Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(79,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 214.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.214 |
Dual form | 735.2.q.d.79.1 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67303 | + | 0.965926i | −1.18301 | + | 0.683013i | −0.956710 | − | 0.291044i | \(-0.905997\pi\) |
−0.226303 | + | 0.974057i | \(0.572664\pi\) | |||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.866025 | − | 1.50000i | 0.433013 | − | 0.750000i | ||||
\(5\) | 2.20711 | + | 0.358719i | 0.987048 | + | 0.160424i | ||||
\(6\) | 1.93185 | 0.788675 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.517638i | − | 0.183013i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −4.03906 | + | 1.53175i | −1.27726 | + | 0.484383i | ||||
\(11\) | 1.73205 | − | 3.00000i | 0.522233 | − | 0.904534i | −0.477432 | − | 0.878668i | \(-0.658432\pi\) |
0.999665 | − | 0.0258656i | \(-0.00823419\pi\) | |||||||
\(12\) | −1.50000 | + | 0.866025i | −0.433013 | + | 0.250000i | ||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.73205 | − | 1.41421i | −0.447214 | − | 0.365148i | ||||
\(16\) | 2.23205 | + | 3.86603i | 0.558013 | + | 0.966506i | ||||
\(17\) | −3.46410 | − | 2.00000i | −0.840168 | − | 0.485071i | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) |
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(18\) | −1.67303 | − | 0.965926i | −0.394338 | − | 0.227671i | ||||
\(19\) | −0.189469 | − | 0.328169i | −0.0434671 | − | 0.0752872i | 0.843473 | − | 0.537171i | \(-0.180507\pi\) |
−0.886940 | + | 0.461884i | \(0.847174\pi\) | |||||||
\(20\) | 2.44949 | − | 3.00000i | 0.547723 | − | 0.670820i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.69213i | 1.42677i | ||||||||
\(23\) | −5.46739 | + | 3.15660i | −1.14003 | + | 0.658196i | −0.946438 | − | 0.322886i | \(-0.895347\pi\) |
−0.193591 | + | 0.981082i | \(0.562013\pi\) | |||||||
\(24\) | −0.258819 | + | 0.448288i | −0.0528312 | + | 0.0915064i | ||||
\(25\) | 4.74264 | + | 1.58346i | 0.948528 | + | 0.316693i | ||||
\(26\) | 3.86370 | + | 6.69213i | 0.757735 | + | 1.31243i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.92820 | −1.65793 | −0.828963 | − | 0.559304i | \(-0.811069\pi\) | ||||
−0.828963 | + | 0.559304i | \(0.811069\pi\) | |||||||
\(30\) | 4.26380 | + | 0.692993i | 0.778460 | + | 0.126523i | ||||
\(31\) | 3.67423 | − | 6.36396i | 0.659912 | − | 1.14300i | −0.320726 | − | 0.947172i | \(-0.603927\pi\) |
0.980638 | − | 0.195829i | \(-0.0627398\pi\) | |||||||
\(32\) | −6.57201 | − | 3.79435i | −1.16178 | − | 0.670753i | ||||
\(33\) | −3.00000 | + | 1.73205i | −0.522233 | + | 0.301511i | ||||
\(34\) | 7.72741 | 1.32524 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.73205 | 0.288675 | ||||||||
\(37\) | −0.656339 | + | 0.378937i | −0.107901 | + | 0.0622969i | −0.552980 | − | 0.833195i | \(-0.686509\pi\) |
0.445078 | + | 0.895492i | \(0.353176\pi\) | |||||||
\(38\) | 0.633975 | + | 0.366025i | 0.102844 | + | 0.0593772i | ||||
\(39\) | −2.00000 | + | 3.46410i | −0.320256 | + | 0.554700i | ||||
\(40\) | 0.185687 | − | 1.14248i | 0.0293597 | − | 0.180642i | ||||
\(41\) | −8.48528 | −1.32518 | −0.662589 | − | 0.748983i | \(-0.730542\pi\) | ||||
−0.662589 | + | 0.748983i | \(0.730542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −3.00000 | − | 5.19615i | −0.452267 | − | 0.783349i | ||||
\(45\) | 0.792893 | + | 2.09077i | 0.118198 | + | 0.311674i | ||||
\(46\) | 6.09808 | − | 10.5622i | 0.899112 | − | 1.55731i | ||||
\(47\) | 5.19615 | − | 3.00000i | 0.757937 | − | 0.437595i | −0.0706177 | − | 0.997503i | \(-0.522497\pi\) |
0.828554 | + | 0.559908i | \(0.189164\pi\) | |||||||
\(48\) | − | 4.46410i | − | 0.644338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.46410 | + | 1.93185i | −1.33843 | + | 0.273205i | ||||
\(51\) | 2.00000 | + | 3.46410i | 0.280056 | + | 0.485071i | ||||
\(52\) | −6.00000 | − | 3.46410i | −0.832050 | − | 0.480384i | ||||
\(53\) | −6.36396 | − | 3.67423i | −0.874157 | − | 0.504695i | −0.00542976 | − | 0.999985i | \(-0.501728\pi\) |
−0.868728 | + | 0.495290i | \(0.835062\pi\) | |||||||
\(54\) | 0.965926 | + | 1.67303i | 0.131446 | + | 0.227671i | ||||
\(55\) | 4.89898 | − | 6.00000i | 0.660578 | − | 0.809040i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.378937i | 0.0501915i | ||||||||
\(58\) | 14.9372 | − | 8.62398i | 1.96135 | − | 1.13238i | ||||
\(59\) | 5.27792 | − | 9.14162i | 0.687126 | − | 1.19014i | −0.285637 | − | 0.958338i | \(-0.592205\pi\) |
0.972764 | − | 0.231800i | \(-0.0744614\pi\) | |||||||
\(60\) | −3.62132 | + | 1.37333i | −0.467510 | + | 0.177296i | ||||
\(61\) | −4.57081 | − | 7.91688i | −0.585232 | − | 1.01365i | −0.994846 | − | 0.101393i | \(-0.967670\pi\) |
0.409614 | − | 0.912259i | \(-0.365663\pi\) | |||||||
\(62\) | 14.1962i | 1.80291i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.73205 | 0.716506 | ||||||||
\(65\) | 1.43488 | − | 8.82843i | 0.177975 | − | 1.09503i | ||||
\(66\) | 3.34607 | − | 5.79555i | 0.411872 | − | 0.713384i | ||||
\(67\) | 6.03579 | + | 3.48477i | 0.737389 | + | 0.425732i | 0.821119 | − | 0.570757i | \(-0.193350\pi\) |
−0.0837300 | + | 0.996488i | \(0.526683\pi\) | |||||||
\(68\) | −6.00000 | + | 3.46410i | −0.727607 | + | 0.420084i | ||||
\(69\) | 6.31319 | 0.760019 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3923 | 1.70805 | 0.854026 | − | 0.520230i | \(-0.174154\pi\) | ||||
0.854026 | + | 0.520230i | \(0.174154\pi\) | |||||||
\(72\) | 0.448288 | − | 0.258819i | 0.0528312 | − | 0.0305021i | ||||
\(73\) | 9.46410 | + | 5.46410i | 1.10769 | + | 0.639525i | 0.938230 | − | 0.346012i | \(-0.112465\pi\) |
0.169459 | + | 0.985537i | \(0.445798\pi\) | |||||||
\(74\) | 0.732051 | − | 1.26795i | 0.0850992 | − | 0.147396i | ||||
\(75\) | −3.31552 | − | 3.74264i | −0.382843 | − | 0.432163i | ||||
\(76\) | −0.656339 | −0.0752872 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 7.72741i | − | 0.874957i | ||||||
\(79\) | −5.73205 | − | 9.92820i | −0.644906 | − | 1.11701i | −0.984323 | − | 0.176374i | \(-0.943563\pi\) |
0.339417 | − | 0.940636i | \(-0.389770\pi\) | |||||||
\(80\) | 3.53956 | + | 9.33341i | 0.395734 | + | 1.04351i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 14.1962 | − | 8.19615i | 1.56770 | − | 0.905114i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.92820 | − | 5.65685i | −0.751469 | − | 0.613572i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.73205 | + | 4.46410i | 0.828963 | + | 0.478602i | ||||
\(88\) | −1.55291 | − | 0.896575i | −0.165541 | − | 0.0955753i | ||||
\(89\) | −2.07055 | − | 3.58630i | −0.219478 | − | 0.380147i | 0.735170 | − | 0.677882i | \(-0.237102\pi\) |
−0.954649 | + | 0.297735i | \(0.903769\pi\) | |||||||
\(90\) | −3.34607 | − | 2.73205i | −0.352706 | − | 0.287983i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.9348i | 1.14003i | ||||||||
\(93\) | −6.36396 | + | 3.67423i | −0.659912 | + | 0.381000i | ||||
\(94\) | −5.79555 | + | 10.0382i | −0.597766 | + | 1.03536i | ||||
\(95\) | −0.300457 | − | 0.792271i | −0.0308262 | − | 0.0812853i | ||||
\(96\) | 3.79435 | + | 6.57201i | 0.387260 | + | 0.670753i | ||||
\(97\) | 5.07180i | 0.514963i | 0.966283 | + | 0.257481i | \(0.0828926\pi\) | ||||
−0.966283 | + | 0.257481i | \(0.917107\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46410 | 0.348155 | ||||||||
\(100\) | 6.48244 | − | 5.74264i | 0.648244 | − | 0.574264i | ||||
\(101\) | 6.31319 | − | 10.9348i | 0.628186 | − | 1.08805i | −0.359729 | − | 0.933057i | \(-0.617131\pi\) |
0.987915 | − | 0.154994i | \(-0.0495357\pi\) | |||||||
\(102\) | −6.69213 | − | 3.86370i | −0.662620 | − | 0.382564i | ||||
\(103\) | 12.0000 | − | 6.92820i | 1.18240 | − | 0.682656i | 0.225828 | − | 0.974167i | \(-0.427491\pi\) |
0.956567 | + | 0.291511i | \(0.0941580\pi\) | |||||||
\(104\) | −2.07055 | −0.203034 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.1962 | 1.37885 | ||||||||
\(107\) | −13.4722 | + | 7.77817i | −1.30241 | + | 0.751945i | −0.980816 | − | 0.194935i | \(-0.937551\pi\) |
−0.321590 | + | 0.946879i | \(0.604217\pi\) | |||||||
\(108\) | −1.50000 | − | 0.866025i | −0.144338 | − | 0.0833333i | ||||
\(109\) | −5.92820 | + | 10.2679i | −0.567819 | + | 0.983491i | 0.428962 | + | 0.903322i | \(0.358879\pi\) |
−0.996781 | + | 0.0801688i | \(0.974454\pi\) | |||||||
\(110\) | −2.40060 | + | 14.7702i | −0.228888 | + | 1.40829i | ||||
\(111\) | 0.757875 | 0.0719343 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.378937i | − | 0.0356474i | −0.999841 | − | 0.0178237i | \(-0.994326\pi\) | ||
0.999841 | − | 0.0178237i | \(-0.00567377\pi\) | |||||||
\(114\) | −0.366025 | − | 0.633975i | −0.0342814 | − | 0.0593772i | ||||
\(115\) | −13.1994 | + | 5.00569i | −1.23085 | + | 0.466783i | ||||
\(116\) | −7.73205 | + | 13.3923i | −0.717903 | + | 1.24344i | ||||
\(117\) | 3.46410 | − | 2.00000i | 0.320256 | − | 0.184900i | ||||
\(118\) | 20.3923i | 1.87726i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.732051 | + | 0.896575i | −0.0668268 | + | 0.0818458i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 15.2942 | + | 8.83013i | 1.38467 | + | 0.799442i | ||||
\(123\) | 7.34847 | + | 4.24264i | 0.662589 | + | 0.382546i | ||||
\(124\) | −6.36396 | − | 11.0227i | −0.571501 | − | 0.989868i | ||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.82843i | − | 0.250982i | −0.992095 | − | 0.125491i | \(-0.959949\pi\) | ||
0.992095 | − | 0.125491i | \(-0.0400507\pi\) | |||||||
\(128\) | 3.55412 | − | 2.05197i | 0.314142 | − | 0.181370i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.12701 | + | 16.1562i | 0.537374 | + | 1.41700i | ||||
\(131\) | −2.82843 | − | 4.89898i | −0.247121 | − | 0.428026i | 0.715605 | − | 0.698505i | \(-0.246151\pi\) |
−0.962726 | + | 0.270479i | \(0.912818\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.4641 | −1.16312 | ||||||||
\(135\) | 0.358719 | − | 2.20711i | 0.0308737 | − | 0.189958i | ||||
\(136\) | −1.03528 | + | 1.79315i | −0.0887742 | + | 0.153761i | ||||
\(137\) | −3.91447 | − | 2.26002i | −0.334436 | − | 0.193087i | 0.323373 | − | 0.946272i | \(-0.395183\pi\) |
−0.657809 | + | 0.753185i | \(0.728517\pi\) | |||||||
\(138\) | −10.5622 | + | 6.09808i | −0.899112 | + | 0.519103i | ||||
\(139\) | −5.27792 | −0.447667 | −0.223834 | − | 0.974627i | \(-0.571857\pi\) | ||||
−0.223834 | + | 0.974627i | \(0.571857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | −24.0788 | + | 13.9019i | −2.02065 | + | 1.16662i | ||||
\(143\) | −12.0000 | − | 6.92820i | −1.00349 | − | 0.579365i | ||||
\(144\) | −2.23205 | + | 3.86603i | −0.186004 | + | 0.322169i | ||||
\(145\) | −19.7055 | − | 3.20272i | −1.63645 | − | 0.265971i | ||||
\(146\) | −21.1117 | −1.74721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.31268i | 0.107901i | ||||||||
\(149\) | 10.4641 | + | 18.1244i | 0.857253 | + | 1.48481i | 0.874539 | + | 0.484954i | \(0.161164\pi\) |
−0.0172868 | + | 0.999851i | \(0.505503\pi\) | |||||||
\(150\) | 9.16208 | + | 3.05902i | 0.748081 | + | 0.249768i | ||||
\(151\) | 6.26795 | − | 10.8564i | 0.510078 | − | 0.883482i | −0.489853 | − | 0.871805i | \(-0.662950\pi\) |
0.999932 | − | 0.0116770i | \(-0.00371698\pi\) | |||||||
\(152\) | −0.169873 | + | 0.0980762i | −0.0137785 | + | 0.00795503i | ||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3923 | − | 12.7279i | 0.834730 | − | 1.02233i | ||||
\(156\) | 3.46410 | + | 6.00000i | 0.277350 | + | 0.480384i | ||||
\(157\) | −16.3923 | − | 9.46410i | −1.30825 | − | 0.755318i | −0.326445 | − | 0.945216i | \(-0.605851\pi\) |
−0.981804 | + | 0.189899i | \(0.939184\pi\) | |||||||
\(158\) | 19.1798 | + | 11.0735i | 1.52586 | + | 0.880958i | ||||
\(159\) | 3.67423 | + | 6.36396i | 0.291386 | + | 0.504695i | ||||
\(160\) | −13.1440 | − | 10.7321i | −1.03913 | − | 0.848443i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.93185i | − | 0.151781i | ||||||
\(163\) | 14.5211 | − | 8.38375i | 1.13738 | − | 0.656666i | 0.191598 | − | 0.981473i | \(-0.438633\pi\) |
0.945780 | + | 0.324808i | \(0.105300\pi\) | |||||||
\(164\) | −7.34847 | + | 12.7279i | −0.573819 | + | 0.993884i | ||||
\(165\) | −7.24264 | + | 2.74666i | −0.563839 | + | 0.213827i | ||||
\(166\) | 5.79555 | + | 10.0382i | 0.449822 | + | 0.779115i | ||||
\(167\) | 5.07180i | 0.392467i | 0.980557 | + | 0.196234i | \(0.0628711\pi\) | ||||
−0.980557 | + | 0.196234i | \(0.937129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 17.0552 | + | 2.77197i | 1.30808 | + | 0.212600i | ||||
\(171\) | 0.189469 | − | 0.328169i | 0.0144890 | − | 0.0250957i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8564 | + | 8.00000i | −1.05348 | + | 0.608229i | −0.923622 | − | 0.383304i | \(-0.874786\pi\) |
−0.129861 | + | 0.991532i | \(0.541453\pi\) | |||||||
\(174\) | −17.2480 | −1.30756 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.4641 | 1.16565 | ||||||||
\(177\) | −9.14162 | + | 5.27792i | −0.687126 | + | 0.396713i | ||||
\(178\) | 6.92820 | + | 4.00000i | 0.519291 | + | 0.299813i | ||||
\(179\) | −5.19615 | + | 9.00000i | −0.388379 | + | 0.672692i | −0.992232 | − | 0.124404i | \(-0.960298\pi\) |
0.603853 | + | 0.797096i | \(0.293631\pi\) | |||||||
\(180\) | 3.82282 | + | 0.621320i | 0.284936 | + | 0.0463105i | ||||
\(181\) | −3.48477 | −0.259021 | −0.129510 | − | 0.991578i | \(-0.541341\pi\) | ||||
−0.129510 | + | 0.991578i | \(0.541341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.14162i | 0.675768i | ||||||||
\(184\) | 1.63397 | + | 2.83013i | 0.120458 | + | 0.208640i | ||||
\(185\) | −1.58454 | + | 0.600914i | −0.116498 | + | 0.0441801i | ||||
\(186\) | 7.09808 | − | 12.2942i | 0.520456 | − | 0.901457i | ||||
\(187\) | −12.0000 | + | 6.92820i | −0.877527 | + | 0.506640i | ||||
\(188\) | − | 10.3923i | − | 0.757937i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.26795 | + | 1.03528i | 0.0919867 | + | 0.0751068i | ||||
\(191\) | 0.267949 | + | 0.464102i | 0.0193881 | + | 0.0335812i | 0.875557 | − | 0.483115i | \(-0.160495\pi\) |
−0.856169 | + | 0.516697i | \(0.827162\pi\) | |||||||
\(192\) | −4.96410 | − | 2.86603i | −0.358253 | − | 0.206838i | ||||
\(193\) | 14.0406 | + | 8.10634i | 1.01066 | + | 0.583507i | 0.911386 | − | 0.411552i | \(-0.135013\pi\) |
0.0992783 | + | 0.995060i | \(0.468347\pi\) | |||||||
\(194\) | −4.89898 | − | 8.48528i | −0.351726 | − | 0.609208i | ||||
\(195\) | −5.65685 | + | 6.92820i | −0.405096 | + | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.4896i | − | 0.818598i | −0.912400 | − | 0.409299i | \(-0.865773\pi\) | ||
0.912400 | − | 0.409299i | \(-0.134227\pi\) | |||||||
\(198\) | −5.79555 | + | 3.34607i | −0.411872 | + | 0.237795i | ||||
\(199\) | −1.60368 | + | 2.77766i | −0.113682 | + | 0.196903i | −0.917252 | − | 0.398307i | \(-0.869598\pi\) |
0.803570 | + | 0.595210i | \(0.202931\pi\) | |||||||
\(200\) | 0.819661 | − | 2.45497i | 0.0579588 | − | 0.173593i | ||||
\(201\) | −3.48477 | − | 6.03579i | −0.245796 | − | 0.425732i | ||||
\(202\) | 24.3923i | 1.71624i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.92820 | 0.485071 | ||||||||
\(205\) | −18.7279 | − | 3.04384i | −1.30801 | − | 0.212591i | ||||
\(206\) | −13.3843 | + | 23.1822i | −0.932526 | + | 1.61518i | ||||
\(207\) | −5.46739 | − | 3.15660i | −0.380010 | − | 0.219399i | ||||
\(208\) | 15.4641 | − | 8.92820i | 1.07224 | − | 0.619060i | ||||
\(209\) | −1.31268 | −0.0907998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0718 | −0.899900 | −0.449950 | − | 0.893054i | \(-0.648558\pi\) | ||||
−0.449950 | + | 0.893054i | \(0.648558\pi\) | |||||||
\(212\) | −11.0227 | + | 6.36396i | −0.757042 | + | 0.437079i | ||||
\(213\) | −12.4641 | − | 7.19615i | −0.854026 | − | 0.493072i | ||||
\(214\) | 15.0263 | − | 26.0263i | 1.02718 | − | 1.77912i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.517638 | −0.0352208 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 22.9048i | − | 1.55131i | ||||||
\(219\) | −5.46410 | − | 9.46410i | −0.369230 | − | 0.639525i | ||||
\(220\) | −4.75736 | − | 12.5446i | −0.320741 | − | 0.845758i | ||||
\(221\) | −8.00000 | + | 13.8564i | −0.538138 | + | 0.932083i | ||||
\(222\) | −1.26795 | + | 0.732051i | −0.0850992 | + | 0.0491320i | ||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 4.89898i | 0.0666667 | + | 0.326599i | ||||
\(226\) | 0.366025 | + | 0.633975i | 0.0243476 | + | 0.0421714i | ||||
\(227\) | −3.46410 | − | 2.00000i | −0.229920 | − | 0.132745i | 0.380615 | − | 0.924734i | \(-0.375712\pi\) |
−0.610535 | + | 0.791989i | \(0.709046\pi\) | |||||||
\(228\) | 0.568406 | + | 0.328169i | 0.0376436 | + | 0.0217335i | ||||
\(229\) | 11.6419 | + | 20.1643i | 0.769317 | + | 1.33250i | 0.937934 | + | 0.346814i | \(0.112737\pi\) |
−0.168617 | + | 0.985682i | \(0.553930\pi\) | |||||||
\(230\) | 17.2480 | − | 21.1244i | 1.13730 | − | 1.39290i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.62158i | 0.303421i | ||||||||
\(233\) | −0.328169 | + | 0.189469i | −0.0214991 | + | 0.0124125i | −0.510711 | − | 0.859752i | \(-0.670618\pi\) |
0.489212 | + | 0.872165i | \(0.337284\pi\) | |||||||
\(234\) | −3.86370 | + | 6.69213i | −0.252578 | + | 0.437478i | ||||
\(235\) | 12.5446 | − | 4.75736i | 0.818321 | − | 0.310336i | ||||
\(236\) | −9.14162 | − | 15.8338i | −0.595069 | − | 1.03069i | ||||
\(237\) | 11.4641i | 0.744673i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4641 | 1.00029 | 0.500145 | − | 0.865942i | \(-0.333280\pi\) | ||||
0.500145 | + | 0.865942i | \(0.333280\pi\) | |||||||
\(240\) | 1.60136 | − | 9.85275i | 0.103367 | − | 0.635992i | ||||
\(241\) | −2.77766 | + | 4.81105i | −0.178925 | + | 0.309907i | −0.941513 | − | 0.336978i | \(-0.890595\pi\) |
0.762588 | + | 0.646885i | \(0.223929\pi\) | |||||||
\(242\) | 1.67303 | + | 0.965926i | 0.107547 | + | 0.0620921i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −15.8338 | −1.01365 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.3923 | −1.04514 | ||||||||
\(247\) | −1.31268 | + | 0.757875i | −0.0835237 | + | 0.0482224i | ||||
\(248\) | −3.29423 | − | 1.90192i | −0.209184 | − | 0.120772i | ||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | −21.5813 | + | 0.868845i | −1.36492 | + | 0.0549506i | ||||
\(251\) | 9.04008 | 0.570605 | 0.285303 | − | 0.958438i | \(-0.407906\pi\) | ||||
0.285303 | + | 0.958438i | \(0.407906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.8695i | 1.37493i | ||||||||
\(254\) | 2.73205 | + | 4.73205i | 0.171424 | + | 0.296915i | ||||
\(255\) | 3.17157 | + | 8.36308i | 0.198612 | + | 0.523716i | ||||
\(256\) | −9.69615 | + | 16.7942i | −0.606010 | + | 1.04964i | ||||
\(257\) | 3.00000 | − | 1.73205i | 0.187135 | − | 0.108042i | −0.403506 | − | 0.914977i | \(-0.632208\pi\) |
0.590641 | + | 0.806935i | \(0.298875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.0000 | − | 9.79796i | −0.744208 | − | 0.607644i | ||||
\(261\) | −4.46410 | − | 7.73205i | −0.276321 | − | 0.478602i | ||||
\(262\) | 9.46410 | + | 5.46410i | 0.584694 | + | 0.337573i | ||||
\(263\) | 18.8516 | + | 10.8840i | 1.16244 | + | 0.671136i | 0.951888 | − | 0.306446i | \(-0.0991398\pi\) |
0.210554 | + | 0.977582i | \(0.432473\pi\) | |||||||
\(264\) | 0.896575 | + | 1.55291i | 0.0551804 | + | 0.0955753i | ||||
\(265\) | −12.7279 | − | 10.3923i | −0.781870 | − | 0.638394i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.14110i | 0.253431i | ||||||||
\(268\) | 10.4543 | − | 6.03579i | 0.638598 | − | 0.368695i | ||||
\(269\) | 4.14110 | − | 7.17260i | 0.252488 | − | 0.437321i | −0.711722 | − | 0.702461i | \(-0.752085\pi\) |
0.964210 | + | 0.265139i | \(0.0854180\pi\) | |||||||
\(270\) | 1.53175 | + | 4.03906i | 0.0932195 | + | 0.245809i | ||||
\(271\) | 6.50266 | + | 11.2629i | 0.395009 | + | 0.684175i | 0.993102 | − | 0.117251i | \(-0.0374083\pi\) |
−0.598094 | + | 0.801426i | \(0.704075\pi\) | |||||||
\(272\) | − | 17.8564i | − | 1.08270i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.73205 | 0.527522 | ||||||||
\(275\) | 12.9649 | − | 11.4853i | 0.781812 | − | 0.692589i | ||||
\(276\) | 5.46739 | − | 9.46979i | 0.329098 | − | 0.570014i | ||||
\(277\) | −9.79796 | − | 5.65685i | −0.588702 | − | 0.339887i | 0.175882 | − | 0.984411i | \(-0.443722\pi\) |
−0.764584 | + | 0.644524i | \(0.777056\pi\) | |||||||
\(278\) | 8.83013 | − | 5.09808i | 0.529596 | − | 0.305762i | ||||
\(279\) | 7.34847 | 0.439941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.143594 | 0.00856607 | 0.00428304 | − | 0.999991i | \(-0.498637\pi\) | ||||
0.00428304 | + | 0.999991i | \(0.498637\pi\) | |||||||
\(282\) | 10.0382 | − | 5.79555i | 0.597766 | − | 0.345120i | ||||
\(283\) | 25.8564 | + | 14.9282i | 1.53700 | + | 0.887390i | 0.999012 | + | 0.0444395i | \(0.0141502\pi\) |
0.537992 | + | 0.842950i | \(0.319183\pi\) | |||||||
\(284\) | 12.4641 | − | 21.5885i | 0.739608 | − | 1.28104i | ||||
\(285\) | −0.135932 | + | 0.836355i | −0.00805193 | + | 0.0495414i | ||||
\(286\) | 26.7685 | 1.58286 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 7.58871i | − | 0.447169i | ||||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 36.0615 | − | 13.6758i | 2.11761 | − | 0.803070i | ||||
\(291\) | 2.53590 | − | 4.39230i | 0.148657 | − | 0.257481i | ||||
\(292\) | 16.3923 | − | 9.46410i | 0.959287 | − | 0.553845i | ||||
\(293\) | − | 4.53590i | − | 0.264990i | −0.991184 | − | 0.132495i | \(-0.957701\pi\) | ||
0.991184 | − | 0.132495i | \(-0.0422989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.9282 | − | 18.2832i | 0.869154 | − | 1.06449i | ||||
\(296\) | 0.196152 | + | 0.339746i | 0.0114011 | + | 0.0197473i | ||||
\(297\) | −3.00000 | − | 1.73205i | −0.174078 | − | 0.100504i | ||||
\(298\) | −35.0136 | − | 20.2151i | −2.02828 | − | 1.17103i | ||||
\(299\) | 12.6264 | + | 21.8695i | 0.730203 | + | 1.26475i | ||||
\(300\) | −8.48528 | + | 1.73205i | −0.489898 | + | 0.100000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 24.2175i | 1.39356i | ||||||||
\(303\) | −10.9348 | + | 6.31319i | −0.628186 | + | 0.362683i | ||||
\(304\) | 0.845807 | − | 1.46498i | 0.0485104 | − | 0.0840225i | ||||
\(305\) | −7.24833 | − | 19.1130i | −0.415038 | − | 1.09441i | ||||
\(306\) | 3.86370 | + | 6.69213i | 0.220873 | + | 0.382564i | ||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.8564 | −0.788263 | ||||||||
\(310\) | −5.09244 | + | 31.3324i | −0.289231 | + | 1.77956i | ||||
\(311\) | −7.72741 | + | 13.3843i | −0.438181 | + | 0.758952i | −0.997549 | − | 0.0699675i | \(-0.977710\pi\) |
0.559368 | + | 0.828919i | \(0.311044\pi\) | |||||||
\(312\) | 1.79315 | + | 1.03528i | 0.101517 | + | 0.0586110i | ||||
\(313\) | −9.46410 | + | 5.46410i | −0.534943 | + | 0.308849i | −0.743027 | − | 0.669262i | \(-0.766611\pi\) |
0.208084 | + | 0.978111i | \(0.433277\pi\) | |||||||
\(314\) | 36.5665 | 2.06357 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.8564 | −1.11701 | ||||||||
\(317\) | 25.3035 | − | 14.6090i | 1.42119 | − | 0.820524i | 0.424788 | − | 0.905293i | \(-0.360349\pi\) |
0.996401 | + | 0.0847694i | \(0.0270154\pi\) | |||||||
\(318\) | −12.2942 | − | 7.09808i | −0.689426 | − | 0.398040i | ||||
\(319\) | −15.4641 | + | 26.7846i | −0.865823 | + | 1.49965i | ||||
\(320\) | 12.6512 | + | 2.05620i | 0.707226 | + | 0.114945i | ||||
\(321\) | 15.5563 | 0.868271 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51575i | 0.0843386i | ||||||||
\(324\) | 0.866025 | + | 1.50000i | 0.0481125 | + | 0.0833333i | ||||
\(325\) | 6.33386 | − | 18.9706i | 0.351339 | − | 1.05230i | ||||
\(326\) | −16.1962 | + | 28.0526i | −0.897022 | + | 1.55369i | ||||
\(327\) | 10.2679 | − | 5.92820i | 0.567819 | − | 0.327830i | ||||
\(328\) | 4.39230i | 0.242524i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.46410 | − | 11.5911i | 0.520982 | − | 0.638070i | ||||
\(331\) | −16.3923 | − | 28.3923i | −0.901003 | − | 1.56058i | −0.826195 | − | 0.563384i | \(-0.809499\pi\) |
−0.0748075 | − | 0.997198i | \(-0.523834\pi\) | |||||||
\(332\) | −9.00000 | − | 5.19615i | −0.493939 | − | 0.285176i | ||||
\(333\) | −0.656339 | − | 0.378937i | −0.0359671 | − | 0.0207656i | ||||
\(334\) | −4.89898 | − | 8.48528i | −0.268060 | − | 0.464294i | ||||
\(335\) | 12.0716 | + | 9.85641i | 0.659541 | + | 0.538513i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.5264i | 1.49946i | 0.661745 | + | 0.749729i | \(0.269816\pi\) | ||||
−0.661745 | + | 0.749729i | \(0.730184\pi\) | |||||||
\(338\) | 5.01910 | − | 2.89778i | 0.273003 | − | 0.157618i | ||||
\(339\) | −0.189469 | + | 0.328169i | −0.0102905 | + | 0.0178237i | ||||
\(340\) | −14.4853 | + | 5.49333i | −0.785575 | + | 0.297917i | ||||
\(341\) | −12.7279 | − | 22.0454i | −0.689256 | − | 1.19383i | ||||
\(342\) | 0.732051i | 0.0395848i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.9339 | + | 2.26467i | 0.750175 | + | 0.121925i | ||||
\(346\) | 15.4548 | − | 26.7685i | 0.830856 | − | 1.43908i | ||||
\(347\) | −9.88589 | − | 5.70762i | −0.530702 | − | 0.306401i | 0.210600 | − | 0.977572i | \(-0.432458\pi\) |
−0.741302 | + | 0.671171i | \(0.765792\pi\) | |||||||
\(348\) | 13.3923 | − | 7.73205i | 0.717903 | − | 0.414481i | ||||
\(349\) | −7.82894 | −0.419074 | −0.209537 | − | 0.977801i | \(-0.567196\pi\) | ||||
−0.209537 | + | 0.977801i | \(0.567196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | −22.7661 | + | 13.1440i | −1.21344 | + | 0.700579i | ||||
\(353\) | 3.92820 | + | 2.26795i | 0.209077 | + | 0.120711i | 0.600882 | − | 0.799337i | \(-0.294816\pi\) |
−0.391805 | + | 0.920048i | \(0.628149\pi\) | |||||||
\(354\) | 10.1962 | − | 17.6603i | 0.541919 | − | 0.938632i | ||||
\(355\) | 31.7654 | + | 5.16280i | 1.68593 | + | 0.274013i | ||||
\(356\) | −7.17260 | −0.380147 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 20.0764i | − | 1.06107i | ||||||
\(359\) | 4.26795 | + | 7.39230i | 0.225254 | + | 0.390151i | 0.956396 | − | 0.292075i | \(-0.0943456\pi\) |
−0.731142 | + | 0.682226i | \(0.761012\pi\) | |||||||
\(360\) | 1.08226 | − | 0.410432i | 0.0570402 | − | 0.0216317i | ||||
\(361\) | 9.42820 | − | 16.3301i | 0.496221 | − | 0.859480i | ||||
\(362\) | 5.83013 | − | 3.36603i | 0.306425 | − | 0.176914i | ||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.9282 | + | 15.4548i | 0.990747 | + | 0.808942i | ||||
\(366\) | −8.83013 | − | 15.2942i | −0.461558 | − | 0.799442i | ||||
\(367\) | −3.46410 | − | 2.00000i | −0.180825 | − | 0.104399i | 0.406855 | − | 0.913493i | \(-0.366625\pi\) |
−0.587680 | + | 0.809093i | \(0.699959\pi\) | |||||||
\(368\) | −24.4070 | − | 14.0914i | −1.27230 | − | 0.734563i | ||||
\(369\) | −4.24264 | − | 7.34847i | −0.220863 | − | 0.382546i | ||||
\(370\) | 2.07055 | − | 2.53590i | 0.107643 | − | 0.131835i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.7279i | 0.659912i | ||||||||
\(373\) | 23.1822 | − | 13.3843i | 1.20033 | − | 0.693011i | 0.239701 | − | 0.970847i | \(-0.422950\pi\) |
0.960629 | + | 0.277836i | \(0.0896172\pi\) | |||||||
\(374\) | 13.3843 | − | 23.1822i | 0.692084 | − | 1.19872i | ||||
\(375\) | −5.97514 | − | 9.44975i | −0.308555 | − | 0.487983i | ||||
\(376\) | −1.55291 | − | 2.68973i | −0.0800854 | − | 0.138712i | ||||
\(377\) | 35.7128i | 1.83930i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.53590 | −0.232993 | −0.116497 | − | 0.993191i | \(-0.537166\pi\) | ||||
−0.116497 | + | 0.993191i | \(0.537166\pi\) | |||||||
\(380\) | −1.44861 | − | 0.235442i | −0.0743121 | − | 0.0120779i | ||||
\(381\) | −1.41421 | + | 2.44949i | −0.0724524 | + | 0.125491i | ||||
\(382\) | −0.896575 | − | 0.517638i | −0.0458728 | − | 0.0264847i | ||||
\(383\) | −3.33975 | + | 1.92820i | −0.170653 | + | 0.0985266i | −0.582894 | − | 0.812548i | \(-0.698080\pi\) |
0.412241 | + | 0.911075i | \(0.364746\pi\) | |||||||
\(384\) | −4.10394 | −0.209428 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −31.3205 | −1.59417 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.60770 | + | 4.39230i | 0.386222 | + | 0.222985i | ||||
\(389\) | 12.4641 | − | 21.5885i | 0.631955 | − | 1.09458i | −0.355197 | − | 0.934792i | \(-0.615586\pi\) |
0.987152 | − | 0.159787i | \(-0.0510806\pi\) | |||||||
\(390\) | 2.77197 | − | 17.0552i | 0.140364 | − | 0.863624i | ||||
\(391\) | 25.2528 | 1.27709 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65685i | 0.285351i | ||||||||
\(394\) | 11.0981 | + | 19.2224i | 0.559113 | + | 0.968412i | ||||
\(395\) | −9.08981 | − | 23.9688i | −0.457358 | − | 1.20600i | ||||
\(396\) | 3.00000 | − | 5.19615i | 0.150756 | − | 0.261116i | ||||
\(397\) | −27.4641 | + | 15.8564i | −1.37838 | + | 0.795810i | −0.991965 | − | 0.126513i | \(-0.959621\pi\) |
−0.386419 | + | 0.922323i | \(0.626288\pi\) | |||||||
\(398\) | − | 6.19615i | − | 0.310585i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.46410 | + | 21.8695i | 0.223205 | + | 1.09348i | ||||
\(401\) | −1.00000 | − | 1.73205i | −0.0499376 | − | 0.0864945i | 0.839976 | − | 0.542623i | \(-0.182569\pi\) |
−0.889914 | + | 0.456129i | \(0.849236\pi\) | |||||||
\(402\) | 11.6603 | + | 6.73205i | 0.581561 | + | 0.335764i | ||||
\(403\) | −25.4558 | − | 14.6969i | −1.26805 | − | 0.732107i | ||||
\(404\) | −10.9348 | − | 18.9396i | −0.544025 | − | 0.942279i | ||||
\(405\) | −1.41421 | + | 1.73205i | −0.0702728 | + | 0.0860663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.62536i | 0.130134i | ||||||||
\(408\) | 1.79315 | − | 1.03528i | 0.0887742 | − | 0.0512538i | ||||
\(409\) | 15.5056 | − | 26.8565i | 0.766702 | − | 1.32797i | −0.172641 | − | 0.984985i | \(-0.555230\pi\) |
0.939342 | − | 0.342981i | \(-0.111437\pi\) | |||||||
\(410\) | 34.2725 | − | 12.9973i | 1.69260 | − | 0.641893i | ||||
\(411\) | 2.26002 | + | 3.91447i | 0.111479 | + | 0.193087i | ||||
\(412\) | − | 24.0000i | − | 1.18240i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.1962 | 0.599408 | ||||||||
\(415\) | 2.15232 | − | 13.2426i | 0.105653 | − | 0.650056i | ||||
\(416\) | −15.1774 | + | 26.2880i | −0.744134 | + | 1.28888i | ||||
\(417\) | 4.57081 | + | 2.63896i | 0.223834 | + | 0.129230i | ||||
\(418\) | 2.19615 | − | 1.26795i | 0.107417 | − | 0.0620174i | ||||
\(419\) | −1.51575 | −0.0740492 | −0.0370246 | − | 0.999314i | \(-0.511788\pi\) | ||||
−0.0370246 | + | 0.999314i | \(0.511788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.7846 | −1.40288 | −0.701438 | − | 0.712730i | \(-0.747458\pi\) | ||||
−0.701438 | + | 0.712730i | \(0.747458\pi\) | |||||||
\(422\) | 21.8695 | − | 12.6264i | 1.06459 | − | 0.614643i | ||||
\(423\) | 5.19615 | + | 3.00000i | 0.252646 | + | 0.145865i | ||||
\(424\) | −1.90192 | + | 3.29423i | −0.0923656 | + | 0.159982i | ||||
\(425\) | −13.2621 | − | 14.9706i | −0.643304 | − | 0.726179i | ||||
\(426\) | 27.8038 | 1.34710 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 26.9444i | 1.30241i | ||||||||
\(429\) | 6.92820 | + | 12.0000i | 0.334497 | + | 0.579365i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.33975 | + | 2.32051i | −0.0645333 | + | 0.111775i | −0.896487 | − | 0.443070i | \(-0.853889\pi\) |
0.831954 | + | 0.554845i | \(0.187223\pi\) | |||||||
\(432\) | 3.86603 | − | 2.23205i | 0.186004 | − | 0.107390i | ||||
\(433\) | − | 9.85641i | − | 0.473669i | −0.971550 | − | 0.236834i | \(-0.923890\pi\) | ||
0.971550 | − | 0.236834i | \(-0.0761099\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.4641 | + | 12.6264i | 0.741447 | + | 0.605389i | ||||
\(436\) | 10.2679 | + | 17.7846i | 0.491746 | + | 0.851728i | ||||
\(437\) | 2.07180 | + | 1.19615i | 0.0991075 | + | 0.0572197i | ||||
\(438\) | 18.2832 | + | 10.5558i | 0.873607 | + | 0.504377i | ||||
\(439\) | 0.845807 | + | 1.46498i | 0.0403682 | + | 0.0699198i | 0.885504 | − | 0.464633i | \(-0.153814\pi\) |
−0.845135 | + | 0.534552i | \(0.820480\pi\) | |||||||
\(440\) | −3.10583 | − | 2.53590i | −0.148065 | − | 0.120894i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 30.9096i | − | 1.47022i | ||||||
\(443\) | −23.0943 | + | 13.3335i | −1.09724 | + | 0.633493i | −0.935495 | − | 0.353339i | \(-0.885046\pi\) |
−0.161747 | + | 0.986832i | \(0.551713\pi\) | |||||||
\(444\) | 0.656339 | − | 1.13681i | 0.0311485 | − | 0.0539507i | ||||
\(445\) | −3.28345 | − | 8.65810i | −0.155651 | − | 0.410433i | ||||
\(446\) | 7.72741 | + | 13.3843i | 0.365903 | + | 0.633763i | ||||
\(447\) | − | 20.9282i | − | 0.989870i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.14359 | −0.384320 | −0.192160 | − | 0.981364i | \(-0.561549\pi\) | ||||
−0.192160 | + | 0.981364i | \(0.561549\pi\) | |||||||
\(450\) | −6.40508 | − | 7.23023i | −0.301939 | − | 0.340836i | ||||
\(451\) | −14.6969 | + | 25.4558i | −0.692052 | + | 1.19867i | ||||
\(452\) | −0.568406 | − | 0.328169i | −0.0267356 | − | 0.0154358i | ||||
\(453\) | −10.8564 | + | 6.26795i | −0.510078 | + | 0.294494i | ||||
\(454\) | 7.72741 | 0.362665 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.196152 | 0.00918568 | ||||||||
\(457\) | 10.4543 | − | 6.03579i | 0.489031 | − | 0.282342i | −0.235141 | − | 0.971961i | \(-0.575555\pi\) |
0.724173 | + | 0.689619i | \(0.242222\pi\) | |||||||
\(458\) | −38.9545 | − | 22.4904i | −1.82022 | − | 1.05091i | ||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | −3.92252 | + | 24.1342i | −0.182888 | + | 1.12526i | ||||
\(461\) | −12.8295 | −0.597527 | −0.298764 | − | 0.954327i | \(-0.596574\pi\) | ||||
−0.298764 | + | 0.954327i | \(0.596574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.7675i | − | 0.779251i | −0.920973 | − | 0.389626i | \(-0.872604\pi\) | ||
0.920973 | − | 0.389626i | \(-0.127396\pi\) | |||||||
\(464\) | −19.9282 | − | 34.5167i | −0.925144 | − | 1.60240i | ||||
\(465\) | −15.3640 | + | 5.82655i | −0.712487 | + | 0.270200i | ||||
\(466\) | 0.366025 | − | 0.633975i | 0.0169558 | − | 0.0293683i | ||||
\(467\) | 15.4641 | − | 8.92820i | 0.715593 | − | 0.413148i | −0.0975353 | − | 0.995232i | \(-0.531096\pi\) |
0.813129 | + | 0.582084i | \(0.197763\pi\) | |||||||
\(468\) | − | 6.92820i | − | 0.320256i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.3923 | + | 20.0764i | −0.756121 | + | 0.926055i | ||||
\(471\) | 9.46410 | + | 16.3923i | 0.436083 | + | 0.755318i | ||||
\(472\) | −4.73205 | − | 2.73205i | −0.217810 | − | 0.125753i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −11.0735 | − | 19.1798i | −0.508621 | − | 0.880958i | ||||
\(475\) | −0.378937 | − | 1.85641i | −0.0173868 | − | 0.0851778i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 7.34847i | − | 0.336463i | ||||||
\(478\) | −25.8719 | + | 14.9372i | −1.18336 | + | 0.683210i | ||||
\(479\) | −6.96953 | + | 12.0716i | −0.318446 | + | 0.551565i | −0.980164 | − | 0.198188i | \(-0.936494\pi\) |
0.661718 | + | 0.749753i | \(0.269828\pi\) | |||||||
\(480\) | 6.01703 | + | 15.8662i | 0.274639 | + | 0.724191i | ||||
\(481\) | 1.51575 | + | 2.62536i | 0.0691122 | + | 0.119706i | ||||
\(482\) | − | 10.7321i | − | 0.488832i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73205 | −0.0787296 | ||||||||
\(485\) | −1.81935 | + | 11.1940i | −0.0826125 | + | 0.508293i | ||||
\(486\) | −0.965926 | + | 1.67303i | −0.0438153 | + | 0.0758903i | ||||
\(487\) | −3.58630 | − | 2.07055i | −0.162511 | − | 0.0938257i | 0.416539 | − | 0.909118i | \(-0.363243\pi\) |
−0.579050 | + | 0.815292i | \(0.696576\pi\) | |||||||
\(488\) | −4.09808 | + | 2.36603i | −0.185511 | + | 0.107105i | ||||
\(489\) | −16.7675 | −0.758252 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.67949 | 0.301441 | 0.150721 | − | 0.988576i | \(-0.451841\pi\) | ||||
0.150721 | + | 0.988576i | \(0.451841\pi\) | |||||||
\(492\) | 12.7279 | − | 7.34847i | 0.573819 | − | 0.331295i | ||||
\(493\) | 30.9282 | + | 17.8564i | 1.39294 | + | 0.804212i | ||||
\(494\) | 1.46410 | − | 2.53590i | 0.0658730 | − | 0.114095i | ||||
\(495\) | 7.64564 | + | 1.24264i | 0.343646 | + | 0.0558525i | ||||
\(496\) | 32.8043 | 1.47296 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 11.5911i | − | 0.519410i | ||||||
\(499\) | 8.12436 | + | 14.0718i | 0.363696 | + | 0.629940i | 0.988566 | − | 0.150789i | \(-0.0481813\pi\) |
−0.624870 | + | 0.780729i | \(0.714848\pi\) | |||||||
\(500\) | 16.3674 | − | 10.3492i | 0.731974 | − | 0.462832i | ||||
\(501\) | 2.53590 | − | 4.39230i | 0.113296 | − | 0.196234i | ||||
\(502\) | −15.1244 | + | 8.73205i | −0.675033 | + | 0.389731i | ||||
\(503\) | 3.85641i | 0.171949i | 0.996297 | + | 0.0859743i | \(0.0274003\pi\) | ||||
−0.996297 | + | 0.0859743i | \(0.972600\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.8564 | − | 21.8695i | 0.794600 | − | 0.973182i | ||||
\(506\) | −21.1244 | − | 36.5885i | −0.939092 | − | 1.62656i | ||||
\(507\) | 2.59808 | + | 1.50000i | 0.115385 | + | 0.0666173i | ||||
\(508\) | −4.24264 | − | 2.44949i | −0.188237 | − | 0.108679i | ||||
\(509\) | 21.1117 | + | 36.5665i | 0.935758 | + | 1.62078i | 0.773276 | + | 0.634069i | \(0.218617\pi\) |
0.162482 | + | 0.986712i | \(0.448050\pi\) | |||||||
\(510\) | −13.3843 | − | 10.9282i | −0.592665 | − | 0.483909i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 29.2552i | − | 1.29291i | ||||||
\(513\) | −0.328169 | + | 0.189469i | −0.0144890 | + | 0.00836525i | ||||
\(514\) | −3.34607 | + | 5.79555i | −0.147589 | + | 0.255631i | ||||
\(515\) | 28.9706 | − | 10.9867i | 1.27660 | − | 0.484130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.7846i | − | 0.914106i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0000 | 0.702322 | ||||||||
\(520\) | −4.56993 | − | 0.742747i | −0.200405 | − | 0.0325716i | ||||
\(521\) | −14.1421 | + | 24.4949i | −0.619578 | + | 1.07314i | 0.369984 | + | 0.929038i | \(0.379363\pi\) |
−0.989563 | + | 0.144103i | \(0.953970\pi\) | |||||||
\(522\) | 14.9372 | + | 8.62398i | 0.653782 | + | 0.377461i | ||||
\(523\) | −10.1436 | + | 5.85641i | −0.443548 | + | 0.256083i | −0.705102 | − | 0.709106i | \(-0.749099\pi\) |
0.261553 | + | 0.965189i | \(0.415765\pi\) | |||||||
\(524\) | −9.79796 | −0.428026 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.0526 | −1.83358 | ||||||||
\(527\) | −25.4558 | + | 14.6969i | −1.10887 | + | 0.640209i | ||||
\(528\) | −13.3923 | − | 7.73205i | −0.582825 | − | 0.336494i | ||||
\(529\) | 8.42820 | − | 14.5981i | 0.366444 | − | 0.634699i | ||||
\(530\) | 31.3324 | + | 5.09244i | 1.36099 | + | 0.221201i | ||||
\(531\) | 10.5558 | 0.458084 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.9411i | 1.47015i | ||||||||
\(534\) | −4.00000 | − | 6.92820i | −0.173097 | − | 0.299813i | ||||
\(535\) | −32.5248 | + | 12.3345i | −1.40617 | + | 0.533268i | ||||
\(536\) | 1.80385 | − | 3.12436i | 0.0779143 | − | 0.134952i | ||||
\(537\) | 9.00000 | − | 5.19615i | 0.388379 | − | 0.224231i | ||||
\(538\) | 16.0000i | 0.689809i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.00000 | − | 2.44949i | −0.129099 | − | 0.105409i | ||||
\(541\) | 21.3205 | + | 36.9282i | 0.916640 | + | 1.58767i | 0.804482 | + | 0.593977i | \(0.202443\pi\) |
0.112158 | + | 0.993690i | \(0.464224\pi\) | |||||||
\(542\) | −21.7583 | − | 12.5622i | −0.934600 | − | 0.539592i | ||||
\(543\) | 3.01790 | + | 1.74238i | 0.129510 | + | 0.0747728i | ||||
\(544\) | 15.1774 | + | 26.2880i | 0.650726 | + | 1.12709i | ||||
\(545\) | −16.7675 | + | 20.5359i | −0.718240 | + | 0.879661i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 29.5969i | − | 1.26547i | −0.774367 | − | 0.632737i | \(-0.781931\pi\) | ||
0.774367 | − | 0.632737i | \(-0.218069\pi\) | |||||||
\(548\) | −6.78006 | + | 3.91447i | −0.289630 | + | 0.167218i | ||||
\(549\) | 4.57081 | − | 7.91688i | 0.195077 | − | 0.337884i | ||||
\(550\) | −10.5967 | + | 31.7384i | −0.451847 | + | 1.35333i | ||||
\(551\) | 1.69161 | + | 2.92996i | 0.0720652 | + | 0.124821i | ||||
\(552\) | − | 3.26795i | − | 0.139093i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.8564 | 0.928590 | ||||||||
\(555\) | 1.67271 | + | 0.271864i | 0.0710026 | + | 0.0115400i | ||||
\(556\) | −4.57081 | + | 7.91688i | −0.193846 | + | 0.335750i | ||||
\(557\) | 11.9193 | + | 6.88160i | 0.505036 | + | 0.291583i | 0.730791 | − | 0.682601i | \(-0.239151\pi\) |
−0.225755 | + | 0.974184i | \(0.572485\pi\) | |||||||
\(558\) | −12.2942 | + | 7.09808i | −0.520456 | + | 0.300486i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.8564 | 0.585018 | ||||||||
\(562\) | −0.240237 | + | 0.138701i | −0.0101338 | + | 0.00585074i | ||||
\(563\) | 27.5885 | + | 15.9282i | 1.16271 | + | 0.671294i | 0.951953 | − | 0.306244i | \(-0.0990723\pi\) |
0.210762 | + | 0.977537i | \(0.432406\pi\) | |||||||
\(564\) | −5.19615 | + | 9.00000i | −0.218797 | + | 0.378968i | ||||
\(565\) | 0.135932 | − | 0.836355i | 0.00571871 | − | 0.0351857i | ||||
\(566\) | −57.6781 | −2.42439 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 7.45001i | − | 0.312595i | ||||||
\(569\) | 5.92820 | + | 10.2679i | 0.248523 | + | 0.430455i | 0.963116 | − | 0.269086i | \(-0.0867214\pi\) |
−0.714593 | + | 0.699540i | \(0.753388\pi\) | |||||||
\(570\) | −0.580438 | − | 1.53055i | −0.0243119 | − | 0.0641077i | ||||
\(571\) | −19.8564 | + | 34.3923i | −0.830965 | + | 1.43927i | 0.0663093 | + | 0.997799i | \(0.478878\pi\) |
−0.897274 | + | 0.441474i | \(0.854456\pi\) | |||||||
\(572\) | −20.7846 | + | 12.0000i | −0.869048 | + | 0.501745i | ||||
\(573\) | − | 0.535898i | − | 0.0223875i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.9282 | + | 6.31319i | −1.28980 | + | 0.263278i | ||||
\(576\) | 2.86603 | + | 4.96410i | 0.119418 | + | 0.206838i | ||||
\(577\) | −3.46410 | − | 2.00000i | −0.144212 | − | 0.0832611i | 0.426158 | − | 0.904649i | \(-0.359867\pi\) |
−0.570370 | + | 0.821388i | \(0.693200\pi\) | |||||||
\(578\) | 1.67303 | + | 0.965926i | 0.0695890 | + | 0.0401772i | ||||
\(579\) | −8.10634 | − | 14.0406i | −0.336888 | − | 0.583507i | ||||
\(580\) | −21.8695 | + | 26.7846i | −0.908083 | + | 1.11217i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.79796i | 0.406138i | ||||||||
\(583\) | −22.0454 | + | 12.7279i | −0.913027 | + | 0.527137i | ||||
\(584\) | 2.82843 | − | 4.89898i | 0.117041 | − | 0.202721i | ||||
\(585\) | 8.36308 | − | 3.17157i | 0.345771 | − | 0.131128i | ||||
\(586\) | 4.38134 | + | 7.58871i | 0.180992 | + | 0.313487i | ||||
\(587\) | − | 31.8564i | − | 1.31485i | −0.753518 | − | 0.657427i | \(-0.771645\pi\) | ||
0.753518 | − | 0.657427i | \(-0.228355\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.78461 | −0.114738 | ||||||||
\(590\) | −7.31512 | + | 45.0080i | −0.301159 | + | 1.85295i | ||||
\(591\) | −5.74479 | + | 9.95026i | −0.236309 | + | 0.409299i | ||||
\(592\) | −2.92996 | − | 1.69161i | −0.120421 | − | 0.0695249i | ||||
\(593\) | 8.07180 | − | 4.66025i | 0.331469 | − | 0.191374i | −0.325024 | − | 0.945706i | \(-0.605372\pi\) |
0.656493 | + | 0.754332i | \(0.272039\pi\) | |||||||
\(594\) | 6.69213 | 0.274581 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.2487 | 1.48481 | ||||||||
\(597\) | 2.77766 | − | 1.60368i | 0.113682 | − | 0.0656343i | ||||
\(598\) | −42.2487 | − | 24.3923i | −1.72768 | − | 0.997476i | ||||
\(599\) | −2.66025 | + | 4.60770i | −0.108695 | + | 0.188265i | −0.915242 | − | 0.402905i | \(-0.868001\pi\) |
0.806547 | + | 0.591170i | \(0.201334\pi\) | |||||||
\(600\) | −1.93733 | + | 1.71624i | −0.0790913 | + | 0.0700651i | ||||
\(601\) | −33.6365 | −1.37206 | −0.686031 | − | 0.727572i | \(-0.740649\pi\) | ||||
−0.686031 | + | 0.727572i | \(0.740649\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.96953i | 0.283821i | ||||||||
\(604\) | −10.8564 | − | 18.8038i | −0.441741 | − | 0.765118i | ||||
\(605\) | −0.792893 | − | 2.09077i | −0.0322357 | − | 0.0850019i | ||||
\(606\) | 12.1962 | − | 21.1244i | 0.495435 | − | 0.858118i | ||||
\(607\) | −10.3923 | + | 6.00000i | −0.421811 | + | 0.243532i | −0.695852 | − | 0.718186i | \(-0.744973\pi\) |
0.274041 | + | 0.961718i | \(0.411640\pi\) | |||||||
\(608\) | 2.87564i | 0.116623i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.5885 | + | 24.9754i | 1.23849 | + | 1.01122i | ||||
\(611\) | −12.0000 | − | 20.7846i | −0.485468 | − | 0.840855i | ||||
\(612\) | −6.00000 | − | 3.46410i | −0.242536 | − | 0.140028i | ||||
\(613\) | 8.48528 | + | 4.89898i | 0.342717 | + | 0.197868i | 0.661473 | − | 0.749969i | \(-0.269932\pi\) |
−0.318756 | + | 0.947837i | \(0.603265\pi\) | |||||||
\(614\) | 3.86370 | + | 6.69213i | 0.155926 | + | 0.270072i | ||||
\(615\) | 14.6969 | + | 12.0000i | 0.592638 | + | 0.483887i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.4505i | − | 0.501239i | −0.968086 | − | 0.250620i | \(-0.919366\pi\) | ||
0.968086 | − | 0.250620i | \(-0.0806343\pi\) | |||||||
\(618\) | 23.1822 | − | 13.3843i | 0.932526 | − | 0.538394i | ||||
\(619\) | −1.88108 | + | 3.25813i | −0.0756071 | + | 0.130955i | −0.901350 | − | 0.433091i | \(-0.857423\pi\) |
0.825743 | + | 0.564047i | \(0.190756\pi\) | |||||||
\(620\) | −10.0919 | − | 26.6112i | −0.405300 | − | 1.06873i | ||||
\(621\) | 3.15660 | + | 5.46739i | 0.126670 | + | 0.219399i | ||||
\(622\) | − | 29.8564i | − | 1.19713i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −17.8564 | −0.714828 | ||||||||
\(625\) | 19.9853 | + | 15.0196i | 0.799411 | + | 0.600784i | ||||
\(626\) | 10.5558 | − | 18.2832i | 0.421896 | − | 0.730745i | ||||
\(627\) | 1.13681 | + | 0.656339i | 0.0453999 | + | 0.0262116i | ||||
\(628\) | −28.3923 | + | 16.3923i | −1.13298 | + | 0.654124i | ||||
\(629\) | 3.03150 | 0.120874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.32051 | 0.371044 | 0.185522 | − | 0.982640i | \(-0.440602\pi\) | ||||
0.185522 | + | 0.982640i | \(0.440602\pi\) | |||||||
\(632\) | −5.13922 | + | 2.96713i | −0.204427 | + | 0.118026i | ||||
\(633\) | 11.3205 | + | 6.53590i | 0.449950 | + | 0.259779i | ||||
\(634\) | −28.2224 | + | 48.8827i | −1.12086 | + | 1.94138i | ||||
\(635\) | 1.01461 | − | 6.24264i | 0.0402636 | − | 0.247732i | ||||
\(636\) | 12.7279 | 0.504695 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 59.7487i | − | 2.36547i | ||||||
\(639\) | 7.19615 | + | 12.4641i | 0.284675 | + | 0.493072i | ||||
\(640\) | 8.58040 | − | 3.25399i | 0.339170 | − | 0.128625i | ||||
\(641\) | −5.00000 | + | 8.66025i | −0.197488 | + | 0.342059i | −0.947713 | − | 0.319123i | \(-0.896612\pi\) |
0.750225 | + | 0.661182i | \(0.229945\pi\) | |||||||
\(642\) | −26.0263 | + | 15.0263i | −1.02718 | + | 0.593040i | ||||
\(643\) | 4.00000i | 0.157745i | 0.996885 | + | 0.0788723i | \(0.0251319\pi\) | ||||
−0.996885 | + | 0.0788723i | \(0.974868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.46410 | − | 2.53590i | −0.0576043 | − | 0.0997736i | ||||
\(647\) | 25.1769 | + | 14.5359i | 0.989807 | + | 0.571465i | 0.905216 | − | 0.424951i | \(-0.139709\pi\) |
0.0845901 | + | 0.996416i | \(0.473042\pi\) | |||||||
\(648\) | 0.448288 | + | 0.258819i | 0.0176104 | + | 0.0101674i | ||||
\(649\) | −18.2832 | − | 31.6675i | −0.717680 | − | 1.24306i | ||||
\(650\) | 7.72741 | + | 37.8564i | 0.303094 | + | 1.48485i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 29.0421i | − | 1.13738i | ||||||
\(653\) | −16.1619 | + | 9.33109i | −0.632465 | + | 0.365154i | −0.781706 | − | 0.623647i | \(-0.785650\pi\) |
0.149241 | + | 0.988801i | \(0.452317\pi\) | |||||||
\(654\) | −11.4524 | + | 19.8362i | −0.447825 | + | 0.775655i | ||||
\(655\) | −4.48528 | − | 11.8272i | −0.175254 | − | 0.462126i | ||||
\(656\) | −18.9396 | − | 32.8043i | −0.739466 | − | 1.28079i | ||||
\(657\) | 10.9282i | 0.426350i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3923 | 0.404827 | 0.202413 | − | 0.979300i | \(-0.435122\pi\) | ||||
0.202413 | + | 0.979300i | \(0.435122\pi\) | |||||||
\(660\) | −2.15232 | + | 13.2426i | −0.0837788 | + | 0.515469i | ||||
\(661\) | 11.6419 | − | 20.1643i | 0.452817 | − | 0.784301i | −0.545743 | − | 0.837953i | \(-0.683753\pi\) |
0.998560 | + | 0.0536512i | \(0.0170859\pi\) | |||||||
\(662\) | 54.8497 | + | 31.6675i | 2.13179 | + | 1.23079i | ||||
\(663\) | 13.8564 | − | 8.00000i | 0.538138 | − | 0.310694i | ||||
\(664\) | −3.10583 | −0.120530 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.46410 | 0.0567328 | ||||||||
\(667\) | 48.8139 | − | 28.1827i | 1.89008 | − | 1.09124i | ||||
\(668\) | 7.60770 | + | 4.39230i | 0.294351 | + | 0.169943i | ||||
\(669\) | −4.00000 | + | 6.92820i | −0.154649 | + | 0.267860i | ||||
\(670\) | −29.7167 | − | 4.82984i | −1.14806 | − | 0.186593i | ||||
\(671\) | −31.6675 | −1.22251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0716i | 0.465325i | 0.972557 | + | 0.232663i | \(0.0747438\pi\) | ||||
−0.972557 | + | 0.232663i | \(0.925256\pi\) | |||||||
\(674\) | −26.5885 | − | 46.0526i | −1.02415 | − | 1.77388i | ||||
\(675\) | 1.58346 | − | 4.74264i | 0.0609476 | − | 0.182544i | ||||
\(676\) | −2.59808 | + | 4.50000i | −0.0999260 | + | 0.173077i | ||||
\(677\) | 33.9282 | − | 19.5885i | 1.30397 | − | 0.752846i | 0.322885 | − | 0.946438i | \(-0.395347\pi\) |
0.981082 | + | 0.193593i | \(0.0620140\pi\) | |||||||
\(678\) | − | 0.732051i | − | 0.0281142i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.92820 | + | 3.58630i | −0.112291 | + | 0.137528i | ||||
\(681\) | 2.00000 | + | 3.46410i | 0.0766402 | + | 0.132745i | ||||
\(682\) | 42.5885 | + | 24.5885i | 1.63080 | + | 0.941541i | ||||
\(683\) | 19.6839 | + | 11.3645i | 0.753182 | + | 0.434850i | 0.826842 | − | 0.562434i | \(-0.190135\pi\) |
−0.0736607 | + | 0.997283i | \(0.523468\pi\) | |||||||
\(684\) | −0.328169 | − | 0.568406i | −0.0125479 | − | 0.0217335i | ||||
\(685\) | −7.82894 | − | 6.39230i | −0.299129 | − | 0.244237i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 23.2838i | − | 0.888331i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.6969 | + | 25.4558i | −0.559909 | + | 0.969790i | ||||
\(690\) | −25.4994 | + | 9.67025i | −0.970744 | + | 0.368140i | ||||
\(691\) | 3.01790 | + | 5.22715i | 0.114806 | + | 0.198850i | 0.917702 | − | 0.397269i | \(-0.130042\pi\) |
−0.802896 | + | 0.596119i | \(0.796709\pi\) | |||||||
\(692\) | 27.7128i | 1.05348i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.0526 | 0.837104 | ||||||||
\(695\) | −11.6489 | − | 1.89329i | −0.441869 | − | 0.0718166i | ||||
\(696\) | 2.31079 | − | 4.00240i | 0.0875902 | − | 0.151711i | ||||
\(697\) | 29.3939 | + | 16.9706i | 1.11337 | + | 0.642806i | ||||
\(698\) | 13.0981 | − | 7.56218i | 0.495769 | − | 0.286233i | ||||
\(699\) | 0.378937 | 0.0143327 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9282 | −0.941525 | −0.470763 | − | 0.882260i | \(-0.656021\pi\) | ||||
−0.470763 | + | 0.882260i | \(0.656021\pi\) | |||||||
\(702\) | 6.69213 | − | 3.86370i | 0.252578 | − | 0.145826i | ||||
\(703\) | 0.248711 | + | 0.143594i | 0.00938032 | + | 0.00541573i | ||||
\(704\) | 9.92820 | − | 17.1962i | 0.374183 | − | 0.648104i | ||||
\(705\) | −13.2426 | − | 2.15232i | −0.498747 | − | 0.0810609i | ||||
\(706\) | −8.76268 | −0.329788 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.2832i | 0.687126i | ||||||||
\(709\) | 1.46410 | + | 2.53590i | 0.0549855 | + | 0.0952377i | 0.892208 | − | 0.451625i | \(-0.149155\pi\) |
−0.837222 | + | 0.546862i | \(0.815822\pi\) | |||||||
\(710\) | −58.1314 | + | 22.0454i | −2.18163 | + | 0.827351i | ||||
\(711\) | 5.73205 | − | 9.92820i | 0.214969 | − | 0.372337i | ||||
\(712\) | −1.85641 | + | 1.07180i | −0.0695718 | + | 0.0401673i | ||||
\(713\) | 46.3923i | 1.73741i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | − | 19.5959i | −0.897549 | − | 0.732846i | ||||
\(716\) | 9.00000 | + | 15.5885i | 0.336346 | + | 0.582568i | ||||
\(717\) | −13.3923 | − | 7.73205i | −0.500145 | − | 0.288759i | ||||
\(718\) | −14.2808 | − | 8.24504i | −0.532956 | − | 0.307702i | ||||
\(719\) | 7.34847 | + | 12.7279i | 0.274052 | + | 0.474671i | 0.969895 | − | 0.243522i | \(-0.0783027\pi\) |
−0.695844 | + | 0.718193i | \(0.744969\pi\) | |||||||
\(720\) | −6.31319 | + | 7.73205i | −0.235279 | + | 0.288157i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 36.4278i | 1.35570i | ||||||||
\(723\) | 4.81105 | − | 2.77766i | 0.178925 | − | 0.103302i | ||||
\(724\) | −3.01790 | + | 5.22715i | −0.112159 | + | 0.194265i | ||||
\(725\) | −42.3433 | − | 14.1375i | −1.57259 | − | 0.525053i | ||||
\(726\) | −0.965926 | − | 1.67303i | −0.0358489 | − | 0.0620921i | ||||
\(727\) | 31.7128i | 1.17616i | 0.808802 | + | 0.588082i | \(0.200117\pi\) | ||||
−0.808802 | + | 0.588082i | \(0.799883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −46.5957 | − | 7.57317i | −1.72458 | − | 0.280295i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 13.7124 | + | 7.91688i | 0.506826 | + | 0.292616i | ||||
\(733\) | 8.53590 | − | 4.92820i | 0.315281 | − | 0.182027i | −0.334006 | − | 0.942571i | \(-0.608401\pi\) |
0.649287 | + | 0.760543i | \(0.275067\pi\) | |||||||
\(734\) | 7.72741 | 0.285224 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 47.9090 | 1.76595 | ||||||||
\(737\) | 20.9086 | − | 12.0716i | 0.770178 | − | 0.444662i | ||||
\(738\) | 14.1962 | + | 8.19615i | 0.522568 | + | 0.301705i | ||||
\(739\) | 0.928203 | − | 1.60770i | 0.0341445 | − | 0.0591400i | −0.848448 | − | 0.529278i | \(-0.822463\pi\) |
0.882593 | + | 0.470138i | \(0.155796\pi\) | |||||||
\(740\) | −0.470883 | + | 2.89722i | −0.0173100 | + | 0.106504i | ||||
\(741\) | 1.51575 | 0.0556825 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.0197i | 1.35812i | 0.734081 | + | 0.679061i | \(0.237613\pi\) | ||||
−0.734081 | + | 0.679061i | \(0.762387\pi\) | |||||||
\(744\) | 1.90192 | + | 3.29423i | 0.0697279 | + | 0.120772i | ||||
\(745\) | 16.5938 | + | 43.7561i | 0.607951 | + | 1.60310i | ||||
\(746\) | −25.8564 | + | 44.7846i | −0.946670 | + | 1.63968i | ||||
\(747\) | 5.19615 | − | 3.00000i | 0.190117 | − | 0.109764i | ||||
\(748\) | 24.0000i | 0.877527i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19.1244 | + | 10.0382i | 0.698323 | + | 0.366543i | ||||
\(751\) | −2.39230 | − | 4.14359i | −0.0872964 | − | 0.151202i | 0.819071 | − | 0.573692i | \(-0.194489\pi\) |
−0.906367 | + | 0.422490i | \(0.861156\pi\) | |||||||
\(752\) | 23.1962 | + | 13.3923i | 0.845877 | + | 0.488367i | ||||
\(753\) | −7.82894 | − | 4.52004i | −0.285303 | − | 0.164719i | ||||
\(754\) | −34.4959 | − | 59.7487i | −1.25627 | − | 2.17592i | ||||
\(755\) | 17.7284 | − | 21.7128i | 0.645204 | − | 0.790210i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.2929i | 1.24640i | 0.782064 | + | 0.623198i | \(0.214167\pi\) | ||||
−0.782064 | + | 0.623198i | \(0.785833\pi\) | |||||||
\(758\) | 7.58871 | − | 4.38134i | 0.275634 | − | 0.159137i | ||||
\(759\) | 10.9348 | − | 18.9396i | 0.396907 | − | 0.687463i | ||||
\(760\) | −0.410110 | + | 0.155528i | −0.0148762 | + | 0.00564159i | ||||
\(761\) | −20.3538 | − | 35.2538i | −0.737824 | − | 1.27795i | −0.953473 | − | 0.301478i | \(-0.902520\pi\) |
0.215649 | − | 0.976471i | \(-0.430813\pi\) | |||||||
\(762\) | − | 5.46410i | − | 0.197944i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.928203 | 0.0335812 | ||||||||
\(765\) | 1.43488 | − | 8.82843i | 0.0518781 | − | 0.319192i | ||||
\(766\) | 3.72500 | − | 6.45189i | 0.134590 | − | 0.233116i | ||||
\(767\) | −36.5665 | − | 21.1117i | −1.32034 | − | 0.762298i | ||||
\(768\) | 16.7942 | − | 9.69615i | 0.606010 | − | 0.349880i | ||||
\(769\) | −19.4944 | −0.702985 | −0.351493 | − | 0.936191i | \(-0.614326\pi\) | ||||
−0.351493 | + | 0.936191i | \(0.614326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.46410 | −0.124757 | ||||||||
\(772\) | 24.3190 | − | 14.0406i | 0.875261 | − | 0.505332i | ||||
\(773\) | 8.78461 | + | 5.07180i | 0.315960 | + | 0.182420i | 0.649591 | − | 0.760284i | \(-0.274940\pi\) |
−0.333630 | + | 0.942704i | \(0.608274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.5027 | − | 24.3640i | 0.987925 | − | 0.875179i | ||||
\(776\) | 2.62536 | 0.0942448 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.1576i | 1.72653i | ||||||||
\(779\) | 1.60770 | + | 2.78461i | 0.0576017 | + | 0.0997690i | ||||
\(780\) | 5.49333 | + | 14.4853i | 0.196693 | + | 0.518656i | ||||
\(781\) | 24.9282 | − | 43.1769i | 0.892001 | − | 1.54499i | ||||
\(782\) | −42.2487 | + | 24.3923i | −1.51081 | + | 0.872267i | ||||
\(783\) | 8.92820i | 0.319068i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.7846 | − | 26.7685i | −1.17013 | − | 0.955410i | ||||
\(786\) | −5.46410 | − | 9.46410i | −0.194898 | − | 0.337573i | ||||
\(787\) | 15.7128 | + | 9.07180i | 0.560101 | + | 0.323375i | 0.753186 | − | 0.657807i | \(-0.228516\pi\) |
−0.193085 | + | 0.981182i | \(0.561849\pi\) | |||||||
\(788\) | −17.2344 | − | 9.95026i | −0.613949 | − | 0.354463i | ||||
\(789\) | −10.8840 | − | 18.8516i | −0.387481 | − | 0.671136i | ||||
\(790\) | 38.3596 | + | 31.3205i | 1.36477 | + | 1.11433i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 1.79315i | − | 0.0637168i | ||||||
\(793\) | −31.6675 | + | 18.2832i | −1.12455 | + | 0.649257i | ||||
\(794\) | 30.6322 | − | 53.0566i | 1.08710 | − | 1.88291i | ||||
\(795\) | 5.82655 | + | 15.3640i | 0.206646 | + | 0.544904i | ||||
\(796\) | 2.77766 | + | 4.81105i | 0.0984515 | + | 0.170523i | ||||
\(797\) | − | 37.8564i | − | 1.34094i | −0.741935 | − | 0.670471i | \(-0.766092\pi\) | ||
0.741935 | − | 0.670471i | \(-0.233908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −25.1605 | − | 28.4018i | −0.889557 | − | 1.00416i | ||||
\(801\) | 2.07055 | − | 3.58630i | 0.0731594 | − | 0.126716i | ||||
\(802\) | 3.34607 | + | 1.93185i | 0.118154 | + | 0.0682161i | ||||
\(803\) | 32.7846 | − | 18.9282i | 1.15694 | − | 0.667962i | ||||
\(804\) | −12.0716 | −0.425732 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 56.7846 | 2.00015 | ||||||||
\(807\) | −7.17260 | + | 4.14110i | −0.252488 | + | 0.145774i | ||||
\(808\) | −5.66025 | − | 3.26795i | −0.199127 | − | 0.114966i | ||||
\(809\) | −16.8564 | + | 29.1962i | −0.592640 | + | 1.02648i | 0.401236 | + | 0.915975i | \(0.368581\pi\) |
−0.993875 | + | 0.110507i | \(0.964752\pi\) | |||||||
\(810\) | 0.692993 | − | 4.26380i | 0.0243493 | − | 0.149815i | ||||
\(811\) | −8.66115 | −0.304134 | −0.152067 | − | 0.988370i | \(-0.548593\pi\) | ||||
−0.152067 | + | 0.988370i | \(0.548593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 13.0053i | − | 0.456117i | ||||||
\(814\) | −2.53590 | − | 4.39230i | −0.0888832 | − | 0.153950i | ||||
\(815\) | 35.0570 | − | 13.2948i | 1.22799 | − | 0.465698i | ||||
\(816\) | −8.92820 | + | 15.4641i | −0.312550 | + | 0.541352i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 59.9090i | 2.09467i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.7846 | + | 25.4558i | −0.725830 | + | 0.888957i | ||||
\(821\) | 11.3923 | + | 19.7321i | 0.397594 | + | 0.688653i | 0.993429 | − | 0.114454i | \(-0.0365119\pi\) |
−0.595834 | + | 0.803107i | \(0.703179\pi\) | |||||||
\(822\) | −7.56218 | − | 4.36603i | −0.263761 | − | 0.152283i | ||||
\(823\) | 41.2896 | + | 23.8386i | 1.43926 | + | 0.830960i | 0.997799 | − | 0.0663179i | \(-0.0211252\pi\) |
0.441466 | + | 0.897278i | \(0.354458\pi\) | |||||||
\(824\) | −3.58630 | − | 6.21166i | −0.124935 | − | 0.216393i | ||||
\(825\) | −16.9706 | + | 3.46410i | −0.590839 | + | 0.120605i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 50.6071i | − | 1.75978i | −0.475177 | − | 0.879890i | \(-0.657616\pi\) | ||
0.475177 | − | 0.879890i | \(-0.342384\pi\) | |||||||
\(828\) | −9.46979 | + | 5.46739i | −0.329098 | + | 0.190005i | ||||
\(829\) | 17.9551 | − | 31.0991i | 0.623605 | − | 1.08012i | −0.365203 | − | 0.930928i | \(-0.619001\pi\) |
0.988809 | − | 0.149188i | \(-0.0476661\pi\) | |||||||
\(830\) | 9.19051 | + | 24.2343i | 0.319007 | + | 0.841187i | ||||
\(831\) | 5.65685 | + | 9.79796i | 0.196234 | + | 0.339887i | ||||
\(832\) | − | 22.9282i | − | 0.794892i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.1962 | −0.353064 | ||||||||
\(835\) | −1.81935 | + | 11.1940i | −0.0629613 | + | 0.387384i | ||||
\(836\) | −1.13681 | + | 1.96902i | −0.0393175 | + | 0.0680999i | ||||
\(837\) | −6.36396 | − | 3.67423i | −0.219971 | − | 0.127000i | ||||
\(838\) | 2.53590 | − | 1.46410i | 0.0876012 | − | 0.0505766i | ||||
\(839\) | 9.04008 | 0.312098 | 0.156049 | − | 0.987749i | \(-0.450124\pi\) | ||||
0.156049 | + | 0.987749i | \(0.450124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.7128 | 1.74872 | ||||||||
\(842\) | 48.1576 | − | 27.8038i | 1.65962 | − | 0.958182i | ||||
\(843\) | −0.124356 | − | 0.0717968i | −0.00428304 | − | 0.00247281i | ||||
\(844\) | −11.3205 | + | 19.6077i | −0.389668 | + | 0.674925i | ||||
\(845\) | −6.62132 | − | 1.07616i | −0.227780 | − | 0.0370210i | ||||
\(846\) | −11.5911 | −0.398511 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 32.8043i | − | 1.12650i | ||||||
\(849\) | −14.9282 | − | 25.8564i | −0.512335 | − | 0.887390i | ||||
\(850\) | 36.6483 | + | 12.2361i | 1.25703 | + | 0.419694i | ||||
\(851\) | 2.39230 | − | 4.14359i | 0.0820072 | − | 0.142041i | ||||
\(852\) | −21.5885 | + | 12.4641i | −0.739608 | + | 0.427013i | ||||
\(853\) | − | 26.9282i | − | 0.922004i | −0.887399 | − | 0.461002i | \(-0.847490\pi\) | ||
0.887399 | − | 0.461002i | \(-0.152510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.535898 | − | 0.656339i | 0.0183273 | − | 0.0224463i | ||||
\(856\) | 4.02628 | + | 6.97372i | 0.137615 | + | 0.238357i | ||||
\(857\) | −15.4641 | − | 8.92820i | −0.528244 | − | 0.304982i | 0.212057 | − | 0.977257i | \(-0.431984\pi\) |
−0.740301 | + | 0.672276i | \(0.765317\pi\) | |||||||
\(858\) | −23.1822 | − | 13.3843i | −0.791428 | − | 0.456931i | ||||
\(859\) | 23.7506 | + | 41.1373i | 0.810361 | + | 1.40359i | 0.912612 | + | 0.408828i | \(0.134062\pi\) |
−0.102251 | + | 0.994759i | \(0.532604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 5.17638i | − | 0.176308i | ||||||
\(863\) | 45.6202 | − | 26.3388i | 1.55293 | − | 0.896584i | 0.555027 | − | 0.831832i | \(-0.312708\pi\) |
0.997901 | − | 0.0647515i | \(-0.0206255\pi\) | |||||||
\(864\) | −3.79435 | + | 6.57201i | −0.129087 | + | 0.223584i | ||||
\(865\) | −33.4523 | + | 12.6863i | −1.13741 | + | 0.431347i | ||||
\(866\) | 9.52056 | + | 16.4901i | 0.323522 | + | 0.560356i | ||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.7128 | −1.34716 | ||||||||
\(870\) | −38.0681 | − | 6.18718i | −1.29063 | − | 0.209765i | ||||
\(871\) | 13.9391 | − | 24.1432i | 0.472307 | − | 0.818060i | ||||
\(872\) | 5.31508 | + | 3.06866i | 0.179991 | + | 0.103918i | ||||
\(873\) | −4.39230 | + | 2.53590i | −0.148657 | + | 0.0858272i | ||||
\(874\) | −4.62158 | −0.156327 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.9282 | −0.639525 | ||||||||
\(877\) | 29.3939 | − | 16.9706i | 0.992561 | − | 0.573055i | 0.0865220 | − | 0.996250i | \(-0.472425\pi\) |
0.906039 | + | 0.423195i | \(0.139091\pi\) | |||||||
\(878\) | −2.83013 | − | 1.63397i | −0.0955122 | − | 0.0551440i | ||||
\(879\) | −2.26795 | + | 3.92820i | −0.0764960 | + | 0.132495i | ||||
\(880\) | 34.1309 | + | 5.54727i | 1.15055 | + | 0.186999i | ||||
\(881\) | 10.0010 | 0.336943 | 0.168472 | − | 0.985707i | \(-0.446117\pi\) | ||||
0.168472 | + | 0.985707i | \(0.446117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.3939i | − | 0.989183i | −0.869126 | − | 0.494591i | \(-0.835318\pi\) | ||
0.869126 | − | 0.494591i | \(-0.164682\pi\) | |||||||
\(884\) | 13.8564 | + | 24.0000i | 0.466041 | + | 0.807207i | ||||
\(885\) | −22.0698 | + | 8.36965i | −0.741869 | + | 0.281343i | ||||
\(886\) | 25.7583 | − | 44.6147i | 0.865368 | − | 1.49886i | ||||
\(887\) | −36.1244 | + | 20.8564i | −1.21294 | + | 0.700290i | −0.963398 | − | 0.268075i | \(-0.913612\pi\) |
−0.249539 | + | 0.968365i | \(0.580279\pi\) | |||||||
\(888\) | − | 0.392305i | − | 0.0131649i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.8564 | + | 11.3137i | 0.464468 | + | 0.379236i | ||||
\(891\) | 1.73205 | + | 3.00000i | 0.0580259 | + | 0.100504i | ||||
\(892\) | −12.0000 | − | 6.92820i | −0.401790 | − | 0.231973i | ||||
\(893\) | −1.96902 | − | 1.13681i | −0.0658906 | − | 0.0380420i | ||||
\(894\) | 20.2151 | + | 35.0136i | 0.676094 | + | 1.17103i | ||||
\(895\) | −14.6969 | + | 18.0000i | −0.491264 | + | 0.601674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 25.2528i | − | 0.843166i | ||||||
\(898\) | 13.6245 | − | 7.86611i | 0.454655 | − | 0.262495i | ||||
\(899\) | −32.8043 | + | 56.8187i | −1.09409 | + | 1.89501i | ||||
\(900\) | 8.21449 | + | 2.74264i | 0.273816 | + | 0.0914214i | ||||
\(901\) | 14.6969 | + | 25.4558i | 0.489626 | + | 0.848057i | ||||
\(902\) | − | 56.7846i | − | 1.89072i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.196152 | −0.00652393 | ||||||||
\(905\) | −7.69125 | − | 1.25005i | −0.255666 | − | 0.0415532i | ||||
\(906\) | 12.1087 | − | 20.9730i | 0.402286 | − | 0.696780i | ||||
\(907\) | −45.0518 | − | 26.0106i | −1.49592 | − | 0.863669i | −0.495930 | − | 0.868362i | \(-0.665173\pi\) |
−0.999989 | + | 0.00469302i | \(0.998506\pi\) | |||||||
\(908\) | −6.00000 | + | 3.46410i | −0.199117 | + | 0.114960i | ||||
\(909\) | 12.6264 | 0.418791 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.3923 | 1.00694 | 0.503471 | − | 0.864012i | \(-0.332056\pi\) | ||||
0.503471 | + | 0.864012i | \(0.332056\pi\) | |||||||
\(912\) | −1.46498 | + | 0.845807i | −0.0485104 | + | 0.0280075i | ||||
\(913\) | −18.0000 | − | 10.3923i | −0.595713 | − | 0.343935i | ||||
\(914\) | −11.6603 | + | 20.1962i | −0.385687 | + | 0.668029i | ||||
\(915\) | −3.27928 | + | 20.1765i | −0.108410 | + | 0.667016i | ||||
\(916\) | 40.3286 | 1.33250 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 7.72741i | − | 0.255042i | ||||||
\(919\) | −11.4641 | − | 19.8564i | −0.378166 | − | 0.655002i | 0.612630 | − | 0.790370i | \(-0.290112\pi\) |
−0.990795 | + | 0.135368i | \(0.956778\pi\) | |||||||
\(920\) | 2.59113 | + | 6.83253i | 0.0854272 | + | 0.225262i | ||||
\(921\) | −2.00000 | + | 3.46410i | −0.0659022 | + | 0.114146i | ||||
\(922\) | 21.4641 | − | 12.3923i | 0.706883 | − | 0.408119i | ||||
\(923\) | − | 57.5692i | − | 1.89491i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.71281 | + | 0.757875i | −0.122077 | + | 0.0249188i | ||||
\(926\) | 16.1962 | + | 28.0526i | 0.532239 | + | 0.921864i | ||||
\(927\) | 12.0000 | + | 6.92820i | 0.394132 | + | 0.227552i | ||||
\(928\) | 58.6763 | + | 33.8768i | 1.92614 | + | 1.11206i | ||||
\(929\) | −20.3538 | − | 35.2538i | −0.667786 | − | 1.15664i | −0.978522 | − | 0.206143i | \(-0.933909\pi\) |
0.310736 | − | 0.950496i | \(-0.399425\pi\) | |||||||
\(930\) | 20.0764 | − | 24.5885i | 0.658331 | − | 0.806287i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.656339i | 0.0214991i | ||||||||
\(933\) | 13.3843 | − | 7.72741i | 0.438181 | − | 0.252984i | ||||
\(934\) | −17.2480 | + | 29.8744i | −0.564371 | + | 0.977519i | ||||
\(935\) | −28.9706 | + | 10.9867i | −0.947439 | + | 0.359302i | ||||
\(936\) | −1.03528 | − | 1.79315i | −0.0338391 | − | 0.0586110i | ||||
\(937\) | 24.7846i | 0.809678i | 0.914388 | + | 0.404839i | \(0.132672\pi\) | ||||
−0.914388 | + | 0.404839i | \(0.867328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.9282 | 0.356628 | ||||||||
\(940\) | 3.72792 | − | 22.9369i | 0.121591 | − | 0.748120i | ||||
\(941\) | 19.6975 | − | 34.1170i | 0.642119 | − | 1.11218i | −0.342840 | − | 0.939394i | \(-0.611389\pi\) |
0.984959 | − | 0.172788i | \(-0.0552777\pi\) | |||||||
\(942\) | −31.6675 | − | 18.2832i | −1.03178 | − | 0.595700i | ||||
\(943\) | 46.3923 | − | 26.7846i | 1.51074 | − | 0.872227i | ||||
\(944\) | 47.1223 | 1.53370 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.9217 | + | 9.19239i | −0.517385 | + | 0.298712i | −0.735864 | − | 0.677129i | \(-0.763224\pi\) |
0.218479 | + | 0.975842i | \(0.429890\pi\) | |||||||
\(948\) | 17.1962 | + | 9.92820i | 0.558505 | + | 0.322453i | ||||
\(949\) | 21.8564 | − | 37.8564i | 0.709489 | − | 1.22887i | ||||
\(950\) | 2.42713 | + | 2.73980i | 0.0787464 | + | 0.0888910i | ||||
\(951\) | −29.2180 | −0.947459 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.6231i | 0.635655i | 0.948148 | + | 0.317828i | \(0.102953\pi\) | ||||
−0.948148 | + | 0.317828i | \(0.897047\pi\) | |||||||
\(954\) | 7.09808 | + | 12.2942i | 0.229809 | + | 0.398040i | ||||
\(955\) | 0.424910 | + | 1.12044i | 0.0137498 | + | 0.0362566i | ||||
\(956\) | 13.3923 | − | 23.1962i | 0.433138 | − | 0.750217i | ||||
\(957\) | 26.7846 | − | 15.4641i | 0.865823 | − | 0.499883i | ||||
\(958\) | − | 26.9282i | − | 0.870011i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.92820 | − | 8.10634i | −0.320431 | − | 0.261631i | ||||
\(961\) | −11.5000 | − | 19.9186i | −0.370968 | − | 0.642535i | ||||
\(962\) | −5.07180 | − | 2.92820i | −0.163521 | − | 0.0944091i | ||||
\(963\) | −13.4722 | − | 7.77817i | −0.434135 | − | 0.250648i | ||||
\(964\) | 4.81105 | + | 8.33298i | 0.154953 | + | 0.268387i | ||||
\(965\) | 28.0812 | + | 22.9282i | 0.903966 | + | 0.738085i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29.5969i | − | 0.951774i | −0.879507 | − | 0.475887i | \(-0.842127\pi\) | ||
0.879507 | − | 0.475887i | \(-0.157873\pi\) | |||||||
\(968\) | −0.448288 | + | 0.258819i | −0.0144085 | + | 0.00831876i | ||||
\(969\) | 0.757875 | − | 1.31268i | 0.0243464 | − | 0.0421693i | ||||
\(970\) | −7.76874 | − | 20.4853i | −0.249439 | − | 0.657743i | ||||
\(971\) | 28.4601 | + | 49.2944i | 0.913329 | + | 1.58193i | 0.809329 | + | 0.587355i | \(0.199831\pi\) |
0.104000 | + | 0.994577i | \(0.466836\pi\) | |||||||
\(972\) | − | 1.73205i | − | 0.0555556i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | −14.9706 | + | 13.2621i | −0.479442 | + | 0.424726i | ||||
\(976\) | 20.4046 | − | 35.3417i | 0.653134 | − | 1.13126i | ||||
\(977\) | 43.7626 | + | 25.2664i | 1.40009 | + | 0.808343i | 0.994401 | − | 0.105668i | \(-0.0336981\pi\) |
0.405690 | + | 0.914011i | \(0.367031\pi\) | |||||||
\(978\) | 28.0526 | − | 16.1962i | 0.897022 | − | 0.517896i | ||||
\(979\) | −14.3452 | −0.458475 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8564 | −0.378546 | ||||||||
\(982\) | −11.1750 | + | 6.45189i | −0.356609 | + | 0.205888i | ||||
\(983\) | 14.5359 | + | 8.39230i | 0.463623 | + | 0.267673i | 0.713566 | − | 0.700588i | \(-0.247079\pi\) |
−0.249943 | + | 0.968260i | \(0.580412\pi\) | |||||||
\(984\) | 2.19615 | − | 3.80385i | 0.0700108 | − | 0.121262i | ||||
\(985\) | 4.12153 | − | 25.3587i | 0.131323 | − | 0.807996i | ||||
\(986\) | −68.9919 | −2.19715 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.62536i | 0.0835237i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −13.9917 | + | 5.30614i | −0.444686 | + | 0.168640i | ||||
\(991\) | 14.3923 | − | 24.9282i | 0.457187 | − | 0.791870i | −0.541624 | − | 0.840621i | \(-0.682190\pi\) |
0.998811 | + | 0.0487502i | \(0.0155238\pi\) | |||||||
\(992\) | −48.2942 | + | 27.8827i | −1.53334 | + | 0.885276i | ||||
\(993\) | 32.7846i | 1.04039i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.53590 | + | 5.55532i | −0.143798 | + | 0.176115i | ||||
\(996\) | 5.19615 | + | 9.00000i | 0.164646 | + | 0.285176i | ||||
\(997\) | −12.2487 | − | 7.07180i | −0.387921 | − | 0.223966i | 0.293338 | − | 0.956009i | \(-0.405234\pi\) |
−0.681259 | + | 0.732043i | \(0.738567\pi\) | |||||||
\(998\) | −27.1846 | − | 15.6950i | −0.860514 | − | 0.496818i | ||||
\(999\) | 0.378937 | + | 0.656339i | 0.0119890 | + | 0.0207656i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 735.2.q.d.214.1 | 8 | ||
5.4 | even | 2 | 735.2.q.c.214.4 | 8 | |||
7.2 | even | 3 | 735.2.q.c.79.4 | 8 | |||
7.3 | odd | 6 | 735.2.d.f.589.1 | ✓ | 8 | ||
7.4 | even | 3 | 735.2.d.f.589.2 | yes | 8 | ||
7.5 | odd | 6 | inner | 735.2.q.d.79.4 | 8 | ||
7.6 | odd | 2 | 735.2.q.c.214.1 | 8 | |||
21.11 | odd | 6 | 2205.2.d.t.1324.8 | 8 | |||
21.17 | even | 6 | 2205.2.d.t.1324.7 | 8 | |||
35.3 | even | 12 | 3675.2.a.bu.1.1 | 4 | |||
35.4 | even | 6 | 735.2.d.f.589.7 | yes | 8 | ||
35.9 | even | 6 | inner | 735.2.q.d.79.1 | 8 | ||
35.17 | even | 12 | 3675.2.a.bs.1.4 | 4 | |||
35.18 | odd | 12 | 3675.2.a.bs.1.1 | 4 | |||
35.19 | odd | 6 | 735.2.q.c.79.1 | 8 | |||
35.24 | odd | 6 | 735.2.d.f.589.8 | yes | 8 | ||
35.32 | odd | 12 | 3675.2.a.bu.1.4 | 4 | |||
35.34 | odd | 2 | inner | 735.2.q.d.214.4 | 8 | ||
105.59 | even | 6 | 2205.2.d.t.1324.1 | 8 | |||
105.74 | odd | 6 | 2205.2.d.t.1324.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.d.f.589.1 | ✓ | 8 | 7.3 | odd | 6 | ||
735.2.d.f.589.2 | yes | 8 | 7.4 | even | 3 | ||
735.2.d.f.589.7 | yes | 8 | 35.4 | even | 6 | ||
735.2.d.f.589.8 | yes | 8 | 35.24 | odd | 6 | ||
735.2.q.c.79.1 | 8 | 35.19 | odd | 6 | |||
735.2.q.c.79.4 | 8 | 7.2 | even | 3 | |||
735.2.q.c.214.1 | 8 | 7.6 | odd | 2 | |||
735.2.q.c.214.4 | 8 | 5.4 | even | 2 | |||
735.2.q.d.79.1 | 8 | 35.9 | even | 6 | inner | ||
735.2.q.d.79.4 | 8 | 7.5 | odd | 6 | inner | ||
735.2.q.d.214.1 | 8 | 1.1 | even | 1 | trivial | ||
735.2.q.d.214.4 | 8 | 35.34 | odd | 2 | inner | ||
2205.2.d.t.1324.1 | 8 | 105.59 | even | 6 | |||
2205.2.d.t.1324.2 | 8 | 105.74 | odd | 6 | |||
2205.2.d.t.1324.7 | 8 | 21.17 | even | 6 | |||
2205.2.d.t.1324.8 | 8 | 21.11 | odd | 6 | |||
3675.2.a.bs.1.1 | 4 | 35.18 | odd | 12 | |||
3675.2.a.bs.1.4 | 4 | 35.17 | even | 12 | |||
3675.2.a.bu.1.1 | 4 | 35.3 | even | 12 | |||
3675.2.a.bu.1.4 | 4 | 35.32 | odd | 12 |