Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (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: | \(10.5642081874\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(1.19343 - 2.06709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.361 |
Dual form | 1323.2.g.f.667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19343 | + | 2.06709i | −0.843886 | + | 1.46165i | 0.0426999 | + | 0.999088i | \(0.486404\pi\) |
−0.886585 | + | 0.462565i | \(0.846929\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.84857 | − | 3.20182i | −0.924286 | − | 1.60091i | ||||
\(5\) | −2.92087 | −1.30625 | −0.653125 | − | 0.757250i | \(-0.726543\pi\) | ||||
−0.653125 | + | 0.757250i | \(0.726543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.05086 | 1.43219 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.48586 | − | 6.03769i | 1.10233 | − | 1.90929i | ||||
\(11\) | 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 | \(-0.768167\pi\) |
0.949589 | + | 0.313497i | \(0.101501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.13729 | + | 1.96984i | −0.284323 | + | 0.492461i | ||||
\(17\) | 1.65514 | − | 2.86678i | 0.401430 | − | 0.695297i | −0.592469 | − | 0.805593i | \(-0.701847\pi\) |
0.993899 | + | 0.110297i | \(0.0351801\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.10329 | + | 1.91096i | 0.253113 | + | 0.438404i | 0.964381 | − | 0.264516i | \(-0.0852123\pi\) |
−0.711268 | + | 0.702921i | \(0.751879\pi\) | |||||||
\(20\) | 5.39943 | + | 9.35209i | 1.20735 | + | 2.09119i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.61557 | + | 2.79825i | −0.344441 | + | 0.596589i | ||||
\(23\) | −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 | ||||||||
\(26\) | 1.74958 | + | 3.03036i | 0.343121 | + | 0.594302i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.521720 | − | 0.903646i | −0.0968810 | − | 0.167803i | 0.813511 | − | 0.581549i | \(-0.197553\pi\) |
−0.910392 | + | 0.413747i | \(0.864220\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.63729 | + | 2.83587i | 0.294066 | + | 0.509337i | 0.974767 | − | 0.223224i | \(-0.0716581\pi\) |
−0.680701 | + | 0.732561i | \(0.738325\pi\) | |||||||
\(32\) | 1.33629 | + | 2.31453i | 0.236226 | + | 0.409155i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.95060 | + | 6.84263i | 0.677521 | + | 1.17350i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.43773 | + | 9.41842i | 0.893957 | + | 1.54838i | 0.835090 | + | 0.550113i | \(0.185415\pi\) |
0.0588664 | + | 0.998266i | \(0.481251\pi\) | |||||||
\(38\) | −5.26683 | −0.854393 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.8320 | −1.87081 | ||||||||
\(41\) | −0.904289 | + | 1.56627i | −0.141226 | + | 0.244611i | −0.927959 | − | 0.372683i | \(-0.878438\pi\) |
0.786732 | + | 0.617294i | \(0.211771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.17129 | − | 3.76078i | −0.331118 | − | 0.573514i | 0.651613 | − | 0.758551i | \(-0.274093\pi\) |
−0.982731 | + | 0.185038i | \(0.940759\pi\) | |||||||
\(44\) | −2.50244 | − | 4.33435i | −0.377257 | − | 0.653428i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.13670 | − | 5.43292i | 0.462481 | − | 0.801041i | ||||
\(47\) | −1.98957 | + | 3.44604i | −0.290209 | + | 0.502656i | −0.973859 | − | 0.227154i | \(-0.927058\pi\) |
0.683650 | + | 0.729810i | \(0.260391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.21456 | + | 7.29984i | −0.596029 | + | 1.03235i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.42002 | −0.751622 | ||||||||
\(53\) | 3.22743 | − | 5.59008i | 0.443322 | − | 0.767856i | −0.554612 | − | 0.832109i | \(-0.687133\pi\) |
0.997934 | + | 0.0642533i | \(0.0204666\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.95402 | −0.533160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.49056 | 0.327026 | ||||||||
\(59\) | 6.10700 | + | 10.5776i | 0.795064 | + | 1.37709i | 0.922799 | + | 0.385283i | \(0.125896\pi\) |
−0.127735 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.279867 | − | 0.484744i | 0.0358333 | − | 0.0620651i | −0.847553 | − | 0.530711i | \(-0.821925\pi\) |
0.883386 | + | 0.468646i | \(0.155258\pi\) | |||||||
\(62\) | −7.81600 | −0.992632 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.9283 | −1.36604 | ||||||||
\(65\) | −2.14100 | + | 3.70832i | −0.265558 | + | 0.459960i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.40588 | − | 11.0953i | −0.782603 | − | 1.35551i | −0.930420 | − | 0.366494i | \(-0.880558\pi\) |
0.147817 | − | 0.989015i | \(-0.452775\pi\) | |||||||
\(68\) | −12.2386 | −1.48414 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | 0.379069 | + | 0.925368i | \(0.376244\pi\) |
−0.990927 | + | 0.134401i | \(0.957089\pi\) | |||||||
\(74\) | −25.9583 | −3.01759 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.07903 | − | 7.06509i | 0.467897 | − | 0.810422i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.383838 | + | 0.664827i | −0.0431852 | + | 0.0747989i | −0.886810 | − | 0.462134i | \(-0.847084\pi\) |
0.843625 | + | 0.536933i | \(0.180417\pi\) | |||||||
\(80\) | 3.32187 | − | 5.75365i | 0.371397 | − | 0.643278i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.15842 | − | 3.73849i | −0.238358 | − | 0.412847i | ||||
\(83\) | −0.983707 | − | 1.70383i | −0.107976 | − | 0.187020i | 0.806974 | − | 0.590587i | \(-0.201104\pi\) |
−0.914950 | + | 0.403567i | \(0.867770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.83443 | + | 8.37348i | −0.524368 | + | 0.908232i | ||||
\(86\) | 10.3652 | 1.11770 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.48371 | 0.584565 | ||||||||
\(89\) | 3.20356 | + | 5.54872i | 0.339576 | + | 0.588163i | 0.984353 | − | 0.176208i | \(-0.0563830\pi\) |
−0.644777 | + | 0.764371i | \(0.723050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.85859 | + | 8.41533i | 0.506543 | + | 0.877359i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.74884 | − | 8.22524i | −0.489806 | − | 0.848369i | ||||
\(95\) | −3.22257 | − | 5.58166i | −0.330629 | − | 0.572666i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.14143 | + | 7.17316i | 0.420498 | + | 0.728324i | 0.995988 | − | 0.0894847i | \(-0.0285220\pi\) |
−0.575490 | + | 0.817809i | \(0.695189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.52815 | − | 11.3071i | −0.652815 | − | 1.13071i | ||||
\(101\) | −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 | \(0.465008\pi\) | |||||||
\(104\) | 2.96929 | − | 5.14295i | 0.291162 | − | 0.504308i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.70346 | + | 13.3428i | 0.748226 | + | 1.29597i | ||||
\(107\) | 8.75403 | + | 15.1624i | 0.846284 | + | 1.46581i | 0.884501 | + | 0.466537i | \(0.154499\pi\) |
−0.0382175 | + | 0.999269i | \(0.512168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.79917 | + | 13.5086i | −0.747025 | + | 1.29388i | 0.202218 | + | 0.979341i | \(0.435185\pi\) |
−0.949243 | + | 0.314544i | \(0.898148\pi\) | |||||||
\(110\) | 4.71886 | − | 8.17331i | 0.449926 | − | 0.779295i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.844555 | − | 1.46281i | 0.0794491 | − | 0.137610i | −0.823563 | − | 0.567224i | \(-0.808017\pi\) |
0.903012 | + | 0.429615i | \(0.141351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.67690 | 0.715875 | ||||||||
\(116\) | −1.92887 | + | 3.34091i | −0.179092 | + | 0.310196i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.1532 | −2.68377 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.16746 | −0.833405 | ||||||||
\(122\) | 0.668005 | + | 1.15702i | 0.0604784 | + | 0.104752i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.05330 | − | 10.4846i | 0.543602 | − | 0.941546i | ||||
\(125\) | 4.28942 | 0.383657 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.96918 | −0.352208 | −0.176104 | − | 0.984372i | \(-0.556350\pi\) | ||||
−0.176104 | + | 0.984372i | \(0.556350\pi\) | |||||||
\(128\) | 10.3696 | − | 17.9607i | 0.916552 | − | 1.58751i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.11028 | − | 8.85127i | −0.448202 | − | 0.776308i | ||||
\(131\) | 5.32863 | 0.465565 | 0.232782 | − | 0.972529i | \(-0.425217\pi\) | ||||
0.232782 | + | 0.972529i | \(0.425217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 30.5800 | 2.64171 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.70473 | − | 11.6129i | 0.574925 | − | 0.995800i | ||||
\(137\) | 7.49543 | 0.640378 | 0.320189 | − | 0.947354i | \(-0.396254\pi\) | ||||
0.320189 | + | 0.947354i | \(0.396254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.03285 | + | 12.1812i | −0.596518 | + | 1.03320i | 0.396812 | + | 0.917900i | \(0.370116\pi\) |
−0.993331 | + | 0.115300i | \(0.963217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.4164 | − | 26.7021i | 1.29372 | − | 2.24079i | ||||
\(143\) | 0.992275 | − | 1.71867i | 0.0829782 | − | 0.143722i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.52388 | + | 2.63943i | 0.126551 | + | 0.219193i | ||||
\(146\) | −12.4779 | − | 21.6123i | −1.03268 | − | 1.78865i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.1041 | − | 34.8212i | 1.65254 | − | 2.86229i | ||||
\(149\) | −2.17971 | −0.178569 | −0.0892846 | − | 0.996006i | \(-0.528458\pi\) | ||||
−0.0892846 | + | 0.996006i | \(0.528458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0277 | 1.14156 | 0.570781 | − | 0.821102i | \(-0.306641\pi\) | ||||
0.570781 | + | 0.821102i | \(0.306641\pi\) | |||||||
\(152\) | 4.46929 | + | 7.74103i | 0.362507 | + | 0.627880i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | \(-0.128901\pi\) |
−0.800755 | + | 0.598993i | \(0.795568\pi\) | |||||||
\(158\) | −0.916172 | − | 1.58686i | −0.0728867 | − | 0.126243i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.90314 | − | 6.76043i | −0.308570 | − | 0.534459i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.194278 | − | 0.336499i | −0.0152170 | − | 0.0263566i | 0.858317 | − | 0.513120i | \(-0.171511\pi\) |
−0.873534 | + | 0.486764i | \(0.838177\pi\) | |||||||
\(164\) | 6.68657 | 0.522133 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.69596 | 0.364477 | ||||||||
\(167\) | 3.64889 | − | 6.32006i | 0.282360 | − | 0.489061i | −0.689606 | − | 0.724185i | \(-0.742216\pi\) |
0.971965 | + | 0.235124i | \(0.0755496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.42542 | + | 9.39710i | 0.417340 | + | 0.722854i | ||||
\(170\) | −11.5392 | − | 19.9864i | −0.885013 | − | 1.53289i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.02756 | + | 13.9041i | −0.612096 | + | 1.06018i | ||||
\(173\) | 2.02754 | − | 3.51181i | 0.154151 | − | 0.266998i | −0.778598 | − | 0.627522i | \(-0.784069\pi\) |
0.932750 | + | 0.360525i | \(0.117402\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.53957 | + | 2.66661i | −0.116049 | + | 0.201003i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.2929 | −1.14625 | ||||||||
\(179\) | −5.29243 | + | 9.16675i | −0.395575 | + | 0.685155i | −0.993174 | − | 0.116639i | \(-0.962788\pi\) |
0.597600 | + | 0.801795i | \(0.296121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6312 | 1.45917 | 0.729586 | − | 0.683889i | \(-0.239713\pi\) | ||||
0.729586 | + | 0.683889i | \(0.239713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.6469 | −0.784896 | ||||||||
\(185\) | −15.8829 | − | 27.5099i | −1.16773 | − | 2.02257i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.24058 | − | 3.88081i | 0.163848 | − | 0.283793i | ||||
\(188\) | 14.7115 | 1.07294 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.3837 | 1.11605 | ||||||||
\(191\) | 4.14357 | − | 7.17688i | 0.299818 | − | 0.519301i | −0.676276 | − | 0.736648i | \(-0.736407\pi\) |
0.976094 | + | 0.217348i | \(0.0697406\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.39242 | + | 16.2682i | 0.676082 | + | 1.17101i | 0.976152 | + | 0.217090i | \(0.0696566\pi\) |
−0.300070 | + | 0.953917i | \(0.597010\pi\) | |||||||
\(194\) | −19.7701 | −1.41941 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.99634 | −0.427222 | −0.213611 | − | 0.976919i | \(-0.568522\pi\) | ||||
−0.213611 | + | 0.976919i | \(0.568522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.20434 | + | 12.4783i | −0.510702 | + | 0.884562i | 0.489221 | + | 0.872160i | \(0.337281\pi\) |
−0.999923 | + | 0.0124022i | \(0.996052\pi\) | |||||||
\(200\) | 14.3054 | 1.01155 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.3654 | − | 33.5419i | 1.36255 | − | 2.36000i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.64131 | − | 4.57488i | 0.184477 | − | 0.319523i | ||||
\(206\) | −2.65758 | + | 4.60306i | −0.185162 | + | 0.320710i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.66727 | + | 2.88780i | 0.115604 | + | 0.200233i | ||||
\(209\) | 1.49354 | + | 2.58690i | 0.103311 | + | 0.178939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.92418 | + | 11.9930i | −0.476680 | + | 0.825634i | −0.999643 | − | 0.0267212i | \(-0.991493\pi\) |
0.522963 | + | 0.852356i | \(0.324827\pi\) | |||||||
\(212\) | −23.8646 | −1.63902 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −41.7894 | −2.85667 | ||||||||
\(215\) | 6.34204 | + | 10.9847i | 0.432523 | + | 0.749153i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.6156 | − | 32.2431i | −1.26081 | − | 2.18378i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.30929 | + | 12.6601i | 0.492792 | + | 0.853541i | ||||
\(221\) | −2.42644 | − | 4.20271i | −0.163220 | − | 0.282705i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.33756 | − | 4.04878i | −0.156535 | − | 0.271126i | 0.777082 | − | 0.629399i | \(-0.216699\pi\) |
−0.933617 | + | 0.358273i | \(0.883366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.01584 | + | 3.49154i | 0.134092 | + | 0.232254i | ||||
\(227\) | 19.7126 | 1.30837 | 0.654187 | − | 0.756333i | \(-0.273011\pi\) | ||||
0.654187 | + | 0.756333i | \(0.273011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.0728 | −1.85510 | −0.927552 | − | 0.373694i | \(-0.878091\pi\) | ||||
−0.927552 | + | 0.373694i | \(0.878091\pi\) | |||||||
\(230\) | −9.16188 | + | 15.8688i | −0.604116 | + | 1.04636i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.11342 | − | 3.66054i | −0.138753 | − | 0.240326i | ||||
\(233\) | 6.90113 | + | 11.9531i | 0.452108 | + | 0.783074i | 0.998517 | − | 0.0544448i | \(-0.0173389\pi\) |
−0.546409 | + | 0.837518i | \(0.684006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.81127 | − | 10.0654i | 0.379085 | − | 0.656595i | ||||
\(236\) | 22.5785 | − | 39.1070i | 1.46973 | − | 2.54565i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.53069 | + | 9.57944i | −0.357751 | + | 0.619642i | −0.987585 | − | 0.157087i | \(-0.949790\pi\) |
0.629834 | + | 0.776730i | \(0.283123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.1697 | 1.49249 | 0.746247 | − | 0.665669i | \(-0.231854\pi\) | ||||
0.746247 | + | 0.665669i | \(0.231854\pi\) | |||||||
\(242\) | 10.9408 | − | 18.9499i | 0.703299 | − | 1.21815i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.06942 | −0.132481 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.23486 | 0.205829 | ||||||||
\(248\) | 6.63243 | + | 11.4877i | 0.421160 | + | 0.729470i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.11914 | + | 8.86660i | −0.323763 | + | 0.560773i | ||||
\(251\) | −7.78402 | −0.491323 | −0.245662 | − | 0.969356i | \(-0.579005\pi\) | ||||
−0.245662 | + | 0.969356i | \(0.579005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55796 | −0.223687 | ||||||||
\(254\) | 4.73696 | − | 8.20466i | 0.297223 | − | 0.514806i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.8226 | + | 23.9414i | 0.863912 | + | 1.49634i | ||||
\(257\) | 10.3760 | 0.647235 | 0.323618 | − | 0.946188i | \(-0.395101\pi\) | ||||
0.323618 | + | 0.946188i | \(0.395101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.8312 | 0.981807 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.35937 | + | 11.0148i | −0.392883 | + | 0.680494i | ||||
\(263\) | 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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.6835 | + | 41.0210i | −1.44670 | + | 2.50576i | ||||
\(269\) | −4.41840 | + | 7.65290i | −0.269395 | + | 0.466605i | −0.968706 | − | 0.248212i | \(-0.920157\pi\) |
0.699311 | + | 0.714818i | \(0.253490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.16955 | + | 15.8821i | 0.557010 | + | 0.964770i | 0.997744 | + | 0.0671321i | \(0.0213849\pi\) |
−0.440734 | + | 0.897638i | \(0.645282\pi\) | |||||||
\(272\) | 3.76474 | + | 6.52073i | 0.228271 | + | 0.395377i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.94531 | + | 15.4937i | −0.540406 | + | 0.936010i | ||||
\(275\) | 4.78059 | 0.288280 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.10482 | 0.306719 | 0.153360 | − | 0.988170i | \(-0.450991\pi\) | ||||
0.153360 | + | 0.988170i | \(0.450991\pi\) | |||||||
\(278\) | −16.7865 | − | 29.0750i | −1.00679 | − | 1.74381i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.853180 | + | 1.47775i | 0.0508964 | + | 0.0881552i | 0.890351 | − | 0.455274i | \(-0.150459\pi\) |
−0.839455 | + | 0.543430i | \(0.817125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.24415 | − | 10.8152i | −0.371176 | − | 0.642896i | 0.618571 | − | 0.785729i | \(-0.287712\pi\) |
−0.989747 | + | 0.142833i | \(0.954379\pi\) | |||||||
\(284\) | 23.8793 | + | 41.3602i | 1.41698 | + | 2.45428i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.36843 | + | 4.10224i | 0.140048 | + | 0.242571i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.02104 | + | 5.23260i | 0.177708 | + | 0.307800i | ||||
\(290\) | −7.27458 | −0.427178 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 38.6552 | 2.26213 | ||||||||
\(293\) | −2.60202 | + | 4.50684i | −0.152012 | + | 0.263292i | −0.931967 | − | 0.362543i | \(-0.881909\pi\) |
0.779955 | + | 0.625835i | \(0.215242\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.8377 | − | 30.8959i | −1.03855 | − | 1.79883i | ||||
\(296\) | 22.0275 | + | 38.1527i | 1.28032 | + | 2.21758i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.60135 | − | 4.50566i | 0.150692 | − | 0.261006i | ||||
\(299\) | −1.92654 | + | 3.33687i | −0.111415 | + | 0.192976i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.7412 | + | 28.9966i | −0.963347 | + | 1.66857i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.01906 | −0.287863 | ||||||||
\(305\) | −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 | 0 | ||||||||
\(310\) | 22.8295 | 1.29663 | ||||||||
\(311\) | 16.1984 | + | 28.0565i | 0.918528 | + | 1.59094i | 0.801652 | + | 0.597791i | \(0.203955\pi\) |
0.116876 | + | 0.993146i | \(0.462712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.759535 | − | 1.31555i | 0.0429315 | − | 0.0743595i | −0.843761 | − | 0.536719i | \(-0.819664\pi\) |
0.886693 | + | 0.462359i | \(0.152997\pi\) | |||||||
\(314\) | −7.08000 | −0.399548 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.83821 | 0.159662 | ||||||||
\(317\) | −10.7544 | + | 18.6272i | −0.604029 | + | 1.04621i | 0.388175 | + | 0.921586i | \(0.373106\pi\) |
−0.992204 | + | 0.124623i | \(0.960228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.706261 | − | 1.22328i | −0.0395430 | − | 0.0684905i | ||||
\(320\) | 31.9200 | 1.78439 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.30441 | 0.406428 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.58856 | − | 4.48352i | 0.143588 | − | 0.248701i | ||||
\(326\) | 0.927430 | 0.0513656 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.66315 | + | 6.34476i | −0.202263 | + | 0.350330i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.73902 | + | 16.8685i | −0.535305 | + | 0.927175i | 0.463844 | + | 0.885917i | \(0.346470\pi\) |
−0.999149 | + | 0.0412580i | \(0.986863\pi\) | |||||||
\(332\) | −3.63691 | + | 6.29931i | −0.199601 | + | 0.345719i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.70942 | + | 15.0852i | 0.476558 | + | 0.825423i | ||||
\(335\) | 18.7107 | + | 32.4079i | 1.02228 | + | 1.77063i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.84742 | − | 8.39598i | 0.264056 | − | 0.457358i | −0.703260 | − | 0.710933i | \(-0.748273\pi\) |
0.967316 | + | 0.253575i | \(0.0816063\pi\) | |||||||
\(338\) | −25.8995 | −1.40875 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 35.7472 | 1.93866 | ||||||||
\(341\) | 2.21642 | + | 3.83896i | 0.120026 | + | 0.207891i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.79558 | − | 15.2344i | −0.474226 | − | 0.821383i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.83948 | + | 8.38222i | 0.260172 | + | 0.450631i | ||||
\(347\) | 1.01302 | + | 1.75460i | 0.0543817 | + | 0.0941919i | 0.891935 | − | 0.452164i | \(-0.149348\pi\) |
−0.837553 | + | 0.546356i | \(0.816015\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.14577 | − | 14.1089i | −0.436033 | − | 0.755231i | 0.561346 | − | 0.827581i | \(-0.310284\pi\) |
−0.997379 | + | 0.0723497i | \(0.976950\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.80896 | + | 3.13321i | 0.0964180 | + | 0.167001i | ||||
\(353\) | 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 | ||||||||
\(356\) | 11.8440 | − | 20.5144i | 0.627731 | − | 1.08726i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.6323 | − | 21.8798i | −0.667639 | − | 1.15639i | ||||
\(359\) | −1.48363 | − | 2.56972i | −0.0783030 | − | 0.135625i | 0.824215 | − | 0.566277i | \(-0.191617\pi\) |
−0.902518 | + | 0.430652i | \(0.858283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.06549 | − | 12.2378i | 0.371868 | − | 0.644094i | ||||
\(362\) | −23.4285 | + | 40.5794i | −1.23137 | + | 2.13280i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | \(0.414592\pi\) | |||||||
\(368\) | 2.98914 | − | 5.17733i | 0.155819 | − | 0.269887i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 75.8207 | 3.94173 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.4846 | −1.31954 | −0.659771 | − | 0.751467i | \(-0.729347\pi\) | ||||
−0.659771 | + | 0.751467i | \(0.729347\pi\) | |||||||
\(374\) | 5.34798 | + | 9.26297i | 0.276537 | + | 0.478977i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.05947 | + | 13.9594i | −0.415635 | + | 0.719902i | ||||
\(377\) | −1.52969 | −0.0787829 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.85497 | 0.506216 | 0.253108 | − | 0.967438i | \(-0.418547\pi\) | ||||
0.253108 | + | 0.967438i | \(0.418547\pi\) | |||||||
\(380\) | −11.9143 | + | 20.6362i | −0.611191 | + | 1.05861i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.89016 | + | 17.1303i | 0.506025 | + | 0.876460i | ||||
\(383\) | −27.3127 | −1.39561 | −0.697806 | − | 0.716286i | \(-0.745840\pi\) | ||||
−0.697806 | + | 0.716286i | \(0.745840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −44.8370 | −2.28214 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.3114 | − | 26.5202i | 0.777321 | − | 1.34636i | ||||
\(389\) | −4.18446 | −0.212161 | −0.106080 | − | 0.994358i | \(-0.533830\pi\) | ||||
−0.106080 | + | 0.994358i | \(0.533830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.35019 | + | 7.53475i | −0.219999 | + | 0.381049i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.15624 | − | 12.3950i | 0.360526 | − | 0.624450i | ||||
\(395\) | 1.12114 | − | 1.94187i | 0.0564107 | − | 0.0977062i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.3354 | − | 26.5618i | −0.769664 | − | 1.33310i | −0.937745 | − | 0.347323i | \(-0.887091\pi\) |
0.168082 | − | 0.985773i | \(-0.446243\pi\) | |||||||
\(398\) | −17.1958 | − | 29.7840i | −0.861948 | − | 1.49294i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.01629 | + | 6.95642i | −0.200815 | + | 0.347821i | ||||
\(401\) | 6.84803 | 0.341974 | 0.170987 | − | 0.985273i | \(-0.445304\pi\) | ||||
0.170987 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.80055 | 0.239132 | ||||||||
\(404\) | 29.9961 | + | 51.9547i | 1.49236 | + | 2.58485i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | \(-0.315846\pi\) |
−0.998491 | + | 0.0549104i | \(0.982513\pi\) | |||||||
\(410\) | 6.30445 | + | 10.9196i | 0.311355 | + | 0.539282i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.11646 | − | 7.12991i | −0.202803 | − | 0.351265i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.87328 | + | 4.97666i | 0.141044 | + | 0.244295i | ||||
\(416\) | 3.91802 | 0.192097 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.12979 | −0.348729 | ||||||||
\(419\) | 11.2310 | − | 19.4526i | 0.548669 | − | 0.950322i | −0.449698 | − | 0.893181i | \(-0.648468\pi\) |
0.998366 | − | 0.0571410i | \(-0.0181984\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4177 | + | 18.0440i | 0.507728 | + | 0.879411i | 0.999960 | + | 0.00894684i | \(0.00284791\pi\) |
−0.492232 | + | 0.870464i | \(0.663819\pi\) | |||||||
\(422\) | −16.5271 | − | 28.6258i | −0.804527 | − | 1.39348i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.0739 | − | 22.6446i | 0.634923 | − | 1.09972i | ||||
\(425\) | 5.84505 | − | 10.1239i | 0.283526 | − | 0.491082i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 32.3649 | − | 56.0577i | 1.56442 | − | 2.70965i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.2752 | −1.46000 | ||||||||
\(431\) | 10.1213 | − | 17.5307i | 0.487527 | − | 0.844422i | −0.512370 | − | 0.858765i | \(-0.671232\pi\) |
0.999897 | + | 0.0143427i | \(0.00456557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6764 | 1.04170 | 0.520851 | − | 0.853648i | \(-0.325615\pi\) | ||||
0.520851 | + | 0.853648i | \(0.325615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 57.6693 | 2.76186 | ||||||||
\(437\) | −2.89978 | − | 5.02257i | −0.138715 | − | 0.240262i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7390 | + | 30.7249i | −0.846639 | + | 1.46642i | 0.0375520 | + | 0.999295i | \(0.488044\pi\) |
−0.884191 | + | 0.467126i | \(0.845289\pi\) | |||||||
\(440\) | −16.0172 | −0.763589 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.5832 | 0.550955 | ||||||||
\(443\) | −9.60313 | + | 16.6331i | −0.456258 | + | 0.790263i | −0.998760 | − | 0.0497923i | \(-0.984144\pi\) |
0.542501 | + | 0.840055i | \(0.317477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.35716 | − | 16.2071i | −0.443572 | − | 0.768289i | ||||
\(446\) | 11.1589 | 0.528390 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6082 | 1.39730 | 0.698648 | − | 0.715465i | \(-0.253785\pi\) | ||||
0.698648 | + | 0.715465i | \(0.253785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.22415 | + | 2.12029i | −0.0576429 | + | 0.0998405i | ||||
\(452\) | −6.24488 | −0.293735 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.5257 | + | 40.7478i | −1.10412 | + | 1.91239i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.78098 | − | 8.28090i | 0.223645 | − | 0.387364i | −0.732267 | − | 0.681017i | \(-0.761538\pi\) |
0.955912 | + | 0.293653i | \(0.0948711\pi\) | |||||||
\(458\) | 33.5031 | − | 58.0290i | 1.56550 | − | 2.71152i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.1913 | − | 24.5800i | −0.661673 | − | 1.14605i | ||||
\(461\) | 10.9187 | + | 18.9118i | 0.508536 | + | 0.880809i | 0.999951 | + | 0.00988416i | \(0.00314628\pi\) |
−0.491416 | + | 0.870925i | \(0.663520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0744 | − | 22.6456i | 0.607621 | − | 1.05243i | −0.384010 | − | 0.923329i | \(-0.625457\pi\) |
0.991631 | − | 0.129102i | \(-0.0412094\pi\) | |||||||
\(464\) | 2.37339 | 0.110182 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.9442 | −1.52611 | ||||||||
\(467\) | −17.4764 | − | 30.2699i | −0.808709 | − | 1.40073i | −0.913758 | − | 0.406258i | \(-0.866833\pi\) |
0.105049 | − | 0.994467i | \(-0.466500\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.8707 | + | 24.0248i | 0.639809 | + | 1.10818i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.7386 | + | 42.8485i | 1.13869 | + | 1.97226i | ||||
\(473\) | −2.93930 | − | 5.09102i | −0.135149 | − | 0.234086i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.89623 | + | 6.74848i | 0.178771 | + | 0.309641i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.2010 | − | 22.8649i | −0.603801 | − | 1.04581i | ||||
\(479\) | −29.8109 | −1.36209 | −0.681047 | − | 0.732240i | \(-0.738475\pi\) | ||||
−0.681047 | + | 0.732240i | \(0.738475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9434 | 0.726959 | ||||||||
\(482\) | −27.6516 | + | 47.8939i | −1.25949 | + | 2.18151i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.9467 | + | 29.3525i | 0.770304 | + | 1.33421i | ||||
\(485\) | −12.0965 | − | 20.9518i | −0.549276 | − | 0.951374i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2253 | + | 19.4428i | −0.508667 | + | 0.881037i | 0.491283 | + | 0.871000i | \(0.336528\pi\) |
−0.999950 | + | 0.0100365i | \(0.996805\pi\) | |||||||
\(488\) | 1.13370 | − | 1.96363i | 0.0513202 | − | 0.0888892i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.5222 | + | 30.3494i | −0.790767 | + | 1.36965i | 0.134726 | + | 0.990883i | \(0.456984\pi\) |
−0.925493 | + | 0.378765i | \(0.876349\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.45407 | −0.155564 | ||||||||
\(494\) | −3.86060 | + | 6.68675i | −0.173696 | + | 0.300851i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.44830 | −0.334438 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.93520 | −0.399994 | −0.199997 | − | 0.979796i | \(-0.564093\pi\) | ||||
−0.199997 | + | 0.979796i | \(0.564093\pi\) | |||||||
\(500\) | −7.92929 | − | 13.7339i | −0.354609 | − | 0.614200i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.28972 | − | 16.0903i | 0.414621 | − | 0.718144i | ||||
\(503\) | −12.6403 | −0.563603 | −0.281802 | − | 0.959473i | \(-0.590932\pi\) | ||||
−0.281802 | + | 0.959473i | \(0.590932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47.3958 | 2.10909 | ||||||||
\(506\) | 4.24620 | − | 7.35463i | 0.188766 | − | 0.326953i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.33732 | + | 12.7086i | 0.325541 | + | 0.563854i | ||||
\(509\) | −28.1110 | −1.24600 | −0.623000 | − | 0.782222i | \(-0.714086\pi\) | ||||
−0.623000 | + | 0.782222i | \(0.714086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −24.5070 | −1.08307 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.3830 | + | 21.4480i | −0.546192 | + | 0.946033i | ||||
\(515\) | −6.50427 | −0.286613 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.69331 | + | 4.66495i | −0.118452 | + | 0.205164i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.67288 | + | 15.0219i | −0.380331 | + | 0.658753i | ||||
\(521\) | 4.23768 | − | 7.33988i | 0.185656 | − | 0.321566i | −0.758141 | − | 0.652090i | \(-0.773892\pi\) |
0.943797 | + | 0.330524i | \(0.107226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7236 | − | 28.9662i | −0.731273 | − | 1.26660i | −0.956339 | − | 0.292259i | \(-0.905593\pi\) |
0.225066 | − | 0.974344i | \(-0.427740\pi\) | |||||||
\(524\) | −9.85035 | − | 17.0613i | −0.430315 | − | 0.745327i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.8341 | + | 39.5498i | −0.995613 | + | 1.72445i | ||||
\(527\) | 10.8398 | 0.472187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0921 | −0.699655 | ||||||||
\(530\) | −22.5008 | − | 38.9725i | −0.977371 | − | 1.69286i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.32569 | + | 2.29616i | 0.0574220 | + | 0.0994579i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.5693 | − | 44.2874i | −1.10546 | − | 1.91471i | ||||
\(536\) | −25.9493 | − | 44.9456i | −1.12084 | − | 1.94135i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.5461 | − | 18.2665i | −0.454677 | − | 0.787523i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.12929 | − | 15.8124i | −0.392499 | − | 0.679828i | 0.600280 | − | 0.799790i | \(-0.295056\pi\) |
−0.992778 | + | 0.119962i | \(0.961723\pi\) | |||||||
\(542\) | −43.7730 | −1.88021 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.84701 | 0.379312 | ||||||||
\(545\) | 22.7803 | − | 39.4567i | 0.975802 | − | 1.69014i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.88599 | − | 4.99869i | −0.123396 | − | 0.213728i | 0.797709 | − | 0.603043i | \(-0.206045\pi\) |
−0.921105 | + | 0.389315i | \(0.872712\pi\) | |||||||
\(548\) | −13.8558 | − | 23.9990i | −0.591892 | − | 1.02519i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.70532 | + | 9.88190i | −0.243276 | + | 0.421366i | ||||
\(551\) | 1.15122 | − | 1.99397i | 0.0490437 | − | 0.0849461i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.09227 | + | 10.5521i | −0.258836 | + | 0.448317i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 52.0029 | 2.20541 | ||||||||
\(557\) | −16.6911 | + | 28.9098i | −0.707223 | + | 1.22495i | 0.258661 | + | 0.965968i | \(0.416719\pi\) |
−0.965883 | + | 0.258977i | \(0.916614\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.36623 | −0.269263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.07286 | −0.171803 | ||||||||
\(563\) | −1.09566 | − | 1.89773i | −0.0461764 | − | 0.0799799i | 0.842013 | − | 0.539457i | \(-0.181370\pi\) |
−0.888190 | + | 0.459477i | \(0.848037\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.46683 | + | 4.27268i | −0.103780 | + | 0.179753i | ||||
\(566\) | 29.8079 | 1.25292 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −52.3278 | −2.19563 | ||||||||
\(569\) | 9.49302 | − | 16.4424i | 0.397968 | − | 0.689301i | −0.595507 | − | 0.803350i | \(-0.703049\pi\) |
0.993475 | + | 0.114049i | \(0.0363822\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8690 | + | 18.8257i | 0.454854 | + | 0.787831i | 0.998680 | − | 0.0513674i | \(-0.0163580\pi\) |
−0.543825 | + | 0.839198i | \(0.683025\pi\) | |||||||
\(572\) | −7.33717 | −0.306782 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.28172 | −0.387074 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.4516 | − | 26.7629i | 0.643258 | − | 1.11416i | −0.341443 | − | 0.939903i | \(-0.610916\pi\) |
0.984701 | − | 0.174253i | \(-0.0557511\pi\) | |||||||
\(578\) | −14.4217 | −0.599862 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.63398 | − | 9.75835i | 0.233938 | − | 0.405193i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.36902 | − | 7.56737i | 0.180946 | − | 0.313408i | ||||
\(584\) | −21.1767 | + | 36.6792i | −0.876299 | + | 1.51780i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.21069 | − | 10.7572i | −0.256561 | − | 0.444377i | ||||
\(587\) | −9.18332 | − | 15.9060i | −0.379036 | − | 0.656510i | 0.611886 | − | 0.790946i | \(-0.290411\pi\) |
−0.990922 | + | 0.134436i | \(0.957078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.61282 | + | 6.25759i | −0.148864 | + | 0.257840i | ||||
\(590\) | 85.1527 | 3.50568 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.7371 | −1.01669 | ||||||||
\(593\) | 13.8775 | + | 24.0365i | 0.569880 | + | 0.987061i | 0.996577 | + | 0.0826662i | \(0.0263435\pi\) |
−0.426698 | + | 0.904394i | \(0.640323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.02936 | + | 6.97905i | 0.165049 | + | 0.285873i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.59841 | − | 7.96468i | −0.188043 | − | 0.325700i | ||||
\(599\) | 0.201412 | + | 0.348855i | 0.00822945 | + | 0.0142538i | 0.870111 | − | 0.492856i | \(-0.164047\pi\) |
−0.861881 | + | 0.507110i | \(0.830714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.3733 | − | 21.4312i | −0.504717 | − | 0.874196i | −0.999985 | − | 0.00545577i | \(-0.998263\pi\) |
0.495268 | − | 0.868740i | \(-0.335070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.9313 | − | 44.9143i | −1.05513 | − | 1.82754i | ||||
\(605\) | 26.7769 | 1.08864 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0697 | −0.976957 | −0.488479 | − | 0.872576i | \(-0.662448\pi\) | ||||
−0.488479 | + | 0.872576i | \(0.662448\pi\) | |||||||
\(608\) | −2.94865 | + | 5.10721i | −0.119584 | + | 0.207125i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.95115 | − | 3.37950i | −0.0789999 | − | 0.136832i | ||||
\(611\) | 2.91672 | + | 5.05190i | 0.117998 | + | 0.204378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1907 | − | 17.6509i | 0.411600 | − | 0.712912i | −0.583465 | − | 0.812138i | \(-0.698303\pi\) |
0.995065 | + | 0.0992261i | \(0.0316367\pi\) | |||||||
\(614\) | 5.96879 | − | 10.3382i | 0.240881 | − | 0.417218i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.9315 | − | 36.2544i | 0.842669 | − | 1.45955i | −0.0449604 | − | 0.998989i | \(-0.514316\pi\) |
0.887630 | − | 0.460558i | \(-0.152350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.8219 | −0.595743 | −0.297871 | − | 0.954606i | \(-0.596277\pi\) | ||||
−0.297871 | + | 0.954606i | \(0.596277\pi\) | |||||||
\(620\) | −17.6809 | + | 30.6242i | −0.710081 | + | 1.22990i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −77.3270 | −3.10053 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1861 | −1.20744 | ||||||||
\(626\) | 1.81291 | + | 3.14005i | 0.0724585 | + | 0.125502i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.48329 | − | 9.49734i | 0.218807 | − | 0.378985i | ||||
\(629\) | 36.0007 | 1.43544 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0294 | −0.837169 | −0.418585 | − | 0.908178i | \(-0.637474\pi\) | ||||
−0.418585 | + | 0.908178i | \(0.637474\pi\) | |||||||
\(632\) | −1.55487 | + | 2.69312i | −0.0618496 | + | 0.107127i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.6694 | − | 44.4607i | −1.01946 | − | 1.76576i | ||||
\(635\) | 11.5935 | 0.460072 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.37150 | 0.133479 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −30.2882 | + | 52.4607i | −1.19725 | + | 2.07369i | ||||
\(641\) | −11.9318 | −0.471279 | −0.235640 | − | 0.971840i | \(-0.575719\pi\) | ||||
−0.235640 | + | 0.971840i | \(0.575719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9678 | − | 34.5852i | 0.787452 | − | 1.36391i | −0.140072 | − | 0.990141i | \(-0.544733\pi\) |
0.927524 | − | 0.373765i | \(-0.121933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.71733 | + | 15.0989i | −0.342979 | + | 0.594057i | ||||
\(647\) | 0.494477 | − | 0.856459i | 0.0194399 | − | 0.0336709i | −0.856142 | − | 0.516741i | \(-0.827145\pi\) |
0.875582 | + | 0.483070i | \(0.160478\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.26714 | + | 14.3191i | 0.324514 | + | 0.562074i | ||||
\(650\) | 6.17856 | + | 10.7016i | 0.242343 | + | 0.419751i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.718272 | + | 1.24408i | −0.0281297 | + | 0.0487221i | ||||
\(653\) | −22.7147 | −0.888894 | −0.444447 | − | 0.895805i | \(-0.646600\pi\) | ||||
−0.444447 | + | 0.895805i | \(0.646600\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5642 | −0.608144 | ||||||||
\(656\) | −2.05688 | − | 3.56262i | −0.0803076 | − | 0.139097i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1943 | + | 33.2454i | 0.747702 | + | 1.29506i | 0.948922 | + | 0.315512i | \(0.102176\pi\) |
−0.201220 | + | 0.979546i | \(0.564491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.9629 | + | 29.3806i | 0.659780 | + | 1.14277i | 0.980672 | + | 0.195657i | \(0.0626839\pi\) |
−0.320892 | + | 0.947116i | \(0.603983\pi\) | |||||||
\(662\) | −23.2458 | − | 40.2628i | −0.903472 | − | 1.56486i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.98486 | − | 6.90198i | −0.154642 | − | 0.267849i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.37124 | + | 2.37505i | 0.0530944 | + | 0.0919623i | ||||
\(668\) | −26.9809 | −1.04392 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −89.3201 | −3.45074 | ||||||||
\(671\) | 0.378860 | − | 0.656205i | 0.0146257 | − | 0.0253325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1030 | − | 27.8912i | −0.620725 | − | 1.07513i | −0.989351 | − | 0.145549i | \(-0.953505\pi\) |
0.368626 | − | 0.929578i | \(-0.379828\pi\) | |||||||
\(674\) | 11.5702 | + | 20.0401i | 0.445666 | + | 0.771916i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.0585 | − | 34.7424i | 0.771483 | − | 1.33625i | ||||
\(677\) | 18.9842 | − | 32.8816i | 0.729622 | − | 1.26374i | −0.227421 | − | 0.973797i | \(-0.573029\pi\) |
0.957043 | − | 0.289946i | \(-0.0936375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −19.5836 | + | 33.9198i | −0.750997 | + | 1.30076i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.5806 | −0.405153 | ||||||||
\(683\) | −7.59357 | + | 13.1525i | −0.290560 | + | 0.503265i | −0.973942 | − | 0.226796i | \(-0.927175\pi\) |
0.683382 | + | 0.730061i | \(0.260508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.8932 | −0.836495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.87754 | 0.376578 | ||||||||
\(689\) | −4.73142 | − | 8.19507i | −0.180253 | − | 0.312207i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.34574 | − | 2.33089i | 0.0511943 | − | 0.0886711i | −0.839293 | − | 0.543680i | \(-0.817031\pi\) |
0.890487 | + | 0.455009i | \(0.150364\pi\) | |||||||
\(692\) | −14.9922 | −0.569919 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.83589 | −0.183568 | ||||||||
\(695\) | 20.5420 | − | 35.5798i | 0.779203 | − | 1.34962i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.99344 | + | 5.18480i | 0.113385 | + | 0.196388i | ||||
\(698\) | 38.8858 | 1.47185 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8515 | 0.447625 | 0.223813 | − | 0.974632i | \(-0.428150\pi\) | ||||
0.223813 | + | 0.974632i | \(0.428150\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9988 | + | 20.7826i | −0.452544 | + | 0.783829i | ||||
\(704\) | −14.7938 | −0.557562 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.3617 | + | 35.2675i | −0.766323 | + | 1.32731i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.5167 | − | 35.5359i | 0.770520 | − | 1.33458i | −0.166759 | − | 0.985998i | \(-0.553330\pi\) |
0.937278 | − | 0.348582i | \(-0.113337\pi\) | |||||||
\(710\) | −45.0294 | + | 77.9931i | −1.68992 | + | 2.92703i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.9772 | + | 22.4771i | 0.486339 | + | 0.842364i | ||||
\(713\) | −4.30328 | − | 7.45351i | −0.161159 | − | 0.279136i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.89830 | + | 5.02001i | −0.108390 | + | 0.187738i | ||||
\(716\) | 39.1337 | 1.46250 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.08246 | 0.264315 | ||||||||
\(719\) | 10.4555 | + | 18.1094i | 0.389923 | + | 0.675366i | 0.992439 | − | 0.122741i | \(-0.0391685\pi\) |
−0.602516 | + | 0.798107i | \(0.705835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.8644 | + | 29.2100i | 0.627628 | + | 1.08708i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −36.2896 | − | 62.8554i | −1.34869 | − | 2.33600i | ||||
\(725\) | −1.84243 | − | 3.19119i | −0.0684263 | − | 0.118518i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.32165 | − | 2.28917i | −0.0490173 | − | 0.0849005i | 0.840476 | − | 0.541849i | \(-0.182276\pi\) |
−0.889493 | + | 0.456949i | \(0.848942\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 36.4462 | + | 63.1267i | 1.34893 | + | 2.33642i | ||||
\(731\) | −14.3751 | −0.531683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.1489 | −0.522602 | −0.261301 | − | 0.965257i | \(-0.584152\pi\) | ||||
−0.261301 | + | 0.965257i | \(0.584152\pi\) | |||||||
\(734\) | −12.1223 | + | 20.9964i | −0.447442 | + | 0.774992i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.51218 | − | 6.08327i | −0.129461 | − | 0.224232i | ||||
\(737\) | −8.67174 | − | 15.0199i | −0.319428 | − | 0.553265i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.85905 | + | 13.6123i | −0.289100 | + | 0.500736i | −0.973595 | − | 0.228282i | \(-0.926689\pi\) |
0.684495 | + | 0.729017i | \(0.260023\pi\) | |||||||
\(740\) | −58.7212 | + | 101.708i | −2.15864 | + | 3.73887i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5496 | + | 18.2724i | −0.387026 | + | 0.670348i | −0.992048 | − | 0.125861i | \(-0.959831\pi\) |
0.605022 | + | 0.796208i | \(0.293164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.36665 | 0.233256 | ||||||||
\(746\) | 30.4142 | − | 52.6789i | 1.11354 | − | 1.92871i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.5675 | −0.605768 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0370 | 0.475725 | 0.237863 | − | 0.971299i | \(-0.423553\pi\) | ||||
0.237863 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(752\) | −4.52544 | − | 7.83829i | −0.165026 | − | 0.285833i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.82558 | − | 3.16200i | 0.0664838 | − | 0.115153i | ||||
\(755\) | −40.9732 | −1.49117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6856 | −0.461065 | −0.230532 | − | 0.973065i | \(-0.574047\pi\) | ||||
−0.230532 | + | 0.973065i | \(0.574047\pi\) | |||||||
\(758\) | −11.7613 | + | 20.3711i | −0.427188 | + | 0.739912i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.0542 | − | 22.6105i | −0.473525 | − | 0.820169i | ||||
\(761\) | −6.04077 | −0.218978 | −0.109489 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109489 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −30.6388 | −1.10847 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5959 | − | 56.4577i | 1.17774 | − | 2.03990i | ||||
\(767\) | 17.9058 | 0.646540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.108129 | + | 0.187285i | −0.00389924 | + | 0.00675368i | −0.867968 | − | 0.496619i | \(-0.834575\pi\) |
0.864069 | + | 0.503373i | \(0.167908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 34.7251 | − | 60.1457i | 1.24979 | − | 2.16469i | ||||
\(773\) | 18.8132 | − | 32.5854i | 0.676663 | − | 1.17202i | −0.299316 | − | 0.954154i | \(-0.596759\pi\) |
0.975980 | − | 0.217861i | \(-0.0699081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.78202 | + | 10.0148i | 0.207696 | + | 0.359741i | ||||
\(776\) | 16.7763 | + | 29.0575i | 0.602235 | + | 1.04310i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.99388 | − | 8.64965i | 0.179039 | − | 0.310105i | ||||
\(779\) | −3.99078 | −0.142985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4869 | −0.625730 | ||||||||
\(782\) | −10.3833 | − | 17.9845i | −0.371307 | − | 0.643123i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.33198 | − | 7.50321i | −0.154615 | − | 0.267801i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.4067 | + | 26.6853i | 0.549191 | + | 0.951226i | 0.998330 | + | 0.0577648i | \(0.0183973\pi\) |
−0.449139 | + | 0.893462i | \(0.648269\pi\) | |||||||
\(788\) | 11.0847 | + | 19.1992i | 0.394875 | + | 0.683943i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.67601 | + | 4.63499i | 0.0952083 | + | 0.164906i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.410286 | − | 0.710636i | −0.0145697 | − | 0.0252354i | ||||
\(794\) | 73.2074 | 2.59803 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53.2710 | 1.88814 | ||||||||
\(797\) | −17.9792 | + | 31.1408i | −0.636855 | + | 1.10306i | 0.349264 | + | 0.937024i | \(0.386431\pi\) |
−0.986119 | + | 0.166040i | \(0.946902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.58602 | + | 11.4073i | 0.232997 | + | 0.403562i | ||||
\(800\) | 4.71907 | + | 8.17367i | 0.166844 | + | 0.288983i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.17268 | + | 14.1555i | −0.288587 | + | 0.499848i | ||||
\(803\) | −7.07684 | + | 12.2574i | −0.249736 | + | 0.432556i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.72914 | + | 9.92315i | −0.201800 | + | 0.349528i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −65.7318 | −2.31244 | ||||||||
\(809\) | 19.4818 | − | 33.7435i | 0.684943 | − | 1.18636i | −0.288511 | − | 0.957477i | \(-0.593160\pi\) |
0.973455 | − | 0.228880i | \(-0.0735065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2811 | 0.993082 | 0.496541 | − | 0.868013i | \(-0.334603\pi\) | ||||
0.496541 | + | 0.868013i | \(0.334603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35.1401 | −1.23166 | ||||||||
\(815\) | 0.567459 | + | 0.982867i | 0.0198772 | + | 0.0344283i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.79113 | − | 8.29849i | 0.167621 | − | 0.290327i | ||||
\(818\) | 43.6076 | 1.52471 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.5306 | −0.682037 | ||||||||
\(821\) | 20.7917 | − | 36.0123i | 0.725635 | − | 1.25684i | −0.233077 | − | 0.972458i | \(-0.574879\pi\) |
0.958712 | − | 0.284378i | \(-0.0917872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.22999 | − | 7.32656i | −0.147448 | − | 0.255388i | 0.782835 | − | 0.622229i | \(-0.213773\pi\) |
−0.930284 | + | 0.366841i | \(0.880439\pi\) | |||||||
\(824\) | 9.02057 | 0.314247 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | \(-0.740064\pi\) |
0.973533 | + | 0.228547i | \(0.0733973\pi\) | |||||||
\(830\) | −13.7163 | −0.476099 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.01045 | + | 13.8745i | −0.277712 | + | 0.481012i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.6579 | + | 18.4601i | −0.368832 | + | 0.638836i | ||||
\(836\) | 5.52185 | − | 9.56412i | 0.190977 | − | 0.330782i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.8068 | + | 46.4308i | 0.926027 | + | 1.60393i | ||||
\(839\) | 14.8006 | + | 25.6354i | 0.510974 | + | 0.885033i | 0.999919 | + | 0.0127182i | \(0.00404843\pi\) |
−0.488945 | + | 0.872314i | \(0.662618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.9556 | − | 24.1718i | 0.481228 | − | 0.833512i | ||||
\(842\) | −49.7314 | −1.71386 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 51.1994 | 1.76236 | ||||||||
\(845\) | −15.8469 | − | 27.4477i | −0.545151 | − | 0.944228i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.34105 | + | 12.7151i | 0.252093 | + | 0.436638i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.9514 | + | 24.1645i | 0.478528 | + | 0.828834i | ||||
\(851\) | −14.2920 | − | 24.7544i | −0.489922 | − | 0.848570i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0619 | + | 26.0880i | 0.515710 | + | 0.893236i | 0.999834 | + | 0.0182366i | \(0.00580520\pi\) |
−0.484124 | + | 0.875000i | \(0.660861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.4613 | + | 61.4208i | 1.21204 | + | 2.09932i | ||||
\(857\) | 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 | \(0.479441\pi\) | |||||||
\(860\) | 23.4474 | − | 40.6121i | 0.799551 | − | 1.38486i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.1583 | + | 41.8434i | 0.822835 | + | 1.42519i | ||||
\(863\) | −0.213559 | − | 0.369895i | −0.00726963 | − | 0.0125914i | 0.862368 | − | 0.506282i | \(-0.168981\pi\) |
−0.869637 | + | 0.493691i | \(0.835647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.92218 | + | 10.2575i | −0.201360 | + | 0.348766i | ||||
\(866\) | −25.8694 | + | 44.8071i | −0.879077 | + | 1.52261i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.519608 | + | 0.899987i | −0.0176265 | + | 0.0305300i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7821 | −0.636407 | ||||||||
\(872\) | −31.5933 | + | 54.7212i | −1.06988 | + | 1.85309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.8428 | 0.468240 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2608 | 0.380249 | 0.190124 | − | 0.981760i | \(-0.439111\pi\) | ||||
0.190124 | + | 0.981760i | \(0.439111\pi\) | |||||||
\(878\) | −42.3408 | − | 73.3364i | −1.42893 | − | 2.47498i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.49687 | − | 7.78881i | 0.151589 | − | 0.262561i | ||||
\(881\) | −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 | \(-0.528429\pi\) | ||||
−0.0891952 | + | 0.996014i | \(0.528429\pi\) | |||||||
\(884\) | −8.97088 | + | 15.5380i | −0.301723 | + | 0.522600i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.9214 | − | 39.7010i | −0.770060 | − | 1.33378i | ||||
\(887\) | 57.5664 | 1.93289 | 0.966446 | − | 0.256870i | \(-0.0826913\pi\) | ||||
0.966446 | + | 0.256870i | \(0.0826913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 44.6686 | 1.49730 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.64231 | + | 14.9689i | −0.289366 | + | 0.501197i | ||||
\(893\) | −8.78032 | −0.293822 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4585 | − | 26.7749i | 0.516720 | − | 0.894985i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.3354 | + | 61.2027i | −1.17916 | + | 2.04236i | ||||
\(899\) | 1.70842 | − | 2.95906i | 0.0569788 | − | 0.0986903i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6837 | − | 18.5047i | −0.355925 | − | 0.616480i | ||||
\(902\) | −2.92188 | − | 5.06085i | −0.0972881 | − | 0.168508i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.42117 | − | 5.92565i | 0.113787 | − | 0.197084i | ||||
\(905\) | −57.3400 | −1.90605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8972 | 0.693879 | 0.346939 | − | 0.937888i | \(-0.387221\pi\) | ||||
0.346939 | + | 0.937888i | \(0.387221\pi\) | |||||||
\(908\) | −36.4402 | − | 63.1163i | −1.20931 | − | 2.09459i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.3819 | − | 19.7141i | −0.377101 | − | 0.653157i | 0.613539 | − | 0.789665i | \(-0.289746\pi\) |
−0.990639 | + | 0.136508i | \(0.956412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.33166 | − | 2.30650i | −0.0440715 | − | 0.0763340i | ||||
\(914\) | 11.4116 | + | 19.7654i | 0.377461 | + | 0.653782i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 51.8946 | + | 89.8841i | 1.71465 | + | 2.96986i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6515 | + | 32.3054i | 0.615257 | + | 1.06566i | 0.990339 | + | 0.138664i | \(0.0442809\pi\) |
−0.375083 | + | 0.926991i | \(0.622386\pi\) | |||||||
\(920\) | 31.0980 | 1.02527 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −52.1231 | −1.71658 | ||||||||
\(923\) | −9.46870 | + | 16.4003i | −0.311666 | + | 0.539822i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.2031 | + | 33.2607i | 0.631394 | + | 1.09361i | ||||
\(926\) | 31.2070 | + | 54.0521i | 1.02553 | + | 1.77626i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.39434 | − | 2.41508i | 0.0457716 | − | 0.0792787i | ||||
\(929\) | −2.83363 | + | 4.90799i | −0.0929683 | + | 0.161026i | −0.908759 | − | 0.417322i | \(-0.862969\pi\) |
0.815791 | + | 0.578347i | \(0.196302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25.5145 | − | 44.1923i | 0.835754 | − | 1.44757i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 83.4275 | 2.72983 | ||||||||
\(935\) | −6.54444 | + | 11.3353i | −0.214026 | + | 0.370704i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.64754 | 0.249834 | 0.124917 | − | 0.992167i | \(-0.460134\pi\) | ||||
0.124917 | + | 0.992167i | \(0.460134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −42.9702 | −1.40153 | ||||||||
\(941\) | −10.2276 | − | 17.7147i | −0.333410 | − | 0.577483i | 0.649768 | − | 0.760132i | \(-0.274866\pi\) |
−0.983178 | + | 0.182650i | \(0.941533\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.37674 | − | 4.11663i | 0.0773973 | − | 0.134056i | ||||
\(944\) | −27.7817 | −0.904219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.0315 | 0.456202 | ||||||||
\(947\) | −2.38343 | + | 4.12823i | −0.0774512 | + | 0.134149i | −0.902150 | − | 0.431423i | \(-0.858012\pi\) |
0.824698 | + | 0.565573i | \(0.191345\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.66385 | + | 13.2742i | 0.248779 | + | 0.430898i | ||||
\(950\) | −18.5996 | −0.603451 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.9412 | 1.58536 | 0.792680 | − | 0.609638i | \(-0.208685\pi\) | ||||
0.792680 | + | 0.609638i | \(0.208685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1028 | + | 20.9627i | −0.391638 | + | 0.678337i | ||||
\(956\) | 40.8955 | 1.32266 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.5773 | − | 61.6217i | 1.14945 | − | 1.99091i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1386 | − | 17.5605i | 0.327050 | − | 0.566468i | ||||
\(962\) | −19.0275 | + | 32.9565i | −0.613470 | + | 1.06256i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −42.8309 | − | 74.1854i | −1.37949 | − | 2.38935i | ||||
\(965\) | −27.4340 | − | 47.5171i | −0.883132 | − | 1.52963i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.95856 | + | 5.12438i | −0.0951409 | + | 0.164789i | −0.909667 | − | 0.415337i | \(-0.863664\pi\) |
0.814526 | + | 0.580126i | \(0.196997\pi\) | |||||||
\(968\) | −37.1361 | −1.19360 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 57.7458 | 1.85410 | ||||||||
\(971\) | 14.4888 | + | 25.0953i | 0.464966 | + | 0.805345i | 0.999200 | − | 0.0399914i | \(-0.0127331\pi\) |
−0.534234 | + | 0.845337i | \(0.679400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −26.7933 | − | 46.4074i | −0.858513 | − | 1.48699i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.636580 | + | 1.10259i | 0.0203764 | + | 0.0352930i | ||||
\(977\) | 11.4228 | + | 19.7848i | 0.365447 | + | 0.632972i | 0.988848 | − | 0.148930i | \(-0.0475830\pi\) |
−0.623401 | + | 0.781902i | \(0.714250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.33670 | + | 7.51139i | 0.138602 | + | 0.240065i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.8232 | − | 72.4400i | −1.33463 | − | 2.31165i | ||||
\(983\) | −31.2703 | −0.997367 | −0.498684 | − | 0.866784i | \(-0.666183\pi\) | ||||
−0.498684 | + | 0.866784i | \(0.666183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5145 | 0.558059 | ||||||||
\(986\) | 4.12221 | − | 7.13988i | 0.131278 | − | 0.227380i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.97988 | − | 10.3574i | −0.190245 | − | 0.329514i | ||||
\(989\) | 5.70679 | + | 9.88444i | 0.181465 | + | 0.314307i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.50732 | − | 6.07485i | 0.111414 | − | 0.192974i | −0.804927 | − | 0.593374i | \(-0.797796\pi\) |
0.916340 | + | 0.400400i | \(0.131129\pi\) | |||||||
\(992\) | −4.37581 | + | 7.57912i | −0.138932 | + | 0.240637i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0429 | − | 36.4474i | 0.667105 | − | 1.15546i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2878 | 0.674191 | 0.337095 | − | 0.941470i | \(-0.390555\pi\) | ||||
0.337095 | + | 0.941470i | \(0.390555\pi\) | |||||||
\(998\) | 10.6636 | − | 18.4698i | 0.337549 | − | 0.584653i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))