Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.14 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.b.769.13 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63529 | −1.15632 | −0.578162 | − | 0.815922i | \(-0.696230\pi\) | ||||
−0.578162 | + | 0.815922i | \(0.696230\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.674169 | 0.337085 | ||||||||
\(5\) | −1.84877 | + | 1.25780i | −0.826794 | + | 0.562505i | ||||
\(6\) | −1.63529 | −0.667604 | ||||||||
\(7\) | 1.79271 | + | 1.94582i | 0.677579 | + | 0.735450i | ||||
\(8\) | 2.16812 | 0.766545 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.02327 | − | 2.05687i | 0.956041 | − | 0.650438i | ||||
\(11\) | −3.27552 | + | 0.520547i | −0.987606 | + | 0.156951i | ||||
\(12\) | 0.674169 | 0.194616 | ||||||||
\(13\) | − | 4.17087i | − | 1.15679i | −0.815756 | − | 0.578396i | \(-0.803679\pi\) | ||
0.815756 | − | 0.578396i | \(-0.196321\pi\) | |||||||
\(14\) | −2.93159 | − | 3.18197i | −0.783501 | − | 0.850418i | ||||
\(15\) | −1.84877 | + | 1.25780i | −0.477350 | + | 0.324763i | ||||
\(16\) | −4.89383 | −1.22346 | ||||||||
\(17\) | − | 7.58089i | − | 1.83864i | −0.393516 | − | 0.919318i | \(-0.628742\pi\) | ||
0.393516 | − | 0.919318i | \(-0.371258\pi\) | |||||||
\(18\) | −1.63529 | −0.385441 | ||||||||
\(19\) | 5.73183 | 1.31497 | 0.657487 | − | 0.753466i | \(-0.271620\pi\) | ||||
0.657487 | + | 0.753466i | \(0.271620\pi\) | |||||||
\(20\) | −1.24638 | + | 0.847970i | −0.278699 | + | 0.189612i | ||||
\(21\) | 1.79271 | + | 1.94582i | 0.391200 | + | 0.424612i | ||||
\(22\) | 5.35642 | − | 0.851244i | 1.14199 | − | 0.181486i | ||||
\(23\) | − | 2.17955i | − | 0.454467i | −0.973840 | − | 0.227233i | \(-0.927032\pi\) | ||
0.973840 | − | 0.227233i | \(-0.0729681\pi\) | |||||||
\(24\) | 2.16812 | 0.442565 | ||||||||
\(25\) | 1.83588 | − | 4.65076i | 0.367176 | − | 0.930152i | ||||
\(26\) | 6.82058i | 1.33763i | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.20859 | + | 1.31181i | 0.228402 | + | 0.247909i | ||||
\(29\) | 5.39200i | 1.00127i | 0.865659 | + | 0.500635i | \(0.166900\pi\) | ||||
−0.865659 | + | 0.500635i | \(0.833100\pi\) | |||||||
\(30\) | 3.02327 | − | 2.05687i | 0.551971 | − | 0.375531i | ||||
\(31\) | 0.864081i | 0.155194i | 0.996985 | + | 0.0775968i | \(0.0247247\pi\) | ||||
−0.996985 | + | 0.0775968i | \(0.975275\pi\) | |||||||
\(32\) | 3.66660 | 0.648169 | ||||||||
\(33\) | −3.27552 | + | 0.520547i | −0.570195 | + | 0.0906155i | ||||
\(34\) | 12.3969i | 2.12606i | ||||||||
\(35\) | −5.76174 | − | 1.34250i | −0.973913 | − | 0.226924i | ||||
\(36\) | 0.674169 | 0.112362 | ||||||||
\(37\) | 2.91371i | 0.479010i | 0.970895 | + | 0.239505i | \(0.0769852\pi\) | ||||
−0.970895 | + | 0.239505i | \(0.923015\pi\) | |||||||
\(38\) | −9.37321 | −1.52053 | ||||||||
\(39\) | − | 4.17087i | − | 0.667874i | ||||||
\(40\) | −4.00834 | + | 2.72706i | −0.633774 | + | 0.431185i | ||||
\(41\) | −3.36581 | −0.525651 | −0.262826 | − | 0.964843i | \(-0.584654\pi\) | ||||
−0.262826 | + | 0.964843i | \(0.584654\pi\) | |||||||
\(42\) | −2.93159 | − | 3.18197i | −0.452354 | − | 0.490989i | ||||
\(43\) | 5.31325 | 0.810263 | 0.405132 | − | 0.914258i | \(-0.367226\pi\) | ||||
0.405132 | + | 0.914258i | \(0.367226\pi\) | |||||||
\(44\) | −2.20825 | + | 0.350936i | −0.332907 | + | 0.0529057i | ||||
\(45\) | −1.84877 | + | 1.25780i | −0.275598 | + | 0.187502i | ||||
\(46\) | 3.56419i | 0.525511i | ||||||||
\(47\) | 10.7554 | 1.56884 | 0.784420 | − | 0.620229i | \(-0.212961\pi\) | ||||
0.784420 | + | 0.620229i | \(0.212961\pi\) | |||||||
\(48\) | −4.89383 | −0.706364 | ||||||||
\(49\) | −0.572412 | + | 6.97656i | −0.0817731 | + | 0.996651i | ||||
\(50\) | −3.00219 | + | 7.60533i | −0.424574 | + | 1.07556i | ||||
\(51\) | − | 7.58089i | − | 1.06154i | ||||||
\(52\) | − | 2.81187i | − | 0.389937i | ||||||
\(53\) | 11.1538i | 1.53209i | 0.642788 | + | 0.766044i | \(0.277777\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722223\pi\) | |||||||
\(54\) | −1.63529 | −0.222535 | ||||||||
\(55\) | 5.40093 | − | 5.08232i | 0.728261 | − | 0.685300i | ||||
\(56\) | 3.88679 | + | 4.21876i | 0.519395 | + | 0.563755i | ||||
\(57\) | 5.73183 | 0.759200 | ||||||||
\(58\) | − | 8.81748i | − | 1.15779i | ||||||
\(59\) | − | 10.8770i | − | 1.41606i | −0.706180 | − | 0.708032i | \(-0.749583\pi\) | ||
0.706180 | − | 0.708032i | \(-0.250417\pi\) | |||||||
\(60\) | −1.24638 | + | 0.847970i | −0.160907 | + | 0.109472i | ||||
\(61\) | 15.3838 | 1.96969 | 0.984846 | − | 0.173430i | \(-0.0554851\pi\) | ||||
0.984846 | + | 0.173430i | \(0.0554851\pi\) | |||||||
\(62\) | − | 1.41302i | − | 0.179454i | ||||||
\(63\) | 1.79271 | + | 1.94582i | 0.225860 | + | 0.245150i | ||||
\(64\) | 3.79172 | 0.473965 | ||||||||
\(65\) | 5.24612 | + | 7.71097i | 0.650701 | + | 0.956428i | ||||
\(66\) | 5.35642 | − | 0.851244i | 0.659330 | − | 0.104781i | ||||
\(67\) | − | 10.6944i | − | 1.30653i | −0.757131 | − | 0.653263i | \(-0.773400\pi\) | ||
0.757131 | − | 0.653263i | \(-0.226600\pi\) | |||||||
\(68\) | − | 5.11080i | − | 0.619776i | ||||||
\(69\) | − | 2.17955i | − | 0.262387i | ||||||
\(70\) | 9.42212 | + | 2.19537i | 1.12616 | + | 0.262397i | ||||
\(71\) | −1.55383 | −0.184405 | −0.0922027 | − | 0.995740i | \(-0.529391\pi\) | ||||
−0.0922027 | + | 0.995740i | \(0.529391\pi\) | |||||||
\(72\) | 2.16812 | 0.255515 | ||||||||
\(73\) | − | 2.25681i | − | 0.264140i | −0.991240 | − | 0.132070i | \(-0.957838\pi\) | ||
0.991240 | − | 0.132070i | \(-0.0421623\pi\) | |||||||
\(74\) | − | 4.76475i | − | 0.553891i | ||||||
\(75\) | 1.83588 | − | 4.65076i | 0.211989 | − | 0.537023i | ||||
\(76\) | 3.86423 | 0.443257 | ||||||||
\(77\) | −6.88493 | − | 5.44038i | −0.784611 | − | 0.619989i | ||||
\(78\) | 6.82058i | 0.772278i | ||||||||
\(79\) | 8.24756i | 0.927923i | 0.885855 | + | 0.463961i | \(0.153572\pi\) | ||||
−0.885855 | + | 0.463961i | \(0.846428\pi\) | |||||||
\(80\) | 9.04756 | − | 6.15546i | 1.01155 | − | 0.688202i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.50407 | 0.607823 | ||||||||
\(83\) | − | 5.54564i | − | 0.608713i | −0.952558 | − | 0.304357i | \(-0.901559\pi\) | ||
0.952558 | − | 0.304357i | \(-0.0984415\pi\) | |||||||
\(84\) | 1.20859 | + | 1.31181i | 0.131868 | + | 0.143130i | ||||
\(85\) | 9.53524 | + | 14.0153i | 1.03424 | + | 1.52017i | ||||
\(86\) | −8.68870 | −0.936926 | ||||||||
\(87\) | 5.39200i | 0.578083i | ||||||||
\(88\) | −7.10171 | + | 1.12861i | −0.757045 | + | 0.120310i | ||||
\(89\) | − | 1.62655i | − | 0.172414i | −0.996277 | − | 0.0862069i | \(-0.972525\pi\) | ||
0.996277 | − | 0.0862069i | \(-0.0274746\pi\) | |||||||
\(90\) | 3.02327 | − | 2.05687i | 0.318680 | − | 0.216813i | ||||
\(91\) | 8.11575 | − | 7.47715i | 0.850762 | − | 0.783818i | ||||
\(92\) | − | 1.46938i | − | 0.153194i | ||||||
\(93\) | 0.864081i | 0.0896010i | ||||||||
\(94\) | −17.5882 | −1.81409 | ||||||||
\(95\) | −10.5968 | + | 7.20950i | −1.08721 | + | 0.739679i | ||||
\(96\) | 3.66660 | 0.374221 | ||||||||
\(97\) | 8.80400 | 0.893911 | 0.446955 | − | 0.894556i | \(-0.352508\pi\) | ||||
0.446955 | + | 0.894556i | \(0.352508\pi\) | |||||||
\(98\) | 0.936058 | − | 11.4087i | 0.0945562 | − | 1.15245i | ||||
\(99\) | −3.27552 | + | 0.520547i | −0.329202 | + | 0.0523169i | ||||
\(100\) | 1.23769 | − | 3.13540i | 0.123769 | − | 0.313540i | ||||
\(101\) | 0.825476 | 0.0821379 | 0.0410690 | − | 0.999156i | \(-0.486924\pi\) | ||||
0.0410690 | + | 0.999156i | \(0.486924\pi\) | |||||||
\(102\) | 12.3969i | 1.22748i | ||||||||
\(103\) | −11.5317 | −1.13625 | −0.568127 | − | 0.822941i | \(-0.692332\pi\) | ||||
−0.568127 | + | 0.822941i | \(0.692332\pi\) | |||||||
\(104\) | − | 9.04293i | − | 0.886733i | ||||||
\(105\) | −5.76174 | − | 1.34250i | −0.562289 | − | 0.131014i | ||||
\(106\) | − | 18.2396i | − | 1.77159i | ||||||
\(107\) | 9.69116 | 0.936880 | 0.468440 | − | 0.883495i | \(-0.344816\pi\) | ||||
0.468440 | + | 0.883495i | \(0.344816\pi\) | |||||||
\(108\) | 0.674169 | 0.0648720 | ||||||||
\(109\) | − | 10.2781i | − | 0.984462i | −0.870465 | − | 0.492231i | \(-0.836181\pi\) | ||
0.870465 | − | 0.492231i | \(-0.163819\pi\) | |||||||
\(110\) | −8.83208 | + | 8.31106i | −0.842106 | + | 0.792428i | ||||
\(111\) | 2.91371i | 0.276557i | ||||||||
\(112\) | −8.77321 | − | 9.52251i | −0.828990 | − | 0.899792i | ||||
\(113\) | 15.0285i | 1.41376i | 0.707333 | + | 0.706881i | \(0.249898\pi\) | ||||
−0.707333 | + | 0.706881i | \(0.750102\pi\) | |||||||
\(114\) | −9.37321 | −0.877881 | ||||||||
\(115\) | 2.74143 | + | 4.02947i | 0.255640 | + | 0.375750i | ||||
\(116\) | 3.63512i | 0.337513i | ||||||||
\(117\) | − | 4.17087i | − | 0.385597i | ||||||
\(118\) | 17.7870i | 1.63743i | ||||||||
\(119\) | 14.7510 | − | 13.5903i | 1.35222 | − | 1.24582i | ||||
\(120\) | −4.00834 | + | 2.72706i | −0.365910 | + | 0.248945i | ||||
\(121\) | 10.4581 | − | 3.41012i | 0.950733 | − | 0.310011i | ||||
\(122\) | −25.1569 | −2.27760 | ||||||||
\(123\) | −3.36581 | −0.303485 | ||||||||
\(124\) | 0.582537i | 0.0523134i | ||||||||
\(125\) | 2.45561 | + | 10.9073i | 0.219637 | + | 0.975582i | ||||
\(126\) | −2.93159 | − | 3.18197i | −0.261167 | − | 0.283473i | ||||
\(127\) | 7.78569 | 0.690868 | 0.345434 | − | 0.938443i | \(-0.387732\pi\) | ||||
0.345434 | + | 0.938443i | \(0.387732\pi\) | |||||||
\(128\) | −13.5338 | −1.19623 | ||||||||
\(129\) | 5.31325 | 0.467806 | ||||||||
\(130\) | −8.57892 | − | 12.6097i | −0.752421 | − | 1.10594i | ||||
\(131\) | 2.89541 | 0.252973 | 0.126486 | − | 0.991968i | \(-0.459630\pi\) | ||||
0.126486 | + | 0.991968i | \(0.459630\pi\) | |||||||
\(132\) | −2.20825 | + | 0.350936i | −0.192204 | + | 0.0305451i | ||||
\(133\) | 10.2755 | + | 11.1531i | 0.890998 | + | 0.967097i | ||||
\(134\) | 17.4884i | 1.51077i | ||||||||
\(135\) | −1.84877 | + | 1.25780i | −0.159117 | + | 0.108254i | ||||
\(136\) | − | 16.4362i | − | 1.40940i | ||||||
\(137\) | − | 9.16402i | − | 0.782935i | −0.920192 | − | 0.391468i | \(-0.871967\pi\) | ||
0.920192 | − | 0.391468i | \(-0.128033\pi\) | |||||||
\(138\) | 3.56419i | 0.303404i | ||||||||
\(139\) | 7.30048 | 0.619218 | 0.309609 | − | 0.950864i | \(-0.399802\pi\) | ||||
0.309609 | + | 0.950864i | \(0.399802\pi\) | |||||||
\(140\) | −3.88439 | − | 0.905071i | −0.328291 | − | 0.0764924i | ||||
\(141\) | 10.7554 | 0.905771 | ||||||||
\(142\) | 2.54096 | 0.213232 | ||||||||
\(143\) | 2.17113 | + | 13.6618i | 0.181559 | + | 1.14245i | ||||
\(144\) | −4.89383 | −0.407820 | ||||||||
\(145\) | −6.78206 | − | 9.96856i | −0.563219 | − | 0.827844i | ||||
\(146\) | 3.69054i | 0.305431i | ||||||||
\(147\) | −0.572412 | + | 6.97656i | −0.0472117 | + | 0.575417i | ||||
\(148\) | 1.96433i | 0.161467i | ||||||||
\(149\) | 16.9556i | 1.38905i | 0.719467 | + | 0.694526i | \(0.244386\pi\) | ||||
−0.719467 | + | 0.694526i | \(0.755614\pi\) | |||||||
\(150\) | −3.00219 | + | 7.60533i | −0.245128 | + | 0.620973i | ||||
\(151\) | − | 16.3343i | − | 1.32927i | −0.747170 | − | 0.664633i | \(-0.768588\pi\) | ||
0.747170 | − | 0.664633i | \(-0.231412\pi\) | |||||||
\(152\) | 12.4273 | 1.00799 | ||||||||
\(153\) | − | 7.58089i | − | 0.612878i | ||||||
\(154\) | 11.2589 | + | 8.89659i | 0.907264 | + | 0.716907i | ||||
\(155\) | −1.08684 | − | 1.59748i | −0.0872972 | − | 0.128313i | ||||
\(156\) | − | 2.81187i | − | 0.225130i | ||||||
\(157\) | −0.510450 | −0.0407384 | −0.0203692 | − | 0.999793i | \(-0.506484\pi\) | ||||
−0.0203692 | + | 0.999793i | \(0.506484\pi\) | |||||||
\(158\) | − | 13.4871i | − | 1.07298i | ||||||
\(159\) | 11.1538i | 0.884551i | ||||||||
\(160\) | −6.77869 | + | 4.61185i | −0.535902 | + | 0.364599i | ||||
\(161\) | 4.24100 | − | 3.90729i | 0.334238 | − | 0.307937i | ||||
\(162\) | −1.63529 | −0.128480 | ||||||||
\(163\) | 24.3951i | 1.91077i | 0.295362 | + | 0.955385i | \(0.404560\pi\) | ||||
−0.295362 | + | 0.955385i | \(0.595440\pi\) | |||||||
\(164\) | −2.26912 | −0.177189 | ||||||||
\(165\) | 5.40093 | − | 5.08232i | 0.420462 | − | 0.395658i | ||||
\(166\) | 9.06873i | 0.703870i | ||||||||
\(167\) | − | 14.6558i | − | 1.13410i | −0.823682 | − | 0.567052i | \(-0.808084\pi\) | ||
0.823682 | − | 0.567052i | \(-0.191916\pi\) | |||||||
\(168\) | 3.88679 | + | 4.21876i | 0.299873 | + | 0.325484i | ||||
\(169\) | −4.39617 | −0.338167 | ||||||||
\(170\) | −15.5929 | − | 22.9191i | −1.19592 | − | 1.75781i | ||||
\(171\) | 5.73183 | 0.438324 | ||||||||
\(172\) | 3.58203 | 0.273127 | ||||||||
\(173\) | − | 17.0484i | − | 1.29617i | −0.761569 | − | 0.648083i | \(-0.775571\pi\) | ||
0.761569 | − | 0.648083i | \(-0.224429\pi\) | |||||||
\(174\) | − | 8.81748i | − | 0.668452i | ||||||
\(175\) | 12.3407 | − | 4.76516i | 0.932870 | − | 0.360212i | ||||
\(176\) | 16.0299 | − | 2.54747i | 1.20830 | − | 0.192023i | ||||
\(177\) | − | 10.8770i | − | 0.817565i | ||||||
\(178\) | 2.65988i | 0.199366i | ||||||||
\(179\) | 19.0830 | 1.42633 | 0.713166 | − | 0.700996i | \(-0.247261\pi\) | ||||
0.713166 | + | 0.700996i | \(0.247261\pi\) | |||||||
\(180\) | −1.24638 | + | 0.847970i | −0.0928998 | + | 0.0632040i | ||||
\(181\) | 7.90098i | 0.587275i | 0.955917 | + | 0.293638i | \(0.0948659\pi\) | ||||
−0.955917 | + | 0.293638i | \(0.905134\pi\) | |||||||
\(182\) | −13.2716 | + | 12.2273i | −0.983757 | + | 0.906347i | ||||
\(183\) | 15.3838 | 1.13720 | ||||||||
\(184\) | − | 4.72551i | − | 0.348369i | ||||||
\(185\) | −3.66486 | − | 5.38676i | −0.269446 | − | 0.396043i | ||||
\(186\) | − | 1.41302i | − | 0.103608i | ||||||
\(187\) | 3.94620 | + | 24.8313i | 0.288575 | + | 1.81585i | ||||
\(188\) | 7.25098 | 0.528832 | ||||||||
\(189\) | 1.79271 | + | 1.94582i | 0.130400 | + | 0.141537i | ||||
\(190\) | 17.3289 | − | 11.7896i | 1.25717 | − | 0.855309i | ||||
\(191\) | 0.577417 | 0.0417804 | 0.0208902 | − | 0.999782i | \(-0.493350\pi\) | ||||
0.0208902 | + | 0.999782i | \(0.493350\pi\) | |||||||
\(192\) | 3.79172 | 0.273644 | ||||||||
\(193\) | −14.2196 | −1.02355 | −0.511776 | − | 0.859119i | \(-0.671012\pi\) | ||||
−0.511776 | + | 0.859119i | \(0.671012\pi\) | |||||||
\(194\) | −14.3971 | −1.03365 | ||||||||
\(195\) | 5.24612 | + | 7.71097i | 0.375683 | + | 0.552194i | ||||
\(196\) | −0.385902 | + | 4.70338i | −0.0275645 | + | 0.335956i | ||||
\(197\) | 2.26374 | 0.161285 | 0.0806425 | − | 0.996743i | \(-0.474303\pi\) | ||||
0.0806425 | + | 0.996743i | \(0.474303\pi\) | |||||||
\(198\) | 5.35642 | − | 0.851244i | 0.380664 | − | 0.0604953i | ||||
\(199\) | 0.287141i | 0.0203549i | 0.999948 | + | 0.0101774i | \(0.00323964\pi\) | ||||
−0.999948 | + | 0.0101774i | \(0.996760\pi\) | |||||||
\(200\) | 3.98040 | − | 10.0834i | 0.281457 | − | 0.713003i | ||||
\(201\) | − | 10.6944i | − | 0.754323i | ||||||
\(202\) | −1.34989 | −0.0949780 | ||||||||
\(203\) | −10.4919 | + | 9.66627i | −0.736384 | + | 0.678439i | ||||
\(204\) | − | 5.11080i | − | 0.357828i | ||||||
\(205\) | 6.22260 | − | 4.23351i | 0.434605 | − | 0.295681i | ||||
\(206\) | 18.8577 | 1.31388 | ||||||||
\(207\) | − | 2.17955i | − | 0.151489i | ||||||
\(208\) | 20.4116i | 1.41529i | ||||||||
\(209\) | −18.7747 | + | 2.98369i | −1.29868 | + | 0.206386i | ||||
\(210\) | 9.42212 | + | 2.19537i | 0.650188 | + | 0.151495i | ||||
\(211\) | 15.6678i | 1.07861i | 0.842109 | + | 0.539307i | \(0.181314\pi\) | ||||
−0.842109 | + | 0.539307i | \(0.818686\pi\) | |||||||
\(212\) | 7.51953i | 0.516443i | ||||||||
\(213\) | −1.55383 | −0.106467 | ||||||||
\(214\) | −15.8478 | −1.08334 | ||||||||
\(215\) | −9.82296 | + | 6.68301i | −0.669920 | + | 0.455777i | ||||
\(216\) | 2.16812 | 0.147522 | ||||||||
\(217\) | −1.68134 | + | 1.54904i | −0.114137 | + | 0.105156i | ||||
\(218\) | 16.8076i | 1.13836i | ||||||||
\(219\) | − | 2.25681i | − | 0.152501i | ||||||
\(220\) | 3.64114 | − | 3.42634i | 0.245486 | − | 0.231004i | ||||
\(221\) | −31.6189 | −2.12692 | ||||||||
\(222\) | − | 4.76475i | − | 0.319789i | ||||||
\(223\) | −21.1236 | −1.41454 | −0.707269 | − | 0.706945i | \(-0.750073\pi\) | ||||
−0.707269 | + | 0.706945i | \(0.750073\pi\) | |||||||
\(224\) | 6.57314 | + | 7.13453i | 0.439186 | + | 0.476696i | ||||
\(225\) | 1.83588 | − | 4.65076i | 0.122392 | − | 0.310051i | ||||
\(226\) | − | 24.5759i | − | 1.63477i | ||||||
\(227\) | 7.65754i | 0.508249i | 0.967172 | + | 0.254124i | \(0.0817873\pi\) | ||||
−0.967172 | + | 0.254124i | \(0.918213\pi\) | |||||||
\(228\) | 3.86423 | 0.255915 | ||||||||
\(229\) | − | 19.9463i | − | 1.31809i | −0.752103 | − | 0.659045i | \(-0.770961\pi\) | ||
0.752103 | − | 0.659045i | \(-0.229039\pi\) | |||||||
\(230\) | −4.48304 | − | 6.58935i | −0.295603 | − | 0.434489i | ||||
\(231\) | −6.88493 | − | 5.44038i | −0.452995 | − | 0.357951i | ||||
\(232\) | 11.6905i | 0.767518i | ||||||||
\(233\) | 5.69495 | 0.373088 | 0.186544 | − | 0.982447i | \(-0.440271\pi\) | ||||
0.186544 | + | 0.982447i | \(0.440271\pi\) | |||||||
\(234\) | 6.82058i | 0.445875i | ||||||||
\(235\) | −19.8843 | + | 13.5282i | −1.29711 | + | 0.882481i | ||||
\(236\) | − | 7.33293i | − | 0.477333i | ||||||
\(237\) | 8.24756i | 0.535736i | ||||||||
\(238\) | −24.1222 | + | 22.2241i | −1.56361 | + | 1.44057i | ||||
\(239\) | − | 9.91495i | − | 0.641345i | −0.947190 | − | 0.320672i | \(-0.896091\pi\) | ||
0.947190 | − | 0.320672i | \(-0.103909\pi\) | |||||||
\(240\) | 9.04756 | − | 6.15546i | 0.584017 | − | 0.397334i | ||||
\(241\) | 2.07373 | 0.133581 | 0.0667903 | − | 0.997767i | \(-0.478724\pi\) | ||||
0.0667903 | + | 0.997767i | \(0.478724\pi\) | |||||||
\(242\) | −17.1020 | + | 5.57653i | −1.09936 | + | 0.358473i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.3713 | 0.663953 | ||||||||
\(245\) | −7.71686 | − | 13.6180i | −0.493012 | − | 0.870023i | ||||
\(246\) | 5.50407 | 0.350927 | ||||||||
\(247\) | − | 23.9067i | − | 1.52115i | ||||||
\(248\) | 1.87343i | 0.118963i | ||||||||
\(249\) | − | 5.54564i | − | 0.351441i | ||||||
\(250\) | −4.01563 | − | 17.8366i | −0.253971 | − | 1.12809i | ||||
\(251\) | − | 9.03128i | − | 0.570049i | −0.958520 | − | 0.285025i | \(-0.907998\pi\) | ||
0.958520 | − | 0.285025i | \(-0.0920018\pi\) | |||||||
\(252\) | 1.20859 | + | 1.31181i | 0.0761338 | + | 0.0826363i | ||||
\(253\) | 1.13456 | + | 7.13915i | 0.0713289 | + | 0.448835i | ||||
\(254\) | −12.7319 | −0.798868 | ||||||||
\(255\) | 9.53524 | + | 14.0153i | 0.597120 | + | 0.877672i | ||||
\(256\) | 14.5482 | 0.909260 | ||||||||
\(257\) | 15.2678 | 0.952376 | 0.476188 | − | 0.879343i | \(-0.342018\pi\) | ||||
0.476188 | + | 0.879343i | \(0.342018\pi\) | |||||||
\(258\) | −8.68870 | −0.540935 | ||||||||
\(259\) | −5.66954 | + | 5.22342i | −0.352288 | + | 0.324567i | ||||
\(260\) | 3.53677 | + | 5.19850i | 0.219341 | + | 0.322397i | ||||
\(261\) | 5.39200i | 0.333757i | ||||||||
\(262\) | −4.73483 | −0.292518 | ||||||||
\(263\) | −6.40729 | −0.395090 | −0.197545 | − | 0.980294i | \(-0.563297\pi\) | ||||
−0.197545 | + | 0.980294i | \(0.563297\pi\) | |||||||
\(264\) | −7.10171 | + | 1.12861i | −0.437080 | + | 0.0694609i | ||||
\(265\) | −14.0292 | − | 20.6207i | −0.861807 | − | 1.26672i | ||||
\(266\) | −16.8034 | − | 18.2385i | −1.03028 | − | 1.11828i | ||||
\(267\) | − | 1.62655i | − | 0.0995432i | ||||||
\(268\) | − | 7.20982i | − | 0.440410i | ||||||
\(269\) | 13.5541i | 0.826410i | 0.910638 | + | 0.413205i | \(0.135591\pi\) | ||||
−0.910638 | + | 0.413205i | \(0.864409\pi\) | |||||||
\(270\) | 3.02327 | − | 2.05687i | 0.183990 | − | 0.125177i | ||||
\(271\) | 13.5515 | 0.823195 | 0.411598 | − | 0.911366i | \(-0.364971\pi\) | ||||
0.411598 | + | 0.911366i | \(0.364971\pi\) | |||||||
\(272\) | 37.0996i | 2.24949i | ||||||||
\(273\) | 8.11575 | − | 7.47715i | 0.491188 | − | 0.452537i | ||||
\(274\) | 14.9858i | 0.905327i | ||||||||
\(275\) | −3.59252 | + | 16.1893i | −0.216637 | + | 0.976252i | ||||
\(276\) | − | 1.46938i | − | 0.0884465i | ||||||
\(277\) | 10.5948 | 0.636580 | 0.318290 | − | 0.947993i | \(-0.396891\pi\) | ||||
0.318290 | + | 0.947993i | \(0.396891\pi\) | |||||||
\(278\) | −11.9384 | −0.716017 | ||||||||
\(279\) | 0.864081i | 0.0517312i | ||||||||
\(280\) | −12.4921 | − | 2.91069i | −0.746548 | − | 0.173947i | ||||
\(281\) | − | 11.4974i | − | 0.685880i | −0.939357 | − | 0.342940i | \(-0.888577\pi\) | ||
0.939357 | − | 0.342940i | \(-0.111423\pi\) | |||||||
\(282\) | −17.5882 | −1.04736 | ||||||||
\(283\) | − | 21.6818i | − | 1.28885i | −0.764668 | − | 0.644424i | \(-0.777097\pi\) | ||
0.764668 | − | 0.644424i | \(-0.222903\pi\) | |||||||
\(284\) | −1.04754 | −0.0621602 | ||||||||
\(285\) | −10.5968 | + | 7.20950i | −0.627702 | + | 0.427054i | ||||
\(286\) | −3.55043 | − | 22.3409i | −0.209941 | − | 1.32105i | ||||
\(287\) | −6.03390 | − | 6.54925i | −0.356170 | − | 0.386590i | ||||
\(288\) | 3.66660 | 0.216056 | ||||||||
\(289\) | −40.4698 | −2.38058 | ||||||||
\(290\) | 11.0906 | + | 16.3015i | 0.651264 | + | 0.957255i | ||||
\(291\) | 8.80400 | 0.516100 | ||||||||
\(292\) | − | 1.52147i | − | 0.0890375i | ||||||
\(293\) | 7.13847i | 0.417034i | 0.978019 | + | 0.208517i | \(0.0668636\pi\) | ||||
−0.978019 | + | 0.208517i | \(0.933136\pi\) | |||||||
\(294\) | 0.936058 | − | 11.4087i | 0.0545920 | − | 0.665368i | ||||
\(295\) | 13.6811 | + | 20.1090i | 0.796543 | + | 1.17079i | ||||
\(296\) | 6.31725i | 0.367183i | ||||||||
\(297\) | −3.27552 | + | 0.520547i | −0.190065 | + | 0.0302052i | ||||
\(298\) | − | 27.7272i | − | 1.60619i | ||||||
\(299\) | −9.09061 | −0.525724 | ||||||||
\(300\) | 1.23769 | − | 3.13540i | 0.0714582 | − | 0.181022i | ||||
\(301\) | 9.52509 | + | 10.3386i | 0.549017 | + | 0.595908i | ||||
\(302\) | 26.7113i | 1.53706i | ||||||||
\(303\) | 0.825476 | 0.0474223 | ||||||||
\(304\) | −28.0507 | −1.60882 | ||||||||
\(305\) | −28.4410 | + | 19.3497i | −1.62853 | + | 1.10796i | ||||
\(306\) | 12.3969i | 0.708686i | ||||||||
\(307\) | − | 15.4378i | − | 0.881081i | −0.897733 | − | 0.440540i | \(-0.854787\pi\) | ||
0.897733 | − | 0.440540i | \(-0.145213\pi\) | |||||||
\(308\) | −4.64161 | − | 3.66774i | −0.264480 | − | 0.208989i | ||||
\(309\) | −11.5317 | −0.656016 | ||||||||
\(310\) | 1.77730 | + | 2.61235i | 0.100944 | + | 0.148371i | ||||
\(311\) | 30.4383i | 1.72600i | 0.505208 | + | 0.862998i | \(0.331416\pi\) | ||||
−0.505208 | + | 0.862998i | \(0.668584\pi\) | |||||||
\(312\) | − | 9.04293i | − | 0.511955i | ||||||
\(313\) | −31.1303 | −1.75959 | −0.879795 | − | 0.475354i | \(-0.842320\pi\) | ||||
−0.879795 | + | 0.475354i | \(0.842320\pi\) | |||||||
\(314\) | 0.834734 | 0.0471068 | ||||||||
\(315\) | −5.76174 | − | 1.34250i | −0.324638 | − | 0.0756412i | ||||
\(316\) | 5.56025i | 0.312789i | ||||||||
\(317\) | − | 28.5646i | − | 1.60435i | −0.597089 | − | 0.802175i | \(-0.703676\pi\) | ||
0.597089 | − | 0.802175i | \(-0.296324\pi\) | |||||||
\(318\) | − | 18.2396i | − | 1.02283i | ||||||
\(319\) | −2.80679 | − | 17.6616i | −0.157150 | − | 0.988860i | ||||
\(320\) | −7.01000 | + | 4.76922i | −0.391871 | + | 0.266608i | ||||
\(321\) | 9.69116 | 0.540908 | ||||||||
\(322\) | −6.93526 | + | 6.38954i | −0.386487 | + | 0.356075i | ||||
\(323\) | − | 43.4524i | − | 2.41776i | ||||||
\(324\) | 0.674169 | 0.0374538 | ||||||||
\(325\) | −19.3977 | − | 7.65721i | −1.07599 | − | 0.424746i | ||||
\(326\) | − | 39.8930i | − | 2.20947i | ||||||
\(327\) | − | 10.2781i | − | 0.568380i | ||||||
\(328\) | −7.29746 | −0.402935 | ||||||||
\(329\) | 19.2813 | + | 20.9281i | 1.06301 | + | 1.15380i | ||||
\(330\) | −8.83208 | + | 8.31106i | −0.486190 | + | 0.457509i | ||||
\(331\) | −26.6099 | −1.46261 | −0.731306 | − | 0.682050i | \(-0.761089\pi\) | ||||
−0.731306 | + | 0.682050i | \(0.761089\pi\) | |||||||
\(332\) | − | 3.73870i | − | 0.205188i | ||||||
\(333\) | 2.91371i | 0.159670i | ||||||||
\(334\) | 23.9665i | 1.31139i | ||||||||
\(335\) | 13.4514 | + | 19.7714i | 0.734927 | + | 1.08023i | ||||
\(336\) | −8.77321 | − | 9.52251i | −0.478618 | − | 0.519495i | ||||
\(337\) | −19.0036 | −1.03519 | −0.517597 | − | 0.855625i | \(-0.673173\pi\) | ||||
−0.517597 | + | 0.855625i | \(0.673173\pi\) | |||||||
\(338\) | 7.18900 | 0.391030 | ||||||||
\(339\) | 15.0285i | 0.816236i | ||||||||
\(340\) | 6.42837 | + | 9.44868i | 0.348627 | + | 0.512427i | ||||
\(341\) | −0.449794 | − | 2.83032i | −0.0243577 | − | 0.153270i | ||||
\(342\) | −9.37321 | −0.506845 | ||||||||
\(343\) | −14.6013 | + | 11.3931i | −0.788395 | + | 0.615170i | ||||
\(344\) | 11.5197 | 0.621103 | ||||||||
\(345\) | 2.74143 | + | 4.02947i | 0.147594 | + | 0.216940i | ||||
\(346\) | 27.8791i | 1.49879i | ||||||||
\(347\) | −7.26940 | −0.390242 | −0.195121 | − | 0.980779i | \(-0.562510\pi\) | ||||
−0.195121 | + | 0.980779i | \(0.562510\pi\) | |||||||
\(348\) | 3.63512i | 0.194863i | ||||||||
\(349\) | 0.888707 | 0.0475714 | 0.0237857 | − | 0.999717i | \(-0.492428\pi\) | ||||
0.0237857 | + | 0.999717i | \(0.492428\pi\) | |||||||
\(350\) | −20.1806 | + | 7.79241i | −1.07870 | + | 0.416522i | ||||
\(351\) | − | 4.17087i | − | 0.222625i | ||||||
\(352\) | −12.0100 | + | 1.90864i | −0.640136 | + | 0.101731i | ||||
\(353\) | 12.9562 | 0.689589 | 0.344794 | − | 0.938678i | \(-0.387949\pi\) | ||||
0.344794 | + | 0.938678i | \(0.387949\pi\) | |||||||
\(354\) | 17.7870i | 0.945370i | ||||||||
\(355\) | 2.87267 | − | 1.95440i | 0.152465 | − | 0.103729i | ||||
\(356\) | − | 1.09657i | − | 0.0581181i | ||||||
\(357\) | 14.7510 | − | 13.5903i | 0.780707 | − | 0.719275i | ||||
\(358\) | −31.2062 | −1.64930 | ||||||||
\(359\) | − | 8.33660i | − | 0.439989i | −0.975501 | − | 0.219994i | \(-0.929396\pi\) | ||
0.975501 | − | 0.219994i | \(-0.0706039\pi\) | |||||||
\(360\) | −4.00834 | + | 2.72706i | −0.211258 | + | 0.143728i | ||||
\(361\) | 13.8539 | 0.729154 | ||||||||
\(362\) | − | 12.9204i | − | 0.679081i | ||||||
\(363\) | 10.4581 | − | 3.41012i | 0.548906 | − | 0.178985i | ||||
\(364\) | 5.47139 | − | 5.04086i | 0.286779 | − | 0.264213i | ||||
\(365\) | 2.83862 | + | 4.17232i | 0.148580 | + | 0.218389i | ||||
\(366\) | −25.1569 | −1.31497 | ||||||||
\(367\) | −22.9597 | −1.19849 | −0.599243 | − | 0.800567i | \(-0.704532\pi\) | ||||
−0.599243 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(368\) | 10.6663i | 0.556022i | ||||||||
\(369\) | −3.36581 | −0.175217 | ||||||||
\(370\) | 5.99310 | + | 8.80892i | 0.311567 | + | 0.457954i | ||||
\(371\) | −21.7032 | + | 19.9954i | −1.12677 | + | 1.03811i | ||||
\(372\) | 0.582537i | 0.0302031i | ||||||||
\(373\) | 35.0778 | 1.81626 | 0.908129 | − | 0.418691i | \(-0.137511\pi\) | ||||
0.908129 | + | 0.418691i | \(0.137511\pi\) | |||||||
\(374\) | −6.45318 | − | 40.6064i | −0.333686 | − | 2.09971i | ||||
\(375\) | 2.45561 | + | 10.9073i | 0.126807 | + | 0.563252i | ||||
\(376\) | 23.3190 | 1.20259 | ||||||||
\(377\) | 22.4893 | 1.15826 | ||||||||
\(378\) | −2.93159 | − | 3.18197i | −0.150785 | − | 0.163663i | ||||
\(379\) | −5.09918 | −0.261928 | −0.130964 | − | 0.991387i | \(-0.541807\pi\) | ||||
−0.130964 | + | 0.991387i | \(0.541807\pi\) | |||||||
\(380\) | −7.14406 | + | 4.86042i | −0.366482 | + | 0.249335i | ||||
\(381\) | 7.78569 | 0.398873 | ||||||||
\(382\) | −0.944243 | −0.0483117 | ||||||||
\(383\) | −2.21160 | −0.113008 | −0.0565038 | − | 0.998402i | \(-0.517995\pi\) | ||||
−0.0565038 | + | 0.998402i | \(0.517995\pi\) | |||||||
\(384\) | −13.5338 | −0.690642 | ||||||||
\(385\) | 19.5715 | + | 1.39812i | 0.997458 | + | 0.0712549i | ||||
\(386\) | 23.2532 | 1.18356 | ||||||||
\(387\) | 5.31325 | 0.270088 | ||||||||
\(388\) | 5.93539 | 0.301324 | ||||||||
\(389\) | 33.7532 | 1.71135 | 0.855677 | − | 0.517510i | \(-0.173141\pi\) | ||||
0.855677 | + | 0.517510i | \(0.173141\pi\) | |||||||
\(390\) | −8.57892 | − | 12.6097i | −0.434411 | − | 0.638515i | ||||
\(391\) | −16.5229 | −0.835599 | ||||||||
\(392\) | −1.24105 | + | 15.1260i | −0.0626827 | + | 0.763978i | ||||
\(393\) | 2.89541 | 0.146054 | ||||||||
\(394\) | −3.70187 | −0.186498 | ||||||||
\(395\) | −10.3738 | − | 15.2478i | −0.521961 | − | 0.767201i | ||||
\(396\) | −2.20825 | + | 0.350936i | −0.110969 | + | 0.0176352i | ||||
\(397\) | −7.81103 | −0.392024 | −0.196012 | − | 0.980601i | \(-0.562799\pi\) | ||||
−0.196012 | + | 0.980601i | \(0.562799\pi\) | |||||||
\(398\) | − | 0.469559i | − | 0.0235368i | ||||||
\(399\) | 10.2755 | + | 11.1531i | 0.514418 | + | 0.558354i | ||||
\(400\) | −8.98448 | + | 22.7600i | −0.449224 | + | 1.13800i | ||||
\(401\) | −14.3745 | −0.717827 | −0.358914 | − | 0.933371i | \(-0.616853\pi\) | ||||
−0.358914 | + | 0.933371i | \(0.616853\pi\) | |||||||
\(402\) | 17.4884i | 0.872241i | ||||||||
\(403\) | 3.60397 | 0.179527 | ||||||||
\(404\) | 0.556510 | 0.0276874 | ||||||||
\(405\) | −1.84877 | + | 1.25780i | −0.0918660 | + | 0.0625006i | ||||
\(406\) | 17.1572 | − | 15.8071i | 0.851498 | − | 0.784496i | ||||
\(407\) | −1.51672 | − | 9.54390i | −0.0751810 | − | 0.473074i | ||||
\(408\) | − | 16.4362i | − | 0.813715i | ||||||
\(409\) | −11.9091 | −0.588866 | −0.294433 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294433 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(410\) | −10.1757 | + | 6.92302i | −0.502544 | + | 0.341903i | ||||
\(411\) | − | 9.16402i | − | 0.452028i | ||||||
\(412\) | −7.77433 | −0.383014 | ||||||||
\(413\) | 21.1646 | − | 19.4992i | 1.04144 | − | 0.959495i | ||||
\(414\) | 3.56419i | 0.175170i | ||||||||
\(415\) | 6.97531 | + | 10.2526i | 0.342404 | + | 0.503280i | ||||
\(416\) | − | 15.2929i | − | 0.749797i | ||||||
\(417\) | 7.30048 | 0.357506 | ||||||||
\(418\) | 30.7021 | − | 4.87919i | 1.50169 | − | 0.238649i | ||||
\(419\) | − | 2.62704i | − | 0.128339i | −0.997939 | − | 0.0641696i | \(-0.979560\pi\) | ||
0.997939 | − | 0.0641696i | \(-0.0204399\pi\) | |||||||
\(420\) | −3.88439 | − | 0.905071i | −0.189539 | − | 0.0441629i | ||||
\(421\) | −13.4735 | −0.656656 | −0.328328 | − | 0.944564i | \(-0.606485\pi\) | ||||
−0.328328 | + | 0.944564i | \(0.606485\pi\) | |||||||
\(422\) | − | 25.6214i | − | 1.24723i | ||||||
\(423\) | 10.7554 | 0.522947 | ||||||||
\(424\) | 24.1827i | 1.17441i | ||||||||
\(425\) | −35.2569 | − | 13.9176i | −1.71021 | − | 0.675102i | ||||
\(426\) | 2.54096 | 0.123110 | ||||||||
\(427\) | 27.5786 | + | 29.9340i | 1.33462 | + | 1.44861i | ||||
\(428\) | 6.53348 | 0.315808 | ||||||||
\(429\) | 2.17113 | + | 13.6618i | 0.104823 | + | 0.659597i | ||||
\(430\) | 16.0634 | − | 10.9286i | 0.774645 | − | 0.527026i | ||||
\(431\) | 17.8620i | 0.860382i | 0.902738 | + | 0.430191i | \(0.141554\pi\) | ||||
−0.902738 | + | 0.430191i | \(0.858446\pi\) | |||||||
\(432\) | −4.89383 | −0.235455 | ||||||||
\(433\) | 0.555819 | 0.0267109 | 0.0133555 | − | 0.999911i | \(-0.495749\pi\) | ||||
0.0133555 | + | 0.999911i | \(0.495749\pi\) | |||||||
\(434\) | 2.74948 | − | 2.53313i | 0.131979 | − | 0.121594i | ||||
\(435\) | −6.78206 | − | 9.96856i | −0.325175 | − | 0.477956i | ||||
\(436\) | − | 6.92917i | − | 0.331847i | ||||||
\(437\) | − | 12.4928i | − | 0.597612i | ||||||
\(438\) | 3.69054i | 0.176341i | ||||||||
\(439\) | 19.6767 | 0.939117 | 0.469558 | − | 0.882901i | \(-0.344413\pi\) | ||||
0.469558 | + | 0.882901i | \(0.344413\pi\) | |||||||
\(440\) | 11.7098 | − | 11.0191i | 0.558245 | − | 0.525313i | ||||
\(441\) | −0.572412 | + | 6.97656i | −0.0272577 | + | 0.332217i | ||||
\(442\) | 51.7060 | 2.45941 | ||||||||
\(443\) | − | 40.6848i | − | 1.93299i | −0.256677 | − | 0.966497i | \(-0.582628\pi\) | ||
0.256677 | − | 0.966497i | \(-0.417372\pi\) | |||||||
\(444\) | 1.96433i | 0.0932230i | ||||||||
\(445\) | 2.04587 | + | 3.00711i | 0.0969837 | + | 0.142551i | ||||
\(446\) | 34.5431 | 1.63566 | ||||||||
\(447\) | 16.9556i | 0.801970i | ||||||||
\(448\) | 6.79744 | + | 7.37799i | 0.321149 | + | 0.348577i | ||||
\(449\) | 15.5339 | 0.733088 | 0.366544 | − | 0.930401i | \(-0.380541\pi\) | ||||
0.366544 | + | 0.930401i | \(0.380541\pi\) | |||||||
\(450\) | −3.00219 | + | 7.60533i | −0.141525 | + | 0.358519i | ||||
\(451\) | 11.0248 | − | 1.75206i | 0.519136 | − | 0.0825013i | ||||
\(452\) | 10.1317i | 0.476557i | ||||||||
\(453\) | − | 16.3343i | − | 0.767453i | ||||||
\(454\) | − | 12.5223i | − | 0.587700i | ||||||
\(455\) | −5.59939 | + | 24.0315i | −0.262503 | + | 1.12661i | ||||
\(456\) | 12.4273 | 0.581961 | ||||||||
\(457\) | −28.8051 | −1.34745 | −0.673724 | − | 0.738983i | \(-0.735306\pi\) | ||||
−0.673724 | + | 0.738983i | \(0.735306\pi\) | |||||||
\(458\) | 32.6180i | 1.52414i | ||||||||
\(459\) | − | 7.58089i | − | 0.353846i | ||||||
\(460\) | 1.84819 | + | 2.71655i | 0.0861723 | + | 0.126660i | ||||
\(461\) | 19.9251 | 0.928005 | 0.464003 | − | 0.885834i | \(-0.346413\pi\) | ||||
0.464003 | + | 0.885834i | \(0.346413\pi\) | |||||||
\(462\) | 11.2589 | + | 8.89659i | 0.523809 | + | 0.413907i | ||||
\(463\) | − | 8.87783i | − | 0.412588i | −0.978490 | − | 0.206294i | \(-0.933860\pi\) | ||
0.978490 | − | 0.206294i | \(-0.0661403\pi\) | |||||||
\(464\) | − | 26.3876i | − | 1.22501i | ||||||
\(465\) | −1.08684 | − | 1.59748i | −0.0504011 | − | 0.0740816i | ||||
\(466\) | −9.31288 | −0.431411 | ||||||||
\(467\) | −31.9600 | −1.47893 | −0.739465 | − | 0.673195i | \(-0.764922\pi\) | ||||
−0.739465 | + | 0.673195i | \(0.764922\pi\) | |||||||
\(468\) | − | 2.81187i | − | 0.129979i | ||||||
\(469\) | 20.8093 | − | 19.1719i | 0.960884 | − | 0.885274i | ||||
\(470\) | 32.5165 | − | 22.1225i | 1.49988 | − | 1.02043i | ||||
\(471\) | −0.510450 | −0.0235203 | ||||||||
\(472\) | − | 23.5826i | − | 1.08548i | ||||||
\(473\) | −17.4037 | + | 2.76579i | −0.800221 | + | 0.127171i | ||||
\(474\) | − | 13.4871i | − | 0.619485i | ||||||
\(475\) | 10.5230 | − | 26.6574i | 0.482826 | − | 1.22312i | ||||
\(476\) | 9.94469 | − | 9.16216i | 0.455814 | − | 0.419947i | ||||
\(477\) | 11.1538i | 0.510696i | ||||||||
\(478\) | 16.2138i | 0.741602i | ||||||||
\(479\) | 9.36547 | 0.427919 | 0.213960 | − | 0.976842i | \(-0.431364\pi\) | ||||
0.213960 | + | 0.976842i | \(0.431364\pi\) | |||||||
\(480\) | −6.77869 | + | 4.61185i | −0.309403 | + | 0.210501i | ||||
\(481\) | 12.1527 | 0.554115 | ||||||||
\(482\) | −3.39115 | −0.154462 | ||||||||
\(483\) | 4.24100 | − | 3.90729i | 0.192972 | − | 0.177788i | ||||
\(484\) | 7.05050 | − | 2.29900i | 0.320477 | − | 0.104500i | ||||
\(485\) | −16.2765 | + | 11.0737i | −0.739080 | + | 0.502830i | ||||
\(486\) | −1.63529 | −0.0741782 | ||||||||
\(487\) | 15.8582i | 0.718602i | 0.933222 | + | 0.359301i | \(0.116985\pi\) | ||||
−0.933222 | + | 0.359301i | \(0.883015\pi\) | |||||||
\(488\) | 33.3538 | 1.50986 | ||||||||
\(489\) | 24.3951i | 1.10318i | ||||||||
\(490\) | 12.6193 | + | 22.2694i | 0.570081 | + | 1.00603i | ||||
\(491\) | 26.6209i | 1.20139i | 0.799480 | + | 0.600693i | \(0.205108\pi\) | ||||
−0.799480 | + | 0.600693i | \(0.794892\pi\) | |||||||
\(492\) | −2.26912 | −0.102300 | ||||||||
\(493\) | 40.8762 | 1.84097 | ||||||||
\(494\) | 39.0944i | 1.75894i | ||||||||
\(495\) | 5.40093 | − | 5.08232i | 0.242754 | − | 0.228433i | ||||
\(496\) | − | 4.22867i | − | 0.189873i | ||||||
\(497\) | −2.78556 | − | 3.02347i | −0.124949 | − | 0.135621i | ||||
\(498\) | 9.06873i | 0.406379i | ||||||||
\(499\) | −12.2258 | −0.547301 | −0.273651 | − | 0.961829i | \(-0.588231\pi\) | ||||
−0.273651 | + | 0.961829i | \(0.588231\pi\) | |||||||
\(500\) | 1.65550 | + | 7.35339i | 0.0740361 | + | 0.328854i | ||||
\(501\) | − | 14.6558i | − | 0.654775i | ||||||
\(502\) | 14.7687i | 0.659161i | ||||||||
\(503\) | − | 0.335068i | − | 0.0149400i | −0.999972 | − | 0.00746998i | \(-0.997622\pi\) | ||
0.999972 | − | 0.00746998i | \(-0.00237779\pi\) | |||||||
\(504\) | 3.88679 | + | 4.21876i | 0.173132 | + | 0.187918i | ||||
\(505\) | −1.52611 | + | 1.03828i | −0.0679111 | + | 0.0462030i | ||||
\(506\) | −1.85533 | − | 11.6746i | −0.0824793 | − | 0.518998i | ||||
\(507\) | −4.39617 | −0.195241 | ||||||||
\(508\) | 5.24887 | 0.232881 | ||||||||
\(509\) | − | 21.9958i | − | 0.974948i | −0.873138 | − | 0.487474i | \(-0.837918\pi\) | ||
0.873138 | − | 0.487474i | \(-0.162082\pi\) | |||||||
\(510\) | −15.5929 | − | 22.9191i | −0.690464 | − | 1.01487i | ||||
\(511\) | 4.39134 | − | 4.04580i | 0.194262 | − | 0.178976i | ||||
\(512\) | 3.27707 | 0.144827 | ||||||||
\(513\) | 5.73183 | 0.253067 | ||||||||
\(514\) | −24.9672 | −1.10126 | ||||||||
\(515\) | 21.3195 | − | 14.5046i | 0.939447 | − | 0.639149i | ||||
\(516\) | 3.58203 | 0.157690 | ||||||||
\(517\) | −35.2296 | + | 5.59870i | −1.54940 | + | 0.246231i | ||||
\(518\) | 9.27134 | − | 8.54180i | 0.407359 | − | 0.375305i | ||||
\(519\) | − | 17.0484i | − | 0.748342i | ||||||
\(520\) | 11.3742 | + | 16.7183i | 0.498792 | + | 0.733145i | ||||
\(521\) | 6.25907i | 0.274215i | 0.990556 | + | 0.137107i | \(0.0437806\pi\) | ||||
−0.990556 | + | 0.137107i | \(0.956219\pi\) | |||||||
\(522\) | − | 8.81748i | − | 0.385931i | ||||||
\(523\) | 36.1671i | 1.58148i | 0.612155 | + | 0.790738i | \(0.290303\pi\) | ||||
−0.612155 | + | 0.790738i | \(0.709697\pi\) | |||||||
\(524\) | 1.95199 | 0.0852732 | ||||||||
\(525\) | 12.3407 | − | 4.76516i | 0.538593 | − | 0.207968i | ||||
\(526\) | 10.4778 | 0.456852 | ||||||||
\(527\) | 6.55050 | 0.285344 | ||||||||
\(528\) | 16.0299 | − | 2.54747i | 0.697610 | − | 0.110864i | ||||
\(529\) | 18.2496 | 0.793460 | ||||||||
\(530\) | 22.9418 | + | 33.7208i | 0.996528 | + | 1.46474i | ||||
\(531\) | − | 10.8770i | − | 0.472021i | ||||||
\(532\) | 6.92742 | + | 7.51908i | 0.300342 | + | 0.325993i | ||||
\(533\) | 14.0384i | 0.608069i | ||||||||
\(534\) | 2.65988i | 0.115104i | ||||||||
\(535\) | −17.9167 | + | 12.1895i | −0.774606 | + | 0.527000i | ||||
\(536\) | − | 23.1866i | − | 1.00151i | ||||||
\(537\) | 19.0830 | 0.823493 | ||||||||
\(538\) | − | 22.1649i | − | 0.955598i | ||||||
\(539\) | −1.75668 | − | 23.1498i | −0.0756654 | − | 0.997133i | ||||
\(540\) | −1.24638 | + | 0.847970i | −0.0536357 | + | 0.0364908i | ||||
\(541\) | 0.696188i | 0.0299315i | 0.999888 | + | 0.0149657i | \(0.00476392\pi\) | ||||
−0.999888 | + | 0.0149657i | \(0.995236\pi\) | |||||||
\(542\) | −22.1606 | −0.951880 | ||||||||
\(543\) | 7.90098i | 0.339064i | ||||||||
\(544\) | − | 27.7961i | − | 1.19175i | ||||||
\(545\) | 12.9278 | + | 19.0018i | 0.553765 | + | 0.813947i | ||||
\(546\) | −13.2716 | + | 12.2273i | −0.567972 | + | 0.523280i | ||||
\(547\) | −27.6211 | −1.18099 | −0.590496 | − | 0.807041i | \(-0.701068\pi\) | ||||
−0.590496 | + | 0.807041i | \(0.701068\pi\) | |||||||
\(548\) | − | 6.17810i | − | 0.263915i | ||||||
\(549\) | 15.3838 | 0.656564 | ||||||||
\(550\) | 5.87481 | − | 26.4742i | 0.250503 | − | 1.12886i | ||||
\(551\) | 30.9061i | 1.31664i | ||||||||
\(552\) | − | 4.72551i | − | 0.201131i | ||||||
\(553\) | −16.0482 | + | 14.7854i | −0.682441 | + | 0.628741i | ||||
\(554\) | −17.3256 | −0.736093 | ||||||||
\(555\) | −3.66486 | − | 5.38676i | −0.155565 | − | 0.228655i | ||||
\(556\) | 4.92176 | 0.208729 | ||||||||
\(557\) | 36.7731 | 1.55813 | 0.779063 | − | 0.626946i | \(-0.215695\pi\) | ||||
0.779063 | + | 0.626946i | \(0.215695\pi\) | |||||||
\(558\) | − | 1.41302i | − | 0.0598180i | ||||||
\(559\) | − | 22.1609i | − | 0.937305i | ||||||
\(560\) | 28.1970 | + | 6.56996i | 1.19154 | + | 0.277632i | ||||
\(561\) | 3.94620 | + | 24.8313i | 0.166609 | + | 1.04838i | ||||
\(562\) | 18.8016i | 0.793099i | ||||||||
\(563\) | − | 3.23737i | − | 0.136439i | −0.997670 | − | 0.0682195i | \(-0.978268\pi\) | ||
0.997670 | − | 0.0682195i | \(-0.0217318\pi\) | |||||||
\(564\) | 7.25098 | 0.305321 | ||||||||
\(565\) | −18.9028 | − | 27.7842i | −0.795248 | − | 1.16889i | ||||
\(566\) | 35.4560i | 1.49033i | ||||||||
\(567\) | 1.79271 | + | 1.94582i | 0.0752866 | + | 0.0817167i | ||||
\(568\) | −3.36888 | −0.141355 | ||||||||
\(569\) | − | 9.36538i | − | 0.392617i | −0.980542 | − | 0.196309i | \(-0.937105\pi\) | ||
0.980542 | − | 0.196309i | \(-0.0628954\pi\) | |||||||
\(570\) | 17.3289 | − | 11.7896i | 0.725827 | − | 0.493813i | ||||
\(571\) | − | 12.0341i | − | 0.503611i | −0.967778 | − | 0.251805i | \(-0.918976\pi\) | ||
0.967778 | − | 0.251805i | \(-0.0810243\pi\) | |||||||
\(572\) | 1.46371 | + | 9.21035i | 0.0612008 | + | 0.385104i | ||||
\(573\) | 0.577417 | 0.0241219 | ||||||||
\(574\) | 9.86718 | + | 10.7099i | 0.411848 | + | 0.447023i | ||||
\(575\) | −10.1365 | − | 4.00138i | −0.422723 | − | 0.166869i | ||||
\(576\) | 3.79172 | 0.157988 | ||||||||
\(577\) | 2.09996 | 0.0874223 | 0.0437111 | − | 0.999044i | \(-0.486082\pi\) | ||||
0.0437111 | + | 0.999044i | \(0.486082\pi\) | |||||||
\(578\) | 66.1799 | 2.75272 | ||||||||
\(579\) | −14.2196 | −0.590948 | ||||||||
\(580\) | −4.57226 | − | 6.72049i | −0.189853 | − | 0.279053i | ||||
\(581\) | 10.7908 | − | 9.94171i | 0.447678 | − | 0.412451i | ||||
\(582\) | −14.3971 | −0.596778 | ||||||||
\(583\) | −5.80605 | − | 36.5344i | −0.240462 | − | 1.51310i | ||||
\(584\) | − | 4.89303i | − | 0.202475i | ||||||
\(585\) | 5.24612 | + | 7.71097i | 0.216900 | + | 0.318809i | ||||
\(586\) | − | 11.6735i | − | 0.482226i | ||||||
\(587\) | 41.4514 | 1.71088 | 0.855441 | − | 0.517901i | \(-0.173286\pi\) | ||||
0.855441 | + | 0.517901i | \(0.173286\pi\) | |||||||
\(588\) | −0.385902 | + | 4.70338i | −0.0159143 | + | 0.193964i | ||||
\(589\) | 4.95277i | 0.204075i | ||||||||
\(590\) | −22.3725 | − | 32.8841i | −0.921062 | − | 1.35382i | ||||
\(591\) | 2.26374 | 0.0931179 | ||||||||
\(592\) | − | 14.2592i | − | 0.586049i | ||||||
\(593\) | − | 35.3731i | − | 1.45260i | −0.687377 | − | 0.726300i | \(-0.741238\pi\) | ||
0.687377 | − | 0.726300i | \(-0.258762\pi\) | |||||||
\(594\) | 5.35642 | − | 0.851244i | 0.219777 | − | 0.0349270i | ||||
\(595\) | −10.1773 | + | 43.6791i | −0.417230 | + | 1.79067i | ||||
\(596\) | 11.4309i | 0.468228i | ||||||||
\(597\) | 0.287141i | 0.0117519i | ||||||||
\(598\) | 14.8658 | 0.607907 | ||||||||
\(599\) | −29.7933 | −1.21732 | −0.608662 | − | 0.793430i | \(-0.708293\pi\) | ||||
−0.608662 | + | 0.793430i | \(0.708293\pi\) | |||||||
\(600\) | 3.98040 | − | 10.0834i | 0.162499 | − | 0.411652i | ||||
\(601\) | −39.9860 | −1.63106 | −0.815531 | − | 0.578713i | \(-0.803555\pi\) | ||||
−0.815531 | + | 0.578713i | \(0.803555\pi\) | |||||||
\(602\) | −15.5763 | − | 16.9066i | −0.634842 | − | 0.689062i | ||||
\(603\) | − | 10.6944i | − | 0.435508i | ||||||
\(604\) | − | 11.0121i | − | 0.448075i | ||||||
\(605\) | −15.0453 | + | 19.4587i | −0.611677 | + | 0.791107i | ||||
\(606\) | −1.34989 | −0.0548356 | ||||||||
\(607\) | 0.361266i | 0.0146634i | 0.999973 | + | 0.00733168i | \(0.00233377\pi\) | ||||
−0.999973 | + | 0.00733168i | \(0.997666\pi\) | |||||||
\(608\) | 21.0163 | 0.852325 | ||||||||
\(609\) | −10.4919 | + | 9.66627i | −0.425151 | + | 0.391697i | ||||
\(610\) | 46.5093 | − | 31.6424i | 1.88311 | − | 1.28116i | ||||
\(611\) | − | 44.8595i | − | 1.81482i | ||||||
\(612\) | − | 5.11080i | − | 0.206592i | ||||||
\(613\) | −26.4191 | −1.06706 | −0.533528 | − | 0.845782i | \(-0.679134\pi\) | ||||
−0.533528 | + | 0.845782i | \(0.679134\pi\) | |||||||
\(614\) | 25.2452i | 1.01881i | ||||||||
\(615\) | 6.22260 | − | 4.23351i | 0.250919 | − | 0.170712i | ||||
\(616\) | −14.9273 | − | 11.7954i | −0.601439 | − | 0.475249i | ||||
\(617\) | 23.7919i | 0.957825i | 0.877863 | + | 0.478912i | \(0.158969\pi\) | ||||
−0.877863 | + | 0.478912i | \(0.841031\pi\) | |||||||
\(618\) | 18.8577 | 0.758567 | ||||||||
\(619\) | 20.1966i | 0.811770i | 0.913924 | + | 0.405885i | \(0.133037\pi\) | ||||
−0.913924 | + | 0.405885i | \(0.866963\pi\) | |||||||
\(620\) | −0.732715 | − | 1.07698i | −0.0294265 | − | 0.0432524i | ||||
\(621\) | − | 2.17955i | − | 0.0874622i | ||||||
\(622\) | − | 49.7753i | − | 1.99581i | ||||||
\(623\) | 3.16497 | − | 2.91592i | 0.126802 | − | 0.116824i | ||||
\(624\) | 20.4116i | 0.817116i | ||||||||
\(625\) | −18.2591 | − | 17.0765i | −0.730364 | − | 0.683058i | ||||
\(626\) | 50.9070 | 2.03465 | ||||||||
\(627\) | −18.7747 | + | 2.98369i | −0.749791 | + | 0.119157i | ||||
\(628\) | −0.344130 | −0.0137323 | ||||||||
\(629\) | 22.0885 | 0.880725 | ||||||||
\(630\) | 9.42212 | + | 2.19537i | 0.375386 | + | 0.0874657i | ||||
\(631\) | −21.8127 | −0.868351 | −0.434175 | − | 0.900828i | \(-0.642960\pi\) | ||||
−0.434175 | + | 0.900828i | \(0.642960\pi\) | |||||||
\(632\) | 17.8817i | 0.711294i | ||||||||
\(633\) | 15.6678i | 0.622739i | ||||||||
\(634\) | 46.7114i | 1.85515i | ||||||||
\(635\) | −14.3939 | + | 9.79284i | −0.571206 | + | 0.388617i | ||||
\(636\) | 7.51953i | 0.298169i | ||||||||
\(637\) | 29.0983 | + | 2.38746i | 1.15292 | + | 0.0945944i | ||||
\(638\) | 4.58991 | + | 28.8818i | 0.181716 | + | 1.14344i | ||||
\(639\) | −1.55383 | −0.0614685 | ||||||||
\(640\) | 25.0208 | − | 17.0228i | 0.989032 | − | 0.672884i | ||||
\(641\) | 16.3512 | 0.645834 | 0.322917 | − | 0.946427i | \(-0.395337\pi\) | ||||
0.322917 | + | 0.946427i | \(0.395337\pi\) | |||||||
\(642\) | −15.8478 | −0.625465 | ||||||||
\(643\) | 18.3877 | 0.725141 | 0.362571 | − | 0.931956i | \(-0.381899\pi\) | ||||
0.362571 | + | 0.931956i | \(0.381899\pi\) | |||||||
\(644\) | 2.85915 | − | 2.63417i | 0.112666 | − | 0.103801i | ||||
\(645\) | −9.82296 | + | 6.68301i | −0.386779 | + | 0.263143i | ||||
\(646\) | 71.0572i | 2.79571i | ||||||||
\(647\) | 2.00293 | 0.0787434 | 0.0393717 | − | 0.999225i | \(-0.487464\pi\) | ||||
0.0393717 | + | 0.999225i | \(0.487464\pi\) | |||||||
\(648\) | 2.16812 | 0.0851716 | ||||||||
\(649\) | 5.66198 | + | 35.6278i | 0.222252 | + | 1.39851i | ||||
\(650\) | 31.7209 | + | 12.5218i | 1.24419 | + | 0.491144i | ||||
\(651\) | −1.68134 | + | 1.54904i | −0.0658971 | + | 0.0607118i | ||||
\(652\) | 16.4464i | 0.644091i | ||||||||
\(653\) | 4.94844i | 0.193647i | 0.995302 | + | 0.0968236i | \(0.0308683\pi\) | ||||
−0.995302 | + | 0.0968236i | \(0.969132\pi\) | |||||||
\(654\) | 16.8076i | 0.657231i | ||||||||
\(655\) | −5.35293 | + | 3.64184i | −0.209156 | + | 0.142299i | ||||
\(656\) | 16.4717 | 0.643112 | ||||||||
\(657\) | − | 2.25681i | − | 0.0880466i | ||||||
\(658\) | −31.5305 | − | 34.2235i | −1.22919 | − | 1.33417i | ||||
\(659\) | − | 4.46793i | − | 0.174046i | −0.996206 | − | 0.0870228i | \(-0.972265\pi\) | ||
0.996206 | − | 0.0870228i | \(-0.0277353\pi\) | |||||||
\(660\) | 3.64114 | − | 3.42634i | 0.141731 | − | 0.133370i | ||||
\(661\) | − | 0.732284i | − | 0.0284826i | −0.999899 | − | 0.0142413i | \(-0.995467\pi\) | ||
0.999899 | − | 0.0142413i | \(-0.00453329\pi\) | |||||||
\(662\) | 43.5149 | 1.69125 | ||||||||
\(663\) | −31.6189 | −1.22798 | ||||||||
\(664\) | − | 12.0236i | − | 0.466606i | ||||||
\(665\) | −33.0254 | − | 7.69498i | −1.28067 | − | 0.298398i | ||||
\(666\) | − | 4.76475i | − | 0.184630i | ||||||
\(667\) | 11.7521 | 0.455044 | ||||||||
\(668\) | − | 9.88052i | − | 0.382289i | ||||||
\(669\) | −21.1236 | −0.816684 | ||||||||
\(670\) | −21.9969 | − | 32.3319i | −0.849814 | − | 1.24909i | ||||
\(671\) | −50.3899 | + | 8.00798i | −1.94528 | + | 0.309145i | ||||
\(672\) | 6.57314 | + | 7.13453i | 0.253564 | + | 0.275221i | ||||
\(673\) | 27.7263 | 1.06877 | 0.534386 | − | 0.845241i | \(-0.320543\pi\) | ||||
0.534386 | + | 0.845241i | \(0.320543\pi\) | |||||||
\(674\) | 31.0764 | 1.19702 | ||||||||
\(675\) | 1.83588 | − | 4.65076i | 0.0706630 | − | 0.179008i | ||||
\(676\) | −2.96376 | −0.113991 | ||||||||
\(677\) | 20.7844i | 0.798809i | 0.916775 | + | 0.399405i | \(0.130783\pi\) | ||||
−0.916775 | + | 0.399405i | \(0.869217\pi\) | |||||||
\(678\) | − | 24.5759i | − | 0.943833i | ||||||
\(679\) | 15.7830 | + | 17.1310i | 0.605695 | + | 0.657427i | ||||
\(680\) | 20.6735 | + | 30.3868i | 0.792793 | + | 1.16528i | ||||
\(681\) | 7.65754i | 0.293438i | ||||||||
\(682\) | 0.735544 | + | 4.62838i | 0.0281654 | + | 0.177230i | ||||
\(683\) | − | 20.6169i | − | 0.788882i | −0.918921 | − | 0.394441i | \(-0.870938\pi\) | ||
0.918921 | − | 0.394441i | \(-0.129062\pi\) | |||||||
\(684\) | 3.86423 | 0.147752 | ||||||||
\(685\) | 11.5265 | + | 16.9421i | 0.440405 | + | 0.647326i | ||||
\(686\) | 23.8773 | − | 18.6310i | 0.911639 | − | 0.711336i | ||||
\(687\) | − | 19.9463i | − | 0.761000i | ||||||
\(688\) | −26.0022 | −0.991323 | ||||||||
\(689\) | 46.5209 | 1.77231 | ||||||||
\(690\) | −4.48304 | − | 6.58935i | −0.170666 | − | 0.250852i | ||||
\(691\) | 2.23979i | 0.0852056i | 0.999092 | + | 0.0426028i | \(0.0135650\pi\) | ||||
−0.999092 | + | 0.0426028i | \(0.986435\pi\) | |||||||
\(692\) | − | 11.4935i | − | 0.436918i | ||||||
\(693\) | −6.88493 | − | 5.44038i | −0.261537 | − | 0.206663i | ||||
\(694\) | 11.8876 | 0.451246 | ||||||||
\(695\) | −13.4969 | + | 9.18254i | −0.511966 | + | 0.348314i | ||||
\(696\) | 11.6905i | 0.443127i | ||||||||
\(697\) | 25.5158i | 0.966480i | ||||||||
\(698\) | −1.45329 | −0.0550080 | ||||||||
\(699\) | 5.69495 | 0.215403 | ||||||||
\(700\) | 8.31973 | − | 3.21252i | 0.314456 | − | 0.121422i | ||||
\(701\) | − | 12.8382i | − | 0.484891i | −0.970165 | − | 0.242446i | \(-0.922050\pi\) | ||
0.970165 | − | 0.242446i | \(-0.0779496\pi\) | |||||||
\(702\) | 6.82058i | 0.257426i | ||||||||
\(703\) | 16.7009i | 0.629886i | ||||||||
\(704\) | −12.4199 | + | 1.97377i | −0.468091 | + | 0.0743891i | ||||
\(705\) | −19.8843 | + | 13.5282i | −0.748885 | + | 0.509501i | ||||
\(706\) | −21.1871 | −0.797388 | ||||||||
\(707\) | 1.47984 | + | 1.60623i | 0.0556549 | + | 0.0604083i | ||||
\(708\) | − | 7.33293i | − | 0.275589i | ||||||
\(709\) | 5.22136 | 0.196092 | 0.0980462 | − | 0.995182i | \(-0.468741\pi\) | ||||
0.0980462 | + | 0.995182i | \(0.468741\pi\) | |||||||
\(710\) | −4.69764 | + | 3.19602i | −0.176299 | + | 0.119944i | ||||
\(711\) | 8.24756i | 0.309308i | ||||||||
\(712\) | − | 3.52655i | − | 0.132163i | ||||||
\(713\) | 1.88331 | 0.0705304 | ||||||||
\(714\) | −24.1222 | + | 22.2241i | −0.902750 | + | 0.831715i | ||||
\(715\) | −21.1977 | − | 22.5266i | −0.792749 | − | 0.842446i | ||||
\(716\) | 12.8652 | 0.480794 | ||||||||
\(717\) | − | 9.91495i | − | 0.370281i | ||||||
\(718\) | 13.6327i | 0.508769i | ||||||||
\(719\) | − | 13.5036i | − | 0.503599i | −0.967779 | − | 0.251800i | \(-0.918978\pi\) | ||
0.967779 | − | 0.251800i | \(-0.0810224\pi\) | |||||||
\(720\) | 9.04756 | − | 6.15546i | 0.337183 | − | 0.229401i | ||||
\(721\) | −20.6730 | − | 22.4386i | −0.769902 | − | 0.835658i | ||||
\(722\) | −22.6552 | −0.843138 | ||||||||
\(723\) | 2.07373 | 0.0771228 | ||||||||
\(724\) | 5.32660i | 0.197962i | ||||||||
\(725\) | 25.0769 | + | 9.89906i | 0.931333 | + | 0.367642i | ||||
\(726\) | −17.1020 | + | 5.57653i | −0.634713 | + | 0.206965i | ||||
\(727\) | −1.97850 | −0.0733786 | −0.0366893 | − | 0.999327i | \(-0.511681\pi\) | ||||
−0.0366893 | + | 0.999327i | \(0.511681\pi\) | |||||||
\(728\) | 17.5959 | − | 16.2113i | 0.652147 | − | 0.600831i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.64196 | − | 6.82295i | −0.171807 | − | 0.252529i | ||||
\(731\) | − | 40.2791i | − | 1.48978i | ||||||
\(732\) | 10.3713 | 0.383333 | ||||||||
\(733\) | − | 3.81876i | − | 0.141049i | −0.997510 | − | 0.0705245i | \(-0.977533\pi\) | ||
0.997510 | − | 0.0705245i | \(-0.0224673\pi\) | |||||||
\(734\) | 37.5457 | 1.38584 | ||||||||
\(735\) | −7.71686 | − | 13.6180i | −0.284641 | − | 0.502308i | ||||
\(736\) | − | 7.99153i | − | 0.294572i | ||||||
\(737\) | 5.56692 | + | 35.0296i | 0.205060 | + | 1.29033i | ||||
\(738\) | 5.50407 | 0.202608 | ||||||||
\(739\) | − | 12.4867i | − | 0.459332i | −0.973270 | − | 0.229666i | \(-0.926237\pi\) | ||
0.973270 | − | 0.229666i | \(-0.0737633\pi\) | |||||||
\(740\) | −2.47074 | − | 3.63159i | −0.0908261 | − | 0.133500i | ||||
\(741\) | − | 23.9067i | − | 0.878236i | ||||||
\(742\) | 35.4910 | − | 32.6983i | 1.30292 | − | 1.20039i | ||||
\(743\) | −37.0586 | −1.35955 | −0.679775 | − | 0.733421i | \(-0.737922\pi\) | ||||
−0.679775 | + | 0.733421i | \(0.737922\pi\) | |||||||
\(744\) | 1.87343i | 0.0686832i | ||||||||
\(745\) | −21.3267 | − | 31.3469i | −0.781350 | − | 1.14846i | ||||
\(746\) | −57.3623 | −2.10018 | ||||||||
\(747\) | − | 5.54564i | − | 0.202904i | ||||||
\(748\) | 2.66041 | + | 16.7405i | 0.0972742 | + | 0.612094i | ||||
\(749\) | 17.3734 | + | 18.8572i | 0.634810 | + | 0.689028i | ||||
\(750\) | −4.01563 | − | 17.8366i | −0.146630 | − | 0.651302i | ||||
\(751\) | 3.95633 | 0.144369 | 0.0721843 | − | 0.997391i | \(-0.477003\pi\) | ||||
0.0721843 | + | 0.997391i | \(0.477003\pi\) | |||||||
\(752\) | −52.6353 | −1.91941 | ||||||||
\(753\) | − | 9.03128i | − | 0.329118i | ||||||
\(754\) | −36.7766 | −1.33932 | ||||||||
\(755\) | 20.5453 | + | 30.1983i | 0.747720 | + | 1.09903i | ||||
\(756\) | 1.20859 | + | 1.31181i | 0.0439559 | + | 0.0477101i | ||||
\(757\) | − | 20.8523i | − | 0.757888i | −0.925420 | − | 0.378944i | \(-0.876287\pi\) | ||
0.925420 | − | 0.378944i | \(-0.123713\pi\) | |||||||
\(758\) | 8.33864 | 0.302873 | ||||||||
\(759\) | 1.13456 | + | 7.13915i | 0.0411818 | + | 0.259135i | ||||
\(760\) | −22.9752 | + | 15.6310i | −0.833396 | + | 0.566997i | ||||
\(761\) | 37.0384 | 1.34264 | 0.671320 | − | 0.741167i | \(-0.265727\pi\) | ||||
0.671320 | + | 0.741167i | \(0.265727\pi\) | |||||||
\(762\) | −12.7319 | −0.461226 | ||||||||
\(763\) | 19.9993 | − | 18.4256i | 0.724023 | − | 0.667051i | ||||
\(764\) | 0.389276 | 0.0140835 | ||||||||
\(765\) | 9.53524 | + | 14.0153i | 0.344747 | + | 0.506724i | ||||
\(766\) | 3.61661 | 0.130673 | ||||||||
\(767\) | −45.3665 | −1.63809 | ||||||||
\(768\) | 14.5482 | 0.524962 | ||||||||
\(769\) | −20.7036 | −0.746590 | −0.373295 | − | 0.927713i | \(-0.621772\pi\) | ||||
−0.373295 | + | 0.927713i | \(0.621772\pi\) | |||||||
\(770\) | −32.0051 | − | 2.28633i | −1.15338 | − | 0.0823937i | ||||
\(771\) | 15.2678 | 0.549855 | ||||||||
\(772\) | −9.58645 | −0.345024 | ||||||||
\(773\) | 9.70891 | 0.349205 | 0.174603 | − | 0.984639i | \(-0.444136\pi\) | ||||
0.174603 | + | 0.984639i | \(0.444136\pi\) | |||||||
\(774\) | −8.68870 | −0.312309 | ||||||||
\(775\) | 4.01863 | + | 1.58635i | 0.144354 | + | 0.0569833i | ||||
\(776\) | 19.0881 | 0.685223 | ||||||||
\(777\) | −5.66954 | + | 5.22342i | −0.203394 | + | 0.187389i | ||||
\(778\) | −55.1962 | −1.97888 | ||||||||
\(779\) | −19.2923 | −0.691217 | ||||||||
\(780\) | 3.53677 | + | 5.19850i | 0.126637 | + | 0.186136i | ||||
\(781\) | 5.08959 | − | 0.808840i | 0.182120 | − | 0.0289426i | ||||
\(782\) | 27.0197 | 0.966223 | ||||||||
\(783\) | 5.39200i | 0.192694i | ||||||||
\(784\) | 2.80129 | − | 34.1421i | 0.100046 | − | 1.21936i | ||||
\(785\) | 0.943704 | − | 0.642045i | 0.0336822 | − | 0.0229156i | ||||
\(786\) | −4.73483 | −0.168886 | ||||||||
\(787\) | − | 7.13561i | − | 0.254357i | −0.991880 | − | 0.127178i | \(-0.959408\pi\) | ||
0.991880 | − | 0.127178i | \(-0.0405921\pi\) | |||||||
\(788\) | 1.52614 | 0.0543667 | ||||||||
\(789\) | −6.40729 | −0.228106 | ||||||||
\(790\) | 16.9641 | + | 24.9346i | 0.603556 | + | 0.887132i | ||||
\(791\) | −29.2427 | + | 26.9417i | −1.03975 | + | 0.957935i | ||||
\(792\) | −7.10171 | + | 1.12861i | −0.252348 | + | 0.0401032i | ||||
\(793\) | − | 64.1638i | − | 2.27852i | ||||||
\(794\) | 12.7733 | 0.453307 | ||||||||
\(795\) | −14.0292 | − | 20.6207i | −0.497565 | − | 0.731341i | ||||
\(796\) | 0.193582i | 0.00686132i | ||||||||
\(797\) | −18.5441 | −0.656866 | −0.328433 | − | 0.944527i | \(-0.606520\pi\) | ||||
−0.328433 | + | 0.944527i | \(0.606520\pi\) | |||||||
\(798\) | −16.8034 | − | 18.2385i | −0.594834 | − | 0.645638i | ||||
\(799\) | − | 81.5357i | − | 2.88453i | ||||||
\(800\) | 6.73143 | − | 17.0525i | 0.237992 | − | 0.602896i | ||||
\(801\) | − | 1.62655i | − | 0.0574713i | ||||||
\(802\) | 23.5064 | 0.830041 | ||||||||
\(803\) | 1.17478 | + | 7.39223i | 0.0414569 | + | 0.260866i | ||||
\(804\) | − | 7.20982i | − | 0.254271i | ||||||
\(805\) | −2.92604 | + | 12.5580i | −0.103129 | + | 0.442611i | ||||
\(806\) | −5.89353 | −0.207591 | ||||||||
\(807\) | 13.5541i | 0.477128i | ||||||||
\(808\) | 1.78973 | 0.0629624 | ||||||||
\(809\) | − | 25.3382i | − | 0.890845i | −0.895320 | − | 0.445422i | \(-0.853053\pi\) | ||
0.895320 | − | 0.445422i | \(-0.146947\pi\) | |||||||
\(810\) | 3.02327 | − | 2.05687i | 0.106227 | − | 0.0722709i | ||||
\(811\) | −14.9314 | −0.524311 | −0.262155 | − | 0.965026i | \(-0.584433\pi\) | ||||
−0.262155 | + | 0.965026i | \(0.584433\pi\) | |||||||
\(812\) | −7.07329 | + | 6.51671i | −0.248224 | + | 0.228692i | ||||
\(813\) | 13.5515 | 0.475272 | ||||||||
\(814\) | 2.48027 | + | 15.6070i | 0.0869336 | + | 0.547026i | ||||
\(815\) | −30.6841 | − | 45.1008i | −1.07482 | − | 1.57981i | ||||
\(816\) | 37.0996i | 1.29875i | ||||||||
\(817\) | 30.4547 | 1.06547 | ||||||||
\(818\) | 19.4748 | 0.680920 | ||||||||
\(819\) | 8.11575 | − | 7.47715i | 0.283587 | − | 0.261273i | ||||
\(820\) | 4.19508 | − | 2.85411i | 0.146499 | − | 0.0996697i | ||||
\(821\) | 31.8707i | 1.11230i | 0.831083 | + | 0.556148i | \(0.187721\pi\) | ||||
−0.831083 | + | 0.556148i | \(0.812279\pi\) | |||||||
\(822\) | 14.9858i | 0.522691i | ||||||||
\(823\) | − | 5.84104i | − | 0.203606i | −0.994805 | − | 0.101803i | \(-0.967539\pi\) | ||
0.994805 | − | 0.101803i | \(-0.0324611\pi\) | |||||||
\(824\) | −25.0021 | −0.870989 | ||||||||
\(825\) | −3.59252 | + | 16.1893i | −0.125076 | + | 0.563639i | ||||
\(826\) | −34.6103 | + | 31.8869i | −1.20425 | + | 1.10949i | ||||
\(827\) | −12.8645 | −0.447341 | −0.223671 | − | 0.974665i | \(-0.571804\pi\) | ||||
−0.223671 | + | 0.974665i | \(0.571804\pi\) | |||||||
\(828\) | − | 1.46938i | − | 0.0510646i | ||||||
\(829\) | − | 4.31992i | − | 0.150037i | −0.997182 | − | 0.0750185i | \(-0.976098\pi\) | ||
0.997182 | − | 0.0750185i | \(-0.0239016\pi\) | |||||||
\(830\) | −11.4066 | − | 16.7660i | −0.395930 | − | 0.581955i | ||||
\(831\) | 10.5948 | 0.367530 | ||||||||
\(832\) | − | 15.8148i | − | 0.548279i | ||||||
\(833\) | 52.8885 | + | 4.33939i | 1.83248 | + | 0.150351i | ||||
\(834\) | −11.9384 | −0.413393 | ||||||||
\(835\) | 18.4341 | + | 27.0952i | 0.637939 | + | 0.937669i | ||||
\(836\) | −12.6574 | + | 2.01151i | −0.437764 | + | 0.0695695i | ||||
\(837\) | 0.864081i | 0.0298670i | ||||||||
\(838\) | 4.29597i | 0.148402i | ||||||||
\(839\) | 46.0836i | 1.59098i | 0.605965 | + | 0.795491i | \(0.292787\pi\) | ||||
−0.605965 | + | 0.795491i | \(0.707213\pi\) | |||||||
\(840\) | −12.4921 | − | 2.91069i | −0.431019 | − | 0.100428i | ||||
\(841\) | −0.0736920 | −0.00254110 | ||||||||
\(842\) | 22.0330 | 0.759307 | ||||||||
\(843\) | − | 11.4974i | − | 0.395993i | ||||||
\(844\) | 10.5627i | 0.363584i | ||||||||
\(845\) | 8.12749 | − | 5.52950i | 0.279594 | − | 0.190221i | ||||
\(846\) | −17.5882 | −0.604696 | ||||||||
\(847\) | 25.3837 | + | 14.2361i | 0.872194 | + | 0.489159i | ||||
\(848\) | − | 54.5847i | − | 1.87445i | ||||||
\(849\) | − | 21.6818i | − | 0.744117i | ||||||
\(850\) | 57.6552 | + | 22.7593i | 1.97756 | + | 0.780637i | ||||
\(851\) | 6.35056 | 0.217694 | ||||||||
\(852\) | −1.04754 | −0.0358882 | ||||||||
\(853\) | 32.2381i | 1.10381i | 0.833907 | + | 0.551906i | \(0.186099\pi\) | ||||
−0.833907 | + | 0.551906i | \(0.813901\pi\) | |||||||
\(854\) | −45.0990 | − | 48.9508i | −1.54326 | − | 1.67506i | ||||
\(855\) | −10.5968 | + | 7.20950i | −0.362404 | + | 0.246560i | ||||
\(856\) | 21.0116 | 0.718160 | ||||||||
\(857\) | 29.0750i | 0.993182i | 0.867985 | + | 0.496591i | \(0.165415\pi\) | ||||
−0.867985 | + | 0.496591i | \(0.834585\pi\) | |||||||
\(858\) | −3.55043 | − | 22.3409i | −0.121210 | − | 0.762707i | ||||
\(859\) | 27.8898i | 0.951588i | 0.879557 | + | 0.475794i | \(0.157839\pi\) | ||||
−0.879557 | + | 0.475794i | \(0.842161\pi\) | |||||||
\(860\) | −6.62234 | + | 4.50548i | −0.225820 | + | 0.153635i | ||||
\(861\) | −6.03390 | − | 6.54925i | −0.205635 | − | 0.223198i | ||||
\(862\) | − | 29.2095i | − | 0.994880i | ||||||
\(863\) | 53.7247i | 1.82881i | 0.404799 | + | 0.914406i | \(0.367342\pi\) | ||||
−0.404799 | + | 0.914406i | \(0.632658\pi\) | |||||||
\(864\) | 3.66660 | 0.124740 | ||||||||
\(865\) | 21.4435 | + | 31.5185i | 0.729100 | + | 1.07166i | ||||
\(866\) | −0.908924 | −0.0308865 | ||||||||
\(867\) | −40.4698 | −1.37443 | ||||||||
\(868\) | −1.13351 | + | 1.04432i | −0.0384739 | + | 0.0354464i | ||||
\(869\) | −4.29324 | − | 27.0150i | −0.145638 | − | 0.916423i | ||||
\(870\) | 11.0906 | + | 16.3015i | 0.376007 | + | 0.552672i | ||||
\(871\) | −44.6048 | −1.51138 | ||||||||
\(872\) | − | 22.2841i | − | 0.754634i | ||||||
\(873\) | 8.80400 | 0.297970 | ||||||||
\(874\) | 20.4293i | 0.691033i | ||||||||
\(875\) | −16.8215 | + | 24.3318i | −0.568670 | + | 0.822566i | ||||
\(876\) | − | 1.52147i | − | 0.0514058i | ||||||
\(877\) | 31.4715 | 1.06272 | 0.531358 | − | 0.847147i | \(-0.321682\pi\) | ||||
0.531358 | + | 0.847147i | \(0.321682\pi\) | |||||||
\(878\) | −32.1770 | −1.08592 | ||||||||
\(879\) | 7.13847i | 0.240774i | ||||||||
\(880\) | −26.4313 | + | 24.8720i | −0.890997 | + | 0.838436i | ||||
\(881\) | 31.4582i | 1.05985i | 0.848044 | + | 0.529926i | \(0.177780\pi\) | ||||
−0.848044 | + | 0.529926i | \(0.822220\pi\) | |||||||
\(882\) | 0.936058 | − | 11.4087i | 0.0315187 | − | 0.384150i | ||||
\(883\) | 33.5011i | 1.12740i | 0.825980 | + | 0.563700i | \(0.190623\pi\) | ||||
−0.825980 | + | 0.563700i | \(0.809377\pi\) | |||||||
\(884\) | −21.3165 | −0.716951 | ||||||||
\(885\) | 13.6811 | + | 20.1090i | 0.459885 | + | 0.675958i | ||||
\(886\) | 66.5314i | 2.23517i | ||||||||
\(887\) | − | 48.3621i | − | 1.62384i | −0.583768 | − | 0.811920i | \(-0.698422\pi\) | ||
0.583768 | − | 0.811920i | \(-0.301578\pi\) | |||||||
\(888\) | 6.31725i | 0.211993i | ||||||||
\(889\) | 13.9575 | + | 15.1495i | 0.468118 | + | 0.508099i | ||||
\(890\) | −3.34559 | − | 4.91749i | −0.112145 | − | 0.164835i | ||||
\(891\) | −3.27552 | + | 0.520547i | −0.109734 | + | 0.0174390i | ||||
\(892\) | −14.2408 | −0.476819 | ||||||||
\(893\) | 61.6484 | 2.06298 | ||||||||
\(894\) | − | 27.7272i | − | 0.927337i | ||||||
\(895\) | −35.2800 | + | 24.0026i | −1.17928 | + | 0.802319i | ||||
\(896\) | −24.2620 | − | 26.3342i | −0.810538 | − | 0.879764i | ||||
\(897\) | −9.09061 | −0.303527 | ||||||||
\(898\) | −25.4024 | −0.847687 | ||||||||
\(899\) | −4.65913 | −0.155391 | ||||||||
\(900\) | 1.23769 | − | 3.13540i | 0.0412564 | − | 0.104513i | ||||
\(901\) | 84.5554 | 2.81695 | ||||||||
\(902\) | −18.0287 | + | 2.86512i | −0.600290 | + | 0.0953982i | ||||
\(903\) | 9.52509 | + | 10.3386i | 0.316975 | + | 0.344048i | ||||
\(904\) | 32.5835i | 1.08371i | ||||||||
\(905\) | −9.93786 | − | 14.6071i | −0.330346 | − | 0.485556i | ||||
\(906\) | 26.7113i | 0.887424i | ||||||||
\(907\) | − | 36.1121i | − | 1.19908i | −0.800344 | − | 0.599541i | \(-0.795350\pi\) | ||
0.800344 | − | 0.599541i | \(-0.204650\pi\) | |||||||
\(908\) | 5.16248i | 0.171323i | ||||||||
\(909\) | 0.825476 | 0.0273793 | ||||||||
\(910\) | 9.15661 | − | 39.2984i | 0.303539 | − | 1.30273i | ||||
\(911\) | −24.7742 | −0.820804 | −0.410402 | − | 0.911905i | \(-0.634612\pi\) | ||||
−0.410402 | + | 0.911905i | \(0.634612\pi\) | |||||||
\(912\) | −28.0507 | −0.928850 | ||||||||
\(913\) | 2.88677 | + | 18.1649i | 0.0955380 | + | 0.601169i | ||||
\(914\) | 47.1047 | 1.55809 | ||||||||
\(915\) | −28.4410 | + | 19.3497i | −0.940232 | + | 0.639682i | ||||
\(916\) | − | 13.4472i | − | 0.444308i | ||||||
\(917\) | 5.19061 | + | 5.63393i | 0.171409 | + | 0.186049i | ||||
\(918\) | 12.3969i | 0.409160i | ||||||||
\(919\) | − | 25.4495i | − | 0.839501i | −0.907639 | − | 0.419751i | \(-0.862118\pi\) | ||
0.907639 | − | 0.419751i | \(-0.137882\pi\) | |||||||
\(920\) | 5.94375 | + | 8.73637i | 0.195960 | + | 0.288030i | ||||
\(921\) | − | 15.4378i | − | 0.508692i | ||||||
\(922\) | −32.5833 | −1.07307 | ||||||||
\(923\) | 6.48082i | 0.213319i | ||||||||
\(924\) | −4.64161 | − | 3.66774i | −0.152698 | − | 0.120660i | ||||
\(925\) | 13.5509 | + | 5.34921i | 0.445552 | + | 0.175881i | ||||
\(926\) | 14.5178i | 0.477085i | ||||||||
\(927\) | −11.5317 | −0.378751 | ||||||||
\(928\) | 19.7703i | 0.648992i | ||||||||
\(929\) | − | 40.7403i | − | 1.33665i | −0.743871 | − | 0.668324i | \(-0.767012\pi\) | ||
0.743871 | − | 0.668324i | \(-0.232988\pi\) | |||||||
\(930\) | 1.77730 | + | 2.61235i | 0.0582799 | + | 0.0856623i | ||||
\(931\) | −3.28097 | + | 39.9885i | −0.107529 | + | 1.31057i | ||||
\(932\) | 3.83936 | 0.125762 | ||||||||
\(933\) | 30.4383i | 0.996504i | ||||||||
\(934\) | 52.2637 | 1.71012 | ||||||||
\(935\) | −38.5285 | − | 40.9438i | −1.26002 | − | 1.33901i | ||||
\(936\) | − | 9.04293i | − | 0.295578i | ||||||
\(937\) | − | 7.83618i | − | 0.255997i | −0.991774 | − | 0.127998i | \(-0.959145\pi\) | ||
0.991774 | − | 0.127998i | \(-0.0408552\pi\) | |||||||
\(938\) | −34.0292 | + | 31.3515i | −1.11109 | + | 1.02366i | ||||
\(939\) | −31.1303 | −1.01590 | ||||||||
\(940\) | −13.4054 | + | 9.12028i | −0.437235 | + | 0.297471i | ||||
\(941\) | −4.89025 | −0.159418 | −0.0797089 | − | 0.996818i | \(-0.525399\pi\) | ||||
−0.0797089 | + | 0.996818i | \(0.525399\pi\) | |||||||
\(942\) | 0.834734 | 0.0271971 | ||||||||
\(943\) | 7.33594i | 0.238891i | ||||||||
\(944\) | 53.2302i | 1.73250i | ||||||||
\(945\) | −5.76174 | − | 1.34250i | −0.187430 | − | 0.0436715i | ||||
\(946\) | 28.4600 | − | 4.52287i | 0.925315 | − | 0.147051i | ||||
\(947\) | 16.5945i | 0.539248i | 0.962966 | + | 0.269624i | \(0.0868995\pi\) | ||||
−0.962966 | + | 0.269624i | \(0.913101\pi\) | |||||||
\(948\) | 5.56025i | 0.180589i | ||||||||
\(949\) | −9.41287 | −0.305555 | ||||||||
\(950\) | −17.2081 | + | 43.5925i | −0.558303 | + | 1.41433i | ||||
\(951\) | − | 28.5646i | − | 0.926272i | ||||||
\(952\) | 31.9819 | − | 29.4653i | 1.03654 | − | 0.954977i | ||||
\(953\) | −38.7567 | −1.25545 | −0.627726 | − | 0.778434i | \(-0.716014\pi\) | ||||
−0.627726 | + | 0.778434i | \(0.716014\pi\) | |||||||
\(954\) | − | 18.2396i | − | 0.590530i | ||||||
\(955\) | −1.06751 | + | 0.726275i | −0.0345438 | + | 0.0235017i | ||||
\(956\) | − | 6.68436i | − | 0.216188i | ||||||
\(957\) | −2.80679 | − | 17.6616i | −0.0907306 | − | 0.570919i | ||||
\(958\) | −15.3153 | −0.494813 | ||||||||
\(959\) | 17.8315 | − | 16.4284i | 0.575810 | − | 0.530501i | ||||
\(960\) | −7.01000 | + | 4.76922i | −0.226247 | + | 0.153926i | ||||
\(961\) | 30.2534 | 0.975915 | ||||||||
\(962\) | −19.8732 | −0.640737 | ||||||||
\(963\) | 9.69116 | 0.312293 | ||||||||
\(964\) | 1.39804 | 0.0450280 | ||||||||
\(965\) | 26.2888 | − | 17.8855i | 0.846267 | − | 0.575754i | ||||
\(966\) | −6.93526 | + | 6.38954i | −0.223138 | + | 0.205580i | ||||
\(967\) | −9.16393 | −0.294692 | −0.147346 | − | 0.989085i | \(-0.547073\pi\) | ||||
−0.147346 | + | 0.989085i | \(0.547073\pi\) | |||||||
\(968\) | 22.6743 | − | 7.39354i | 0.728779 | − | 0.237637i | ||||
\(969\) | − | 43.4524i | − | 1.39589i | ||||||
\(970\) | 26.6169 | − | 18.1087i | 0.854616 | − | 0.581434i | ||||
\(971\) | 23.3469i | 0.749237i | 0.927179 | + | 0.374619i | \(0.122226\pi\) | ||||
−0.927179 | + | 0.374619i | \(0.877774\pi\) | |||||||
\(972\) | 0.674169 | 0.0216240 | ||||||||
\(973\) | 13.0876 | + | 14.2054i | 0.419570 | + | 0.455404i | ||||
\(974\) | − | 25.9327i | − | 0.830936i | ||||||
\(975\) | −19.3977 | − | 7.65721i | −0.621224 | − | 0.245227i | ||||
\(976\) | −75.2857 | −2.40984 | ||||||||
\(977\) | 29.9628i | 0.958596i | 0.877652 | + | 0.479298i | \(0.159109\pi\) | ||||
−0.877652 | + | 0.479298i | \(0.840891\pi\) | |||||||
\(978\) | − | 39.8930i | − | 1.27564i | ||||||
\(979\) | 0.846694 | + | 5.32779i | 0.0270605 | + | 0.170277i | ||||
\(980\) | −5.20247 | − | 9.18084i | −0.166187 | − | 0.293271i | ||||
\(981\) | − | 10.2781i | − | 0.328154i | ||||||
\(982\) | − | 43.5329i | − | 1.38919i | ||||||
\(983\) | 24.6226 | 0.785338 | 0.392669 | − | 0.919680i | \(-0.371552\pi\) | ||||
0.392669 | + | 0.919680i | \(0.371552\pi\) | |||||||
\(984\) | −7.29746 | −0.232635 | ||||||||
\(985\) | −4.18513 | + | 2.84733i | −0.133349 | + | 0.0907236i | ||||
\(986\) | −66.8443 | −2.12876 | ||||||||
\(987\) | 19.2813 | + | 20.9281i | 0.613731 | + | 0.666149i | ||||
\(988\) | − | 16.1172i | − | 0.512756i | ||||||
\(989\) | − | 11.5805i | − | 0.368238i | ||||||
\(990\) | −8.83208 | + | 8.31106i | −0.280702 | + | 0.264143i | ||||
\(991\) | 12.5327 | 0.398115 | 0.199058 | − | 0.979988i | \(-0.436212\pi\) | ||||
0.199058 | + | 0.979988i | \(0.436212\pi\) | |||||||
\(992\) | 3.16824i | 0.100592i | ||||||||
\(993\) | −26.6099 | −0.844439 | ||||||||
\(994\) | 4.55519 | + | 4.94424i | 0.144482 | + | 0.156822i | ||||
\(995\) | −0.361166 | − | 0.530857i | −0.0114497 | − | 0.0168293i | ||||
\(996\) | − | 3.73870i | − | 0.118465i | ||||||
\(997\) | − | 17.7248i | − | 0.561349i | −0.959803 | − | 0.280675i | \(-0.909442\pi\) | ||
0.959803 | − | 0.280675i | \(-0.0905582\pi\) | |||||||
\(998\) | 19.9927 | 0.632857 | ||||||||
\(999\) | 2.91371i | 0.0921856i |
(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 | 1155.2.k.b.769.14 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.a.769.35 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.a.769.13 | ✓ | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.b.769.35 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.b.769.36 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.a.769.14 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.a.769.36 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.b.769.13 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.13 | ✓ | 48 | 7.6 | odd | 2 | ||
1155.2.k.a.769.14 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.a.769.35 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.a.769.36 | yes | 48 | 77.76 | even | 2 | ||
1155.2.k.b.769.13 | yes | 48 | 385.384 | even | 2 | inner | |
1155.2.k.b.769.14 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.b.769.35 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.b.769.36 | yes | 48 | 35.34 | odd | 2 | inner |