Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(118,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 9, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.ce (of order \(12\), degree \(4\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Relative dimension: | \(44\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 748.34 | ||
Character | \(\chi\) | \(=\) | 945.748 |
Dual form | 945.2.ce.a.307.34 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.377876 | + | 1.41025i | 0.267198 | + | 0.997198i | 0.960891 | + | 0.276927i | \(0.0893160\pi\) |
−0.693692 | + | 0.720271i | \(0.744017\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.113968 | + | 0.0657996i | −0.0569841 | + | 0.0328998i | ||||
\(5\) | 2.18439 | − | 0.477942i | 0.976890 | − | 0.213742i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.573911 | − | 2.58276i | −0.216918 | − | 0.976190i | ||||
\(8\) | 1.92889 | + | 1.92889i | 0.681966 | + | 0.681966i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.49945 | + | 2.89994i | 0.474167 | + | 0.917042i | ||||
\(11\) | 1.95430 | − | 3.38495i | 0.589245 | − | 1.02060i | −0.405087 | − | 0.914278i | \(-0.632759\pi\) |
0.994332 | − | 0.106324i | \(-0.0339079\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.354054 | + | 0.0948685i | 0.0981969 | + | 0.0263118i | 0.307583 | − | 0.951521i | \(-0.400480\pi\) |
−0.209386 | + | 0.977833i | \(0.567147\pi\) | |||||||
\(14\) | 3.42547 | − | 1.78532i | 0.915495 | − | 0.477147i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.12294 | + | 3.67704i | −0.530735 | + | 0.919260i | ||||
\(17\) | −1.41297 | − | 1.41297i | −0.342696 | − | 0.342696i | 0.514684 | − | 0.857380i | \(-0.327909\pi\) |
−0.857380 | + | 0.514684i | \(0.827909\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.83464 | −0.879727 | −0.439863 | − | 0.898065i | \(-0.644973\pi\) | ||||
−0.439863 | + | 0.898065i | \(0.644973\pi\) | |||||||
\(20\) | −0.217503 | + | 0.198202i | −0.0486351 | + | 0.0443194i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.51212 | + | 1.47697i | 1.17519 | + | 0.314891i | ||||
\(23\) | 1.67073 | − | 6.23526i | 0.348372 | − | 1.30014i | −0.540251 | − | 0.841504i | \(-0.681671\pi\) |
0.888623 | − | 0.458638i | \(-0.151663\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.54314 | − | 2.08803i | 0.908629 | − | 0.417605i | ||||
\(26\) | 0.535154i | 0.104952i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.235352 | + | 0.256589i | 0.0444773 | + | 0.0484907i | ||||
\(29\) | 3.97286 | + | 2.29373i | 0.737741 | + | 0.425935i | 0.821247 | − | 0.570572i | \(-0.193279\pi\) |
−0.0835066 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.80914 | + | 1.04451i | −0.324931 | + | 0.187599i | −0.653588 | − | 0.756850i | \(-0.726737\pi\) |
0.328658 | + | 0.944449i | \(0.393404\pi\) | |||||||
\(32\) | −0.717928 | − | 0.192368i | −0.126913 | − | 0.0340062i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.45872 | − | 2.52657i | 0.250168 | − | 0.433303i | ||||
\(35\) | −2.48805 | − | 5.36746i | −0.420558 | − | 0.907266i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0303530 | + | 0.0303530i | −0.00499001 | + | 0.00499001i | −0.709597 | − | 0.704607i | \(-0.751123\pi\) |
0.704607 | + | 0.709597i | \(0.251123\pi\) | |||||||
\(38\) | −1.44902 | − | 5.40781i | −0.235062 | − | 0.877262i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.13535 | + | 3.29156i | 0.811971 | + | 0.520441i | ||||
\(41\) | −9.89957 | + | 5.71552i | −1.54605 | + | 0.892614i | −0.547616 | + | 0.836730i | \(0.684465\pi\) |
−0.998437 | + | 0.0558847i | \(0.982202\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.456457 | − | 0.122307i | 0.0696090 | − | 0.0186517i | −0.223846 | − | 0.974624i | \(-0.571861\pi\) |
0.293455 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(44\) | 0.514369i | 0.0775441i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.42462 | 1.38958 | ||||||||
\(47\) | 11.3193 | − | 3.03299i | 1.65108 | − | 0.442406i | 0.691167 | − | 0.722695i | \(-0.257097\pi\) |
0.959916 | + | 0.280288i | \(0.0904301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.34125 | + | 2.96454i | −0.905893 | + | 0.423506i | ||||
\(50\) | 4.66138 | + | 5.61796i | 0.659219 | + | 0.794500i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0465932 | + | 0.0124846i | −0.00646132 | + | 0.00173130i | ||||
\(53\) | 8.71292 | + | 8.71292i | 1.19681 | + | 1.19681i | 0.975116 | + | 0.221696i | \(0.0711591\pi\) |
0.221696 | + | 0.975116i | \(0.428841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.65116 | − | 8.32811i | 0.357482 | − | 1.12296i | ||||
\(56\) | 3.87484 | − | 6.08887i | 0.517798 | − | 0.813659i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.73349 | + | 6.46947i | −0.227618 | + | 0.849483i | ||||
\(59\) | 4.90552 | + | 8.49662i | 0.638645 | + | 1.10617i | 0.985730 | + | 0.168332i | \(0.0538380\pi\) |
−0.347086 | + | 0.937833i | \(0.612829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.75087 | − | 3.32027i | −0.736323 | − | 0.425116i | 0.0844077 | − | 0.996431i | \(-0.473100\pi\) |
−0.820731 | + | 0.571315i | \(0.806434\pi\) | |||||||
\(62\) | −2.15664 | − | 2.15664i | −0.273894 | − | 0.273894i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.40661i | 0.925826i | ||||||||
\(65\) | 0.818735 | + | 0.0380128i | 0.101552 | + | 0.00471491i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.81623 | − | 1.02256i | −0.466227 | − | 0.124925i | 0.0180555 | − | 0.999837i | \(-0.494252\pi\) |
−0.484282 | + | 0.874912i | \(0.660919\pi\) | |||||||
\(68\) | 0.254006 | + | 0.0680608i | 0.0308028 | + | 0.00825359i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.62929 | − | 5.53701i | 0.792351 | − | 0.661800i | ||||
\(71\) | −2.12555 | −0.252256 | −0.126128 | − | 0.992014i | \(-0.540255\pi\) | ||||
−0.126128 | + | 0.992014i | \(0.540255\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.94714 | + | 8.94714i | −1.04718 | + | 1.04718i | −0.0483534 | + | 0.998830i | \(0.515397\pi\) |
−0.998830 | + | 0.0483534i | \(0.984603\pi\) | |||||||
\(74\) | −0.0542751 | − | 0.0313357i | −0.00630935 | − | 0.00364270i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.437027 | − | 0.252318i | 0.0501304 | − | 0.0289428i | ||||
\(77\) | −9.86410 | − | 3.10483i | −1.12412 | − | 0.353828i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.15769 | − | 1.82309i | −0.355268 | − | 0.205114i | 0.311735 | − | 0.950169i | \(-0.399090\pi\) |
−0.667003 | + | 0.745055i | \(0.732423\pi\) | |||||||
\(80\) | −2.87992 | + | 9.04674i | −0.321985 | + | 1.01146i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.8011 | − | 11.8011i | −1.30322 | − | 1.30322i | ||||
\(83\) | 3.53109 | + | 13.1782i | 0.387587 | + | 1.44649i | 0.834048 | + | 0.551692i | \(0.186018\pi\) |
−0.446461 | + | 0.894803i | \(0.647316\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.76180 | − | 2.41116i | −0.408024 | − | 0.261528i | ||||
\(86\) | 0.344968 | + | 0.597502i | 0.0371988 | + | 0.0644303i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.2988 | − | 2.75957i | 1.09786 | − | 0.294171i | ||||
\(89\) | −1.00672 | −0.106712 | −0.0533561 | − | 0.998576i | \(-0.516992\pi\) | ||||
−0.0533561 | + | 0.998576i | \(0.516992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0418267 | − | 0.968881i | 0.00438463 | − | 0.101566i | ||||
\(92\) | 0.219867 | + | 0.820555i | 0.0229227 | + | 0.0855488i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.55454 | + | 14.8169i | 0.882334 | + | 1.52825i | ||||
\(95\) | −8.37636 | + | 1.83273i | −0.859396 | + | 0.188035i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7802 | − | 3.15650i | 1.19610 | − | 0.320494i | 0.394806 | − | 0.918765i | \(-0.370812\pi\) |
0.801294 | + | 0.598271i | \(0.204145\pi\) | |||||||
\(98\) | −6.57696 | − | 7.82253i | −0.664373 | − | 0.790195i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.380383 | + | 0.536905i | −0.0380383 | + | 0.0536905i | ||||
\(101\) | −5.32516 | − | 3.07448i | −0.529873 | − | 0.305923i | 0.211091 | − | 0.977466i | \(-0.432298\pi\) |
−0.740965 | + | 0.671544i | \(0.765632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.90090 | + | 1.04524i | 0.384367 | + | 0.102991i | 0.445828 | − | 0.895119i | \(-0.352909\pi\) |
−0.0614609 | + | 0.998109i | \(0.519576\pi\) | |||||||
\(104\) | 0.499941 | + | 0.865923i | 0.0490232 | + | 0.0849108i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.99501 | + | 15.5798i | −0.873672 | + | 1.51324i | ||||
\(107\) | 2.19807 | − | 2.19807i | 0.212495 | − | 0.212495i | −0.592831 | − | 0.805327i | \(-0.701990\pi\) |
0.805327 | + | 0.592831i | \(0.201990\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.35559i | 0.800320i | 0.916445 | + | 0.400160i | \(0.131045\pi\) | ||||
−0.916445 | + | 0.400160i | \(0.868955\pi\) | |||||||
\(110\) | 12.7465 | + | 0.591806i | 1.21533 | + | 0.0564265i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.7153 | + | 3.37274i | 1.01250 | + | 0.318694i | ||||
\(113\) | −3.45767 | + | 12.9042i | −0.325271 | + | 1.21393i | 0.588769 | + | 0.808301i | \(0.299613\pi\) |
−0.914040 | + | 0.405625i | \(0.867054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.669446 | − | 14.4188i | 0.0624261 | − | 1.34456i | ||||
\(116\) | −0.603705 | −0.0560526 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1287 | + | 10.1287i | −0.932421 | + | 0.932421i | ||||
\(119\) | −2.83844 | + | 4.46028i | −0.260199 | + | 0.408873i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.13861 | − | 3.70417i | −0.194419 | − | 0.336743i | ||||
\(122\) | 2.50930 | − | 9.36482i | 0.227181 | − | 0.847851i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.137456 | − | 0.238081i | 0.0123439 | − | 0.0213803i | ||||
\(125\) | 8.92605 | − | 6.73243i | 0.798371 | − | 0.602166i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.18444 | + | 9.18444i | −0.814987 | + | 0.814987i | −0.985377 | − | 0.170390i | \(-0.945497\pi\) |
0.170390 | + | 0.985377i | \(0.445497\pi\) | |||||||
\(128\) | −11.8810 | + | 3.18351i | −1.05015 | + | 0.281386i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.255772 | + | 1.16899i | 0.0224327 | + | 0.102527i | ||||
\(131\) | −9.99028 | + | 5.76789i | −0.872855 | + | 0.503943i | −0.868296 | − | 0.496047i | \(-0.834784\pi\) |
−0.00455882 | + | 0.999990i | \(0.501451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.20074 | + | 9.90394i | 0.190828 | + | 0.858780i | ||||
\(134\) | − | 5.76824i | − | 0.498300i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.45093i | − | 0.467414i | ||||||
\(137\) | −1.36307 | − | 5.08704i | −0.116455 | − | 0.434615i | 0.882937 | − | 0.469492i | \(-0.155563\pi\) |
−0.999392 | + | 0.0348765i | \(0.988896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.20435 | + | 9.01419i | 0.441427 | + | 0.764574i | 0.997796 | − | 0.0663616i | \(-0.0211391\pi\) |
−0.556369 | + | 0.830936i | \(0.687806\pi\) | |||||||
\(140\) | 0.636735 | + | 0.448006i | 0.0538139 | + | 0.0378635i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.803193 | − | 2.99756i | −0.0674025 | − | 0.251549i | ||||
\(143\) | 1.01305 | − | 1.01305i | 0.0847159 | − | 0.0847159i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.77455 | + | 3.11161i | 0.811732 | + | 0.258405i | ||||
\(146\) | −15.9986 | − | 9.23681i | −1.32406 | − | 0.764444i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.00146206 | − | 0.00545649i | 0.000120181 | − | 0.000448521i | ||||
\(149\) | −0.639215 | + | 0.369051i | −0.0523665 | + | 0.0302338i | −0.525955 | − | 0.850513i | \(-0.676292\pi\) |
0.473588 | + | 0.880746i | \(0.342959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1772 | − | 17.6275i | 0.828211 | − | 1.43450i | −0.0712291 | − | 0.997460i | \(-0.522692\pi\) |
0.899440 | − | 0.437044i | \(-0.143975\pi\) | |||||||
\(152\) | −7.39660 | − | 7.39660i | −0.599944 | − | 0.599944i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.651182 | − | 15.0841i | 0.0524737 | − | 1.21551i | ||||
\(155\) | −3.45265 | + | 3.14627i | −0.277324 | + | 0.252715i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.47340 | − | 9.23084i | 0.197399 | − | 0.736701i | −0.794234 | − | 0.607612i | \(-0.792128\pi\) |
0.991633 | − | 0.129090i | \(-0.0412056\pi\) | |||||||
\(158\) | 1.37781 | − | 5.14204i | 0.109612 | − | 0.409079i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.66018 | − | 0.0770800i | −0.131249 | − | 0.00609371i | ||||
\(161\) | −17.0630 | − | 0.736612i | −1.34475 | − | 0.0580531i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.94454 | − | 6.94454i | −0.543938 | − | 0.543938i | 0.380743 | − | 0.924681i | \(-0.375668\pi\) |
−0.924681 | + | 0.380743i | \(0.875668\pi\) | |||||||
\(164\) | 0.752158 | − | 1.30278i | 0.0587336 | − | 0.101730i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.2503 | + | 9.95944i | −1.33888 | + | 0.773003i | ||||
\(167\) | 4.73607 | − | 17.6752i | 0.366488 | − | 1.36775i | −0.498905 | − | 0.866657i | \(-0.666264\pi\) |
0.865393 | − | 0.501095i | \(-0.167069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1420 | − | 6.43282i | −0.857075 | − | 0.494833i | ||||
\(170\) | 1.97886 | − | 6.21620i | 0.151771 | − | 0.476761i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0439738 | + | 0.0439738i | −0.00335297 | + | 0.00335297i | ||||
\(173\) | −3.98957 | − | 14.8893i | −0.303321 | − | 1.13201i | −0.934381 | − | 0.356276i | \(-0.884046\pi\) |
0.631059 | − | 0.775735i | \(-0.282621\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.00022 | − | 10.5355i | −0.604760 | − | 0.796408i | ||||
\(176\) | 8.29774 | + | 14.3721i | 0.625466 | + | 1.08334i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.380415 | − | 1.41973i | −0.0285133 | − | 0.106413i | ||||
\(179\) | 2.84155i | 0.212388i | 0.994345 | + | 0.106194i | \(0.0338664\pi\) | ||||
−0.994345 | + | 0.106194i | \(0.966134\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2943i | 1.50846i | 0.656609 | + | 0.754231i | \(0.271990\pi\) | ||||
−0.656609 | + | 0.754231i | \(0.728010\pi\) | |||||||
\(182\) | 1.38217 | − | 0.307131i | 0.102453 | − | 0.0227660i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.2498 | − | 8.80448i | 1.12423 | − | 0.649075i | ||||
\(185\) | −0.0517959 | + | 0.0808099i | −0.00380811 | + | 0.00594126i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.54421 | + | 2.02147i | −0.551687 | + | 0.147824i | ||||
\(188\) | −1.09047 | + | 1.09047i | −0.0795304 | + | 0.0795304i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.74984 | − | 11.1202i | −0.417137 | − | 0.806746i | ||||
\(191\) | −6.13621 | + | 10.6282i | −0.444000 | + | 0.769031i | −0.997982 | − | 0.0634977i | \(-0.979774\pi\) |
0.553982 | + | 0.832529i | \(0.313108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.09344 | − | 7.81281i | 0.150689 | − | 0.562378i | −0.848747 | − | 0.528799i | \(-0.822643\pi\) |
0.999436 | − | 0.0335796i | \(-0.0106907\pi\) | |||||||
\(194\) | 8.90292 | + | 15.4203i | 0.639192 | + | 1.10711i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.527635 | − | 0.755115i | 0.0376882 | − | 0.0539368i | ||||
\(197\) | 1.52429 | − | 1.52429i | 0.108601 | − | 0.108601i | −0.650718 | − | 0.759319i | \(-0.725532\pi\) |
0.759319 | + | 0.650718i | \(0.225532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3535 | −0.804828 | −0.402414 | − | 0.915458i | \(-0.631829\pi\) | ||||
−0.402414 | + | 0.915458i | \(0.631829\pi\) | |||||||
\(200\) | 12.7908 | + | 4.73566i | 0.904447 | + | 0.334861i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.32355 | − | 8.67159i | 0.163484 | − | 0.610131i | ||||
\(203\) | 3.64408 | − | 11.5773i | 0.255764 | − | 0.812568i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.8929 | + | 17.2164i | −1.31954 | + | 1.20244i | ||||
\(206\) | 5.89622i | 0.410809i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.10047 | + | 1.10047i | −0.0763039 | + | 0.0763039i | ||||
\(209\) | −7.49405 | + | 12.9801i | −0.518374 | + | 0.897851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.887630 | − | 1.53742i | −0.0611069 | − | 0.105840i | 0.833854 | − | 0.551986i | \(-0.186130\pi\) |
−0.894960 | + | 0.446145i | \(0.852796\pi\) | |||||||
\(212\) | −1.56630 | − | 0.419689i | −0.107574 | − | 0.0288244i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.93043 | + | 2.26923i | 0.268678 | + | 0.155122i | ||||
\(215\) | 0.938625 | − | 0.485327i | 0.0640137 | − | 0.0330990i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.73599 | + | 4.07310i | 0.253615 | + | 0.276500i | ||||
\(218\) | −11.7835 | + | 3.15737i | −0.798078 | + | 0.213844i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.245839 | + | 1.12358i | 0.0165744 | + | 0.0757521i | ||||
\(221\) | −0.366222 | − | 0.634314i | −0.0246347 | − | 0.0426686i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.15894 | − | 19.2534i | −0.345468 | − | 1.28930i | −0.892065 | − | 0.451908i | \(-0.850744\pi\) |
0.546597 | − | 0.837396i | \(-0.315923\pi\) | |||||||
\(224\) | −0.0848135 | + | 1.96464i | −0.00566684 | + | 0.131268i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.5048 | −1.29744 | ||||||||
\(227\) | 11.6212 | − | 3.11388i | 0.771325 | − | 0.206676i | 0.148368 | − | 0.988932i | \(-0.452598\pi\) |
0.622957 | + | 0.782256i | \(0.285931\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.78689 | − | 8.29114i | −0.316327 | − | 0.547894i | 0.663392 | − | 0.748272i | \(-0.269116\pi\) |
−0.979719 | + | 0.200378i | \(0.935783\pi\) | |||||||
\(230\) | 20.5871 | − | 4.50442i | 1.35747 | − | 0.297013i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.23885 | + | 12.0876i | 0.212641 | + | 0.793587i | ||||
\(233\) | −6.37266 | − | 6.37266i | −0.417487 | − | 0.417487i | 0.466850 | − | 0.884337i | \(-0.345389\pi\) |
−0.884337 | + | 0.466850i | \(0.845389\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.2761 | − | 12.0352i | 1.51837 | − | 0.785088i | ||||
\(236\) | −1.11815 | − | 0.645563i | −0.0727852 | − | 0.0420226i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.36269 | − | 2.31748i | −0.477252 | − | 0.150220i | ||||
\(239\) | 5.05325 | − | 2.91749i | 0.326867 | − | 0.188717i | −0.327582 | − | 0.944823i | \(-0.606234\pi\) |
0.654449 | + | 0.756106i | \(0.272900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.01801 | − | 4.05185i | −0.452070 | − | 0.261003i | 0.256634 | − | 0.966509i | \(-0.417386\pi\) |
−0.708704 | + | 0.705506i | \(0.750720\pi\) | |||||||
\(242\) | 4.41569 | − | 4.41569i | 0.283851 | − | 0.283851i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.873888 | 0.0559450 | ||||||||
\(245\) | −12.4349 | + | 9.50648i | −0.794437 | + | 0.607346i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.35767 | − | 0.363787i | −0.0863865 | − | 0.0231472i | ||||
\(248\) | −5.50437 | − | 1.47489i | −0.349528 | − | 0.0936556i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.8674 | + | 10.0440i | 0.813803 | + | 0.635236i | ||||
\(251\) | 7.52743i | 0.475127i | 0.971372 | + | 0.237564i | \(0.0763488\pi\) | ||||
−0.971372 | + | 0.237564i | \(0.923651\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.8410 | − | 17.8410i | −1.12165 | − | 1.12165i | ||||
\(254\) | −16.4229 | − | 9.48179i | −1.03047 | − | 0.594940i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.57250 | − | 2.72365i | −0.0982814 | − | 0.170228i | ||||
\(257\) | 3.22856 | − | 12.0491i | 0.201392 | − | 0.751604i | −0.789127 | − | 0.614230i | \(-0.789467\pi\) |
0.990519 | − | 0.137375i | \(-0.0438665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0958144 | + | 0.0609745i | 0.00595362 | + | 0.00378877i | ||||
\(260\) | −0.0958110 | + | 0.0495401i | −0.00594194 | + | 0.00307235i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.9093 | − | 11.9093i | −0.735756 | − | 0.735756i | ||||
\(263\) | 0.495319 | − | 0.132720i | 0.0305427 | − | 0.00818389i | −0.243515 | − | 0.969897i | \(-0.578301\pi\) |
0.274058 | + | 0.961713i | \(0.411634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.1967 | + | 14.8682i | 1.42496 | + | 0.913344i | ||||
\(266\) | −13.1354 | + | 6.84606i | −0.805385 | + | 0.419759i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.502212 | − | 0.134567i | 0.0306775 | − | 0.00822001i | ||||
\(269\) | 5.16747 | 0.315066 | 0.157533 | − | 0.987514i | \(-0.449646\pi\) | ||||
0.157533 | + | 0.987514i | \(0.449646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.0214709i | − | 0.00130426i | −1.00000 | 0.000652132i | \(-0.999792\pi\) | |||
1.00000 | 0.000652132i | \(-0.000207580\pi\) | ||||||||
\(272\) | 8.19520 | − | 2.19590i | 0.496907 | − | 0.133146i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.65894 | − | 3.84454i | 0.402281 | − | 0.232257i | ||||
\(275\) | 1.81081 | − | 19.4590i | 0.109196 | − | 1.17342i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.94340 | − | 10.9849i | −0.176851 | − | 0.660019i | −0.996229 | − | 0.0867643i | \(-0.972347\pi\) |
0.819377 | − | 0.573254i | \(-0.194319\pi\) | |||||||
\(278\) | −10.7457 | + | 10.7457i | −0.644483 | + | 0.644483i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.55406 | − | 15.1524i | 0.331918 | − | 0.905531i | ||||
\(281\) | −6.07820 | + | 10.5278i | −0.362595 | + | 0.628033i | −0.988387 | − | 0.151957i | \(-0.951443\pi\) |
0.625792 | + | 0.779990i | \(0.284776\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6739 | + | 6.87930i | 1.52615 | + | 0.408932i | 0.921762 | − | 0.387756i | \(-0.126750\pi\) |
0.604392 | + | 0.796687i | \(0.293416\pi\) | |||||||
\(284\) | 0.242245 | − | 0.139860i | 0.0143746 | − | 0.00829917i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.81147 | + | 1.04585i | 0.107115 | + | 0.0618426i | ||||
\(287\) | 20.4433 | + | 22.2880i | 1.20673 | + | 1.31562i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.0070i | − | 0.765119i | ||||||
\(290\) | −0.694591 | + | 14.9604i | −0.0407878 | + | 0.878503i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.430971 | − | 1.60841i | 0.0252207 | − | 0.0941249i | ||||
\(293\) | −22.2897 | − | 5.97252i | −1.30218 | − | 0.348918i | −0.459907 | − | 0.887967i | \(-0.652117\pi\) |
−0.842274 | + | 0.539049i | \(0.818784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7765 | + | 16.2154i | 0.860320 | + | 0.944097i | ||||
\(296\) | −0.117095 | −0.00680603 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.761999 | − | 0.761999i | −0.0441414 | − | 0.0441414i | ||||
\(299\) | 1.18306 | − | 2.04912i | 0.0684181 | − | 0.118504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.577855 | − | 1.10872i | −0.0333070 | − | 0.0639057i | ||||
\(302\) | 28.7049 | + | 7.69146i | 1.65178 | + | 0.442594i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.14071 | − | 14.1001i | 0.466902 | − | 0.808698i | ||||
\(305\) | −14.1491 | − | 4.50418i | −0.810172 | − | 0.257909i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.6287 | − | 14.6287i | −0.834902 | − | 0.834902i | 0.153281 | − | 0.988183i | \(-0.451016\pi\) |
−0.988183 | + | 0.153281i | \(0.951016\pi\) | |||||||
\(308\) | 1.32849 | − | 0.295202i | 0.0756978 | − | 0.0168207i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.74171 | − | 3.68021i | −0.326107 | − | 0.209022i | ||||
\(311\) | 12.9578 | − | 7.48121i | 0.734772 | − | 0.424221i | −0.0853935 | − | 0.996347i | \(-0.527215\pi\) |
0.820165 | + | 0.572127i | \(0.193881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.35233 | + | 12.5111i | 0.189485 | + | 0.707167i | 0.993626 | + | 0.112728i | \(0.0359590\pi\) |
−0.804141 | + | 0.594439i | \(0.797374\pi\) | |||||||
\(314\) | 13.9524 | 0.787382 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.479835 | 0.0269929 | ||||||||
\(317\) | 6.73734 | + | 25.1441i | 0.378407 | + | 1.41223i | 0.848303 | + | 0.529512i | \(0.177625\pi\) |
−0.469896 | + | 0.882722i | \(0.655709\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.5283 | − | 8.96529i | 0.869420 | − | 0.501960i | ||||
\(320\) | 3.53993 | + | 16.1789i | 0.197888 | + | 0.904430i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.40889 | − | 24.3415i | −0.301426 | − | 1.35650i | ||||
\(323\) | 5.41823 | + | 5.41823i | 0.301479 | + | 0.301479i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.80661 | − | 0.308273i | 0.100212 | − | 0.0170999i | ||||
\(326\) | 7.16937 | − | 12.4177i | 0.397075 | − | 0.687754i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −30.1198 | − | 8.07058i | −1.66309 | − | 0.445623i | ||||
\(329\) | −14.3297 | − | 27.4942i | −0.790022 | − | 1.51580i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.19019 | − | 5.52557i | 0.175349 | − | 0.303713i | −0.764933 | − | 0.644110i | \(-0.777228\pi\) |
0.940282 | + | 0.340397i | \(0.110561\pi\) | |||||||
\(332\) | −1.26955 | − | 1.26955i | −0.0696757 | − | 0.0696757i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 26.7162 | 1.46184 | ||||||||
\(335\) | −8.82486 | − | 0.409727i | −0.482154 | − | 0.0223858i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.47444 | + | 0.663023i | 0.134791 | + | 0.0361172i | 0.325584 | − | 0.945513i | \(-0.394439\pi\) |
−0.190793 | + | 0.981630i | \(0.561106\pi\) | |||||||
\(338\) | 4.86162 | − | 18.1438i | 0.264437 | − | 0.986892i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.587379 | + | 0.0272713i | 0.0318551 | + | 0.00147899i | ||||
\(341\) | 8.16512i | 0.442166i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.2960 | + | 14.6765i | 0.609927 | + | 0.792458i | ||||
\(344\) | 1.11637 | + | 0.644538i | 0.0601908 | + | 0.0347512i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.4901 | − | 11.2526i | 1.04779 | − | 0.604943i | ||||
\(347\) | −7.93384 | − | 2.12587i | −0.425911 | − | 0.114122i | 0.0394952 | − | 0.999220i | \(-0.487425\pi\) |
−0.465406 | + | 0.885097i | \(0.654092\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.03047 | + | 13.9092i | −0.429861 | + | 0.744541i | −0.996861 | − | 0.0791769i | \(-0.974771\pi\) |
0.567000 | + | 0.823718i | \(0.308104\pi\) | |||||||
\(350\) | 11.8346 | − | 15.2634i | 0.632586 | − | 0.815864i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.05421 | + | 2.05421i | −0.109490 | + | 0.109490i | ||||
\(353\) | 1.62567 | + | 6.06709i | 0.0865257 | + | 0.322918i | 0.995599 | − | 0.0937184i | \(-0.0298753\pi\) |
−0.909073 | + | 0.416637i | \(0.863209\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.64303 | + | 1.01589i | −0.246427 | + | 0.0539178i | ||||
\(356\) | 0.114734 | − | 0.0662417i | 0.00608089 | − | 0.00351080i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.00730 | + | 1.07375i | −0.211792 | + | 0.0567496i | ||||
\(359\) | 29.1921i | 1.54070i | 0.637620 | + | 0.770351i | \(0.279919\pi\) | ||||
−0.637620 | + | 0.770351i | \(0.720081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.29554 | −0.226081 | ||||||||
\(362\) | −28.6201 | + | 7.66872i | −1.50424 | + | 0.403059i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0589851 | + | 0.113174i | 0.00309166 | + | 0.00593192i | ||||
\(365\) | −15.2679 | + | 23.8203i | −0.799156 | + | 1.24681i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.4620 | + | 4.94689i | −0.963711 | + | 0.258226i | −0.706170 | − | 0.708042i | \(-0.749579\pi\) |
−0.257541 | + | 0.966267i | \(0.582912\pi\) | |||||||
\(368\) | 19.3804 | + | 19.3804i | 1.01028 | + | 1.01028i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.133535 | − | 0.0425092i | −0.00694214 | − | 0.00220995i | ||||
\(371\) | 17.5029 | − | 27.5038i | 0.908705 | − | 1.42793i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.68146 | + | 36.1317i | −0.501287 | + | 1.87083i | −0.00978595 | + | 0.999952i | \(0.503115\pi\) |
−0.491501 | + | 0.870877i | \(0.663552\pi\) | |||||||
\(374\) | −5.70155 | − | 9.87537i | −0.294820 | − | 0.510643i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.6839 | + | 15.9833i | 1.42769 | + | 0.824277i | ||||
\(377\) | 1.18900 | + | 1.18900i | 0.0612368 | + | 0.0612368i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0974i | 1.08370i | 0.840474 | + | 0.541851i | \(0.182276\pi\) | ||||
−0.840474 | + | 0.541851i | \(0.817724\pi\) | |||||||
\(380\) | 0.834045 | − | 0.760034i | 0.0427856 | − | 0.0389889i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.3072 | − | 4.63745i | −0.885513 | − | 0.237272i | ||||
\(383\) | 3.93021 | + | 1.05310i | 0.200824 | + | 0.0538107i | 0.357829 | − | 0.933787i | \(-0.383517\pi\) |
−0.157005 | + | 0.987598i | \(0.550184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.0310 | − | 2.06769i | −1.17377 | − | 0.105379i | ||||
\(386\) | 11.8091 | 0.601067 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.13487 | + | 1.13487i | −0.0576145 | + | 0.0576145i | ||||
\(389\) | −26.8857 | − | 15.5225i | −1.36316 | − | 0.787021i | −0.373118 | − | 0.927784i | \(-0.621711\pi\) |
−0.990043 | + | 0.140763i | \(0.955045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.1709 | + | 6.44954i | −0.564939 | + | 0.326167i | ||||
\(392\) | −17.9499 | − | 6.51331i | −0.906605 | − | 0.328972i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.72562 | + | 1.57364i | 0.137315 | + | 0.0792786i | ||||
\(395\) | −7.76898 | − | 2.47316i | −0.390900 | − | 0.124438i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.43818 | + | 4.43818i | 0.222746 | + | 0.222746i | 0.809654 | − | 0.586908i | \(-0.199655\pi\) |
−0.586908 | + | 0.809654i | \(0.699655\pi\) | |||||||
\(398\) | −4.29021 | − | 16.0113i | −0.215049 | − | 0.802573i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.96707 | + | 21.1381i | −0.0983534 | + | 1.05690i | ||||
\(401\) | 19.1412 | + | 33.1535i | 0.955866 | + | 1.65561i | 0.732375 | + | 0.680902i | \(0.238412\pi\) |
0.223491 | + | 0.974706i | \(0.428255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.739623 | + | 0.198181i | −0.0368432 | + | 0.00987212i | ||||
\(404\) | 0.809199 | 0.0402591 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.7039 | + | 0.764280i | 0.878631 | + | 0.0379306i | ||||
\(407\) | 0.0434245 | + | 0.162063i | 0.00215247 | + | 0.00803314i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0631 | − | 26.0901i | −0.744823 | − | 1.29007i | −0.950277 | − | 0.311404i | \(-0.899201\pi\) |
0.205455 | − | 0.978667i | \(-0.434133\pi\) | |||||||
\(410\) | −31.4186 | − | 20.1380i | −1.55165 | − | 0.994547i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.513355 | + | 0.137553i | −0.0252912 | + | 0.00677676i | ||||
\(413\) | 19.1294 | − | 17.5461i | 0.941294 | − | 0.863386i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0117 | + | 27.0987i | 0.687807 | + | 1.33022i | ||||
\(416\) | −0.235936 | − | 0.136218i | −0.0115677 | − | 0.00667862i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.1370 | − | 5.66364i | −1.03384 | − | 0.277018i | ||||
\(419\) | −5.18972 | − | 8.98886i | −0.253534 | − | 0.439134i | 0.710962 | − | 0.703230i | \(-0.248260\pi\) |
−0.964496 | + | 0.264096i | \(0.914926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.30441 | + | 16.1157i | −0.453469 | + | 0.785432i | −0.998599 | − | 0.0529202i | \(-0.983147\pi\) |
0.545130 | + | 0.838352i | \(0.316480\pi\) | |||||||
\(422\) | 1.83273 | − | 1.83273i | 0.0892161 | − | 0.0892161i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 33.6126i | 1.63237i | ||||||||
\(425\) | −9.36964 | − | 3.46901i | −0.454495 | − | 0.168272i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.27495 | + | 16.7586i | −0.255273 | + | 0.811007i | ||||
\(428\) | −0.105878 | + | 0.395142i | −0.00511780 | + | 0.0190999i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.03912 | + | 1.14030i | 0.0501106 | + | 0.0549904i | ||||
\(431\) | −25.3205 | −1.21964 | −0.609822 | − | 0.792538i | \(-0.708759\pi\) | ||||
−0.609822 | + | 0.792538i | \(0.708759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.9170 | − | 13.9170i | 0.668810 | − | 0.668810i | −0.288630 | − | 0.957441i | \(-0.593200\pi\) |
0.957441 | + | 0.288630i | \(0.0931999\pi\) | |||||||
\(434\) | −4.33236 | + | 6.80781i | −0.207960 | + | 0.326785i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.549794 | − | 0.952271i | −0.0263304 | − | 0.0456055i | ||||
\(437\) | −6.40666 | + | 23.9100i | −0.306472 | + | 1.14377i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7353 | − | 25.5223i | 0.703278 | − | 1.21811i | −0.264031 | − | 0.964514i | \(-0.585052\pi\) |
0.967309 | − | 0.253599i | \(-0.0816144\pi\) | |||||||
\(440\) | 21.1778 | − | 10.9502i | 1.00961 | − | 0.522032i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.756157 | − | 0.756157i | 0.0359667 | − | 0.0359667i | ||||
\(443\) | 14.7465 | − | 3.95131i | 0.700627 | − | 0.187732i | 0.109116 | − | 0.994029i | \(-0.465198\pi\) |
0.591512 | + | 0.806297i | \(0.298531\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.19907 | + | 0.481154i | −0.104246 | + | 0.0228089i | ||||
\(446\) | 25.2027 | − | 14.5508i | 1.19338 | − | 0.689000i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.1295 | − | 4.25073i | 0.903782 | − | 0.200828i | ||||
\(449\) | 3.06142i | 0.144478i | 0.997387 | + | 0.0722388i | \(0.0230144\pi\) | ||||
−0.997387 | + | 0.0722388i | \(0.976986\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.6795i | 2.10387i | ||||||||
\(452\) | −0.455027 | − | 1.69818i | −0.0214027 | − | 0.0798758i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.78272 | + | 15.2121i | 0.412194 | + | 0.713940i | ||||
\(455\) | −0.371703 | − | 2.13641i | −0.0174257 | − | 0.100156i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.19133 | + | 4.44611i | 0.0557282 | + | 0.207980i | 0.988176 | − | 0.153325i | \(-0.0489980\pi\) |
−0.932448 | + | 0.361305i | \(0.882331\pi\) | |||||||
\(458\) | 9.88374 | − | 9.88374i | 0.461837 | − | 0.461837i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.872454 | + | 1.68733i | 0.0406784 | + | 0.0786722i | ||||
\(461\) | 31.5764 | + | 18.2307i | 1.47066 | + | 0.849087i | 0.999457 | − | 0.0329376i | \(-0.0104863\pi\) |
0.471204 | + | 0.882024i | \(0.343820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.97859 | + | 26.0444i | −0.324323 | + | 1.21039i | 0.590669 | + | 0.806914i | \(0.298864\pi\) |
−0.914991 | + | 0.403474i | \(0.867803\pi\) | |||||||
\(464\) | −16.8683 | + | 9.73890i | −0.783090 | + | 0.452117i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.57898 | − | 11.3951i | 0.304765 | − | 0.527869i | ||||
\(467\) | −26.5122 | − | 26.5122i | −1.22684 | − | 1.22684i | −0.965153 | − | 0.261688i | \(-0.915721\pi\) |
−0.261688 | − | 0.965153i | \(-0.584279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.450836 | + | 10.4432i | −0.0208177 | + | 0.482224i | ||||
\(470\) | 25.7681 | + | 28.2774i | 1.18859 | + | 1.30434i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.92683 | + | 25.8513i | −0.318833 | + | 1.18990i | ||||
\(473\) | 0.478051 | − | 1.78411i | 0.0219808 | − | 0.0820335i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.4213 | + | 8.00682i | −0.799345 | + | 0.367378i | ||||
\(476\) | 0.0300074 | − | 0.695098i | 0.00137539 | − | 0.0318597i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.02390 | + | 6.02390i | 0.275527 | + | 0.275527i | ||||
\(479\) | 4.24052 | − | 7.34480i | 0.193754 | − | 0.335592i | −0.752737 | − | 0.658321i | \(-0.771267\pi\) |
0.946491 | + | 0.322729i | \(0.104600\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0136262 | + | 0.00786707i | −0.000621299 | + | 0.000358707i | ||||
\(482\) | 3.06219 | − | 11.4283i | 0.139479 | − | 0.520543i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.487466 | + | 0.281439i | 0.0221575 | + | 0.0127927i | ||||
\(485\) | 24.2240 | − | 12.5253i | 1.09996 | − | 0.568744i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.65490 | − | 2.65490i | 0.120305 | − | 0.120305i | −0.644391 | − | 0.764696i | \(-0.722889\pi\) |
0.764696 | + | 0.644391i | \(0.222889\pi\) | |||||||
\(488\) | −4.68837 | − | 17.4972i | −0.212233 | − | 0.792063i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.1054 | − | 13.9441i | −0.817917 | − | 0.629929i | ||||
\(491\) | 2.01799 | + | 3.49526i | 0.0910707 | + | 0.157739i | 0.907962 | − | 0.419053i | \(-0.137638\pi\) |
−0.816891 | + | 0.576792i | \(0.804304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.37256 | − | 8.85450i | −0.106855 | − | 0.398787i | ||||
\(494\) | − | 2.05212i | − | 0.0923293i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.86969i | − | 0.398261i | ||||||
\(497\) | 1.21988 | + | 5.48977i | 0.0547189 | + | 0.246250i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.03591 | − | 3.48484i | 0.270205 | − | 0.156003i | −0.358776 | − | 0.933424i | \(-0.616806\pi\) |
0.628981 | + | 0.777421i | \(0.283472\pi\) | |||||||
\(500\) | −0.574296 | + | 1.35461i | −0.0256833 | + | 0.0605801i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.6156 | + | 2.84443i | −0.473796 | + | 0.126953i | ||||
\(503\) | −12.3235 | + | 12.3235i | −0.549477 | + | 0.549477i | −0.926290 | − | 0.376812i | \(-0.877020\pi\) |
0.376812 | + | 0.926290i | \(0.377020\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.1017 | − | 4.17076i | −0.583017 | − | 0.185597i | ||||
\(506\) | 18.4186 | − | 31.9019i | 0.818805 | − | 1.41821i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.442402 | − | 1.65107i | 0.0196284 | − | 0.0732542i | ||||
\(509\) | 15.1933 | + | 26.3156i | 0.673433 | + | 1.16642i | 0.976924 | + | 0.213586i | \(0.0685145\pi\) |
−0.303491 | + | 0.952834i | \(0.598152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.2431 | + | 17.9734i | 1.24940 | + | 0.795097i | ||||
\(512\) | −14.1482 | + | 14.1482i | −0.625269 | + | 0.625269i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.2123 | 0.803310 | ||||||||
\(515\) | 9.02067 | + | 0.418818i | 0.397498 | + | 0.0184553i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.8547 | − | 44.2425i | 0.521371 | − | 1.94578i | ||||
\(518\) | −0.0497835 | + | 0.158163i | −0.00218736 | + | 0.00694929i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.50593 | + | 1.65257i | 0.0660393 | + | 0.0724701i | ||||
\(521\) | − | 41.4003i | − | 1.81378i | −0.421367 | − | 0.906890i | \(-0.638450\pi\) | ||
0.421367 | − | 0.906890i | \(-0.361550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.38267 | − | 4.38267i | 0.191641 | − | 0.191641i | −0.604764 | − | 0.796405i | \(-0.706733\pi\) |
0.796405 | + | 0.604764i | \(0.206733\pi\) | |||||||
\(524\) | 0.759049 | − | 1.31471i | 0.0331592 | − | 0.0574335i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.374338 | + | 0.648373i | 0.0163219 | + | 0.0282704i | ||||
\(527\) | 4.03211 | + | 1.08040i | 0.175642 | + | 0.0470630i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1686 | − | 9.33493i | −0.702981 | − | 0.405866i | ||||
\(530\) | −12.2024 | + | 38.3315i | −0.530038 | + | 1.66501i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.902489 | − | 0.983926i | −0.0391279 | − | 0.0426586i | ||||
\(533\) | −4.04721 | + | 1.08445i | −0.175304 | + | 0.0469726i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.75090 | − | 5.85200i | 0.162165 | − | 0.253004i | ||||
\(536\) | −5.38869 | − | 9.33349i | −0.232756 | − | 0.403145i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.95266 | + | 7.28744i | 0.0841853 | + | 0.314184i | ||||
\(539\) | −2.35789 | + | 27.2585i | −0.101562 | + | 1.17411i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.6955 | 1.01875 | 0.509374 | − | 0.860545i | \(-0.329877\pi\) | ||||
0.509374 | + | 0.860545i | \(0.329877\pi\) | |||||||
\(542\) | 0.0302794 | − | 0.00811333i | 0.00130061 | − | 0.000348497i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.742601 | + | 1.28622i | 0.0318387 | + | 0.0551463i | ||||
\(545\) | 3.99348 | + | 18.2519i | 0.171062 | + | 0.781825i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.66691 | + | 21.1492i | 0.242300 | + | 0.904275i | 0.974721 | + | 0.223424i | \(0.0717233\pi\) |
−0.732422 | + | 0.680851i | \(0.761610\pi\) | |||||||
\(548\) | 0.490072 | + | 0.490072i | 0.0209348 | + | 0.0209348i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 28.1263 | − | 4.79937i | 1.19931 | − | 0.204646i | ||||
\(551\) | −15.2345 | − | 8.79562i | −0.649010 | − | 0.374706i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.89637 | + | 9.20184i | −0.123166 | + | 0.391302i | ||||
\(554\) | 14.3792 | − | 8.30185i | 0.610915 | − | 0.352712i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.18626 | − | 0.684888i | −0.0503086 | − | 0.0290457i | ||||
\(557\) | 22.0540 | − | 22.0540i | 0.934458 | − | 0.934458i | −0.0635225 | − | 0.997980i | \(-0.520233\pi\) |
0.997980 | + | 0.0635225i | \(0.0202335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.173214 | 0.00732615 | ||||||||
\(560\) | 25.0183 | + | 2.24612i | 1.05722 | + | 0.0949157i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.1436 | − | 4.59361i | −0.723158 | − | 0.193770i | ||||
\(563\) | −3.72139 | − | 0.997144i | −0.156838 | − | 0.0420246i | 0.179546 | − | 0.983750i | \(-0.442537\pi\) |
−0.336384 | + | 0.941725i | \(0.609204\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.38545 | + | 29.8404i | −0.0582865 | + | 1.25540i | ||||
\(566\) | 38.8061i | 1.63114i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.09995 | − | 4.09995i | −0.172030 | − | 0.172030i | ||||
\(569\) | 10.4167 | + | 6.01410i | 0.436692 | + | 0.252124i | 0.702193 | − | 0.711986i | \(-0.252204\pi\) |
−0.265502 | + | 0.964110i | \(0.585538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7271 | + | 27.2401i | 0.658158 | + | 1.13996i | 0.981092 | + | 0.193541i | \(0.0619973\pi\) |
−0.322935 | + | 0.946421i | \(0.604669\pi\) | |||||||
\(572\) | −0.0487975 | + | 0.182115i | −0.00204032 | + | 0.00761459i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.7066 | + | 37.2522i | −0.989496 | + | 1.55488i | ||||
\(575\) | −5.42900 | − | 31.8162i | −0.226405 | − | 1.32683i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5174 | + | 22.5174i | 0.937411 | + | 0.937411i | 0.998153 | − | 0.0607420i | \(-0.0193467\pi\) |
−0.0607420 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(578\) | 18.3432 | − | 4.91504i | 0.762976 | − | 0.204439i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.31873 | + | 0.288536i | −0.0547573 | + | 0.0119808i | ||||
\(581\) | 32.0095 | − | 16.6830i | 1.32798 | − | 0.692129i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.5205 | − | 12.4651i | 1.92668 | − | 0.516253i | ||||
\(584\) | −34.5161 | −1.42829 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 33.6910i | − | 1.39176i | ||||||
\(587\) | −6.32026 | + | 1.69351i | −0.260865 | + | 0.0698986i | −0.386881 | − | 0.922130i | \(-0.626448\pi\) |
0.126016 | + | 0.992028i | \(0.459781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.93739 | − | 4.00530i | 0.285850 | − | 0.165036i | ||||
\(590\) | −17.2841 | + | 26.9660i | −0.711575 | + | 1.11017i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.0471716 | − | 0.176047i | −0.00193874 | − | 0.00723548i | ||||
\(593\) | −25.4392 | + | 25.4392i | −1.04466 | + | 1.04466i | −0.0457067 | + | 0.998955i | \(0.514554\pi\) |
−0.998955 | + | 0.0457067i | \(0.985446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.06851 | + | 11.0996i | −0.166793 | + | 0.455039i | ||||
\(596\) | 0.0485668 | − | 0.0841201i | 0.00198937 | − | 0.00344570i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.33683 | + | 0.894100i | 0.136453 | + | 0.0365625i | ||||
\(599\) | 38.3139 | − | 22.1205i | 1.56546 | − | 0.903820i | 0.568775 | − | 0.822493i | \(-0.307417\pi\) |
0.996687 | − | 0.0813272i | \(-0.0259159\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.6353 | − | 9.02705i | −0.637778 | − | 0.368221i | 0.145980 | − | 0.989288i | \(-0.453366\pi\) |
−0.783758 | + | 0.621066i | \(0.786700\pi\) | |||||||
\(602\) | 1.34522 | − | 1.23388i | 0.0548271 | − | 0.0502892i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.67863i | 0.108992i | ||||||||
\(605\) | −6.44193 | − | 7.06924i | −0.261902 | − | 0.287405i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.0006 | − | 37.3229i | 0.405913 | − | 1.51489i | −0.396452 | − | 0.918055i | \(-0.629759\pi\) |
0.802365 | − | 0.596833i | \(-0.203575\pi\) | |||||||
\(608\) | 2.75300 | + | 0.737663i | 0.111649 | + | 0.0299162i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.00545 | − | 21.6557i | 0.0407094 | − | 0.876815i | ||||
\(611\) | 4.29536 | 0.173772 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5939 | − | 23.5939i | −0.952949 | − | 0.952949i | 0.0459926 | − | 0.998942i | \(-0.485355\pi\) |
−0.998942 | + | 0.0459926i | \(0.985355\pi\) | |||||||
\(614\) | 15.1023 | − | 26.1579i | 0.609478 | − | 1.05565i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.0379 | − | 25.0157i | −0.525312 | − | 1.00791i | ||||
\(617\) | −18.1190 | − | 4.85497i | −0.729444 | − | 0.195454i | −0.125062 | − | 0.992149i | \(-0.539913\pi\) |
−0.604382 | + | 0.796695i | \(0.706580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.29505 | − | 10.9033i | 0.253019 | − | 0.438243i | −0.711336 | − | 0.702852i | \(-0.751910\pi\) |
0.964356 | + | 0.264609i | \(0.0852430\pi\) | |||||||
\(620\) | 0.186469 | − | 0.585758i | 0.00748878 | − | 0.0235246i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.4468 | + | 15.4468i | 0.619362 | + | 0.619362i | ||||
\(623\) | 0.577768 | + | 2.60011i | 0.0231478 | + | 0.104171i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.2803 | − | 18.9724i | 0.651212 | − | 0.758896i | ||||
\(626\) | −16.3770 | + | 9.45525i | −0.654556 | + | 0.377908i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.325497 | + | 1.21477i | 0.0129887 | + | 0.0484746i | ||||
\(629\) | 0.0857758 | 0.00342011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.280570 | 0.0111693 | 0.00558466 | − | 0.999984i | \(-0.498222\pi\) | ||||
0.00558466 | + | 0.999984i | \(0.498222\pi\) | |||||||
\(632\) | −2.57430 | − | 9.60740i | −0.102400 | − | 0.382162i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −32.9136 | + | 19.0027i | −1.30717 | + | 0.754693i | ||||
\(635\) | −15.6728 | + | 24.4520i | −0.621956 | + | 0.970350i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.52639 | + | 0.448023i | −0.100099 | + | 0.0177513i | ||||
\(638\) | 18.5111 | + | 18.5111i | 0.732861 | + | 0.732861i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.4313 | + | 12.6325i | −0.965733 | + | 0.499343i | ||||
\(641\) | 3.24741 | − | 5.62468i | 0.128265 | − | 0.222162i | −0.794739 | − | 0.606951i | \(-0.792393\pi\) |
0.923004 | + | 0.384789i | \(0.125726\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1017 | + | 3.51060i | 0.516683 | + | 0.138445i | 0.507732 | − | 0.861515i | \(-0.330484\pi\) |
0.00895086 | + | 0.999960i | \(0.497151\pi\) | |||||||
\(644\) | 1.99311 | − | 1.03879i | 0.0785395 | − | 0.0409340i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.59365 | + | 9.68849i | −0.220079 | + | 0.381188i | ||||
\(647\) | 22.4871 | + | 22.4871i | 0.884059 | + | 0.884059i | 0.993944 | − | 0.109886i | \(-0.0350484\pi\) |
−0.109886 | + | 0.993944i | \(0.535048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.3475 | 1.50527 | ||||||||
\(650\) | 1.11741 | + | 2.43128i | 0.0438286 | + | 0.0953627i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.24840 | + | 0.334509i | 0.0488913 | + | 0.0131004i | ||||
\(653\) | −6.27826 | + | 23.4308i | −0.245687 | + | 0.916917i | 0.727350 | + | 0.686267i | \(0.240752\pi\) |
−0.973037 | + | 0.230650i | \(0.925915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.0660 | + | 17.3741i | −0.744969 | + | 0.678863i | ||||
\(656\) | − | 48.5348i | − | 1.89497i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 33.3589 | − | 30.5979i | 1.30047 | − | 1.19283i | ||||
\(659\) | −15.5047 | − | 8.95163i | −0.603977 | − | 0.348706i | 0.166628 | − | 0.986020i | \(-0.446712\pi\) |
−0.770604 | + | 0.637314i | \(0.780046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2369 | − | 7.64232i | 0.514855 | − | 0.297252i | −0.219972 | − | 0.975506i | \(-0.570597\pi\) |
0.734827 | + | 0.678254i | \(0.237263\pi\) | |||||||
\(662\) | 8.99794 | + | 2.41099i | 0.349715 | + | 0.0937058i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.6082 | + | 32.2304i | −0.722139 | + | 1.25078i | ||||
\(665\) | 9.54079 | + | 20.5823i | 0.369976 | + | 0.798146i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.9396 | − | 20.9396i | 0.810784 | − | 0.810784i | ||||
\(668\) | 0.623262 | + | 2.32605i | 0.0241147 | + | 0.0899974i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.75688 | − | 12.6001i | −0.106508 | − | 0.486784i | ||||
\(671\) | −22.4779 | + | 12.9776i | −0.867749 | + | 0.500995i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.09576 | + | 2.43720i | −0.350616 | + | 0.0939472i | −0.429829 | − | 0.902911i | \(-0.641426\pi\) |
0.0792128 | + | 0.996858i | \(0.474759\pi\) | |||||||
\(674\) | 3.74012i | 0.144064i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.69311 | 0.0651195 | ||||||||
\(677\) | 30.3503 | − | 8.13234i | 1.16646 | − | 0.312551i | 0.376915 | − | 0.926248i | \(-0.376985\pi\) |
0.789542 | + | 0.613697i | \(0.210318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.9133 | − | 28.6139i | −0.572319 | − | 1.09810i | ||||
\(680\) | −2.60523 | − | 11.9070i | −0.0999060 | − | 0.456612i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.5149 | + | 3.08540i | −0.440927 | + | 0.118146i | ||||
\(683\) | −23.8050 | − | 23.8050i | −0.910874 | − | 0.910874i | 0.0854672 | − | 0.996341i | \(-0.472762\pi\) |
−0.996341 | + | 0.0854672i | \(0.972762\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.40879 | − | 10.4606i | −0.206659 | − | 0.399680i | ||||
\(686\) | −16.4291 | + | 21.4761i | −0.627266 | + | 0.819962i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.519302 | + | 1.93806i | −0.0197982 | + | 0.0738879i | ||||
\(689\) | 2.25826 | + | 3.91143i | 0.0860330 | + | 0.149013i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.6309 | − | 18.2621i | −1.20330 | − | 0.694724i | −0.242011 | − | 0.970274i | \(-0.577807\pi\) |
−0.961287 | + | 0.275549i | \(0.911140\pi\) | |||||||
\(692\) | 1.43439 | + | 1.43439i | 0.0545274 | + | 0.0545274i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 11.9920i | − | 0.455211i | ||||||
\(695\) | 15.6766 | + | 17.2032i | 0.594647 | + | 0.652553i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.0637 | + | 5.91194i | 0.835721 | + | 0.223931i | ||||
\(698\) | −22.6500 | − | 6.06904i | −0.857313 | − | 0.229716i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.60500 | + | 0.674300i | 0.0606633 | + | 0.0254861i | ||||
\(701\) | −18.2879 | −0.690725 | −0.345363 | − | 0.938469i | \(-0.612244\pi\) | ||||
−0.345363 | + | 0.938469i | \(0.612244\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.116393 | − | 0.116393i | 0.00438984 | − | 0.00438984i | ||||
\(704\) | 25.0710 | + | 14.4748i | 0.944900 | + | 0.545538i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.94182 | + | 4.58521i | −0.298894 | + | 0.172567i | ||||
\(707\) | −4.88447 | + | 15.5181i | −0.183699 | + | 0.583617i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.14195 | + | 4.12341i | 0.268222 | + | 0.154858i | 0.628079 | − | 0.778149i | \(-0.283841\pi\) |
−0.359858 | + | 0.933007i | \(0.617175\pi\) | |||||||
\(710\) | −3.18715 | − | 6.16396i | −0.119611 | − | 0.231329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.94185 | − | 1.94185i | −0.0727740 | − | 0.0727740i | ||||
\(713\) | 3.49018 | + | 13.0255i | 0.130708 | + | 0.487810i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.72873 | − | 2.69709i | 0.0646508 | − | 0.100865i | ||||
\(716\) | −0.186973 | − | 0.323846i | −0.00698750 | − | 0.0121027i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41.1682 | + | 11.0310i | −1.53638 | + | 0.411673i | ||||
\(719\) | 25.4661 | 0.949724 | 0.474862 | − | 0.880060i | \(-0.342498\pi\) | ||||
0.474862 | + | 0.880060i | \(0.342498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.460838 | − | 10.6750i | 0.0171625 | − | 0.397556i | ||||
\(722\) | −1.62318 | − | 6.05779i | −0.0604085 | − | 0.225448i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.33536 | − | 2.31290i | −0.0496281 | − | 0.0859584i | ||||
\(725\) | 22.8386 | + | 2.12532i | 0.848205 | + | 0.0789323i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.7819 | − | 5.30055i | 0.733671 | − | 0.196586i | 0.127407 | − | 0.991850i | \(-0.459334\pi\) |
0.606263 | + | 0.795264i | \(0.292668\pi\) | |||||||
\(728\) | 1.94955 | − | 1.78819i | 0.0722550 | − | 0.0662747i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −39.3619 | − | 12.5304i | −1.45685 | − | 0.463771i | ||||
\(731\) | −0.817776 | − | 0.472143i | −0.0302466 | − | 0.0174629i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7597 | − | 5.56254i | −0.766776 | − | 0.205457i | −0.145829 | − | 0.989310i | \(-0.546585\pi\) |
−0.620947 | + | 0.783853i | \(0.713252\pi\) | |||||||
\(734\) | −13.9527 | − | 24.1668i | −0.515004 | − | 0.892013i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.39893 | + | 4.15508i | −0.0884259 | + | 0.153158i | ||||
\(737\) | −10.9194 | + | 10.9194i | −0.402220 | + | 0.402220i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 43.5443i | − | 1.60180i | −0.598796 | − | 0.800901i | \(-0.704354\pi\) | ||
0.598796 | − | 0.800901i | \(-0.295646\pi\) | |||||||
\(740\) | 0.000585834 | − | 0.0126179i | 2.15357e−5 | − | 0.000463844i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 45.4012 | + | 14.2905i | 1.66673 | + | 0.524620i | ||||
\(743\) | 10.1722 | − | 37.9631i | 0.373181 | − | 1.39273i | −0.482803 | − | 0.875729i | \(-0.660381\pi\) |
0.855984 | − | 0.517002i | \(-0.172952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.21991 | + | 1.11166i | −0.0446941 | + | 0.0407281i | ||||
\(746\) | −54.6132 | −1.99953 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.726789 | − | 0.726789i | 0.0265740 | − | 0.0265740i | ||||
\(749\) | −6.93857 | − | 4.41558i | −0.253530 | − | 0.161342i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6732 | − | 21.9506i | −0.462452 | − | 0.800990i | 0.536631 | − | 0.843817i | \(-0.319697\pi\) |
−0.999082 | + | 0.0428274i | \(0.986363\pi\) | |||||||
\(752\) | −12.8777 | + | 48.0602i | −0.469601 | + | 1.75258i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.22750 | + | 2.12609i | −0.0447028 | + | 0.0774276i | ||||
\(755\) | 13.8062 | − | 43.3695i | 0.502457 | − | 1.57838i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.86625 | + | 2.86625i | −0.104176 | + | 0.104176i | −0.757273 | − | 0.653098i | \(-0.773469\pi\) |
0.653098 | + | 0.757273i | \(0.273469\pi\) | |||||||
\(758\) | −29.7527 | + | 7.97221i | −1.08067 | + | 0.289564i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.6922 | − | 12.6219i | −0.714312 | − | 0.457846i | ||||
\(761\) | 13.3875 | − | 7.72926i | 0.485295 | − | 0.280185i | −0.237325 | − | 0.971430i | \(-0.576271\pi\) |
0.722621 | + | 0.691245i | \(0.242937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.5804 | − | 4.79536i | 0.781264 | − | 0.173604i | ||||
\(764\) | − | 1.61504i | − | 0.0584301i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.94052i | 0.214640i | ||||||||
\(767\) | 0.930760 | + | 3.47364i | 0.0336078 | + | 0.125426i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.41964 | − | 12.8512i | −0.267559 | − | 0.463426i | 0.700672 | − | 0.713484i | \(-0.252884\pi\) |
−0.968231 | + | 0.250058i | \(0.919550\pi\) | |||||||
\(770\) | −5.78689 | − | 33.2608i | −0.208545 | − | 1.19864i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.275494 | + | 1.02816i | 0.00991526 | + | 0.0370043i | ||||
\(773\) | −6.14208 | + | 6.14208i | −0.220915 | + | 0.220915i | −0.808884 | − | 0.587969i | \(-0.799928\pi\) |
0.587969 | + | 0.808884i | \(0.299928\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.03821 | + | 8.52286i | −0.216899 | + | 0.306150i | ||||
\(776\) | 28.8113 | + | 16.6342i | 1.03427 | + | 0.597134i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.7311 | − | 43.7812i | 0.420582 | − | 1.56963i | ||||
\(779\) | 37.9613 | − | 21.9170i | 1.36010 | − | 0.785257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.15397 | + | 7.19488i | −0.148641 | + | 0.257453i | ||||
\(782\) | −13.3167 | − | 13.3167i | −0.476204 | − | 0.476204i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.56136 | − | 29.6106i | 0.0914770 | − | 1.05752i | ||||
\(785\) | 0.991064 | − | 21.3459i | 0.0353726 | − | 0.761869i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.1760 | + | 45.4416i | −0.434029 | + | 1.61982i | 0.309352 | + | 0.950948i | \(0.399888\pi\) |
−0.743380 | + | 0.668869i | \(0.766779\pi\) | |||||||
\(788\) | −0.0734228 | + | 0.274017i | −0.00261558 | + | 0.00976147i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.552073 | − | 11.8908i | 0.0196419 | − | 0.423054i | ||||
\(791\) | 35.3128 | + | 1.52446i | 1.25558 | + | 0.0542035i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.72113 | − | 1.72113i | −0.0611191 | − | 0.0611191i | ||||
\(794\) | −4.58186 | + | 7.93602i | −0.162604 | + | 0.281639i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.29394 | − | 0.747055i | 0.0458624 | − | 0.0264787i | ||||
\(797\) | −4.98780 | + | 18.6147i | −0.176677 | + | 0.659367i | 0.819583 | + | 0.572960i | \(0.194205\pi\) |
−0.996260 | + | 0.0864066i | \(0.972462\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.2793 | − | 11.7083i | −0.717430 | − | 0.414208i | ||||
\(800\) | −3.66332 | + | 0.625096i | −0.129518 | + | 0.0221005i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −39.5218 | + | 39.5218i | −1.39556 | + | 1.39556i | ||||
\(803\) | 12.8002 | + | 47.7711i | 0.451710 | + | 1.68581i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.6244 | + | 6.54608i | −1.32609 | + | 0.230719i | ||||
\(806\) | −0.558971 | − | 0.968166i | −0.0196889 | − | 0.0341022i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.34132 | − | 16.2020i | −0.152727 | − | 0.569985i | ||||
\(809\) | − | 27.6394i | − | 0.971751i | −0.874028 | − | 0.485876i | \(-0.838501\pi\) | ||
0.874028 | − | 0.485876i | \(-0.161499\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.5840i | 0.476997i | 0.971143 | + | 0.238499i | \(0.0766552\pi\) | ||||
−0.971143 | + | 0.238499i | \(0.923345\pi\) | |||||||
\(812\) | 0.346473 | + | 1.55922i | 0.0121588 | + | 0.0547180i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.212140 | + | 0.122479i | −0.00743550 | + | 0.00429289i | ||||
\(815\) | −18.4887 | − | 11.8505i | −0.647630 | − | 0.415105i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.75035 | + | 0.469004i | −0.0612369 | + | 0.0164084i | ||||
\(818\) | 31.1016 | − | 31.1016i | 1.08744 | − | 1.08744i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.02036 | − | 3.20526i | 0.0356324 | − | 0.111933i | ||||
\(821\) | 4.88248 | − | 8.45670i | 0.170400 | − | 0.295141i | −0.768160 | − | 0.640258i | \(-0.778827\pi\) |
0.938560 | + | 0.345117i | \(0.112161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0194 | − | 41.1250i | 0.384113 | − | 1.43353i | −0.455448 | − | 0.890262i | \(-0.650521\pi\) |
0.839561 | − | 0.543266i | \(-0.182812\pi\) | |||||||
\(824\) | 5.50825 | + | 9.54058i | 0.191889 | + | 0.332362i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.9729 | + | 20.3470i | 1.11248 | + | 0.707961i | ||||
\(827\) | 35.2828 | − | 35.2828i | 1.22690 | − | 1.22690i | 0.261774 | − | 0.965129i | \(-0.415693\pi\) |
0.965129 | − | 0.261774i | \(-0.0843075\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6110 | −1.06316 | −0.531582 | − | 0.847007i | \(-0.678402\pi\) | ||||
−0.531582 | + | 0.847007i | \(0.678402\pi\) | |||||||
\(830\) | −32.9213 | + | 30.0000i | −1.14272 | + | 1.04131i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.702654 | + | 2.62234i | −0.0243601 | + | 0.0909133i | ||||
\(833\) | 13.1488 | + | 4.77119i | 0.455579 | + | 0.165312i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.89769 | − | 40.8732i | 0.0656724 | − | 1.41448i | ||||
\(836\) | − | 1.97242i | − | 0.0682176i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.7155 | − | 10.7155i | 0.370160 | − | 0.370160i | ||||
\(839\) | 8.60220 | − | 14.8995i | 0.296981 | − | 0.514386i | −0.678463 | − | 0.734635i | \(-0.737354\pi\) |
0.975444 | + | 0.220249i | \(0.0706868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.97761 | − | 6.88943i | −0.137159 | − | 0.237567i | ||||
\(842\) | −26.2431 | − | 7.03182i | −0.904397 | − | 0.242333i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.202323 | + | 0.116811i | 0.00696425 | + | 0.00402081i | ||||
\(845\) | −27.4130 | − | 8.72660i | −0.943035 | − | 0.300204i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.33961 | + | 7.64936i | −0.286552 | + | 0.262835i | ||||
\(848\) | −50.5348 | + | 13.5407i | −1.73537 | + | 0.464991i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.35161 | − | 14.5244i | 0.0463600 | − | 0.498183i | ||||
\(851\) | 0.138547 | + | 0.239971i | 0.00474934 | + | 0.00822610i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.23563 | − | 15.8076i | −0.145025 | − | 0.541241i | −0.999754 | − | 0.0221670i | \(-0.992943\pi\) |
0.854729 | − | 0.519074i | \(-0.173723\pi\) | |||||||
\(854\) | −25.6272 | − | 1.10633i | −0.876943 | − | 0.0378577i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.47967 | 0.289829 | ||||||||
\(857\) | −3.46122 | + | 0.927430i | −0.118233 | + | 0.0316804i | −0.317450 | − | 0.948275i | \(-0.602827\pi\) |
0.199217 | + | 0.979955i | \(0.436160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.69388 | − | 15.0582i | −0.296631 | − | 0.513781i | 0.678732 | − | 0.734386i | \(-0.262530\pi\) |
−0.975363 | + | 0.220606i | \(0.929197\pi\) | |||||||
\(860\) | −0.0750391 | + | 0.117073i | −0.00255881 | + | 0.00399215i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.56800 | − | 35.7082i | −0.325887 | − | 1.21623i | ||||
\(863\) | 4.87607 | + | 4.87607i | 0.165984 | + | 0.165984i | 0.785211 | − | 0.619228i | \(-0.212554\pi\) |
−0.619228 | + | 0.785211i | \(0.712554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.8310 | − | 30.6173i | −0.538270 | − | 1.04102i | ||||
\(866\) | 24.8854 | + | 14.3676i | 0.845642 | + | 0.488231i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.693792 | − | 0.218378i | −0.0235488 | − | 0.00741224i | ||||
\(869\) | −12.3422 | + | 7.12576i | −0.418680 | + | 0.241725i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.25414 | − | 0.724080i | −0.0424950 | − | 0.0245345i | ||||
\(872\) | −16.1170 | + | 16.1170i | −0.545791 | + | 0.545791i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36.1400 | −1.22245 | ||||||||
\(875\) | −22.5110 | − | 19.1900i | −0.761010 | − | 0.648741i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.4733 | + | 11.9166i | 1.50176 | + | 0.402394i | 0.913688 | − | 0.406417i | \(-0.133222\pi\) |
0.588068 | + | 0.808811i | \(0.299889\pi\) | |||||||
\(878\) | 41.5610 | + | 11.1362i | 1.40262 | + | 0.375830i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 24.9945 | + | 27.4285i | 0.842566 | + | 0.924614i | ||||
\(881\) | 23.7070i | 0.798708i | 0.916797 | + | 0.399354i | \(0.130766\pi\) | ||||
−0.916797 | + | 0.399354i | \(0.869234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8246 | + | 10.8246i | 0.364276 | + | 0.364276i | 0.865384 | − | 0.501109i | \(-0.167074\pi\) |
−0.501109 | + | 0.865384i | \(0.667074\pi\) | |||||||
\(884\) | 0.0834752 | + | 0.0481944i | 0.00280758 | + | 0.00162095i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.1447 | + | 19.3032i | 0.374413 | + | 0.648502i | ||||
\(887\) | −1.04539 | + | 3.90146i | −0.0351009 | + | 0.130998i | −0.981253 | − | 0.192724i | \(-0.938268\pi\) |
0.946152 | + | 0.323722i | \(0.104934\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.9922 | + | 18.4501i | 0.972367 | + | 0.618797i | ||||
\(890\) | −1.50952 | − | 2.91943i | −0.0505993 | − | 0.0978594i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.85482 | + | 1.85482i | 0.0621040 | + | 0.0621040i | ||||
\(893\) | −43.4053 | + | 11.6304i | −1.45250 | + | 0.389197i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.35810 | + | 6.20706i | 0.0453961 | + | 0.207479i | ||||
\(896\) | 15.0409 | + | 28.8588i | 0.502481 | + | 0.964104i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.31738 | + | 1.15684i | −0.144073 | + | 0.0386042i | ||||
\(899\) | −9.58325 | −0.319619 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 24.6222i | − | 0.820284i | ||||||
\(902\) | −63.0093 | + | 16.8833i | −2.09798 | + | 0.562152i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −31.5603 | + | 18.2214i | −1.04968 | + | 0.606033i | ||||
\(905\) | 9.69949 | + | 44.3307i | 0.322422 | + | 1.47360i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.69211 | + | 21.2432i | 0.189003 | + | 0.705370i | 0.993738 | + | 0.111735i | \(0.0356409\pi\) |
−0.804735 | + | 0.593635i | \(0.797692\pi\) | |||||||
\(908\) | −1.11955 | + | 1.11955i | −0.0371536 | + | 0.0371536i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.87242 | − | 1.33149i | 0.0952196 | − | 0.0441385i | ||||
\(911\) | 4.61287 | − | 7.98972i | 0.152831 | − | 0.264711i | −0.779436 | − | 0.626482i | \(-0.784494\pi\) |
0.932267 | + | 0.361770i | \(0.117828\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.5084 | + | 13.8016i | 1.70468 | + | 0.456767i | ||||
\(914\) | −5.81996 | + | 3.36016i | −0.192507 | + | 0.111144i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.09111 | + | 0.629951i | 0.0360512 | + | 0.0208142i | ||||
\(917\) | 20.6306 | + | 22.4922i | 0.681282 | + | 0.742758i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1931i | 0.962991i | 0.876449 | + | 0.481496i | \(0.159906\pi\) | ||||
−0.876449 | + | 0.481496i | \(0.840094\pi\) | |||||||
\(920\) | 29.1035 | − | 26.5210i | 0.959516 | − | 0.874370i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.7779 | + | 51.4196i | −0.453749 | + | 1.69342i | ||||
\(923\) | −0.752559 | − | 0.201648i | −0.0247708 | − | 0.00663731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0745203 | + | 0.201276i | −0.00245021 | + | 0.00661791i | ||||
\(926\) | −39.3663 | −1.29366 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.41098 | − | 2.41098i | −0.0791444 | − | 0.0791444i | ||||
\(929\) | 18.9546 | − | 32.8304i | 0.621882 | − | 1.07713i | −0.367253 | − | 0.930121i | \(-0.619702\pi\) |
0.989135 | − | 0.147010i | \(-0.0469649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.3164 | − | 11.3680i | 0.796938 | − | 0.372570i | ||||
\(932\) | 1.14560 | + | 0.306962i | 0.0375253 | + | 0.0100549i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.3706 | − | 47.4073i | 0.895593 | − | 1.55121i | ||||
\(935\) | −15.5134 | + | 8.02137i | −0.507342 | + | 0.262327i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.2007 | + | 38.2007i | 1.24796 | + | 1.24796i | 0.956619 | + | 0.291343i | \(0.0941022\pi\) |
0.291343 | + | 0.956619i | \(0.405898\pi\) | |||||||
\(938\) | −14.8980 | + | 3.31046i | −0.486436 | + | 0.108090i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.86083 | + | 2.90319i | −0.0606935 | + | 0.0946915i | ||||
\(941\) | 24.9324 | − | 14.3947i | 0.812774 | − | 0.469255i | −0.0351445 | − | 0.999382i | \(-0.511189\pi\) |
0.847918 | + | 0.530127i | \(0.177856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.0982 | + | 71.2755i | 0.621924 | + | 2.32105i | ||||
\(944\) | −41.6565 | −1.35580 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.69669 | 0.0876769 | ||||||||
\(947\) | −6.96236 | − | 25.9839i | −0.226246 | − | 0.844363i | −0.981901 | − | 0.189393i | \(-0.939348\pi\) |
0.755655 | − | 0.654970i | \(-0.227319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.01657 | + | 2.31897i | −0.130384 | + | 0.0752770i | ||||
\(950\) | −17.8747 | − | 21.5429i | −0.579933 | − | 0.698942i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.0784 | + | 3.12835i | −0.456284 | + | 0.101390i | ||||
\(953\) | 20.7929 | + | 20.7929i | 0.673548 | + | 0.673548i | 0.958532 | − | 0.284984i | \(-0.0919884\pi\) |
−0.284984 | + | 0.958532i | \(0.591988\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.32422 | + | 26.1490i | −0.269365 | + | 0.846161i | ||||
\(956\) | −0.383940 | + | 0.665003i | −0.0124175 | + | 0.0215077i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.9604 | + | 3.20478i | 0.386423 | + | 0.103542i | ||||
\(959\) | −12.3563 | + | 6.43998i | −0.399006 | + | 0.207958i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.3180 | + | 23.0675i | −0.429613 | + | 0.744112i | ||||
\(962\) | −0.0162435 | − | 0.0162435i | −0.000523713 | − | 0.000523713i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.06644 | 0.0343477 | ||||||||
\(965\) | 0.838818 | − | 18.0668i | 0.0270025 | − | 0.581591i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.2366 | − | 8.10188i | −0.972345 | − | 0.260539i | −0.262527 | − | 0.964925i | \(-0.584556\pi\) |
−0.709817 | + | 0.704386i | \(0.751223\pi\) | |||||||
\(968\) | 3.01981 | − | 11.2701i | 0.0970604 | − | 0.362234i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 26.8175 | + | 29.4289i | 0.861057 | + | 0.944906i | ||||
\(971\) | − | 0.191830i | − | 0.00615612i | −0.999995 | − | 0.00307806i | \(-0.999020\pi\) | ||
0.999995 | − | 0.00307806i | \(-0.000979779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.2946 | − | 18.6149i | 0.650616 | − | 0.596766i | ||||
\(974\) | 4.74729 | + | 2.74085i | 0.152113 | + | 0.0878225i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.4175 | − | 14.0974i | 0.781585 | − | 0.451248i | ||||
\(977\) | −30.9571 | − | 8.29492i | −0.990404 | − | 0.265378i | −0.272984 | − | 0.962019i | \(-0.588011\pi\) |
−0.717420 | + | 0.696640i | \(0.754677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.96744 | + | 3.40770i | −0.0628795 | + | 0.108911i | ||||
\(980\) | 0.791662 | − | 1.90165i | 0.0252887 | − | 0.0607459i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.16665 | + | 4.16665i | −0.132963 | + | 0.132963i | ||||
\(983\) | −6.91122 | − | 25.7930i | −0.220434 | − | 0.822670i | −0.984183 | − | 0.177156i | \(-0.943310\pi\) |
0.763749 | − | 0.645513i | \(-0.223357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.60112 | − | 4.05816i | 0.0828786 | − | 0.129304i | ||||
\(986\) | 11.5905 | − | 6.69180i | 0.369118 | − | 0.213110i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.178668 | − | 0.0478740i | 0.00568419 | − | 0.00152307i | ||||
\(989\) | − | 3.05047i | − | 0.0969993i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.6436 | −1.83111 | −0.915554 | − | 0.402194i | \(-0.868248\pi\) | ||||
−0.915554 | + | 0.402194i | \(0.868248\pi\) | |||||||
\(992\) | 1.49976 | − | 0.401859i | 0.0476174 | − | 0.0127591i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.28100 | + | 3.79478i | −0.230939 | + | 0.120363i | ||||
\(995\) | −24.8005 | + | 5.42631i | −0.786228 | + | 0.172026i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5152 | + | 7.64061i | −0.903084 | + | 0.241981i | −0.680340 | − | 0.732896i | \(-0.738168\pi\) |
−0.222744 | + | 0.974877i | \(0.571501\pi\) | |||||||
\(998\) | 7.19532 | + | 7.19532i | 0.227764 | + | 0.227764i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.ce.a.748.34 | 176 | ||
3.2 | odd | 2 | 315.2.cb.a.223.11 | yes | 176 | ||
5.2 | odd | 4 | inner | 945.2.ce.a.937.12 | 176 | ||
7.6 | odd | 2 | inner | 945.2.ce.a.748.33 | 176 | ||
9.4 | even | 3 | inner | 945.2.ce.a.118.11 | 176 | ||
9.5 | odd | 6 | 315.2.cb.a.13.34 | yes | 176 | ||
15.2 | even | 4 | 315.2.cb.a.97.33 | yes | 176 | ||
21.20 | even | 2 | 315.2.cb.a.223.12 | yes | 176 | ||
35.27 | even | 4 | inner | 945.2.ce.a.937.11 | 176 | ||
45.22 | odd | 12 | inner | 945.2.ce.a.307.33 | 176 | ||
45.32 | even | 12 | 315.2.cb.a.202.12 | yes | 176 | ||
63.13 | odd | 6 | inner | 945.2.ce.a.118.12 | 176 | ||
63.41 | even | 6 | 315.2.cb.a.13.33 | ✓ | 176 | ||
105.62 | odd | 4 | 315.2.cb.a.97.34 | yes | 176 | ||
315.167 | odd | 12 | 315.2.cb.a.202.11 | yes | 176 | ||
315.202 | even | 12 | inner | 945.2.ce.a.307.34 | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.cb.a.13.33 | ✓ | 176 | 63.41 | even | 6 | ||
315.2.cb.a.13.34 | yes | 176 | 9.5 | odd | 6 | ||
315.2.cb.a.97.33 | yes | 176 | 15.2 | even | 4 | ||
315.2.cb.a.97.34 | yes | 176 | 105.62 | odd | 4 | ||
315.2.cb.a.202.11 | yes | 176 | 315.167 | odd | 12 | ||
315.2.cb.a.202.12 | yes | 176 | 45.32 | even | 12 | ||
315.2.cb.a.223.11 | yes | 176 | 3.2 | odd | 2 | ||
315.2.cb.a.223.12 | yes | 176 | 21.20 | even | 2 | ||
945.2.ce.a.118.11 | 176 | 9.4 | even | 3 | inner | ||
945.2.ce.a.118.12 | 176 | 63.13 | odd | 6 | inner | ||
945.2.ce.a.307.33 | 176 | 45.22 | odd | 12 | inner | ||
945.2.ce.a.307.34 | 176 | 315.202 | even | 12 | inner | ||
945.2.ce.a.748.33 | 176 | 7.6 | odd | 2 | inner | ||
945.2.ce.a.748.34 | 176 | 1.1 | even | 1 | trivial | ||
945.2.ce.a.937.11 | 176 | 35.27 | even | 4 | inner | ||
945.2.ce.a.937.12 | 176 | 5.2 | odd | 4 | inner |