | 0.361035 | − | 0.625331i | −0.627096 | − | 0.778942i | \(-0.715757\pi\) |
0.988131 | + | 0.153611i | \(0.0490902\pi\) | |||||||
\(492\) | 6.92820 | 0.312348 | ||||||||
\(493\) | 1.00000 | + | 1.73205i | 0.0450377 | + | 0.0780076i | ||||
\(494\) | −48.0000 | − | 32.0000i | −2.15962 | − | 1.43975i | ||||
\(495\) | −9.00000 | − | 15.5885i | −0.404520 | − | 0.700649i | ||||
\(496\) | 32.0000i | 1.43684i | ||||||||
\(497\) | 10.0000 | + | 17.3205i | 0.448561 | + | 0.776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487 | + | 14.0000i | 1.08552 | + | 0.626726i | 0.932381 | − | 0.361478i | \(-0.117728\pi\) |
0.153141 | + | 0.988204i | \(0.451061\pi\) | |||||||
\(500\) | −1.73205 | − | 1.00000i | −0.0774597 | − | 0.0447214i | ||||
\(501\) | 1.73205 | + | 3.00000i | 0.0773823 | + | 0.134030i | ||||
\(502\) | −5.19615 | + | 3.00000i | −0.231916 | + | 0.133897i | ||||
\(503\) | −25.0000 | −1.11469 | −0.557347 | − | 0.830279i | \(-0.688181\pi\) | ||||
−0.557347 | + | 0.830279i | \(0.688181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.00000i | 0.311496i | ||||||||
\(506\) | −6.00000 | − | 10.3923i | −0.266733 | − | 0.461994i | ||||
\(507\) | 20.7846 | − | 8.66025i | 0.923077 | − | 0.384615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.19615 | − | 3.00000i | −0.230315 | − | 0.132973i | 0.380402 | − | 0.924821i | \(-0.375786\pi\) |
−0.610718 | + | 0.791849i | \(0.709119\pi\) | |||||||
\(510\) | −3.00000 | − | 1.73205i | −0.132842 | − | 0.0766965i | ||||
\(511\) | −4.00000 | − | 6.92820i | −0.176950 | − | 0.306486i | ||||
\(512\) | − | 32.0000i | − | 1.41421i | ||||||
\(513\) | −41.5692 | −1.83533 | ||||||||
\(514\) | 6.00000i | 0.264649i | ||||||||
\(515\) | 13.8564 | − | 8.00000i | 0.610586 | − | 0.352522i | ||||
\(516\) | −15.0000 | − | 8.66025i | −0.660338 | − | 0.381246i | ||||
\(517\) | −30.0000 | + | 51.9615i | −1.31940 | + | 2.28527i | ||||
\(518\) | −6.92820 | − | 4.00000i | −0.304408 | − | 0.175750i | ||||
\(519\) | − | 22.5167i | − | 0.988372i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 12.0000i | 0.525226i | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 15.0000 | + | 25.9808i | 0.655278 | + | 1.13497i | ||||
\(525\) | −1.73205 | − | 3.00000i | −0.0755929 | − | 0.130931i | ||||
\(526\) | 15.5885 | + | 9.00000i | 0.679689 | + | 0.392419i | ||||
\(527\) | −6.92820 | − | 4.00000i | −0.301797 | − | 0.174243i | ||||
\(528\) | 20.7846 | + | 36.0000i | 0.904534 | + | 1.56670i | ||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 18.0000 | 0.781870 | ||||||||
\(531\) | 18.0000i | 0.781133i | ||||||||
\(532\) | −32.0000 | −1.38738 | ||||||||
\(533\) | 7.19615 | + | 0.464102i | 0.311700 | + | 0.0201025i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.7224 | − | 8.50000i | −0.636506 | − | 0.367487i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.5000 | + | 12.9904i | 0.970947 | + | 0.560576i | ||||
\(538\) | 24.2487 | − | 14.0000i | 1.04544 | − | 0.603583i | ||||
\(539\) | 18.0000i | 0.775315i | ||||||||
\(540\) | −5.19615 | − | 9.00000i | −0.223607 | − | 0.387298i | ||||
\(541\) | − | 32.0000i | − | 1.37579i | −0.725811 | − | 0.687894i | \(-0.758536\pi\) | ||
0.725811 | − | 0.687894i | \(-0.241464\pi\) | |||||||
\(542\) | −28.0000 | − | 48.4974i | −1.20270 | − | 2.08314i | ||||
\(543\) | 31.5000 | + | 18.1865i | 1.35179 | + | 0.780459i | ||||
\(544\) | 6.92820 | + | 4.00000i | 0.297044 | + | 0.171499i | ||||
\(545\) | −10.0000 | + | 17.3205i | −0.428353 | + | 0.741929i | ||||
\(546\) | 13.8564 | − | 20.7846i | 0.592999 | − | 0.889499i | ||||
\(547\) | 2.00000 | + | 3.46410i | 0.0855138 | + | 0.148114i | 0.905610 | − | 0.424111i | \(-0.139413\pi\) |
−0.820096 | + | 0.572226i | \(0.806080\pi\) | |||||||
\(548\) | 12.0000i | 0.512615i | ||||||||
\(549\) | −7.50000 | + | 12.9904i | −0.320092 | + | 0.554416i | ||||
\(550\) | −12.0000 | −0.511682 | ||||||||
\(551\) | 13.8564 | − | 8.00000i | 0.590303 | − | 0.340811i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.73205 | + | 1.00000i | 0.0736543 | + | 0.0425243i | ||||
\(554\) | 17.3205 | + | 10.0000i | 0.735878 | + | 0.424859i | ||||
\(555\) | −3.00000 | + | 1.73205i | −0.127343 | + | 0.0735215i | ||||
\(556\) | −11.0000 | − | 19.0526i | −0.466504 | − | 0.808008i | ||||
\(557\) | 12.0000i | 0.508456i | 0.967144 | + | 0.254228i | \(0.0818214\pi\) | ||||
−0.967144 | + | 0.254228i | \(0.918179\pi\) | |||||||
\(558\) | −24.0000 | − | 41.5692i | −1.01600 | − | 1.75977i | ||||
\(559\) | −15.0000 | − | 10.0000i | −0.634432 | − | 0.422955i | ||||
\(560\) | 4.00000 | + | 6.92820i | 0.169031 | + | 0.292770i | ||||
\(561\) | −10.3923 | −0.438763 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5000 | + | 33.7750i | −0.821827 | + | 1.42345i | 0.0824933 | + | 0.996592i | \(0.473712\pi\) |
−0.904320 | + | 0.426855i | \(0.859622\pi\) | |||||||
\(564\) | −17.3205 | + | 30.0000i | −0.729325 | + | 1.26323i | ||||
\(565\) | 16.4545 | − | 9.50000i | 0.692245 | − | 0.399668i | ||||
\(566\) | 62.0000i | 2.60605i | ||||||||
\(567\) | − | 18.0000i | − | 0.755929i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0000 | − | 25.9808i | −0.628833 | − | 1.08917i | −0.987786 | − | 0.155815i | \(-0.950200\pi\) |
0.358954 | − | 0.933355i | \(-0.383134\pi\) | |||||||
\(570\) | −13.8564 | + | 24.0000i | −0.580381 | + | 1.00525i | ||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −19.1769 | − | 38.7846i | −0.801827 | − | 1.62167i | ||||
\(573\) | − | 32.9090i | − | 1.37479i | ||||||
\(574\) | 6.92820 | − | 4.00000i | 0.289178 | − | 0.166957i | ||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.500000 | + | 0.866025i | ||||
\(577\) | 28.0000i | 1.16566i | 0.812596 | + | 0.582828i | \(0.198054\pi\) | ||||
−0.812596 | + | 0.582828i | \(0.801946\pi\) | |||||||
\(578\) | 27.7128 | − | 16.0000i | 1.15270 | − | 0.665512i | ||||
\(579\) | −3.46410 | − | 6.00000i | −0.143963 | − | 0.249351i | ||||
\(580\) | 3.46410 | + | 2.00000i | 0.143839 | + | 0.0830455i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −30.0000 | + | 17.3205i | −1.24354 | + | 0.717958i | ||||
\(583\) | 46.7654 | − | 27.0000i | 1.93682 | − | 1.11823i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.79423 | − | 9.69615i | −0.198217 | − | 0.400887i | ||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 24.2487 | − | 14.0000i | 1.00085 | − | 0.577842i | 0.0923513 | − | 0.995726i | \(-0.470562\pi\) |
0.908500 | + | 0.417885i | \(0.137228\pi\) | |||||||
\(588\) | 10.3923i | 0.428571i | ||||||||
\(589\) | −32.0000 | + | 55.4256i | −1.31854 | + | 2.28377i | ||||
\(590\) | 10.3923 | + | 6.00000i | 0.427844 | + | 0.247016i | ||||
\(591\) | 17.3205 | − | 30.0000i | 0.712470 | − | 1.23404i | ||||
\(592\) | 6.92820 | − | 4.00000i | 0.284747 | − | 0.164399i | ||||
\(593\) | − | 16.0000i | − | 0.657041i | −0.944497 | − | 0.328521i | \(-0.893450\pi\) | ||
0.944497 | − | 0.328521i | \(-0.106550\pi\) | |||||||
\(594\) | −54.0000 | − | 31.1769i | −2.21565 | − | 1.27920i | ||||
\(595\) | −2.00000 | −0.0819920 | ||||||||
\(596\) | 3.46410 | − | 2.00000i | 0.141895 | − | 0.0819232i | ||||
\(597\) | 4.50000 | + | 2.59808i | 0.184173 | + | 0.106332i | ||||
\(598\) | −3.19615 | − | 6.46410i | −0.130700 | − | 0.264337i | ||||
\(599\) | −3.50000 | + | 6.06218i | −0.143006 | + | 0.247694i | −0.928627 | − | 0.371014i | \(-0.879010\pi\) |
0.785621 | + | 0.618708i | \(0.212344\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.50000 | − | 4.33013i | −0.101977 | − | 0.176630i | 0.810522 | − | 0.585708i | \(-0.199184\pi\) |
−0.912499 | + | 0.409079i | \(0.865850\pi\) | |||||||
\(602\) | −20.0000 | −0.815139 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000i | 0.325515i | ||||||||
\(605\) | −21.6506 | + | 12.5000i | −0.880223 | + | 0.508197i | ||||
\(606\) | 12.1244 | + | 21.0000i | 0.492518 | + | 0.853067i | ||||
\(607\) | 5.50000 | − | 9.52628i | 0.223238 | − | 0.386660i | −0.732551 | − | 0.680712i | \(-0.761671\pi\) |
0.955789 | + | 0.294052i | \(0.0950039\pi\) | |||||||
\(608\) | 32.0000 | − | 55.4256i | 1.29777 | − | 2.24781i | ||||
\(609\) | 3.46410 | + | 6.00000i | 0.140372 | + | 0.243132i | ||||
\(610\) | 5.00000 | + | 8.66025i | 0.202444 | + | 0.350643i | ||||
\(611\) | −20.0000 | + | 30.0000i | −0.809113 | + | 1.21367i | ||||
\(612\) | −6.00000 | −0.242536 | ||||||||
\(613\) | 28.0000i | 1.13091i | 0.824779 | + | 0.565455i | \(0.191299\pi\) | ||||
−0.824779 | + | 0.565455i | \(0.808701\pi\) | |||||||
\(614\) | 4.00000 | + | 6.92820i | 0.161427 | + | 0.279600i | ||||
\(615\) | − | 3.46410i | − | 0.139686i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.73205 | − | 1.00000i | −0.0697297 | − | 0.0402585i | 0.464730 | − | 0.885453i | \(-0.346151\pi\) |
−0.534460 | + | 0.845194i | \(0.679485\pi\) | |||||||
\(618\) | 27.7128 | − | 48.0000i | 1.11477 | − | 1.93084i | ||||
\(619\) | −8.66025 | + | 5.00000i | −0.348085 | + | 0.200967i | −0.663842 | − | 0.747873i | \(-0.731075\pi\) |
0.315757 | + | 0.948840i | \(0.397742\pi\) | |||||||
\(620\) | −16.0000 | −0.642575 | ||||||||
\(621\) | −4.50000 | − | 2.59808i | −0.180579 | − | 0.104257i | ||||
\(622\) | 16.0000i | 0.641542i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.0718 | + | 22.3923i | 0.443227 | + | 0.896410i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −17.3205 | − | 10.0000i | −0.692267 | − | 0.399680i | ||||
\(627\) | 83.1384i | 3.32023i | ||||||||
\(628\) | −13.0000 | − | 22.5167i | −0.518756 | − | 0.898513i | ||||
\(629\) | 2.00000i | 0.0797452i | ||||||||
\(630\) | −10.3923 | − | 6.00000i | −0.414039 | − | 0.239046i | ||||
\(631\) | 2.00000i | 0.0796187i | 0.999207 | + | 0.0398094i | \(0.0126751\pi\) | ||||
−0.999207 | + | 0.0398094i | \(0.987325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.5000 | − | 12.9904i | 0.894295 | − | 0.516321i | ||||
\(634\) | 26.0000 | − | 45.0333i | 1.03259 | − | 1.78850i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 27.0000 | − | 15.5885i | 1.07062 | − | 0.618123i | ||||
\(637\) | −0.696152 | + | 10.7942i | −0.0275826 | + | 0.427683i | ||||
\(638\) | 24.0000 | 0.950169 | ||||||||
\(639\) | 25.9808 | − | 15.0000i | 1.02778 | − | 0.593391i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.00000 | + | 5.19615i | 0.118493 | + | 0.205236i | 0.919171 | − | 0.393860i | \(-0.128860\pi\) |
−0.800678 | + | 0.599095i | \(0.795527\pi\) | |||||||
\(642\) | −58.8897 | −2.32419 | ||||||||
\(643\) | 27.7128 | + | 16.0000i | 1.09289 | + | 0.630978i | 0.934344 | − | 0.356374i | \(-0.115987\pi\) |
0.158543 | + | 0.987352i | \(0.449320\pi\) | |||||||
\(644\) | −3.46410 | − | 2.00000i | −0.136505 | − | 0.0788110i | ||||
\(645\) | −4.33013 | + | 7.50000i | −0.170499 | + | 0.295312i | ||||
\(646\) | 8.00000 | + | 13.8564i | 0.314756 | + | 0.545173i | ||||
\(647\) | −17.0000 | −0.668339 | −0.334169 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334169 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.0000 | 1.41312 | ||||||||
\(650\) | −7.19615 | − | 0.464102i | −0.282256 | − | 0.0182036i | ||||
\(651\) | −24.0000 | − | 13.8564i | −0.940634 | − | 0.543075i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.0000 | + | 29.4449i | −0.665261 | + | 1.15227i | 0.313953 | + | 0.949439i | \(0.398347\pi\) |
−0.979214 | + | 0.202828i | \(0.934987\pi\) | |||||||
\(654\) | 69.2820i | 2.70914i | ||||||||
\(655\) | 12.9904 | − | 7.50000i | 0.507576 | − | 0.293049i | ||||
\(656\) | 8.00000i | 0.312348i | ||||||||
\(657\) | −10.3923 | + | 6.00000i | −0.405442 | + | 0.234082i | ||||
\(658\) | 40.0000i | 1.55936i | ||||||||
\(659\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(660\) | −18.0000 | + | 10.3923i | −0.700649 | + | 0.404520i | ||||
\(661\) | −1.73205 | − | 1.00000i | −0.0673690 | − | 0.0388955i | 0.465937 | − | 0.884818i | \(-0.345717\pi\) |
−0.533306 | + | 0.845922i | \(0.679051\pi\) | |||||||
\(662\) | 8.00000 | − | 13.8564i | 0.310929 | − | 0.538545i | ||||
\(663\) | −6.23205 | − | 0.401924i | −0.242033 | − | 0.0156094i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000i | 0.620453i | ||||||||
\(666\) | −6.00000 | + | 10.3923i | −0.232495 | + | 0.402694i | ||||
\(667\) | 2.00000 | 0.0774403 | ||||||||
\(668\) | 3.46410 | − | 2.00000i | 0.134030 | − | 0.0773823i | ||||
\(669\) | 24.2487 | 0.937509 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.9808 | + | 15.0000i | 1.00298 | + | 0.579069i | ||||
\(672\) | 24.0000 | + | 13.8564i | 0.925820 | + | 0.534522i | ||||
\(673\) | −15.5000 | − | 26.8468i | −0.597481 | − | 1.03487i | −0.993192 | − | 0.116492i | \(-0.962835\pi\) |
0.395711 | − | 0.918375i | \(-0.370498\pi\) | |||||||
\(674\) | − | 6.00000i | − | 0.231111i | ||||||
\(675\) | −4.50000 | + | 2.59808i | −0.173205 | + | 0.100000i | ||||
\(676\) | −10.0000 | − | 24.0000i | −0.384615 | − | 0.923077i | ||||
\(677\) | 3.00000 | + | 5.19615i | 0.115299 | + | 0.199704i | 0.917899 | − | 0.396813i | \(-0.129884\pi\) |
−0.802600 | + | 0.596518i | \(0.796551\pi\) | |||||||
\(678\) | 32.9090 | − | 57.0000i | 1.26386 | − | 2.18907i | ||||
\(679\) | −10.0000 | + | 17.3205i | −0.383765 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −83.1384 | + | 48.0000i | −3.18354 | + | 1.83801i | ||||
\(683\) | − | 34.0000i | − | 1.30097i | −0.759517 | − | 0.650487i | \(-0.774565\pi\) | ||
0.759517 | − | 0.650487i | \(-0.225435\pi\) | |||||||
\(684\) | 48.0000i | 1.83533i | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 20.0000 | + | 34.6410i | 0.763604 | + | 1.32260i | ||||
\(687\) | −22.5167 | − | 39.0000i | −0.859064 | − | 1.48794i | ||||
\(688\) | 10.0000 | − | 17.3205i | 0.381246 | − | 0.660338i | ||||
\(689\) | 29.0885 | − | 14.3827i | 1.10818 | − | 0.547937i | ||||
\(690\) | −3.00000 | + | 1.73205i | −0.114208 | + | 0.0659380i | ||||
\(691\) | −8.66025 | + | 5.00000i | −0.329452 | + | 0.190209i | −0.655598 | − | 0.755110i | \(-0.727583\pi\) |
0.326146 | + | 0.945319i | \(0.394250\pi\) | |||||||
\(692\) | −26.0000 | −0.988372 | ||||||||
\(693\) | −36.0000 | −1.36753 | ||||||||
\(694\) | 10.0000i | 0.379595i | ||||||||
\(695\) | −9.52628 | + | 5.50000i | −0.361352 | + | 0.208627i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.73205 | − | 1.00000i | −0.0656061 | − | 0.0378777i | ||||
\(698\) | 2.00000 | − | 3.46410i | 0.0757011 | − | 0.131118i | ||||
\(699\) | −28.5000 | − | 16.4545i | −1.07797 | − | 0.622366i | ||||
\(700\) | −3.46410 | + | 2.00000i | −0.130931 | + | 0.0755929i | ||||
\(701\) | −39.0000 | −1.47301 | −0.736505 | − | 0.676432i | \(-0.763525\pi\) | ||||
−0.736505 | + | 0.676432i | \(0.763525\pi\) | |||||||
\(702\) | −31.1769 | − | 20.7846i | −1.17670 | − | 0.784465i | ||||
\(703\) | 16.0000 | 0.603451 | ||||||||
\(704\) | 41.5692 | − | 24.0000i | 1.56670 | − | 0.904534i | ||||
\(705\) | 15.0000 | + | 8.66025i | 0.564933 | + | 0.326164i | ||||
\(706\) | 6.00000 | − | 10.3923i | 0.225813 | − | 0.391120i | ||||
\(707\) | 12.1244 | + | 7.00000i | 0.455983 | + | 0.263262i | ||||
\(708\) | 20.7846 | 0.781133 | ||||||||
\(709\) | −6.92820 | + | 4.00000i | −0.260194 | + | 0.150223i | −0.624423 | − | 0.781086i | \(-0.714666\pi\) |
0.364229 | + | 0.931309i | \(0.381333\pi\) | |||||||
\(710\) | − | 20.0000i | − | 0.750587i | ||||||
\(711\) | 1.50000 | − | 2.59808i | 0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.92820 | + | 4.00000i | −0.259463 | + | 0.149801i | ||||
\(714\) | −6.00000 | + | 3.46410i | −0.224544 | + | 0.129641i | ||||
\(715\) | −19.3923 | + | 9.58846i | −0.725231 | + | 0.358588i | ||||
\(716\) | 15.0000 | − | 25.9808i | 0.560576 | − | 0.970947i | ||||
\(717\) | −17.3205 | − | 30.0000i | −0.646846 | − | 1.12037i | ||||
\(718\) | −10.0000 | − | 17.3205i | −0.373197 | − | 0.646396i | ||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 10.3923 | − | 6.00000i | 0.387298 | − | 0.223607i | ||||
\(721\) | − | 32.0000i | − | 1.19174i | ||||||
\(722\) | 77.9423 | − | 45.0000i | 2.90071 | − | 1.67473i | ||||
\(723\) | −51.9615 | −1.93247 | ||||||||
\(724\) | 21.0000 | − | 36.3731i | 0.780459 | − | 1.35179i | ||||
\(725\) | 1.00000 | − | 1.73205i | 0.0371391 | − | 0.0643268i | ||||
\(726\) | −43.3013 | + | 75.0000i | −1.60706 | + | 2.78351i | ||||
\(727\) | 18.5000 | + | 32.0429i | 0.686127 | + | 1.18841i | 0.973081 | + | 0.230463i | \(0.0740239\pi\) |
−0.286954 | + | 0.957944i | \(0.592643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 8.00000i | 0.296093i | ||||||||
\(731\) | 2.50000 | + | 4.33013i | 0.0924658 | + | 0.160156i | ||||
\(732\) | 15.0000 | + | 8.66025i | 0.554416 | + | 0.320092i | ||||
\(733\) | −20.7846 | − | 12.0000i | −0.767697 | − | 0.443230i | 0.0643554 | − | 0.997927i | \(-0.479501\pi\) |
−0.832052 | + | 0.554697i | \(0.812834\pi\) | |||||||
\(734\) | 36.3731 | + | 21.0000i | 1.34255 | + | 0.775124i | ||||
\(735\) | 5.19615 | 0.191663 | ||||||||
\(736\) | 6.92820 | − | 4.00000i | 0.255377 | − | 0.147442i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.00000 | − | 10.3923i | −0.220863 | − | 0.382546i | ||||
\(739\) | 12.0000i | 0.441427i | 0.975339 | + | 0.220714i | \(0.0708386\pi\) | ||||
−0.975339 | + | 0.220714i | \(0.929161\pi\) | |||||||
\(740\) | 2.00000 | + | 3.46410i | 0.0735215 | + | 0.127343i | ||||
\(741\) | −3.21539 | + | 49.8564i | −0.118120 | + | 1.83152i | ||||
\(742\) | 18.0000 | − | 31.1769i | 0.660801 | − | 1.14454i | ||||
\(743\) | 38.1051 | + | 22.0000i | 1.39794 | + | 0.807102i | 0.994177 | − | 0.107761i | \(-0.0343682\pi\) |
0.403764 | + | 0.914863i | \(0.367702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.00000 | − | 1.73205i | −0.0366372 | − | 0.0634574i | ||||
\(746\) | − | 38.0000i | − | 1.39128i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.0000i | 0.438763i | ||||||||
\(749\) | −29.4449 | + | 17.0000i | −1.07589 | + | 0.621166i | ||||
\(750\) | 3.46410i | 0.126491i | ||||||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | −34.6410 | − | 20.0000i | −1.26323 | − | 0.729325i | ||||
\(753\) | 4.50000 | + | 2.59808i | 0.163989 | + | 0.0946792i | ||||
\(754\) | 14.3923 | + | 0.928203i | 0.524137 | + | 0.0338032i | ||||
\(755\) | 4.00000 | 0.145575 | ||||||||
\(756\) | −20.7846 | −0.755929 | ||||||||
\(757\) | 29.0000 | 1.05402 | 0.527011 | − | 0.849858i | \(-0.323312\pi\) | ||||
0.527011 | + | 0.849858i | \(0.323312\pi\) | |||||||
\(758\) | 18.0000 | + | 31.1769i | 0.653789 | + | 1.13240i | ||||
\(759\) | −5.19615 | + | 9.00000i | −0.188608 | + | 0.326679i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.8372 | − | 23.0000i | −1.44410 | − | 0.833749i | −0.445977 | − | 0.895045i | \(-0.647144\pi\) |
−0.998120 | + | 0.0612953i | \(0.980477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0000 | + | 34.6410i | 0.724049 | + | 1.25409i | ||||
\(764\) | −38.0000 | −1.37479 | ||||||||
\(765\) | 3.00000i | 0.108465i | ||||||||
\(766\) | −52.0000 | −1.87884 | ||||||||
\(767\) | 21.5885 | + | 1.39230i | 0.779514 | + | 0.0502732i | ||||
\(768\) | −24.0000 | + | 13.8564i | −0.866025 | + | 0.500000i | ||||
\(769\) | −34.6410 | − | 20.0000i | −1.24919 | − | 0.721218i | −0.278240 | − | 0.960512i | \(-0.589751\pi\) |
−0.970947 | + | 0.239293i | \(0.923084\pi\) | |||||||
\(770\) | −12.0000 | + | 20.7846i | −0.432450 | + | 0.749025i | ||||
\(771\) | 4.50000 | − | 2.59808i | 0.162064 | − | 0.0935674i | ||||
\(772\) | −6.92820 | + | 4.00000i | −0.249351 | + | 0.143963i | ||||
\(773\) | − | 18.0000i | − | 0.647415i | −0.946157 | − | 0.323708i | \(-0.895071\pi\) | ||
0.946157 | − | 0.323708i | \(-0.104929\pi\) | |||||||
\(774\) | 30.0000i | 1.07833i | ||||||||
\(775\) | 8.00000i | 0.287368i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.92820i | 0.248548i | ||||||||
\(778\) | −39.8372 | − | 23.0000i | −1.42823 | − | 0.824590i | ||||
\(779\) | −8.00000 | + | 13.8564i | −0.286630 | + | 0.496457i | ||||
\(780\) | −11.1962 | + | 5.53590i | −0.400887 | + | 0.198217i | ||||
\(781\) | −30.0000 | − | 51.9615i | −1.07348 | − | 1.85933i | ||||
\(782\) | 2.00000i | 0.0715199i | ||||||||
\(783\) | 9.00000 | − | 5.19615i | 0.321634 | − | 0.185695i | ||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | −11.2583 | + | 6.50000i | −0.401827 | + | 0.231995i | ||||
\(786\) | 25.9808 | − | 45.0000i | 0.926703 | − | 1.60510i | ||||
\(787\) | 1.73205 | + | 1.00000i | 0.0617409 | + | 0.0356462i | 0.530553 | − | 0.847652i | \(-0.321984\pi\) |
−0.468812 | + | 0.883298i | \(0.655318\pi\) | |||||||
\(788\) | −34.6410 | − | 20.0000i | −1.23404 | − | 0.712470i | ||||
\(789\) | − | 15.5885i | − | 0.554964i | ||||||
\(790\) | −1.00000 | − | 1.73205i | −0.0355784 | − | 0.0616236i | ||||
\(791\) | − | 38.0000i | − | 1.35112i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.0000 | + | 10.0000i | 0.532666 | + | 0.355110i | ||||
\(794\) | 28.0000 | + | 48.4974i | 0.993683 | + | 1.72111i | ||||
\(795\) | −7.79423 | − | 13.5000i | −0.276433 | − | 0.478796i | ||||
\(796\) | 3.00000 | − | 5.19615i | 0.106332 | − | 0.184173i | ||||
\(797\) | −17.0000 | + | 29.4449i | −0.602171 | + | 1.04299i | 0.390321 | + | 0.920679i | \(0.372364\pi\) |
−0.992492 | + | 0.122312i | \(0.960969\pi\) | |||||||
\(798\) | 27.7128 | + | 48.0000i | 0.981023 | + | 1.69918i | ||||
\(799\) | 8.66025 | − | 5.00000i | 0.306378 | − | 0.176887i | ||||
\(800\) | − | 8.00000i | − | 0.282843i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 64.0000 | 2.25992 | ||||||||
\(803\) | 12.0000 | + | 20.7846i | 0.423471 | + | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00000 | + | 1.73205i | −0.0352454 | + | 0.0610468i | ||||
\(806\) | −51.7128 | + | 25.5692i | −1.82151 | + | 0.900637i | ||||
\(807\) | −21.0000 | − | 12.1244i | −0.739235 | − | 0.426798i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.0000 | 1.58212 | 0.791058 | − | 0.611741i | \(-0.209531\pi\) | ||||
0.791058 | + | 0.611741i | \(0.209531\pi\) | |||||||
\(810\) | −9.00000 | + | 15.5885i | −0.316228 | + | 0.547723i | ||||
\(811\) | − | 32.0000i | − | 1.12367i | −0.827249 | − | 0.561836i | \(-0.810095\pi\) | ||
0.827249 | − | 0.561836i | \(-0.189905\pi\) | |||||||
\(812\) | 6.92820 | − | 4.00000i | 0.243132 | − | 0.140372i | ||||
\(813\) | −24.2487 | + | 42.0000i | −0.850439 | + | 1.47300i | ||||
\(814\) | 20.7846 | + | 12.0000i | 0.728500 | + | 0.420600i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 6.92820i | − | 0.242536i | ||||||
\(817\) | 34.6410 | − | 20.0000i | 1.21194 | − | 0.699711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.5885 | − | 1.39230i | −0.754362 | − | 0.0486511i | ||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | −15.5885 | + | 9.00000i | −0.544041 | + | 0.314102i | −0.746715 | − | 0.665144i | \(-0.768370\pi\) |
0.202674 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(822\) | 18.0000 | − | 10.3923i | 0.627822 | − | 0.362473i | ||||
\(823\) | 16.5000 | − | 28.5788i | 0.575154 | − | 0.996196i | −0.420871 | − | 0.907120i | \(-0.638276\pi\) |
0.996025 | − | 0.0890752i | \(-0.0283911\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.19615 | + | 9.00000i | 0.180907 | + | 0.313340i | ||||
\(826\) | 20.7846 | − | 12.0000i | 0.723189 | − | 0.417533i | ||||
\(827\) | − | 4.00000i | − | 0.139094i | −0.997579 | − | 0.0695468i | \(-0.977845\pi\) | ||
0.997579 | − | 0.0695468i | \(-0.0221553\pi\) | |||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 17.3205i | − | 0.600842i | ||||||
\(832\) | 25.8564 | − | 12.7846i | 0.896410 | − | 0.443227i | ||||
\(833\) | 1.50000 | − | 2.59808i | 0.0519719 | − | 0.0900180i | ||||
\(834\) | −19.0526 | + | 33.0000i | −0.659736 | + | 1.14270i | ||||
\(835\) | −1.00000 | − | 1.73205i | −0.0346064 | − | 0.0599401i | ||||
\(836\) | 96.0000 | 3.32023 | ||||||||
\(837\) | −20.7846 | + | 36.0000i | −0.718421 | + | 1.24434i | ||||
\(838\) | − | 30.0000i | − | 1.03633i | ||||||
\(839\) | 31.1769 | − | 18.0000i | 1.07635 | − | 0.621429i | 0.146438 | − | 0.989220i | \(-0.453219\pi\) |
0.929909 | + | 0.367791i | \(0.119886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | −8.00000 | + | 13.8564i | −0.275698 | + | 0.477523i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.0000 | − | 25.9808i | −0.516321 | − | 0.894295i | ||||
\(845\) | −12.0000 | + | 5.00000i | −0.412813 | + | 0.172005i | ||||
\(846\) | 60.0000 | 2.06284 | ||||||||
\(847\) | 50.0000i | 1.71802i | ||||||||
\(848\) | 18.0000 | + | 31.1769i | 0.618123 | + | 1.07062i | ||||
\(849\) | 46.5000 | − | 26.8468i | 1.59588 | − | 0.921379i | ||||
\(850\) | 1.73205 | + | 1.00000i | 0.0594089 | + | 0.0342997i | ||||
\(851\) | 1.73205 | + | 1.00000i | 0.0593739 | + | 0.0342796i | ||||
\(852\) | −17.3205 | − | 30.0000i | −0.593391 | − | 1.02778i | ||||
\(853\) | 15.5885 | − | 9.00000i | 0.533739 | − | 0.308154i | −0.208799 | − | 0.977959i | \(-0.566955\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(854\) | 20.0000 | 0.684386 | ||||||||
\(855\) | 24.0000 | 0.820783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.00000 | + | 8.66025i | 0.170797 | + | 0.295829i | 0.938699 | − | 0.344739i | \(-0.112033\pi\) |
−0.767902 | + | 0.640567i | \(0.778699\pi\) | |||||||
\(858\) | −41.5692 | + | 62.3538i | −1.41915 | + | 2.12872i | ||||
\(859\) | 24.5000 | − | 42.4352i | 0.835929 | − | 1.44787i | −0.0573424 | − | 0.998355i | \(-0.518263\pi\) |
0.893272 | − | 0.449517i | \(-0.148404\pi\) | |||||||
\(860\) | 8.66025 | + | 5.00000i | 0.295312 | + | 0.170499i | ||||
\(861\) | −6.00000 | − | 3.46410i | −0.204479 | − | 0.118056i | ||||
\(862\) | 24.0000 | + | 41.5692i | 0.817443 | + | 1.41585i | ||||
\(863\) | 18.0000i | 0.612727i | 0.951915 | + | 0.306364i | \(0.0991123\pi\) | ||||
−0.951915 | + | 0.306364i | \(0.900888\pi\) | |||||||
\(864\) | 20.7846 | − | 36.0000i | 0.707107 | − | 1.22474i | ||||
\(865\) | 13.0000i | 0.442013i | ||||||||
\(866\) | −8.66025 | + | 5.00000i | −0.294287 | + | 0.169907i | ||||
\(867\) | −24.0000 | − | 13.8564i | −0.815083 | − | 0.470588i | ||||
\(868\) | −16.0000 | + | 27.7128i | −0.543075 | + | 0.940634i | ||||
\(869\) | −5.19615 | − | 3.00000i | −0.176267 | − | 0.101768i | ||||
\(870\) | − | 6.92820i | − | 0.234888i | ||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.9808 | + | 15.0000i | 0.879316 | + | 0.507673i | ||||
\(874\) | 16.0000 | 0.541208 | ||||||||
\(875\) | 1.00000 | + | 1.73205i | 0.0338062 | + | 0.0585540i | ||||
\(876\) | 6.92820 | + | 12.0000i | 0.234082 | + | 0.405442i | ||||
\(877\) | −27.7128 | − | 16.0000i | −0.935795 | − | 0.540282i | −0.0471555 | − | 0.998888i | \(-0.515016\pi\) |
−0.888640 | + | 0.458606i | \(0.848349\pi\) | |||||||
\(878\) | 43.3013 | + | 25.0000i | 1.46135 | + | 0.843709i | ||||
\(879\) | −5.19615 | − | 9.00000i | −0.175262 | − | 0.303562i | ||||
\(880\) | −12.0000 | − | 20.7846i | −0.404520 | − | 0.700649i | ||||
\(881\) | 27.0000 | 0.909653 | 0.454827 | − | 0.890580i | \(-0.349701\pi\) | ||||
0.454827 | + | 0.890580i | \(0.349701\pi\) | |||||||
\(882\) | 15.5885 | − | 9.00000i | 0.524891 | − | 0.303046i | ||||
\(883\) | 52.0000 | 1.74994 | 0.874970 | − | 0.484178i | \(-0.160881\pi\) | ||||
0.874970 | + | 0.484178i | \(0.160881\pi\) | |||||||
\(884\) | −0.464102 | + | 7.19615i | −0.0156094 | + | 0.242033i | ||||
\(885\) | − | 10.3923i | − | 0.349334i | ||||||
\(886\) | 36.3731 | + | 21.0000i | 1.22198 | + | 0.705509i | ||||
\(887\) | 12.5000 | − | 21.6506i | 0.419709 | − | 0.726957i | −0.576201 | − | 0.817308i | \(-0.695465\pi\) |
0.995910 | + | 0.0903508i | \(0.0287988\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54.0000i | 1.80907i | ||||||||
\(892\) | − | 28.0000i | − | 0.937509i | ||||||
\(893\) | −40.0000 | − | 69.2820i | −1.33855 | − | 2.31843i | ||||
\(894\) | −6.00000 | − | 3.46410i | −0.200670 | − | 0.115857i | ||||
\(895\) | −12.9904 | − | 7.50000i | −0.434221 | − | 0.250697i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.46410 | + | 5.19615i | −0.115663 | + | 0.173494i | ||||
\(898\) | −36.0000 | − | 62.3538i | −1.20134 | − | 2.08077i | ||||
\(899\) | − | 16.0000i | − | 0.533630i | ||||||
\(900\) | 3.00000 | + | 5.19615i | 0.100000 | + | 0.173205i | ||||
\(901\) | −9.00000 | −0.299833 | ||||||||
\(902\) | −20.7846 | + | 12.0000i | −0.692052 | + | 0.399556i | ||||
\(903\) | 8.66025 | + | 15.0000i | 0.288195 | + | 0.499169i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.1865 | − | 10.5000i | −0.604541 | − | 0.349032i | ||||
\(906\) | 12.0000 | − | 6.92820i | 0.398673 | − | 0.230174i | ||||
\(907\) | 11.5000 | + | 19.9186i | 0.381851 | + | 0.661386i | 0.991327 | − | 0.131419i | \(-0.0419533\pi\) |
−0.609476 | + | 0.792805i | \(0.708620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.5000 | − | 18.1865i | 0.348263 | − | 0.603209i | ||||
\(910\) | −8.00000 | + | 12.0000i | −0.265197 | + | 0.397796i | ||||
\(911\) | −11.5000 | − | 19.9186i | −0.381012 | − | 0.659932i | 0.610195 | − | 0.792251i | \(-0.291091\pi\) |
−0.991207 | + | 0.132319i | \(0.957758\pi\) | |||||||
\(912\) | −55.4256 | −1.83533 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −8.00000 | + | 13.8564i | −0.264616 | + | 0.458329i | ||||
\(915\) | 4.33013 | − | 7.50000i | 0.143150 | − | 0.247942i | ||||
\(916\) | −45.0333 | + | 26.0000i | −1.48794 | + | 0.859064i | ||||
\(917\) | − | 30.0000i | − | 0.990687i | ||||||
\(918\) | 5.19615 | + | 9.00000i | 0.171499 | + | 0.297044i | ||||
\(919\) | −5.00000 | −0.164935 | −0.0824674 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824674 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.46410 | − | 6.00000i | 0.114146 | − | 0.197707i | ||||
\(922\) | −2.00000 | + | 3.46410i | −0.0658665 | + | 0.114084i | ||||
\(923\) | −15.9808 | − | 32.3205i | −0.526013 | − | 1.06384i | ||||
\(924\) | 41.5692i | 1.36753i | ||||||||
\(925\) | 1.73205 | − | 1.00000i | 0.0569495 | − | 0.0328798i | ||||
\(926\) | −44.0000 | −1.44593 | ||||||||
\(927\) | −48.0000 | −1.57653 | ||||||||
\(928\) | 16.0000i | 0.525226i | ||||||||
\(929\) | 3.46410 | − | 2.00000i | 0.113653 | − | 0.0656179i | −0.442096 | − | 0.896968i | \(-0.645765\pi\) |
0.555749 | + | 0.831350i | \(0.312431\pi\) | |||||||
\(930\) | 13.8564 | + | 24.0000i | 0.454369 | + | 0.786991i | ||||
\(931\) | −20.7846 | − | 12.0000i | −0.681188 | − | 0.393284i | ||||
\(932\) | −19.0000 | + | 32.9090i | −0.622366 | + | 1.07797i | ||||
\(933\) | 12.0000 | − | 6.92820i | 0.392862 | − | 0.226819i | ||||
\(934\) | 36.3731 | − | 21.0000i | 1.19016 | − | 0.687141i | ||||
\(935\) | 6.00000 | 0.196221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0000 | 0.555366 | 0.277683 | − | 0.960673i | \(-0.410434\pi\) | ||||
0.277683 | + | 0.960673i | \(0.410434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.3205i | 0.565233i | ||||||||
\(940\) | 10.0000 | − | 17.3205i | 0.326164 | − | 0.564933i | ||||
\(941\) | 24.2487 | + | 14.0000i | 0.790485 | + | 0.456387i | 0.840133 | − | 0.542380i | \(-0.182477\pi\) |
−0.0496480 | + | 0.998767i | \(0.515810\pi\) | |||||||
\(942\) | −22.5167 | + | 39.0000i | −0.733632 | + | 1.27069i | ||||
\(943\) | −1.73205 | + | 1.00000i | −0.0564033 | + | 0.0325645i | ||||
\(944\) | 24.0000i | 0.781133i | ||||||||
\(945\) | 10.3923i | 0.338062i | ||||||||
\(946\) | 60.0000 | 1.95077 | ||||||||
\(947\) | 25.9808 | − | 15.0000i | 0.844261 | − | 0.487435i | −0.0144491 | − | 0.999896i | \(-0.504599\pi\) |
0.858710 | + | 0.512461i | \(0.171266\pi\) | |||||||
\(948\) | −3.00000 | − | 1.73205i | −0.0974355 | − | 0.0562544i | ||||
\(949\) | 6.39230 | + | 12.9282i | 0.207503 | + | 0.419667i | ||||
\(950\) | 8.00000 | − | 13.8564i | 0.259554 | − | 0.449561i | ||||
\(951\) | −45.0333 | −1.46031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | −46.7654 | − | 27.0000i | −1.51408 | − | 0.874157i | ||||
\(955\) | 19.0000i | 0.614826i | ||||||||
\(956\) | −34.6410 | + | 20.0000i | −1.12037 | + | 0.646846i | ||||
\(957\) | −10.3923 | − | 18.0000i | −0.335936 | − | 0.581857i | ||||
\(958\) | −18.0000 | + | 31.1769i | −0.581554 | + | 1.00728i | ||||
\(959\) | 6.00000 | − | 10.3923i | 0.193750 | − | 0.335585i | ||||
\(960\) | −6.92820 | − | 12.0000i | −0.223607 | − | 0.387298i | ||||
\(961\) | 16.5000 | + | 28.5788i | 0.532258 | + | 0.921898i | ||||
\(962\) | 12.0000 | + | 8.00000i | 0.386896 | + | 0.257930i | ||||
\(963\) | 25.5000 | + | 44.1673i | 0.821726 | + | 1.42327i | ||||
\(964\) | 60.0000i | 1.93247i | ||||||||
\(965\) | 2.00000 | + | 3.46410i | 0.0643823 | + | 0.111513i | ||||
\(966\) | 6.92820i | 0.222911i | ||||||||
\(967\) | 17.3205 | + | 10.0000i | 0.556990 | + | 0.321578i | 0.751936 | − | 0.659236i | \(-0.229120\pi\) |
−0.194946 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.92820 | − | 12.0000i | 0.222566 | − | 0.385496i | ||||
\(970\) | 17.3205 | − | 10.0000i | 0.556128 | − | 0.321081i | ||||
\(971\) | 60.0000 | 1.92549 | 0.962746 | − | 0.270408i | \(-0.0871586\pi\) | ||||
0.962746 | + | 0.270408i | \(0.0871586\pi\) | |||||||
\(972\) | 31.1769i | 1.00000i | ||||||||
\(973\) | 22.0000i | 0.705288i | ||||||||
\(974\) | −24.0000 | − | 41.5692i | −0.769010 | − | 1.33196i | ||||
\(975\) | 2.76795 | + | 5.59808i | 0.0886453 | + | 0.179282i | ||||
\(976\) | −10.0000 | + | 17.3205i | −0.320092 | + | 0.554416i | ||||
\(977\) | 17.3205 | + | 10.0000i | 0.554132 | + | 0.319928i | 0.750787 | − | 0.660544i | \(-0.229674\pi\) |
−0.196655 | + | 0.980473i | \(0.563008\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 6.00000i | − | 0.191663i | ||||||
\(981\) | 51.9615 | − | 30.0000i | 1.65900 | − | 0.957826i | ||||
\(982\) | 32.0000i | 1.02116i | ||||||||
\(983\) | 17.3205 | − | 10.0000i | 0.552438 | − | 0.318950i | −0.197666 | − | 0.980269i | \(-0.563336\pi\) |
0.750105 | + | 0.661319i | \(0.230003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | + | 17.3205i | −0.318626 | + | 0.551877i | ||||
\(986\) | −3.46410 | − | 2.00000i | −0.110319 | − | 0.0636930i | ||||
\(987\) | 30.0000 | − | 17.3205i | 0.954911 | − | 0.551318i | ||||
\(988\) | 57.5692 | + | 3.71281i | 1.83152 | + | 0.118120i | ||||
\(989\) | 5.00000 | 0.158991 | ||||||||
\(990\) | 31.1769 | + | 18.0000i | 0.990867 | + | 0.572078i | ||||
\(991\) | 25.0000 | 0.794151 | 0.397076 | − | 0.917786i | \(-0.370025\pi\) | ||||
0.397076 | + | 0.917786i | \(0.370025\pi\) | |||||||
\(992\) | −32.0000 | − | 55.4256i | −1.01600 | − | 1.75977i | ||||
\(993\) | −13.8564 | −0.439720 | ||||||||
\(994\) | −34.6410 | − | 20.0000i | −1.09875 | − | 0.634361i | ||||
\(995\) | −2.59808 | − | 1.50000i | −0.0823646 | − | 0.0475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5000 | − | 49.3634i | −0.902604 | − | 1.56336i | −0.824101 | − | 0.566442i | \(-0.808319\pi\) |
−0.0785026 | − | 0.996914i | \(-0.525014\pi\) | |||||||
\(998\) | −56.0000 | −1.77265 | ||||||||
\(999\) | 10.3923 | 0.328798 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 585.2.bt.a.571.1 | yes | 4 | |
9.7 | even | 3 | inner | 585.2.bt.a.376.2 | yes | 4 | |
13.12 | even | 2 | inner | 585.2.bt.a.571.2 | yes | 4 | |
117.25 | even | 6 | inner | 585.2.bt.a.376.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.a.376.1 | ✓ | 4 | 117.25 | even | 6 | inner | |
585.2.bt.a.376.2 | yes | 4 | 9.7 | even | 3 | inner | |
585.2.bt.a.571.1 | yes | 4 | 1.1 | even | 1 | trivial | |
585.2.bt.a.571.2 | yes | 4 | 13.12 | even | 2 | inner |