Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(37,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 181.8 | ||
Root | \(1.05026 + 0.947078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.181 |
Dual form | 216.2.n.b.37.8 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34532 | + | 0.436011i | 0.951287 | + | 0.308307i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.61979 | + | 1.17315i | 0.809894 | + | 0.586576i | ||||
\(5\) | 0.602794 | − | 0.348023i | 0.269578 | − | 0.155641i | −0.359118 | − | 0.933292i | \(-0.616922\pi\) |
0.628696 | + | 0.777651i | \(0.283589\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.795065 | − | 1.37709i | 0.300506 | − | 0.520492i | −0.675745 | − | 0.737136i | \(-0.736178\pi\) |
0.976251 | + | 0.216644i | \(0.0695111\pi\) | |||||||
\(8\) | 1.66763 | + | 2.28452i | 0.589596 | + | 0.807698i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.962695 | − | 0.205379i | 0.304431 | − | 0.0649464i | ||||
\(11\) | −2.37222 | − | 1.36960i | −0.715252 | − | 0.412951i | 0.0977506 | − | 0.995211i | \(-0.468835\pi\) |
−0.813003 | + | 0.582260i | \(0.802169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.76780 | + | 2.75269i | −1.32235 | + | 0.763460i | −0.984103 | − | 0.177597i | \(-0.943168\pi\) |
−0.338248 | + | 0.941057i | \(0.609834\pi\) | |||||||
\(14\) | 1.67005 | − | 1.50598i | 0.446339 | − | 0.402489i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.24743 | + | 3.80052i | 0.311857 | + | 0.950129i | ||||
\(17\) | 5.65175 | 1.37075 | 0.685375 | − | 0.728190i | \(-0.259638\pi\) | ||||
0.685375 | + | 0.728190i | \(0.259638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.963328i | 0.221003i | 0.993876 | + | 0.110501i | \(0.0352457\pi\) | ||||
−0.993876 | + | 0.110501i | \(0.964754\pi\) | |||||||
\(20\) | 1.38468 | + | 0.143445i | 0.309625 | + | 0.0320753i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.59424 | − | 2.87688i | −0.553095 | − | 0.613352i | ||||
\(23\) | −3.28857 | − | 5.69597i | −0.685714 | − | 1.18769i | −0.973212 | − | 0.229910i | \(-0.926157\pi\) |
0.287498 | − | 0.957781i | \(-0.407177\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.25776 | + | 3.91055i | −0.451552 | + | 0.782111i | ||||
\(26\) | −7.61444 | + | 1.62444i | −1.49332 | + | 0.318580i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.90338 | − | 1.29787i | 0.548686 | − | 0.245274i | ||||
\(29\) | −2.85076 | − | 1.64589i | −0.529373 | − | 0.305634i | 0.211388 | − | 0.977402i | \(-0.432202\pi\) |
−0.740761 | + | 0.671768i | \(0.765535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.69844 | − | 6.40589i | −0.664259 | − | 1.15053i | −0.979486 | − | 0.201514i | \(-0.935414\pi\) |
0.315226 | − | 0.949017i | \(-0.397920\pi\) | |||||||
\(32\) | 0.0211236 | + | 5.65681i | 0.00373416 | + | 0.999993i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.60343 | + | 2.46423i | 1.30398 | + | 0.422611i | ||||
\(35\) | − | 1.10680i | − | 0.187084i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.25538i | − | 1.02838i | −0.857677 | − | 0.514189i | \(-0.828093\pi\) | ||
0.857677 | − | 0.514189i | \(-0.171907\pi\) | |||||||
\(38\) | −0.420022 | + | 1.29599i | −0.0681366 | + | 0.210237i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.80030 | + | 0.796718i | 0.284653 | + | 0.125972i | ||||
\(41\) | 0.931886 | + | 1.61407i | 0.145536 | + | 0.252076i | 0.929573 | − | 0.368639i | \(-0.120176\pi\) |
−0.784037 | + | 0.620714i | \(0.786843\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.99838 | − | 1.73111i | −0.457248 | − | 0.263992i | 0.253638 | − | 0.967299i | \(-0.418373\pi\) |
−0.710886 | + | 0.703307i | \(0.751706\pi\) | |||||||
\(44\) | −2.23574 | − | 5.00145i | −0.337051 | − | 0.753996i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.94068 | − | 9.09677i | −0.286138 | − | 1.34125i | ||||
\(47\) | −3.85668 | + | 6.67997i | −0.562555 | + | 0.974374i | 0.434717 | + | 0.900567i | \(0.356848\pi\) |
−0.997273 | + | 0.0738070i | \(0.976485\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.23574 | + | 3.87242i | 0.319392 | + | 0.553203i | ||||
\(50\) | −4.74246 | + | 4.27655i | −0.670685 | + | 0.604795i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.9522 | − | 1.13458i | −1.51879 | − | 0.157338i | ||||
\(53\) | 2.54179i | 0.349141i | 0.984645 | + | 0.174571i | \(0.0558537\pi\) | ||||
−0.984645 | + | 0.174571i | \(0.944146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.90662 | −0.257088 | ||||||||
\(56\) | 4.47186 | − | 0.480144i | 0.597578 | − | 0.0641619i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.11757 | − | 3.45722i | −0.409357 | − | 0.453955i | ||||
\(59\) | 4.62019 | − | 2.66747i | 0.601498 | − | 0.347275i | −0.168133 | − | 0.985764i | \(-0.553774\pi\) |
0.769631 | + | 0.638489i | \(0.220440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.93715 | + | 4.58252i | 1.01625 | + | 0.586731i | 0.913015 | − | 0.407926i | \(-0.133748\pi\) |
0.103233 | + | 0.994657i | \(0.467081\pi\) | |||||||
\(62\) | −2.18256 | − | 10.2305i | −0.277185 | − | 1.29928i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.43802 | + | 7.61945i | −0.304752 | + | 0.952432i | ||||
\(65\) | −1.91600 | + | 3.31861i | −0.237651 | + | 0.411623i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.95780 | − | 3.43974i | 0.727861 | − | 0.420231i | −0.0897783 | − | 0.995962i | \(-0.528616\pi\) |
0.817639 | + | 0.575731i | \(0.195283\pi\) | |||||||
\(68\) | 9.15463 | + | 6.63036i | 1.11016 | + | 0.804049i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.482579 | − | 1.48901i | 0.0576792 | − | 0.177971i | ||||
\(71\) | −3.68351 | −0.437153 | −0.218576 | − | 0.975820i | \(-0.570141\pi\) | ||||
−0.218576 | + | 0.975820i | \(0.570141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.83201 | 0.331461 | 0.165731 | − | 0.986171i | \(-0.447002\pi\) | ||||
0.165731 | + | 0.986171i | \(0.447002\pi\) | |||||||
\(74\) | 2.72742 | − | 8.41550i | 0.317056 | − | 0.978282i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.13013 | + | 1.56039i | −0.129635 | + | 0.178989i | ||||
\(77\) | −3.77214 | + | 2.17785i | −0.429875 | + | 0.248189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.87870 | − | 4.98605i | 0.323879 | − | 0.560975i | −0.657406 | − | 0.753537i | \(-0.728346\pi\) |
0.981285 | + | 0.192562i | \(0.0616797\pi\) | |||||||
\(80\) | 2.07461 | + | 1.85680i | 0.231948 | + | 0.207596i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.549933 | + | 2.57776i | 0.0607299 | + | 0.284666i | ||||
\(83\) | 5.74968 | + | 3.31958i | 0.631110 | + | 0.364371i | 0.781182 | − | 0.624304i | \(-0.214617\pi\) |
−0.150072 | + | 0.988675i | \(0.547951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.40684 | − | 1.96694i | 0.369524 | − | 0.213345i | ||||
\(86\) | −3.27900 | − | 3.63623i | −0.353584 | − | 0.392105i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.827111 | − | 7.70337i | −0.0881703 | − | 0.821182i | ||||
\(89\) | 2.98701 | 0.316622 | 0.158311 | − | 0.987389i | \(-0.449395\pi\) | ||||
0.158311 | + | 0.987389i | \(0.449395\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.75427i | 0.917697i | ||||||||
\(92\) | 1.35545 | − | 13.0843i | 0.141316 | − | 1.36413i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.10103 | + | 7.30516i | −0.835557 | + | 0.753470i | ||||
\(95\) | 0.335261 | + | 0.580689i | 0.0343970 | + | 0.0595774i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.24837 | + | 2.16224i | −0.126753 | + | 0.219543i | −0.922417 | − | 0.386196i | \(-0.873789\pi\) |
0.795664 | + | 0.605738i | \(0.207122\pi\) | |||||||
\(98\) | 1.31938 | + | 6.18447i | 0.133277 | + | 0.624726i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.24477 | + | 3.68557i | −0.824477 | + | 0.368557i | ||||
\(101\) | 8.22136 | + | 4.74661i | 0.818056 | + | 0.472305i | 0.849746 | − | 0.527193i | \(-0.176755\pi\) |
−0.0316896 | + | 0.999498i | \(0.510089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.37220 | + | 12.7690i | 0.726405 | + | 1.25817i | 0.958393 | + | 0.285451i | \(0.0921435\pi\) |
−0.231989 | + | 0.972719i | \(0.574523\pi\) | |||||||
\(104\) | −14.2395 | − | 6.30165i | −1.39630 | − | 0.617927i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.10825 | + | 3.41952i | −0.107643 | + | 0.332134i | ||||
\(107\) | 7.83384i | 0.757325i | 0.925535 | + | 0.378663i | \(0.123616\pi\) | ||||
−0.925535 | + | 0.378663i | \(0.876384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.242400i | 0.0232177i | 0.999933 | + | 0.0116089i | \(0.00369529\pi\) | ||||
−0.999933 | + | 0.0116089i | \(0.996305\pi\) | |||||||
\(110\) | −2.56501 | − | 0.831306i | −0.244565 | − | 0.0792619i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.22545 | + | 1.30383i | 0.588249 | + | 0.123201i | ||||
\(113\) | −4.34789 | − | 7.53076i | −0.409015 | − | 0.708435i | 0.585765 | − | 0.810481i | \(-0.300794\pi\) |
−0.994780 | + | 0.102046i | \(0.967461\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.96466 | − | 2.28900i | −0.369706 | − | 0.213450i | ||||
\(116\) | −2.68675 | − | 6.01037i | −0.249459 | − | 0.558049i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.37870 | − | 1.57415i | 0.679264 | − | 0.144912i | ||||
\(119\) | 4.49350 | − | 7.78298i | 0.411919 | − | 0.713464i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.74837 | − | 3.02827i | −0.158943 | − | 0.275297i | ||||
\(122\) | 8.68000 | + | 9.62565i | 0.785850 | + | 0.871466i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.52439 | − | 14.7150i | 0.136894 | − | 1.32145i | ||||
\(125\) | 6.62325i | 0.592401i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.72754 | −0.153295 | −0.0766473 | − | 0.997058i | \(-0.524422\pi\) | ||||
−0.0766473 | + | 0.997058i | \(0.524422\pi\) | |||||||
\(128\) | −6.60209 | + | 9.18762i | −0.583548 | + | 0.812079i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.02460 | + | 3.62921i | −0.352980 | + | 0.318303i | ||||
\(131\) | −5.74968 | + | 3.31958i | −0.502352 | + | 0.290033i | −0.729684 | − | 0.683784i | \(-0.760333\pi\) |
0.227332 | + | 0.973817i | \(0.427000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.32659 | + | 0.765908i | 0.115030 | + | 0.0664127i | ||||
\(134\) | 9.51493 | − | 2.02989i | 0.821964 | − | 0.175356i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.42503 | + | 12.9115i | 0.808189 | + | 1.10715i | ||||
\(137\) | −1.81325 | + | 3.14063i | −0.154916 | + | 0.268322i | −0.933028 | − | 0.359803i | \(-0.882844\pi\) |
0.778112 | + | 0.628125i | \(0.216177\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.9919 | − | 8.65556i | 1.27159 | − | 0.734155i | 0.296307 | − | 0.955093i | \(-0.404245\pi\) |
0.975288 | + | 0.220937i | \(0.0709117\pi\) | |||||||
\(140\) | 1.29845 | − | 1.79279i | 0.109739 | − | 0.151518i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.95552 | − | 1.60605i | −0.415858 | − | 0.134777i | ||||
\(143\) | 15.0804 | 1.26109 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.29123 | −0.190276 | ||||||||
\(146\) | 3.80996 | + | 1.23479i | 0.315315 | + | 0.102192i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.33851 | − | 10.1324i | 0.603222 | − | 0.832877i | ||||
\(149\) | 18.7251 | − | 10.8109i | 1.53402 | − | 0.885665i | 0.534846 | − | 0.844949i | \(-0.320369\pi\) |
0.999171 | − | 0.0407158i | \(-0.0129638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.35019 | + | 10.9988i | −0.516771 | + | 0.895073i | 0.483039 | + | 0.875599i | \(0.339533\pi\) |
−0.999810 | + | 0.0194749i | \(0.993801\pi\) | |||||||
\(152\) | −2.20074 | + | 1.60648i | −0.178503 | + | 0.130302i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.02431 | + | 1.28521i | −0.485453 | + | 0.103565i | ||||
\(155\) | −4.45880 | − | 2.57429i | −0.358139 | − | 0.206772i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.1285 | + | 8.73443i | −1.20738 | + | 0.697083i | −0.962187 | − | 0.272390i | \(-0.912186\pi\) |
−0.245197 | + | 0.969473i | \(0.578853\pi\) | |||||||
\(158\) | 6.04675 | − | 5.45270i | 0.481054 | − | 0.433794i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.98144 | + | 3.40254i | 0.156646 | + | 0.268995i | ||||
\(161\) | −10.4585 | −0.824245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.56748i | 0.671057i | 0.942030 | + | 0.335528i | \(0.108915\pi\) | ||||
−0.942030 | + | 0.335528i | \(0.891085\pi\) | |||||||
\(164\) | −0.384097 | + | 3.70770i | −0.0299929 | + | 0.289523i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.28781 | + | 6.97284i | 0.488028 | + | 0.541197i | ||||
\(167\) | 5.97532 | + | 10.3496i | 0.462384 | + | 0.800873i | 0.999079 | − | 0.0429032i | \(-0.0136607\pi\) |
−0.536695 | + | 0.843776i | \(0.680327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.65464 | − | 14.9903i | 0.665741 | − | 1.15310i | ||||
\(170\) | 5.44091 | − | 1.16075i | 0.417299 | − | 0.0890254i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.82587 | − | 6.32159i | −0.215471 | − | 0.482017i | ||||
\(173\) | −11.2973 | − | 6.52248i | −0.858916 | − | 0.495895i | 0.00473326 | − | 0.999989i | \(-0.498493\pi\) |
−0.863649 | + | 0.504094i | \(0.831827\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.59013 | + | 6.21829i | 0.271388 | + | 0.470058i | ||||
\(176\) | 2.24603 | − | 10.7242i | 0.169301 | − | 0.808363i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.01849 | + | 1.30237i | 0.301199 | + | 0.0976167i | ||||
\(179\) | − | 3.31875i | − | 0.248055i | −0.992279 | − | 0.124028i | \(-0.960419\pi\) | ||
0.992279 | − | 0.124028i | \(-0.0395811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.9128i | − | 1.10846i | −0.832363 | − | 0.554231i | \(-0.813013\pi\) | ||
0.832363 | − | 0.554231i | \(-0.186987\pi\) | |||||||
\(182\) | −3.81696 | + | 11.7773i | −0.282932 | + | 0.872994i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.52841 | − | 17.0116i | 0.555002 | − | 1.25411i | ||||
\(185\) | −2.17702 | − | 3.77070i | −0.160058 | − | 0.277228i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4072 | − | 7.74065i | −0.980432 | − | 0.566053i | ||||
\(188\) | −14.0836 | + | 6.29566i | −1.02715 | + | 0.459158i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.197847 | + | 0.927391i | 0.0143533 | + | 0.0672800i | ||||
\(191\) | −3.65884 | + | 6.33729i | −0.264744 | + | 0.458550i | −0.967497 | − | 0.252884i | \(-0.918621\pi\) |
0.702752 | + | 0.711434i | \(0.251954\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.2354 | − | 17.7282i | −0.736759 | − | 1.27610i | −0.953947 | − | 0.299974i | \(-0.903022\pi\) |
0.217189 | − | 0.976130i | \(-0.430311\pi\) | |||||||
\(194\) | −2.62223 | + | 2.36461i | −0.188265 | + | 0.169769i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.921510 | + | 8.89537i | −0.0658222 | + | 0.635384i | ||||
\(197\) | − | 20.5437i | − | 1.46368i | −0.681479 | − | 0.731838i | \(-0.738663\pi\) | ||
0.681479 | − | 0.731838i | \(-0.261337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.95597 | 0.138655 | 0.0693275 | − | 0.997594i | \(-0.477915\pi\) | ||||
0.0693275 | + | 0.997594i | \(0.477915\pi\) | |||||||
\(200\) | −12.6988 | + | 1.36347i | −0.897943 | + | 0.0964121i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.99081 | + | 9.97033i | 0.632591 | + | 0.701510i | ||||
\(203\) | −4.53308 | + | 2.61718i | −0.318160 | + | 0.183690i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.12347 | + | 0.648636i | 0.0784666 | + | 0.0453027i | ||||
\(206\) | 4.35055 | + | 20.3928i | 0.303117 | + | 1.42084i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.4091 | − | 14.6863i | −1.13777 | − | 1.01831i | ||||
\(209\) | 1.31938 | − | 2.28523i | 0.0912633 | − | 0.158073i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.10981 | + | 5.25955i | −0.627145 | + | 0.362082i | −0.779646 | − | 0.626221i | \(-0.784601\pi\) |
0.152501 | + | 0.988303i | \(0.451267\pi\) | |||||||
\(212\) | −2.98190 | + | 4.11716i | −0.204798 | + | 0.282767i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.41564 | + | 10.5390i | −0.233488 | + | 0.720434i | ||||
\(215\) | −2.40987 | −0.164352 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.7620 | −0.798456 | ||||||||
\(218\) | −0.105689 | + | 0.326106i | −0.00715817 | + | 0.0220867i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.08831 | − | 2.23675i | −0.208214 | − | 0.150802i | ||||
\(221\) | −26.9464 | + | 15.5575i | −1.81261 | + | 1.04651i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.93129 | − | 3.34510i | 0.129329 | − | 0.224004i | −0.794088 | − | 0.607803i | \(-0.792051\pi\) |
0.923417 | + | 0.383799i | \(0.125384\pi\) | |||||||
\(224\) | 7.80675 | + | 4.46844i | 0.521610 | + | 0.298560i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.56582 | − | 12.0270i | −0.170676 | − | 0.800027i | ||||
\(227\) | −13.9183 | − | 8.03574i | −0.923790 | − | 0.533351i | −0.0389481 | − | 0.999241i | \(-0.512401\pi\) |
−0.884842 | + | 0.465891i | \(0.845734\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.46319 | − | 4.30888i | 0.493182 | − | 0.284739i | −0.232712 | − | 0.972546i | \(-0.574760\pi\) |
0.725893 | + | 0.687807i | \(0.241427\pi\) | |||||||
\(230\) | −4.33572 | − | 4.80808i | −0.285889 | − | 0.317035i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.993962 | − | 9.25735i | −0.0652568 | − | 0.607775i | ||||
\(233\) | −24.1535 | −1.58235 | −0.791176 | − | 0.611589i | \(-0.790531\pi\) | ||||
−0.791176 | + | 0.611589i | \(0.790531\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.36886i | 0.350226i | ||||||||
\(236\) | 10.6131 | + | 1.09945i | 0.690853 | + | 0.0715684i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.43868 | − | 8.51140i | 0.611819 | − | 0.551712i | ||||
\(239\) | 2.01493 | + | 3.48996i | 0.130335 | + | 0.225746i | 0.923806 | − | 0.382862i | \(-0.125061\pi\) |
−0.793471 | + | 0.608608i | \(0.791728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.81649 | − | 4.87830i | 0.181426 | − | 0.314239i | −0.760940 | − | 0.648822i | \(-0.775262\pi\) |
0.942366 | + | 0.334583i | \(0.108595\pi\) | |||||||
\(242\) | −1.03177 | − | 4.83631i | −0.0663244 | − | 0.310890i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.48051 | + | 16.7342i | 0.478891 | + | 1.07130i | ||||
\(245\) | 2.69539 | + | 1.55618i | 0.172202 | + | 0.0994209i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.65175 | − | 4.59296i | −0.168727 | − | 0.292243i | ||||
\(248\) | 8.46671 | − | 19.1318i | 0.537637 | − | 1.21487i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.88781 | + | 8.91040i | −0.182641 | + | 0.563543i | ||||
\(251\) | − | 13.8828i | − | 0.876276i | −0.898908 | − | 0.438138i | \(-0.855638\pi\) | ||
0.898908 | − | 0.438138i | \(-0.144362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0161i | 1.13267i | ||||||||
\(254\) | −2.32410 | − | 0.753228i | −0.145827 | − | 0.0472618i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.8879 | + | 9.48173i | −0.805491 | + | 0.592608i | ||||
\(257\) | 5.42539 | + | 9.39705i | 0.338427 | + | 0.586172i | 0.984137 | − | 0.177410i | \(-0.0567720\pi\) |
−0.645710 | + | 0.763582i | \(0.723439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.61423 | − | 4.97343i | −0.535262 | − | 0.309034i | ||||
\(260\) | −6.99676 | + | 3.12769i | −0.433921 | + | 0.193971i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.18256 | + | 1.95898i | −0.567300 | + | 0.121026i | ||||
\(263\) | 11.6051 | − | 20.1005i | 0.715598 | − | 1.23945i | −0.247130 | − | 0.968982i | \(-0.579487\pi\) |
0.962728 | − | 0.270470i | \(-0.0871792\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.884601 | + | 1.53217i | 0.0543406 | + | 0.0941207i | ||||
\(266\) | 1.45075 | + | 1.60880i | 0.0889512 | + | 0.0986421i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.6857 | + | 1.41776i | 0.835987 | + | 0.0866035i | ||||
\(269\) | − | 4.01966i | − | 0.245083i | −0.992463 | − | 0.122541i | \(-0.960896\pi\) | ||
0.992463 | − | 0.122541i | \(-0.0391044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.75621 | −0.410411 | −0.205205 | − | 0.978719i | \(-0.565786\pi\) | ||||
−0.205205 | + | 0.978719i | \(0.565786\pi\) | |||||||
\(272\) | 7.05014 | + | 21.4796i | 0.427478 | + | 1.30239i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.80875 | + | 3.43457i | −0.230095 | + | 0.207490i | ||||
\(275\) | 10.7118 | − | 6.18447i | 0.645947 | − | 0.372938i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.83595 | + | 1.05999i | 0.110312 | + | 0.0636885i | 0.554141 | − | 0.832423i | \(-0.313047\pi\) |
−0.443829 | + | 0.896111i | \(0.646380\pi\) | |||||||
\(278\) | 23.9428 | − | 5.10790i | 1.43600 | − | 0.306352i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.52851 | − | 1.84574i | 0.151107 | − | 0.110304i | ||||
\(281\) | 13.0580 | − | 22.6171i | 0.778976 | − | 1.34923i | −0.153557 | − | 0.988140i | \(-0.549073\pi\) |
0.932533 | − | 0.361086i | \(-0.117594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5376 | + | 9.54799i | −0.983058 | + | 0.567569i | −0.903192 | − | 0.429237i | \(-0.858783\pi\) |
−0.0798661 | + | 0.996806i | \(0.525449\pi\) | |||||||
\(284\) | −5.96651 | − | 4.32132i | −0.354047 | − | 0.256423i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.2880 | + | 6.57522i | 1.19965 | + | 0.388801i | ||||
\(287\) | 2.96364 | 0.174938 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9423 | 0.878956 | ||||||||
\(290\) | −3.08245 | − | 0.999003i | −0.181007 | − | 0.0586635i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.58725 | + | 3.32237i | 0.268448 | + | 0.194427i | ||||
\(293\) | 5.07116 | − | 2.92784i | 0.296261 | − | 0.171046i | −0.344501 | − | 0.938786i | \(-0.611952\pi\) |
0.640762 | + | 0.767740i | \(0.278619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.85668 | − | 3.21587i | 0.108100 | − | 0.187235i | ||||
\(296\) | 14.2905 | − | 10.4317i | 0.830619 | − | 0.606328i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 29.9049 | − | 6.37984i | 1.73235 | − | 0.369574i | ||||
\(299\) | 31.3585 | + | 18.1048i | 1.81351 | + | 1.04703i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.76780 | + | 2.75269i | −0.274812 | + | 0.158663i | ||||
\(302\) | −13.3387 | + | 12.0282i | −0.767555 | + | 0.692148i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.66115 | + | 1.20168i | −0.209981 | + | 0.0689212i | ||||
\(305\) | 6.37929 | 0.365277 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.7071i | − | 0.782305i | −0.920326 | − | 0.391152i | \(-0.872077\pi\) | ||
0.920326 | − | 0.391152i | \(-0.127923\pi\) | |||||||
\(308\) | −8.66501 | − | 0.897646i | −0.493735 | − | 0.0511481i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.87610 | − | 5.40733i | −0.276944 | − | 0.307116i | ||||
\(311\) | 9.57980 | + | 16.5927i | 0.543221 | + | 0.940886i | 0.998717 | + | 0.0506479i | \(0.0161286\pi\) |
−0.455496 | + | 0.890238i | \(0.650538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6102 | + | 21.8416i | −0.712773 | + | 1.23456i | 0.251039 | + | 0.967977i | \(0.419228\pi\) |
−0.963812 | + | 0.266582i | \(0.914106\pi\) | |||||||
\(314\) | −24.1610 | + | 5.15444i | −1.36348 | + | 0.290882i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.5123 | − | 4.69919i | 0.591362 | − | 0.264350i | ||||
\(317\) | −2.13931 | − | 1.23513i | −0.120156 | − | 0.0693719i | 0.438718 | − | 0.898625i | \(-0.355433\pi\) |
−0.558873 | + | 0.829253i | \(0.688766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50843 | + | 7.80883i | 0.252424 | + | 0.437211i | ||||
\(320\) | 1.18212 | + | 5.44145i | 0.0660828 | + | 0.304186i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.0701 | − | 4.56002i | −0.784094 | − | 0.254120i | ||||
\(323\) | 5.44449i | 0.302939i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 24.8597i | − | 1.37897i | ||||||
\(326\) | −3.73552 | + | 11.5260i | −0.206891 | + | 0.638368i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.13333 | + | 4.82058i | −0.117794 | + | 0.266172i | ||||
\(329\) | 6.13262 | + | 10.6220i | 0.338103 | + | 0.585611i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4404 | + | 14.1107i | 1.34336 | + | 0.775592i | 0.987300 | − | 0.158869i | \(-0.0507848\pi\) |
0.356065 | + | 0.934461i | \(0.384118\pi\) | |||||||
\(332\) | 5.41889 | + | 12.1223i | 0.297400 | + | 0.665296i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.52621 | + | 16.5288i | 0.192946 | + | 0.904416i | ||||
\(335\) | 2.39422 | − | 4.14691i | 0.130810 | − | 0.226570i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.60565 | + | 9.70927i | 0.305359 | + | 0.528897i | 0.977341 | − | 0.211670i | \(-0.0678902\pi\) |
−0.671982 | + | 0.740567i | \(0.734557\pi\) | |||||||
\(338\) | 18.1792 | − | 16.3932i | 0.988819 | − | 0.891675i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.82588 | + | 0.810717i | 0.424418 | + | 0.0439673i | ||||
\(341\) | 20.2616i | 1.09723i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2411 | 0.984929 | ||||||||
\(344\) | −1.04543 | − | 9.73669i | −0.0563657 | − | 0.524967i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.3546 | − | 13.7006i | −0.664188 | − | 0.736548i | ||||
\(347\) | −17.8303 | + | 10.2943i | −0.957180 | + | 0.552628i | −0.895304 | − | 0.445455i | \(-0.853042\pi\) |
−0.0618763 | + | 0.998084i | \(0.519708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.93968 | + | 1.69723i | 0.157358 | + | 0.0908505i | 0.576611 | − | 0.817019i | \(-0.304375\pi\) |
−0.419253 | + | 0.907869i | \(0.637708\pi\) | |||||||
\(350\) | 2.11864 | + | 9.93094i | 0.113246 | + | 0.530831i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.69748 | − | 13.4482i | 0.410277 | − | 0.716789i | ||||
\(353\) | 0.503241 | − | 0.871639i | 0.0267848 | − | 0.0463926i | −0.852322 | − | 0.523017i | \(-0.824806\pi\) |
0.879107 | + | 0.476624i | \(0.158140\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.22040 | + | 1.28195i | −0.117847 | + | 0.0680388i | ||||
\(356\) | 4.83832 | + | 3.50422i | 0.256430 | + | 0.185723i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.44701 | − | 4.46479i | 0.0764770 | − | 0.235972i | ||||
\(359\) | −31.4772 | −1.66131 | −0.830653 | − | 0.556791i | \(-0.812032\pi\) | ||||
−0.830653 | + | 0.556791i | \(0.812032\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0720 | 0.951158 | ||||||||
\(362\) | 6.50216 | − | 20.0626i | 0.341746 | − | 1.05446i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.2701 | + | 14.1801i | −0.538299 | + | 0.743238i | ||||
\(365\) | 1.70712 | − | 0.985604i | 0.0893546 | − | 0.0515889i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.66667 | + | 15.0111i | −0.452397 | + | 0.783574i | −0.998534 | − | 0.0541214i | \(-0.982764\pi\) |
0.546138 | + | 0.837695i | \(0.316098\pi\) | |||||||
\(368\) | 17.5454 | − | 19.6036i | 0.914616 | − | 1.02191i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.28472 | − | 6.02202i | −0.0667895 | − | 0.313070i | ||||
\(371\) | 3.50027 | + | 2.02088i | 0.181725 | + | 0.104919i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2742 | − | 6.50917i | 0.583757 | − | 0.337032i | −0.178868 | − | 0.983873i | \(-0.557244\pi\) |
0.762625 | + | 0.646841i | \(0.223910\pi\) | |||||||
\(374\) | −14.6620 | − | 16.2594i | −0.758154 | − | 0.840752i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.6920 | + | 2.32907i | −1.11868 | + | 0.120113i | ||||
\(377\) | 18.1225 | 0.933357 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.8643i | − | 1.17446i | −0.809421 | − | 0.587229i | \(-0.800219\pi\) | ||
0.809421 | − | 0.587229i | \(-0.199781\pi\) | |||||||
\(380\) | −0.138185 | + | 1.33390i | −0.00708874 | + | 0.0684279i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.68545 | + | 6.93041i | −0.393222 | + | 0.354590i | ||||
\(383\) | −15.0117 | − | 26.0010i | −0.767061 | − | 1.32859i | −0.939150 | − | 0.343508i | \(-0.888385\pi\) |
0.172089 | − | 0.985081i | \(-0.444948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.51588 | + | 2.62559i | −0.0772565 | + | 0.133812i | ||||
\(386\) | −6.04020 | − | 28.3129i | −0.307438 | − | 1.44109i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.55874 | + | 2.03785i | −0.231435 | + | 0.103456i | ||||
\(389\) | 32.9474 | + | 19.0222i | 1.67050 | + | 0.964463i | 0.967358 | + | 0.253412i | \(0.0815528\pi\) |
0.703140 | + | 0.711051i | \(0.251780\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.5862 | − | 32.1922i | −0.939943 | − | 1.62803i | ||||
\(392\) | −5.11821 | + | 11.5654i | −0.258509 | + | 0.584139i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.95728 | − | 27.6379i | 0.451261 | − | 1.39238i | ||||
\(395\) | − | 4.00742i | − | 0.201635i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.4510i | 1.87961i | 0.341709 | + | 0.939806i | \(0.388994\pi\) | ||||
−0.341709 | + | 0.939806i | \(0.611006\pi\) | |||||||
\(398\) | 2.63141 | + | 0.852825i | 0.131901 | + | 0.0427483i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.6785 | − | 3.70252i | −0.883926 | − | 0.185126i | ||||
\(401\) | 2.35402 | + | 4.07728i | 0.117554 | + | 0.203610i | 0.918798 | − | 0.394728i | \(-0.129161\pi\) |
−0.801244 | + | 0.598338i | \(0.795828\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.2669 | + | 20.3613i | 1.75677 | + | 1.01427i | ||||
\(404\) | 7.74837 | + | 17.3334i | 0.385496 | + | 0.862369i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.23958 | + | 1.54447i | −0.359294 | + | 0.0766508i | ||||
\(407\) | −8.56739 | + | 14.8391i | −0.424670 | + | 0.735549i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.36377 | + | 9.29032i | 0.265221 | + | 0.459377i | 0.967622 | − | 0.252405i | \(-0.0812216\pi\) |
−0.702400 | + | 0.711782i | \(0.747888\pi\) | |||||||
\(410\) | 1.22862 | + | 1.36247i | 0.0606771 | + | 0.0672876i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.03861 | + | 29.3318i | −0.149702 | + | 1.44508i | ||||
\(413\) | − | 8.48324i | − | 0.417433i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.62117 | 0.226844 | ||||||||
\(416\) | −15.6722 | − | 26.9124i | −0.768392 | − | 1.31949i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.77138 | − | 2.49911i | 0.135552 | − | 0.122235i | ||||
\(419\) | 3.57600 | − | 2.06460i | 0.174699 | − | 0.100863i | −0.410101 | − | 0.912040i | \(-0.634506\pi\) |
0.584800 | + | 0.811178i | \(0.301173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7321 | − | 7.92824i | −0.669262 | − | 0.386399i | 0.126535 | − | 0.991962i | \(-0.459614\pi\) |
−0.795797 | + | 0.605563i | \(0.792948\pi\) | |||||||
\(422\) | −14.5489 | + | 3.10381i | −0.708227 | + | 0.151091i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.80675 | + | 4.23876i | −0.282001 | + | 0.205852i | ||||
\(425\) | −12.7603 | + | 22.1015i | −0.618965 | + | 1.07208i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.6211 | − | 7.28679i | 0.610778 | − | 0.352633i | ||||
\(428\) | −9.19028 | + | 12.6892i | −0.444229 | + | 0.613353i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.24205 | − | 1.05073i | −0.156346 | − | 0.0506708i | ||||
\(431\) | −16.1853 | −0.779619 | −0.389810 | − | 0.920895i | \(-0.627459\pi\) | ||||
−0.389810 | + | 0.920895i | \(0.627459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.8306 | −1.57774 | −0.788868 | − | 0.614563i | \(-0.789332\pi\) | ||||
−0.788868 | + | 0.614563i | \(0.789332\pi\) | |||||||
\(434\) | −15.8237 | − | 5.12836i | −0.759561 | − | 0.246169i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.284372 | + | 0.392636i | −0.0136190 | + | 0.0188039i | ||||
\(437\) | 5.48709 | − | 3.16797i | 0.262483 | − | 0.151545i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9273 | − | 18.9267i | 0.521533 | − | 0.903321i | −0.478154 | − | 0.878276i | \(-0.658694\pi\) |
0.999686 | − | 0.0250450i | \(-0.00797290\pi\) | |||||||
\(440\) | −3.17953 | − | 4.35569i | −0.151578 | − | 0.207650i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −43.0349 | + | 9.18095i | −2.04696 | + | 0.436693i | ||||
\(443\) | −30.4500 | − | 17.5803i | −1.44672 | − | 0.835265i | −0.448436 | − | 0.893815i | \(-0.648019\pi\) |
−0.998284 | + | 0.0585501i | \(0.981352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.80055 | − | 1.03955i | 0.0853543 | − | 0.0492793i | ||||
\(446\) | 4.05671 | − | 3.65817i | 0.192091 | − | 0.173219i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.55431 | + | 9.41533i | 0.404153 | + | 0.444833i | ||||
\(449\) | −3.21851 | −0.151891 | −0.0759453 | − | 0.997112i | \(-0.524197\pi\) | ||||
−0.0759453 | + | 0.997112i | \(0.524197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.10526i | − | 0.240397i | ||||||
\(452\) | 1.79208 | − | 17.2990i | 0.0842921 | − | 0.813675i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.2209 | − | 16.8792i | −0.714354 | − | 0.792180i | ||||
\(455\) | 3.04669 | + | 5.27703i | 0.142831 | + | 0.247391i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.05512 | − | 7.02368i | 0.189691 | − | 0.328554i | −0.755456 | − | 0.655199i | \(-0.772585\pi\) |
0.945147 | + | 0.326645i | \(0.105918\pi\) | |||||||
\(458\) | 11.9191 | − | 2.54279i | 0.556944 | − | 0.118817i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.73657 | − | 8.35884i | −0.174218 | − | 0.389733i | ||||
\(461\) | −18.1813 | − | 10.4970i | −0.846789 | − | 0.488894i | 0.0127771 | − | 0.999918i | \(-0.495933\pi\) |
−0.859566 | + | 0.511024i | \(0.829266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.45005 | − | 7.70772i | −0.206812 | − | 0.358208i | 0.743897 | − | 0.668294i | \(-0.232975\pi\) |
−0.950708 | + | 0.310086i | \(0.899642\pi\) | |||||||
\(464\) | 2.69911 | − | 12.8875i | 0.125303 | − | 0.598287i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.4943 | − | 10.5312i | −1.50527 | − | 0.487849i | ||||
\(467\) | 26.0527i | 1.20557i | 0.797902 | + | 0.602787i | \(0.205943\pi\) | ||||
−0.797902 | + | 0.602787i | \(0.794057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.9392i | − | 0.505128i | ||||||
\(470\) | −2.34089 | + | 7.22285i | −0.107977 | + | 0.333165i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.7986 | + | 6.10655i | 0.635134 | + | 0.281077i | ||||
\(473\) | 4.74188 | + | 8.21317i | 0.218032 | + | 0.377642i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.76715 | − | 2.17496i | −0.172849 | − | 0.0997942i | ||||
\(476\) | 16.4091 | − | 7.33521i | 0.752112 | − | 0.336209i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.18907 | + | 5.57365i | 0.0543866 | + | 0.254933i | ||||
\(479\) | −8.71143 | + | 15.0886i | −0.398035 | + | 0.689418i | −0.993483 | − | 0.113976i | \(-0.963641\pi\) |
0.595448 | + | 0.803394i | \(0.296975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2191 | + | 29.8244i | 0.785125 | + | 1.35988i | ||||
\(482\) | 5.91608 | − | 5.33487i | 0.269470 | − | 0.242997i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.720629 | − | 6.95626i | 0.0327559 | − | 0.316194i | ||||
\(485\) | 1.73785i | 0.0789118i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.7367 | −1.34750 | −0.673750 | − | 0.738959i | \(-0.735318\pi\) | ||||
−0.673750 | + | 0.738959i | \(0.735318\pi\) | |||||||
\(488\) | 2.76741 | + | 25.7745i | 0.125275 | + | 1.16676i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.94765 | + | 3.26879i | 0.133161 | + | 0.147669i | ||||
\(491\) | 20.6346 | − | 11.9134i | 0.931229 | − | 0.537645i | 0.0440286 | − | 0.999030i | \(-0.485981\pi\) |
0.887200 | + | 0.461385i | \(0.152647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.1118 | − | 9.30215i | −0.725639 | − | 0.418948i | ||||
\(494\) | −1.56487 | − | 7.33521i | −0.0704070 | − | 0.330027i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.7321 | − | 22.0469i | 0.885999 | − | 0.989933i | ||||
\(497\) | −2.92863 | + | 5.07254i | −0.131367 | + | 0.227534i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8622 | − | 9.73540i | 0.754856 | − | 0.435816i | −0.0725899 | − | 0.997362i | \(-0.523126\pi\) |
0.827446 | + | 0.561546i | \(0.189793\pi\) | |||||||
\(500\) | −7.77008 | + | 10.7283i | −0.347488 | + | 0.479782i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.05307 | − | 18.6769i | 0.270162 | − | 0.833590i | ||||
\(503\) | −1.23494 | −0.0550631 | −0.0275316 | − | 0.999621i | \(-0.508765\pi\) | ||||
−0.0275316 | + | 0.999621i | \(0.508765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.60772 | 0.294040 | ||||||||
\(506\) | −7.85524 | + | 24.2375i | −0.349208 | + | 1.07749i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.79825 | − | 2.02667i | −0.124152 | − | 0.0899190i | ||||
\(509\) | 0.392870 | − | 0.226823i | 0.0174136 | − | 0.0100538i | −0.491268 | − | 0.871009i | \(-0.663466\pi\) |
0.508682 | + | 0.860955i | \(0.330133\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.25163 | − | 3.89993i | 0.0996061 | − | 0.172523i | ||||
\(512\) | −21.4725 | + | 7.13674i | −0.948958 | + | 0.315403i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.20168 | + | 15.0076i | 0.141220 | + | 0.661957i | ||||
\(515\) | 8.88784 | + | 5.13140i | 0.391645 | + | 0.226116i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.2978 | − | 10.5643i | 0.804737 | − | 0.464615i | ||||
\(518\) | −9.42045 | − | 10.4468i | −0.413911 | − | 0.459005i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.7766 | + | 1.15708i | −0.472586 | + | 0.0507415i | ||||
\(521\) | 29.0873 | 1.27434 | 0.637170 | − | 0.770724i | \(-0.280105\pi\) | ||||
0.637170 | + | 0.770724i | \(0.280105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.95874i | − | 0.129377i | −0.997906 | − | 0.0646883i | \(-0.979395\pi\) | ||
0.997906 | − | 0.0646883i | \(-0.0206053\pi\) | |||||||
\(524\) | −13.2076 | − | 1.36824i | −0.576979 | − | 0.0597717i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.3766 | − | 21.9818i | 1.06287 | − | 0.958452i | ||||
\(527\) | −20.9026 | − | 36.2044i | −0.910534 | − | 1.57709i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.1294 | + | 17.5446i | −0.440407 | + | 0.762808i | ||||
\(530\) | 0.522029 | + | 2.44697i | 0.0226755 | + | 0.106289i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.25027 | + | 2.79690i | 0.0542061 | + | 0.121261i | ||||
\(533\) | −8.88610 | − | 5.13039i | −0.384900 | − | 0.222222i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.72636 | + | 4.72219i | 0.117871 | + | 0.204158i | ||||
\(536\) | 17.7935 | + | 7.87447i | 0.768564 | + | 0.340125i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.75262 | − | 5.40774i | 0.0755607 | − | 0.233144i | ||||
\(539\) | − | 12.2483i | − | 0.527573i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9753i | 0.643838i | 0.946767 | + | 0.321919i | \(0.104328\pi\) | ||||
−0.946767 | + | 0.321919i | \(0.895672\pi\) | |||||||
\(542\) | −9.08929 | − | 2.94578i | −0.390418 | − | 0.126532i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.119385 | + | 31.9709i | 0.00511861 | + | 1.37074i | ||||
\(545\) | 0.0843608 | + | 0.146117i | 0.00361362 | + | 0.00625897i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7731 | − | 9.10661i | −0.674409 | − | 0.389370i | 0.123336 | − | 0.992365i | \(-0.460641\pi\) |
−0.797745 | + | 0.602995i | \(0.793974\pi\) | |||||||
\(548\) | −6.62152 | + | 2.95995i | −0.282857 | + | 0.126443i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.1074 | − | 3.64964i | 0.729460 | − | 0.155621i | ||||
\(551\) | 1.58553 | − | 2.74622i | 0.0675459 | − | 0.116993i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.57750 | − | 7.92846i | −0.194655 | − | 0.337153i | ||||
\(554\) | 2.00778 | + | 2.22652i | 0.0853025 | + | 0.0945958i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 34.4380 | + | 3.56758i | 1.46049 | + | 0.151299i | ||||
\(557\) | 35.7359i | 1.51418i | 0.653310 | + | 0.757090i | \(0.273380\pi\) | ||||
−0.653310 | + | 0.757090i | \(0.726620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0609 | 0.806190 | ||||||||
\(560\) | 4.20643 | − | 1.38066i | 0.177754 | − | 0.0583434i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.4286 | − | 24.7339i | 1.15700 | − | 1.04334i | ||||
\(563\) | −8.04256 | + | 4.64337i | −0.338953 | + | 0.195695i | −0.659809 | − | 0.751433i | \(-0.729363\pi\) |
0.320856 | + | 0.947128i | \(0.396030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.24176 | − | 3.02633i | −0.220523 | − | 0.127319i | ||||
\(566\) | −26.4114 | + | 5.63454i | −1.11016 | + | 0.236838i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.14274 | − | 8.41504i | −0.257744 | − | 0.353087i | ||||
\(569\) | 5.66727 | − | 9.81599i | 0.237584 | − | 0.411508i | −0.722436 | − | 0.691437i | \(-0.756978\pi\) |
0.960021 | + | 0.279930i | \(0.0903111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.7843 | + | 21.8148i | −1.58122 | + | 0.912920i | −0.586543 | + | 0.809918i | \(0.699511\pi\) |
−0.994681 | + | 0.103002i | \(0.967155\pi\) | |||||||
\(572\) | 24.4270 | + | 17.6916i | 1.02135 | + | 0.739723i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.98705 | + | 1.29218i | 0.166416 | + | 0.0539345i | ||||
\(575\) | 29.6992 | 1.23854 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.98123 | 0.290632 | 0.145316 | − | 0.989385i | \(-0.453580\pi\) | ||||
0.145316 | + | 0.989385i | \(0.453580\pi\) | |||||||
\(578\) | 20.1022 | + | 6.51499i | 0.836139 | + | 0.270988i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.71131 | − | 2.68796i | −0.154104 | − | 0.111612i | ||||
\(581\) | 9.14274 | − | 5.27856i | 0.379305 | − | 0.218992i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.48124 | − | 6.02968i | 0.144178 | − | 0.249724i | ||||
\(584\) | 4.72274 | + | 6.46976i | 0.195428 | + | 0.267721i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.09892 | − | 1.72780i | 0.334563 | − | 0.0713749i | ||||
\(587\) | 7.34574 | + | 4.24107i | 0.303191 | + | 0.175048i | 0.643876 | − | 0.765130i | \(-0.277325\pi\) |
−0.340684 | + | 0.940178i | \(0.610659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.17097 | − | 3.56281i | 0.254270 | − | 0.146803i | ||||
\(590\) | 3.89999 | − | 3.51685i | 0.160560 | − | 0.144786i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.7737 | − | 7.80313i | 0.977092 | − | 0.320707i | ||||
\(593\) | 9.40869 | 0.386368 | 0.193184 | − | 0.981163i | \(-0.438119\pi\) | ||||
0.193184 | + | 0.981163i | \(0.438119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.25538i | − | 0.256445i | ||||||
\(596\) | 43.0135 | + | 4.45595i | 1.76190 | + | 0.182523i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.2934 | + | 38.0295i | 1.40236 | + | 1.55514i | ||||
\(599\) | 14.9623 | + | 25.9155i | 0.611344 | + | 1.05888i | 0.991014 | + | 0.133757i | \(0.0427043\pi\) |
−0.379670 | + | 0.925122i | \(0.623962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.81973 | − | 3.15186i | 0.0742282 | − | 0.128567i | −0.826522 | − | 0.562904i | \(-0.809684\pi\) |
0.900750 | + | 0.434337i | \(0.143017\pi\) | |||||||
\(602\) | −7.61444 | + | 1.62444i | −0.310342 | + | 0.0662074i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −23.1893 | + | 10.3661i | −0.943558 | + | 0.421789i | ||||
\(605\) | −2.10782 | − | 1.21695i | −0.0856950 | − | 0.0494760i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.63358 | + | 6.29355i | 0.147482 | + | 0.255447i | 0.930296 | − | 0.366809i | \(-0.119550\pi\) |
−0.782814 | + | 0.622256i | \(0.786216\pi\) | |||||||
\(608\) | −5.44937 | + | 0.0203490i | −0.221001 | + | 0.000825260i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.58221 | + | 2.78144i | 0.347483 | + | 0.112617i | ||||
\(611\) | − | 42.4651i | − | 1.71795i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.6469i | 1.31859i | 0.751882 | + | 0.659297i | \(0.229146\pi\) | ||||
−0.751882 | + | 0.659297i | \(0.770854\pi\) | |||||||
\(614\) | 5.97645 | − | 18.4405i | 0.241190 | − | 0.744197i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.2659 | − | 4.98567i | −0.453914 | − | 0.200878i | ||||
\(617\) | −15.6751 | − | 27.1501i | −0.631056 | − | 1.09302i | −0.987336 | − | 0.158642i | \(-0.949288\pi\) |
0.356280 | − | 0.934379i | \(-0.384045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.72589 | − | 0.996445i | −0.0693695 | − | 0.0400505i | 0.464914 | − | 0.885356i | \(-0.346085\pi\) |
−0.534284 | + | 0.845305i | \(0.679419\pi\) | |||||||
\(620\) | −4.20227 | − | 9.40065i | −0.168767 | − | 0.377539i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.65332 | + | 26.4994i | 0.226677 | + | 1.06253i | ||||
\(623\) | 2.37486 | − | 4.11339i | 0.0951469 | − | 0.164799i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.98375 | − | 15.5603i | −0.359350 | − | 0.622413i | ||||
\(626\) | −26.4880 | + | 23.8858i | −1.05867 | + | 0.954668i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −34.7517 | − | 3.60008i | −1.38675 | − | 0.143659i | ||||
\(629\) | − | 35.3538i | − | 1.40965i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4643 | −0.615623 | −0.307812 | − | 0.951447i | \(-0.599597\pi\) | ||||
−0.307812 | + | 0.951447i | \(0.599597\pi\) | |||||||
\(632\) | 16.1913 | − | 1.73846i | 0.644056 | − | 0.0691523i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.33953 | − | 2.59441i | −0.0929147 | − | 0.103037i | ||||
\(635\) | −1.04135 | + | 0.601225i | −0.0413248 | + | 0.0238589i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.3192 | − | 12.3086i | −0.844697 | − | 0.487686i | ||||
\(638\) | 2.66056 | + | 12.4711i | 0.105332 | + | 0.493737i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.782194 | + | 7.83593i | −0.0309189 | + | 0.309742i | ||||
\(641\) | 12.3638 | − | 21.4147i | 0.488340 | − | 0.845829i | −0.511570 | − | 0.859241i | \(-0.670936\pi\) |
0.999910 | + | 0.0134123i | \(0.00426940\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.0176 | + | 23.1042i | −1.57814 | + | 0.911141i | −0.583023 | + | 0.812456i | \(0.698130\pi\) |
−0.995119 | + | 0.0986850i | \(0.968536\pi\) | |||||||
\(644\) | −16.9406 | − | 12.2694i | −0.667551 | − | 0.483483i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.37386 | + | 7.32460i | −0.0933983 | + | 0.288182i | ||||
\(647\) | 6.36971 | 0.250419 | 0.125210 | − | 0.992130i | \(-0.460040\pi\) | ||||
0.125210 | + | 0.992130i | \(0.460040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.6135 | −0.573630 | ||||||||
\(650\) | 10.8391 | − | 33.4443i | 0.425145 | − | 1.31179i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0510 | + | 13.8775i | −0.393626 | + | 0.543485i | ||||
\(653\) | −31.8848 | + | 18.4087i | −1.24775 | + | 0.720389i | −0.970660 | − | 0.240455i | \(-0.922703\pi\) |
−0.277090 | + | 0.960844i | \(0.589370\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.31058 | + | 4.00205i | −0.0902820 | + | 0.156373i | ||||
\(656\) | −4.97185 | + | 5.55509i | −0.194118 | + | 0.216890i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.61904 | + | 16.9639i | 0.141085 | + | 0.661323i | ||||
\(659\) | −6.46565 | − | 3.73294i | −0.251866 | − | 0.145415i | 0.368752 | − | 0.929528i | \(-0.379785\pi\) |
−0.620618 | + | 0.784113i | \(0.713118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.51984 | − | 1.45483i | 0.0980102 | − | 0.0565862i | −0.450194 | − | 0.892931i | \(-0.648645\pi\) |
0.548204 | + | 0.836345i | \(0.315312\pi\) | |||||||
\(662\) | 26.7278 | + | 29.6397i | 1.03881 | + | 1.15198i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.00471 | + | 18.6711i | 0.0777980 | + | 0.724578i | ||||
\(665\) | 1.06622 | 0.0413461 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.6505i | 0.838310i | ||||||||
\(668\) | −2.46286 | + | 23.7741i | −0.0952908 | + | 0.919846i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.02909 | − | 4.53502i | 0.194291 | − | 0.175203i | ||||
\(671\) | −12.5525 | − | 21.7415i | −0.484582 | − | 0.839321i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0527 | − | 36.4643i | 0.811522 | − | 1.40560i | −0.100277 | − | 0.994960i | \(-0.531973\pi\) |
0.911799 | − | 0.410637i | \(-0.134694\pi\) | |||||||
\(674\) | 3.30806 | + | 15.5062i | 0.127422 | + | 0.597278i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.6046 | − | 14.1279i | 1.21556 | − | 0.543379i | ||||
\(677\) | −32.9941 | − | 19.0492i | −1.26807 | − | 0.732119i | −0.293445 | − | 0.955976i | \(-0.594802\pi\) |
−0.974622 | + | 0.223858i | \(0.928135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.98507 | + | 3.43825i | 0.0761801 | + | 0.131948i | ||||
\(680\) | 10.1749 | + | 4.50285i | 0.390188 | + | 0.172676i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.83428 | + | 27.2584i | −0.338282 | + | 1.04378i | ||||
\(683\) | 47.0728i | 1.80119i | 0.434659 | + | 0.900595i | \(0.356869\pi\) | ||||
−0.434659 | + | 0.900595i | \(0.643131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.52421i | 0.0964450i | ||||||||
\(686\) | 24.5402 | + | 7.95335i | 0.936951 | + | 0.303660i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.83887 | − | 13.5548i | 0.108231 | − | 0.516772i | ||||
\(689\) | −6.99676 | − | 12.1187i | −0.266555 | − | 0.461687i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.38522 | + | 1.95446i | 0.128780 | + | 0.0743512i | 0.563006 | − | 0.826453i | \(-0.309645\pi\) |
−0.434226 | + | 0.900804i | \(0.642978\pi\) | |||||||
\(692\) | −10.6473 | − | 23.8185i | −0.404750 | − | 0.905442i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.4760 | + | 6.07498i | −1.08093 | + | 0.230603i | ||||
\(695\) | 6.02468 | − | 10.4350i | 0.228529 | − | 0.395824i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.26678 | + | 9.12234i | 0.199494 | + | 0.345533i | ||||
\(698\) | 3.21481 | + | 3.56505i | 0.121683 | + | 0.134939i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.47975 | + | 14.2841i | −0.0559292 | + | 0.539887i | ||||
\(701\) | − | 16.4480i | − | 0.621231i | −0.950536 | − | 0.310615i | \(-0.899465\pi\) | ||
0.950536 | − | 0.310615i | \(-0.100535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.02598 | 0.227274 | ||||||||
\(704\) | 16.2192 | − | 14.7359i | 0.611282 | − | 0.555381i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.05707 | − | 0.953217i | 0.0397832 | − | 0.0358748i | ||||
\(707\) | 13.0730 | − | 7.54772i | 0.491662 | − | 0.283861i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.84805 | − | 3.95372i | −0.257184 | − | 0.148485i | 0.365865 | − | 0.930668i | \(-0.380773\pi\) |
−0.623049 | + | 0.782183i | \(0.714106\pi\) | |||||||
\(710\) | −3.54610 | + | 0.756515i | −0.133083 | + | 0.0283915i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.98123 | + | 6.82387i | 0.186679 | + | 0.255735i | ||||
\(713\) | −24.3251 | + | 42.1324i | −0.910984 | + | 1.57787i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.09037 | − | 5.24833i | 0.339961 | − | 0.196276i | ||||
\(716\) | 3.89340 | − | 5.37567i | 0.145503 | − | 0.200898i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −42.3471 | − | 13.7244i | −1.58038 | − | 0.512191i | ||||
\(719\) | 37.0556 | 1.38194 | 0.690970 | − | 0.722884i | \(-0.257184\pi\) | ||||
0.690970 | + | 0.722884i | \(0.257184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.4455 | 0.873156 | ||||||||
\(722\) | 24.3127 | + | 7.87960i | 0.904824 | + | 0.293248i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.4950 | − | 24.1556i | 0.650197 | − | 0.897736i | ||||
\(725\) | 12.8727 | − | 7.43204i | 0.478079 | − | 0.276019i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.83467 | − | 4.90979i | 0.105132 | − | 0.182094i | −0.808660 | − | 0.588276i | \(-0.799807\pi\) |
0.913792 | + | 0.406182i | \(0.133140\pi\) | |||||||
\(728\) | −19.9993 | + | 14.5989i | −0.741222 | + | 0.541071i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.72636 | − | 0.581634i | 0.100907 | − | 0.0215272i | ||||
\(731\) | −16.9461 | − | 9.78381i | −0.626773 | − | 0.361867i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.8544 | − | 6.26677i | 0.400915 | − | 0.231469i | −0.285964 | − | 0.958240i | \(-0.592314\pi\) |
0.686879 | + | 0.726772i | \(0.258980\pi\) | |||||||
\(734\) | −18.2045 | + | 16.4160i | −0.671940 | + | 0.605927i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32.1516 | − | 18.7231i | 1.18512 | − | 0.690144i | ||||
\(737\) | −18.8443 | −0.694139 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.83358i | 0.0674492i | 0.999431 | + | 0.0337246i | \(0.0107369\pi\) | ||||
−0.999431 | + | 0.0337246i | \(0.989263\pi\) | |||||||
\(740\) | 0.897304 | − | 8.66172i | 0.0329856 | − | 0.318411i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.82787 | + | 4.24490i | 0.140526 | + | 0.155835i | ||||
\(743\) | 15.6588 | + | 27.1219i | 0.574467 | + | 0.995006i | 0.996099 | + | 0.0882391i | \(0.0281240\pi\) |
−0.421632 | + | 0.906767i | \(0.638543\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.52491 | − | 13.0335i | 0.275691 | − | 0.477511i | ||||
\(746\) | 18.0055 | − | 3.84125i | 0.659230 | − | 0.140638i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.6359 | − | 28.2669i | −0.462013 | − | 1.03354i | ||||
\(749\) | 10.7879 | + | 6.22841i | 0.394182 | + | 0.227581i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.64466 | + | 6.31274i | 0.132996 | + | 0.230355i | 0.924830 | − | 0.380381i | \(-0.124207\pi\) |
−0.791834 | + | 0.610736i | \(0.790874\pi\) | |||||||
\(752\) | −30.1983 | − | 6.32461i | −1.10122 | − | 0.230635i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.3806 | + | 7.90162i | 0.887890 | + | 0.287760i | ||||
\(755\) | 8.84005i | 0.321722i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8156i | 0.465792i | 0.972502 | + | 0.232896i | \(0.0748202\pi\) | ||||
−0.972502 | + | 0.232896i | \(0.925180\pi\) | |||||||
\(758\) | 9.96908 | − | 30.7598i | 0.362093 | − | 1.11725i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.767501 | + | 1.73428i | −0.0278402 | + | 0.0629090i | ||||
\(761\) | −12.5800 | − | 21.7892i | −0.456025 | − | 0.789859i | 0.542721 | − | 0.839913i | \(-0.317394\pi\) |
−0.998747 | + | 0.0500541i | \(0.984061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.333807 | + | 0.192724i | 0.0120846 | + | 0.00697706i | ||||
\(764\) | −13.3611 | + | 5.97269i | −0.483389 | + | 0.216084i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.85883 | − | 41.5250i | −0.320083 | − | 1.50036i | ||||
\(767\) | −14.6854 | + | 25.4359i | −0.530261 | + | 0.918439i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7318 | − | 18.5880i | −0.386998 | − | 0.670300i | 0.605046 | − | 0.796190i | \(-0.293155\pi\) |
−0.992044 | + | 0.125890i | \(0.959821\pi\) | |||||||
\(770\) | −3.18414 | + | 2.87132i | −0.114748 | + | 0.103475i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.21873 | − | 40.7236i | 0.151835 | − | 1.46567i | ||||
\(773\) | 20.2122i | 0.726981i | 0.931598 | + | 0.363491i | \(0.118415\pi\) | ||||
−0.931598 | + | 0.363491i | \(0.881585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.4007 | 1.19979 | ||||||||
\(776\) | −7.02150 | + | 0.753899i | −0.252057 | + | 0.0270634i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36.0310 | + | 39.9564i | 1.29177 | + | 1.43251i | ||||
\(779\) | −1.55488 | + | 0.897712i | −0.0557095 | + | 0.0321639i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.73811 | + | 5.04495i | 0.312674 | + | 0.180523i | ||||
\(782\) | −10.9682 | − | 51.4127i | −0.392223 | − | 1.83851i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.9283 | + | 13.3276i | −0.426010 | + | 0.475984i | ||||
\(785\) | −6.07957 | + | 10.5301i | −0.216989 | + | 0.375836i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5726 | − | 10.1455i | 0.626395 | − | 0.361649i | −0.152960 | − | 0.988232i | \(-0.548880\pi\) |
0.779355 | + | 0.626583i | \(0.215547\pi\) | |||||||
\(788\) | 24.1009 | − | 33.2764i | 0.858558 | − | 1.18542i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.74728 | − | 5.39127i | 0.0621654 | − | 0.191813i | ||||
\(791\) | −13.8274 | −0.491646 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.4570 | −1.79178 | ||||||||
\(794\) | −16.3291 | + | 50.3837i | −0.579497 | + | 1.78805i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.16826 | + | 2.29465i | 0.112296 | + | 0.0813318i | ||||
\(797\) | 28.8758 | − | 16.6715i | 1.02283 | − | 0.590533i | 0.107910 | − | 0.994161i | \(-0.465584\pi\) |
0.914924 | + | 0.403627i | \(0.132251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.7970 | + | 37.7535i | −0.771122 | + | 1.33562i | ||||
\(800\) | −22.1690 | − | 12.6891i | −0.783792 | − | 0.448628i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.38918 | + | 6.51164i | 0.0490535 | + | 0.229934i | ||||
\(803\) | −6.71815 | − | 3.87873i | −0.237078 | − | 0.136877i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.30432 | + | 3.63980i | −0.222198 | + | 0.128286i | ||||
\(806\) | 38.5676 | + | 42.7693i | 1.35848 | + | 1.50649i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.86650 | + | 26.6974i | 0.100843 | + | 0.939212i | ||||
\(809\) | −30.6920 | −1.07907 | −0.539536 | − | 0.841962i | \(-0.681400\pi\) | ||||
−0.539536 | + | 0.841962i | \(0.681400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 49.5457i | − | 1.73978i | −0.493241 | − | 0.869892i | \(-0.664188\pi\) | ||
0.493241 | − | 0.869892i | \(-0.335812\pi\) | |||||||
\(812\) | −10.4130 | − | 1.07873i | −0.365424 | − | 0.0378558i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.9959 | + | 16.2280i | −0.630757 | + | 0.568790i | ||||
\(815\) | 2.98168 | + | 5.16443i | 0.104444 | + | 0.180902i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.66763 | − | 2.88842i | 0.0583430 | − | 0.101053i | ||||
\(818\) | 3.16532 | + | 14.8372i | 0.110673 | + | 0.518769i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.05884 | + | 2.36865i | 0.0369761 | + | 0.0827170i | ||||
\(821\) | 32.9739 | + | 19.0375i | 1.15080 | + | 0.664414i | 0.949082 | − | 0.315030i | \(-0.102015\pi\) |
0.201716 | + | 0.979444i | \(0.435348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.2626 | + | 19.5074i | 0.392589 | + | 0.679984i | 0.992790 | − | 0.119865i | \(-0.0382461\pi\) |
−0.600201 | + | 0.799849i | \(0.704913\pi\) | |||||||
\(824\) | −16.8769 | + | 38.1359i | −0.587936 | + | 1.32853i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.69879 | − | 11.4127i | 0.128697 | − | 0.397099i | ||||
\(827\) | − | 33.5317i | − | 1.16601i | −0.812468 | − | 0.583006i | \(-0.801876\pi\) | ||
0.812468 | − | 0.583006i | \(-0.198124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.7559i | − | 1.31132i | −0.755058 | − | 0.655658i | \(-0.772391\pi\) | ||
0.755058 | − | 0.655658i | \(-0.227609\pi\) | |||||||
\(830\) | 6.21696 | + | 2.01488i | 0.215794 | + | 0.0699376i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.35003 | − | 43.0392i | −0.324154 | − | 1.49212i | ||||
\(833\) | 12.6359 | + | 21.8860i | 0.437807 | + | 0.758304i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.20378 | + | 4.15910i | 0.249297 | + | 0.143932i | ||||
\(836\) | 4.81804 | − | 2.15376i | 0.166635 | − | 0.0744892i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.71107 | − | 1.21838i | 0.197286 | − | 0.0420884i | ||||
\(839\) | 9.90604 | − | 17.1578i | 0.341994 | − | 0.592352i | −0.642809 | − | 0.766027i | \(-0.722231\pi\) |
0.984803 | + | 0.173675i | \(0.0555643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.08210 | − | 15.7307i | −0.313176 | − | 0.542436i | ||||
\(842\) | −15.0173 | − | 16.6534i | −0.517531 | − | 0.573914i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.9262 | − | 2.16784i | −0.720310 | − | 0.0746200i | ||||
\(845\) | − | 12.0481i | − | 0.414466i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.56028 | −0.191053 | ||||||||
\(848\) | −9.66010 | + | 3.17069i | −0.331729 | + | 0.108882i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −26.8032 | + | 24.1700i | −0.919342 | + | 0.829023i | ||||
\(851\) | −35.6304 | + | 20.5712i | −1.22140 | + | 0.705173i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.95424 | − | 3.43768i | −0.203869 | − | 0.117704i | 0.394590 | − | 0.918857i | \(-0.370887\pi\) |
−0.598459 | + | 0.801153i | \(0.704220\pi\) | |||||||
\(854\) | 20.1566 | − | 4.30015i | 0.689744 | − | 0.147148i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.8965 | + | 13.0639i | −0.611690 | + | 0.446516i | ||||
\(857\) | 3.87316 | − | 6.70851i | 0.132305 | − | 0.229158i | −0.792260 | − | 0.610184i | \(-0.791096\pi\) |
0.924565 | + | 0.381025i | \(0.124429\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.594592 | − | 0.343288i | 0.0202872 | − | 0.0117128i | −0.489822 | − | 0.871822i | \(-0.662938\pi\) |
0.510109 | + | 0.860110i | \(0.329605\pi\) | |||||||
\(860\) | −3.90348 | − | 2.82715i | −0.133108 | − | 0.0964049i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.7745 | − | 7.05698i | −0.741642 | − | 0.240362i | ||||
\(863\) | 42.9194 | 1.46099 | 0.730496 | − | 0.682917i | \(-0.239289\pi\) | ||||
0.730496 | + | 0.682917i | \(0.239289\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.07991 | −0.308726 | ||||||||
\(866\) | −44.1677 | − | 14.3145i | −1.50088 | − | 0.486426i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19.0519 | − | 13.7986i | −0.646665 | − | 0.468355i | ||||
\(869\) | −13.6578 | + | 7.88535i | −0.463310 | + | 0.267492i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.9371 | + | 32.8000i | −0.641658 | + | 1.11138i | ||||
\(872\) | −0.553766 | + | 0.404233i | −0.0187529 | + | 0.0136891i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.76318 | − | 1.86951i | 0.296419 | − | 0.0632372i | ||||
\(875\) | 9.12082 | + | 5.26591i | 0.308340 | + | 0.178020i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.7508 | − | 8.51640i | 0.498100 | − | 0.287578i | −0.229828 | − | 0.973231i | \(-0.573817\pi\) |
0.727929 | + | 0.685653i | \(0.240483\pi\) | |||||||
\(878\) | 22.9530 | − | 20.6981i | 0.774627 | − | 0.698526i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.37836 | − | 7.24613i | −0.0801746 | − | 0.244267i | ||||
\(881\) | 7.90546 | 0.266342 | 0.133171 | − | 0.991093i | \(-0.457484\pi\) | ||||
0.133171 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.53298i | − | 0.253505i | −0.991934 | − | 0.126752i | \(-0.959545\pi\) | ||
0.991934 | − | 0.126752i | \(-0.0404554\pi\) | |||||||
\(884\) | −61.8989 | − | 6.41237i | −2.08188 | − | 0.215671i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.2998 | − | 36.9277i | −1.11873 | − | 1.24061i | ||||
\(887\) | −7.02719 | − | 12.1715i | −0.235950 | − | 0.408677i | 0.723598 | − | 0.690221i | \(-0.242487\pi\) |
−0.959548 | + | 0.281544i | \(0.909153\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.37351 | + | 2.37899i | −0.0460660 | + | 0.0797886i | ||||
\(890\) | 2.87558 | − | 0.613468i | 0.0963896 | − | 0.0205635i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.05260 | − | 3.15265i | 0.236138 | − | 0.105558i | ||||
\(893\) | −6.43501 | − | 3.71525i | −0.215339 | − | 0.124326i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.15500 | − | 2.00052i | −0.0386075 | − | 0.0668701i | ||||
\(896\) | 7.40312 | + | 16.3964i | 0.247321 | + | 0.547767i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.32993 | − | 1.40331i | −0.144492 | − | 0.0468289i | ||||
\(899\) | 24.3489i | 0.812081i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.3655i | 0.478585i | ||||||||
\(902\) | 2.22595 | − | 6.86822i | 0.0741160 | − | 0.228687i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.95347 | − | 22.4913i | 0.331048 | − | 0.748051i | ||||
\(905\) | −5.19001 | − | 8.98936i | −0.172522 | − | 0.298816i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7958 | + | 22.9761i | 1.32140 | + | 0.762910i | 0.983952 | − | 0.178435i | \(-0.0571034\pi\) |
0.337447 | + | 0.941345i | \(0.390437\pi\) | |||||||
\(908\) | −13.1176 | − | 29.3445i | −0.435322 | − | 0.973831i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.79794 | + | 8.42770i | 0.0596012 | + | 0.279375i | ||||
\(911\) | −25.7911 | + | 44.6715i | −0.854497 | + | 1.48003i | 0.0226136 | + | 0.999744i | \(0.492801\pi\) |
−0.877111 | + | 0.480288i | \(0.840532\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.09302 | − | 15.7496i | −0.300935 | − | 0.521235i | ||||
\(914\) | 8.51785 | − | 7.68104i | 0.281746 | − | 0.254066i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.1438 | + | 1.77600i | 0.566446 | + | 0.0586805i | ||||
\(917\) | 10.5571i | 0.348627i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2048 | −0.699481 | −0.349741 | − | 0.936847i | \(-0.613730\pi\) | ||||
−0.349741 | + | 0.936847i | \(0.613730\pi\) | |||||||
\(920\) | −1.38234 | − | 12.8745i | −0.0455743 | − | 0.424461i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.8830 | − | 22.0491i | −0.654810 | − | 0.726149i | ||||
\(923\) | 17.5623 | − | 10.1396i | 0.578069 | − | 0.333748i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.4620 | + | 14.1231i | 0.804305 | + | 0.464366i | ||||
\(926\) | −2.62611 | − | 12.3096i | −0.0862992 | − | 0.404520i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.25027 | − | 16.1610i | 0.303655 | − | 0.530511i | ||||
\(929\) | −1.70516 | + | 2.95343i | −0.0559446 | + | 0.0968989i | −0.892641 | − | 0.450767i | \(-0.851150\pi\) |
0.836697 | + | 0.547666i | \(0.184484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.73042 | + | 2.15376i | −0.122259 | + | 0.0705865i | ||||
\(932\) | −39.1236 | − | 28.3358i | −1.28154 | − | 0.928170i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.3593 | + | 35.0493i | −0.371687 | + | 1.14685i | ||||
\(935\) | −10.7757 | −0.352403 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4448 | 0.961919 | 0.480959 | − | 0.876743i | \(-0.340288\pi\) | ||||
0.480959 | + | 0.876743i | \(0.340288\pi\) | |||||||
\(938\) | 4.76964 | − | 14.7168i | 0.155734 | − | 0.480521i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.29849 | + | 8.69642i | −0.205434 | + | 0.283646i | ||||
\(941\) | 40.5880 | − | 23.4335i | 1.32313 | − | 0.763910i | 0.338904 | − | 0.940821i | \(-0.389944\pi\) |
0.984227 | + | 0.176911i | \(0.0566106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.12914 | − | 10.6160i | 0.199592 | − | 0.345704i | ||||
\(944\) | 15.9011 | + | 14.2316i | 0.517537 | + | 0.463201i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.79832 | + | 13.1169i | 0.0909812 | + | 0.426467i | ||||
\(947\) | 31.5821 | + | 18.2340i | 1.02628 | + | 0.592524i | 0.915917 | − | 0.401367i | \(-0.131465\pi\) |
0.110365 | + | 0.993891i | \(0.464798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.5024 | + | 7.79564i | −0.438308 | + | 0.253057i | ||||
\(950\) | −4.11972 | − | 4.56855i | −0.133661 | − | 0.148223i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 25.2738 | − | 2.71365i | 0.819130 | − | 0.0879500i | ||||
\(953\) | −38.0590 | −1.23285 | −0.616426 | − | 0.787413i | \(-0.711420\pi\) | ||||
−0.616426 | + | 0.787413i | \(0.711420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.09344i | 0.164820i | ||||||||
\(956\) | −0.830495 | + | 8.01680i | −0.0268601 | + | 0.259282i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.2985 | + | 16.5008i | −0.591198 | + | 0.533117i | ||||
\(959\) | 2.88330 | + | 4.99401i | 0.0931065 | + | 0.161265i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.8569 | + | 20.5368i | −0.382481 | + | 0.662477i | ||||
\(962\) | 10.1615 | + | 47.6312i | 0.327620 | + | 1.53569i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.2851 | − | 4.59764i | 0.331261 | − | 0.148080i | ||||
\(965\) | −12.3397 | − | 7.12430i | −0.397228 | − | 0.229339i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.4864 | + | 19.8951i | 0.369378 | + | 0.639782i | 0.989468 | − | 0.144749i | \(-0.0462374\pi\) |
−0.620090 | + | 0.784531i | \(0.712904\pi\) | |||||||
\(968\) | 4.00249 | − | 9.04422i | 0.128645 | − | 0.290692i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.757723 | + | 2.33797i | −0.0243290 | + | 0.0750677i | ||||
\(971\) | 53.8829i | 1.72919i | 0.502474 | + | 0.864593i | \(0.332423\pi\) | ||||
−0.502474 | + | 0.864593i | \(0.667577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 27.5269i | − | 0.882473i | ||||||
\(974\) | −40.0055 | − | 12.9656i | −1.28186 | − | 0.415443i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.51491 | + | 35.8816i | −0.240546 | + | 1.14854i | ||||
\(977\) | −19.1024 | − | 33.0863i | −0.611140 | − | 1.05853i | −0.991049 | − | 0.133501i | \(-0.957378\pi\) |
0.379909 | − | 0.925024i | \(-0.375955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.08585 | − | 4.09102i | −0.226465 | − | 0.130749i | ||||
\(980\) | 2.54032 | + | 5.68279i | 0.0811475 | + | 0.181530i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32.9547 | − | 7.03045i | 1.05163 | − | 0.224351i | ||||
\(983\) | 24.3307 | − | 42.1420i | 0.776028 | − | 1.34412i | −0.158186 | − | 0.987409i | \(-0.550565\pi\) |
0.934215 | − | 0.356711i | \(-0.116102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.14968 | − | 12.3836i | −0.227808 | − | 0.394574i | ||||
\(986\) | −17.6197 | − | 19.5393i | −0.561126 | − | 0.622259i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.09297 | − | 10.5505i | 0.0347722 | − | 0.335657i | ||||
\(989\) | 22.7715i | 0.724093i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7822 | −0.406040 | −0.203020 | − | 0.979175i | \(-0.565076\pi\) | ||||
−0.203020 | + | 0.979175i | \(0.565076\pi\) | |||||||
\(992\) | 36.1588 | − | 21.0567i | 1.14804 | − | 0.668551i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.15164 | + | 5.54728i | −0.195118 | + | 0.175949i | ||||
\(995\) | 1.17905 | − | 0.680723i | 0.0373783 | − | 0.0215804i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.1161 | + | 12.1914i | 0.668752 | + | 0.386104i | 0.795604 | − | 0.605817i | \(-0.207154\pi\) |
−0.126851 | + | 0.991922i | \(0.540487\pi\) | |||||||
\(998\) | 26.9299 | − | 5.74514i | 0.852450 | − | 0.181859i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 216.2.n.b.181.8 | 16 | ||
3.2 | odd | 2 | 72.2.n.b.61.1 | yes | 16 | ||
4.3 | odd | 2 | 864.2.r.b.721.5 | 16 | |||
8.3 | odd | 2 | 864.2.r.b.721.4 | 16 | |||
8.5 | even | 2 | inner | 216.2.n.b.181.2 | 16 | ||
9.2 | odd | 6 | 648.2.d.j.325.6 | 8 | |||
9.4 | even | 3 | inner | 216.2.n.b.37.2 | 16 | ||
9.5 | odd | 6 | 72.2.n.b.13.7 | yes | 16 | ||
9.7 | even | 3 | 648.2.d.k.325.3 | 8 | |||
12.11 | even | 2 | 288.2.r.b.241.2 | 16 | |||
24.5 | odd | 2 | 72.2.n.b.61.7 | yes | 16 | ||
24.11 | even | 2 | 288.2.r.b.241.7 | 16 | |||
36.7 | odd | 6 | 2592.2.d.k.1297.5 | 8 | |||
36.11 | even | 6 | 2592.2.d.j.1297.4 | 8 | |||
36.23 | even | 6 | 288.2.r.b.49.7 | 16 | |||
36.31 | odd | 6 | 864.2.r.b.145.4 | 16 | |||
72.5 | odd | 6 | 72.2.n.b.13.1 | ✓ | 16 | ||
72.11 | even | 6 | 2592.2.d.j.1297.5 | 8 | |||
72.13 | even | 6 | inner | 216.2.n.b.37.8 | 16 | ||
72.29 | odd | 6 | 648.2.d.j.325.5 | 8 | |||
72.43 | odd | 6 | 2592.2.d.k.1297.4 | 8 | |||
72.59 | even | 6 | 288.2.r.b.49.2 | 16 | |||
72.61 | even | 6 | 648.2.d.k.325.4 | 8 | |||
72.67 | odd | 6 | 864.2.r.b.145.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.n.b.13.1 | ✓ | 16 | 72.5 | odd | 6 | ||
72.2.n.b.13.7 | yes | 16 | 9.5 | odd | 6 | ||
72.2.n.b.61.1 | yes | 16 | 3.2 | odd | 2 | ||
72.2.n.b.61.7 | yes | 16 | 24.5 | odd | 2 | ||
216.2.n.b.37.2 | 16 | 9.4 | even | 3 | inner | ||
216.2.n.b.37.8 | 16 | 72.13 | even | 6 | inner | ||
216.2.n.b.181.2 | 16 | 8.5 | even | 2 | inner | ||
216.2.n.b.181.8 | 16 | 1.1 | even | 1 | trivial | ||
288.2.r.b.49.2 | 16 | 72.59 | even | 6 | |||
288.2.r.b.49.7 | 16 | 36.23 | even | 6 | |||
288.2.r.b.241.2 | 16 | 12.11 | even | 2 | |||
288.2.r.b.241.7 | 16 | 24.11 | even | 2 | |||
648.2.d.j.325.5 | 8 | 72.29 | odd | 6 | |||
648.2.d.j.325.6 | 8 | 9.2 | odd | 6 | |||
648.2.d.k.325.3 | 8 | 9.7 | even | 3 | |||
648.2.d.k.325.4 | 8 | 72.61 | even | 6 | |||
864.2.r.b.145.4 | 16 | 36.31 | odd | 6 | |||
864.2.r.b.145.5 | 16 | 72.67 | odd | 6 | |||
864.2.r.b.721.4 | 16 | 8.3 | odd | 2 | |||
864.2.r.b.721.5 | 16 | 4.3 | odd | 2 | |||
2592.2.d.j.1297.4 | 8 | 36.11 | even | 6 | |||
2592.2.d.j.1297.5 | 8 | 72.11 | even | 6 | |||
2592.2.d.k.1297.4 | 8 | 72.43 | odd | 6 | |||
2592.2.d.k.1297.5 | 8 | 36.7 | odd | 6 |