Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.991381711347.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(1.19343 + 2.06709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.961 |
Dual form | 1008.2.t.i.193.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.266999 | + | 1.71135i | −0.154152 | + | 0.988047i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.92087 | −1.30625 | −0.653125 | − | 0.757250i | \(-0.726543\pi\) | ||||
−0.653125 | + | 0.757250i | \(0.726543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.35742 | + | 1.20106i | −0.891022 | + | 0.453959i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.85742 | − | 0.913855i | −0.952475 | − | 0.304618i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.35371 | 0.408160 | 0.204080 | − | 0.978954i | \(-0.434580\pi\) | ||||
0.204080 | + | 0.978954i | \(0.434580\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.733001 | − | 1.26960i | −0.203298 | − | 0.352123i | 0.746291 | − | 0.665620i | \(-0.231833\pi\) |
−0.949589 | + | 0.313497i | \(0.898499\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.779867 | − | 4.99862i | 0.201361 | − | 1.29064i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.65514 | + | 2.86678i | 0.401430 | + | 0.695297i | 0.993899 | − | 0.110297i | \(-0.0351801\pi\) |
−0.592469 | + | 0.805593i | \(0.701847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.10329 | − | 1.91096i | 0.253113 | − | 0.438404i | −0.711268 | − | 0.702921i | \(-0.751879\pi\) |
0.964381 | + | 0.264516i | \(0.0852123\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.42601 | − | 4.35505i | −0.311181 | − | 0.950351i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.62830 | −0.548038 | −0.274019 | − | 0.961724i | \(-0.588353\pi\) | ||||
−0.274019 | + | 0.961724i | \(0.588353\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.53146 | 0.706292 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.32685 | − | 4.64605i | 0.447803 | − | 0.894132i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.521720 | − | 0.903646i | 0.0968810 | − | 0.167803i | −0.813511 | − | 0.581549i | \(-0.802447\pi\) |
0.910392 | + | 0.413747i | \(0.135780\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.63729 | − | 2.83587i | 0.294066 | − | 0.509337i | −0.680701 | − | 0.732561i | \(-0.738325\pi\) |
0.974767 | + | 0.223224i | \(0.0716581\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.361440 | + | 2.31668i | −0.0629186 | + | 0.403282i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.88572 | − | 3.50815i | 1.16390 | − | 0.592985i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.43773 | − | 9.41842i | 0.893957 | − | 1.54838i | 0.0588664 | − | 0.998266i | \(-0.481251\pi\) |
0.835090 | − | 0.550113i | \(-0.185415\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.36843 | − | 0.915440i | 0.379252 | − | 0.146588i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.904289 | − | 1.56627i | −0.141226 | − | 0.244611i | 0.786732 | − | 0.617294i | \(-0.211771\pi\) |
−0.927959 | + | 0.372683i | \(0.878438\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.17129 | − | 3.76078i | 0.331118 | − | 0.573514i | −0.651613 | − | 0.758551i | \(-0.725907\pi\) |
0.982731 | + | 0.185038i | \(0.0592408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.34615 | + | 2.66925i | 1.24417 | + | 0.397908i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.98957 | + | 3.44604i | 0.290209 | + | 0.502656i | 0.973859 | − | 0.227154i | \(-0.0729419\pi\) |
−0.683650 | + | 0.729810i | \(0.739609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.11489 | − | 5.66283i | 0.587842 | − | 0.808976i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.34798 | + | 2.06709i | −0.748867 | + | 0.289450i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.22743 | − | 5.59008i | −0.443322 | − | 0.767856i | 0.554612 | − | 0.832109i | \(-0.312867\pi\) |
−0.997934 | + | 0.0642533i | \(0.979533\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.95402 | −0.533160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.97574 | + | 2.39834i | 0.394146 | + | 0.317668i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.10700 | + | 10.5776i | −0.795064 | + | 1.37709i | 0.127735 | + | 0.991808i | \(0.459229\pi\) |
−0.922799 | + | 0.385283i | \(0.874104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.279867 | − | 0.484744i | −0.0358333 | − | 0.0620651i | 0.847553 | − | 0.530711i | \(-0.178075\pi\) |
−0.883386 | + | 0.468646i | \(0.844742\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.83376 | − | 1.27761i | 0.986960 | − | 0.160963i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.14100 | + | 3.70832i | 0.265558 | + | 0.459960i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.40588 | − | 11.0953i | 0.782603 | − | 1.35551i | −0.147817 | − | 0.989015i | \(-0.547225\pi\) |
0.930420 | − | 0.366494i | \(-0.119442\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.701751 | − | 4.49793i | 0.0844809 | − | 0.541487i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9177 | −1.53305 | −0.766525 | − | 0.642214i | \(-0.778016\pi\) | ||||
−0.766525 | + | 0.642214i | \(0.778016\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.22772 | + | 9.05467i | 0.611858 | + | 1.05977i | 0.990927 | + | 0.134401i | \(0.0429109\pi\) |
−0.379069 | + | 0.925368i | \(0.623756\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.942894 | + | 6.04355i | −0.108876 | + | 0.697849i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.19128 | + | 1.62590i | −0.363680 | + | 0.185288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.383838 | + | 0.664827i | 0.0431852 | + | 0.0747989i | 0.886810 | − | 0.462134i | \(-0.152916\pi\) |
−0.843625 | + | 0.536933i | \(0.819583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.32974 | + | 5.22254i | 0.814415 | + | 0.580282i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.983707 | − | 1.70383i | 0.107976 | − | 0.187020i | −0.806974 | − | 0.590587i | \(-0.798896\pi\) |
0.914950 | + | 0.403567i | \(0.132230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.83443 | − | 8.37348i | −0.524368 | − | 0.908232i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.40715 | + | 1.13412i | 0.150863 | + | 0.121590i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.20356 | − | 5.54872i | 0.339576 | − | 0.588163i | −0.644777 | − | 0.764371i | \(-0.723050\pi\) |
0.984353 | + | 0.176208i | \(0.0563830\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.25286 | + | 2.11259i | 0.340992 | + | 0.221460i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.41601 | + | 3.55915i | 0.457919 | + | 0.369066i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.22257 | + | 5.58166i | −0.330629 | + | 0.572666i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.14143 | + | 7.17316i | −0.420498 | + | 0.728324i | −0.995988 | − | 0.0894847i | \(-0.971478\pi\) |
0.575490 | + | 0.817809i | \(0.304811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.86814 | − | 1.23710i | −0.388762 | − | 0.124333i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2266 | −1.61461 | −0.807305 | − | 0.590134i | \(-0.799075\pi\) | ||||
−0.807305 | + | 0.590134i | \(0.799075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.22683 | 0.219416 | 0.109708 | − | 0.993964i | \(-0.465008\pi\) | ||||
0.109708 | + | 0.993964i | \(0.465008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.16518 | + | 12.7205i | 0.406480 | + | 1.24140i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.75403 | − | 15.1624i | 0.846284 | − | 1.46581i | −0.0382175 | − | 0.999269i | \(-0.512168\pi\) |
0.884501 | − | 0.466537i | \(-0.154499\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.79917 | − | 13.5086i | −0.747025 | − | 1.29388i | −0.949243 | − | 0.314544i | \(-0.898148\pi\) |
0.202218 | − | 0.979341i | \(-0.435185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.6663 | + | 11.8205i | 1.39207 | + | 1.12196i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.844555 | − | 1.46281i | −0.0794491 | − | 0.137610i | 0.823563 | − | 0.567224i | \(-0.191983\pi\) |
−0.903012 | + | 0.429615i | \(0.858649\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.67690 | 0.715875 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.934270 | + | 4.29763i | 0.0863733 | + | 0.397316i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.34505 | − | 4.77029i | −0.673319 | − | 0.437292i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.16746 | −0.833405 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92188 | − | 1.12936i | 0.263457 | − | 0.101831i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.28942 | 0.383657 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.96918 | 0.352208 | 0.176104 | − | 0.984372i | \(-0.443650\pi\) | ||||
0.176104 | + | 0.984372i | \(0.443650\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.85627 | + | 4.71995i | 0.515616 | + | 0.415569i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.32863 | −0.465565 | −0.232782 | − | 0.972529i | \(-0.574783\pi\) | ||||
−0.232782 | + | 0.972529i | \(0.574783\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.305745 | + | 5.83007i | −0.0265115 | + | 0.505531i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.79642 | + | 13.5705i | −0.584943 | + | 1.16796i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.49543 | −0.640378 | −0.320189 | − | 0.947354i | \(-0.603746\pi\) | ||||
−0.320189 | + | 0.947354i | \(0.603746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.03285 | − | 12.1812i | −0.596518 | − | 1.03320i | −0.993331 | − | 0.115300i | \(-0.963217\pi\) |
0.396812 | − | 0.917900i | \(-0.370116\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.42858 | + | 2.48476i | −0.541384 | + | 0.209255i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.992275 | − | 1.71867i | −0.0829782 | − | 0.143722i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.52388 | + | 2.63943i | −0.126551 | + | 0.219193i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.59241 | + | 8.55398i | 0.708690 | + | 0.705520i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.17971 | 0.178569 | 0.0892846 | − | 0.996006i | \(-0.471542\pi\) | ||||
0.0892846 | + | 0.996006i | \(0.471542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0277 | −1.14156 | −0.570781 | − | 0.821102i | \(-0.693359\pi\) | ||||
−0.570781 | + | 0.821102i | \(0.693359\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.10961 | − | 9.70416i | −0.170552 | − | 0.784535i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.78231 | + | 8.28320i | −0.384124 | + | 0.665322i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.48312 | + | 2.56883i | −0.118365 | + | 0.205015i | −0.919120 | − | 0.393978i | \(-0.871099\pi\) |
0.800755 | + | 0.598993i | \(0.204432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4283 | − | 4.03072i | 0.827017 | − | 0.319657i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.19601 | − | 3.15675i | 0.488314 | − | 0.248787i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.194278 | − | 0.336499i | 0.0152170 | − | 0.0263566i | −0.858317 | − | 0.513120i | \(-0.828489\pi\) |
0.873534 | + | 0.486764i | \(0.161823\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.05572 | − | 6.76670i | 0.0821875 | − | 0.526787i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.64889 | − | 6.32006i | −0.282360 | − | 0.489061i | 0.689606 | − | 0.724185i | \(-0.257784\pi\) |
−0.971965 | + | 0.235124i | \(0.924450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.42542 | − | 9.39710i | 0.417340 | − | 0.722854i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.89892 | + | 4.45217i | −0.374630 | + | 0.340466i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.02754 | + | 3.51181i | 0.154151 | + | 0.266998i | 0.932750 | − | 0.360525i | \(-0.117402\pi\) |
−0.778598 | + | 0.627522i | \(0.784069\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.32514 | + | 4.24151i | −0.629322 | + | 0.320628i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.4715 | − | 13.2754i | −1.23807 | − | 0.997842i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.29243 | − | 9.16675i | −0.395575 | − | 0.685155i | 0.597600 | − | 0.801795i | \(-0.296121\pi\) |
−0.993174 | + | 0.116639i | \(0.962788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6312 | −1.45917 | −0.729586 | − | 0.683889i | \(-0.760287\pi\) | ||||
−0.729586 | + | 0.683889i | \(0.760287\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.904289 | − | 0.349524i | 0.0668470 | − | 0.0258375i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.8829 | + | 27.5099i | −1.16773 | + | 2.02257i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.24058 | + | 3.88081i | 0.163848 | + | 0.283793i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.0948259 | + | 13.7474i | 0.00689757 | + | 0.999976i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.14357 | + | 7.17688i | 0.299818 | + | 0.519301i | 0.976094 | − | 0.217348i | \(-0.0697406\pi\) |
−0.676276 | + | 0.736648i | \(0.736407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.39242 | − | 16.2682i | 0.676082 | − | 1.17101i | −0.300070 | − | 0.953917i | \(-0.597010\pi\) |
0.976152 | − | 0.217090i | \(-0.0696566\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.91787 | + | 2.67388i | −0.495399 | + | 0.191480i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.99634 | 0.427222 | 0.213611 | − | 0.976919i | \(-0.431478\pi\) | ||||
0.213611 | + | 0.976919i | \(0.431478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.20434 | − | 12.4783i | −0.510702 | − | 0.884562i | −0.999923 | − | 0.0124022i | \(-0.996052\pi\) |
0.489221 | − | 0.872160i | \(-0.337281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.2776 | + | 13.9251i | 1.21867 | + | 0.982203i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.144579 | + | 2.75690i | −0.0101475 | + | 0.193496i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.64131 | + | 4.57488i | 0.184477 | + | 0.319523i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.51015 | + | 2.40188i | 0.521992 | + | 0.166942i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.49354 | − | 2.58690i | 0.103311 | − | 0.178939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.92418 | + | 11.9930i | 0.476680 | + | 0.825634i | 0.999643 | − | 0.0267212i | \(-0.00850663\pi\) |
−0.522963 | + | 0.852356i | \(0.675173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.44901 | − | 22.1067i | 0.236322 | − | 1.51473i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.34204 | + | 10.9847i | −0.432523 | + | 0.749153i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.453726 | + | 8.65184i | −0.0308010 | + | 0.587325i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.8915 | + | 6.52886i | −1.14142 | + | 0.441179i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.42644 | − | 4.20271i | 0.163220 | − | 0.282705i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.33756 | + | 4.04878i | −0.156535 | + | 0.271126i | −0.933617 | − | 0.358273i | \(-0.883366\pi\) |
0.777082 | + | 0.629399i | \(0.216699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0909 | − | 3.22724i | −0.672725 | − | 0.215149i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.7126 | −1.30837 | −0.654187 | − | 0.756333i | \(-0.726989\pi\) | ||||
−0.654187 | + | 0.756333i | \(0.726989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.0728 | 1.85510 | 0.927552 | − | 0.373694i | \(-0.121909\pi\) | ||||
0.927552 | + | 0.373694i | \(0.121909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.93041 | − | 5.89550i | −0.127012 | − | 0.387896i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.90113 | + | 11.9531i | −0.452108 | + | 0.783074i | −0.998517 | − | 0.0544448i | \(-0.982661\pi\) |
0.546409 | + | 0.837518i | \(0.315994\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.81127 | − | 10.0654i | −0.379085 | − | 0.656595i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.24024 | + | 0.479373i | −0.0805619 | + | 0.0311386i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.53069 | − | 9.57944i | −0.357751 | − | 0.619642i | 0.629834 | − | 0.776730i | \(-0.283123\pi\) |
−0.987585 | + | 0.157087i | \(0.949790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1697 | −1.49249 | −0.746247 | − | 0.665669i | \(-0.768146\pi\) | ||||
−0.746247 | + | 0.665669i | \(0.768146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.8946 | + | 11.1493i | −0.698890 | + | 0.715229i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.0190 | + | 16.5404i | −0.767869 | + | 1.05673i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.23486 | −0.205829 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.65320 | + | 2.13839i | 0.168140 | + | 0.135515i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.78402 | 0.491323 | 0.245662 | − | 0.969356i | \(-0.420995\pi\) | ||||
0.245662 | + | 0.969356i | \(0.420995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55796 | −0.223687 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.6207 | − | 6.03769i | 0.978208 | − | 0.378095i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3760 | 0.647235 | 0.323618 | − | 0.946188i | \(-0.395101\pi\) | ||||
0.323618 | + | 0.946188i | \(0.395101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.50690 | + | 28.7343i | −0.0936345 | + | 1.78546i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.31658 | + | 2.10532i | −0.143393 | + | 0.130316i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.1331 | 1.17980 | 0.589898 | − | 0.807478i | \(-0.299168\pi\) | ||||
0.589898 | + | 0.807478i | \(0.299168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.42689 | + | 16.3279i | 0.579090 | + | 1.00301i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.64045 | + | 6.96390i | 0.528787 | + | 0.426184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.41840 | − | 7.65290i | −0.269395 | − | 0.466605i | 0.699311 | − | 0.714818i | \(-0.253490\pi\) |
−0.968706 | + | 0.248212i | \(0.920157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.16955 | − | 15.8821i | 0.557010 | − | 0.964770i | −0.440734 | − | 0.897638i | \(-0.645282\pi\) |
0.997744 | − | 0.0671321i | \(-0.0213849\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.48389 | + | 5.00272i | −0.271377 | + | 0.302778i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.78059 | 0.288280 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.10482 | 0.306719 | 0.153360 | − | 0.988170i | \(-0.450991\pi\) | ||||
0.153360 | + | 0.988170i | \(0.450991\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.27001 | + | 6.60704i | −0.435244 | + | 0.395553i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.853180 | + | 1.47775i | −0.0508964 | + | 0.0881552i | −0.890351 | − | 0.455274i | \(-0.849541\pi\) |
0.839455 | + | 0.543430i | \(0.182875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.24415 | + | 10.8152i | −0.371176 | + | 0.642896i | −0.989747 | − | 0.142833i | \(-0.954379\pi\) |
0.618571 | + | 0.785729i | \(0.287712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.69174 | − | 7.00524i | −0.514854 | − | 0.414954i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.01299 | + | 2.60626i | 0.236879 | + | 0.153843i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.02104 | − | 5.23260i | 0.177708 | − | 0.307800i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.1700 | − | 9.00264i | −0.654798 | − | 0.527744i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.60202 | − | 4.50684i | −0.152012 | − | 0.263292i | 0.779955 | − | 0.625835i | \(-0.215242\pi\) |
−0.931967 | + | 0.362543i | \(0.881909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.8377 | − | 30.8959i | 1.03855 | − | 1.79883i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.14989 | − | 6.28942i | 0.182775 | − | 0.364949i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.92654 | + | 3.33687i | 0.111415 | + | 0.192976i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.601708 | + | 11.4736i | −0.0346819 | + | 0.661328i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.33249 | − | 27.7694i | 0.248895 | − | 1.59531i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.817453 | + | 1.41587i | 0.0468072 | + | 0.0810725i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00136 | −0.285442 | −0.142721 | − | 0.989763i | \(-0.545585\pi\) | ||||
−0.142721 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.594560 | + | 3.81088i | −0.0338234 | + | 0.216793i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1984 | + | 28.0565i | −0.918528 | + | 1.59094i | −0.116876 | + | 0.993146i | \(0.537288\pi\) |
−0.801652 | + | 0.597791i | \(0.796045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.759535 | − | 1.31555i | −0.0429315 | − | 0.0743595i | 0.843761 | − | 0.536719i | \(-0.180336\pi\) |
−0.886693 | + | 0.462359i | \(0.847003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −22.8813 | + | 3.73171i | −1.28922 | + | 0.210258i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7544 | + | 18.6272i | 0.604029 | + | 1.04621i | 0.992204 | + | 0.124623i | \(0.0397723\pi\) |
−0.388175 | + | 0.921586i | \(0.626894\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.706261 | − | 1.22328i | 0.0395430 | − | 0.0684905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.6109 | + | 19.0295i | 1.31783 | + | 1.06213i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.30441 | 0.406428 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.58856 | − | 4.48352i | −0.143588 | − | 0.248701i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.2002 | − | 9.74032i | 1.39357 | − | 0.538641i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.82917 | − | 5.73417i | −0.486768 | − | 0.316135i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.73902 | + | 16.8685i | 0.535305 | + | 0.927175i | 0.999149 | + | 0.0412580i | \(0.0131366\pi\) |
−0.463844 | + | 0.885917i | \(0.653530\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.1450 | + | 21.9431i | −1.32314 | + | 1.20248i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.7107 | + | 32.4079i | −1.02228 | + | 1.77063i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.84742 | + | 8.39598i | 0.264056 | + | 0.457358i | 0.967316 | − | 0.253575i | \(-0.0816063\pi\) |
−0.703260 | + | 0.710933i | \(0.748273\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.72888 | − | 1.05476i | 0.148212 | − | 0.0572867i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.21642 | − | 3.83896i | 0.120026 | − | 0.207891i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.89912 | + | 18.2919i | −0.156538 | + | 0.987672i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.04972 | + | 13.1378i | −0.110353 | + | 0.707318i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.01302 | − | 1.75460i | 0.0543817 | − | 0.0941919i | −0.837553 | − | 0.546356i | \(-0.816015\pi\) |
0.891935 | + | 0.452164i | \(0.149348\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.14577 | − | 14.1089i | 0.436033 | − | 0.755231i | −0.561346 | − | 0.827581i | \(-0.689716\pi\) |
0.997379 | + | 0.0723497i | \(0.0230498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.60419 | + | 0.451400i | −0.405882 | + | 0.0240939i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.0614 | 0.908089 | 0.454045 | − | 0.890979i | \(-0.349981\pi\) | ||||
0.454045 | + | 0.890979i | \(0.349981\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.7309 | 2.00255 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.1247 | − | 11.2963i | 0.535859 | − | 0.597862i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.48363 | + | 2.56972i | −0.0783030 | + | 0.135625i | −0.902518 | − | 0.430652i | \(-0.858283\pi\) |
0.824215 | + | 0.566277i | \(0.191617\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.06549 | + | 12.2378i | 0.371868 | + | 0.644094i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.44770 | − | 15.6887i | 0.128471 | − | 0.823444i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2695 | − | 26.4475i | −0.799240 | − | 1.38432i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1575 | 0.530216 | 0.265108 | − | 0.964219i | \(-0.414592\pi\) | ||||
0.265108 | + | 0.964219i | \(0.414592\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.15259 | + | 5.30190i | 0.0600014 | + | 0.276006i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.3225 | + | 9.30182i | 0.743585 | + | 0.482927i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.4846 | −1.31954 | −0.659771 | − | 0.751467i | \(-0.729347\pi\) | ||||
−0.659771 | + | 0.751467i | \(0.729347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.14527 | + | 7.34068i | −0.0591414 | + | 0.379071i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.52969 | −0.0787829 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.85497 | −0.506216 | −0.253108 | − | 0.967438i | \(-0.581453\pi\) | ||||
−0.253108 | + | 0.967438i | \(0.581453\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.05977 | + | 6.79266i | −0.0542935 | + | 0.347998i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.3127 | 1.39561 | 0.697806 | − | 0.716286i | \(-0.254160\pi\) | ||||
0.697806 | + | 0.716286i | \(0.254160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.32130 | − | 4.74903i | 0.475057 | − | 0.242033i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.64109 | + | 8.76190i | −0.490084 | + | 0.445392i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.18446 | 0.212161 | 0.106080 | − | 0.994358i | \(-0.466170\pi\) | ||||
0.106080 | + | 0.994358i | \(0.466170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.35019 | − | 7.53475i | −0.219999 | − | 0.381049i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.42274 | − | 9.11914i | 0.0717676 | − | 0.460000i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.12114 | − | 1.94187i | −0.0564107 | − | 0.0977062i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.3354 | − | 26.5618i | 0.769664 | − | 1.33310i | −0.168082 | − | 0.985773i | \(-0.553757\pi\) |
0.937745 | − | 0.347323i | \(-0.112909\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.89564 | − | 2.07986i | −0.495402 | − | 0.104123i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.84803 | −0.341974 | −0.170987 | − | 0.985273i | \(-0.554696\pi\) | ||||
−0.170987 | + | 0.985273i | \(0.554696\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.80055 | −0.239132 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.4092 | − | 15.2543i | −1.06383 | − | 0.757994i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.36113 | − | 12.7499i | 0.364878 | − | 0.631987i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.13490 | − | 15.8221i | 0.451692 | − | 0.782353i | −0.546799 | − | 0.837264i | \(-0.684154\pi\) |
0.998491 | + | 0.0549104i | \(0.0174873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00127 | − | 12.8273i | 0.0987154 | − | 0.632724i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.69237 | − | 32.2709i | 0.0832763 | − | 1.58795i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.87328 | + | 4.97666i | −0.141044 | + | 0.244295i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.7241 | − | 8.78327i | 1.11280 | − | 0.430119i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.2310 | − | 19.4526i | −0.548669 | − | 0.950322i | −0.998366 | − | 0.0571410i | \(-0.981802\pi\) |
0.449698 | − | 0.893181i | \(-0.351532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4177 | − | 18.0440i | 0.507728 | − | 0.879411i | −0.492232 | − | 0.870464i | \(-0.663819\pi\) |
0.999960 | − | 0.00894684i | \(-0.00284791\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.53587 | − | 11.6650i | −0.123298 | − | 0.567170i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.84505 | + | 10.1239i | 0.283526 | + | 0.491082i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.24197 | + | 0.806608i | 0.0601033 | + | 0.0390345i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.20618 | − | 1.23925i | 0.154796 | − | 0.0598313i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.1213 | + | 17.5307i | 0.487527 | + | 0.844422i | 0.999897 | − | 0.0143427i | \(-0.00456557\pi\) |
−0.512370 | + | 0.858765i | \(0.671232\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.6764 | −1.04170 | −0.520851 | − | 0.853648i | \(-0.674385\pi\) | ||||
−0.520851 | + | 0.853648i | \(0.674385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.11011 | − | 3.31260i | −0.197065 | − | 0.158827i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.89978 | + | 5.02257i | −0.138715 | + | 0.240262i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7390 | − | 30.7249i | −0.846639 | − | 1.46642i | −0.884191 | − | 0.467126i | \(-0.845289\pi\) |
0.0375520 | − | 0.999295i | \(-0.488044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.9330 | + | 12.4207i | −0.806333 | + | 0.591462i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.60313 | − | 16.6331i | −0.456258 | − | 0.790263i | 0.542501 | − | 0.840055i | \(-0.317477\pi\) |
−0.998760 | + | 0.0497923i | \(0.984144\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.35716 | + | 16.2071i | −0.443572 | + | 0.768289i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.581980 | + | 3.73025i | −0.0275267 | + | 0.176435i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.6082 | −1.39730 | −0.698648 | − | 0.715465i | \(-0.746215\pi\) | ||||
−0.698648 | + | 0.715465i | \(0.746215\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.22415 | − | 2.12029i | −0.0576429 | − | 0.0998405i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.74539 | − | 24.0064i | 0.175974 | − | 1.12792i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.50117 | − | 6.17060i | −0.445422 | − | 0.289282i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.78098 | + | 8.28090i | 0.223645 | + | 0.387364i | 0.955912 | − | 0.293653i | \(-0.0948711\pi\) |
−0.732267 | + | 0.681017i | \(0.761538\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.1705 | − | 1.01927i | 0.801449 | − | 0.0475756i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.9187 | − | 18.9118i | 0.508536 | − | 0.880809i | −0.491416 | − | 0.870925i | \(-0.663520\pi\) |
0.999951 | − | 0.00988416i | \(-0.00314628\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0744 | − | 22.6456i | −0.607621 | − | 1.05243i | −0.991631 | − | 0.129102i | \(-0.958791\pi\) |
0.384010 | − | 0.923329i | \(-0.374543\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.8986 | − | 10.3958i | −0.598157 | − | 0.482093i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.4764 | − | 30.2699i | 0.808709 | − | 1.40073i | −0.105049 | − | 0.994467i | \(-0.533500\pi\) |
0.913758 | − | 0.406258i | \(-0.133167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.77520 | + | 33.8502i | −0.0819711 | + | 1.56306i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.00017 | − | 3.22400i | −0.184318 | − | 0.148554i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.93930 | − | 5.09102i | 0.135149 | − | 0.234086i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.89623 | − | 6.74848i | 0.178771 | − | 0.309641i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.11362 | + | 18.9226i | 0.188350 | + | 0.866407i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.8109 | 1.36209 | 0.681047 | − | 0.732240i | \(-0.261525\pi\) | ||||
0.681047 | + | 0.732240i | \(0.261525\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.9434 | −0.726959 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.74797 | + | 11.4464i | 0.170539 | + | 0.520828i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0965 | − | 20.9518i | 0.549276 | − | 0.951374i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.2253 | + | 19.4428i | 0.508667 | + | 0.881037i | 0.999950 | + | 0.0100365i | \(0.00319477\pi\) |
−0.491283 | + | 0.871000i | \(0.663472\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.523994 | + | 0.422321i | 0.0236958 | + | 0.0190980i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.5222 | − | 30.3494i | −0.790767 | − | 1.36965i | −0.925493 | − | 0.378765i | \(-0.876349\pi\) |
0.134726 | − | 0.990883i | \(-0.456984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.45407 | 0.155564 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.2983 | + | 3.61340i | 0.507821 | + | 0.162410i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.4525 | − | 15.5150i | 1.36598 | − | 0.695943i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.93520 | 0.399994 | 0.199997 | − | 0.979796i | \(-0.435907\pi\) | ||||
0.199997 | + | 0.979796i | \(0.435907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.7901 | − | 4.55707i | 0.526742 | − | 0.203595i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6403 | 0.563603 | 0.281802 | − | 0.959473i | \(-0.409068\pi\) | ||||
0.281802 | + | 0.959473i | \(0.409068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47.3958 | 2.10909 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.6331 | + | 11.7938i | 0.649880 | + | 0.523781i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.1110 | −1.24600 | −0.623000 | − | 0.782222i | \(-0.714086\pi\) | ||||
−0.623000 | + | 0.782222i | \(0.714086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.1992 | − | 15.0669i | −1.02627 | − | 0.666519i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.31121 | − | 9.57247i | −0.278647 | − | 0.422635i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.50427 | −0.286613 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.69331 | + | 4.66495i | 0.118452 | + | 0.205164i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.55127 | + | 2.53218i | −0.287569 | + | 0.111150i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.23768 | + | 7.33988i | 0.185656 | + | 0.321566i | 0.943797 | − | 0.330524i | \(-0.107226\pi\) |
−0.758141 | + | 0.652090i | \(0.773892\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7236 | + | 28.9662i | −0.731273 | + | 1.26660i | 0.225066 | + | 0.974344i | \(0.427740\pi\) |
−0.956339 | + | 0.292259i | \(0.905593\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.03589 | − | 15.3797i | −0.219784 | − | 0.671225i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.8398 | 0.472187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0921 | −0.699655 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.1167 | − | 24.6439i | 1.17677 | − | 1.06945i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.32569 | + | 2.29616i | −0.0574220 | + | 0.0994579i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.5693 | + | 44.2874i | −1.10546 | + | 1.91471i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.1006 | − | 6.60968i | 0.737944 | − | 0.285229i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.57039 | − | 7.66586i | 0.239934 | − | 0.330192i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.12929 | + | 15.8124i | −0.392499 | + | 0.679828i | −0.992778 | − | 0.119962i | \(-0.961723\pi\) |
0.600280 | + | 0.799790i | \(0.295056\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.24149 | − | 33.5957i | 0.224934 | − | 1.44173i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.7803 | + | 39.4567i | 0.975802 | + | 1.69014i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.88599 | − | 4.99869i | 0.123396 | − | 0.213728i | −0.797709 | − | 0.603043i | \(-0.793955\pi\) |
0.921105 | + | 0.389315i | \(0.127288\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.356713 | + | 1.64088i | 0.0152241 | + | 0.0700309i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.15122 | − | 1.99397i | −0.0490437 | − | 0.0849461i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.70337 | − | 1.10627i | −0.0724346 | − | 0.0470432i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −42.8384 | − | 34.5262i | −1.81839 | − | 1.46556i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.6911 | + | 28.9098i | 0.707223 | + | 1.22495i | 0.965883 | + | 0.258977i | \(0.0833855\pi\) |
−0.258661 | + | 0.965968i | \(0.583281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.36623 | −0.269263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.23964 | + | 2.79825i | −0.305658 | + | 0.118142i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.09566 | − | 1.89773i | 0.0461764 | − | 0.0799799i | −0.842013 | − | 0.539457i | \(-0.818630\pi\) |
0.888190 | + | 0.459477i | \(0.151963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.46683 | + | 4.27268i | 0.103780 | + | 0.179753i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.5519 | − | 3.50826i | −0.989087 | − | 0.147333i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.49302 | − | 16.4424i | −0.397968 | − | 0.689301i | 0.595507 | − | 0.803350i | \(-0.296951\pi\) |
−0.993475 | + | 0.114049i | \(0.963618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8690 | + | 18.8257i | −0.454854 | + | 0.787831i | −0.998680 | − | 0.0513674i | \(-0.983642\pi\) |
0.543825 | + | 0.839198i | \(0.316975\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.3885 | + | 5.17488i | −0.559311 | + | 0.216184i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.28172 | −0.387074 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.4516 | − | 26.7629i | −0.643258 | − | 1.11416i | −0.984701 | − | 0.174253i | \(-0.944249\pi\) |
0.341443 | − | 0.939903i | \(-0.389084\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.3327 | + | 20.4173i | 1.05279 | + | 0.848513i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.272605 | + | 5.19815i | −0.0113096 | + | 0.215655i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.36902 | − | 7.56737i | −0.180946 | − | 0.313408i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.72888 | − | 12.5528i | −0.112825 | − | 0.518994i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.18332 | − | 15.9060i | 0.379036 | − | 0.656510i | −0.611886 | − | 0.790946i | \(-0.709589\pi\) |
0.990922 | + | 0.134436i | \(0.0429222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.61282 | − | 6.25759i | −0.148864 | − | 0.257840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.60101 | + | 10.2618i | −0.0658569 | + | 0.422115i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.8775 | − | 24.0365i | 0.569880 | − | 0.987061i | −0.426698 | − | 0.904394i | \(-0.640323\pi\) |
0.996577 | − | 0.0826662i | \(-0.0263435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.4539 | + | 13.9334i | 0.879524 | + | 0.571213i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.2782 | − | 8.99745i | 0.952715 | − | 0.368241i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.201412 | − | 0.348855i | 0.00822945 | − | 0.0142538i | −0.861881 | − | 0.507110i | \(-0.830714\pi\) |
0.870111 | + | 0.492856i | \(0.164047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3733 | − | 21.4312i | 0.504717 | − | 0.874196i | −0.495268 | − | 0.868740i | \(-0.664930\pi\) |
0.999985 | − | 0.00545577i | \(-0.00173663\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.4438 | + | 25.8500i | −1.15832 | + | 1.05269i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.7769 | 1.08864 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0697 | −0.976957 | −0.488479 | − | 0.872576i | \(-0.662448\pi\) | ||||
−0.488479 | + | 0.872576i | \(0.662448\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.67941 | − | 0.983513i | −0.189619 | − | 0.0398539i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.91672 | − | 5.05190i | 0.117998 | − | 0.204378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1907 | + | 17.6509i | 0.411600 | + | 0.712912i | 0.995065 | − | 0.0992261i | \(-0.0316367\pi\) |
−0.583465 | + | 0.812138i | \(0.698303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.53443 | + | 3.29871i | −0.344142 | + | 0.133017i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.9315 | − | 36.2544i | −0.842669 | − | 1.45955i | −0.887630 | − | 0.460558i | \(-0.847650\pi\) |
0.0449604 | − | 0.998989i | \(-0.485684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.8219 | −0.595743 | −0.297871 | − | 0.954606i | \(-0.596277\pi\) | ||||
−0.297871 | + | 0.954606i | \(0.596277\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.11565 | + | 12.2112i | −0.245413 | + | 0.490018i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.887770 | + | 16.9284i | −0.0355678 | + | 0.678221i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1861 | −1.20744 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.02830 | + | 3.24667i | 0.160875 | + | 0.129660i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.0007 | 1.43544 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.0294 | 0.837169 | 0.418585 | − | 0.908178i | \(-0.362526\pi\) | ||||
0.418585 | + | 0.908178i | \(0.362526\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.3730 | + | 8.64756i | −0.889247 | + | 0.343710i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.5935 | −0.460072 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.2057 | − | 1.07339i | −0.404366 | − | 0.0425291i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.9114 | + | 11.8049i | 1.46019 | + | 0.466995i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.9318 | 0.471279 | 0.235640 | − | 0.971840i | \(-0.424281\pi\) | ||||
0.235640 | + | 0.971840i | \(0.424281\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9678 | + | 34.5852i | 0.787452 | + | 1.36391i | 0.927524 | + | 0.373765i | \(0.121933\pi\) |
−0.140072 | + | 0.990141i | \(0.544733\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1054 | − | 13.7863i | −0.673524 | − | 0.542837i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.494477 | − | 0.856459i | −0.0194399 | − | 0.0336709i | 0.856142 | − | 0.516741i | \(-0.172855\pi\) |
−0.875582 | + | 0.483070i | \(0.839522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.26714 | + | 14.3191i | −0.324514 | + | 0.562074i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.6852 | − | 3.08651i | −0.575557 | − | 0.120970i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.7147 | 0.888894 | 0.444447 | − | 0.895805i | \(-0.353400\pi\) | ||||
0.444447 | + | 0.895805i | \(0.353400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5642 | 0.608144 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.66315 | − | 30.6504i | −0.259954 | − | 1.19579i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1943 | − | 33.2454i | 0.747702 | − | 1.29506i | −0.201220 | − | 0.979546i | \(-0.564491\pi\) |
0.948922 | − | 0.315512i | \(-0.102176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.9629 | + | 29.3806i | −0.659780 | + | 1.14277i | 0.320892 | + | 0.947116i | \(0.396017\pi\) |
−0.980672 | + | 0.195657i | \(0.937316\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.54444 | + | 5.27459i | 0.254165 | + | 0.204848i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.893040 | − | 17.0288i | 0.0346306 | − | 0.660350i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.37124 | + | 2.37505i | −0.0530944 | + | 0.0919623i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.30475 | − | 5.08140i | −0.243756 | − | 0.196458i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.378860 | − | 0.656205i | −0.0146257 | − | 0.0253325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1030 | + | 27.8912i | −0.620725 | + | 1.07513i | 0.368626 | + | 0.929578i | \(0.379828\pi\) |
−0.989351 | + | 0.145549i | \(0.953505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.21718 | − | 16.4073i | 0.316279 | − | 0.631518i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.9842 | + | 32.8816i | 0.729622 | + | 1.26374i | 0.957043 | + | 0.289946i | \(0.0936375\pi\) |
−0.227421 | + | 0.973797i | \(0.573029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.14767 | − | 21.8843i | 0.0440436 | − | 0.839842i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.26324 | − | 33.7352i | 0.201688 | − | 1.29273i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.59357 | − | 13.1525i | −0.290560 | − | 0.503265i | 0.683382 | − | 0.730061i | \(-0.260508\pi\) |
−0.973942 | + | 0.226796i | \(0.927175\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.8932 | 0.836495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.49540 | + | 48.0424i | −0.285967 | + | 1.83293i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.73142 | + | 8.19507i | −0.180253 | + | 0.312207i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.34574 | + | 2.33089i | 0.0511943 | + | 0.0886711i | 0.890487 | − | 0.455009i | \(-0.150364\pi\) |
−0.839293 | + | 0.543680i | \(0.817031\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.6047 | − | 1.72951i | 0.402838 | − | 0.0656988i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.5420 | + | 35.5798i | 0.779203 | + | 1.34962i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.99344 | − | 5.18480i | 0.113385 | − | 0.196388i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.6133 | − | 15.0017i | −0.704021 | − | 0.567416i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.8515 | −0.447625 | −0.223813 | − | 0.974632i | \(-0.571850\pi\) | ||||
−0.223813 | + | 0.974632i | \(0.571850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9988 | − | 20.7826i | −0.452544 | − | 0.783829i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.7770 | − | 7.25765i | 0.707184 | − | 0.273339i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.2530 | − | 19.4892i | 1.43865 | − | 0.732967i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.5167 | + | 35.5359i | 0.770520 | + | 1.33458i | 0.937278 | + | 0.348582i | \(0.113337\pi\) |
−0.166759 | + | 0.985998i | \(0.553330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.489233 | − | 2.25047i | −0.0183477 | − | 0.0843991i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.30328 | + | 7.45351i | −0.161159 | + | 0.279136i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.89830 | + | 5.02001i | 0.108390 | + | 0.187738i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.8704 | − | 6.90724i | 0.667384 | − | 0.257956i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.4555 | + | 18.1094i | −0.389923 | + | 0.675366i | −0.992439 | − | 0.122741i | \(-0.960832\pi\) |
0.602516 | + | 0.798107i | \(0.294165\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.24958 | + | 2.67457i | −0.195505 | + | 0.0996060i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.18629 | − | 39.6515i | 0.230071 | − | 1.47466i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.84243 | − | 3.19119i | 0.0684263 | − | 0.118518i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.32165 | + | 2.28917i | −0.0490173 | + | 0.0849005i | −0.889493 | − | 0.456949i | \(-0.848942\pi\) |
0.840476 | + | 0.541849i | \(0.182276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.1715 | − | 21.6213i | −0.598945 | − | 0.800790i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.3751 | 0.531683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.1489 | 0.522602 | 0.261301 | − | 0.965257i | \(-0.415848\pi\) | ||||
0.261301 | + | 0.965257i | \(0.415848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25.0973 | − | 24.9850i | −0.925727 | − | 0.921587i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.67174 | − | 15.0199i | 0.319428 | − | 0.553265i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.85905 | + | 13.6123i | 0.289100 | + | 0.500736i | 0.973595 | − | 0.228282i | \(-0.0733107\pi\) |
−0.684495 | + | 0.729017i | \(0.739977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.863704 | − | 5.53598i | 0.0317289 | − | 0.203369i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5496 | − | 18.2724i | −0.387026 | − | 0.670348i | 0.605022 | − | 0.796208i | \(-0.293164\pi\) |
−0.992048 | + | 0.125861i | \(0.959831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.36665 | −0.233256 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.36792 | + | 3.96960i | −0.159814 | + | 0.145240i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.42592 | + | 46.2584i | −0.0886412 | + | 1.69025i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0370 | −0.475725 | −0.237863 | − | 0.971299i | \(-0.576447\pi\) | ||||
−0.237863 | + | 0.971299i | \(0.576447\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.07832 | + | 13.3212i | −0.0757383 | + | 0.485451i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.9732 | 1.49117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6856 | −0.461065 | −0.230532 | − | 0.973065i | \(-0.574047\pi\) | ||||
−0.230532 | + | 0.973065i | \(0.574047\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.949971 | − | 6.08891i | 0.0344818 | − | 0.221014i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.04077 | −0.218978 | −0.109489 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109489 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.6106 | + | 22.4781i | 1.25299 | + | 0.813761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.16188 | + | 28.3446i | 0.222783 | + | 1.02480i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9058 | 0.646540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.108129 | + | 0.187285i | 0.00389924 | + | 0.00675368i | 0.867968 | − | 0.496619i | \(-0.165425\pi\) |
−0.864069 | + | 0.503373i | \(0.832092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.77037 | + | 17.7569i | −0.0997724 | + | 0.639499i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8132 | + | 32.5854i | 0.676663 | + | 1.17202i | 0.975980 | + | 0.217861i | \(0.0699081\pi\) |
−0.299316 | + | 0.954154i | \(0.596759\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.78202 | − | 10.0148i | 0.207696 | − | 0.359741i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −48.7720 | − | 10.2508i | −1.74968 | − | 0.367747i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.99078 | −0.142985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4869 | −0.625730 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.98442 | − | 4.52659i | −0.106654 | − | 0.161767i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.33198 | − | 7.50321i | 0.154615 | − | 0.267801i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.4067 | − | 26.6853i | 0.549191 | − | 0.951226i | −0.449139 | − | 0.893462i | \(-0.648269\pi\) |
0.998330 | − | 0.0577648i | \(-0.0183973\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.10850 | + | 32.7433i | −0.181867 | + | 1.16569i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.74791 | + | 2.43410i | 0.133260 | + | 0.0865468i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.410286 | + | 0.710636i | −0.0145697 | + | 0.0252354i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.4596 | + | 11.7732i | −1.08029 | + | 0.417552i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.9792 | − | 31.1408i | −0.636855 | − | 1.10306i | −0.986119 | − | 0.166040i | \(-0.946902\pi\) |
0.349264 | − | 0.937024i | \(-0.386431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.58602 | + | 11.4073i | −0.232997 | + | 0.403562i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.2246 | + | 12.9275i | −0.502603 | + | 0.456770i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.07684 | + | 12.2574i | 0.249736 | + | 0.432556i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.0977 | + | 9.22045i | −0.637860 | + | 0.324978i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.2765 | − | 5.51811i | 0.502556 | − | 0.194247i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.4818 | − | 33.7435i | −0.684943 | − | 1.18636i | −0.973455 | − | 0.228880i | \(-0.926494\pi\) |
0.288511 | − | 0.957477i | \(-0.406840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2811 | 0.993082 | 0.496541 | − | 0.868013i | \(-0.334603\pi\) | ||||
0.496541 | + | 0.868013i | \(0.334603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.7316 | + | 19.9328i | 0.867374 | + | 0.699073i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.567459 | + | 0.982867i | −0.0198772 | + | 0.0344283i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.79113 | − | 8.29849i | −0.167621 | − | 0.290327i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.36420 | − | 9.00922i | −0.257326 | − | 0.314808i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.7917 | − | 36.0123i | −0.725635 | − | 1.25684i | −0.958712 | − | 0.284378i | \(-0.908213\pi\) |
0.233077 | − | 0.972458i | \(-0.425121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.22999 | − | 7.32656i | 0.147448 | − | 0.255388i | −0.782835 | − | 0.622229i | \(-0.786227\pi\) |
0.930284 | + | 0.366841i | \(0.119561\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.27641 | + | 8.18125i | −0.0444389 | + | 0.284834i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.2823 | −1.53985 | −0.769923 | − | 0.638137i | \(-0.779706\pi\) | ||||
−0.769923 | + | 0.638137i | \(0.779706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.31637 | − | 14.4044i | −0.288839 | − | 0.500284i | 0.684694 | − | 0.728831i | \(-0.259936\pi\) |
−0.973533 | + | 0.228547i | \(0.926603\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.36298 | + | 8.73613i | −0.0472813 | + | 0.303053i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.0448 | + | 2.42373i | 0.798455 | + | 0.0839774i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.6579 | + | 18.4601i | 0.368832 | + | 0.638836i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.36586 | − | 14.2056i | −0.323731 | − | 0.491017i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.8006 | + | 25.6354i | −0.510974 | + | 0.885033i | 0.488945 | + | 0.872314i | \(0.337382\pi\) |
−0.999919 | + | 0.0127182i | \(0.995952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.9556 | + | 24.1718i | 0.481228 | + | 0.833512i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.30115 | − | 1.85464i | −0.0792557 | − | 0.0638773i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.8469 | + | 27.4477i | −0.545151 | + | 0.944228i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.6116 | − | 11.0107i | 0.742583 | − | 0.378332i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.8414 | − | 13.5736i | −0.577994 | − | 0.465843i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.2920 | + | 24.7544i | −0.489922 | + | 0.848570i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0619 | + | 26.0880i | −0.515710 | + | 0.893236i | 0.484124 | + | 0.875000i | \(0.339139\pi\) |
−0.999834 | + | 0.0182366i | \(0.994195\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.3091 | − | 13.0042i | 0.489360 | − | 0.444734i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.0894 | 1.26695 | 0.633475 | − | 0.773763i | \(-0.281628\pi\) | ||||
0.633475 | + | 0.773763i | \(0.281628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.78333 | 0.129085 | 0.0645427 | − | 0.997915i | \(-0.479441\pi\) | ||||
0.0645427 | + | 0.997915i | \(0.479441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.53169 | + | 6.17175i | −0.188519 | + | 0.210333i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.213559 | + | 0.369895i | −0.00726963 | + | 0.0125914i | −0.869637 | − | 0.493691i | \(-0.835647\pi\) |
0.862368 | + | 0.506282i | \(0.168981\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.92218 | − | 10.2575i | −0.201360 | − | 0.348766i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.14818 | + | 6.56715i | 0.276727 | + | 0.223032i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.519608 | + | 0.899987i | 0.0176265 | + | 0.0305300i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7821 | −0.636407 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.3890 | − | 16.7121i | 0.622374 | − | 0.565619i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1120 | + | 5.15186i | −0.341847 | + | 0.174165i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2608 | 0.380249 | 0.190124 | − | 0.981760i | \(-0.439111\pi\) | ||||
0.190124 | + | 0.981760i | \(0.439111\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.40750 | − | 3.24965i | 0.283578 | − | 0.109608i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.4810 | −1.19538 | −0.597692 | − | 0.801726i | \(-0.703916\pi\) | ||||
−0.597692 | + | 0.801726i | \(0.703916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.30092 | 0.178390 | 0.0891952 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891952 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 48.1109 | + | 38.7757i | 1.61723 | + | 1.30343i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.5664 | −1.93289 | −0.966446 | − | 0.256870i | \(-0.917309\pi\) | ||||
−0.966446 | + | 0.256870i | \(0.917309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.35705 | + | 4.76724i | −0.313825 | + | 0.159888i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.92238 | + | 7.06983i | 0.332412 | + | 0.236848i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.78032 | 0.293822 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4585 | + | 26.7749i | 0.516720 | + | 0.894985i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.22494 | + | 2.40605i | −0.207845 | + | 0.0803356i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.70842 | − | 2.95906i | −0.0569788 | − | 0.0986903i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6837 | − | 18.5047i | 0.355925 | − | 0.616480i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.4747 | − | 4.09317i | −0.648077 | − | 0.136212i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 57.3400 | 1.90605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.8972 | −0.693879 | −0.346939 | − | 0.937888i | \(-0.612779\pi\) | ||||
−0.346939 | + | 0.937888i | \(0.612779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.3664 | + | 14.8288i | 1.53787 | + | 0.491840i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.3819 | + | 19.7141i | −0.377101 | + | 0.653157i | −0.990639 | − | 0.136508i | \(-0.956412\pi\) |
0.613539 | + | 0.789665i | \(0.289746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.33166 | − | 2.30650i | 0.0440715 | − | 0.0763340i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.64131 | + | 1.02091i | −0.0873189 | + | 0.0337503i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.5618 | − | 6.40002i | 0.414828 | − | 0.211347i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.6515 | + | 32.3054i | −0.615257 | + | 1.06566i | 0.375083 | + | 0.926991i | \(0.377614\pi\) |
−0.990339 | + | 0.138664i | \(0.955719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.33535 | − | 8.55906i | 0.0440014 | − | 0.282031i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.46870 | + | 16.4003i | 0.311666 | + | 0.539822i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.2031 | − | 33.2607i | 0.631394 | − | 1.09361i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.36300 | − | 2.03500i | −0.208988 | − | 0.0668381i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.83363 | − | 4.90799i | −0.0929683 | − | 0.161026i | 0.815791 | − | 0.578347i | \(-0.196302\pi\) |
−0.908759 | + | 0.417322i | \(0.862969\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.28151 | − | 14.1112i | −0.205868 | − | 0.462475i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −43.6895 | − | 35.2122i | −1.43033 | − | 1.15279i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.54444 | − | 11.3353i | −0.214026 | − | 0.370704i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.64754 | −0.249834 | −0.124917 | − | 0.992167i | \(-0.539866\pi\) | ||||
−0.124917 | + | 0.992167i | \(0.539866\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.45416 | − | 0.948578i | 0.0800886 | − | 0.0309557i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.2276 | + | 17.7147i | −0.333410 | + | 0.577483i | −0.983178 | − | 0.182650i | \(-0.941533\pi\) |
0.649768 | + | 0.760132i | \(0.274866\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.37674 | + | 4.11663i | 0.0773973 | + | 0.134056i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.276974 | − | 40.1543i | −0.00900996 | − | 1.30622i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.38343 | − | 4.12823i | −0.0774512 | − | 0.134149i | 0.824698 | − | 0.565573i | \(-0.191345\pi\) |
−0.902150 | + | 0.431423i | \(0.858012\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.66385 | − | 13.2742i | 0.248779 | − | 0.430898i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.7491 | + | 13.4311i | −1.12682 | + | 0.435534i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.9412 | −1.58536 | −0.792680 | − | 0.609638i | \(-0.791315\pi\) | ||||
−0.792680 | + | 0.609638i | \(0.791315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1028 | − | 20.9627i | −0.391638 | − | 0.678337i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.90489 | + | 1.53527i | 0.0615762 | + | 0.0496283i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.6699 | − | 9.00249i | 0.570591 | − | 0.290706i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1386 | + | 17.5605i | 0.327050 | + | 0.566468i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.8702 | + | 35.3256i | −1.25258 | + | 1.13835i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.4340 | + | 47.5171i | −0.883132 | + | 1.52963i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.95856 | + | 5.12438i | 0.0951409 | + | 0.164789i | 0.909667 | − | 0.415337i | \(-0.136336\pi\) |
−0.814526 | + | 0.580126i | \(0.803003\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.95027 | + | 12.5004i | −0.0626516 | + | 0.401570i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4888 | + | 25.0953i | −0.464966 | + | 0.805345i | −0.999200 | − | 0.0399914i | \(-0.987267\pi\) |
0.534234 | + | 0.845337i | \(0.320600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.2099 | + | 20.2695i | 1.00054 | + | 0.649809i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.36401 | − | 3.23284i | 0.267863 | − | 0.103534i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.4228 | + | 19.7848i | −0.365447 | + | 0.632972i | −0.988848 | − | 0.148930i | \(-0.952417\pi\) |
0.623401 | + | 0.781902i | \(0.285750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.33670 | − | 7.51139i | 0.138602 | − | 0.240065i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.94067 | + | 45.7270i | 0.317381 | + | 1.45995i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.2703 | 0.997367 | 0.498684 | − | 0.866784i | \(-0.333817\pi\) | ||||
0.498684 | + | 0.866784i | \(0.333817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.5145 | −0.558059 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.1705 | − | 13.5788i | 0.387392 | − | 0.432217i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.70679 | + | 9.88444i | −0.181465 | + | 0.314307i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.50732 | − | 6.07485i | −0.111414 | − | 0.192974i | 0.804927 | − | 0.593374i | \(-0.202204\pi\) |
−0.916340 | + | 0.400400i | \(0.868871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.4681 | + | 12.1630i | −0.998611 | + | 0.385981i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0429 | + | 36.4474i | 0.667105 | + | 1.15546i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.2878 | −0.674191 | −0.337095 | − | 0.941470i | \(-0.609445\pi\) | ||||
−0.337095 | + | 0.941470i | \(0.609445\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.1056 | − | 47.1792i | −0.984139 | − | 1.49268i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))