Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(49,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.bf (of order \(18\), degree \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(204\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 49.20 | ||
Character | \(\chi\) | \(=\) | 864.49 |
Dual form | 864.2.bf.a.529.20 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{9}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.368292 | − | 1.69244i | 0.212633 | − | 0.977132i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.355965 | + | 0.978005i | 0.159192 | + | 0.437377i | 0.993488 | − | 0.113941i | \(-0.0363474\pi\) |
−0.834295 | + | 0.551318i | \(0.814125\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.272085 | + | 1.54307i | 0.102839 | + | 0.583227i | 0.992062 | + | 0.125753i | \(0.0401346\pi\) |
−0.889223 | + | 0.457474i | \(0.848754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.72872 | − | 1.24663i | −0.909574 | − | 0.415542i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.44773 | + | 3.97760i | −0.436507 | + | 1.19929i | 0.505243 | + | 0.862977i | \(0.331403\pi\) |
−0.941750 | + | 0.336315i | \(0.890819\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.33941 | + | 5.17151i | −1.20354 | + | 1.43432i | −0.332497 | + | 0.943104i | \(0.607891\pi\) |
−0.871039 | + | 0.491214i | \(0.836553\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.78632 | − | 0.242259i | 0.461225 | − | 0.0625509i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.494959 | + | 0.857294i | −0.120045 | + | 0.207924i | −0.919785 | − | 0.392422i | \(-0.871637\pi\) |
0.799740 | + | 0.600346i | \(0.204971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.70129 | + | 1.55959i | −0.619719 | + | 0.357795i | −0.776759 | − | 0.629797i | \(-0.783138\pi\) |
0.157041 | + | 0.987592i | \(0.449805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.71177 | + | 0.107812i | 0.591757 | + | 0.0235266i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17888 | + | 6.68573i | −0.245812 | + | 1.39407i | 0.572786 | + | 0.819705i | \(0.305863\pi\) |
−0.818598 | + | 0.574367i | \(0.805248\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00044 | − | 2.51767i | 0.600088 | − | 0.503533i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.11481 | + | 4.15908i | −0.599445 | + | 0.800416i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.84964 | − | 3.39607i | −0.529166 | − | 0.630635i | 0.433557 | − | 0.901126i | \(-0.357258\pi\) |
−0.962722 | + | 0.270491i | \(0.912814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.409166 | − | 2.32049i | 0.0734883 | − | 0.416773i | −0.925764 | − | 0.378103i | \(-0.876577\pi\) |
0.999252 | − | 0.0386704i | \(-0.0123123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.19868 | + | 3.91512i | 1.07905 | + | 0.681534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41228 | + | 0.815381i | −0.238719 | + | 0.137825i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.19157 | − | 1.84266i | −0.524691 | − | 0.302931i | 0.214161 | − | 0.976798i | \(-0.431298\pi\) |
−0.738852 | + | 0.673868i | \(0.764632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.15431 | + | 9.24883i | 1.14561 | + | 1.48100i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.44191 | − | 2.04900i | −0.381362 | − | 0.320000i | 0.431875 | − | 0.901933i | \(-0.357852\pi\) |
−0.813237 | + | 0.581933i | \(0.802297\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.71087 | − | 10.1955i | 0.565903 | − | 1.55481i | −0.244938 | − | 0.969539i | \(-0.578767\pi\) |
0.810841 | − | 0.585267i | \(-0.199010\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.247877 | − | 3.11246i | 0.0369513 | − | 0.463978i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.155220 | + | 0.880296i | 0.0226411 | + | 0.128404i | 0.994033 | − | 0.109077i | \(-0.0347894\pi\) |
−0.971392 | + | 0.237481i | \(0.923678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.27080 | − | 1.55445i | 0.610115 | − | 0.222064i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.26863 | + | 1.15342i | 0.177644 | + | 0.161512i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00251i | 0.687148i | 0.939126 | + | 0.343574i | \(0.111638\pi\) | ||||
−0.939126 | + | 0.343574i | \(0.888362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.40546 | −0.594032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.64465 | + | 5.14616i | 0.217840 | + | 0.681626i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.85475 | + | 10.5908i | 0.501846 | + | 1.37881i | 0.889470 | + | 0.456993i | \(0.151073\pi\) |
−0.387625 | + | 0.921817i | \(0.626704\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.41575 | + | 0.954943i | −0.693416 | + | 0.122268i | −0.509239 | − | 0.860625i | \(-0.670073\pi\) |
−0.184177 | + | 0.982893i | \(0.558962\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.18119 | − | 4.54981i | 0.148816 | − | 0.573222i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.60244 | − | 2.40309i | −0.818932 | − | 0.298067i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.467287 | − | 0.556891i | 0.0570882 | − | 0.0680351i | −0.736745 | − | 0.676171i | \(-0.763638\pi\) |
0.793833 | + | 0.608136i | \(0.208082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.8810 | + | 4.45748i | 1.30992 | + | 0.536617i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.52073 | − | 4.36603i | 0.299155 | − | 0.518152i | −0.676788 | − | 0.736178i | \(-0.736628\pi\) |
0.975943 | + | 0.218026i | \(0.0699618\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.01816 | + | 12.1558i | 0.821413 | + | 1.42273i | 0.904630 | + | 0.426198i | \(0.140147\pi\) |
−0.0832165 | + | 0.996531i | \(0.526519\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.15597 | − | 6.00531i | −0.364420 | − | 0.693433i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.53164 | − | 1.15170i | −0.744349 | − | 0.131249i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.78017 | − | 5.68924i | 0.762829 | − | 0.640090i | −0.176032 | − | 0.984384i | \(-0.556326\pi\) |
0.938862 | + | 0.344295i | \(0.111882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.89185 | + | 6.80339i | 0.654650 | + | 0.755932i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.03223 | + | 4.80543i | 0.442595 | + | 0.527464i | 0.940512 | − | 0.339760i | \(-0.110346\pi\) |
−0.497917 | + | 0.867225i | \(0.665902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.01463 | − | 0.178906i | −0.110052 | − | 0.0194051i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.79716 | + | 3.57211i | −0.728732 | + | 0.382971i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.02279 | + | 6.96768i | 0.426415 | + | 0.738573i | 0.996551 | − | 0.0829775i | \(-0.0264430\pi\) |
−0.570136 | + | 0.821550i | \(0.693110\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.16071 | − | 5.28894i | −0.960303 | − | 0.554431i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.77661 | − | 1.54711i | −0.391616 | − | 0.160428i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.48685 | − | 2.08672i | −0.255146 | − | 0.214093i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1365 | − | 3.68937i | −1.02920 | − | 0.374599i | −0.228425 | − | 0.973561i | \(-0.573358\pi\) |
−0.800777 | + | 0.598963i | \(0.795580\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.90903 | − | 9.04900i | 0.895391 | − | 0.909458i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.50659 | − | 1.14729i | 0.647430 | − | 0.114159i | 0.159716 | − | 0.987163i | \(-0.448942\pi\) |
0.487714 | + | 0.873004i | \(0.337831\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.9315 | − | 5.43464i | 1.47125 | − | 0.535491i | 0.522809 | − | 0.852450i | \(-0.324884\pi\) |
0.948439 | + | 0.316959i | \(0.102662\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.859854 | + | 2.69050i | 0.0839131 | + | 0.262566i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.85513i | 0.372689i | 0.982484 | + | 0.186345i | \(0.0596641\pi\) | ||||
−0.982484 | + | 0.186345i | \(0.940336\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.32803i | − | 0.318767i | −0.987217 | − | 0.159384i | \(-0.949049\pi\) | ||
0.987217 | − | 0.159384i | \(-0.0509507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.29402 | + | 4.72292i | −0.407570 | + | 0.448279i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.85208 | − | 2.85792i | 0.738662 | − | 0.268851i | 0.0548351 | − | 0.998495i | \(-0.482537\pi\) |
0.683827 | + | 0.729645i | \(0.260314\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.95832 | + | 1.22694i | −0.648867 | + | 0.114413i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.2880 | − | 8.70199i | 1.69072 | − | 0.804499i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.45754 | − | 0.530501i | −0.133612 | − | 0.0486309i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.29891 | − | 4.44632i | −0.481719 | − | 0.404211i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.36715 | + | 3.37815i | −0.393773 | + | 0.304598i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.03702 | + | 4.64017i | 0.718853 | + | 0.415030i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.83012 | − | 3.16986i | −0.162397 | − | 0.281280i | 0.773331 | − | 0.634003i | \(-0.218589\pi\) |
−0.935728 | + | 0.352723i | \(0.885256\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.8887 | − | 10.0354i | −1.39892 | − | 0.883566i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.66082 | − | 1.70346i | −0.844070 | − | 0.148832i | −0.265140 | − | 0.964210i | \(-0.585418\pi\) |
−0.578930 | + | 0.815378i | \(0.696529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.14155 | − | 3.74395i | −0.272407 | − | 0.324641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.17637 | − | 1.56581i | −0.445511 | − | 0.134764i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.9231 | + | 14.2001i | −1.44583 | + | 1.21320i | −0.510284 | + | 0.860006i | \(0.670460\pi\) |
−0.935550 | + | 0.353193i | \(0.885096\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.68849 | + | 0.826707i | 0.397672 | + | 0.0701203i | 0.368908 | − | 0.929466i | \(-0.379732\pi\) |
0.0287641 | + | 0.999586i | \(0.490843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.54702 | + | 0.0615050i | 0.130282 | + | 0.00517966i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.2879 | − | 24.7474i | −1.19482 | − | 2.06948i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.30701 | − | 3.99585i | 0.191586 | − | 0.331837i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.05791 | − | 7.80058i | −0.0872547 | − | 0.643381i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.7916 | + | 17.6280i | −1.21178 | + | 1.44414i | −0.350076 | + | 0.936721i | \(0.613844\pi\) |
−0.861700 | + | 0.507418i | \(0.830600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.6779 | − | 6.79819i | −1.51998 | − | 0.553229i | −0.558840 | − | 0.829276i | \(-0.688753\pi\) |
−0.961144 | + | 0.276047i | \(0.910975\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.41933 | − | 1.72229i | 0.195591 | − | 0.139239i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.41510 | − | 0.425848i | 0.193986 | − | 0.0342049i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.67263 | − | 4.59552i | −0.133491 | − | 0.366762i | 0.854880 | − | 0.518825i | \(-0.173631\pi\) |
−0.988371 | + | 0.152063i | \(0.951408\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.46647 | + | 1.84239i | 0.671435 | + | 0.146111i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6373 | −0.838339 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.18081i | 0.327466i | 0.986505 | + | 0.163733i | \(0.0523536\pi\) | ||||
−0.986505 | + | 0.163733i | \(0.947646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.62249 | + | 7.45598i | −0.126311 | + | 0.580447i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.72775 | + | 2.08473i | −0.443227 | + | 0.161321i | −0.553986 | − | 0.832526i | \(-0.686894\pi\) |
0.110759 | + | 0.993847i | \(0.464672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.65659 | − | 32.0801i | −0.435122 | − | 2.46770i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.31530 | − | 0.888193i | 0.712359 | − | 0.0679218i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.453627 | + | 1.24633i | −0.0344886 | + | 0.0947567i | −0.955742 | − | 0.294207i | \(-0.904945\pi\) |
0.921253 | + | 0.388964i | \(0.127167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.70132 | + | 3.94488i | 0.355386 | + | 0.298205i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.3441 | − | 2.62342i | 1.45399 | − | 0.197189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.68622 | + | 5.59234i | 0.723982 | + | 0.417991i | 0.816217 | − | 0.577746i | \(-0.196068\pi\) |
−0.0922343 | + | 0.995737i | \(0.529401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.21058 | − | 1.85363i | 0.238641 | − | 0.137779i | −0.375911 | − | 0.926656i | \(-0.622670\pi\) |
0.614552 | + | 0.788876i | \(0.289337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.378391 | + | 9.51754i | −0.0279714 | + | 0.703557i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.666039 | − | 3.77730i | 0.0489682 | − | 0.277712i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.69341 | − | 3.20988i | −0.196961 | − | 0.234730i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.26526 | − | 3.67475i | −0.528470 | − | 0.267299i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8306 | + | 11.6053i | −1.00075 | + | 0.839729i | −0.987088 | − | 0.160178i | \(-0.948793\pi\) |
−0.0136618 | + | 0.999907i | \(0.504349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.770660 | − | 4.37063i | 0.0554733 | − | 0.314605i | −0.944427 | − | 0.328721i | \(-0.893382\pi\) |
0.999900 | + | 0.0141163i | \(0.00449352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.49872 | + | 10.2892i | −0.465383 | + | 0.736826i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1519 | − | 8.17063i | 1.00828 | − | 0.582133i | 0.0975957 | − | 0.995226i | \(-0.468885\pi\) |
0.910689 | + | 0.413093i | \(0.135551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.458824 | − | 0.794707i | 0.0325252 | − | 0.0563353i | −0.849305 | − | 0.527903i | \(-0.822978\pi\) |
0.881830 | + | 0.471568i | \(0.156312\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.770408 | − | 0.995955i | −0.0543404 | − | 0.0702493i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.46504 | − | 5.32123i | 0.313385 | − | 0.373477i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.13470 | − | 3.11757i | 0.0792511 | − | 0.217741i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.5514 | − | 16.7739i | 0.802880 | − | 1.16587i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.29270 | − | 13.0025i | −0.158589 | − | 0.899403i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.09734 | + | 5.76240i | 0.144387 | + | 0.396700i | 0.990714 | − | 0.135964i | \(-0.0434131\pi\) |
−0.846327 | + | 0.532664i | \(0.821191\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.46089 | − | 5.87416i | −0.442693 | − | 0.402491i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.2922 | 0.770124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.69202 | 0.250631 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.1577 | − | 7.40094i | 1.56485 | − | 0.500109i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.28567 | − | 6.27983i | −0.153751 | − | 0.422427i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.72326 | + | 21.1156i | 0.249328 | + | 1.41401i | 0.810223 | + | 0.586121i | \(0.199346\pi\) |
−0.560896 | + | 0.827887i | \(0.689543\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.3260 | + | 3.12959i | −0.755063 | + | 0.208639i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.36438 | − | 17.4860i | 0.422419 | − | 1.16059i | −0.527900 | − | 0.849307i | \(-0.677020\pi\) |
0.950319 | − | 0.311279i | \(-0.100757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.70813 | − | 6.80268i | 0.377204 | − | 0.449534i | −0.543726 | − | 0.839263i | \(-0.682987\pi\) |
0.920930 | + | 0.389729i | \(0.127431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.35474 | + | 10.6303i | −0.286521 | + | 0.699420i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.39731 | − | 16.2766i | 0.615638 | − | 1.06632i | −0.374634 | − | 0.927173i | \(-0.622232\pi\) |
0.990272 | − | 0.139144i | \(-0.0444350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.805681 | + | 0.465160i | −0.0525568 | + | 0.0303437i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.13163 | − | 13.5704i | −0.463249 | − | 0.881489i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.56653 | + | 20.2268i | −0.230700 | + | 1.30836i | 0.620784 | + | 0.783982i | \(0.286815\pi\) |
−0.851483 | + | 0.524382i | \(0.824297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5529 | + | 8.85497i | −0.679775 | + | 0.570399i | −0.915941 | − | 0.401314i | \(-0.868554\pi\) |
0.236166 | + | 0.971713i | \(0.424109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.6843 | − | 7.46598i | 0.877846 | − | 0.478943i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.04051 | + | 3.62354i | 0.194251 | + | 0.231499i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.65657 | − | 20.7374i | 0.232662 | − | 1.31949i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.61795 | − | 5.05452i | 0.609513 | − | 0.320317i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.419101 | − | 0.241968i | 0.0264534 | − | 0.0152729i | −0.486715 | − | 0.873561i | \(-0.661805\pi\) |
0.513168 | + | 0.858288i | \(0.328472\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.8865 | − | 14.3682i | −1.56460 | − | 0.903323i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.676466 | + | 1.65131i | −0.0423620 | + | 0.103409i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5896 | + | 11.4030i | 0.847695 | + | 0.711300i | 0.959281 | − | 0.282454i | \(-0.0911486\pi\) |
−0.111586 | + | 0.993755i | \(0.535593\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.97497 | − | 5.42619i | 0.122719 | − | 0.337167i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.54226 | + | 12.8194i | 0.219260 | + | 0.793500i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.39832 | − | 7.93029i | −0.0862243 | − | 0.489002i | −0.997086 | − | 0.0762899i | \(-0.975693\pi\) |
0.910861 | − | 0.412712i | \(-0.135419\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.89249 | + | 1.78072i | −0.300543 | + | 0.109389i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2740 | − | 4.24220i | 0.812353 | − | 0.259619i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.56538i | 0.400298i | 0.979765 | + | 0.200149i | \(0.0641426\pi\) | ||||
−0.979765 | + | 0.200149i | \(0.935857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8623 | −0.659839 | −0.329919 | − | 0.944009i | \(-0.607022\pi\) | ||||
−0.329919 | + | 0.944009i | \(0.607022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.3250 | + | 13.5561i | −0.745945 | + | 0.820452i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.67046 | + | 15.5795i | 0.341941 | + | 0.939476i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.2235 | − | 5.50555i | 1.87604 | − | 0.330796i | 0.885131 | − | 0.465342i | \(-0.154069\pi\) |
0.990907 | + | 0.134546i | \(0.0429575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00929 | + | 5.82191i | −0.240030 | + | 0.348549i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.4488 | − | 6.71481i | −1.10056 | − | 0.400572i | −0.273039 | − | 0.962003i | \(-0.588029\pi\) |
−0.827523 | + | 0.561431i | \(0.810251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6768 | + | 15.1076i | −0.753556 | + | 0.898053i | −0.997422 | − | 0.0717558i | \(-0.977140\pi\) |
0.243866 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.44754 | + | 3.44033i | −0.263449 | + | 0.203788i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.49735 | − | 4.32554i | 0.147414 | − | 0.255329i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.01003 | + | 13.8738i | 0.471178 | + | 0.816105i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.97723 | + | 15.7966i | −0.584875 | + | 0.926014i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1866 | + | 4.61741i | 1.52984 | + | 0.269752i | 0.874292 | − | 0.485401i | \(-0.161326\pi\) |
0.655549 | + | 0.755153i | \(0.272437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.98574 | + | 7.53993i | −0.523170 | + | 0.438992i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.0338 | − | 18.4107i | −0.698271 | − | 1.06830i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.4597 | − | 35.1087i | −1.70370 | − | 2.03039i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.7421 | + | 2.95209i | 0.965001 | + | 0.170156i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.454606 | − | 11.4346i | 0.0261164 | − | 0.656898i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.86175 | − | 4.95671i | −0.163864 | − | 0.283820i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0407 | − | 11.5705i | −1.14379 | − | 0.660365i | −0.196420 | − | 0.980520i | \(-0.562932\pi\) |
−0.947365 | + | 0.320155i | \(0.896265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.69864 | − | 27.2723i | −0.210409 | − | 1.55147i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.6806 | + | 15.6749i | 1.05928 | + | 0.888842i | 0.994039 | − | 0.109027i | \(-0.0347735\pi\) |
0.0652424 | + | 0.997869i | \(0.479218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.2156 | + | 8.81377i | 1.36875 | + | 0.498184i | 0.918748 | − | 0.394845i | \(-0.129202\pi\) |
0.450000 | + | 0.893028i | \(0.351424\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.87020 | − | 0.464362i | 0.274405 | − | 0.0261639i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.1371 | + | 3.19806i | −1.01868 | + | 0.179621i | −0.657960 | − | 0.753053i | \(-0.728580\pi\) |
−0.360721 | + | 0.932674i | \(0.617469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6337 | − | 6.41816i | 0.987300 | − | 0.359348i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.52458 | + | 1.41981i | 0.364167 | + | 0.0792462i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.08773i | − | 0.171806i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.4420i | 1.46674i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.63249 | − | 1.22568i | −0.311478 | − | 0.0677805i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.31613 | + | 0.479031i | −0.0725605 | + | 0.0264099i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2370 | − | 2.68670i | 0.837502 | − | 0.147674i | 0.261583 | − | 0.965181i | \(-0.415755\pi\) |
0.575919 | + | 0.817507i | \(0.304644\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.41181 | + | 9.00679i | 0.351365 | + | 0.493569i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.710980 | + | 0.258776i | 0.0388450 | + | 0.0141384i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.32566 | + | 7.82516i | 0.508001 | + | 0.426264i | 0.860425 | − | 0.509577i | \(-0.170198\pi\) |
−0.352424 | + | 0.935840i | \(0.614643\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.94501 | − | 14.3417i | −0.105639 | − | 0.778937i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.63764 | + | 4.98695i | 0.467755 | + | 0.270058i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.04472 | + | 15.6659i | 0.488369 | + | 0.845880i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.486168 | + | 12.2284i | −0.0261744 | + | 0.658356i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.2143 | − | 4.09332i | −1.24621 | − | 0.219741i | −0.488636 | − | 0.872488i | \(-0.662505\pi\) |
−0.757576 | + | 0.652747i | \(0.773616\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.7087 | − | 17.5291i | −0.787338 | − | 0.938312i | 0.211902 | − | 0.977291i | \(-0.432034\pi\) |
−0.999240 | + | 0.0389784i | \(0.987590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.99230 | − | 34.1562i | −0.426598 | − | 1.82312i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.541929 | − | 0.454733i | 0.0288440 | − | 0.0242030i | −0.628252 | − | 0.778010i | \(-0.716229\pi\) |
0.657096 | + | 0.753807i | \(0.271785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16729 | + | 0.911132i | 0.274251 | + | 0.0483579i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.43464 | + | 2.27142i | −0.0759293 | + | 0.120216i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.07907 | + | 8.79721i | 0.268063 | + | 0.464299i | 0.968362 | − | 0.249551i | \(-0.0802831\pi\) |
−0.700298 | + | 0.713850i | \(0.746950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.63535 | + | 8.02867i | −0.243966 | + | 0.422561i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.47668 | + | 7.33056i | −0.497397 | + | 0.384755i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.39023 | + | 11.1908i | −0.491507 | + | 0.585755i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.79478 | + | 0.653245i | 0.0936866 | + | 0.0340991i | 0.388438 | − | 0.921475i | \(-0.373015\pi\) |
−0.294752 | + | 0.955574i | \(0.595237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.10894 | + | 8.63530i | 0.213903 | + | 0.449536i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.71925 | + | 1.36111i | −0.400763 | + | 0.0706654i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8307 | + | 32.5046i | 0.612571 | + | 1.68303i | 0.724470 | + | 0.689306i | \(0.242084\pi\) |
−0.111899 | + | 0.993720i | \(0.535693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.8132 | − | 11.8932i | 0.558391 | − | 0.614165i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.9286 | 1.54140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.1937i | 1.39685i | 0.715685 | + | 0.698423i | \(0.246114\pi\) | ||||
−0.715685 | + | 0.698423i | \(0.753886\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.03883 | + | 1.92994i | −0.309378 | + | 0.0988738i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.67775 | − | 2.06653i | 0.290120 | − | 0.105595i | −0.192861 | − | 0.981226i | \(-0.561777\pi\) |
0.482980 | + | 0.875631i | \(0.339554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.19866 | − | 6.79794i | −0.0610894 | − | 0.346455i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.8360 | + | 23.1947i | −1.16082 | + | 1.17905i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.99747 | − | 10.9830i | 0.202680 | − | 0.556858i | −0.796156 | − | 0.605091i | \(-0.793137\pi\) |
0.998836 | + | 0.0482330i | \(0.0153590\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.14814 | − | 4.31980i | −0.260353 | − | 0.218462i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.44102 | + | 15.7230i | −0.324906 | + | 0.793121i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.97761 | + | 4.60588i | 0.401397 | + | 0.231747i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.31327 | + | 1.33556i | −0.116099 | + | 0.0670301i | −0.556925 | − | 0.830563i | \(-0.688019\pi\) |
0.440826 | + | 0.897593i | \(0.354686\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.49342 | + | 3.93802i | −0.375140 | + | 0.197148i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.15776 | + | 12.2372i | −0.107753 | + | 0.611099i | 0.882332 | + | 0.470628i | \(0.155973\pi\) |
−0.990085 | + | 0.140470i | \(0.955138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.2249 | + | 12.1856i | 0.509339 | + | 0.607007i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.55646 | + | 8.18403i | −0.226412 | + | 0.406668i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.9499 | − | 10.0271i | 0.592334 | − | 0.497027i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.895032 | + | 5.07598i | −0.0442565 | + | 0.250991i | −0.998907 | − | 0.0467370i | \(-0.985118\pi\) |
0.954651 | + | 0.297728i | \(0.0962288\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.8003 | + | 33.8711i | 0.878023 | + | 1.67074i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.2936 | + | 8.82978i | −0.752550 | + | 0.434485i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.26440 | + | 5.65411i | −0.160243 | + | 0.277549i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.12588 | − | 7.63052i | 0.153075 | − | 0.373668i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84481 | + | 2.19856i | −0.0901248 | + | 0.107407i | −0.809222 | − | 0.587503i | \(-0.800111\pi\) |
0.719097 | + | 0.694909i | \(0.244556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.61049 | − | 12.6672i | 0.224701 | − | 0.617362i | −0.775195 | − | 0.631721i | \(-0.782349\pi\) |
0.999897 | + | 0.0143594i | \(0.00457089\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.673847 | − | 2.59558i | 0.0327636 | − | 0.126202i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.673287 | + | 3.81840i | 0.0326592 | + | 0.185220i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.94709 | − | 8.09707i | −0.142620 | − | 0.391845i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −47.1457 | + | 15.0672i | −2.27621 | + | 0.727452i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.2153 | −1.21458 | −0.607290 | − | 0.794480i | \(-0.707743\pi\) | ||||
−0.607290 | + | 0.794480i | \(0.707743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.5658 | −0.748046 | −0.374023 | − | 0.927419i | \(-0.622022\pi\) | ||||
−0.374023 | + | 0.927419i | \(0.622022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.91309 | − | 5.37611i | −0.283511 | − | 0.257765i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.24252 | − | 19.8987i | −0.346457 | − | 0.951882i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.53290 | − | 31.3787i | −0.264071 | − | 1.49762i | −0.771667 | − | 0.636026i | \(-0.780577\pi\) |
0.507596 | − | 0.861595i | \(-0.330534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.5916 | − | 1.08244i | −0.647221 | − | 0.0515449i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.16330 | + | 5.94362i | −0.102782 | + | 0.282390i | −0.980415 | − | 0.196942i | \(-0.936899\pi\) |
0.877634 | + | 0.479332i | \(0.159121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.38246 | + | 6.41456i | −0.255153 | + | 0.304079i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.3867 | + | 31.5262i | 1.15345 | + | 1.49114i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.18149 | + | 7.24256i | −0.197337 | + | 0.341797i | −0.947664 | − | 0.319269i | \(-0.896563\pi\) |
0.750327 | + | 0.661067i | \(0.229896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6853 | − | 6.74653i | 0.550241 | − | 0.317682i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.3845 | + | 29.1075i | −0.863777 | + | 1.36759i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.91172 | − | 10.8419i | 0.0896228 | − | 0.508276i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.5741 | + | 18.1028i | −1.00919 | + | 0.846812i | −0.988231 | − | 0.152968i | \(-0.951117\pi\) |
−0.0209605 | + | 0.999780i | \(0.506672\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.02385 | − | 4.72888i | −0.0944655 | − | 0.220725i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.8013 | − | 20.0230i | −0.782513 | − | 0.932563i | 0.216531 | − | 0.976276i | \(-0.430526\pi\) |
−0.999044 | + | 0.0437126i | \(0.986081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.84612 | + | 21.8124i | −0.178744 | + | 1.01371i | 0.754988 | + | 0.655738i | \(0.227642\pi\) |
−0.933733 | + | 0.357971i | \(0.883469\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.168740 | − | 4.24426i | 0.00782513 | − | 0.196823i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1663 | − | 11.0657i | 0.886910 | − | 0.512058i | 0.0139792 | − | 0.999902i | \(-0.495550\pi\) |
0.872930 | + | 0.487845i | \(0.162217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.986466 | + | 0.569536i | 0.0455508 | + | 0.0262987i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.39367 | + | 1.13834i | −0.386760 | + | 0.0524520i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.1815 | + | 29.5208i | 1.61765 | + | 1.35737i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.17853 | + | 11.4804i | −0.191724 | + | 0.526757i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.23626 | − | 13.6505i | 0.285539 | − | 0.625012i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.06488 | + | 11.7105i | 0.0943470 | + | 0.535068i | 0.994946 | + | 0.100416i | \(0.0320175\pi\) |
−0.900599 | + | 0.434652i | \(0.856871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.3788 | − | 8.50920i | 1.06598 | − | 0.387986i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.91764 | + | 18.0031i | −0.178259 | + | 0.819168i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 11.2268i | − | 0.509783i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.1183 | −1.00228 | −0.501138 | − | 0.865367i | \(-0.667085\pi\) | ||||
−0.501138 | + | 0.865367i | \(0.667085\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.07578 | + | 1.53976i | 0.319978 | + | 0.0696303i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.55319 | − | 7.01484i | −0.115224 | − | 0.316575i | 0.868653 | − | 0.495421i | \(-0.164986\pi\) |
−0.983877 | + | 0.178845i | \(0.942764\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.32189 | − | 0.762066i | 0.194648 | − | 0.0343217i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0213 | + | 5.49195i | 0.540316 | + | 0.246845i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.42295 | + | 2.70173i | 0.332965 | + | 0.121189i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.65452 | − | 7.93054i | 0.297897 | − | 0.355020i | −0.596246 | − | 0.802802i | \(-0.703342\pi\) |
0.894143 | + | 0.447782i | \(0.147786\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.41880 | + | 10.4617i | 0.0633874 | + | 0.467393i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9435 | − | 29.3471i | 0.755475 | − | 1.30852i | −0.189663 | − | 0.981849i | \(-0.560739\pi\) |
0.945138 | − | 0.326672i | \(-0.105927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.43817 | + | 5.95508i | 0.152997 | + | 0.264998i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −56.3770 | − | 2.24139i | −2.50379 | − | 0.0995436i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7517 | + | 2.95378i | 0.742508 | + | 0.130924i | 0.532090 | − | 0.846688i | \(-0.321407\pi\) |
0.210417 | + | 0.977612i | \(0.432518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.8478 | + | 14.1370i | −0.745301 | + | 0.625382i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.92753 | − | 16.0927i | 0.0851026 | − | 0.710511i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.6302 | + | 12.6686i | 0.468423 | + | 0.558245i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.72618 | − | 0.657026i | −0.163877 | − | 0.0288960i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.94227 | + | 1.22675i | 0.0852564 | + | 0.0538484i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.6553 | − | 25.3837i | −0.642060 | − | 1.11208i | −0.984972 | − | 0.172714i | \(-0.944746\pi\) |
0.342912 | − | 0.939368i | \(-0.388587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.33680 | + | 1.92651i | 0.145908 | + | 0.0842402i | 0.571177 | − | 0.820827i | \(-0.306487\pi\) |
−0.425269 | + | 0.905067i | \(0.639820\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.40793 | − | 6.50385i | 0.366952 | − | 0.283851i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.78683 | + | 1.49932i | 0.0778353 | + | 0.0653116i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6963 | − | 7.89682i | −0.943319 | − | 0.343340i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.68427 | − | 33.7049i | 0.116487 | − | 1.46267i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.1929 | − | 3.73687i | 0.917965 | − | 0.161862i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.77033 | + | 1.37229i | −0.163006 | + | 0.0593292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.0321 | − | 14.3338i | 0.562376 | − | 0.618547i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.2380i | 0.828638i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.51542i | 0.194133i | 0.995278 | + | 0.0970665i | \(0.0309460\pi\) | ||||
−0.995278 | + | 0.0970665i | \(0.969054\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.95473 | − | 6.11640i | −0.0838856 | − | 0.262480i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.25483 | − | 1.18466i | 0.139421 | − | 0.0507453i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.3037 | − | 2.16948i | 0.526069 | − | 0.0927602i | 0.0956949 | − | 0.995411i | \(-0.469493\pi\) |
0.430374 | + | 0.902651i | \(0.358382\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.9685 | + | 4.14564i | 0.681520 | + | 0.176931i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.9942 | + | 4.72950i | 0.553572 | + | 0.201484i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6237 | + | 8.91435i | 0.451766 | + | 0.379077i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.14756 | − | 2.51838i | −0.260949 | − | 0.106899i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.03004 | − | 1.74940i | −0.128387 | − | 0.0741243i | 0.434431 | − | 0.900705i | \(-0.356949\pi\) |
−0.562818 | + | 0.826581i | \(0.690283\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.6233 | + | 63.4335i | 1.54900 | + | 2.68295i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.42449 | + | 3.37627i | −0.271242 | + | 0.142546i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.9436 | − | 4.75088i | −1.13554 | − | 0.200226i | −0.425885 | − | 0.904777i | \(-0.640037\pi\) |
−0.709653 | + | 0.704552i | \(0.751148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.59013 | + | 6.66206i | 0.235179 | + | 0.280275i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.89504 | + | 10.9427i | −0.373557 | + | 0.459549i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.15771 | − | 2.64963i | 0.132378 | − | 0.111078i | −0.574195 | − | 0.818719i | \(-0.694685\pi\) |
0.706573 | + | 0.707640i | \(0.250240\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.91629 | − | 0.514220i | −0.122043 | − | 0.0215194i | 0.112293 | − | 0.993675i | \(-0.464180\pi\) |
−0.234336 | + | 0.972156i | \(0.575292\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.5476 | + | 27.6817i | 0.607733 | + | 1.15642i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.2953 | + | 23.0281i | 0.554453 | + | 0.960340i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.23106 | + | 7.32841i | −0.176141 | + | 0.305086i | −0.940556 | − | 0.339640i | \(-0.889695\pi\) |
0.764414 | + | 0.644725i | \(0.223028\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.11321 | − | 2.91396i | −0.295615 | − | 0.121100i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.31802 | + | 7.52952i | −0.262115 | + | 0.312377i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.8980 | − | 7.24228i | −0.824092 | − | 0.299945i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0205 | + | 14.7881i | 0.621020 | + | 0.611414i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.4714 | − | 8.01784i | 1.87681 | − | 0.330932i | 0.885727 | − | 0.464206i | \(-0.153660\pi\) |
0.991079 | + | 0.133275i | \(0.0425493\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.51375 | + | 6.90646i | 0.103577 | + | 0.284576i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.61628 | − | 26.9605i | −0.354426 | − | 1.10901i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.0816 | 0.906784 | 0.453392 | − | 0.891311i | \(-0.350214\pi\) | ||||
0.453392 | + | 0.891311i | \(0.350214\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.61432i | − | 0.0661807i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.17601 | − | 1.06922i | −0.0481311 | − | 0.0437602i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.2555 | − | 8.46431i | 0.950194 | − | 0.345842i | 0.180010 | − | 0.983665i | \(-0.442387\pi\) |
0.770184 | + | 0.637822i | \(0.220165\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.55983 | + | 14.5175i | 0.104418 | + | 0.592182i | 0.991451 | + | 0.130477i | \(0.0416509\pi\) |
−0.887034 | + | 0.461705i | \(0.847238\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.96933 | + | 0.937069i | −0.0801974 | + | 0.0381604i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.46229 | − | 6.76510i | 0.100107 | − | 0.275040i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.2768 | + | 19.5315i | 0.944775 | + | 0.792761i | 0.978410 | − | 0.206674i | \(-0.0662638\pi\) |
−0.0336346 | + | 0.999434i | \(0.510708\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.36144 | − | 9.51660i | −0.298301 | − | 0.385632i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.22602 | − | 3.01724i | −0.211422 | − | 0.122065i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.97166 | − | 5.17979i | 0.362362 | − | 0.209210i | −0.307754 | − | 0.951466i | \(-0.599578\pi\) |
0.670116 | + | 0.742256i | \(0.266244\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.85841 | − | 3.06859i | −0.195910 | − | 0.123738i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.09885 | − | 11.9032i | 0.0844965 | − | 0.479204i | −0.912968 | − | 0.408032i | \(-0.866215\pi\) |
0.997464 | − | 0.0711715i | \(-0.0226738\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.25371 | + | 1.49411i | 0.0503908 | + | 0.0600535i | 0.790651 | − | 0.612267i | \(-0.209742\pi\) |
−0.740260 | + | 0.672320i | \(0.765298\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.1345 | − | 25.7278i | −0.968486 | − | 1.03242i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.65710 | + | 8.10327i | −0.386904 | + | 0.324651i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.72350 | − | 9.77447i | 0.0689401 | − | 0.390979i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.8504 | − | 0.908468i | −0.912557 | − | 0.0362807i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.15939 | − | 1.82408i | 0.125973 | − | 0.0727307i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.64702 | − | 11.5130i | 0.264614 | − | 0.458325i | −0.702849 | − | 0.711340i | \(-0.748089\pi\) |
0.967462 | + | 0.253015i | \(0.0814222\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5250 | − | 1.42739i | 0.418330 | − | 0.0567335i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.44868 | − | 2.91823i | 0.0971730 | − | 0.115806i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4939 | + | 28.8319i | −0.415785 | + | 1.14236i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.3212 | + | 8.77127i | −0.487418 | + | 0.346986i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.99251 | + | 28.3139i | 0.197192 | + | 1.11833i | 0.909262 | + | 0.416225i | \(0.136647\pi\) |
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8078 | + | 35.1891i | 0.505090 | + | 1.38772i | 0.886247 | + | 0.463213i | \(0.153303\pi\) |
−0.381157 | + | 0.924510i | \(0.624474\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.15884 | − | 19.1115i | 0.163754 | − | 0.752513i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.8383 | 0.937182 | 0.468591 | − | 0.883415i | \(-0.344762\pi\) | ||||
0.468591 | + | 0.883415i | \(0.344762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.7068 | −1.87266 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.35974 | − | 6.24853i | 0.0532925 | − | 0.244899i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.8138 | − | 46.1955i | −0.657974 | − | 1.80777i | −0.585921 | − | 0.810368i | \(-0.699267\pi\) |
−0.0720526 | − | 0.997401i | \(-0.522955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.77292 | − | 10.0547i | −0.0692736 | − | 0.392870i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.99687 | − | 41.9188i | −0.155933 | − | 1.63541i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.01137 | − | 24.7585i | 0.351033 | − | 0.964456i | −0.631006 | − | 0.775778i | \(-0.717358\pi\) |
0.982039 | − | 0.188678i | \(-0.0604202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.937603 | − | 1.11739i | 0.0364685 | − | 0.0434615i | −0.747502 | − | 0.664260i | \(-0.768747\pi\) |
0.783970 | + | 0.620798i | \(0.213191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.4701 | + | 1.55556i | −0.445460 | + | 0.0604128i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.54332 | − | 4.40516i | 0.0986258 | − | 0.170825i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.0646 | − | 15.0484i | 1.00923 | − | 0.582677i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.1082 | + | 1.47532i | 1.43469 | + | 0.0570392i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.04215 | − | 22.9242i | 0.156046 | − | 0.884979i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.2562 | − | 11.9623i | 0.549534 | − | 0.461114i | −0.325249 | − | 0.945628i | \(-0.605448\pi\) |
0.874783 | + | 0.484514i | \(0.161004\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.12540 | + | 20.3211i | 0.0433165 | + | 0.782160i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.04257 | − | 2.43424i | −0.0785022 | − | 0.0935553i | 0.725364 | − | 0.688366i | \(-0.241672\pi\) |
−0.803866 | + | 0.594810i | \(0.797227\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.93499 | − | 16.6451i | 0.112634 | − | 0.638782i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.2501 | − | 17.2113i | −1.04423 | − | 0.659538i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.95770 | − | 4.59438i | 0.304493 | − | 0.175799i | −0.339967 | − | 0.940437i | \(-0.610416\pi\) |
0.644459 | + | 0.764639i | \(0.277082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.9118 | − | 11.4961i | −0.760792 | − | 0.439243i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.41089 | − | 12.1660i | −0.359048 | − | 0.464164i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.8705 | − | 21.7080i | −0.985589 | − | 0.827008i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.14708 | − | 16.8890i | 0.233846 | − | 0.642487i | −0.766154 | − | 0.642657i | \(-0.777832\pi\) |
1.00000 | 0.000170287i | \(5.42042e-5\pi\) | ||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.3873 | + | 11.2852i | 0.622501 | + | 0.428689i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.860413 | + | 4.87964i | 0.0326373 | + | 0.185095i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.96524 | − | 1.07926i | 0.112316 | − | 0.0408799i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.0863 | − | 21.8989i | −0.911027 | − | 0.828294i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.1567i | − | 0.723538i | −0.932268 | − | 0.361769i | \(-0.882173\pi\) | ||
0.932268 | − | 0.361769i | \(-0.117827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4952 | 0.433548 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.490531 | + | 1.53488i | 0.0184745 | + | 0.0578070i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.54070 | + | 9.72798i | 0.133162 | + | 0.365858i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.23990 | + | 1.62924i | −0.347012 | + | 0.0611875i | −0.344438 | − | 0.938809i | \(-0.611930\pi\) |
−0.00257396 | + | 0.999997i | \(0.500819\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.5936 | + | 7.07202i | −0.959834 | + | 0.265222i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.0318 | + | 5.47115i | 0.562947 | + | 0.204896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.1171 | − | 22.7829i | 0.714938 | − | 0.852031i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.9192 | + | 13.4855i | 1.22939 | + | 0.503626i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7417 | + | 18.6051i | −0.400596 | + | 0.693853i | −0.993798 | − | 0.111201i | \(-0.964530\pi\) |
0.593202 | + | 0.805054i | \(0.297864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.4487 | + | 21.5618i | 0.463614 | + | 0.803003i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.1000 | + | 21.1215i | 0.412812 | + | 0.785516i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.1004 | − | 3.01526i | −0.635092 | − | 0.111984i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5451 | − | 18.9176i | 0.836151 | − | 0.701614i | −0.120543 | − | 0.992708i | \(-0.538464\pi\) |
0.956694 | + | 0.291094i | \(0.0940193\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.59595 | − | 25.9095i | −0.281331 | − | 0.959611i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.90385 | + | 8.22768i | 0.255348 | + | 0.304312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.1488 | + | 7.60829i | 1.59374 | + | 0.281019i | 0.898901 | − | 0.438151i | \(-0.144366\pi\) |
0.694835 | + | 0.719170i | \(0.255478\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.25243 | − | 3.81137i | 0.267510 | − | 0.140584i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.53859 | + | 2.66491i | 0.0566746 | + | 0.0981632i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9574 | − | 12.6771i | −0.807716 | − | 0.466335i | 0.0384462 | − | 0.999261i | \(-0.487759\pi\) |
−0.846162 | + | 0.532926i | \(0.821093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.7503 | − | 13.8260i | −1.23985 | − | 0.507910i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.44991 | + | 2.89482i | 0.126565 | + | 0.106201i | 0.703873 | − | 0.710326i | \(-0.251452\pi\) |
−0.577308 | + | 0.816526i | \(0.695897\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.5055 | − | 8.19135i | −0.824539 | − | 0.300108i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.01228 | − | 18.1394i | −0.183390 | − | 0.663685i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.94874 | + | 1.04892i | −0.217362 | + | 0.0383268i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.9941 | + | 13.4647i | −1.34993 | + | 0.491335i | −0.912927 | − | 0.408124i | \(-0.866183\pi\) |
−0.437006 | + | 0.899459i | \(0.643961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.255166 | − | 0.798419i | −0.00929875 | − | 0.0290960i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 20.6870i | − | 0.752876i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.7213i | 1.22562i | 0.790229 | + | 0.612811i | \(0.209961\pi\) | ||||
−0.790229 | + | 0.612811i | \(0.790039\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33.4829 | + | 36.8273i | −1.21535 | + | 1.33674i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.7776 | + | 12.6580i | −1.26069 | + | 0.458852i | −0.883999 | − | 0.467489i | \(-0.845159\pi\) |
−0.376687 | + | 0.926341i | \(0.622937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.13539 | − | 0.905508i | 0.185914 | − | 0.0327816i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.54560 | + | 1.75304i | 0.0920365 | + | 0.0633814i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −71.4980 | − | 26.0231i | −2.58164 | − | 0.939641i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.44297 | − | 3.72810i | −0.160218 | − | 0.134439i | 0.559154 | − | 0.829064i | \(-0.311126\pi\) |
−0.719372 | + | 0.694625i | \(0.755570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.3039 | − | 18.7999i | 0.875283 | − | 0.677064i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.8149 | − | 21.2551i | −1.32414 | − | 0.764492i | −0.339753 | − | 0.940515i | \(-0.610344\pi\) |
−0.984386 | + | 0.176022i | \(0.943677\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.61456 | − | 7.99264i | −0.165760 | − | 0.287104i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.45615 | − | 5.34095i | −0.303363 | − | 0.191605i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.79190 | + | 1.72658i | 0.350831 | + | 0.0618610i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7170 | + | 16.3473i | 0.490833 | + | 0.584951i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.0006 | − | 1.27379i | 0.821976 | − | 0.0455216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.89904 | − | 3.27169i | 0.139163 | − | 0.116771i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.8983 | + | 2.97963i | 0.602359 | + | 0.106212i | 0.466508 | − | 0.884517i | \(-0.345512\pi\) |
0.135851 | + | 0.990729i | \(0.456623\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.9365 | − | 0.554078i | −0.496154 | − | 0.0197257i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.54642 | + | 11.3387i | 0.232764 | + | 0.403159i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.5627 | − | 32.1515i | 0.659179 | − | 1.14173i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.21190 | + | 8.93607i | 0.0429817 | + | 0.316930i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.53298 | + | 5.40220i | −0.160567 | + | 0.191356i | −0.840329 | − | 0.542076i | \(-0.817638\pi\) |
0.679763 | + | 0.733432i | \(0.262083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.831499 | − | 0.302641i | −0.0294163 | − | 0.0107067i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.29100 | − | 24.0278i | −0.0809483 | − | 0.848980i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −58.5114 | + | 10.3171i | −2.06482 | + | 0.364084i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.78652 | − | 10.4034i | −0.133457 | − | 0.366670i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.1115 | + | 2.41797i | 0.391144 | + | 0.0851167i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.2649 | −1.20469 | −0.602345 | − | 0.798236i | \(-0.705767\pi\) | ||||
−0.602345 | + | 0.798236i | \(0.705767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.06146i | − | 0.177732i | −0.996044 | − | 0.0888659i | \(-0.971676\pi\) | ||
0.996044 | − | 0.0888659i | \(-0.0283243\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.00050 | + | 18.3839i | −0.140304 | + | 0.644750i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.08885 | + | 1.48822i | −0.143226 | + | 0.0521301i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.87673 | + | 33.3286i | 0.205601 | + | 1.16602i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.4037 | + | 25.8520i | 0.643077 | + | 0.903342i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.19050 | − | 14.2608i | 0.181150 | − | 0.497705i | −0.815568 | − | 0.578661i | \(-0.803575\pi\) |
0.996718 | + | 0.0809566i | \(0.0257975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8496 | − | 19.1731i | −0.796487 | − | 0.668332i | 0.150855 | − | 0.988556i | \(-0.451797\pi\) |
−0.947342 | + | 0.320224i | \(0.896242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.4557 | − | 3.85914i | 0.990701 | − | 0.134358i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.24554 | + | 4.18322i | 0.251952 | + | 0.145465i | 0.620658 | − | 0.784082i | \(-0.286866\pi\) |
−0.368706 | + | 0.929546i | \(0.620199\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.4946 | − | 15.2967i | 0.920196 | − | 0.531276i | 0.0364987 | − | 0.999334i | \(-0.488380\pi\) |
0.883698 | + | 0.468058i | \(0.155046\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.18154 | − | 54.8716i | 0.0756768 | − | 1.90348i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.781255 | + | 4.43072i | −0.0270689 | + | 0.153515i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.07776 | − | 4.85968i | −0.141117 | − | 0.168176i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.37666 | + | 8.92965i | 0.289540 | + | 0.308654i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.60536 | + | 4.70346i | −0.193519 | + | 0.162381i | −0.734399 | − | 0.678718i | \(-0.762536\pi\) |
0.540880 | + | 0.841100i | \(0.318091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.62295 | − | 9.20422i | 0.0559639 | − | 0.317387i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.1590 | + | 28.7505i | −0.625428 | + | 0.990219i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.3610 | − | 16.9516i | 1.01005 | − | 0.583151i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.41924 | − | 9.38639i | 0.186207 | − | 0.322520i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.9000 | + | 27.0187i | 0.717285 | + | 0.927280i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0820 | − | 19.1657i | 0.551283 | − | 0.656993i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5473 | − | 42.7160i | 0.532331 | − | 1.46257i | −0.323959 | − | 0.946071i | \(-0.605014\pi\) |
0.856290 | − | 0.516496i | \(-0.172764\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.18458 | + | 8.79424i | 0.143109 | + | 0.300757i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.84017 | − | 21.7787i | −0.131178 | − | 0.743946i | −0.977445 | − | 0.211188i | \(-0.932267\pi\) |
0.846268 | − | 0.532758i | \(-0.178844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5655 | + | 29.0285i | 0.360491 | + | 0.990441i | 0.978856 | + | 0.204550i | \(0.0655730\pi\) |
−0.618365 | + | 0.785891i | \(0.712205\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.40098 | − | 5.81969i | −0.218145 | − | 0.198335i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.4661 | 0.934956 | 0.467478 | − | 0.884005i | \(-0.345163\pi\) | ||||
0.467478 | + | 0.884005i | \(0.345163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.38039 | −0.0469348 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.4306 | − | 8.44692i | 0.897630 | − | 0.286872i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.8137 | + | 35.2053i | 0.434675 | + | 1.19426i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.852216 | + | 4.83316i | 0.0288762 | + | 0.163765i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.0603 | + | 22.7036i | 0.780474 | + | 0.768402i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.97337 | + | 13.6642i | −0.168131 | + | 0.461935i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.68788 | + | 9.16206i | −0.259601 | + | 0.309381i | −0.880064 | − | 0.474855i | \(-0.842500\pi\) |
0.620463 | + | 0.784236i | \(0.286945\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.4590 | − | 42.6188i | 0.588879 | − | 1.43750i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.8243 | − | 32.6046i | 0.634205 | − | 1.09848i | −0.352478 | − | 0.935820i | \(-0.614661\pi\) |
0.986683 | − | 0.162655i | \(-0.0520059\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8345 | − | 11.4515i | 0.667485 | − | 0.385373i | −0.127638 | − | 0.991821i | \(-0.540739\pi\) |
0.795123 | + | 0.606448i | \(0.207406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.45153 | + | 17.9847i | 0.317710 | + | 0.604551i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.995710 | + | 5.64695i | −0.0334327 | + | 0.189606i | −0.996950 | − | 0.0780387i | \(-0.975134\pi\) |
0.963518 | + | 0.267645i | \(0.0862454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.39338 | − | 3.68648i | 0.147349 | − | 0.123641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.5910 | + | 13.5860i | −1.19234 | + | 0.455147i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.79219 | − | 2.13585i | −0.0599735 | − | 0.0714737i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.02139 | + | 11.4639i | −0.0675675 | + | 0.383194i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −70.2692 | + | 36.9286i | −2.34622 | + | 1.23301i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.04655 | + | 5.22303i | −0.301719 | + | 0.174198i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.28862 | − | 2.47604i | −0.142875 | − | 0.0824888i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.1622 | − | 27.2479i | 0.371456 | − | 0.906753i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.95572 | + | 2.48014i | 0.0982513 | + | 0.0824426i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.42248 | − | 23.1406i | 0.279664 | − | 0.768370i | −0.717737 | − | 0.696315i | \(-0.754822\pi\) |
0.997401 | − | 0.0720557i | \(-0.0229559\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.1849 | − | 4.98065i | −0.636323 | − | 0.165198i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.32793 | − | 35.8875i | −0.209654 | − | 1.18901i | −0.889947 | − | 0.456065i | \(-0.849259\pi\) |
0.680293 | − | 0.732940i | \(-0.261853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.9517 | + | 9.08166i | −0.825780 | + | 0.300559i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.44290 | + | 3.01784i | −0.312173 | + | 0.0997668i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 15.3708i | − | 0.507590i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.8245 | −0.917845 | −0.458923 | − | 0.888476i | \(-0.651764\pi\) | ||||
−0.458923 | + | 0.888476i | \(0.651764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.9633 | + | 29.6565i | −0.888470 | + | 0.977213i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.6405 | + | 31.9819i | 0.383151 | + | 1.05270i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.2153 | + | 2.50654i | −0.467397 | + | 0.0824146i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −47.5190 | − | 3.78443i | −1.56073 | − | 0.124297i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0864 | + | 5.12703i | 0.462160 | + | 0.168212i | 0.562598 | − | 0.826731i | \(-0.309802\pi\) |
−0.100438 | + | 0.994943i | \(0.532024\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.11238 | + | 10.8597i | −0.298646 | + | 0.355913i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.4088 | − | 25.8429i | 1.09375 | − | 0.846060i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.18052 | − | 3.77677i | 0.0713106 | − | 0.123514i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.57278 | − | 16.5805i | −0.312729 | − | 0.541663i | 0.666223 | − | 0.745753i | \(-0.267910\pi\) |
−0.978952 | + | 0.204090i | \(0.934577\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.8352 | − | 37.7375i | 0.777833 | − | 1.23152i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.4053 | + | 6.41923i | 1.18678 | + | 0.209261i | 0.731975 | − | 0.681331i | \(-0.238599\pi\) |
0.454803 | + | 0.890592i | \(0.349710\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.5778 | − | 13.9104i | 0.539847 | − | 0.452985i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00775 | − | 8.41355i | 0.0327820 | − | 0.273693i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0406 | + | 19.1164i | 0.521248 | + | 0.621199i | 0.960875 | − | 0.276981i | \(-0.0893340\pi\) |
−0.439627 | + | 0.898180i | \(0.644890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −93.3185 | − | 16.4546i | −3.02925 | − | 0.534138i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.26721 | + | 31.8738i | −0.0410922 | + | 1.03358i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.31014 | − | 12.6615i | −0.236799 | − | 0.410147i | 0.722995 | − | 0.690853i | \(-0.242765\pi\) |
−0.959794 | + | 0.280706i | \(0.909432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.2733 | − | 9.39537i | −0.526590 | − | 0.304027i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.36800 | − | 32.2079i | −0.141197 | − | 1.04113i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.5164 | − | 22.2499i | −0.856258 | − | 0.718486i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.9132 | + | 8.70369i | 0.771393 | + | 0.280764i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.80590 | − | 10.5196i | 0.154868 | − | 0.338988i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.54883 | − | 0.802081i | 0.146432 | − | 0.0258199i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.8192 | + | 17.7687i | −1.56992 | + | 0.571404i | −0.972981 | − | 0.230884i | \(-0.925838\pi\) |
−0.596937 | + | 0.802288i | \(0.703616\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.22581 | − | 1.13719i | −0.167877 | − | 0.0365317i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.4952i | − | 0.657724i | −0.944378 | − | 0.328862i | \(-0.893335\pi\) | ||
0.944378 | − | 0.328862i | \(-0.106665\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.45961i | 0.239144i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 44.7515 | + | 9.73837i | 1.43320 | + | 0.311877i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.72505 | + | 2.81169i | −0.247146 | + | 0.0899539i | −0.462623 | − | 0.886555i | \(-0.653092\pi\) |
0.215477 | + | 0.976509i | \(0.430869\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.5386 | + | 5.91376i | −1.07190 | + | 0.189004i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.14880 | + | 9.08126i | −0.132461 | + | 0.289942i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5289 | + | 8.19984i | 0.718559 | + | 0.261534i | 0.675314 | − | 0.737530i | \(-0.264008\pi\) |
0.0432453 | + | 0.999064i | \(0.486230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0285 | + | 10.9322i | 0.415123 | + | 0.348330i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.326014 | + | 2.40389i | 0.0103771 | + | 0.0765168i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.7900 | + | 36.8292i | 2.02840 | + | 1.17110i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.43544 | − | 14.6106i | −0.267960 | − | 0.464121i | 0.700375 | − | 0.713776i | \(-0.253016\pi\) |
−0.968335 | + | 0.249654i | \(0.919683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.06459 | − | 26.7773i | 0.0337837 | − | 0.849751i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.940553 | + | 0.165845i | 0.0298175 | + | 0.00525763i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.3234 | + | 25.4122i | 0.675317 | + | 0.804812i | 0.989497 | − | 0.144552i | \(-0.0461740\pi\) |
−0.314180 | + | 0.949363i | \(0.601730\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.6049 | − | 7.53450i | 0.556994 | − | 0.238381i |
(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 | 864.2.bf.a.49.20 | 204 | ||
4.3 | odd | 2 | 216.2.t.a.157.32 | yes | 204 | ||
8.3 | odd | 2 | 216.2.t.a.157.18 | ✓ | 204 | ||
8.5 | even | 2 | inner | 864.2.bf.a.49.15 | 204 | ||
12.11 | even | 2 | 648.2.t.a.37.3 | 204 | |||
24.11 | even | 2 | 648.2.t.a.37.17 | 204 | |||
27.16 | even | 9 | inner | 864.2.bf.a.529.15 | 204 | ||
108.11 | even | 18 | 648.2.t.a.613.17 | 204 | |||
108.43 | odd | 18 | 216.2.t.a.205.18 | yes | 204 | ||
216.11 | even | 18 | 648.2.t.a.613.3 | 204 | |||
216.43 | odd | 18 | 216.2.t.a.205.32 | yes | 204 | ||
216.205 | even | 18 | inner | 864.2.bf.a.529.20 | 204 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.t.a.157.18 | ✓ | 204 | 8.3 | odd | 2 | ||
216.2.t.a.157.32 | yes | 204 | 4.3 | odd | 2 | ||
216.2.t.a.205.18 | yes | 204 | 108.43 | odd | 18 | ||
216.2.t.a.205.32 | yes | 204 | 216.43 | odd | 18 | ||
648.2.t.a.37.3 | 204 | 12.11 | even | 2 | |||
648.2.t.a.37.17 | 204 | 24.11 | even | 2 | |||
648.2.t.a.613.3 | 204 | 216.11 | even | 18 | |||
648.2.t.a.613.17 | 204 | 108.11 | even | 18 | |||
864.2.bf.a.49.15 | 204 | 8.5 | even | 2 | inner | ||
864.2.bf.a.49.20 | 204 | 1.1 | even | 1 | trivial | ||
864.2.bf.a.529.15 | 204 | 27.16 | even | 9 | inner | ||
864.2.bf.a.529.20 | 204 | 216.205 | even | 18 | inner |