Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,2,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), 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: | \(1.17380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.2.e.d.79.2 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20711 | + | 2.09077i | 0.853553 | + | 1.47840i | 0.877981 | + | 0.478696i | \(0.158890\pi\) |
−0.0244272 | + | 0.999702i | \(0.507776\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.91421 | + | 3.31552i | −0.957107 | + | 1.65776i | ||||
\(5\) | −0.292893 | − | 0.507306i | −0.130986 | − | 0.226874i | 0.793071 | − | 0.609129i | \(-0.208481\pi\) |
−0.924057 | + | 0.382255i | \(0.875148\pi\) | |||||||
\(6\) | −2.41421 | −0.985599 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.707107 | − | 1.22474i | 0.223607 | − | 0.387298i | ||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | −1.91421 | − | 3.31552i | −0.552586 | − | 0.957107i | ||||
\(13\) | 5.41421 | 1.50163 | 0.750816 | − | 0.660511i | \(-0.229660\pi\) | ||||
0.750816 | + | 0.660511i | \(0.229660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.585786 | 0.151249 | ||||||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −3.12132 | + | 5.40629i | −0.757031 | + | 1.31122i | 0.187327 | + | 0.982298i | \(0.440018\pi\) |
−0.944358 | + | 0.328919i | \(0.893316\pi\) | |||||||
\(18\) | 1.20711 | − | 2.09077i | 0.284518 | − | 0.492799i | ||||
\(19\) | −1.41421 | − | 2.44949i | −0.324443 | − | 0.561951i | 0.656957 | − | 0.753928i | \(-0.271843\pi\) |
−0.981399 | + | 0.191977i | \(0.938510\pi\) | |||||||
\(20\) | 2.24264 | 0.501470 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.82843 | 1.02942 | ||||||||
\(23\) | −1.82843 | − | 3.16693i | −0.381253 | − | 0.660350i | 0.609988 | − | 0.792410i | \(-0.291174\pi\) |
−0.991242 | + | 0.132060i | \(0.957841\pi\) | |||||||
\(24\) | 2.20711 | − | 3.82282i | 0.450524 | − | 0.780330i | ||||
\(25\) | 2.32843 | − | 4.03295i | 0.465685 | − | 0.806591i | ||||
\(26\) | 6.53553 | + | 11.3199i | 1.28172 | + | 2.22001i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | 0.707107 | + | 1.22474i | 0.129099 | + | 0.223607i | ||||
\(31\) | 3.41421 | − | 5.91359i | 0.613211 | − | 1.06211i | −0.377485 | − | 0.926016i | \(-0.623211\pi\) |
0.990696 | − | 0.136097i | \(-0.0434557\pi\) | |||||||
\(32\) | −0.792893 | + | 1.37333i | −0.140165 | + | 0.242773i | ||||
\(33\) | 1.00000 | + | 1.73205i | 0.174078 | + | 0.301511i | ||||
\(34\) | −15.0711 | −2.58467 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | 3.41421 | − | 5.91359i | 0.553859 | − | 0.959311i | ||||
\(39\) | −2.70711 | + | 4.68885i | −0.433484 | + | 0.750816i | ||||
\(40\) | 1.29289 | + | 2.23936i | 0.204424 | + | 0.354073i | ||||
\(41\) | −2.24264 | −0.350242 | −0.175121 | − | 0.984547i | \(-0.556032\pi\) | ||||
−0.175121 | + | 0.984547i | \(0.556032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.65685 | −0.862662 | −0.431331 | − | 0.902194i | \(-0.641956\pi\) | ||||
−0.431331 | + | 0.902194i | \(0.641956\pi\) | |||||||
\(44\) | 3.82843 | + | 6.63103i | 0.577157 | + | 0.999665i | ||||
\(45\) | −0.292893 | + | 0.507306i | −0.0436619 | + | 0.0756247i | ||||
\(46\) | 4.41421 | − | 7.64564i | 0.650840 | − | 1.12729i | ||||
\(47\) | −1.41421 | − | 2.44949i | −0.206284 | − | 0.357295i | 0.744257 | − | 0.667893i | \(-0.232804\pi\) |
−0.950541 | + | 0.310599i | \(0.899470\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.2426 | 1.58995 | ||||||||
\(51\) | −3.12132 | − | 5.40629i | −0.437072 | − | 0.757031i | ||||
\(52\) | −10.3640 | + | 17.9509i | −1.43722 | + | 2.48934i | ||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | 1.20711 | + | 2.09077i | 0.164266 | + | 0.284518i | ||||
\(55\) | −1.17157 | −0.157975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | −1.41421 | − | 2.44949i | −0.185695 | − | 0.321634i | ||||
\(59\) | 3.41421 | − | 5.91359i | 0.444493 | − | 0.769884i | −0.553524 | − | 0.832833i | \(-0.686717\pi\) |
0.998017 | + | 0.0629492i | \(0.0200506\pi\) | |||||||
\(60\) | −1.12132 | + | 1.94218i | −0.144762 | + | 0.250735i | ||||
\(61\) | −1.87868 | − | 3.25397i | −0.240540 | − | 0.416628i | 0.720328 | − | 0.693634i | \(-0.243991\pi\) |
−0.960868 | + | 0.277006i | \(0.910658\pi\) | |||||||
\(62\) | 16.4853 | 2.09363 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −1.58579 | − | 2.74666i | −0.196693 | − | 0.340682i | ||||
\(66\) | −2.41421 | + | 4.18154i | −0.297169 | + | 0.514712i | ||||
\(67\) | −2.82843 | + | 4.89898i | −0.345547 | + | 0.598506i | −0.985453 | − | 0.169948i | \(-0.945640\pi\) |
0.639906 | + | 0.768453i | \(0.278973\pi\) | |||||||
\(68\) | −11.9497 | − | 20.6976i | −1.44912 | − | 2.50995i | ||||
\(69\) | 3.65685 | 0.440234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.3137 | −1.58005 | −0.790023 | − | 0.613077i | \(-0.789932\pi\) | ||||
−0.790023 | + | 0.613077i | \(0.789932\pi\) | |||||||
\(72\) | 2.20711 | + | 3.82282i | 0.260110 | + | 0.450524i | ||||
\(73\) | 2.94975 | − | 5.10911i | 0.345242 | − | 0.597976i | −0.640156 | − | 0.768245i | \(-0.721130\pi\) |
0.985398 | + | 0.170269i | \(0.0544636\pi\) | |||||||
\(74\) | −4.82843 | + | 8.36308i | −0.561293 | + | 0.972188i | ||||
\(75\) | 2.32843 | + | 4.03295i | 0.268864 | + | 0.465685i | ||||
\(76\) | 10.8284 | 1.24211 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.0711 | −1.48001 | ||||||||
\(79\) | −1.17157 | − | 2.02922i | −0.131812 | − | 0.228306i | 0.792563 | − | 0.609790i | \(-0.208746\pi\) |
−0.924375 | + | 0.381485i | \(0.875413\pi\) | |||||||
\(80\) | −0.878680 | + | 1.52192i | −0.0982394 | + | 0.170156i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.70711 | − | 4.68885i | −0.298950 | − | 0.517796i | ||||
\(83\) | −15.3137 | −1.68090 | −0.840449 | − | 0.541891i | \(-0.817709\pi\) | ||||
−0.840449 | + | 0.541891i | \(0.817709\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | 0.396642 | ||||||||
\(86\) | −6.82843 | − | 11.8272i | −0.736328 | − | 1.27536i | ||||
\(87\) | 0.585786 | − | 1.01461i | 0.0628029 | − | 0.108778i | ||||
\(88\) | −4.41421 | + | 7.64564i | −0.470557 | + | 0.815028i | ||||
\(89\) | 2.87868 | + | 4.98602i | 0.305139 | + | 0.528517i | 0.977292 | − | 0.211895i | \(-0.0679636\pi\) |
−0.672153 | + | 0.740412i | \(0.734630\pi\) | |||||||
\(90\) | −1.41421 | −0.149071 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.0000 | 1.45960 | ||||||||
\(93\) | 3.41421 | + | 5.91359i | 0.354037 | + | 0.613211i | ||||
\(94\) | 3.41421 | − | 5.91359i | 0.352149 | − | 0.609940i | ||||
\(95\) | −0.828427 | + | 1.43488i | −0.0849948 | + | 0.147215i | ||||
\(96\) | −0.792893 | − | 1.37333i | −0.0809243 | − | 0.140165i | ||||
\(97\) | 5.41421 | 0.549730 | 0.274865 | − | 0.961483i | \(-0.411367\pi\) | ||||
0.274865 | + | 0.961483i | \(0.411367\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 8.91421 | + | 15.4399i | 0.891421 | + | 1.54399i | ||||
\(101\) | −8.53553 | + | 14.7840i | −0.849317 | + | 1.47106i | 0.0325010 | + | 0.999472i | \(0.489653\pi\) |
−0.881818 | + | 0.471589i | \(0.843681\pi\) | |||||||
\(102\) | 7.53553 | − | 13.0519i | 0.746129 | − | 1.29233i | ||||
\(103\) | 6.24264 | + | 10.8126i | 0.615106 | + | 1.06539i | 0.990366 | + | 0.138475i | \(0.0442200\pi\) |
−0.375260 | + | 0.926919i | \(0.622447\pi\) | |||||||
\(104\) | −23.8995 | −2.34354 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.82843 | 0.468978 | ||||||||
\(107\) | 5.82843 | + | 10.0951i | 0.563455 | + | 0.975933i | 0.997192 | + | 0.0748933i | \(0.0238616\pi\) |
−0.433736 | + | 0.901040i | \(0.642805\pi\) | |||||||
\(108\) | −1.91421 | + | 3.31552i | −0.184195 | + | 0.319036i | ||||
\(109\) | −2.82843 | + | 4.89898i | −0.270914 | + | 0.469237i | −0.969096 | − | 0.246683i | \(-0.920659\pi\) |
0.698182 | + | 0.715920i | \(0.253993\pi\) | |||||||
\(110\) | −1.41421 | − | 2.44949i | −0.134840 | − | 0.233550i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3137 | 1.62874 | 0.814368 | − | 0.580348i | \(-0.197084\pi\) | ||||
0.814368 | + | 0.580348i | \(0.197084\pi\) | |||||||
\(114\) | 3.41421 | + | 5.91359i | 0.319770 | + | 0.553859i | ||||
\(115\) | −1.07107 | + | 1.85514i | −0.0998776 | + | 0.172993i | ||||
\(116\) | 2.24264 | − | 3.88437i | 0.208224 | − | 0.360654i | ||||
\(117\) | −2.70711 | − | 4.68885i | −0.250272 | − | 0.433484i | ||||
\(118\) | 16.4853 | 1.51759 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.58579 | −0.236049 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 4.53553 | − | 7.85578i | 0.410628 | − | 0.711228i | ||||
\(123\) | 1.12132 | − | 1.94218i | 0.101106 | − | 0.175121i | ||||
\(124\) | 13.0711 | + | 22.6398i | 1.17382 | + | 2.03311i | ||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.65685 | 0.856907 | 0.428454 | − | 0.903564i | \(-0.359059\pi\) | ||||
0.428454 | + | 0.903564i | \(0.359059\pi\) | |||||||
\(128\) | −10.2782 | − | 17.8023i | −0.908471 | − | 1.57352i | ||||
\(129\) | 2.82843 | − | 4.89898i | 0.249029 | − | 0.431331i | ||||
\(130\) | 3.82843 | − | 6.63103i | 0.335775 | − | 0.581580i | ||||
\(131\) | −3.65685 | − | 6.33386i | −0.319501 | − | 0.553392i | 0.660883 | − | 0.750489i | \(-0.270182\pi\) |
−0.980384 | + | 0.197097i | \(0.936849\pi\) | |||||||
\(132\) | −7.65685 | −0.666444 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.6569 | −1.17977 | ||||||||
\(135\) | −0.292893 | − | 0.507306i | −0.0252082 | − | 0.0436619i | ||||
\(136\) | 13.7782 | − | 23.8645i | 1.18147 | − | 2.04636i | ||||
\(137\) | 7.07107 | − | 12.2474i | 0.604122 | − | 1.04637i | −0.388067 | − | 0.921631i | \(-0.626857\pi\) |
0.992190 | − | 0.124739i | \(-0.0398094\pi\) | |||||||
\(138\) | 4.41421 | + | 7.64564i | 0.375763 | + | 0.650840i | ||||
\(139\) | −6.34315 | −0.538019 | −0.269009 | − | 0.963138i | \(-0.586696\pi\) | ||||
−0.269009 | + | 0.963138i | \(0.586696\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843 | 0.238197 | ||||||||
\(142\) | −16.0711 | − | 27.8359i | −1.34865 | − | 2.33594i | ||||
\(143\) | 5.41421 | − | 9.37769i | 0.452759 | − | 0.784202i | ||||
\(144\) | −1.50000 | + | 2.59808i | −0.125000 | + | 0.216506i | ||||
\(145\) | 0.343146 | + | 0.594346i | 0.0284967 | + | 0.0493577i | ||||
\(146\) | 14.2426 | 1.17873 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.3137 | −1.25878 | ||||||||
\(149\) | 2.65685 | + | 4.60181i | 0.217658 | + | 0.376995i | 0.954092 | − | 0.299515i | \(-0.0968249\pi\) |
−0.736434 | + | 0.676510i | \(0.763492\pi\) | |||||||
\(150\) | −5.62132 | + | 9.73641i | −0.458979 | + | 0.794975i | ||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | 6.24264 | + | 10.8126i | 0.506345 | + | 0.877015i | ||||
\(153\) | 6.24264 | 0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | −10.3640 | − | 17.9509i | −0.829781 | − | 1.43722i | ||||
\(157\) | −10.1213 | + | 17.5306i | −0.807769 | + | 1.39910i | 0.106636 | + | 0.994298i | \(0.465992\pi\) |
−0.914406 | + | 0.404799i | \(0.867341\pi\) | |||||||
\(158\) | 2.82843 | − | 4.89898i | 0.225018 | − | 0.389742i | ||||
\(159\) | 1.00000 | + | 1.73205i | 0.0793052 | + | 0.137361i | ||||
\(160\) | 0.928932 | 0.0734385 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.41421 | −0.189679 | ||||||||
\(163\) | −5.65685 | − | 9.79796i | −0.443079 | − | 0.767435i | 0.554837 | − | 0.831959i | \(-0.312781\pi\) |
−0.997916 | + | 0.0645236i | \(0.979447\pi\) | |||||||
\(164\) | 4.29289 | − | 7.43551i | 0.335219 | − | 0.580616i | ||||
\(165\) | 0.585786 | − | 1.01461i | 0.0456034 | − | 0.0789874i | ||||
\(166\) | −18.4853 | − | 32.0174i | −1.43474 | − | 2.48504i | ||||
\(167\) | 19.7990 | 1.53209 | 0.766046 | − | 0.642786i | \(-0.222221\pi\) | ||||
0.766046 | + | 0.642786i | \(0.222221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.3137 | 1.25490 | ||||||||
\(170\) | 4.41421 | + | 7.64564i | 0.338555 | + | 0.586394i | ||||
\(171\) | −1.41421 | + | 2.44949i | −0.108148 | + | 0.187317i | ||||
\(172\) | 10.8284 | − | 18.7554i | 0.825660 | − | 1.43008i | ||||
\(173\) | −3.46447 | − | 6.00063i | −0.263398 | − | 0.456220i | 0.703744 | − | 0.710453i | \(-0.251510\pi\) |
−0.967143 | + | 0.254234i | \(0.918177\pi\) | |||||||
\(174\) | 2.82843 | 0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 3.41421 | + | 5.91359i | 0.256628 | + | 0.444493i | ||||
\(178\) | −6.94975 | + | 12.0373i | −0.520906 | + | 0.902235i | ||||
\(179\) | 4.17157 | − | 7.22538i | 0.311798 | − | 0.540050i | −0.666954 | − | 0.745099i | \(-0.732402\pi\) |
0.978752 | + | 0.205049i | \(0.0657354\pi\) | |||||||
\(180\) | −1.12132 | − | 1.94218i | −0.0835783 | − | 0.144762i | ||||
\(181\) | −5.41421 | −0.402435 | −0.201218 | − | 0.979547i | \(-0.564490\pi\) | ||||
−0.201218 | + | 0.979547i | \(0.564490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.75736 | 0.277752 | ||||||||
\(184\) | 8.07107 | + | 13.9795i | 0.595007 | + | 1.03058i | ||||
\(185\) | 1.17157 | − | 2.02922i | 0.0861358 | − | 0.149191i | ||||
\(186\) | −8.24264 | + | 14.2767i | −0.604380 | + | 1.04682i | ||||
\(187\) | 6.24264 | + | 10.8126i | 0.456507 | + | 0.790693i | ||||
\(188\) | 10.8284 | 0.789744 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 4.91421 | − | 8.51167i | 0.354653 | − | 0.614277i | ||||
\(193\) | 8.65685 | − | 14.9941i | 0.623134 | − | 1.07930i | −0.365765 | − | 0.930707i | \(-0.619192\pi\) |
0.988899 | − | 0.148592i | \(-0.0474742\pi\) | |||||||
\(194\) | 6.53553 | + | 11.3199i | 0.469224 | + | 0.812720i | ||||
\(195\) | 3.17157 | 0.227121 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | −2.41421 | − | 4.18154i | −0.171571 | − | 0.297169i | ||||
\(199\) | −5.17157 | + | 8.95743i | −0.366603 | + | 0.634975i | −0.989032 | − | 0.147701i | \(-0.952813\pi\) |
0.622429 | + | 0.782676i | \(0.286146\pi\) | |||||||
\(200\) | −10.2782 | + | 17.8023i | −0.726777 | + | 1.25881i | ||||
\(201\) | −2.82843 | − | 4.89898i | −0.199502 | − | 0.345547i | ||||
\(202\) | −41.2132 | −2.89975 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 23.8995 | 1.67330 | ||||||||
\(205\) | 0.656854 | + | 1.13770i | 0.0458767 | + | 0.0794608i | ||||
\(206\) | −15.0711 | + | 26.1039i | −1.05005 | + | 1.81874i | ||||
\(207\) | −1.82843 | + | 3.16693i | −0.127084 | + | 0.220117i | ||||
\(208\) | −8.12132 | − | 14.0665i | −0.563112 | − | 0.975339i | ||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9706 | −1.44367 | −0.721837 | − | 0.692064i | \(-0.756702\pi\) | ||||
−0.721837 | + | 0.692064i | \(0.756702\pi\) | |||||||
\(212\) | 3.82843 | + | 6.63103i | 0.262937 | + | 0.455421i | ||||
\(213\) | 6.65685 | − | 11.5300i | 0.456120 | − | 0.790023i | ||||
\(214\) | −14.0711 | + | 24.3718i | −0.961878 | + | 1.66602i | ||||
\(215\) | 1.65685 | + | 2.86976i | 0.112997 | + | 0.195716i | ||||
\(216\) | −4.41421 | −0.300349 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −13.6569 | −0.924959 | ||||||||
\(219\) | 2.94975 | + | 5.10911i | 0.199325 | + | 0.345242i | ||||
\(220\) | 2.24264 | − | 3.88437i | 0.151199 | − | 0.261884i | ||||
\(221\) | −16.8995 | + | 29.2708i | −1.13678 | + | 1.96897i | ||||
\(222\) | −4.82843 | − | 8.36308i | −0.324063 | − | 0.561293i | ||||
\(223\) | −8.97056 | −0.600713 | −0.300357 | − | 0.953827i | \(-0.597106\pi\) | ||||
−0.300357 | + | 0.953827i | \(0.597106\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 20.8995 | + | 36.1990i | 1.39021 | + | 2.40792i | ||||
\(227\) | 7.89949 | − | 13.6823i | 0.524308 | − | 0.908128i | −0.475292 | − | 0.879828i | \(-0.657657\pi\) |
0.999599 | − | 0.0282996i | \(-0.00900924\pi\) | |||||||
\(228\) | −5.41421 | + | 9.37769i | −0.358565 | + | 0.621053i | ||||
\(229\) | −4.12132 | − | 7.13834i | −0.272345 | − | 0.471715i | 0.697117 | − | 0.716957i | \(-0.254466\pi\) |
−0.969462 | + | 0.245243i | \(0.921132\pi\) | |||||||
\(230\) | −5.17157 | −0.341003 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.17157 | 0.339530 | ||||||||
\(233\) | −11.0711 | − | 19.1757i | −0.725290 | − | 1.25624i | −0.958855 | − | 0.283898i | \(-0.908372\pi\) |
0.233565 | − | 0.972341i | \(-0.424961\pi\) | |||||||
\(234\) | 6.53553 | − | 11.3199i | 0.427241 | − | 0.740003i | ||||
\(235\) | −0.828427 | + | 1.43488i | −0.0540406 | + | 0.0936011i | ||||
\(236\) | 13.0711 | + | 22.6398i | 0.850854 | + | 1.47372i | ||||
\(237\) | 2.34315 | 0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.34315 | −0.280935 | −0.140467 | − | 0.990085i | \(-0.544861\pi\) | ||||
−0.140467 | + | 0.990085i | \(0.544861\pi\) | |||||||
\(240\) | −0.878680 | − | 1.52192i | −0.0567185 | − | 0.0982394i | ||||
\(241\) | 3.87868 | − | 6.71807i | 0.249848 | − | 0.432749i | −0.713636 | − | 0.700517i | \(-0.752953\pi\) |
0.963483 | + | 0.267768i | \(0.0862861\pi\) | |||||||
\(242\) | −8.44975 | + | 14.6354i | −0.543170 | + | 0.940799i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 14.3848 | 0.920891 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.41421 | 0.345198 | ||||||||
\(247\) | −7.65685 | − | 13.2621i | −0.487194 | − | 0.843845i | ||||
\(248\) | −15.0711 | + | 26.1039i | −0.957014 | + | 1.65760i | ||||
\(249\) | 7.65685 | − | 13.2621i | 0.485233 | − | 0.840449i | ||||
\(250\) | −6.82843 | − | 11.8272i | −0.431868 | − | 0.748017i | ||||
\(251\) | 4.48528 | 0.283108 | 0.141554 | − | 0.989931i | \(-0.454790\pi\) | ||||
0.141554 | + | 0.989931i | \(0.454790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.31371 | −0.459809 | ||||||||
\(254\) | 11.6569 | + | 20.1903i | 0.731416 | + | 1.26685i | ||||
\(255\) | −1.82843 | + | 3.16693i | −0.114501 | + | 0.198321i | ||||
\(256\) | 14.9853 | − | 25.9553i | 0.936580 | − | 1.62220i | ||||
\(257\) | 9.60660 | + | 16.6391i | 0.599243 | + | 1.03792i | 0.992933 | + | 0.118677i | \(0.0378651\pi\) |
−0.393690 | + | 0.919243i | \(0.628802\pi\) | |||||||
\(258\) | 13.6569 | 0.850239 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.1421 | 0.753023 | ||||||||
\(261\) | 0.585786 | + | 1.01461i | 0.0362593 | + | 0.0628029i | ||||
\(262\) | 8.82843 | − | 15.2913i | 0.545422 | − | 0.944699i | ||||
\(263\) | 8.65685 | − | 14.9941i | 0.533805 | − | 0.924577i | −0.465416 | − | 0.885092i | \(-0.654095\pi\) |
0.999220 | − | 0.0394843i | \(-0.0125715\pi\) | |||||||
\(264\) | −4.41421 | − | 7.64564i | −0.271676 | − | 0.470557i | ||||
\(265\) | −1.17157 | −0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.75736 | −0.352345 | ||||||||
\(268\) | −10.8284 | − | 18.7554i | −0.661451 | − | 1.14567i | ||||
\(269\) | −5.36396 | + | 9.29065i | −0.327046 | + | 0.566461i | −0.981924 | − | 0.189274i | \(-0.939387\pi\) |
0.654878 | + | 0.755735i | \(0.272720\pi\) | |||||||
\(270\) | 0.707107 | − | 1.22474i | 0.0430331 | − | 0.0745356i | ||||
\(271\) | −9.07107 | − | 15.7116i | −0.551028 | − | 0.954409i | −0.998201 | − | 0.0599610i | \(-0.980902\pi\) |
0.447173 | − | 0.894448i | \(-0.352431\pi\) | |||||||
\(272\) | 18.7279 | 1.13555 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 34.1421 | 2.06260 | ||||||||
\(275\) | −4.65685 | − | 8.06591i | −0.280819 | − | 0.486393i | ||||
\(276\) | −7.00000 | + | 12.1244i | −0.421350 | + | 0.729800i | ||||
\(277\) | −6.65685 | + | 11.5300i | −0.399972 | + | 0.692771i | −0.993722 | − | 0.111878i | \(-0.964313\pi\) |
0.593750 | + | 0.804649i | \(0.297647\pi\) | |||||||
\(278\) | −7.65685 | − | 13.2621i | −0.459228 | − | 0.795406i | ||||
\(279\) | −6.82843 | −0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4853 | −0.983429 | −0.491715 | − | 0.870756i | \(-0.663630\pi\) | ||||
−0.491715 | + | 0.870756i | \(0.663630\pi\) | |||||||
\(282\) | 3.41421 | + | 5.91359i | 0.203313 | + | 0.352149i | ||||
\(283\) | −4.24264 | + | 7.34847i | −0.252199 | + | 0.436821i | −0.964131 | − | 0.265427i | \(-0.914487\pi\) |
0.711932 | + | 0.702248i | \(0.247820\pi\) | |||||||
\(284\) | 25.4853 | − | 44.1418i | 1.51227 | − | 2.61933i | ||||
\(285\) | −0.828427 | − | 1.43488i | −0.0490718 | − | 0.0849948i | ||||
\(286\) | 26.1421 | 1.54582 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | −10.9853 | − | 19.0271i | −0.646193 | − | 1.11924i | ||||
\(290\) | −0.828427 | + | 1.43488i | −0.0486469 | + | 0.0842589i | ||||
\(291\) | −2.70711 | + | 4.68885i | −0.158693 | + | 0.274865i | ||||
\(292\) | 11.2929 | + | 19.5599i | 0.660867 | + | 1.14465i | ||||
\(293\) | 19.4142 | 1.13419 | 0.567095 | − | 0.823652i | \(-0.308067\pi\) | ||||
0.567095 | + | 0.823652i | \(0.308067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | −8.82843 | − | 15.2913i | −0.513142 | − | 0.888788i | ||||
\(297\) | 1.00000 | − | 1.73205i | 0.0580259 | − | 0.100504i | ||||
\(298\) | −6.41421 | + | 11.1097i | −0.371565 | + | 0.643570i | ||||
\(299\) | −9.89949 | − | 17.1464i | −0.572503 | − | 0.991604i | ||||
\(300\) | −17.8284 | −1.02932 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −28.9706 | −1.66707 | ||||||||
\(303\) | −8.53553 | − | 14.7840i | −0.490354 | − | 0.849317i | ||||
\(304\) | −4.24264 | + | 7.34847i | −0.243332 | + | 0.421464i | ||||
\(305\) | −1.10051 | + | 1.90613i | −0.0630147 | + | 0.109145i | ||||
\(306\) | 7.53553 | + | 13.0519i | 0.430778 | + | 0.746129i | ||||
\(307\) | 1.85786 | 0.106034 | 0.0530170 | − | 0.998594i | \(-0.483116\pi\) | ||||
0.0530170 | + | 0.998594i | \(0.483116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4853 | −0.710263 | ||||||||
\(310\) | −4.82843 | − | 8.36308i | −0.274236 | − | 0.474991i | ||||
\(311\) | 11.0711 | − | 19.1757i | 0.627783 | − | 1.08735i | −0.360213 | − | 0.932870i | \(-0.617296\pi\) |
0.987996 | − | 0.154481i | \(-0.0493707\pi\) | |||||||
\(312\) | 11.9497 | − | 20.6976i | 0.676521 | − | 1.17177i | ||||
\(313\) | 8.94975 | + | 15.5014i | 0.505870 | + | 0.876192i | 0.999977 | + | 0.00679098i | \(0.00216165\pi\) |
−0.494107 | + | 0.869401i | \(0.664505\pi\) | |||||||
\(314\) | −48.8701 | −2.75790 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.97056 | 0.504634 | ||||||||
\(317\) | −5.00000 | − | 8.66025i | −0.280828 | − | 0.486408i | 0.690761 | − | 0.723083i | \(-0.257276\pi\) |
−0.971589 | + | 0.236675i | \(0.923942\pi\) | |||||||
\(318\) | −2.41421 | + | 4.18154i | −0.135382 | + | 0.234489i | ||||
\(319\) | −1.17157 | + | 2.02922i | −0.0655955 | + | 0.113615i | ||||
\(320\) | 2.87868 | + | 4.98602i | 0.160923 | + | 0.278727i | ||||
\(321\) | −11.6569 | −0.650622 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.6569 | 0.982454 | ||||||||
\(324\) | −1.91421 | − | 3.31552i | −0.106345 | − | 0.184195i | ||||
\(325\) | 12.6066 | − | 21.8353i | 0.699288 | − | 1.21120i | ||||
\(326\) | 13.6569 | − | 23.6544i | 0.756383 | − | 1.31009i | ||||
\(327\) | −2.82843 | − | 4.89898i | −0.156412 | − | 0.270914i | ||||
\(328\) | 9.89949 | 0.546608 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.82843 | 0.155700 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 29.3137 | − | 50.7728i | 1.60880 | − | 2.78652i | ||||
\(333\) | 2.00000 | − | 3.46410i | 0.109599 | − | 0.189832i | ||||
\(334\) | 23.8995 | + | 41.3951i | 1.30772 | + | 2.26504i | ||||
\(335\) | 3.31371 | 0.181047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3431 | −0.999215 | −0.499607 | − | 0.866252i | \(-0.666522\pi\) | ||||
−0.499607 | + | 0.866252i | \(0.666522\pi\) | |||||||
\(338\) | 19.6924 | + | 34.1082i | 1.07112 | + | 1.85524i | ||||
\(339\) | −8.65685 | + | 14.9941i | −0.470176 | + | 0.814368i | ||||
\(340\) | −7.00000 | + | 12.1244i | −0.379628 | + | 0.657536i | ||||
\(341\) | −6.82843 | − | 11.8272i | −0.369780 | − | 0.640478i | ||||
\(342\) | −6.82843 | −0.369239 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 24.9706 | 1.34632 | ||||||||
\(345\) | −1.07107 | − | 1.85514i | −0.0576644 | − | 0.0998776i | ||||
\(346\) | 8.36396 | − | 14.4868i | 0.449649 | − | 0.778815i | ||||
\(347\) | −5.34315 | + | 9.25460i | −0.286835 | + | 0.496813i | −0.973053 | − | 0.230584i | \(-0.925937\pi\) |
0.686217 | + | 0.727396i | \(0.259270\pi\) | |||||||
\(348\) | 2.24264 | + | 3.88437i | 0.120218 | + | 0.208224i | ||||
\(349\) | 9.89949 | 0.529908 | 0.264954 | − | 0.964261i | \(-0.414643\pi\) | ||||
0.264954 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.41421 | 0.288989 | ||||||||
\(352\) | 1.58579 | + | 2.74666i | 0.0845227 | + | 0.146398i | ||||
\(353\) | −5.36396 | + | 9.29065i | −0.285495 | + | 0.494492i | −0.972729 | − | 0.231944i | \(-0.925491\pi\) |
0.687234 | + | 0.726436i | \(0.258825\pi\) | |||||||
\(354\) | −8.24264 | + | 14.2767i | −0.438091 | + | 0.758797i | ||||
\(355\) | 3.89949 | + | 6.75412i | 0.206964 | + | 0.358472i | ||||
\(356\) | −22.0416 | −1.16820 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.1421 | 1.06454 | ||||||||
\(359\) | 5.82843 | + | 10.0951i | 0.307613 | + | 0.532801i | 0.977840 | − | 0.209355i | \(-0.0671366\pi\) |
−0.670227 | + | 0.742156i | \(0.733803\pi\) | |||||||
\(360\) | 1.29289 | − | 2.23936i | 0.0681415 | − | 0.118024i | ||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | −6.53553 | − | 11.3199i | −0.343500 | − | 0.594960i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.45584 | −0.180887 | ||||||||
\(366\) | 4.53553 | + | 7.85578i | 0.237076 | + | 0.410628i | ||||
\(367\) | −9.65685 | + | 16.7262i | −0.504084 | + | 0.873099i | 0.495905 | + | 0.868377i | \(0.334836\pi\) |
−0.999989 | + | 0.00472187i | \(0.998497\pi\) | |||||||
\(368\) | −5.48528 | + | 9.50079i | −0.285940 | + | 0.495263i | ||||
\(369\) | 1.12132 | + | 1.94218i | 0.0583736 | + | 0.101106i | ||||
\(370\) | 5.65685 | 0.294086 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.1421 | −1.35541 | ||||||||
\(373\) | 16.6569 | + | 28.8505i | 0.862459 | + | 1.49382i | 0.869548 | + | 0.493848i | \(0.164410\pi\) |
−0.00708885 | + | 0.999975i | \(0.502256\pi\) | |||||||
\(374\) | −15.0711 | + | 26.1039i | −0.779306 | + | 1.34980i | ||||
\(375\) | 2.82843 | − | 4.89898i | 0.146059 | − | 0.252982i | ||||
\(376\) | 6.24264 | + | 10.8126i | 0.321940 | + | 0.557616i | ||||
\(377\) | −6.34315 | −0.326689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.3137 | 1.60848 | 0.804239 | − | 0.594307i | \(-0.202573\pi\) | ||||
0.804239 | + | 0.594307i | \(0.202573\pi\) | |||||||
\(380\) | −3.17157 | − | 5.49333i | −0.162698 | − | 0.281802i | ||||
\(381\) | −4.82843 | + | 8.36308i | −0.247368 | + | 0.428454i | ||||
\(382\) | −21.7279 | + | 37.6339i | −1.11170 | + | 1.92552i | ||||
\(383\) | 14.8284 | + | 25.6836i | 0.757697 | + | 1.31237i | 0.944022 | + | 0.329882i | \(0.107009\pi\) |
−0.186325 | + | 0.982488i | \(0.559658\pi\) | |||||||
\(384\) | 20.5563 | 1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.7990 | 2.12751 | ||||||||
\(387\) | 2.82843 | + | 4.89898i | 0.143777 | + | 0.249029i | ||||
\(388\) | −10.3640 | + | 17.9509i | −0.526150 | + | 0.911319i | ||||
\(389\) | −5.07107 | + | 8.78335i | −0.257113 | + | 0.445333i | −0.965467 | − | 0.260524i | \(-0.916105\pi\) |
0.708354 | + | 0.705857i | \(0.249438\pi\) | |||||||
\(390\) | 3.82843 | + | 6.63103i | 0.193860 | + | 0.335775i | ||||
\(391\) | 22.8284 | 1.15448 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.31371 | 0.368928 | ||||||||
\(394\) | 2.41421 | + | 4.18154i | 0.121626 | + | 0.210663i | ||||
\(395\) | −0.686292 | + | 1.18869i | −0.0345311 | + | 0.0598096i | ||||
\(396\) | 3.82843 | − | 6.63103i | 0.192386 | − | 0.333222i | ||||
\(397\) | −17.1924 | − | 29.7781i | −0.862861 | − | 1.49452i | −0.869155 | − | 0.494539i | \(-0.835337\pi\) |
0.00629405 | − | 0.999980i | \(-0.497997\pi\) | |||||||
\(398\) | −24.9706 | −1.25166 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.9706 | −0.698528 | ||||||||
\(401\) | −11.0711 | − | 19.1757i | −0.552863 | − | 0.957586i | −0.998066 | − | 0.0621570i | \(-0.980202\pi\) |
0.445204 | − | 0.895429i | \(-0.353131\pi\) | |||||||
\(402\) | 6.82843 | − | 11.8272i | 0.340571 | − | 0.589886i | ||||
\(403\) | 18.4853 | − | 32.0174i | 0.920817 | − | 1.59490i | ||||
\(404\) | −32.6777 | − | 56.5994i | −1.62577 | − | 2.81592i | ||||
\(405\) | 0.585786 | 0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 13.7782 | + | 23.8645i | 0.682121 | + | 1.18147i | ||||
\(409\) | 9.29289 | − | 16.0958i | 0.459504 | − | 0.795884i | −0.539431 | − | 0.842030i | \(-0.681361\pi\) |
0.998935 | + | 0.0461457i | \(0.0146939\pi\) | |||||||
\(410\) | −1.58579 | + | 2.74666i | −0.0783164 | + | 0.135648i | ||||
\(411\) | 7.07107 | + | 12.2474i | 0.348790 | + | 0.604122i | ||||
\(412\) | −47.7990 | −2.35489 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.82843 | −0.433894 | ||||||||
\(415\) | 4.48528 | + | 7.76874i | 0.220174 | + | 0.381352i | ||||
\(416\) | −4.29289 | + | 7.43551i | −0.210476 | + | 0.364556i | ||||
\(417\) | 3.17157 | − | 5.49333i | 0.155313 | − | 0.269009i | ||||
\(418\) | −6.82843 | − | 11.8272i | −0.333989 | − | 0.578486i | ||||
\(419\) | 38.8284 | 1.89689 | 0.948446 | − | 0.316938i | \(-0.102655\pi\) | ||||
0.948446 | + | 0.316938i | \(0.102655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.6274 | −1.39521 | −0.697607 | − | 0.716480i | \(-0.745752\pi\) | ||||
−0.697607 | + | 0.716480i | \(0.745752\pi\) | |||||||
\(422\) | −25.3137 | − | 43.8446i | −1.23225 | − | 2.13432i | ||||
\(423\) | −1.41421 | + | 2.44949i | −0.0687614 | + | 0.119098i | ||||
\(424\) | −4.41421 | + | 7.64564i | −0.214373 | + | 0.371305i | ||||
\(425\) | 14.5355 | + | 25.1763i | 0.705077 | + | 1.22123i | ||||
\(426\) | 32.1421 | 1.55729 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −44.6274 | −2.15715 | ||||||||
\(429\) | 5.41421 | + | 9.37769i | 0.261401 | + | 0.452759i | ||||
\(430\) | −4.00000 | + | 6.92820i | −0.192897 | + | 0.334108i | ||||
\(431\) | −3.48528 | + | 6.03668i | −0.167880 | + | 0.290777i | −0.937674 | − | 0.347515i | \(-0.887025\pi\) |
0.769794 | + | 0.638292i | \(0.220359\pi\) | |||||||
\(432\) | −1.50000 | − | 2.59808i | −0.0721688 | − | 0.125000i | ||||
\(433\) | −11.7574 | −0.565023 | −0.282511 | − | 0.959264i | \(-0.591167\pi\) | ||||
−0.282511 | + | 0.959264i | \(0.591167\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.686292 | −0.0329052 | ||||||||
\(436\) | −10.8284 | − | 18.7554i | −0.518588 | − | 0.898220i | ||||
\(437\) | −5.17157 | + | 8.95743i | −0.247390 | + | 0.428492i | ||||
\(438\) | −7.12132 | + | 12.3345i | −0.340270 | + | 0.589365i | ||||
\(439\) | −17.6569 | − | 30.5826i | −0.842716 | − | 1.45963i | −0.887590 | − | 0.460634i | \(-0.847622\pi\) |
0.0448746 | − | 0.998993i | \(-0.485711\pi\) | |||||||
\(440\) | 5.17157 | 0.246545 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −81.5980 | −3.88122 | ||||||||
\(443\) | −0.514719 | − | 0.891519i | −0.0244550 | − | 0.0423573i | 0.853539 | − | 0.521029i | \(-0.174452\pi\) |
−0.877994 | + | 0.478672i | \(0.841118\pi\) | |||||||
\(444\) | 7.65685 | − | 13.2621i | 0.363378 | − | 0.629390i | ||||
\(445\) | 1.68629 | − | 2.92074i | 0.0799379 | − | 0.138456i | ||||
\(446\) | −10.8284 | − | 18.7554i | −0.512741 | − | 0.888093i | ||||
\(447\) | −5.31371 | −0.251330 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.3137 | 0.817084 | 0.408542 | − | 0.912739i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912739i | \(0.366037\pi\) | |||||||
\(450\) | −5.62132 | − | 9.73641i | −0.264992 | − | 0.458979i | ||||
\(451\) | −2.24264 | + | 3.88437i | −0.105602 | + | 0.182908i | ||||
\(452\) | −33.1421 | + | 57.4039i | −1.55887 | + | 2.70005i | ||||
\(453\) | −6.00000 | − | 10.3923i | −0.281905 | − | 0.488273i | ||||
\(454\) | 38.1421 | 1.79010 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4853 | −0.584677 | ||||||||
\(457\) | 9.00000 | + | 15.5885i | 0.421002 | + | 0.729197i | 0.996038 | − | 0.0889312i | \(-0.0283451\pi\) |
−0.575036 | + | 0.818128i | \(0.695012\pi\) | |||||||
\(458\) | 9.94975 | − | 17.2335i | 0.464921 | − | 0.805267i | ||||
\(459\) | −3.12132 | + | 5.40629i | −0.145691 | + | 0.252344i | ||||
\(460\) | −4.10051 | − | 7.10228i | −0.191187 | − | 0.331146i | ||||
\(461\) | −19.4142 | −0.904210 | −0.452105 | − | 0.891965i | \(-0.649327\pi\) | ||||
−0.452105 | + | 0.891965i | \(0.649327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6274 | 0.865689 | 0.432845 | − | 0.901468i | \(-0.357510\pi\) | ||||
0.432845 | + | 0.901468i | \(0.357510\pi\) | |||||||
\(464\) | 1.75736 | + | 3.04384i | 0.0815834 | + | 0.141307i | ||||
\(465\) | 2.00000 | − | 3.46410i | 0.0927478 | − | 0.160644i | ||||
\(466\) | 26.7279 | − | 46.2941i | 1.23815 | − | 2.14453i | ||||
\(467\) | −19.8995 | − | 34.4669i | −0.920839 | − | 1.59494i | −0.798120 | − | 0.602498i | \(-0.794172\pi\) |
−0.122718 | − | 0.992442i | \(-0.539161\pi\) | |||||||
\(468\) | 20.7279 | 0.958149 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.00000 | −0.184506 | ||||||||
\(471\) | −10.1213 | − | 17.5306i | −0.466366 | − | 0.807769i | ||||
\(472\) | −15.0711 | + | 26.1039i | −0.693702 | + | 1.20153i | ||||
\(473\) | −5.65685 | + | 9.79796i | −0.260102 | + | 0.450511i | ||||
\(474\) | 2.82843 | + | 4.89898i | 0.129914 | + | 0.225018i | ||||
\(475\) | −13.1716 | −0.604353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | −5.24264 | − | 9.08052i | −0.239793 | − | 0.415333i | ||||
\(479\) | −15.0711 | + | 26.1039i | −0.688615 | + | 1.19272i | 0.283671 | + | 0.958922i | \(0.408447\pi\) |
−0.972286 | + | 0.233794i | \(0.924886\pi\) | |||||||
\(480\) | −0.464466 | + | 0.804479i | −0.0211999 | + | 0.0367193i | ||||
\(481\) | 10.8284 | + | 18.7554i | 0.493734 | + | 0.855172i | ||||
\(482\) | 18.7279 | 0.853033 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.7990 | −1.21814 | ||||||||
\(485\) | −1.58579 | − | 2.74666i | −0.0720069 | − | 0.124720i | ||||
\(486\) | 1.20711 | − | 2.09077i | 0.0547555 | − | 0.0948393i | ||||
\(487\) | 9.31371 | − | 16.1318i | 0.422044 | − | 0.731002i | −0.574095 | − | 0.818789i | \(-0.694646\pi\) |
0.996139 | + | 0.0877864i | \(0.0279793\pi\) | |||||||
\(488\) | 8.29289 | + | 14.3637i | 0.375402 | + | 0.650215i | ||||
\(489\) | 11.3137 | 0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.9706 | 1.75872 | 0.879358 | − | 0.476160i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476160i | \(0.157972\pi\) | |||||||
\(492\) | 4.29289 | + | 7.43551i | 0.193539 | + | 0.335219i | ||||
\(493\) | 3.65685 | − | 6.33386i | 0.164696 | − | 0.285263i | ||||
\(494\) | 18.4853 | − | 32.0174i | 0.831692 | − | 1.44053i | ||||
\(495\) | 0.585786 | + | 1.01461i | 0.0263291 | + | 0.0456034i | ||||
\(496\) | −20.4853 | −0.919816 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 36.9706 | 1.65669 | ||||||||
\(499\) | 9.65685 | + | 16.7262i | 0.432300 | + | 0.748766i | 0.997071 | − | 0.0764820i | \(-0.0243688\pi\) |
−0.564771 | + | 0.825248i | \(0.691035\pi\) | |||||||
\(500\) | 10.8284 | − | 18.7554i | 0.484262 | − | 0.838766i | ||||
\(501\) | −9.89949 | + | 17.1464i | −0.442277 | + | 0.766046i | ||||
\(502\) | 5.41421 | + | 9.37769i | 0.241648 | + | 0.418547i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | −8.82843 | − | 15.2913i | −0.392471 | − | 0.679781i | ||||
\(507\) | −8.15685 | + | 14.1281i | −0.362259 | + | 0.627450i | ||||
\(508\) | −18.4853 | + | 32.0174i | −0.820152 | + | 1.42054i | ||||
\(509\) | 12.7782 | + | 22.1324i | 0.566383 | + | 0.981003i | 0.996920 | + | 0.0784305i | \(0.0249909\pi\) |
−0.430537 | + | 0.902573i | \(0.641676\pi\) | |||||||
\(510\) | −8.82843 | −0.390929 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | −1.41421 | − | 2.44949i | −0.0624391 | − | 0.108148i | ||||
\(514\) | −23.1924 | + | 40.1704i | −1.02297 | + | 1.77184i | ||||
\(515\) | 3.65685 | − | 6.33386i | 0.161140 | − | 0.279103i | ||||
\(516\) | 10.8284 | + | 18.7554i | 0.476695 | + | 0.825660i | ||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.92893 | 0.304146 | ||||||||
\(520\) | 7.00000 | + | 12.1244i | 0.306970 | + | 0.531688i | ||||
\(521\) | 16.2929 | − | 28.2201i | 0.713805 | − | 1.23635i | −0.249614 | − | 0.968345i | \(-0.580304\pi\) |
0.963419 | − | 0.268000i | \(-0.0863629\pi\) | |||||||
\(522\) | −1.41421 | + | 2.44949i | −0.0618984 | + | 0.107211i | ||||
\(523\) | 7.17157 | + | 12.4215i | 0.313591 | + | 0.543156i | 0.979137 | − | 0.203201i | \(-0.0651346\pi\) |
−0.665546 | + | 0.746357i | \(0.731801\pi\) | |||||||
\(524\) | 28.0000 | 1.22319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 41.7990 | 1.82252 | ||||||||
\(527\) | 21.3137 | + | 36.9164i | 0.928440 | + | 1.60810i | ||||
\(528\) | 3.00000 | − | 5.19615i | 0.130558 | − | 0.226134i | ||||
\(529\) | 4.81371 | − | 8.33759i | 0.209292 | − | 0.362504i | ||||
\(530\) | −1.41421 | − | 2.44949i | −0.0614295 | − | 0.106399i | ||||
\(531\) | −6.82843 | −0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1421 | −0.525934 | ||||||||
\(534\) | −6.94975 | − | 12.0373i | −0.300745 | − | 0.520906i | ||||
\(535\) | 3.41421 | − | 5.91359i | 0.147609 | − | 0.255667i | ||||
\(536\) | 12.4853 | − | 21.6251i | 0.539282 | − | 0.934064i | ||||
\(537\) | 4.17157 | + | 7.22538i | 0.180017 | + | 0.311798i | ||||
\(538\) | −25.8995 | −1.11661 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.24264 | 0.0965079 | ||||||||
\(541\) | 2.65685 | + | 4.60181i | 0.114227 | + | 0.197847i | 0.917471 | − | 0.397804i | \(-0.130228\pi\) |
−0.803243 | + | 0.595651i | \(0.796894\pi\) | |||||||
\(542\) | 21.8995 | − | 37.9310i | 0.940664 | − | 1.62928i | ||||
\(543\) | 2.70711 | − | 4.68885i | 0.116173 | − | 0.201218i | ||||
\(544\) | −4.94975 | − | 8.57321i | −0.212219 | − | 0.367574i | ||||
\(545\) | 3.31371 | 0.141944 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.02944 | −0.129529 | −0.0647647 | − | 0.997901i | \(-0.520630\pi\) | ||||
−0.0647647 | + | 0.997901i | \(0.520630\pi\) | |||||||
\(548\) | 27.0711 | + | 46.8885i | 1.15642 | + | 2.00298i | ||||
\(549\) | −1.87868 | + | 3.25397i | −0.0801801 | + | 0.138876i | ||||
\(550\) | 11.2426 | − | 19.4728i | 0.479388 | − | 0.830324i | ||||
\(551\) | 1.65685 | + | 2.86976i | 0.0705844 | + | 0.122256i | ||||
\(552\) | −16.1421 | −0.687055 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −32.1421 | −1.36559 | ||||||||
\(555\) | 1.17157 | + | 2.02922i | 0.0497305 | + | 0.0861358i | ||||
\(556\) | 12.1421 | − | 21.0308i | 0.514941 | − | 0.891904i | ||||
\(557\) | −13.0000 | + | 22.5167i | −0.550828 | + | 0.954062i | 0.447387 | + | 0.894340i | \(0.352355\pi\) |
−0.998215 | + | 0.0597213i | \(0.980979\pi\) | |||||||
\(558\) | −8.24264 | − | 14.2767i | −0.348939 | − | 0.604380i | ||||
\(559\) | −30.6274 | −1.29540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.4853 | −0.527129 | ||||||||
\(562\) | −19.8995 | − | 34.4669i | −0.839410 | − | 1.45390i | ||||
\(563\) | 3.41421 | − | 5.91359i | 0.143892 | − | 0.249228i | −0.785067 | − | 0.619411i | \(-0.787372\pi\) |
0.928959 | + | 0.370183i | \(0.120705\pi\) | |||||||
\(564\) | −5.41421 | + | 9.37769i | −0.227980 | + | 0.394872i | ||||
\(565\) | −5.07107 | − | 8.78335i | −0.213341 | − | 0.369518i | ||||
\(566\) | −20.4853 | −0.861061 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 58.7696 | 2.46592 | ||||||||
\(569\) | −0.242641 | − | 0.420266i | −0.0101720 | − | 0.0176185i | 0.860895 | − | 0.508783i | \(-0.169905\pi\) |
−0.871067 | + | 0.491165i | \(0.836571\pi\) | |||||||
\(570\) | 2.00000 | − | 3.46410i | 0.0837708 | − | 0.145095i | ||||
\(571\) | −16.8284 | + | 29.1477i | −0.704248 | + | 1.21979i | 0.262715 | + | 0.964874i | \(0.415382\pi\) |
−0.966962 | + | 0.254919i | \(0.917951\pi\) | |||||||
\(572\) | 20.7279 | + | 35.9018i | 0.866678 | + | 1.50113i | ||||
\(573\) | −18.0000 | −0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.0294 | −0.710177 | ||||||||
\(576\) | 4.91421 | + | 8.51167i | 0.204759 | + | 0.354653i | ||||
\(577\) | 7.05025 | − | 12.2114i | 0.293506 | − | 0.508367i | −0.681130 | − | 0.732162i | \(-0.738511\pi\) |
0.974636 | + | 0.223795i | \(0.0718446\pi\) | |||||||
\(578\) | 26.5208 | − | 45.9354i | 1.10312 | − | 1.91066i | ||||
\(579\) | 8.65685 | + | 14.9941i | 0.359767 | + | 0.623134i | ||||
\(580\) | −2.62742 | −0.109098 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.0711 | −0.541813 | ||||||||
\(583\) | −2.00000 | − | 3.46410i | −0.0828315 | − | 0.143468i | ||||
\(584\) | −13.0208 | + | 22.5527i | −0.538805 | + | 0.933238i | ||||
\(585\) | −1.58579 | + | 2.74666i | −0.0655642 | + | 0.113561i | ||||
\(586\) | 23.4350 | + | 40.5907i | 0.968092 | + | 1.67678i | ||||
\(587\) | −17.1716 | −0.708747 | −0.354373 | − | 0.935104i | \(-0.615306\pi\) | ||||
−0.354373 | + | 0.935104i | \(0.615306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3137 | −0.795807 | ||||||||
\(590\) | −4.82843 | − | 8.36308i | −0.198783 | − | 0.344303i | ||||
\(591\) | −1.00000 | + | 1.73205i | −0.0411345 | + | 0.0712470i | ||||
\(592\) | 6.00000 | − | 10.3923i | 0.246598 | − | 0.427121i | ||||
\(593\) | 10.5355 | + | 18.2481i | 0.432643 | + | 0.749359i | 0.997100 | − | 0.0761034i | \(-0.0242479\pi\) |
−0.564457 | + | 0.825462i | \(0.690915\pi\) | |||||||
\(594\) | 4.82843 | 0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.3431 | −0.833288 | ||||||||
\(597\) | −5.17157 | − | 8.95743i | −0.211658 | − | 0.366603i | ||||
\(598\) | 23.8995 | − | 41.3951i | 0.977323 | − | 1.69277i | ||||
\(599\) | 1.00000 | − | 1.73205i | 0.0408589 | − | 0.0707697i | −0.844873 | − | 0.534967i | \(-0.820324\pi\) |
0.885732 | + | 0.464198i | \(0.153657\pi\) | |||||||
\(600\) | −10.2782 | − | 17.8023i | −0.419605 | − | 0.726777i | ||||
\(601\) | −0.928932 | −0.0378919 | −0.0189460 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189460 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.65685 | 0.230365 | ||||||||
\(604\) | −22.9706 | − | 39.7862i | −0.934659 | − | 1.61888i | ||||
\(605\) | 2.05025 | − | 3.55114i | 0.0833546 | − | 0.144374i | ||||
\(606\) | 20.6066 | − | 35.6917i | 0.837086 | − | 1.44988i | ||||
\(607\) | 14.8284 | + | 25.6836i | 0.601867 | + | 1.04246i | 0.992538 | + | 0.121934i | \(0.0389097\pi\) |
−0.390671 | + | 0.920530i | \(0.627757\pi\) | |||||||
\(608\) | 4.48528 | 0.181902 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.31371 | −0.215146 | ||||||||
\(611\) | −7.65685 | − | 13.2621i | −0.309763 | − | 0.536526i | ||||
\(612\) | −11.9497 | + | 20.6976i | −0.483040 | + | 0.836650i | ||||
\(613\) | −13.6569 | + | 23.6544i | −0.551595 | + | 0.955391i | 0.446565 | + | 0.894751i | \(0.352647\pi\) |
−0.998160 | + | 0.0606394i | \(0.980686\pi\) | |||||||
\(614\) | 2.24264 | + | 3.88437i | 0.0905056 | + | 0.156760i | ||||
\(615\) | −1.31371 | −0.0529738 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.51472 | −0.302531 | −0.151266 | − | 0.988493i | \(-0.548335\pi\) | ||||
−0.151266 | + | 0.988493i | \(0.548335\pi\) | |||||||
\(618\) | −15.0711 | − | 26.1039i | −0.606247 | − | 1.05005i | ||||
\(619\) | 2.48528 | − | 4.30463i | 0.0998919 | − | 0.173018i | −0.811748 | − | 0.584008i | \(-0.801484\pi\) |
0.911640 | + | 0.410990i | \(0.134817\pi\) | |||||||
\(620\) | 7.65685 | − | 13.2621i | 0.307507 | − | 0.532617i | ||||
\(621\) | −1.82843 | − | 3.16693i | −0.0733723 | − | 0.127084i | ||||
\(622\) | 53.4558 | 2.14338 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 16.2426 | 0.650226 | ||||||||
\(625\) | −9.98528 | − | 17.2950i | −0.399411 | − | 0.691801i | ||||
\(626\) | −21.6066 | + | 37.4237i | −0.863573 | + | 1.49575i | ||||
\(627\) | 2.82843 | − | 4.89898i | 0.112956 | − | 0.195646i | ||||
\(628\) | −38.7487 | − | 67.1148i | −1.54624 | − | 2.67817i | ||||
\(629\) | −24.9706 | −0.995642 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.686292 | 0.0273208 | 0.0136604 | − | 0.999907i | \(-0.495652\pi\) | ||||
0.0136604 | + | 0.999907i | \(0.495652\pi\) | |||||||
\(632\) | 5.17157 | + | 8.95743i | 0.205714 | + | 0.356307i | ||||
\(633\) | 10.4853 | − | 18.1610i | 0.416753 | − | 0.721837i | ||||
\(634\) | 12.0711 | − | 20.9077i | 0.479403 | − | 0.830351i | ||||
\(635\) | −2.82843 | − | 4.89898i | −0.112243 | − | 0.194410i | ||||
\(636\) | −7.65685 | −0.303614 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.65685 | −0.223957 | ||||||||
\(639\) | 6.65685 | + | 11.5300i | 0.263341 | + | 0.456120i | ||||
\(640\) | −6.02082 | + | 10.4284i | −0.237994 | + | 0.412217i | ||||
\(641\) | 2.58579 | − | 4.47871i | 0.102132 | − | 0.176899i | −0.810431 | − | 0.585835i | \(-0.800767\pi\) |
0.912563 | + | 0.408936i | \(0.134100\pi\) | |||||||
\(642\) | −14.0711 | − | 24.3718i | −0.555341 | − | 0.961878i | ||||
\(643\) | 50.4264 | 1.98862 | 0.994312 | − | 0.106510i | \(-0.0339675\pi\) | ||||
0.994312 | + | 0.106510i | \(0.0339675\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.31371 | −0.130477 | ||||||||
\(646\) | 21.3137 | + | 36.9164i | 0.838577 | + | 1.45246i | ||||
\(647\) | −10.5858 | + | 18.3351i | −0.416170 | + | 0.720828i | −0.995551 | − | 0.0942294i | \(-0.969961\pi\) |
0.579380 | + | 0.815057i | \(0.303295\pi\) | |||||||
\(648\) | 2.20711 | − | 3.82282i | 0.0867033 | − | 0.150175i | ||||
\(649\) | −6.82843 | − | 11.8272i | −0.268039 | − | 0.464258i | ||||
\(650\) | 60.8701 | 2.38752 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 43.3137 | 1.69630 | ||||||||
\(653\) | −9.75736 | − | 16.9002i | −0.381835 | − | 0.661358i | 0.609490 | − | 0.792794i | \(-0.291374\pi\) |
−0.991325 | + | 0.131436i | \(0.958041\pi\) | |||||||
\(654\) | 6.82843 | − | 11.8272i | 0.267013 | − | 0.462479i | ||||
\(655\) | −2.14214 | + | 3.71029i | −0.0837002 | + | 0.144973i | ||||
\(656\) | 3.36396 | + | 5.82655i | 0.131341 | + | 0.227489i | ||||
\(657\) | −5.89949 | −0.230161 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3137 | −0.518628 | −0.259314 | − | 0.965793i | \(-0.583497\pi\) | ||||
−0.259314 | + | 0.965793i | \(0.583497\pi\) | |||||||
\(660\) | 2.24264 | + | 3.88437i | 0.0872947 | + | 0.151199i | ||||
\(661\) | −3.77817 | + | 6.54399i | −0.146954 | + | 0.254532i | −0.930100 | − | 0.367306i | \(-0.880280\pi\) |
0.783146 | + | 0.621838i | \(0.213614\pi\) | |||||||
\(662\) | −4.82843 | + | 8.36308i | −0.187662 | + | 0.325040i | ||||
\(663\) | −16.8995 | − | 29.2708i | −0.656322 | − | 1.13678i | ||||
\(664\) | 67.5980 | 2.62331 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.65685 | 0.374196 | ||||||||
\(667\) | 2.14214 | + | 3.71029i | 0.0829438 | + | 0.143663i | ||||
\(668\) | −37.8995 | + | 65.6439i | −1.46638 | + | 2.53984i | ||||
\(669\) | 4.48528 | − | 7.76874i | 0.173411 | − | 0.300357i | ||||
\(670\) | 4.00000 | + | 6.92820i | 0.154533 | + | 0.267660i | ||||
\(671\) | −7.51472 | −0.290102 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.686292 | 0.0264546 | 0.0132273 | − | 0.999913i | \(-0.495789\pi\) | ||||
0.0132273 | + | 0.999913i | \(0.495789\pi\) | |||||||
\(674\) | −22.1421 | − | 38.3513i | −0.852883 | − | 1.47724i | ||||
\(675\) | 2.32843 | − | 4.03295i | 0.0896212 | − | 0.155228i | ||||
\(676\) | −31.2279 | + | 54.0883i | −1.20107 | + | 2.08032i | ||||
\(677\) | −14.2929 | − | 24.7560i | −0.549321 | − | 0.951451i | −0.998321 | − | 0.0579196i | \(-0.981553\pi\) |
0.449001 | − | 0.893531i | \(-0.351780\pi\) | |||||||
\(678\) | −41.7990 | −1.60528 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.1421 | −0.619023 | ||||||||
\(681\) | 7.89949 | + | 13.6823i | 0.302709 | + | 0.524308i | ||||
\(682\) | 16.4853 | − | 28.5533i | 0.631254 | − | 1.09336i | ||||
\(683\) | 4.17157 | − | 7.22538i | 0.159621 | − | 0.276471i | −0.775111 | − | 0.631825i | \(-0.782306\pi\) |
0.934732 | + | 0.355354i | \(0.115640\pi\) | |||||||
\(684\) | −5.41421 | − | 9.37769i | −0.207018 | − | 0.358565i | ||||
\(685\) | −8.28427 | −0.316526 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.24264 | 0.314476 | ||||||||
\(688\) | 8.48528 | + | 14.6969i | 0.323498 | + | 0.560316i | ||||
\(689\) | 5.41421 | − | 9.37769i | 0.206265 | − | 0.357262i | ||||
\(690\) | 2.58579 | − | 4.47871i | 0.0984392 | − | 0.170502i | ||||
\(691\) | 11.6569 | + | 20.1903i | 0.443448 | + | 0.768074i | 0.997943 | − | 0.0641132i | \(-0.0204219\pi\) |
−0.554495 | + | 0.832187i | \(0.687089\pi\) | |||||||
\(692\) | 26.5269 | 1.00840 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.7990 | −0.979316 | ||||||||
\(695\) | 1.85786 | + | 3.21792i | 0.0704728 | + | 0.122062i | ||||
\(696\) | −2.58579 | + | 4.47871i | −0.0980140 | + | 0.169765i | ||||
\(697\) | 7.00000 | − | 12.1244i | 0.265144 | − | 0.459243i | ||||
\(698\) | 11.9497 | + | 20.6976i | 0.452305 | + | 0.783415i | ||||
\(699\) | 22.1421 | 0.837492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.8284 | −0.862218 | −0.431109 | − | 0.902300i | \(-0.641878\pi\) | ||||
−0.431109 | + | 0.902300i | \(0.641878\pi\) | |||||||
\(702\) | 6.53553 | + | 11.3199i | 0.246668 | + | 0.427241i | ||||
\(703\) | 5.65685 | − | 9.79796i | 0.213352 | − | 0.369537i | ||||
\(704\) | −9.82843 | + | 17.0233i | −0.370423 | + | 0.641591i | ||||
\(705\) | −0.828427 | − | 1.43488i | −0.0312004 | − | 0.0540406i | ||||
\(706\) | −25.8995 | −0.974740 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −26.1421 | −0.982482 | ||||||||
\(709\) | −10.1421 | − | 17.5667i | −0.380896 | − | 0.659731i | 0.610295 | − | 0.792174i | \(-0.291051\pi\) |
−0.991191 | + | 0.132443i | \(0.957718\pi\) | |||||||
\(710\) | −9.41421 | + | 16.3059i | −0.353309 | + | 0.611949i | ||||
\(711\) | −1.17157 | + | 2.02922i | −0.0439374 | + | 0.0761018i | ||||
\(712\) | −12.7071 | − | 22.0094i | −0.476219 | − | 0.824835i | ||||
\(713\) | −24.9706 | −0.935155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.34315 | −0.237220 | ||||||||
\(716\) | 15.9706 | + | 27.6618i | 0.596848 | + | 1.03377i | ||||
\(717\) | 2.17157 | − | 3.76127i | 0.0810989 | − | 0.140467i | ||||
\(718\) | −14.0711 | + | 24.3718i | −0.525128 | + | 0.909548i | ||||
\(719\) | 12.9706 | + | 22.4657i | 0.483720 | + | 0.837828i | 0.999825 | − | 0.0186972i | \(-0.00595184\pi\) |
−0.516105 | + | 0.856525i | \(0.672619\pi\) | |||||||
\(720\) | 1.75736 | 0.0654929 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.5563 | 0.988325 | ||||||||
\(723\) | 3.87868 | + | 6.71807i | 0.144250 | + | 0.249848i | ||||
\(724\) | 10.3640 | − | 17.9509i | 0.385174 | − | 0.667140i | ||||
\(725\) | −2.72792 | + | 4.72490i | −0.101312 | + | 0.175478i | ||||
\(726\) | −8.44975 | − | 14.6354i | −0.313600 | − | 0.543170i | ||||
\(727\) | −4.48528 | −0.166350 | −0.0831749 | − | 0.996535i | \(-0.526506\pi\) | ||||
−0.0831749 | + | 0.996535i | \(0.526506\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.17157 | − | 7.22538i | −0.154397 | − | 0.267423i | ||||
\(731\) | 17.6569 | − | 30.5826i | 0.653062 | − | 1.13114i | ||||
\(732\) | −7.19239 | + | 12.4576i | −0.265838 | + | 0.460445i | ||||
\(733\) | 4.84924 | + | 8.39913i | 0.179111 | + | 0.310229i | 0.941576 | − | 0.336800i | \(-0.109345\pi\) |
−0.762465 | + | 0.647029i | \(0.776011\pi\) | |||||||
\(734\) | −46.6274 | −1.72105 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.79899 | 0.213754 | ||||||||
\(737\) | 5.65685 | + | 9.79796i | 0.208373 | + | 0.360912i | ||||
\(738\) | −2.70711 | + | 4.68885i | −0.0996500 | + | 0.172599i | ||||
\(739\) | −13.6569 | + | 23.6544i | −0.502376 | + | 0.870140i | 0.497621 | + | 0.867395i | \(0.334207\pi\) |
−0.999996 | + | 0.00274517i | \(0.999126\pi\) | |||||||
\(740\) | 4.48528 | + | 7.76874i | 0.164882 | + | 0.285584i | ||||
\(741\) | 15.3137 | 0.562563 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.0294 | −0.624749 | −0.312375 | − | 0.949959i | \(-0.601124\pi\) | ||||
−0.312375 | + | 0.949959i | \(0.601124\pi\) | |||||||
\(744\) | −15.0711 | − | 26.1039i | −0.552532 | − | 0.957014i | ||||
\(745\) | 1.55635 | − | 2.69568i | 0.0570202 | − | 0.0987619i | ||||
\(746\) | −40.2132 | + | 69.6513i | −1.47231 | + | 2.55012i | ||||
\(747\) | 7.65685 | + | 13.2621i | 0.280150 | + | 0.485233i | ||||
\(748\) | −47.7990 | −1.74770 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.6569 | 0.498678 | ||||||||
\(751\) | −1.17157 | − | 2.02922i | −0.0427513 | − | 0.0740474i | 0.843858 | − | 0.536567i | \(-0.180279\pi\) |
−0.886609 | + | 0.462519i | \(0.846946\pi\) | |||||||
\(752\) | −4.24264 | + | 7.34847i | −0.154713 | + | 0.267971i | ||||
\(753\) | −2.24264 | + | 3.88437i | −0.0817264 | + | 0.141554i | ||||
\(754\) | −7.65685 | − | 13.2621i | −0.278846 | − | 0.482976i | ||||
\(755\) | 7.02944 | 0.255827 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6569 | 1.36866 | 0.684331 | − | 0.729172i | \(-0.260094\pi\) | ||||
0.684331 | + | 0.729172i | \(0.260094\pi\) | |||||||
\(758\) | 37.7990 | + | 65.4698i | 1.37292 | + | 2.37797i | ||||
\(759\) | 3.65685 | − | 6.33386i | 0.132735 | − | 0.229904i | ||||
\(760\) | 3.65685 | − | 6.33386i | 0.132648 | − | 0.229753i | ||||
\(761\) | −23.2635 | − | 40.2935i | −0.843300 | − | 1.46064i | −0.887090 | − | 0.461597i | \(-0.847277\pi\) |
0.0437901 | − | 0.999041i | \(-0.486057\pi\) | |||||||
\(762\) | −23.3137 | −0.844567 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −68.9117 | −2.49314 | ||||||||
\(765\) | −1.82843 | − | 3.16693i | −0.0661069 | − | 0.114501i | ||||
\(766\) | −35.7990 | + | 62.0057i | −1.29347 | + | 2.24036i | ||||
\(767\) | 18.4853 | − | 32.0174i | 0.667465 | − | 1.15608i | ||||
\(768\) | 14.9853 | + | 25.9553i | 0.540735 | + | 0.936580i | ||||
\(769\) | −29.6985 | −1.07095 | −0.535477 | − | 0.844550i | \(-0.679868\pi\) | ||||
−0.535477 | + | 0.844550i | \(0.679868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2132 | −0.691947 | ||||||||
\(772\) | 33.1421 | + | 57.4039i | 1.19281 | + | 2.06601i | ||||
\(773\) | −10.7782 | + | 18.6683i | −0.387664 | + | 0.671454i | −0.992135 | − | 0.125174i | \(-0.960051\pi\) |
0.604471 | + | 0.796627i | \(0.293385\pi\) | |||||||
\(774\) | −6.82843 | + | 11.8272i | −0.245443 | + | 0.425119i | ||||
\(775\) | −15.8995 | − | 27.5387i | −0.571127 | − | 0.989220i | ||||
\(776\) | −23.8995 | −0.857942 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.4853 | −0.877840 | ||||||||
\(779\) | 3.17157 | + | 5.49333i | 0.113633 | + | 0.196819i | ||||
\(780\) | −6.07107 | + | 10.5154i | −0.217379 | + | 0.376512i | ||||
\(781\) | −13.3137 | + | 23.0600i | −0.476402 | + | 0.825152i | ||||
\(782\) | 27.5563 | + | 47.7290i | 0.985413 | + | 1.70679i | ||||
\(783\) | −1.17157 | −0.0418686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8579 | 0.423225 | ||||||||
\(786\) | 8.82843 | + | 15.2913i | 0.314900 | + | 0.545422i | ||||
\(787\) | −23.6569 | + | 40.9749i | −0.843276 | + | 1.46060i | 0.0438344 | + | 0.999039i | \(0.486043\pi\) |
−0.887110 | + | 0.461558i | \(0.847291\pi\) | |||||||
\(788\) | −3.82843 | + | 6.63103i | −0.136382 | + | 0.236221i | ||||
\(789\) | 8.65685 | + | 14.9941i | 0.308192 | + | 0.533805i | ||||
\(790\) | −3.31371 | −0.117896 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.82843 | 0.313704 | ||||||||
\(793\) | −10.1716 | − | 17.6177i | −0.361203 | − | 0.625622i | ||||
\(794\) | 41.5061 | − | 71.8907i | 1.47300 | − | 2.55130i | ||||
\(795\) | 0.585786 | − | 1.01461i | 0.0207757 | − | 0.0359846i | ||||
\(796\) | −19.7990 | − | 34.2929i | −0.701757 | − | 1.21548i | ||||
\(797\) | 28.3848 | 1.00544 | 0.502720 | − | 0.864449i | \(-0.332333\pi\) | ||||
0.502720 | + | 0.864449i | \(0.332333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.6569 | 0.624655 | ||||||||
\(800\) | 3.69239 | + | 6.39540i | 0.130546 | + | 0.226112i | ||||
\(801\) | 2.87868 | − | 4.98602i | 0.101713 | − | 0.176172i | ||||
\(802\) | 26.7279 | − | 46.2941i | 0.943796 | − | 1.63470i | ||||
\(803\) | −5.89949 | − | 10.2182i | −0.208189 | − | 0.360593i | ||||
\(804\) | 21.6569 | 0.763778 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 89.2548 | 3.14387 | ||||||||
\(807\) | −5.36396 | − | 9.29065i | −0.188820 | − | 0.327046i | ||||
\(808\) | 37.6777 | − | 65.2596i | 1.32550 | − | 2.29583i | ||||
\(809\) | 23.9706 | − | 41.5182i | 0.842760 | − | 1.45970i | −0.0447922 | − | 0.998996i | \(-0.514263\pi\) |
0.887552 | − | 0.460707i | \(-0.152404\pi\) | |||||||
\(810\) | 0.707107 | + | 1.22474i | 0.0248452 | + | 0.0430331i | ||||
\(811\) | −6.34315 | −0.222738 | −0.111369 | − | 0.993779i | \(-0.535524\pi\) | ||||
−0.111369 | + | 0.993779i | \(0.535524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.1421 | 0.636272 | ||||||||
\(814\) | 9.65685 | + | 16.7262i | 0.338473 | + | 0.586252i | ||||
\(815\) | −3.31371 | + | 5.73951i | −0.116074 | + | 0.201046i | ||||
\(816\) | −9.36396 | + | 16.2189i | −0.327804 | + | 0.567774i | ||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | 44.8701 | 1.56884 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.02944 | −0.175636 | ||||||||
\(821\) | 16.6569 | + | 28.8505i | 0.581328 | + | 1.00689i | 0.995322 | + | 0.0966104i | \(0.0308001\pi\) |
−0.413994 | + | 0.910280i | \(0.635867\pi\) | |||||||
\(822\) | −17.0711 | + | 29.5680i | −0.595422 | + | 1.03130i | ||||
\(823\) | 12.4853 | − | 21.6251i | 0.435210 | − | 0.753805i | −0.562103 | − | 0.827067i | \(-0.690008\pi\) |
0.997313 | + | 0.0732621i | \(0.0233410\pi\) | |||||||
\(824\) | −27.5563 | − | 47.7290i | −0.959971 | − | 1.66272i | ||||
\(825\) | 9.31371 | 0.324262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.3431 | 1.26378 | 0.631888 | − | 0.775060i | \(-0.282280\pi\) | ||||
0.631888 | + | 0.775060i | \(0.282280\pi\) | |||||||
\(828\) | −7.00000 | − | 12.1244i | −0.243267 | − | 0.421350i | ||||
\(829\) | −12.3640 | + | 21.4150i | −0.429418 | + | 0.743774i | −0.996822 | − | 0.0796659i | \(-0.974615\pi\) |
0.567404 | + | 0.823440i | \(0.307948\pi\) | |||||||
\(830\) | −10.8284 | + | 18.7554i | −0.375860 | + | 0.651009i | ||||
\(831\) | −6.65685 | − | 11.5300i | −0.230924 | − | 0.399972i | ||||
\(832\) | −53.2132 | −1.84484 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.3137 | 0.530270 | ||||||||
\(835\) | −5.79899 | − | 10.0441i | −0.200682 | − | 0.347592i | ||||
\(836\) | 10.8284 | − | 18.7554i | 0.374509 | − | 0.648669i | ||||
\(837\) | 3.41421 | − | 5.91359i | 0.118012 | − | 0.204404i | ||||
\(838\) | 46.8701 | + | 81.1813i | 1.61910 | + | 2.80436i | ||||
\(839\) | 45.1716 | 1.55950 | 0.779748 | − | 0.626094i | \(-0.215347\pi\) | ||||
0.779748 | + | 0.626094i | \(0.215347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | −34.5563 | − | 59.8534i | −1.19089 | − | 2.06268i | ||||
\(843\) | 8.24264 | − | 14.2767i | 0.283892 | − | 0.491715i | ||||
\(844\) | 40.1421 | − | 69.5282i | 1.38175 | − | 2.39326i | ||||
\(845\) | −4.77817 | − | 8.27604i | −0.164374 | − | 0.284704i | ||||
\(846\) | −6.82843 | −0.234766 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −4.24264 | − | 7.34847i | −0.145607 | − | 0.252199i | ||||
\(850\) | −35.0919 | + | 60.7809i | −1.20364 | + | 2.08477i | ||||
\(851\) | 7.31371 | − | 12.6677i | 0.250711 | − | 0.434244i | ||||
\(852\) | 25.4853 | + | 44.1418i | 0.873111 | + | 1.51227i | ||||
\(853\) | 49.4975 | 1.69476 | 0.847381 | − | 0.530986i | \(-0.178178\pi\) | ||||
0.847381 | + | 0.530986i | \(0.178178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.65685 | 0.0566632 | ||||||||
\(856\) | −25.7279 | − | 44.5621i | −0.879362 | − | 1.52310i | ||||
\(857\) | −6.29289 | + | 10.8996i | −0.214961 | + | 0.372324i | −0.953261 | − | 0.302149i | \(-0.902296\pi\) |
0.738299 | + | 0.674473i | \(0.235629\pi\) | |||||||
\(858\) | −13.0711 | + | 22.6398i | −0.446239 | + | 0.772908i | ||||
\(859\) | −3.27208 | − | 5.66741i | −0.111642 | − | 0.193369i | 0.804791 | − | 0.593559i | \(-0.202278\pi\) |
−0.916432 | + | 0.400190i | \(0.868944\pi\) | |||||||
\(860\) | −12.6863 | −0.432599 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.8284 | −0.573179 | ||||||||
\(863\) | 2.65685 | + | 4.60181i | 0.0904404 | + | 0.156647i | 0.907697 | − | 0.419627i | \(-0.137839\pi\) |
−0.817256 | + | 0.576275i | \(0.804506\pi\) | |||||||
\(864\) | −0.792893 | + | 1.37333i | −0.0269748 | + | 0.0467217i | ||||
\(865\) | −2.02944 | + | 3.51509i | −0.0690029 | + | 0.119517i | ||||
\(866\) | −14.1924 | − | 24.5819i | −0.482277 | − | 0.835328i | ||||
\(867\) | 21.9706 | 0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.68629 | −0.158972 | ||||||||
\(870\) | −0.828427 | − | 1.43488i | −0.0280863 | − | 0.0486469i | ||||
\(871\) | −15.3137 | + | 26.5241i | −0.518885 | + | 0.898736i | ||||
\(872\) | 12.4853 | − | 21.6251i | 0.422805 | − | 0.732320i | ||||
\(873\) | −2.70711 | − | 4.68885i | −0.0916217 | − | 0.158693i | ||||
\(874\) | −24.9706 | −0.844642 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.5858 | −0.763103 | ||||||||
\(877\) | −5.65685 | − | 9.79796i | −0.191018 | − | 0.330854i | 0.754570 | − | 0.656220i | \(-0.227846\pi\) |
−0.945588 | + | 0.325366i | \(0.894512\pi\) | |||||||
\(878\) | 42.6274 | − | 73.8329i | 1.43861 | − | 2.49174i | ||||
\(879\) | −9.70711 | + | 16.8132i | −0.327413 | + | 0.567095i | ||||
\(880\) | 1.75736 | + | 3.04384i | 0.0592406 | + | 0.102608i | ||||
\(881\) | 30.2426 | 1.01890 | 0.509450 | − | 0.860500i | \(-0.329849\pi\) | ||||
0.509450 | + | 0.860500i | \(0.329849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.3137 | −0.919179 | −0.459590 | − | 0.888131i | \(-0.652004\pi\) | ||||
−0.459590 | + | 0.888131i | \(0.652004\pi\) | |||||||
\(884\) | −64.6985 | − | 112.061i | −2.17605 | − | 3.76902i | ||||
\(885\) | 2.00000 | − | 3.46410i | 0.0672293 | − | 0.116445i | ||||
\(886\) | 1.24264 | − | 2.15232i | 0.0417473 | − | 0.0723085i | ||||
\(887\) | −1.41421 | − | 2.44949i | −0.0474846 | − | 0.0822458i | 0.841306 | − | 0.540559i | \(-0.181787\pi\) |
−0.888791 | + | 0.458313i | \(0.848454\pi\) | |||||||
\(888\) | 17.6569 | 0.592525 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.14214 | 0.272925 | ||||||||
\(891\) | 1.00000 | + | 1.73205i | 0.0335013 | + | 0.0580259i | ||||
\(892\) | 17.1716 | − | 29.7420i | 0.574947 | − | 0.995837i | ||||
\(893\) | −4.00000 | + | 6.92820i | −0.133855 | + | 0.231843i | ||||
\(894\) | −6.41421 | − | 11.1097i | −0.214523 | − | 0.371565i | ||||
\(895\) | −4.88730 | −0.163364 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.7990 | 0.661069 | ||||||||
\(898\) | 20.8995 | + | 36.1990i | 0.697425 | + | 1.20798i | ||||
\(899\) | −4.00000 | + | 6.92820i | −0.133407 | + | 0.231069i | ||||
\(900\) | 8.91421 | − | 15.4399i | 0.297140 | − | 0.514662i | ||||
\(901\) | 6.24264 | + | 10.8126i | 0.207973 | + | 0.360219i | ||||
\(902\) | −10.8284 | −0.360547 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −76.4264 | −2.54190 | ||||||||
\(905\) | 1.58579 | + | 2.74666i | 0.0527133 | + | 0.0913022i | ||||
\(906\) | 14.4853 | − | 25.0892i | 0.481241 | − | 0.833534i | ||||
\(907\) | 8.00000 | − | 13.8564i | 0.265636 | − | 0.460094i | −0.702094 | − | 0.712084i | \(-0.747752\pi\) |
0.967730 | + | 0.251990i | \(0.0810849\pi\) | |||||||
\(908\) | 30.2426 | + | 52.3818i | 1.00364 | + | 1.73835i | ||||
\(909\) | 17.0711 | 0.566212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.9706 | −1.15863 | −0.579313 | − | 0.815105i | \(-0.696679\pi\) | ||||
−0.579313 | + | 0.815105i | \(0.696679\pi\) | |||||||
\(912\) | −4.24264 | − | 7.34847i | −0.140488 | − | 0.243332i | ||||
\(913\) | −15.3137 | + | 26.5241i | −0.506810 | + | 0.877820i | ||||
\(914\) | −21.7279 | + | 37.6339i | −0.718696 | + | 1.24482i | ||||
\(915\) | −1.10051 | − | 1.90613i | −0.0363816 | − | 0.0630147i | ||||
\(916\) | 31.5563 | 1.04265 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −15.0711 | −0.497419 | ||||||||
\(919\) | −24.1421 | − | 41.8154i | −0.796376 | − | 1.37936i | −0.921962 | − | 0.387280i | \(-0.873415\pi\) |
0.125586 | − | 0.992083i | \(-0.459919\pi\) | |||||||
\(920\) | 4.72792 | − | 8.18900i | 0.155875 | − | 0.269983i | ||||
\(921\) | −0.928932 | + | 1.60896i | −0.0306094 | + | 0.0530170i | ||||
\(922\) | −23.4350 | − | 40.5907i | −0.771792 | − | 1.33678i | ||||
\(923\) | −72.0833 | −2.37265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6274 | 0.612466 | ||||||||
\(926\) | 22.4853 | + | 38.9456i | 0.738912 | + | 1.27983i | ||||
\(927\) | 6.24264 | − | 10.8126i | 0.205035 | − | 0.355131i | ||||
\(928\) | 0.928932 | − | 1.60896i | 0.0304937 | − | 0.0528166i | ||||
\(929\) | −1.60660 | − | 2.78272i | −0.0527109 | − | 0.0912979i | 0.838466 | − | 0.544954i | \(-0.183453\pi\) |
−0.891177 | + | 0.453656i | \(0.850120\pi\) | |||||||
\(930\) | 9.65685 | 0.316661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 84.7696 | 2.77672 | ||||||||
\(933\) | 11.0711 | + | 19.1757i | 0.362450 | + | 0.627783i | ||||
\(934\) | 48.0416 | − | 83.2105i | 1.57197 | − | 2.72273i | ||||
\(935\) | 3.65685 | − | 6.33386i | 0.119592 | − | 0.207139i | ||||
\(936\) | 11.9497 | + | 20.6976i | 0.390590 | + | 0.676521i | ||||
\(937\) | 33.4142 | 1.09159 | 0.545797 | − | 0.837917i | \(-0.316227\pi\) | ||||
0.545797 | + | 0.837917i | \(0.316227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.8995 | −0.584128 | ||||||||
\(940\) | −3.17157 | − | 5.49333i | −0.103445 | − | 0.179173i | ||||
\(941\) | 3.60660 | − | 6.24682i | 0.117572 | − | 0.203640i | −0.801233 | − | 0.598352i | \(-0.795822\pi\) |
0.918805 | + | 0.394712i | \(0.129156\pi\) | |||||||
\(942\) | 24.4350 | − | 42.3227i | 0.796136 | − | 1.37895i | ||||
\(943\) | 4.10051 | + | 7.10228i | 0.133531 | + | 0.231282i | ||||
\(944\) | −20.4853 | −0.666739 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.3137 | −0.888045 | ||||||||
\(947\) | −26.6569 | − | 46.1710i | −0.866231 | − | 1.50036i | −0.865819 | − | 0.500357i | \(-0.833202\pi\) |
−0.000412082 | − | 1.00000i | \(-0.500131\pi\) | |||||||
\(948\) | −4.48528 | + | 7.76874i | −0.145675 | + | 0.252317i | ||||
\(949\) | 15.9706 | − | 27.6618i | 0.518426 | − | 0.897941i | ||||
\(950\) | −15.8995 | − | 27.5387i | −0.515848 | − | 0.893474i | ||||
\(951\) | 10.0000 | 0.324272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | −2.41421 | − | 4.18154i | −0.0781631 | − | 0.135382i | ||||
\(955\) | 5.27208 | − | 9.13151i | 0.170600 | − | 0.295489i | ||||
\(956\) | 8.31371 | − | 14.3998i | 0.268885 | − | 0.465722i | ||||
\(957\) | −1.17157 | − | 2.02922i | −0.0378716 | − | 0.0655955i | ||||
\(958\) | −72.7696 | −2.35108 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.75736 | −0.185818 | ||||||||
\(961\) | −7.81371 | − | 13.5337i | −0.252055 | − | 0.436572i | ||||
\(962\) | −26.1421 | + | 45.2795i | −0.842856 | + | 1.45987i | ||||
\(963\) | 5.82843 | − | 10.0951i | 0.187818 | − | 0.325311i | ||||
\(964\) | 14.8492 | + | 25.7196i | 0.478262 | + | 0.828374i | ||||
\(965\) | −10.1421 | −0.326487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.3431 | 0.718507 | 0.359254 | − | 0.933240i | \(-0.383031\pi\) | ||||
0.359254 | + | 0.933240i | \(0.383031\pi\) | |||||||
\(968\) | −15.4497 | − | 26.7597i | −0.496574 | − | 0.860091i | ||||
\(969\) | −8.82843 | + | 15.2913i | −0.283610 | + | 0.491227i | ||||
\(970\) | 3.82843 | − | 6.63103i | 0.122923 | − | 0.212910i | ||||
\(971\) | 2.68629 | + | 4.65279i | 0.0862072 | + | 0.149315i | 0.905905 | − | 0.423481i | \(-0.139192\pi\) |
−0.819698 | + | 0.572796i | \(0.805859\pi\) | |||||||
\(972\) | 3.82843 | 0.122797 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 44.9706 | 1.44095 | ||||||||
\(975\) | 12.6066 | + | 21.8353i | 0.403734 | + | 0.699288i | ||||
\(976\) | −5.63604 | + | 9.76191i | −0.180405 | + | 0.312471i | ||||
\(977\) | 13.4142 | − | 23.2341i | 0.429159 | − | 0.743325i | −0.567640 | − | 0.823277i | \(-0.692143\pi\) |
0.996799 | + | 0.0799522i | \(0.0254768\pi\) | |||||||
\(978\) | 13.6569 | + | 23.6544i | 0.436698 | + | 0.756383i | ||||
\(979\) | 11.5147 | 0.368012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.65685 | 0.180609 | ||||||||
\(982\) | 47.0416 | + | 81.4785i | 1.50116 | + | 2.60008i | ||||
\(983\) | −18.6274 | + | 32.2636i | −0.594122 | + | 1.02905i | 0.399548 | + | 0.916712i | \(0.369167\pi\) |
−0.993670 | + | 0.112338i | \(0.964166\pi\) | |||||||
\(984\) | −4.94975 | + | 8.57321i | −0.157792 | + | 0.273304i | ||||
\(985\) | −0.585786 | − | 1.01461i | −0.0186647 | − | 0.0323282i | ||||
\(986\) | 17.6569 | 0.562309 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 58.6274 | 1.86519 | ||||||||
\(989\) | 10.3431 | + | 17.9149i | 0.328893 | + | 0.569659i | ||||
\(990\) | −1.41421 | + | 2.44949i | −0.0449467 | + | 0.0778499i | ||||
\(991\) | −10.4853 | + | 18.1610i | −0.333076 | + | 0.576904i | −0.983113 | − | 0.182998i | \(-0.941420\pi\) |
0.650037 | + | 0.759902i | \(0.274753\pi\) | |||||||
\(992\) | 5.41421 | + | 9.37769i | 0.171901 | + | 0.297742i | ||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.05887 | 0.192079 | ||||||||
\(996\) | 29.3137 | + | 50.7728i | 0.928840 | + | 1.60880i | ||||
\(997\) | 5.19239 | − | 8.99348i | 0.164445 | − | 0.284826i | −0.772013 | − | 0.635606i | \(-0.780750\pi\) |
0.936458 | + | 0.350780i | \(0.114083\pi\) | |||||||
\(998\) | −23.3137 | + | 40.3805i | −0.737983 | + | 1.27822i | ||||
\(999\) | 2.00000 | + | 3.46410i | 0.0632772 | + | 0.109599i |
(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 | 147.2.e.d.67.2 | 4 | ||
3.2 | odd | 2 | 441.2.e.g.361.1 | 4 | |||
4.3 | odd | 2 | 2352.2.q.bd.1537.2 | 4 | |||
7.2 | even | 3 | inner | 147.2.e.d.79.2 | 4 | ||
7.3 | odd | 6 | 147.2.a.d.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 147.2.a.e.1.1 | yes | 2 | ||
7.5 | odd | 6 | 147.2.e.e.79.2 | 4 | |||
7.6 | odd | 2 | 147.2.e.e.67.2 | 4 | |||
21.2 | odd | 6 | 441.2.e.g.226.1 | 4 | |||
21.5 | even | 6 | 441.2.e.f.226.1 | 4 | |||
21.11 | odd | 6 | 441.2.a.i.1.2 | 2 | |||
21.17 | even | 6 | 441.2.a.j.1.2 | 2 | |||
21.20 | even | 2 | 441.2.e.f.361.1 | 4 | |||
28.3 | even | 6 | 2352.2.a.be.1.2 | 2 | |||
28.11 | odd | 6 | 2352.2.a.bc.1.1 | 2 | |||
28.19 | even | 6 | 2352.2.q.bb.961.1 | 4 | |||
28.23 | odd | 6 | 2352.2.q.bd.961.2 | 4 | |||
28.27 | even | 2 | 2352.2.q.bb.1537.1 | 4 | |||
35.4 | even | 6 | 3675.2.a.bd.1.2 | 2 | |||
35.24 | odd | 6 | 3675.2.a.bf.1.2 | 2 | |||
56.3 | even | 6 | 9408.2.a.dq.1.1 | 2 | |||
56.11 | odd | 6 | 9408.2.a.dt.1.2 | 2 | |||
56.45 | odd | 6 | 9408.2.a.ef.1.1 | 2 | |||
56.53 | even | 6 | 9408.2.a.di.1.2 | 2 | |||
84.11 | even | 6 | 7056.2.a.cf.1.2 | 2 | |||
84.59 | odd | 6 | 7056.2.a.cv.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.2.a.d.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
147.2.a.e.1.1 | yes | 2 | 7.4 | even | 3 | ||
147.2.e.d.67.2 | 4 | 1.1 | even | 1 | trivial | ||
147.2.e.d.79.2 | 4 | 7.2 | even | 3 | inner | ||
147.2.e.e.67.2 | 4 | 7.6 | odd | 2 | |||
147.2.e.e.79.2 | 4 | 7.5 | odd | 6 | |||
441.2.a.i.1.2 | 2 | 21.11 | odd | 6 | |||
441.2.a.j.1.2 | 2 | 21.17 | even | 6 | |||
441.2.e.f.226.1 | 4 | 21.5 | even | 6 | |||
441.2.e.f.361.1 | 4 | 21.20 | even | 2 | |||
441.2.e.g.226.1 | 4 | 21.2 | odd | 6 | |||
441.2.e.g.361.1 | 4 | 3.2 | odd | 2 | |||
2352.2.a.bc.1.1 | 2 | 28.11 | odd | 6 | |||
2352.2.a.be.1.2 | 2 | 28.3 | even | 6 | |||
2352.2.q.bb.961.1 | 4 | 28.19 | even | 6 | |||
2352.2.q.bb.1537.1 | 4 | 28.27 | even | 2 | |||
2352.2.q.bd.961.2 | 4 | 28.23 | odd | 6 | |||
2352.2.q.bd.1537.2 | 4 | 4.3 | odd | 2 | |||
3675.2.a.bd.1.2 | 2 | 35.4 | even | 6 | |||
3675.2.a.bf.1.2 | 2 | 35.24 | odd | 6 | |||
7056.2.a.cf.1.2 | 2 | 84.11 | even | 6 | |||
7056.2.a.cv.1.1 | 2 | 84.59 | odd | 6 | |||
9408.2.a.di.1.2 | 2 | 56.53 | even | 6 | |||
9408.2.a.dq.1.1 | 2 | 56.3 | even | 6 | |||
9408.2.a.dt.1.2 | 2 | 56.11 | odd | 6 | |||
9408.2.a.ef.1.1 | 2 | 56.45 | odd | 6 |