Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [270,2,Mod(17,270)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(270, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("270.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.m (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.15596085457\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 143.3 | ||
Root | \(0.500000 - 2.00333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 270.143 |
Dual form | 270.2.m.b.17.3 |
$q$-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 \(\left(\mathbb{Z}/270\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(217\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0.139908 | − | 2.23169i | 0.0625688 | − | 0.998041i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.622279 | − | 2.32238i | −0.235199 | − | 0.877776i | −0.978059 | − | 0.208328i | \(-0.933198\pi\) |
0.742860 | − | 0.669447i | \(-0.233469\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.442462 | − | 2.19185i | −0.139919 | − | 0.693125i | ||||
\(11\) | −0.991757 | − | 0.572591i | −0.299026 | − | 0.172643i | 0.342979 | − | 0.939343i | \(-0.388564\pi\) |
−0.642005 | + | 0.766700i | \(0.721897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.640322 | + | 2.38971i | −0.177593 | + | 0.662788i | 0.818502 | + | 0.574504i | \(0.194805\pi\) |
−0.996095 | + | 0.0882838i | \(0.971862\pi\) | |||||||
\(14\) | −1.20215 | − | 2.08219i | −0.321288 | − | 0.556487i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 4.99855 | + | 4.99855i | 1.21233 | + | 1.21233i | 0.970259 | + | 0.242068i | \(0.0778258\pi\) |
0.242068 | + | 0.970259i | \(0.422174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.78390i | − | 0.638671i | −0.947642 | − | 0.319336i | \(-0.896540\pi\) | ||
0.947642 | − | 0.319336i | \(-0.103460\pi\) | |||||||
\(20\) | −0.994679 | − | 2.00265i | −0.222417 | − | 0.447806i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.10616 | − | 0.296395i | −0.235834 | − | 0.0631917i | ||||
\(23\) | 5.95746 | + | 1.59630i | 1.24222 | + | 0.332851i | 0.819325 | − | 0.573330i | \(-0.194349\pi\) |
0.422891 | + | 0.906181i | \(0.361015\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96085 | − | 0.624462i | −0.992170 | − | 0.124892i | ||||
\(26\) | 2.47401i | 0.485194i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.70010 | − | 1.70010i | −0.321288 | − | 0.321288i | ||||
\(29\) | −0.672250 | + | 1.16437i | −0.124834 | + | 0.216218i | −0.921668 | − | 0.387980i | \(-0.873173\pi\) |
0.796834 | + | 0.604198i | \(0.206506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25223 | + | 2.16892i | 0.224907 | + | 0.389550i | 0.956292 | − | 0.292415i | \(-0.0944589\pi\) |
−0.731385 | + | 0.681965i | \(0.761126\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.12195 | + | 3.53451i | 1.04991 | + | 0.606164i | ||||
\(35\) | −5.26988 | + | 1.06381i | −0.890772 | + | 0.179817i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.16761 | + | 8.16761i | −1.34275 | + | 1.34275i | −0.449434 | + | 0.893314i | \(0.648374\pi\) |
−0.893314 | + | 0.449434i | \(0.851626\pi\) | |||||||
\(38\) | −0.720527 | − | 2.68904i | −0.116885 | − | 0.436221i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.47911 | − | 1.67697i | −0.233868 | − | 0.265152i | ||||
\(41\) | 1.70826 | − | 0.986264i | 0.266785 | − | 0.154029i | −0.360641 | − | 0.932705i | \(-0.617442\pi\) |
0.627426 | + | 0.778676i | \(0.284109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.68498 | − | 2.32713i | 1.32445 | − | 0.354885i | 0.473805 | − | 0.880630i | \(-0.342880\pi\) |
0.850642 | + | 0.525745i | \(0.176213\pi\) | |||||||
\(44\) | −1.14518 | −0.172643 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.16761 | 0.909365 | ||||||||
\(47\) | −11.9118 | + | 3.19175i | −1.73751 | + | 0.465565i | −0.981891 | − | 0.189445i | \(-0.939331\pi\) |
−0.755621 | + | 0.655010i | \(0.772665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.05598 | − | 0.609669i | 0.150854 | − | 0.0870956i | ||||
\(50\) | −4.95344 | + | 0.680779i | −0.700522 | + | 0.0962767i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.640322 | + | 2.38971i | 0.0887967 | + | 0.331394i | ||||
\(53\) | −1.84828 | + | 1.84828i | −0.253881 | + | 0.253881i | −0.822560 | − | 0.568679i | \(-0.807455\pi\) |
0.568679 | + | 0.822560i | \(0.307455\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41660 | + | 2.13318i | −0.191014 | + | 0.287638i | ||||
\(56\) | −2.08219 | − | 1.20215i | −0.278244 | − | 0.160644i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.347982 | + | 1.29869i | −0.0456923 | + | 0.170526i | ||||
\(59\) | −1.31456 | − | 2.27688i | −0.171141 | − | 0.296424i | 0.767678 | − | 0.640835i | \(-0.221412\pi\) |
−0.938819 | + | 0.344411i | \(0.888079\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.54275 | + | 6.13623i | −0.453603 | + | 0.785664i | −0.998607 | − | 0.0527700i | \(-0.983195\pi\) |
0.545004 | + | 0.838434i | \(0.316528\pi\) | |||||||
\(62\) | 1.77092 | + | 1.77092i | 0.224907 | + | 0.224907i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 5.24351 | + | 1.76334i | 0.650377 | + | 0.218715i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0545285 | + | 0.0146109i | 0.00666172 | + | 0.00178500i | 0.262148 | − | 0.965028i | \(-0.415569\pi\) |
−0.255487 | + | 0.966813i | \(0.582236\pi\) | |||||||
\(68\) | 6.82815 | + | 1.82960i | 0.828035 | + | 0.221871i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.81498 | + | 2.39151i | −0.575500 | + | 0.285840i | ||||
\(71\) | − | 9.10005i | − | 1.07998i | −0.841672 | − | 0.539989i | \(-0.818429\pi\) | ||
0.841672 | − | 0.539989i | \(-0.181571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.82779 | + | 7.82779i | 0.916174 | + | 0.916174i | 0.996749 | − | 0.0805747i | \(-0.0256756\pi\) |
−0.0805747 | + | 0.996749i | \(0.525676\pi\) | |||||||
\(74\) | −5.77537 | + | 10.0032i | −0.671374 | + | 1.16285i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.39195 | − | 2.41093i | −0.159668 | − | 0.276553i | ||||
\(77\) | −0.712623 | + | 2.65955i | −0.0812109 | + | 0.303083i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.46375 | − | 4.88655i | −0.952246 | − | 0.549779i | −0.0584679 | − | 0.998289i | \(-0.518622\pi\) |
−0.893778 | + | 0.448510i | \(0.851955\pi\) | |||||||
\(80\) | −1.86274 | − | 1.23701i | −0.208261 | − | 0.138302i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.39479 | − | 1.39479i | 0.154029 | − | 0.154029i | ||||
\(83\) | −0.724794 | − | 2.70497i | −0.0795565 | − | 0.296909i | 0.914671 | − | 0.404198i | \(-0.132449\pi\) |
−0.994228 | + | 0.107290i | \(0.965783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8545 | − | 10.4559i | 1.28581 | − | 1.13410i | ||||
\(86\) | 7.78674 | − | 4.49568i | 0.839666 | − | 0.484781i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.10616 | + | 0.296395i | −0.117917 | + | 0.0315958i | ||||
\(89\) | 4.87832 | 0.517100 | 0.258550 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258550 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.94827 | 0.623549 | ||||||||
\(92\) | 5.95746 | − | 1.59630i | 0.621108 | − | 0.166425i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.6798 | + | 6.16599i | −1.10154 | + | 0.635974i | ||||
\(95\) | −6.21280 | − | 0.389491i | −0.637420 | − | 0.0399609i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.08981 | + | 7.79929i | 0.212188 | + | 0.791898i | 0.987137 | + | 0.159874i | \(0.0511088\pi\) |
−0.774949 | + | 0.632024i | \(0.782225\pi\) | |||||||
\(98\) | 0.862203 | − | 0.862203i | 0.0870956 | − | 0.0870956i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.60845 | + | 1.93963i | −0.460845 | + | 0.193963i | ||||
\(101\) | 0.631074 | + | 0.364351i | 0.0627942 | + | 0.0362543i | 0.531068 | − | 0.847329i | \(-0.321791\pi\) |
−0.468274 | + | 0.883583i | \(0.655124\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.353393 | − | 1.31888i | 0.0348209 | − | 0.129953i | −0.946327 | − | 0.323209i | \(-0.895238\pi\) |
0.981148 | + | 0.193256i | \(0.0619048\pi\) | |||||||
\(104\) | 1.23701 | + | 2.14256i | 0.121299 | + | 0.210095i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.30693 | + | 2.26367i | −0.126940 | + | 0.219867i | ||||
\(107\) | 0.399208 | + | 0.399208i | 0.0385929 | + | 0.0385929i | 0.726140 | − | 0.687547i | \(-0.241312\pi\) |
−0.687547 | + | 0.726140i | \(0.741312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.5974i | − | 1.30239i | −0.758909 | − | 0.651196i | \(-0.774268\pi\) | ||
0.758909 | − | 0.651196i | \(-0.225732\pi\) | |||||||
\(110\) | −0.816222 | + | 2.42714i | −0.0778237 | + | 0.231419i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.32238 | − | 0.622279i | −0.219444 | − | 0.0587998i | ||||
\(113\) | −4.94392 | − | 1.32472i | −0.465084 | − | 0.124619i | 0.0186645 | − | 0.999826i | \(-0.494059\pi\) |
−0.483749 | + | 0.875207i | \(0.660725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.39593 | − | 13.0718i | 0.409922 | − | 1.21896i | ||||
\(116\) | 1.34450i | 0.124834i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.85906 | − | 1.85906i | −0.171141 | − | 0.171141i | ||||
\(119\) | 8.49803 | − | 14.7190i | 0.779013 | − | 1.34929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.84428 | − | 8.39054i | −0.440389 | − | 0.762776i | ||||
\(122\) | −1.83386 | + | 6.84408i | −0.166030 | + | 0.619633i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.16892 | + | 1.25223i | 0.194775 | + | 0.112453i | ||||
\(125\) | −2.08767 | + | 10.9837i | −0.186727 | + | 0.982412i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.88817 | + | 4.88817i | −0.433755 | + | 0.433755i | −0.889904 | − | 0.456149i | \(-0.849228\pi\) |
0.456149 | + | 0.889904i | \(0.349228\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.52123 | + | 0.346135i | 0.484244 | + | 0.0303580i | ||||
\(131\) | −4.98351 | + | 2.87723i | −0.435412 | + | 0.251385i | −0.701649 | − | 0.712522i | \(-0.747553\pi\) |
0.266238 | + | 0.963907i | \(0.414219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.46527 | + | 1.73236i | −0.560610 | + | 0.150215i | ||||
\(134\) | 0.0564521 | 0.00487672 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.06902 | 0.606164 | ||||||||
\(137\) | 10.0458 | − | 2.69177i | 0.858272 | − | 0.229973i | 0.197262 | − | 0.980351i | \(-0.436795\pi\) |
0.661010 | + | 0.750377i | \(0.270128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.19537 | + | 1.26750i | −0.186209 | + | 0.107508i | −0.590207 | − | 0.807252i | \(-0.700954\pi\) |
0.403998 | + | 0.914760i | \(0.367620\pi\) | |||||||
\(140\) | −4.03194 | + | 3.55623i | −0.340761 | + | 0.300556i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.35527 | − | 8.78997i | −0.197650 | − | 0.737638i | ||||
\(143\) | 2.00337 | − | 2.00337i | 0.167531 | − | 0.167531i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50446 | + | 1.66316i | 0.207984 | + | 0.138118i | ||||
\(146\) | 9.58705 | + | 5.53509i | 0.793430 | + | 0.458087i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.98955 | + | 11.1572i | −0.245740 | + | 0.917114i | ||||
\(149\) | −6.49294 | − | 11.2461i | −0.531922 | − | 0.921316i | −0.999306 | − | 0.0372613i | \(-0.988137\pi\) |
0.467384 | − | 0.884055i | \(-0.345197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.58502 | − | 2.74534i | 0.128987 | − | 0.223412i | −0.794297 | − | 0.607529i | \(-0.792161\pi\) |
0.923284 | + | 0.384117i | \(0.125494\pi\) | |||||||
\(152\) | −1.96852 | − | 1.96852i | −0.159668 | − | 0.159668i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.75336i | 0.221872i | ||||||||
\(155\) | 5.01556 | − | 2.49113i | 0.402859 | − | 0.200093i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3186 | + | 2.76487i | 0.823515 | + | 0.220660i | 0.645883 | − | 0.763437i | \(-0.276489\pi\) |
0.177633 | + | 0.984097i | \(0.443156\pi\) | |||||||
\(158\) | −9.44008 | − | 2.52946i | −0.751013 | − | 0.201233i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.11943 | − | 0.712744i | −0.167556 | − | 0.0563473i | ||||
\(161\) | − | 14.8288i | − | 1.16867i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7354 | − | 15.7354i | −1.23249 | − | 1.23249i | −0.963003 | − | 0.269490i | \(-0.913145\pi\) |
−0.269490 | − | 0.963003i | \(-0.586855\pi\) | |||||||
\(164\) | 0.986264 | − | 1.70826i | 0.0770143 | − | 0.133393i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.40019 | − | 2.42521i | −0.108676 | − | 0.188233i | ||||
\(167\) | 1.05230 | − | 3.92724i | 0.0814295 | − | 0.303899i | −0.913185 | − | 0.407546i | \(-0.866385\pi\) |
0.994614 | + | 0.103647i | \(0.0330512\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.95761 | + | 3.43963i | 0.458277 | + | 0.264587i | ||||
\(170\) | 8.74443 | − | 13.1678i | 0.670667 | − | 1.00992i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.35785 | − | 6.35785i | 0.484781 | − | 0.484781i | ||||
\(173\) | 1.44105 | + | 5.37809i | 0.109561 | + | 0.408889i | 0.998823 | − | 0.0485110i | \(-0.0154476\pi\) |
−0.889261 | + | 0.457400i | \(0.848781\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.63680 | + | 11.9096i | 0.123730 | + | 0.900278i | ||||
\(176\) | −0.991757 | + | 0.572591i | −0.0747565 | + | 0.0431607i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.71209 | − | 1.26260i | 0.353186 | − | 0.0946359i | ||||
\(179\) | 0.310192 | 0.0231848 | 0.0115924 | − | 0.999933i | \(-0.496310\pi\) | ||||
0.0115924 | + | 0.999933i | \(0.496310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.07416 | 0.228501 | 0.114250 | − | 0.993452i | \(-0.463553\pi\) | ||||
0.114250 | + | 0.993452i | \(0.463553\pi\) | |||||||
\(182\) | 5.74559 | − | 1.53953i | 0.425892 | − | 0.114117i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.34131 | − | 3.08381i | 0.393767 | − | 0.227341i | ||||
\(185\) | 17.0848 | + | 19.3703i | 1.25610 | + | 1.42413i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.09522 | − | 7.81948i | −0.153218 | − | 0.571817i | ||||
\(188\) | −8.72003 | + | 8.72003i | −0.635974 | + | 0.635974i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.10191 | + | 1.23177i | −0.442679 | + | 0.0893622i | ||||
\(191\) | 12.3541 | + | 7.13262i | 0.893909 | + | 0.516098i | 0.875219 | − | 0.483727i | \(-0.160717\pi\) |
0.0186896 | + | 0.999825i | \(0.494051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.48506 | + | 9.27437i | −0.178879 | + | 0.667584i | 0.816980 | + | 0.576666i | \(0.195647\pi\) |
−0.995858 | + | 0.0909176i | \(0.971020\pi\) | |||||||
\(194\) | 4.03721 | + | 6.99265i | 0.289855 | + | 0.502043i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.609669 | − | 1.05598i | 0.0435478 | − | 0.0754270i | ||||
\(197\) | −4.62495 | − | 4.62495i | −0.329514 | − | 0.329514i | 0.522887 | − | 0.852402i | \(-0.324855\pi\) |
−0.852402 | + | 0.522887i | \(0.824855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.07227i | − | 0.288675i | −0.989528 | − | 0.144338i | \(-0.953895\pi\) | ||
0.989528 | − | 0.144338i | \(-0.0461051\pi\) | |||||||
\(200\) | −3.94941 | + | 3.06629i | −0.279266 | + | 0.216819i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.703872 | + | 0.188602i | 0.0495243 | + | 0.0132700i | ||||
\(203\) | 3.12243 | + | 0.836654i | 0.219152 | + | 0.0587216i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.96203 | − | 3.95029i | −0.137034 | − | 0.275900i | ||||
\(206\) | − | 1.36541i | − | 0.0951324i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.74939 | + | 1.74939i | 0.121299 | + | 0.121299i | ||||
\(209\) | −1.59404 | + | 2.76096i | −0.110262 | + | 0.190979i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.58800 | − | 13.1428i | −0.522379 | − | 0.904788i | −0.999661 | − | 0.0260371i | \(-0.991711\pi\) |
0.477282 | − | 0.878750i | \(-0.341622\pi\) | |||||||
\(212\) | −0.676517 | + | 2.52480i | −0.0464634 | + | 0.173404i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.488928 | + | 0.282283i | 0.0334224 | + | 0.0192964i | ||||
\(215\) | −3.97833 | − | 19.7077i | −0.271320 | − | 1.34406i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.25782 | − | 4.25782i | 0.289040 | − | 0.289040i | ||||
\(218\) | −3.51926 | − | 13.1341i | −0.238354 | − | 0.889551i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.160220 | + | 2.55569i | −0.0108021 | + | 0.172305i | ||||
\(221\) | −15.1458 | + | 8.74443i | −1.01882 | + | 0.588214i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.21978 | − | 2.20248i | 0.550437 | − | 0.147489i | 0.0271279 | − | 0.999632i | \(-0.491364\pi\) |
0.523309 | + | 0.852143i | \(0.324697\pi\) | |||||||
\(224\) | −2.40430 | −0.160644 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.11832 | −0.340465 | ||||||||
\(227\) | −19.6687 | + | 5.27021i | −1.30546 | + | 0.349796i | −0.843511 | − | 0.537112i | \(-0.819515\pi\) |
−0.461946 | + | 0.886908i | \(0.652849\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2032 | + | 7.04551i | −0.806409 | + | 0.465580i | −0.845707 | − | 0.533647i | \(-0.820821\pi\) |
0.0392983 | + | 0.999228i | \(0.487488\pi\) | |||||||
\(230\) | 0.862899 | − | 13.7642i | 0.0568979 | − | 0.907583i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.347982 | + | 1.29869i | 0.0228461 | + | 0.0852630i | ||||
\(233\) | −0.643009 | + | 0.643009i | −0.0421249 | + | 0.0421249i | −0.727855 | − | 0.685731i | \(-0.759483\pi\) |
0.685731 | + | 0.727855i | \(0.259483\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.45644 | + | 27.0299i | 0.355939 | + | 1.76324i | ||||
\(236\) | −2.27688 | − | 1.31456i | −0.148212 | − | 0.0855703i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.39890 | − | 16.4169i | 0.285139 | − | 1.06415i | ||||
\(239\) | 5.34131 | + | 9.25142i | 0.345501 | + | 0.598425i | 0.985445 | − | 0.169997i | \(-0.0543758\pi\) |
−0.639944 | + | 0.768422i | \(0.721042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5666 | + | 18.3019i | −0.680654 | + | 1.17893i | 0.294127 | + | 0.955766i | \(0.404971\pi\) |
−0.974782 | + | 0.223161i | \(0.928362\pi\) | |||||||
\(242\) | −6.85084 | − | 6.85084i | −0.440389 | − | 0.440389i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.08551i | 0.453603i | ||||||||
\(245\) | −1.21285 | − | 2.44191i | −0.0774862 | − | 0.156008i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.65274 | + | 1.78260i | 0.423303 | + | 0.113424i | ||||
\(248\) | 2.41912 | + | 0.648201i | 0.153614 | + | 0.0411608i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.826260 | + | 11.1498i | 0.0522573 | + | 0.705173i | ||||
\(251\) | 24.6952i | 1.55874i | 0.626561 | + | 0.779372i | \(0.284462\pi\) | ||||
−0.626561 | + | 0.779372i | \(0.715538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.99433 | − | 4.99433i | −0.313991 | − | 0.313991i | ||||
\(254\) | −3.45646 | + | 5.98676i | −0.216877 | + | 0.375643i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.36020 | − | 5.07632i | 0.0848467 | − | 0.316652i | −0.910438 | − | 0.413645i | \(-0.864256\pi\) |
0.995285 | + | 0.0969925i | \(0.0309223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.0508 | + | 13.8857i | 1.49444 | + | 0.862818i | ||||
\(260\) | 5.42268 | − | 1.09466i | 0.336300 | − | 0.0678878i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.06902 | + | 4.06902i | −0.251385 | + | 0.251385i | ||||
\(263\) | 3.86551 | + | 14.4263i | 0.238358 | + | 0.889563i | 0.976606 | + | 0.215034i | \(0.0689864\pi\) |
−0.738249 | + | 0.674529i | \(0.764347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.86619 | + | 4.38337i | 0.237498 | + | 0.269268i | ||||
\(266\) | −5.79660 | + | 3.34667i | −0.355413 | + | 0.205198i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0545285 | − | 0.0146109i | 0.00333086 | − | 0.000892501i | ||||
\(269\) | −20.0071 | −1.21985 | −0.609927 | − | 0.792457i | \(-0.708801\pi\) | ||||
−0.609927 | + | 0.792457i | \(0.708801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.02714 | −0.183886 | −0.0919428 | − | 0.995764i | \(-0.529308\pi\) | ||||
−0.0919428 | + | 0.995764i | \(0.529308\pi\) | |||||||
\(272\) | 6.82815 | − | 1.82960i | 0.414018 | − | 0.110936i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.00683 | − | 5.20010i | 0.544123 | − | 0.314149i | ||||
\(275\) | 4.56240 | + | 3.45986i | 0.275123 | + | 0.208637i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.723941 | − | 2.70178i | −0.0434974 | − | 0.162334i | 0.940761 | − | 0.339071i | \(-0.110113\pi\) |
−0.984258 | + | 0.176736i | \(0.943446\pi\) | |||||||
\(278\) | −1.79251 | + | 1.79251i | −0.107508 | + | 0.107508i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.97414 | + | 4.47860i | −0.177739 | + | 0.267647i | ||||
\(281\) | −13.0998 | − | 7.56319i | −0.781470 | − | 0.451182i | 0.0554808 | − | 0.998460i | \(-0.482331\pi\) |
−0.836951 | + | 0.547278i | \(0.815664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.22154 | + | 23.2191i | −0.369832 | + | 1.38023i | 0.490918 | + | 0.871206i | \(0.336661\pi\) |
−0.860750 | + | 0.509027i | \(0.830005\pi\) | |||||||
\(284\) | −4.55002 | − | 7.88087i | −0.269994 | − | 0.467644i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.41660 | − | 2.45362i | 0.0837653 | − | 0.145086i | ||||
\(287\) | −3.35349 | − | 3.35349i | −0.197950 | − | 0.197950i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.9711i | 1.93948i | ||||||||
\(290\) | 2.84958 | + | 0.958284i | 0.167333 | + | 0.0562724i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.6930 | + | 2.86517i | 0.625758 | + | 0.167671i | ||||
\(293\) | −14.5851 | − | 3.90805i | −0.852068 | − | 0.228311i | −0.193750 | − | 0.981051i | \(-0.562065\pi\) |
−0.658318 | + | 0.752740i | \(0.728732\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.26519 | + | 2.61512i | −0.306551 | + | 0.152258i | ||||
\(296\) | 11.5507i | 0.671374i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.18240 | − | 9.18240i | −0.531922 | − | 0.531922i | ||||
\(299\) | −7.62938 | + | 13.2145i | −0.441219 | + | 0.764213i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.8090 | − | 18.7217i | −0.623018 | − | 1.07910i | ||||
\(302\) | 0.820468 | − | 3.06203i | 0.0472126 | − | 0.176200i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.41093 | − | 1.39195i | −0.138276 | − | 0.0798339i | ||||
\(305\) | 13.1985 | + | 8.76483i | 0.755743 | + | 0.501872i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.29531 | − | 8.29531i | 0.473438 | − | 0.473438i | −0.429587 | − | 0.903025i | \(-0.641341\pi\) |
0.903025 | + | 0.429587i | \(0.141341\pi\) | |||||||
\(308\) | 0.712623 | + | 2.65955i | 0.0406055 | + | 0.151542i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.19990 | − | 3.70437i | 0.238538 | − | 0.210394i | ||||
\(311\) | −10.8857 | + | 6.28488i | −0.617274 | + | 0.356383i | −0.775807 | − | 0.630971i | \(-0.782657\pi\) |
0.158533 | + | 0.987354i | \(0.449324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5304 | − | 3.08956i | 0.651737 | − | 0.174632i | 0.0822229 | − | 0.996614i | \(-0.473798\pi\) |
0.569514 | + | 0.821982i | \(0.307131\pi\) | |||||||
\(314\) | 10.6826 | 0.602855 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.77309 | −0.549779 | ||||||||
\(317\) | 1.87547 | − | 0.502531i | 0.105337 | − | 0.0282249i | −0.205766 | − | 0.978601i | \(-0.565968\pi\) |
0.311102 | + | 0.950376i | \(0.399302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.33342 | − | 0.769849i | 0.0746570 | − | 0.0431033i | ||||
\(320\) | −2.23169 | − | 0.139908i | −0.124755 | − | 0.00782110i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.83797 | − | 14.3235i | −0.213882 | − | 0.798218i | ||||
\(323\) | 13.9155 | − | 13.9155i | 0.774279 | − | 0.774279i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.66883 | − | 11.4552i | 0.258980 | − | 0.635418i | ||||
\(326\) | −19.2719 | − | 11.1266i | −1.06737 | − | 0.616247i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.510528 | − | 1.90532i | 0.0281892 | − | 0.105203i | ||||
\(329\) | 14.8249 | + | 25.6775i | 0.817323 | + | 1.41565i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9811 | + | 19.0198i | −0.603575 | + | 1.04542i | 0.388700 | + | 0.921364i | \(0.372924\pi\) |
−0.992275 | + | 0.124058i | \(0.960409\pi\) | |||||||
\(332\) | −1.98017 | − | 1.98017i | −0.108676 | − | 0.108676i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 4.06578i | − | 0.222470i | ||||||
\(335\) | 0.0402359 | − | 0.119646i | 0.00219832 | − | 0.00653698i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.8842 | − | 6.93565i | −1.41000 | − | 0.377809i | −0.528076 | − | 0.849197i | \(-0.677086\pi\) |
−0.881926 | + | 0.471388i | \(0.843753\pi\) | |||||||
\(338\) | 6.64485 | + | 1.78048i | 0.361432 | + | 0.0968454i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.03840 | − | 14.9823i | 0.273246 | − | 0.812530i | ||||
\(341\) | − | 2.86806i | − | 0.155314i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.9737 | − | 13.9737i | −0.754508 | − | 0.754508i | ||||
\(344\) | 4.49568 | − | 7.78674i | 0.242391 | − | 0.419833i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.78390 | + | 4.82186i | 0.149664 | + | 0.259225i | ||||
\(347\) | 7.78712 | − | 29.0619i | 0.418035 | − | 1.56013i | −0.360644 | − | 0.932704i | \(-0.617443\pi\) |
0.778679 | − | 0.627423i | \(-0.215890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.2846 | − | 12.8660i | −1.19287 | − | 0.688702i | −0.233911 | − | 0.972258i | \(-0.575152\pi\) |
−0.958956 | + | 0.283556i | \(0.908486\pi\) | |||||||
\(350\) | 4.66344 | + | 11.0801i | 0.249272 | + | 0.592257i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.809767 | + | 0.809767i | −0.0431607 | + | 0.0431607i | ||||
\(353\) | 4.03627 | + | 15.0636i | 0.214829 | + | 0.801752i | 0.986227 | + | 0.165399i | \(0.0528912\pi\) |
−0.771398 | + | 0.636353i | \(0.780442\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.3085 | − | 1.27317i | −1.07786 | − | 0.0675728i | ||||
\(356\) | 4.22474 | − | 2.43916i | 0.223911 | − | 0.129275i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.299622 | − | 0.0802835i | 0.0158355 | − | 0.00424312i | ||||
\(359\) | 22.9830 | 1.21300 | 0.606498 | − | 0.795085i | \(-0.292574\pi\) | ||||
0.606498 | + | 0.795085i | \(0.292574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2499 | 0.592099 | ||||||||
\(362\) | 2.96941 | − | 0.795652i | 0.156069 | − | 0.0418185i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.15136 | − | 2.97414i | 0.270004 | − | 0.155887i | ||||
\(365\) | 18.5644 | − | 16.3740i | 0.971703 | − | 0.857055i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.901720 | − | 3.36526i | −0.0470694 | − | 0.175665i | 0.938389 | − | 0.345580i | \(-0.112318\pi\) |
−0.985459 | + | 0.169914i | \(0.945651\pi\) | |||||||
\(368\) | 4.36116 | − | 4.36116i | 0.227341 | − | 0.227341i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.5161 | + | 14.2884i | 1.11857 | + | 0.742817i | ||||
\(371\) | 5.44254 | + | 3.14225i | 0.282563 | + | 0.163138i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.91894 | − | 22.0898i | 0.306471 | − | 1.14377i | −0.625200 | − | 0.780464i | \(-0.714983\pi\) |
0.931671 | − | 0.363302i | \(-0.118351\pi\) | |||||||
\(374\) | −4.04766 | − | 7.01076i | −0.209300 | − | 0.362518i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.16599 | + | 10.6798i | −0.317987 | + | 0.550769i | ||||
\(377\) | −2.35206 | − | 2.35206i | −0.121137 | − | 0.121137i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 36.3113i | − | 1.86519i | −0.360927 | − | 0.932594i | \(-0.617540\pi\) | ||
0.360927 | − | 0.932594i | \(-0.382460\pi\) | |||||||
\(380\) | −5.57519 | + | 2.76909i | −0.286001 | + | 0.142051i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.7792 | + | 3.69212i | 0.705003 | + | 0.188905i | ||||
\(383\) | −16.0342 | − | 4.29635i | −0.819308 | − | 0.219533i | −0.175264 | − | 0.984521i | \(-0.556078\pi\) |
−0.644044 | + | 0.764988i | \(0.722745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.83557 | + | 1.96244i | 0.297408 | + | 0.100015i | ||||
\(386\) | 9.60153i | 0.488705i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.70947 | + | 5.70947i | 0.289855 | + | 0.289855i | ||||
\(389\) | 11.7878 | − | 20.4171i | 0.597667 | − | 1.03519i | −0.395497 | − | 0.918467i | \(-0.629428\pi\) |
0.993164 | − | 0.116723i | \(-0.0372390\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.7995 | + | 37.7578i | 1.10245 | + | 1.90950i | ||||
\(392\) | 0.315588 | − | 1.17779i | 0.0159396 | − | 0.0594874i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.66439 | − | 3.27034i | −0.285368 | − | 0.164757i | ||||
\(395\) | −12.0894 | + | 18.2048i | −0.608283 | + | 0.915981i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.6509 | − | 27.6509i | 1.38776 | − | 1.38776i | 0.557748 | − | 0.830011i | \(-0.311666\pi\) |
0.830011 | − | 0.557748i | \(-0.188334\pi\) | |||||||
\(398\) | −1.05398 | − | 3.93351i | −0.0528312 | − | 0.197169i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.02123 | + | 3.98399i | −0.151061 | + | 0.199200i | ||||
\(401\) | 26.4658 | − | 15.2801i | 1.32164 | − | 0.763050i | 0.337651 | − | 0.941272i | \(-0.390368\pi\) |
0.983990 | + | 0.178222i | \(0.0570344\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.98494 | + | 1.60366i | −0.298131 | + | 0.0798840i | ||||
\(404\) | 0.728702 | 0.0362543 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.23258 | 0.160430 | ||||||||
\(407\) | 12.7770 | − | 3.42359i | 0.633332 | − | 0.169701i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.43668 | + | 1.40682i | −0.120486 | + | 0.0695626i | −0.559032 | − | 0.829146i | \(-0.688827\pi\) |
0.438546 | + | 0.898709i | \(0.355494\pi\) | |||||||
\(410\) | −2.91759 | − | 3.30787i | −0.144089 | − | 0.163364i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.353393 | − | 1.31888i | −0.0174104 | − | 0.0649766i | ||||
\(413\) | −4.46974 | + | 4.46974i | −0.219942 | + | 0.219942i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.13805 | + | 1.23907i | −0.301305 | + | 0.0608234i | ||||
\(416\) | 2.14256 | + | 1.23701i | 0.105048 | + | 0.0606493i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.825136 | + | 3.07945i | −0.0403587 | + | 0.150621i | ||||
\(419\) | 2.23812 | + | 3.87654i | 0.109339 | + | 0.189381i | 0.915503 | − | 0.402311i | \(-0.131793\pi\) |
−0.806163 | + | 0.591693i | \(0.798460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.85177 | − | 4.93941i | 0.138987 | − | 0.240732i | −0.788127 | − | 0.615513i | \(-0.788949\pi\) |
0.927113 | + | 0.374781i | \(0.122282\pi\) | |||||||
\(422\) | −10.7310 | − | 10.7310i | −0.522379 | − | 0.522379i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.61386i | 0.126940i | ||||||||
\(425\) | −21.6757 | − | 27.9185i | −1.05142 | − | 1.35425i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.4552 | + | 4.40916i | 0.796324 | + | 0.213374i | ||||
\(428\) | 0.545328 | + | 0.146120i | 0.0263594 | + | 0.00706299i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.94351 | − | 18.0065i | −0.431295 | − | 0.868353i | ||||
\(431\) | 28.4120i | 1.36856i | 0.729221 | + | 0.684278i | \(0.239883\pi\) | ||||
−0.729221 | + | 0.684278i | \(0.760117\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2290 | + | 20.2290i | 0.972142 | + | 0.972142i | 0.999622 | − | 0.0274806i | \(-0.00874844\pi\) |
−0.0274806 | + | 0.999622i | \(0.508748\pi\) | |||||||
\(434\) | 3.01073 | − | 5.21475i | 0.144520 | − | 0.250316i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.79869 | − | 11.7757i | −0.325598 | − | 0.563952i | ||||
\(437\) | 4.44393 | − | 16.5850i | 0.212582 | − | 0.793368i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4785 | + | 7.20447i | 0.595567 | + | 0.343851i | 0.767296 | − | 0.641293i | \(-0.221602\pi\) |
−0.171729 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(440\) | 0.506700 | + | 2.51007i | 0.0241560 | + | 0.119663i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.3665 | + | 12.3665i | −0.588214 | + | 0.588214i | ||||
\(443\) | −6.94511 | − | 25.9195i | −0.329972 | − | 1.23147i | −0.909218 | − | 0.416320i | \(-0.863320\pi\) |
0.579246 | − | 0.815153i | \(-0.303347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.682516 | − | 10.8869i | 0.0323543 | − | 0.516087i | ||||
\(446\) | 7.36965 | − | 4.25487i | 0.348963 | − | 0.201474i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.32238 | + | 0.622279i | −0.109722 | + | 0.0293999i | ||||
\(449\) | 1.72288 | 0.0813077 | 0.0406538 | − | 0.999173i | \(-0.487056\pi\) | ||||
0.0406538 | + | 0.999173i | \(0.487056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.25891 | −0.106368 | ||||||||
\(452\) | −4.94392 | + | 1.32472i | −0.232542 | + | 0.0623095i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.6345 | + | 10.1813i | −0.827626 | + | 0.477830i | ||||
\(455\) | 0.832211 | − | 13.2747i | 0.0390147 | − | 0.622327i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.30155 | − | 12.3215i | −0.154440 | − | 0.576377i | −0.999153 | − | 0.0411576i | \(-0.986895\pi\) |
0.844713 | − | 0.535220i | \(-0.179771\pi\) | |||||||
\(458\) | −9.96386 | + | 9.96386i | −0.465580 | + | 0.465580i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.72894 | − | 13.5185i | −0.127237 | − | 0.630304i | ||||
\(461\) | −8.72418 | − | 5.03691i | −0.406326 | − | 0.234592i | 0.282884 | − | 0.959154i | \(-0.408709\pi\) |
−0.689210 | + | 0.724562i | \(0.742042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.90706 | − | 36.9737i | 0.460420 | − | 1.71831i | −0.211224 | − | 0.977438i | \(-0.567745\pi\) |
0.671644 | − | 0.740874i | \(-0.265588\pi\) | |||||||
\(464\) | 0.672250 | + | 1.16437i | 0.0312084 | + | 0.0540546i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.454676 | + | 0.787522i | −0.0210625 | + | 0.0364813i | ||||
\(467\) | 14.5094 | + | 14.5094i | 0.671413 | + | 0.671413i | 0.958042 | − | 0.286629i | \(-0.0925347\pi\) |
−0.286629 | + | 0.958042i | \(0.592535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.135728i | − | 0.00626733i | ||||||
\(470\) | 12.2664 | + | 24.6967i | 0.565806 | + | 1.13917i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.53953 | − | 0.680464i | −0.116891 | − | 0.0313209i | ||||
\(473\) | −9.94589 | − | 2.66499i | −0.457313 | − | 0.122537i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.73844 | + | 13.8105i | −0.0797652 | + | 0.633671i | ||||
\(476\) | − | 16.9961i | − | 0.779013i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.55375 | + | 7.55375i | 0.345501 | + | 0.345501i | ||||
\(479\) | −2.27813 | + | 3.94584i | −0.104091 | + | 0.180290i | −0.913366 | − | 0.407139i | \(-0.866527\pi\) |
0.809276 | + | 0.587429i | \(0.199860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.2884 | − | 24.7482i | −0.651493 | − | 1.12842i | ||||
\(482\) | −5.46967 | + | 20.4131i | −0.249137 | + | 0.929791i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.39054 | − | 4.84428i | −0.381388 | − | 0.220194i | ||||
\(485\) | 17.6979 | − | 3.57262i | 0.803622 | − | 0.162225i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.4889 | + | 18.4889i | −0.837814 | + | 0.837814i | −0.988571 | − | 0.150757i | \(-0.951829\pi\) |
0.150757 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(488\) | 1.83386 | + | 6.84408i | 0.0830151 | + | 0.309817i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.80354 | − | 2.04480i | −0.0814755 | − | 0.0923744i | ||||
\(491\) | 0.730071 | − | 0.421507i | 0.0329476 | − | 0.0190223i | −0.483436 | − | 0.875380i | \(-0.660611\pi\) |
0.516383 | + | 0.856358i | \(0.327278\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.18045 | + | 2.45989i | −0.413467 | + | 0.110788i | ||||
\(494\) | 6.88742 | 0.309880 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.50446 | 0.112453 | ||||||||
\(497\) | −21.1337 | + | 5.66277i | −0.947978 | + | 0.254010i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.45869 | + | 4.88363i | −0.378663 | + | 0.218621i | −0.677236 | − | 0.735765i | \(-0.736823\pi\) |
0.298573 | + | 0.954387i | \(0.403489\pi\) | |||||||
\(500\) | 3.68388 | + | 10.5560i | 0.164748 | + | 0.472078i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.39158 | + | 23.8537i | 0.285270 | + | 1.06464i | ||||
\(503\) | −22.3161 | + | 22.3161i | −0.995025 | + | 0.995025i | −0.999988 | − | 0.00496279i | \(-0.998420\pi\) |
0.00496279 | + | 0.999988i | \(0.498420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.901410 | − | 1.35738i | 0.0401122 | − | 0.0604028i | ||||
\(506\) | −6.11678 | − | 3.53152i | −0.271924 | − | 0.156995i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.78919 | + | 6.67736i | −0.0793826 | + | 0.296260i | ||||
\(509\) | −3.83647 | − | 6.64497i | −0.170049 | − | 0.294533i | 0.768388 | − | 0.639984i | \(-0.221059\pi\) |
−0.938437 | + | 0.345451i | \(0.887726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.3080 | − | 23.0501i | 0.588712 | − | 1.01968i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 5.25539i | − | 0.231805i | ||||||
\(515\) | −2.89389 | − | 0.973185i | −0.127520 | − | 0.0428837i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6412 | + | 3.65514i | 0.599938 | + | 0.160753i | ||||
\(518\) | 26.8252 | + | 7.18779i | 1.17863 | + | 0.315813i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.95459 | − | 2.46085i | 0.217273 | − | 0.107915i | ||||
\(521\) | − | 23.2333i | − | 1.01787i | −0.860805 | − | 0.508934i | \(-0.830040\pi\) | ||
0.860805 | − | 0.508934i | \(-0.169960\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.86103 | − | 3.86103i | −0.168831 | − | 0.168831i | 0.617634 | − | 0.786465i | \(-0.288091\pi\) |
−0.786465 | + | 0.617634i | \(0.788091\pi\) | |||||||
\(524\) | −2.87723 | + | 4.98351i | −0.125693 | + | 0.217706i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.46760 | + | 12.9343i | 0.325603 | + | 0.563960i | ||||
\(527\) | −4.58215 | + | 17.1008i | −0.199602 | + | 0.744923i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0246 | + | 7.51973i | 0.566285 | + | 0.326945i | ||||
\(530\) | 4.86895 | + | 3.23336i | 0.211494 | + | 0.140448i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.73291 | + | 4.73291i | −0.205198 | + | 0.205198i | ||||
\(533\) | 1.26305 | + | 4.71378i | 0.0547089 | + | 0.204176i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.946759 | − | 0.835055i | 0.0409320 | − | 0.0361026i | ||||
\(536\) | 0.0488889 | − | 0.0282260i | 0.00211168 | − | 0.00121918i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.3254 | + | 5.17822i | −0.833176 | + | 0.223249i | ||||
\(539\) | −1.39637 | −0.0601457 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.3692 | −0.918732 | −0.459366 | − | 0.888247i | \(-0.651923\pi\) | ||||
−0.459366 | + | 0.888247i | \(0.651923\pi\) | |||||||
\(542\) | −2.92399 | + | 0.783481i | −0.125596 | + | 0.0336534i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.12195 | − | 3.53451i | 0.262477 | − | 0.151541i | ||||
\(545\) | −30.3451 | − | 1.90238i | −1.29984 | − | 0.0814891i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.10984 | + | 26.5343i | 0.303995 | + | 1.13452i | 0.933807 | + | 0.357777i | \(0.116465\pi\) |
−0.629812 | + | 0.776747i | \(0.716868\pi\) | |||||||
\(548\) | 7.35405 | − | 7.35405i | 0.314149 | − | 0.314149i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.30242 | + | 2.16113i | 0.226096 | + | 0.0921508i | ||||
\(551\) | 3.24150 | + | 1.87148i | 0.138092 | + | 0.0797277i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.08159 | + | 22.6968i | −0.258615 | + | 0.965166i | ||||
\(554\) | −1.39855 | − | 2.42235i | −0.0594185 | − | 0.102916i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.26750 | + | 2.19537i | −0.0537539 | + | 0.0931045i | ||||
\(557\) | 13.7347 | + | 13.7347i | 0.581958 | + | 0.581958i | 0.935441 | − | 0.353483i | \(-0.115003\pi\) |
−0.353483 | + | 0.935441i | \(0.615003\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2447i | 0.940852i | ||||||||
\(560\) | −1.71365 | + | 5.09575i | −0.0724149 | + | 0.215335i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.6110 | − | 3.91500i | −0.616326 | − | 0.165144i | ||||
\(563\) | 14.3759 | + | 3.85201i | 0.605872 | + | 0.162343i | 0.548697 | − | 0.836021i | \(-0.315124\pi\) |
0.0571749 | + | 0.998364i | \(0.481791\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.64805 | + | 10.8479i | −0.153475 | + | 0.456376i | ||||
\(566\) | 24.0382i | 1.01040i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.43471 | − | 6.43471i | −0.269994 | − | 0.269994i | ||||
\(569\) | −14.7082 | + | 25.4753i | −0.616599 | + | 1.06798i | 0.373503 | + | 0.927629i | \(0.378157\pi\) |
−0.990102 | + | 0.140351i | \(0.955177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2909 | + | 26.4847i | 0.639906 | + | 1.10835i | 0.985453 | + | 0.169948i | \(0.0543599\pi\) |
−0.345548 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(572\) | 0.733286 | − | 2.73666i | 0.0306602 | − | 0.114426i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.10717 | − | 2.37128i | −0.171430 | − | 0.0989751i | ||||
\(575\) | −28.5572 | − | 11.6392i | −1.19092 | − | 0.485388i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.75877 | + | 2.75877i | −0.114849 | + | 0.114849i | −0.762196 | − | 0.647347i | \(-0.775879\pi\) |
0.647347 | + | 0.762196i | \(0.275879\pi\) | |||||||
\(578\) | 8.53354 | + | 31.8476i | 0.354949 | + | 1.32469i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.00050 | + | 0.188106i | 0.124589 | + | 0.00781069i | ||||
\(581\) | −5.83093 | + | 3.36649i | −0.241908 | + | 0.139665i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.89135 | − | 0.774736i | 0.119748 | − | 0.0320863i | ||||
\(584\) | 11.0702 | 0.458087 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0996 | −0.623757 | ||||||||
\(587\) | 15.5484 | − | 4.16617i | 0.641750 | − | 0.171956i | 0.0767539 | − | 0.997050i | \(-0.475544\pi\) |
0.564996 | + | 0.825094i | \(0.308878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.03808 | − | 3.48608i | 0.248795 | − | 0.143642i | ||||
\(590\) | −4.40894 | + | 3.88875i | −0.181513 | + | 0.160097i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.98955 | + | 11.1572i | 0.122870 | + | 0.458557i | ||||
\(593\) | 31.4829 | − | 31.4829i | 1.29285 | − | 1.29285i | 0.359830 | − | 0.933018i | \(-0.382835\pi\) |
0.933018 | − | 0.359830i | \(-0.117165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −31.6593 | − | 21.0242i | −1.29790 | − | 0.861910i | ||||
\(596\) | −11.2461 | − | 6.49294i | −0.460658 | − | 0.265961i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.94926 | + | 14.7388i | −0.161497 | + | 0.602716i | ||||
\(599\) | 0.0708577 | + | 0.122729i | 0.00289517 | + | 0.00501457i | 0.867469 | − | 0.497491i | \(-0.165745\pi\) |
−0.864574 | + | 0.502505i | \(0.832412\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.9425 | − | 38.0055i | 0.895052 | − | 1.55028i | 0.0613115 | − | 0.998119i | \(-0.480472\pi\) |
0.833740 | − | 0.552157i | \(-0.186195\pi\) | |||||||
\(602\) | −15.2862 | − | 15.2862i | −0.623018 | − | 0.623018i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 3.17004i | − | 0.128987i | ||||||
\(605\) | −19.4028 | + | 9.63701i | −0.788836 | + | 0.391800i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.2841 | − | 8.65049i | −1.31037 | − | 0.351113i | −0.465008 | − | 0.885306i | \(-0.653949\pi\) |
−0.845362 | + | 0.534194i | \(0.820615\pi\) | |||||||
\(608\) | −2.68904 | − | 0.720527i | −0.109055 | − | 0.0292212i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0173 | + | 5.05015i | 0.608031 | + | 0.204475i | ||||
\(611\) | − | 30.5095i | − | 1.23428i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.75021 | + | 6.75021i | 0.272638 | + | 0.272638i | 0.830161 | − | 0.557523i | \(-0.188248\pi\) |
−0.557523 | + | 0.830161i | \(0.688248\pi\) | |||||||
\(614\) | 5.86567 | − | 10.1596i | 0.236719 | − | 0.410010i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.37668 | + | 2.38448i | 0.0554681 | + | 0.0960736i | ||||
\(617\) | −8.53953 | + | 31.8700i | −0.343789 | + | 1.28304i | 0.550232 | + | 0.835012i | \(0.314539\pi\) |
−0.894021 | + | 0.448025i | \(0.852128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2360 | + | 7.64183i | 0.532001 | + | 0.307151i | 0.741831 | − | 0.670587i | \(-0.233958\pi\) |
−0.209830 | + | 0.977738i | \(0.567291\pi\) | |||||||
\(620\) | 3.09803 | − | 4.66516i | 0.124420 | − | 0.187357i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.88817 | + | 8.88817i | −0.356383 | + | 0.356383i | ||||
\(623\) | −3.03567 | − | 11.3293i | −0.121622 | − | 0.453898i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2201 | + | 6.19573i | 0.968804 | + | 0.247829i | ||||
\(626\) | 10.3379 | − | 5.96858i | 0.413185 | − | 0.238552i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.3186 | − | 2.76487i | 0.411758 | − | 0.110330i | ||||
\(629\) | −81.6525 | −3.25570 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.8347 | 0.431321 | 0.215660 | − | 0.976468i | \(-0.430810\pi\) | ||||
0.215660 | + | 0.976468i | \(0.430810\pi\) | |||||||
\(632\) | −9.44008 | + | 2.52946i | −0.375506 | + | 0.100617i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.68150 | − | 0.970815i | 0.0667809 | − | 0.0385560i | ||||
\(635\) | 10.2250 | + | 11.5928i | 0.405765 | + | 0.460044i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.780770 | + | 2.91387i | 0.0309352 | + | 0.115452i | ||||
\(638\) | 1.08873 | − | 1.08873i | 0.0431033 | − | 0.0431033i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.19185 | + | 0.442462i | −0.0866407 | + | 0.0174899i | ||||
\(641\) | 23.0771 | + | 13.3236i | 0.911491 | + | 0.526250i | 0.880911 | − | 0.473283i | \(-0.156931\pi\) |
0.0305804 | + | 0.999532i | \(0.490264\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.67008 | + | 13.6969i | −0.144734 | + | 0.540153i | 0.855033 | + | 0.518573i | \(0.173537\pi\) |
−0.999767 | + | 0.0215806i | \(0.993130\pi\) | |||||||
\(644\) | −7.41440 | − | 12.8421i | −0.292168 | − | 0.506050i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.83974 | − | 17.0429i | 0.387139 | − | 0.670545i | ||||
\(647\) | 22.3507 | + | 22.3507i | 0.878698 | + | 0.878698i | 0.993400 | − | 0.114702i | \(-0.0365912\pi\) |
−0.114702 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.01081i | 0.118185i | ||||||||
\(650\) | 1.54493 | − | 12.2732i | 0.0605971 | − | 0.481395i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.4950 | − | 5.75956i | −0.841809 | − | 0.225562i | ||||
\(653\) | −24.6425 | − | 6.60293i | −0.964334 | − | 0.258393i | −0.257900 | − | 0.966172i | \(-0.583031\pi\) |
−0.706434 | + | 0.707779i | \(0.749697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.72385 | + | 11.5242i | 0.223649 | + | 0.450287i | ||||
\(656\) | − | 1.97253i | − | 0.0770143i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.9656 | + | 20.9656i | 0.817323 | + | 0.817323i | ||||
\(659\) | 10.2346 | − | 17.7269i | 0.398684 | − | 0.690540i | −0.594880 | − | 0.803814i | \(-0.702800\pi\) |
0.993564 | + | 0.113274i | \(0.0361338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.883223 | − | 1.52979i | −0.0343534 | − | 0.0595018i | 0.848338 | − | 0.529456i | \(-0.177604\pi\) |
−0.882691 | + | 0.469954i | \(0.844271\pi\) | |||||||
\(662\) | −5.68423 | + | 21.2138i | −0.220924 | + | 0.824499i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.42521 | − | 1.40019i | −0.0941163 | − | 0.0543381i | ||||
\(665\) | 2.96155 | + | 14.6708i | 0.114844 | + | 0.568911i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.86358 | + | 5.86358i | −0.227039 | + | 0.227039i | ||||
\(668\) | −1.05230 | − | 3.92724i | −0.0407148 | − | 0.151950i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.00789810 | − | 0.125983i | 0.000305130 | − | 0.00486716i | ||||
\(671\) | 7.02711 | − | 4.05710i | 0.271278 | − | 0.156623i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4819 | + | 3.61246i | −0.519688 | + | 0.139250i | −0.509122 | − | 0.860694i | \(-0.670030\pi\) |
−0.0105656 | + | 0.999944i | \(0.503363\pi\) | |||||||
\(674\) | −26.7973 | −1.03219 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.87925 | 0.264587 | ||||||||
\(677\) | 1.70954 | − | 0.458071i | 0.0657031 | − | 0.0176051i | −0.225818 | − | 0.974170i | \(-0.572505\pi\) |
0.291521 | + | 0.956564i | \(0.405839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8124 | − | 9.70666i | 0.645202 | − | 0.372508i | ||||
\(680\) | 0.989013 | − | 15.7758i | 0.0379269 | − | 0.604976i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.742309 | − | 2.77034i | −0.0284245 | − | 0.106082i | ||||
\(683\) | 22.8964 | − | 22.8964i | 0.876105 | − | 0.876105i | −0.117024 | − | 0.993129i | \(-0.537335\pi\) |
0.993129 | + | 0.117024i | \(0.0373354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.60169 | − | 22.7957i | −0.175822 | − | 0.870980i | ||||
\(686\) | −17.1142 | − | 9.88088i | −0.653423 | − | 0.377254i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.32713 | − | 8.68498i | 0.0887211 | − | 0.331112i | ||||
\(689\) | −3.23336 | − | 5.60035i | −0.123181 | − | 0.213356i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.3908 | − | 19.7295i | 0.433327 | − | 0.750545i | −0.563830 | − | 0.825891i | \(-0.690673\pi\) |
0.997157 | + | 0.0753461i | \(0.0240062\pi\) | |||||||
\(692\) | 3.93703 | + | 3.93703i | 0.149664 | + | 0.149664i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 30.0871i | − | 1.14209i | ||||||
\(695\) | 2.52151 | + | 5.07672i | 0.0956463 | + | 0.192571i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4687 | + | 3.60893i | 0.510164 | + | 0.136698i | ||||
\(698\) | −24.8552 | − | 6.65994i | −0.940784 | − | 0.252082i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.37228 | + | 9.49558i | 0.278646 | + | 0.358899i | ||||
\(701\) | − | 26.0321i | − | 0.983220i | −0.870816 | − | 0.491610i | \(-0.836409\pi\) | ||
0.870816 | − | 0.491610i | \(-0.163591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.7379 | + | 22.7379i | 0.857574 | + | 0.857574i | ||||
\(704\) | −0.572591 | + | 0.991757i | −0.0215804 | + | 0.0373783i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.79747 | + | 13.5056i | 0.293462 | + | 0.508291i | ||||
\(707\) | 0.453456 | − | 1.69232i | 0.0170540 | − | 0.0636462i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.58254 | − | 1.49103i | −0.0969892 | − | 0.0559968i | 0.450721 | − | 0.892665i | \(-0.351167\pi\) |
−0.547710 | + | 0.836668i | \(0.684500\pi\) | |||||||
\(710\) | −19.9460 | + | 4.02643i | −0.748559 | + | 0.151109i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.44949 | − | 3.44949i | 0.129275 | − | 0.129275i | ||||
\(713\) | 3.99786 | + | 14.9202i | 0.149721 | + | 0.558766i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.19062 | − | 4.75119i | −0.156720 | − | 0.177685i | ||||
\(716\) | 0.268634 | − | 0.155096i | 0.0100393 | − | 0.00579621i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.1999 | − | 5.94843i | 0.828491 | − | 0.221994i | ||||
\(719\) | 7.38853 | 0.275546 | 0.137773 | − | 0.990464i | \(-0.456006\pi\) | ||||
0.137773 | + | 0.990464i | \(0.456006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.28285 | −0.122260 | ||||||||
\(722\) | 10.8665 | − | 2.91168i | 0.404411 | − | 0.108362i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.66230 | − | 1.53708i | 0.0989437 | − | 0.0571252i | ||||
\(725\) | 4.06204 | − | 5.35648i | 0.150860 | − | 0.198935i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.57881 | − | 20.8204i | −0.206906 | − | 0.772185i | −0.988860 | − | 0.148849i | \(-0.952443\pi\) |
0.781954 | − | 0.623337i | \(-0.214223\pi\) | |||||||
\(728\) | 4.20607 | − | 4.20607i | 0.155887 | − | 0.155887i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.6939 | − | 20.6209i | 0.506833 | − | 0.763213i | ||||
\(731\) | 55.0446 | + | 31.7800i | 2.03590 | + | 1.17543i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.74734 | + | 6.52116i | −0.0645395 | + | 0.240865i | −0.990658 | − | 0.136367i | \(-0.956457\pi\) |
0.926119 | + | 0.377232i | \(0.123124\pi\) | |||||||
\(734\) | −1.74199 | − | 3.01721i | −0.0642980 | − | 0.111367i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.08381 | − | 5.34131i | 0.113671 | − | 0.196883i | ||||
\(737\) | −0.0457130 | − | 0.0457130i | −0.00168386 | − | 0.00168386i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.8637i | 0.473200i | 0.971607 | + | 0.236600i | \(0.0760331\pi\) | ||||
−0.971607 | + | 0.236600i | \(0.923967\pi\) | |||||||
\(740\) | 24.4810 | + | 8.23273i | 0.899941 | + | 0.302641i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.07037 | + | 1.62655i | 0.222850 | + | 0.0597125i | ||||
\(743\) | 32.7401 | + | 8.77270i | 1.20112 | + | 0.321839i | 0.803272 | − | 0.595613i | \(-0.203091\pi\) |
0.397848 | + | 0.917452i | \(0.369757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.0062 | + | 12.9168i | −0.952792 | + | 0.473234i | ||||
\(746\) | − | 22.8690i | − | 0.837295i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.72426 | − | 5.72426i | −0.209300 | − | 0.209300i | ||||
\(749\) | 0.678692 | − | 1.17553i | 0.0247989 | − | 0.0429529i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.70415 | + | 11.6119i | 0.244638 | + | 0.423725i | 0.962030 | − | 0.272945i | \(-0.0879975\pi\) |
−0.717392 | + | 0.696670i | \(0.754664\pi\) | |||||||
\(752\) | −3.19175 | + | 11.9118i | −0.116391 | + | 0.434378i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.88067 | − | 1.66316i | −0.104908 | − | 0.0605686i | ||||
\(755\) | −5.90498 | − | 3.92137i | −0.214904 | − | 0.142713i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.11492 | + | 1.11492i | −0.0405223 | + | 0.0405223i | −0.727078 | − | 0.686555i | \(-0.759122\pi\) |
0.686555 | + | 0.727078i | \(0.259122\pi\) | |||||||
\(758\) | −9.39806 | − | 35.0741i | −0.341353 | − | 1.27395i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.66853 | + | 4.11770i | −0.169345 | + | 0.149365i | ||||
\(761\) | 29.7531 | − | 17.1780i | 1.07855 | − | 0.622702i | 0.148046 | − | 0.988981i | \(-0.452702\pi\) |
0.930505 | + | 0.366279i | \(0.119368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.5782 | + | 8.46136i | −1.14321 | + | 0.306322i | ||||
\(764\) | 14.2652 | 0.516098 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.5998 | −0.599775 | ||||||||
\(767\) | 6.28282 | − | 1.68348i | 0.226860 | − | 0.0607869i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.4890 | − | 8.36522i | 0.522486 | − | 0.301658i | −0.215465 | − | 0.976512i | \(-0.569127\pi\) |
0.737951 | + | 0.674854i | \(0.235793\pi\) | |||||||
\(770\) | 6.14465 | + | 0.385218i | 0.221438 | + | 0.0138823i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.48506 | + | 9.27437i | 0.0894393 | + | 0.333792i | ||||
\(773\) | −5.20827 | + | 5.20827i | −0.187328 | + | 0.187328i | −0.794540 | − | 0.607212i | \(-0.792288\pi\) |
0.607212 | + | 0.794540i | \(0.292288\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.85771 | − | 11.5417i | −0.174494 | − | 0.414589i | ||||
\(776\) | 6.99265 | + | 4.03721i | 0.251022 | + | 0.144927i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.10184 | − | 22.7724i | 0.218761 | − | 0.816429i | ||||
\(779\) | −2.74567 | − | 4.75563i | −0.0983737 | − | 0.170388i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.21061 | + | 9.02504i | −0.186450 | + | 0.322941i | ||||
\(782\) | 30.8291 | + | 30.8291i | 1.10245 | + | 1.10245i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.21934i | − | 0.0435478i | ||||||
\(785\) | 7.61397 | − | 22.6411i | 0.271754 | − | 0.808095i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.6815 | − | 11.9724i | −1.59272 | − | 0.426769i | −0.649888 | − | 0.760030i | \(-0.725184\pi\) |
−0.942834 | + | 0.333262i | \(0.891851\pi\) | |||||||
\(788\) | −6.31780 | − | 1.69285i | −0.225062 | − | 0.0603053i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.96571 | + | 20.7134i | −0.247829 | + | 0.736950i | ||||
\(791\) | 12.3060i | 0.437550i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.3953 | − | 12.3953i | −0.440171 | − | 0.440171i | ||||
\(794\) | 19.5521 | − | 33.8653i | 0.693879 | − | 1.20183i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.03613 | − | 3.52669i | −0.0721688 | − | 0.125000i | ||||
\(797\) | −13.3339 | + | 49.7628i | −0.472311 | + | 1.76269i | 0.159123 | + | 0.987259i | \(0.449134\pi\) |
−0.631434 | + | 0.775430i | \(0.717533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75.4958 | − | 43.5875i | −2.67085 | − | 1.54202i | ||||
\(800\) | −1.88715 | + | 4.63019i | −0.0667207 | + | 0.163702i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.6093 | − | 21.6093i | 0.763050 | − | 0.763050i | ||||
\(803\) | −3.28114 | − | 12.2454i | −0.115789 | − | 0.432131i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.0932 | − | 2.07467i | −1.16638 | − | 0.0731224i | ||||
\(806\) | −5.36595 | + | 3.09803i | −0.189008 | + | 0.109124i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.703872 | − | 0.188602i | 0.0247621 | − | 0.00663499i | ||||
\(809\) | 18.0260 | 0.633762 | 0.316881 | − | 0.948465i | \(-0.397364\pi\) | ||||
0.316881 | + | 0.948465i | \(0.397364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.7969 | 1.64326 | 0.821630 | − | 0.570021i | \(-0.193065\pi\) | ||||
0.821630 | + | 0.570021i | \(0.193065\pi\) | |||||||
\(812\) | 3.12243 | − | 0.836654i | 0.109576 | − | 0.0293608i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.4555 | − | 6.61386i | 0.401517 | − | 0.231816i | ||||
\(815\) | −37.3180 | + | 32.9150i | −1.30719 | + | 1.15296i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.47852 | − | 24.1782i | −0.226655 | − | 0.845886i | ||||
\(818\) | −1.98954 | + | 1.98954i | −0.0695626 | + | 0.0695626i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.67431 | − | 2.44003i | −0.128313 | − | 0.0852096i | ||||
\(821\) | −5.91006 | − | 3.41218i | −0.206263 | − | 0.119086i | 0.393311 | − | 0.919406i | \(-0.371330\pi\) |
−0.599573 | + | 0.800320i | \(0.704663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.27529 | − | 19.6876i | 0.183885 | − | 0.686268i | −0.810982 | − | 0.585072i | \(-0.801066\pi\) |
0.994866 | − | 0.101196i | \(-0.0322670\pi\) | |||||||
\(824\) | −0.682703 | − | 1.18248i | −0.0237831 | − | 0.0411935i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.16059 | + | 5.47430i | −0.109971 | + | 0.190475i | ||||
\(827\) | −29.8425 | − | 29.8425i | −1.03773 | − | 1.03773i | −0.999260 | − | 0.0384654i | \(-0.987753\pi\) |
−0.0384654 | − | 0.999260i | \(-0.512247\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.4152i | 0.709050i | 0.935047 | + | 0.354525i | \(0.115357\pi\) | ||||
−0.935047 | + | 0.354525i | \(0.884643\pi\) | |||||||
\(830\) | −5.60820 | + | 2.78549i | −0.194664 | + | 0.0966857i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.38971 | + | 0.640322i | 0.0828484 | + | 0.0221992i | ||||
\(833\) | 8.32583 | + | 2.23090i | 0.288473 | + | 0.0772961i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.61715 | − | 2.89786i | −0.298209 | − | 0.100285i | ||||
\(836\) | 3.18808i | 0.110262i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.16518 | + | 3.16518i | 0.109339 | + | 0.109339i | ||||
\(839\) | −9.70261 | + | 16.8054i | −0.334971 | + | 0.580187i | −0.983479 | − | 0.181021i | \(-0.942060\pi\) |
0.648508 | + | 0.761208i | \(0.275393\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5962 | + | 23.5492i | 0.468833 | + | 0.812043i | ||||
\(842\) | 1.47618 | − | 5.50919i | 0.0508726 | − | 0.189859i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.1428 | − | 7.58800i | −0.452394 | − | 0.261190i | ||||
\(845\) | 8.50968 | − | 12.8143i | 0.292742 | − | 0.440825i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.4715 | + | 16.4715i | −0.565967 | + | 0.565967i | ||||
\(848\) | 0.676517 | + | 2.52480i | 0.0232317 | + | 0.0867018i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28.1629 | − | 21.3571i | −0.965981 | − | 0.732543i | ||||
\(851\) | −61.6961 | + | 35.6203i | −2.11492 | + | 1.22105i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.496213 | + | 0.132960i | −0.0169900 | + | 0.00455246i | −0.267304 | − | 0.963612i | \(-0.586133\pi\) |
0.250314 | + | 0.968165i | \(0.419466\pi\) | |||||||
\(854\) | 17.0357 | 0.582949 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.564565 | 0.0192964 | ||||||||
\(857\) | 43.0427 | − | 11.5332i | 1.47031 | − | 0.393968i | 0.567272 | − | 0.823530i | \(-0.307999\pi\) |
0.903037 | + | 0.429562i | \(0.141332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5432 | − | 14.7474i | 0.871522 | − | 0.503174i | 0.00366859 | − | 0.999993i | \(-0.498832\pi\) |
0.867854 | + | 0.496820i | \(0.165499\pi\) | |||||||
\(860\) | −13.2992 | − | 15.0782i | −0.453499 | − | 0.514164i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.35356 | + | 27.4438i | 0.250463 | + | 0.934741i | ||||
\(863\) | 6.17951 | − | 6.17951i | 0.210353 | − | 0.210353i | −0.594064 | − | 0.804417i | \(-0.702478\pi\) |
0.804417 | + | 0.594064i | \(0.202478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.2038 | − | 2.46354i | 0.414943 | − | 0.0837630i | ||||
\(866\) | 24.7753 | + | 14.3040i | 0.841899 | + | 0.486071i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.55847 | − | 5.81629i | 0.0528979 | − | 0.197418i | ||||
\(869\) | 5.59599 | + | 9.69254i | 0.189831 | + | 0.328797i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0698316 | + | 0.120952i | −0.00236615 | + | 0.00409830i | ||||
\(872\) | −9.61480 | − | 9.61480i | −0.325598 | − | 0.325598i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 17.1700i | − | 0.580785i | ||||||
\(875\) | 26.8074 | − | 1.98658i | 0.906255 | − | 0.0671586i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0896 | + | 5.38298i | 0.678376 | + | 0.181770i | 0.581525 | − | 0.813528i | \(-0.302456\pi\) |
0.0968513 | + | 0.995299i | \(0.469123\pi\) | |||||||
\(878\) | 13.9180 | + | 3.72931i | 0.469709 | + | 0.125858i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.13909 | + | 2.29340i | 0.0383987 | + | 0.0773106i | ||||
\(881\) | 28.3087i | 0.953745i | 0.878972 | + | 0.476873i | \(0.158230\pi\) | ||||
−0.878972 | + | 0.476873i | \(0.841770\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1647 | + | 15.1647i | 0.510333 | + | 0.510333i | 0.914629 | − | 0.404295i | \(-0.132483\pi\) |
−0.404295 | + | 0.914629i | \(0.632483\pi\) | |||||||
\(884\) | −8.74443 | + | 15.1458i | −0.294107 | + | 0.509408i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.4169 | − | 23.2388i | −0.450750 | − | 0.780723i | ||||
\(887\) | 12.4339 | − | 46.4040i | 0.417490 | − | 1.55809i | −0.362306 | − | 0.932059i | \(-0.618011\pi\) |
0.779796 | − | 0.626034i | \(-0.215323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3940 | + | 8.31036i | 0.482758 | + | 0.278721i | ||||
\(890\) | −2.15847 | − | 10.6926i | −0.0723521 | − | 0.358415i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.01730 | − | 6.01730i | 0.201474 | − | 0.201474i | ||||
\(893\) | 8.88553 | + | 33.1613i | 0.297343 | + | 1.10970i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0433983 | − | 0.692251i | 0.00145065 | − | 0.0231394i | ||||
\(896\) | −2.08219 | + | 1.20215i | −0.0695609 | + | 0.0401610i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.66417 | − | 0.445914i | 0.0555342 | − | 0.0148803i | ||||
\(899\) | −3.36724 | −0.112304 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.4774 | −0.615573 | ||||||||
\(902\) | −2.18194 | + | 0.584648i | −0.0726505 | + | 0.0194666i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.43259 | + | 2.55916i | −0.147426 | + | 0.0851164i | ||||
\(905\) | 0.430100 | − | 6.86057i | 0.0142970 | − | 0.228053i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.66001 | + | 36.0516i | 0.320755 | + | 1.19707i | 0.918511 | + | 0.395396i | \(0.129393\pi\) |
−0.597755 | + | 0.801679i | \(0.703941\pi\) | |||||||
\(908\) | −14.3985 | + | 14.3985i | −0.477830 | + | 0.477830i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.63189 | − | 13.0378i | −0.0872462 | − | 0.432197i | ||||
\(911\) | −46.5957 | − | 26.9020i | −1.54378 | − | 0.891304i | −0.998595 | − | 0.0529906i | \(-0.983125\pi\) |
−0.545189 | − | 0.838313i | \(-0.683542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.830022 | + | 3.09768i | −0.0274697 | + | 0.102518i | ||||
\(914\) | −6.37810 | − | 11.0472i | −0.210969 | − | 0.365409i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.04551 | + | 12.2032i | −0.232790 | + | 0.403204i | ||||
\(917\) | 9.78315 | + | 9.78315i | 0.323068 | + | 0.323068i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.1668i | 0.764203i | 0.924120 | + | 0.382101i | \(0.124799\pi\) | ||||
−0.924120 | + | 0.382101i | \(0.875201\pi\) | |||||||
\(920\) | −6.13480 | − | 12.3516i | −0.202258 | − | 0.407220i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.73056 | − | 2.60729i | −0.320459 | − | 0.0858667i | ||||
\(923\) | 21.7465 | + | 5.82696i | 0.715795 | + | 0.191797i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.6187 | − | 35.4180i | 1.49993 | − | 1.16454i | ||||
\(926\) | − | 38.2779i | − | 1.25789i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.950705 | + | 0.950705i | 0.0312084 | + | 0.0312084i | ||||
\(929\) | 6.78350 | − | 11.7494i | 0.222559 | − | 0.385484i | −0.733025 | − | 0.680202i | \(-0.761892\pi\) |
0.955584 | + | 0.294717i | \(0.0952255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.69726 | − | 2.93974i | −0.0556255 | − | 0.0963462i | ||||
\(932\) | −0.235358 | + | 0.878367i | −0.00770940 | + | 0.0287719i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.7703 | + | 10.2597i | 0.581461 | + | 0.335706i | ||||
\(935\) | −17.7438 | + | 3.58188i | −0.580283 | + | 0.117140i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.94086 | + | 6.94086i | −0.226748 | + | 0.226748i | −0.811333 | − | 0.584585i | \(-0.801258\pi\) |
0.584585 | + | 0.811333i | \(0.301258\pi\) | |||||||
\(938\) | −0.0351289 | − | 0.131103i | −0.00114700 | − | 0.00428066i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.2404 | + | 20.6804i | 0.594935 | + | 0.674520i | ||||
\(941\) | 14.5976 | − | 8.42791i | 0.475867 | − | 0.274742i | −0.242825 | − | 0.970070i | \(-0.578074\pi\) |
0.718693 | + | 0.695328i | \(0.244741\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.7513 | − | 3.14874i | 0.382673 | − | 0.102537i | ||||
\(944\) | −2.62911 | −0.0855703 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.2967 | −0.334776 | ||||||||
\(947\) | −37.0498 | + | 9.92745i | −1.20396 | + | 0.322599i | −0.804388 | − | 0.594105i | \(-0.797506\pi\) |
−0.399568 | + | 0.916704i | \(0.630840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.7185 | + | 13.6939i | −0.769935 | + | 0.444522i | ||||
\(950\) | 1.89522 | + | 13.7899i | 0.0614892 | + | 0.447403i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.39890 | − | 16.4169i | −0.142569 | − | 0.532076i | ||||
\(953\) | −18.8861 | + | 18.8861i | −0.611780 | + | 0.611780i | −0.943410 | − | 0.331630i | \(-0.892402\pi\) |
0.331630 | + | 0.943410i | \(0.392402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.6462 | − | 26.5725i | 0.571018 | − | 0.859865i | ||||
\(956\) | 9.25142 | + | 5.34131i | 0.299212 | + | 0.172750i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.17925 | + | 4.40102i | −0.0380998 | + | 0.142190i | ||||
\(959\) | −12.5026 | − | 21.6551i | −0.403730 | − | 0.699281i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3638 | − | 21.4148i | 0.398834 | − | 0.690800i | ||||
\(962\) | −20.2068 | − | 20.2068i | −0.651493 | − | 0.651493i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.1332i | 0.680654i | ||||||||
\(965\) | 20.3498 | + | 6.84343i | 0.655084 | + | 0.220298i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.9494 | + | 8.29288i | 0.995267 | + | 0.266681i | 0.719461 | − | 0.694533i | \(-0.244389\pi\) |
0.275805 | + | 0.961213i | \(0.411055\pi\) | |||||||
\(968\) | −9.35843 | − | 2.50758i | −0.300791 | − | 0.0805968i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.1702 | − | 8.03146i | 0.519195 | − | 0.257875i | ||||
\(971\) | − | 29.2201i | − | 0.937716i | −0.883274 | − | 0.468858i | \(-0.844666\pi\) | ||
0.883274 | − | 0.468858i | \(-0.155334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.30974 | + | 4.30974i | 0.138164 | + | 0.138164i | ||||
\(974\) | −13.0737 | + | 22.6442i | −0.418907 | + | 0.725568i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.54275 | + | 6.13623i | 0.113401 | + | 0.196416i | ||||
\(977\) | 10.1124 | − | 37.7399i | 0.323523 | − | 1.20741i | −0.592265 | − | 0.805743i | \(-0.701766\pi\) |
0.915788 | − | 0.401662i | \(-0.131567\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.83811 | − | 2.79328i | −0.154627 | − | 0.0892737i | ||||
\(980\) | −2.27132 | − | 1.50833i | −0.0725545 | − | 0.0481819i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.596101 | − | 0.596101i | 0.0190223 | − | 0.0190223i | ||||
\(983\) | −2.96514 | − | 11.0660i | −0.0945732 | − | 0.352952i | 0.902381 | − | 0.430939i | \(-0.141818\pi\) |
−0.996954 | + | 0.0779867i | \(0.975151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.9685 | + | 9.67438i | −0.349486 | + | 0.308251i | ||||
\(986\) | −8.23096 | + | 4.75215i | −0.262127 | + | 0.151339i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.65274 | − | 1.78260i | 0.211652 | − | 0.0567119i | ||||
\(989\) | 55.4552 | 1.76337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.7986 | −0.851286 | −0.425643 | − | 0.904891i | \(-0.639952\pi\) | ||||
−0.425643 | + | 0.904891i | \(0.639952\pi\) | |||||||
\(992\) | 2.41912 | − | 0.648201i | 0.0768071 | − | 0.0205804i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.9480 | + | 10.9396i | −0.600994 | + | 0.346984i | ||||
\(995\) | −9.08802 | − | 0.569743i | −0.288110 | − | 0.0180621i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2233 | + | 53.0819i | 0.450455 | + | 1.68112i | 0.701116 | + | 0.713047i | \(0.252685\pi\) |
−0.250661 | + | 0.968075i | \(0.580648\pi\) | |||||||
\(998\) | −6.90650 | + | 6.90650i | −0.218621 | + | 0.218621i | ||||
\(999\) | 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 | 270.2.m.b.143.3 | 16 | ||
3.2 | odd | 2 | 90.2.l.b.83.2 | yes | 16 | ||
5.2 | odd | 4 | inner | 270.2.m.b.197.4 | 16 | ||
5.3 | odd | 4 | 1350.2.q.h.1007.2 | 16 | |||
5.4 | even | 2 | 1350.2.q.h.143.1 | 16 | |||
9.2 | odd | 6 | 810.2.f.c.323.6 | 16 | |||
9.4 | even | 3 | 90.2.l.b.23.2 | ✓ | 16 | ||
9.5 | odd | 6 | inner | 270.2.m.b.233.4 | 16 | ||
9.7 | even | 3 | 810.2.f.c.323.3 | 16 | |||
12.11 | even | 2 | 720.2.cu.b.353.1 | 16 | |||
15.2 | even | 4 | 90.2.l.b.47.2 | yes | 16 | ||
15.8 | even | 4 | 450.2.p.h.407.3 | 16 | |||
15.14 | odd | 2 | 450.2.p.h.443.3 | 16 | |||
36.31 | odd | 6 | 720.2.cu.b.113.2 | 16 | |||
45.2 | even | 12 | 810.2.f.c.647.3 | 16 | |||
45.4 | even | 6 | 450.2.p.h.293.3 | 16 | |||
45.7 | odd | 12 | 810.2.f.c.647.6 | 16 | |||
45.13 | odd | 12 | 450.2.p.h.257.3 | 16 | |||
45.14 | odd | 6 | 1350.2.q.h.1043.2 | 16 | |||
45.22 | odd | 12 | 90.2.l.b.77.2 | yes | 16 | ||
45.23 | even | 12 | 1350.2.q.h.557.1 | 16 | |||
45.32 | even | 12 | inner | 270.2.m.b.17.3 | 16 | ||
60.47 | odd | 4 | 720.2.cu.b.497.2 | 16 | |||
180.67 | even | 12 | 720.2.cu.b.257.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.l.b.23.2 | ✓ | 16 | 9.4 | even | 3 | ||
90.2.l.b.47.2 | yes | 16 | 15.2 | even | 4 | ||
90.2.l.b.77.2 | yes | 16 | 45.22 | odd | 12 | ||
90.2.l.b.83.2 | yes | 16 | 3.2 | odd | 2 | ||
270.2.m.b.17.3 | 16 | 45.32 | even | 12 | inner | ||
270.2.m.b.143.3 | 16 | 1.1 | even | 1 | trivial | ||
270.2.m.b.197.4 | 16 | 5.2 | odd | 4 | inner | ||
270.2.m.b.233.4 | 16 | 9.5 | odd | 6 | inner | ||
450.2.p.h.257.3 | 16 | 45.13 | odd | 12 | |||
450.2.p.h.293.3 | 16 | 45.4 | even | 6 | |||
450.2.p.h.407.3 | 16 | 15.8 | even | 4 | |||
450.2.p.h.443.3 | 16 | 15.14 | odd | 2 | |||
720.2.cu.b.113.2 | 16 | 36.31 | odd | 6 | |||
720.2.cu.b.257.1 | 16 | 180.67 | even | 12 | |||
720.2.cu.b.353.1 | 16 | 12.11 | even | 2 | |||
720.2.cu.b.497.2 | 16 | 60.47 | odd | 4 | |||
810.2.f.c.323.3 | 16 | 9.7 | even | 3 | |||
810.2.f.c.323.6 | 16 | 9.2 | odd | 6 | |||
810.2.f.c.647.3 | 16 | 45.2 | even | 12 | |||
810.2.f.c.647.6 | 16 | 45.7 | odd | 12 | |||
1350.2.q.h.143.1 | 16 | 5.4 | even | 2 | |||
1350.2.q.h.557.1 | 16 | 45.23 | even | 12 | |||
1350.2.q.h.1007.2 | 16 | 5.3 | odd | 4 | |||
1350.2.q.h.1043.2 | 16 | 45.14 | odd | 6 |