Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(49,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([14, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.u (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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Character | \(\chi\) | \(=\) | 675.49 |
Dual form | 675.2.u.b.124.2 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.267057 | − | 0.318266i | −0.188837 | − | 0.225048i | 0.663316 | − | 0.748339i | \(-0.269148\pi\) |
−0.852154 | + | 0.523291i | \(0.824704\pi\) | |||||||
\(3\) | −1.72466 | − | 0.159815i | −0.995734 | − | 0.0922690i | ||||
\(4\) | 0.317323 | − | 1.79963i | 0.158661 | − | 0.899813i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.409719 | + | 0.591580i | 0.167267 | + | 0.241512i | ||||
\(7\) | 1.29958 | − | 0.229151i | 0.491195 | − | 0.0866110i | 0.0774361 | − | 0.996997i | \(-0.475327\pi\) |
0.413759 | + | 0.910386i | \(0.364216\pi\) | |||||||
\(8\) | −1.37711 | + | 0.795075i | −0.486882 | + | 0.281102i | ||||
\(9\) | 2.94892 | + | 0.551252i | 0.982973 | + | 0.183751i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.90067 | + | 1.78370i | 1.47761 | + | 0.537805i | 0.950155 | − | 0.311778i | \(-0.100925\pi\) |
0.527454 | + | 0.849584i | \(0.323147\pi\) | |||||||
\(12\) | −0.834881 | + | 3.05303i | −0.241009 | + | 0.881335i | ||||
\(13\) | −0.0116078 | + | 0.0138336i | −0.00321942 | + | 0.00383676i | −0.767652 | − | 0.640867i | \(-0.778575\pi\) |
0.764432 | + | 0.644704i | \(0.223019\pi\) | |||||||
\(14\) | −0.419993 | − | 0.352416i | −0.112248 | − | 0.0941870i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.81355 | − | 1.02405i | −0.703389 | − | 0.256012i | ||||
\(17\) | 2.71308 | + | 1.56640i | 0.658019 | + | 0.379907i | 0.791522 | − | 0.611141i | \(-0.209289\pi\) |
−0.133503 | + | 0.991048i | \(0.542623\pi\) | |||||||
\(18\) | −0.612083 | − | 1.08575i | −0.144269 | − | 0.255915i | ||||
\(19\) | 0.208676 | + | 0.361438i | 0.0478736 | + | 0.0829195i | 0.888969 | − | 0.457967i | \(-0.151422\pi\) |
−0.841096 | + | 0.540886i | \(0.818089\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.27796 | + | 0.187516i | −0.497092 | + | 0.0409194i | ||||
\(22\) | −0.741067 | − | 2.03606i | −0.157996 | − | 0.434090i | ||||
\(23\) | 1.01867 | + | 0.179619i | 0.212408 | + | 0.0374532i | 0.278839 | − | 0.960338i | \(-0.410050\pi\) |
−0.0664316 | + | 0.997791i | \(0.521161\pi\) | |||||||
\(24\) | 2.50212 | − | 1.15115i | 0.510742 | − | 0.234978i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.00750270 | 0.00147140 | ||||||||
\(27\) | −4.99779 | − | 1.42200i | −0.961825 | − | 0.273665i | ||||
\(28\) | − | 2.41147i | − | 0.455726i | ||||||
\(29\) | 5.98068 | − | 5.01839i | 1.11058 | − | 0.931891i | 0.112493 | − | 0.993652i | \(-0.464116\pi\) |
0.998091 | + | 0.0617615i | \(0.0196718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.647649 | − | 3.67300i | 0.116321 | − | 0.659691i | −0.869766 | − | 0.493464i | \(-0.835730\pi\) |
0.986088 | − | 0.166227i | \(-0.0531584\pi\) | |||||||
\(32\) | 1.51319 | + | 4.15744i | 0.267496 | + | 0.734939i | ||||
\(33\) | −8.16694 | − | 3.85948i | −1.42168 | − | 0.671849i | ||||
\(34\) | −0.226015 | − | 1.28180i | −0.0387613 | − | 0.219826i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.92781 | − | 5.13202i | 0.321301 | − | 0.855337i | ||||
\(37\) | −3.83195 | − | 2.21238i | −0.629969 | − | 0.363713i | 0.150771 | − | 0.988569i | \(-0.451824\pi\) |
−0.780740 | + | 0.624856i | \(0.785158\pi\) | |||||||
\(38\) | 0.0593049 | − | 0.162939i | 0.00962052 | − | 0.0264322i | ||||
\(39\) | 0.0222303 | − | 0.0220032i | 0.00355970 | − | 0.00352334i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.81517 | − | 2.36221i | −0.439655 | − | 0.368915i | 0.395925 | − | 0.918283i | \(-0.370424\pi\) |
−0.835580 | + | 0.549368i | \(0.814868\pi\) | |||||||
\(42\) | 0.668024 | + | 0.674919i | 0.103078 | + | 0.104142i | ||||
\(43\) | 2.84146 | − | 7.80685i | 0.433319 | − | 1.19053i | −0.510445 | − | 0.859911i | \(-0.670519\pi\) |
0.943763 | − | 0.330622i | \(-0.107259\pi\) | |||||||
\(44\) | 4.76508 | − | 8.25337i | 0.718363 | − | 1.24424i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.214876 | − | 0.372177i | −0.0316818 | − | 0.0548745i | ||||
\(47\) | 6.99008 | − | 1.23254i | 1.01961 | − | 0.179784i | 0.361234 | − | 0.932475i | \(-0.382356\pi\) |
0.658374 | + | 0.752691i | \(0.271245\pi\) | |||||||
\(48\) | 4.68877 | + | 2.21579i | 0.676766 | + | 0.319821i | ||||
\(49\) | −4.94145 | + | 1.79854i | −0.705921 | + | 0.256934i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.42881 | − | 3.13510i | −0.620158 | − | 0.439001i | ||||
\(52\) | 0.0212119 | + | 0.0252794i | 0.00294157 | + | 0.00350562i | ||||
\(53\) | 1.30057i | 0.178648i | 0.996003 | + | 0.0893238i | \(0.0284706\pi\) | ||||
−0.996003 | + | 0.0893238i | \(0.971529\pi\) | |||||||
\(54\) | 0.882118 | + | 1.97038i | 0.120041 | + | 0.268135i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.60747 | + | 1.34883i | −0.214808 | + | 0.180245i | ||||
\(57\) | −0.302133 | − | 0.656707i | −0.0400185 | − | 0.0869830i | ||||
\(58\) | −3.19436 | − | 0.563252i | −0.419440 | − | 0.0739586i | ||||
\(59\) | −3.47856 | + | 1.26609i | −0.452871 | + | 0.164831i | −0.558377 | − | 0.829587i | \(-0.688576\pi\) |
0.105507 | + | 0.994419i | \(0.466354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.20064 | + | 6.80919i | 0.153727 | + | 0.871828i | 0.959941 | + | 0.280204i | \(0.0904020\pi\) |
−0.806214 | + | 0.591624i | \(0.798487\pi\) | |||||||
\(62\) | −1.34195 | + | 0.774775i | −0.170428 | + | 0.0983965i | ||||
\(63\) | 3.95868 | + | 0.0406486i | 0.498747 | + | 0.00512125i | ||||
\(64\) | −2.07506 | + | 3.59410i | −0.259382 | + | 0.449263i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.952697 | + | 3.62996i | 0.117269 | + | 0.446817i | ||||
\(67\) | 7.08789 | − | 8.44702i | 0.865923 | − | 1.03197i | −0.133241 | − | 0.991084i | \(-0.542538\pi\) |
0.999164 | − | 0.0408835i | \(-0.0130172\pi\) | |||||||
\(68\) | 3.67985 | − | 4.38548i | 0.446247 | − | 0.531817i | ||||
\(69\) | −1.72816 | − | 0.472581i | −0.208046 | − | 0.0568921i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.04214 | − | 5.26914i | 0.361035 | − | 0.625332i | −0.627096 | − | 0.778942i | \(-0.715757\pi\) |
0.988132 | + | 0.153610i | \(0.0490900\pi\) | |||||||
\(72\) | −4.49927 | + | 1.58548i | −0.530245 | + | 0.186850i | ||||
\(73\) | 0.473692 | − | 0.273486i | 0.0554415 | − | 0.0320092i | −0.472023 | − | 0.881586i | \(-0.656476\pi\) |
0.527465 | + | 0.849577i | \(0.323143\pi\) | |||||||
\(74\) | 0.319224 | + | 1.81041i | 0.0371090 | + | 0.210456i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.716670 | − | 0.260847i | 0.0822077 | − | 0.0299212i | ||||
\(77\) | 6.77756 | + | 1.19507i | 0.772374 | + | 0.136190i | ||||
\(78\) | −0.0129396 | − | 0.00119904i | −0.00146512 | − | 0.000135765i | ||||
\(79\) | −0.374706 | + | 0.314416i | −0.0421577 | + | 0.0353745i | −0.663623 | − | 0.748067i | \(-0.730982\pi\) |
0.621465 | + | 0.783442i | \(0.286538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.39224 | + | 3.25120i | 0.932471 | + | 0.361244i | ||||
\(82\) | 1.52681i | 0.168608i | ||||||||
\(83\) | −2.96561 | − | 3.53428i | −0.325518 | − | 0.387937i | 0.578321 | − | 0.815809i | \(-0.303708\pi\) |
−0.903839 | + | 0.427872i | \(0.859263\pi\) | |||||||
\(84\) | −0.385389 | + | 4.15898i | −0.0420493 | + | 0.453782i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.24348 | + | 1.18053i | −0.349754 | + | 0.127300i | ||||
\(87\) | −11.1167 | + | 7.69922i | −1.19183 | + | 0.825443i | ||||
\(88\) | −8.16694 | + | 1.44005i | −0.870599 | + | 0.153510i | ||||
\(89\) | −1.68653 | − | 2.92116i | −0.178772 | − | 0.309642i | 0.762688 | − | 0.646766i | \(-0.223879\pi\) |
−0.941460 | + | 0.337124i | \(0.890546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0119153 | + | 0.0206379i | −0.00124906 | + | 0.00216344i | ||||
\(92\) | 0.646495 | − | 1.77623i | 0.0674018 | − | 0.185185i | ||||
\(93\) | −1.70398 | + | 6.23118i | −0.176694 | + | 0.646144i | ||||
\(94\) | −2.25902 | − | 1.89554i | −0.233000 | − | 0.195510i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.94531 | − | 7.41201i | −0.198543 | − | 0.756485i | ||||
\(97\) | 3.40014 | − | 9.34182i | 0.345232 | − | 0.948518i | −0.638618 | − | 0.769524i | \(-0.720493\pi\) |
0.983850 | − | 0.178994i | \(-0.0572843\pi\) | |||||||
\(98\) | 1.89206 | + | 1.09238i | 0.191127 | + | 0.110347i | ||||
\(99\) | 13.4684 | + | 7.96149i | 1.35363 | + | 0.800160i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.39626 | + | 13.5898i | 0.238436 | + | 1.35224i | 0.835255 | + | 0.549863i | \(0.185320\pi\) |
−0.596818 | + | 0.802377i | \(0.703569\pi\) | |||||||
\(102\) | 0.184950 | + | 2.24679i | 0.0183128 | + | 0.222465i | ||||
\(103\) | 1.56136 | + | 4.28981i | 0.153846 | + | 0.422687i | 0.992541 | − | 0.121914i | \(-0.0389032\pi\) |
−0.838695 | + | 0.544601i | \(0.816681\pi\) | |||||||
\(104\) | 0.00498644 | − | 0.0282795i | 0.000488961 | − | 0.00277303i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.413928 | − | 0.347327i | 0.0402042 | − | 0.0337354i | ||||
\(107\) | − | 11.2965i | − | 1.09207i | −0.837762 | − | 0.546035i | \(-0.816136\pi\) | ||
0.837762 | − | 0.546035i | \(-0.183864\pi\) | |||||||
\(108\) | −4.14499 | + | 8.54292i | −0.398851 | + | 0.822043i | ||||
\(109\) | −14.5032 | −1.38915 | −0.694577 | − | 0.719419i | \(-0.744408\pi\) | ||||
−0.694577 | + | 0.719419i | \(0.744408\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.25525 | + | 4.42801i | 0.593722 | + | 0.420288i | ||||
\(112\) | −3.89110 | − | 0.686107i | −0.367675 | − | 0.0648310i | ||||
\(113\) | 4.29523 | + | 11.8011i | 0.404062 | + | 1.11015i | 0.960262 | + | 0.279102i | \(0.0900367\pi\) |
−0.556200 | + | 0.831049i | \(0.687741\pi\) | |||||||
\(114\) | −0.128321 | + | 0.271536i | −0.0120183 | + | 0.0254317i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.13341 | − | 12.3554i | −0.662321 | − | 1.14717i | ||||
\(117\) | −0.0418563 | + | 0.0343954i | −0.00386961 | + | 0.00317986i | ||||
\(118\) | 1.33193 | + | 0.768989i | 0.122614 | + | 0.0707912i | ||||
\(119\) | 3.88481 | + | 1.41395i | 0.356120 | + | 0.129617i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4085 | + | 10.4120i | 1.12805 | + | 0.946544i | ||||
\(122\) | 1.84649 | − | 2.20056i | 0.167174 | − | 0.199230i | ||||
\(123\) | 4.47770 | + | 4.52391i | 0.403740 | + | 0.407907i | ||||
\(124\) | −6.40452 | − | 2.33105i | −0.575143 | − | 0.209335i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.04425 | − | 1.27077i | −0.0930295 | − | 0.113209i | ||||
\(127\) | −7.27027 | + | 4.19749i | −0.645132 | + | 0.372467i | −0.786589 | − | 0.617477i | \(-0.788155\pi\) |
0.141456 | + | 0.989944i | \(0.454821\pi\) | |||||||
\(128\) | 10.4121 | − | 1.83594i | 0.920310 | − | 0.162276i | ||||
\(129\) | −6.14821 | + | 13.0101i | −0.541319 | + | 1.14547i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.69761 | + | 15.2989i | −0.235691 | + | 1.33667i | 0.605463 | + | 0.795874i | \(0.292988\pi\) |
−0.841154 | + | 0.540796i | \(0.818123\pi\) | |||||||
\(132\) | −9.53717 | + | 13.4727i | −0.830104 | + | 1.17265i | ||||
\(133\) | 0.354015 | + | 0.421899i | 0.0306970 | + | 0.0365833i | ||||
\(134\) | −4.58126 | −0.395761 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.98162 | −0.427170 | ||||||||
\(137\) | 7.71820 | + | 9.19820i | 0.659411 | + | 0.785855i | 0.987301 | − | 0.158861i | \(-0.0507821\pi\) |
−0.327890 | + | 0.944716i | \(0.606338\pi\) | |||||||
\(138\) | 0.311110 | + | 0.676219i | 0.0264834 | + | 0.0575636i | ||||
\(139\) | −1.06709 | + | 6.05176i | −0.0905093 | + | 0.513304i | 0.905522 | + | 0.424299i | \(0.139480\pi\) |
−0.996031 | + | 0.0890042i | \(0.971632\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.2525 | + | 1.00860i | −1.03185 | + | 0.0849392i | ||||
\(142\) | −2.48941 | + | 0.438950i | −0.208907 | + | 0.0368359i | ||||
\(143\) | −0.0815610 | + | 0.0470893i | −0.00682047 | + | 0.00393780i | ||||
\(144\) | −7.73243 | − | 4.57082i | −0.644369 | − | 0.380901i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.213544 | − | 0.0777237i | −0.0176730 | − | 0.00643246i | ||||
\(147\) | 8.80976 | − | 2.31216i | 0.726617 | − | 0.190704i | ||||
\(148\) | −5.19742 | + | 6.19404i | −0.427225 | + | 0.509147i | ||||
\(149\) | −0.676280 | − | 0.567466i | −0.0554030 | − | 0.0464886i | 0.614666 | − | 0.788788i | \(-0.289291\pi\) |
−0.670069 | + | 0.742299i | \(0.733735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.72942 | − | 2.81328i | −0.629011 | − | 0.228941i | 0.00778980 | − | 0.999970i | \(-0.497520\pi\) |
−0.636801 | + | 0.771028i | \(0.719743\pi\) | |||||||
\(152\) | −0.574740 | − | 0.331826i | −0.0466176 | − | 0.0269147i | ||||
\(153\) | 7.13717 | + | 6.11477i | 0.577006 | + | 0.494350i | ||||
\(154\) | −1.42964 | − | 2.47621i | −0.115204 | − | 0.199539i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0325434 | − | 0.0469884i | −0.00260556 | − | 0.00376208i | ||||
\(157\) | −4.29571 | − | 11.8024i | −0.342835 | − | 0.941932i | −0.984568 | − | 0.175003i | \(-0.944006\pi\) |
0.641733 | − | 0.766928i | \(-0.278216\pi\) | |||||||
\(158\) | 0.200135 | + | 0.0352893i | 0.0159219 | + | 0.00280746i | ||||
\(159\) | 0.207851 | − | 2.24305i | 0.0164836 | − | 0.177886i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.36501 | 0.107578 | ||||||||
\(162\) | −1.20646 | − | 3.53922i | −0.0947884 | − | 0.278067i | ||||
\(163\) | − | 3.31466i | − | 0.259624i | −0.991539 | − | 0.129812i | \(-0.958563\pi\) | ||
0.991539 | − | 0.129812i | \(-0.0414374\pi\) | |||||||
\(164\) | −5.14440 | + | 4.31667i | −0.401710 | + | 0.337075i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.332853 | + | 1.88770i | −0.0258344 | + | 0.146514i | ||||
\(167\) | 7.03295 | + | 19.3229i | 0.544226 | + | 1.49525i | 0.841393 | + | 0.540424i | \(0.181736\pi\) |
−0.297167 | + | 0.954826i | \(0.596042\pi\) | |||||||
\(168\) | 2.98791 | − | 2.06938i | 0.230522 | − | 0.159656i | ||||
\(169\) | 2.25737 | + | 12.8022i | 0.173644 | + | 0.984783i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.416126 | + | 1.18088i | 0.0318219 | + | 0.0903044i | ||||
\(172\) | −13.1477 | − | 7.59085i | −1.00251 | − | 0.578797i | ||||
\(173\) | −4.79966 | + | 13.1870i | −0.364911 | + | 1.00259i | 0.612357 | + | 0.790581i | \(0.290221\pi\) |
−0.977269 | + | 0.212005i | \(0.932001\pi\) | |||||||
\(174\) | 5.41917 | + | 1.48192i | 0.410827 | + | 0.112344i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.9617 | − | 10.0371i | −0.901648 | − | 0.756572i | ||||
\(177\) | 6.20169 | − | 1.62766i | 0.466148 | − | 0.122342i | ||||
\(178\) | −0.479305 | + | 1.31688i | −0.0359254 | + | 0.0987043i | ||||
\(179\) | 5.09500 | − | 8.82479i | 0.380818 | − | 0.659596i | −0.610361 | − | 0.792123i | \(-0.708976\pi\) |
0.991179 | + | 0.132527i | \(0.0423091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0274 | − | 20.8320i | −0.893987 | − | 1.54843i | −0.835054 | − | 0.550169i | \(-0.814563\pi\) |
−0.0589331 | − | 0.998262i | \(-0.518770\pi\) | |||||||
\(182\) | 0.00975037 | − | 0.00171925i | 0.000722746 | − | 0.000127440i | ||||
\(183\) | −0.982498 | − | 11.9354i | −0.0726283 | − | 0.882293i | ||||
\(184\) | −1.54563 | + | 0.562565i | −0.113946 | + | 0.0414728i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.43823 | − | 1.12176i | 0.178780 | − | 0.0822516i | ||||
\(187\) | 10.5019 | + | 12.5157i | 0.767978 | + | 0.915240i | ||||
\(188\) | − | 12.9706i | − | 0.945981i | ||||||
\(189\) | −6.82089 | − | 0.702760i | −0.496146 | − | 0.0511182i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.38541 | − | 7.03619i | 0.606747 | − | 0.509121i | −0.286860 | − | 0.957973i | \(-0.592611\pi\) |
0.893606 | + | 0.448852i | \(0.148167\pi\) | |||||||
\(192\) | 4.15316 | − | 5.86699i | 0.299729 | − | 0.423414i | ||||
\(193\) | 10.6418 | + | 1.87644i | 0.766013 | + | 0.135069i | 0.542984 | − | 0.839743i | \(-0.317294\pi\) |
0.223029 | + | 0.974812i | \(0.428405\pi\) | |||||||
\(194\) | −3.88121 | + | 1.41265i | −0.278655 | + | 0.101422i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.66867 | + | 9.46347i | 0.119190 | + | 0.675962i | ||||
\(197\) | −19.1161 | + | 11.0367i | −1.36196 | + | 0.786331i | −0.989885 | − | 0.141870i | \(-0.954689\pi\) |
−0.372080 | + | 0.928201i | \(0.621355\pi\) | |||||||
\(198\) | −1.06296 | − | 6.41270i | −0.0755413 | − | 0.455731i | ||||
\(199\) | 6.44338 | − | 11.1603i | 0.456759 | − | 0.791130i | −0.542028 | − | 0.840360i | \(-0.682343\pi\) |
0.998787 | + | 0.0492301i | \(0.0156768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5742 | + | 13.4355i | −0.957448 | + | 0.947667i | ||||
\(202\) | 3.68524 | − | 4.39190i | 0.259293 | − | 0.309013i | ||||
\(203\) | 6.62241 | − | 7.89228i | 0.464802 | − | 0.553929i | ||||
\(204\) | −7.04736 | + | 6.97537i | −0.493414 | + | 0.488374i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.948326 | − | 1.64255i | 0.0660730 | − | 0.114442i | ||||
\(207\) | 2.90496 | + | 1.09123i | 0.201909 | + | 0.0758456i | ||||
\(208\) | 0.0468255 | − | 0.0270347i | 0.00324676 | − | 0.00187452i | ||||
\(209\) | 0.377957 | + | 2.14350i | 0.0261439 | + | 0.148269i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5485 | − | 8.20699i | 1.55230 | − | 0.564992i | 0.583347 | − | 0.812223i | \(-0.301743\pi\) |
0.968957 | + | 0.247230i | \(0.0795204\pi\) | |||||||
\(212\) | 2.34055 | + | 0.412702i | 0.160749 | + | 0.0283445i | ||||
\(213\) | −6.08875 | + | 8.60131i | −0.417194 | + | 0.589352i | ||||
\(214\) | −3.59528 | + | 3.01680i | −0.245768 | + | 0.206224i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.01311 | − | 2.01536i | 0.545223 | − | 0.137128i | ||||
\(217\) | − | 4.92177i | − | 0.334112i | ||||||
\(218\) | 3.87317 | + | 4.61587i | 0.262324 | + | 0.312626i | ||||
\(219\) | −0.860667 | + | 0.395969i | −0.0581585 | + | 0.0267571i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0531618 | + | 0.0193493i | −0.00357605 | + | 0.00130158i | ||||
\(222\) | −0.261224 | − | 3.17336i | −0.0175322 | − | 0.212982i | ||||
\(223\) | 21.3331 | − | 3.76160i | 1.42857 | − | 0.251895i | 0.594740 | − | 0.803918i | \(-0.297255\pi\) |
0.833829 | + | 0.552023i | \(0.186144\pi\) | |||||||
\(224\) | 2.91919 | + | 5.05618i | 0.195047 | + | 0.337831i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.60880 | − | 4.51858i | 0.173535 | − | 0.300571i | ||||
\(227\) | 7.40196 | − | 20.3367i | 0.491285 | − | 1.34979i | −0.408220 | − | 0.912884i | \(-0.633850\pi\) |
0.899505 | − | 0.436911i | \(-0.143928\pi\) | |||||||
\(228\) | −1.27770 | + | 0.335338i | −0.0846178 | + | 0.0222083i | ||||
\(229\) | 8.27739 | + | 6.94555i | 0.546985 | + | 0.458975i | 0.873919 | − | 0.486072i | \(-0.161571\pi\) |
−0.326934 | + | 0.945047i | \(0.606015\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.4980 | − | 3.14424i | −0.756513 | − | 0.206876i | ||||
\(232\) | −4.24606 | + | 11.6660i | −0.278768 | + | 0.765908i | ||||
\(233\) | 6.61557 | + | 3.81950i | 0.433400 | + | 0.250224i | 0.700794 | − | 0.713364i | \(-0.252829\pi\) |
−0.267394 | + | 0.963587i | \(0.586162\pi\) | |||||||
\(234\) | 0.0221249 | + | 0.00413588i | 0.00144635 | + | 0.000270371i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.17467 | + | 6.66187i | 0.0764644 | + | 0.433651i | ||||
\(237\) | 0.696490 | − | 0.482377i | 0.0452419 | − | 0.0313338i | ||||
\(238\) | −0.587451 | − | 1.61401i | −0.0380788 | − | 0.104621i | ||||
\(239\) | 0.561143 | − | 3.18240i | 0.0362973 | − | 0.205852i | −0.961266 | − | 0.275623i | \(-0.911116\pi\) |
0.997563 | + | 0.0697711i | \(0.0222269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3346 | + | 17.0628i | −1.30987 | + | 1.09911i | −0.321518 | + | 0.946903i | \(0.604193\pi\) |
−0.988349 | + | 0.152206i | \(0.951362\pi\) | |||||||
\(242\) | − | 6.72979i | − | 0.432608i | ||||||
\(243\) | −13.9542 | − | 6.94842i | −0.895162 | − | 0.445741i | ||||
\(244\) | 12.6350 | 0.808873 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.244007 | − | 2.63324i | 0.0155573 | − | 0.167889i | ||||
\(247\) | −0.00742226 | − | 0.00130875i | −0.000472267 | − | 8.32735e-5i | ||||
\(248\) | 2.02843 | + | 5.57306i | 0.128805 | + | 0.353890i | ||||
\(249\) | 4.54985 | + | 6.56938i | 0.288335 | + | 0.416318i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.24965 | + | 3.89651i | 0.141997 | + | 0.245945i | 0.928248 | − | 0.371961i | \(-0.121314\pi\) |
−0.786252 | + | 0.617906i | \(0.787981\pi\) | |||||||
\(252\) | 1.32933 | − | 7.11124i | 0.0837399 | − | 0.447966i | ||||
\(253\) | 4.67179 | + | 2.69726i | 0.293713 | + | 0.169575i | ||||
\(254\) | 3.27749 | + | 1.19291i | 0.205648 | + | 0.0748498i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.99340 | + | 2.51176i | 0.187088 | + | 0.156985i | ||||
\(257\) | −8.82895 | + | 10.5219i | −0.550735 | + | 0.656340i | −0.967559 | − | 0.252647i | \(-0.918699\pi\) |
0.416824 | + | 0.908987i | \(0.363143\pi\) | |||||||
\(258\) | 5.78258 | − | 1.51766i | 0.360007 | − | 0.0944854i | ||||
\(259\) | −5.48690 | − | 1.99707i | −0.340939 | − | 0.124092i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.4029 | − | 11.5020i | 1.26291 | − | 0.711953i | ||||
\(262\) | 5.58952 | − | 3.22711i | 0.345322 | − | 0.199372i | ||||
\(263\) | −23.8349 | + | 4.20273i | −1.46972 | + | 0.259151i | −0.850462 | − | 0.526036i | \(-0.823678\pi\) |
−0.619258 | + | 0.785187i | \(0.712567\pi\) | |||||||
\(264\) | 14.3154 | − | 1.17841i | 0.881049 | − | 0.0725260i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0397339 | − | 0.225342i | 0.00243624 | − | 0.0138166i | ||||
\(267\) | 2.44185 | + | 5.30755i | 0.149439 | + | 0.324817i | ||||
\(268\) | −12.9523 | − | 15.4360i | −0.791189 | − | 0.942902i | ||||
\(269\) | −12.0062 | −0.732032 | −0.366016 | − | 0.930609i | \(-0.619278\pi\) | ||||
−0.366016 | + | 0.930609i | \(0.619278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.71777 | 0.225839 | 0.112919 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112919 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(272\) | −6.02933 | − | 7.18547i | −0.365582 | − | 0.435683i | ||||
\(273\) | 0.0238481 | − | 0.0336891i | 0.00144335 | − | 0.00203896i | ||||
\(274\) | 0.866273 | − | 4.91288i | 0.0523335 | − | 0.296798i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.39885 | + | 2.96008i | −0.0842011 | + | 0.178176i | ||||
\(277\) | 23.1264 | − | 4.07780i | 1.38953 | − | 0.245011i | 0.571695 | − | 0.820466i | \(-0.306286\pi\) |
0.817833 | + | 0.575455i | \(0.195175\pi\) | |||||||
\(278\) | 2.21104 | − | 1.27654i | 0.132609 | − | 0.0765621i | ||||
\(279\) | 3.93462 | − | 10.4744i | 0.235559 | − | 0.627084i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1432 | + | 6.96754i | 1.14199 | + | 0.415649i | 0.842630 | − | 0.538493i | \(-0.181006\pi\) |
0.299356 | + | 0.954142i | \(0.403228\pi\) | |||||||
\(282\) | 3.59311 | + | 3.63020i | 0.213967 | + | 0.216175i | ||||
\(283\) | 7.45630 | − | 8.88607i | 0.443231 | − | 0.528222i | −0.497460 | − | 0.867487i | \(-0.665734\pi\) |
0.940691 | + | 0.339265i | \(0.110178\pi\) | |||||||
\(284\) | −8.51714 | − | 7.14673i | −0.505399 | − | 0.424080i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0367683 | + | 0.0133826i | 0.00217416 | + | 0.000791328i | ||||
\(287\) | −4.19984 | − | 2.42478i | −0.247909 | − | 0.143130i | ||||
\(288\) | 2.17046 | + | 13.0941i | 0.127896 | + | 0.771578i | ||||
\(289\) | −3.59280 | − | 6.22291i | −0.211341 | − | 0.366053i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.35706 | + | 15.5681i | −0.431279 | + | 0.912618i | ||||
\(292\) | −0.341860 | − | 0.939253i | −0.0200058 | − | 0.0549656i | ||||
\(293\) | −31.0945 | − | 5.48280i | −1.81656 | − | 0.320308i | −0.841165 | − | 0.540779i | \(-0.818130\pi\) |
−0.975394 | + | 0.220470i | \(0.929241\pi\) | |||||||
\(294\) | −3.08858 | − | 2.18637i | −0.180130 | − | 0.127511i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.03603 | 0.408961 | ||||||||
\(297\) | −21.9561 | − | 15.8833i | −1.27402 | − | 0.921644i | ||||
\(298\) | 0.366782i | 0.0212471i | ||||||||
\(299\) | −0.0143093 | + | 0.0120069i | −0.000827529 | + | 0.000694379i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.90376 | − | 10.7968i | 0.109731 | − | 0.622315i | ||||
\(302\) | 1.16882 | + | 3.21131i | 0.0672581 | + | 0.184790i | ||||
\(303\) | −1.96088 | − | 23.8208i | −0.112649 | − | 1.36847i | ||||
\(304\) | −0.216991 | − | 1.23062i | −0.0124453 | − | 0.0705809i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.0400924 | − | 3.90451i | 0.00229193 | − | 0.223206i | ||||
\(307\) | 7.03259 | + | 4.06027i | 0.401371 | + | 0.231732i | 0.687075 | − | 0.726586i | \(-0.258894\pi\) |
−0.285704 | + | 0.958318i | \(0.592227\pi\) | |||||||
\(308\) | 4.30134 | − | 11.8178i | 0.245092 | − | 0.673384i | ||||
\(309\) | −2.00725 | − | 7.64800i | −0.114188 | − | 0.435079i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.2691 | − | 15.3296i | −1.03594 | − | 0.869259i | −0.0443970 | − | 0.999014i | \(-0.514137\pi\) |
−0.991546 | + | 0.129754i | \(0.958581\pi\) | |||||||
\(312\) | −0.0131194 | + | 0.0479757i | −0.000742740 | + | 0.00271609i | ||||
\(313\) | −9.20392 | + | 25.2876i | −0.520236 | + | 1.42934i | 0.350022 | + | 0.936742i | \(0.386174\pi\) |
−0.870258 | + | 0.492596i | \(0.836048\pi\) | |||||||
\(314\) | −2.60909 | + | 4.51908i | −0.147240 | + | 0.255026i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.446928 | + | 0.774102i | 0.0251417 | + | 0.0435466i | ||||
\(317\) | 8.20574 | − | 1.44689i | 0.460881 | − | 0.0812657i | 0.0616130 | − | 0.998100i | \(-0.480376\pi\) |
0.399268 | + | 0.916834i | \(0.369264\pi\) | |||||||
\(318\) | −0.769394 | + | 0.532870i | −0.0431455 | + | 0.0298819i | ||||
\(319\) | 38.2606 | − | 13.9257i | 2.14218 | − | 0.779692i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.80534 | + | 19.4826i | −0.100764 | + | 1.08741i | ||||
\(322\) | −0.364534 | − | 0.434435i | −0.0203147 | − | 0.0242101i | ||||
\(323\) | 1.30748i | 0.0727501i | ||||||||
\(324\) | 8.51398 | − | 14.0712i | 0.472999 | − | 0.781734i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.05494 | + | 0.885201i | −0.0584278 | + | 0.0490268i | ||||
\(327\) | 25.0131 | + | 2.31782i | 1.38323 | + | 0.128176i | ||||
\(328\) | 5.75493 | + | 1.01475i | 0.317763 | + | 0.0560301i | ||||
\(329\) | 8.80173 | − | 3.20357i | 0.485255 | − | 0.176618i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.11487 | − | 6.32272i | −0.0612786 | − | 0.347528i | −0.999996 | − | 0.00284030i | \(-0.999096\pi\) |
0.938717 | − | 0.344688i | \(-0.112015\pi\) | |||||||
\(332\) | −7.30143 | + | 4.21548i | −0.400718 | + | 0.231355i | ||||
\(333\) | −10.0805 | − | 8.63650i | −0.552410 | − | 0.473277i | ||||
\(334\) | 4.27161 | − | 7.39865i | 0.233732 | − | 0.404836i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.60119 | + | 1.80516i | 0.360124 | + | 0.0984794i | ||||
\(337\) | −4.80477 | + | 5.72610i | −0.261732 | + | 0.311921i | −0.880867 | − | 0.473365i | \(-0.843039\pi\) |
0.619134 | + | 0.785285i | \(0.287484\pi\) | |||||||
\(338\) | 3.47165 | − | 4.13735i | 0.188833 | − | 0.225042i | ||||
\(339\) | −5.52185 | − | 21.0393i | −0.299906 | − | 1.14270i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.72545 | − | 16.8450i | 0.526663 | − | 0.912206i | ||||
\(342\) | 0.264706 | − | 0.447801i | 0.0143136 | − | 0.0242143i | ||||
\(343\) | −14.0095 | + | 8.08839i | −0.756442 | + | 0.436732i | ||||
\(344\) | 2.29403 | + | 13.0101i | 0.123686 | + | 0.701456i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.47874 | − | 1.99410i | 0.294539 | − | 0.107203i | ||||
\(347\) | −30.9766 | − | 5.46202i | −1.66291 | − | 0.293216i | −0.738399 | − | 0.674364i | \(-0.764418\pi\) |
−0.924514 | + | 0.381148i | \(0.875529\pi\) | |||||||
\(348\) | 10.3281 | + | 22.4490i | 0.553647 | + | 1.20339i | ||||
\(349\) | −9.07988 | + | 7.61893i | −0.486035 | + | 0.407832i | −0.852603 | − | 0.522560i | \(-0.824977\pi\) |
0.366568 | + | 0.930391i | \(0.380533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0776848 | − | 0.0526312i | 0.00414651 | − | 0.00280925i | ||||
\(352\) | 23.0733i | 1.22981i | ||||||||
\(353\) | 5.27541 | + | 6.28699i | 0.280782 | + | 0.334623i | 0.887941 | − | 0.459958i | \(-0.152135\pi\) |
−0.607159 | + | 0.794580i | \(0.707691\pi\) | |||||||
\(354\) | −2.17423 | − | 1.53911i | −0.115559 | − | 0.0818026i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.79217 | + | 2.10818i | −0.306984 | + | 0.111733i | ||||
\(357\) | −6.47401 | − | 3.05944i | −0.342641 | − | 0.161923i | ||||
\(358\) | −4.16928 | + | 0.735157i | −0.220353 | + | 0.0388542i | ||||
\(359\) | 8.86365 | + | 15.3523i | 0.467806 | + | 0.810263i | 0.999323 | − | 0.0367840i | \(-0.0117114\pi\) |
−0.531517 | + | 0.847047i | \(0.678378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.41291 | − | 16.3036i | 0.495416 | − | 0.858086i | ||||
\(362\) | −3.41812 | + | 9.39122i | −0.179653 | + | 0.493591i | ||||
\(363\) | −19.7365 | − | 19.9402i | −1.03590 | − | 1.04659i | ||||
\(364\) | 0.0333594 | + | 0.0279919i | 0.00174851 | + | 0.00146717i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.53626 | + | 3.50013i | −0.184843 | + | 0.182955i | ||||
\(367\) | −6.94969 | + | 19.0941i | −0.362771 | + | 0.996704i | 0.615275 | + | 0.788313i | \(0.289045\pi\) |
−0.978045 | + | 0.208392i | \(0.933177\pi\) | |||||||
\(368\) | −2.68215 | − | 1.54854i | −0.139817 | − | 0.0807232i | ||||
\(369\) | −6.99953 | − | 8.51782i | −0.364381 | − | 0.443420i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.298028 | + | 1.69020i | 0.0154728 | + | 0.0877509i | ||||
\(372\) | 10.6731 | + | 5.04381i | 0.553374 | + | 0.261510i | ||||
\(373\) | −3.31125 | − | 9.09758i | −0.171450 | − | 0.471055i | 0.823972 | − | 0.566630i | \(-0.191753\pi\) |
−0.995422 | + | 0.0955754i | \(0.969531\pi\) | |||||||
\(374\) | 1.17871 | − | 6.68481i | 0.0609498 | − | 0.345663i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.64615 | + | 7.25498i | −0.445891 | + | 0.374147i | ||||
\(377\) | 0.140987i | 0.00726119i | ||||||||
\(378\) | 1.59790 | + | 2.35853i | 0.0821870 | + | 0.121310i | ||||
\(379\) | 4.12905 | 0.212095 | 0.106048 | − | 0.994361i | \(-0.466180\pi\) | ||||
0.106048 | + | 0.994361i | \(0.466180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.2096 | − | 6.07736i | 0.676748 | − | 0.311353i | ||||
\(382\) | −4.47876 | − | 0.789725i | −0.229153 | − | 0.0404059i | ||||
\(383\) | 1.62466 | + | 4.46371i | 0.0830162 | + | 0.228085i | 0.974255 | − | 0.225450i | \(-0.0723851\pi\) |
−0.891239 | + | 0.453535i | \(0.850163\pi\) | |||||||
\(384\) | −18.2508 | + | 1.50236i | −0.931357 | + | 0.0766672i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.24476 | − | 3.88803i | −0.114255 | − | 0.197896i | ||||
\(387\) | 12.6828 | − | 21.4554i | 0.644702 | − | 1.09064i | ||||
\(388\) | −15.7328 | − | 9.08336i | −0.798714 | − | 0.461138i | ||||
\(389\) | −20.4978 | − | 7.46059i | −1.03928 | − | 0.378267i | −0.234673 | − | 0.972074i | \(-0.575402\pi\) |
−0.804607 | + | 0.593807i | \(0.797624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.48238 | + | 2.08297i | 0.125539 | + | 0.105340i | ||||
\(392\) | 5.37495 | − | 6.40561i | 0.271476 | − | 0.323532i | ||||
\(393\) | 7.09745 | − | 25.9543i | 0.358019 | − | 1.30922i | ||||
\(394\) | 8.61767 | + | 3.13658i | 0.434152 | + | 0.158018i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 18.6015 | − | 21.7117i | 0.934762 | − | 1.09106i | ||||
\(397\) | −30.1802 | + | 17.4245i | −1.51470 | + | 0.874512i | −0.514847 | + | 0.857282i | \(0.672151\pi\) |
−0.999852 | + | 0.0172294i | \(0.994515\pi\) | |||||||
\(398\) | −5.27268 | + | 0.929715i | −0.264295 | + | 0.0466024i | ||||
\(399\) | −0.543131 | − | 0.784210i | −0.0271906 | − | 0.0392596i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.26911 | + | 18.5401i | −0.163252 | + | 0.925847i | 0.787597 | + | 0.616191i | \(0.211325\pi\) |
−0.950849 | + | 0.309656i | \(0.899786\pi\) | |||||||
\(402\) | 7.90113 | + | 0.732152i | 0.394072 | + | 0.0365164i | ||||
\(403\) | 0.0432932 | + | 0.0515948i | 0.00215659 | + | 0.00257012i | ||||
\(404\) | 25.2170 | 1.25459 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.28040 | −0.212433 | ||||||||
\(407\) | −14.8329 | − | 17.6772i | −0.735241 | − | 0.876226i | ||||
\(408\) | 8.59160 | + | 0.796135i | 0.425348 | + | 0.0394145i | ||||
\(409\) | 1.10439 | − | 6.26334i | 0.0546088 | − | 0.309702i | −0.945253 | − | 0.326339i | \(-0.894185\pi\) |
0.999862 | + | 0.0166371i | \(0.00529599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8413 | − | 17.0973i | −0.584088 | − | 0.843346i | ||||
\(412\) | 8.21551 | − | 1.44862i | 0.404749 | − | 0.0713682i | ||||
\(413\) | −4.23055 | + | 2.44251i | −0.208172 | + | 0.120188i | ||||
\(414\) | −0.428490 | − | 1.21597i | −0.0210591 | − | 0.0597617i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0750772 | − | 0.0273259i | −0.00368096 | − | 0.00133976i | ||||
\(417\) | 2.80753 | − | 10.2667i | 0.137485 | − | 0.502763i | ||||
\(418\) | 0.581267 | − | 0.692727i | 0.0284307 | − | 0.0338824i | ||||
\(419\) | 18.6286 | + | 15.6313i | 0.910069 | + | 0.763638i | 0.972132 | − | 0.234434i | \(-0.0753236\pi\) |
−0.0620632 | + | 0.998072i | \(0.519768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.50818 | + | 2.73275i | 0.365926 | + | 0.133186i | 0.518438 | − | 0.855115i | \(-0.326514\pi\) |
−0.152511 | + | 0.988302i | \(0.548736\pi\) | |||||||
\(422\) | −8.63373 | − | 4.98469i | −0.420283 | − | 0.242651i | ||||
\(423\) | 21.2926 | + | 0.218637i | 1.03528 | + | 0.0106305i | ||||
\(424\) | −1.03405 | − | 1.79103i | −0.0502181 | − | 0.0869803i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.36354 | − | 0.359197i | 0.211414 | − | 0.0174031i | ||||
\(427\) | 3.12067 | + | 8.57397i | 0.151020 | + | 0.414924i | ||||
\(428\) | −20.3294 | − | 3.58462i | −0.982659 | − | 0.173269i | ||||
\(429\) | 0.148191 | − | 0.0681784i | 0.00715472 | − | 0.00329169i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.87124 | 0.475481 | 0.237740 | − | 0.971329i | \(-0.423593\pi\) | ||||
0.237740 | + | 0.971329i | \(0.423593\pi\) | |||||||
\(432\) | 12.6053 | + | 9.11887i | 0.606475 | + | 0.438732i | ||||
\(433\) | 6.10369i | 0.293325i | 0.989187 | + | 0.146662i | \(0.0468531\pi\) | ||||
−0.989187 | + | 0.146662i | \(0.953147\pi\) | |||||||
\(434\) | −1.56643 | + | 1.31439i | −0.0751911 | + | 0.0630928i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.60219 | + | 26.1003i | −0.220405 | + | 1.24998i | ||||
\(437\) | 0.147651 | + | 0.405669i | 0.00706312 | + | 0.0194058i | ||||
\(438\) | 0.355870 | + | 0.168174i | 0.0170041 | + | 0.00803569i | ||||
\(439\) | 2.62800 | + | 14.9041i | 0.125427 | + | 0.711334i | 0.981053 | + | 0.193739i | \(0.0620615\pi\) |
−0.855626 | + | 0.517595i | \(0.826827\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.5634 | + | 2.57976i | −0.741113 | + | 0.122846i | ||||
\(442\) | 0.0203554 | + | 0.0117522i | 0.000968210 | + | 0.000558996i | ||||
\(443\) | 0.247210 | − | 0.679204i | 0.0117453 | − | 0.0322699i | −0.933681 | − | 0.358105i | \(-0.883423\pi\) |
0.945427 | + | 0.325835i | \(0.105645\pi\) | |||||||
\(444\) | 9.95369 | − | 9.85201i | 0.472381 | − | 0.467555i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.89432 | − | 5.78502i | −0.326456 | − | 0.273929i | ||||
\(447\) | 1.07566 | + | 1.08677i | 0.0508772 | + | 0.0514023i | ||||
\(448\) | −1.87311 | + | 5.14633i | −0.0884962 | + | 0.243141i | ||||
\(449\) | 0.834224 | − | 1.44492i | 0.0393695 | − | 0.0681899i | −0.845669 | − | 0.533707i | \(-0.820798\pi\) |
0.885039 | + | 0.465517i | \(0.154132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.58275 | − | 16.5978i | −0.451234 | − | 0.781560i | ||||
\(452\) | 22.6005 | − | 3.98507i | 1.06304 | − | 0.187442i | ||||
\(453\) | 12.8810 | + | 6.08723i | 0.605204 | + | 0.286003i | ||||
\(454\) | −8.44922 | + | 3.07526i | −0.396541 | + | 0.144329i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.938202 | + | 0.664140i | 0.0439353 | + | 0.0311012i | ||||
\(457\) | 7.12430 | + | 8.49041i | 0.333261 | + | 0.397165i | 0.906488 | − | 0.422232i | \(-0.138753\pi\) |
−0.573227 | + | 0.819397i | \(0.694309\pi\) | |||||||
\(458\) | − | 4.48926i | − | 0.209769i | ||||||
\(459\) | −11.3320 | − | 11.6865i | −0.528932 | − | 0.545481i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.7644 | + | 14.0670i | −0.780797 | + | 0.655166i | −0.943449 | − | 0.331517i | \(-0.892439\pi\) |
0.162653 | + | 0.986683i | \(0.447995\pi\) | |||||||
\(462\) | 2.06992 | + | 4.49911i | 0.0963012 | + | 0.209318i | ||||
\(463\) | −24.4742 | − | 4.31546i | −1.13741 | − | 0.200556i | −0.426938 | − | 0.904281i | \(-0.640408\pi\) |
−0.710473 | + | 0.703724i | \(0.751519\pi\) | |||||||
\(464\) | −21.9660 | + | 7.99499i | −1.01975 | + | 0.371158i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.551115 | − | 3.12553i | −0.0255299 | − | 0.144787i | ||||
\(467\) | −10.2499 | + | 5.91777i | −0.474308 | + | 0.273842i | −0.718041 | − | 0.696001i | \(-0.754961\pi\) |
0.243734 | + | 0.969842i | \(0.421628\pi\) | |||||||
\(468\) | 0.0486170 | + | 0.0862400i | 0.00224732 | + | 0.00398645i | ||||
\(469\) | 7.27564 | − | 12.6018i | 0.335958 | − | 0.581896i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.52246 | + | 21.0416i | 0.254462 | + | 0.969547i | ||||
\(472\) | 3.78373 | − | 4.50927i | 0.174160 | − | 0.207556i | ||||
\(473\) | 27.8501 | − | 33.1905i | 1.28055 | − | 1.52610i | ||||
\(474\) | −0.339526 | − | 0.0928466i | −0.0155950 | − | 0.00426459i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.77733 | − | 6.54252i | 0.173134 | − | 0.299876i | ||||
\(477\) | −0.716944 | + | 3.83529i | −0.0328266 | + | 0.175606i | ||||
\(478\) | −1.16270 | + | 0.671288i | −0.0531809 | + | 0.0307040i | ||||
\(479\) | −0.501383 | − | 2.84349i | −0.0229088 | − | 0.129922i | 0.971209 | − | 0.238231i | \(-0.0765676\pi\) |
−0.994117 | + | 0.108309i | \(0.965456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0750857 | − | 0.0273290i | 0.00342361 | − | 0.00124609i | ||||
\(482\) | 10.8610 | + | 1.91508i | 0.494704 | + | 0.0872297i | ||||
\(483\) | −2.35417 | − | 0.218148i | −0.107119 | − | 0.00992607i | ||||
\(484\) | 22.6752 | − | 19.0267i | 1.03069 | − | 0.864852i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.51512 | + | 6.29676i | 0.0687271 | + | 0.285627i | ||||
\(487\) | 8.75903i | 0.396910i | 0.980110 | + | 0.198455i | \(0.0635923\pi\) | ||||
−0.980110 | + | 0.198455i | \(0.936408\pi\) | |||||||
\(488\) | −7.06724 | − | 8.42241i | −0.319919 | − | 0.381265i | ||||
\(489\) | −0.529731 | + | 5.71667i | −0.0239553 | + | 0.258517i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.2117 | − | 7.72044i | 0.957272 | − | 0.348418i | 0.184308 | − | 0.982869i | \(-0.440996\pi\) |
0.772964 | + | 0.634450i | \(0.218773\pi\) | |||||||
\(492\) | 9.56222 | − | 6.62264i | 0.431098 | − | 0.298572i | ||||
\(493\) | 24.0869 | − | 4.24716i | 1.08482 | − | 0.191283i | ||||
\(494\) | 0.00156564 | + | 0.00271176i | 7.04413e−5 | + | 0.000122008i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.58354 | + | 9.67097i | −0.250708 | + | 0.434239i | ||||
\(497\) | 2.74608 | − | 7.54478i | 0.123178 | − | 0.338430i | ||||
\(498\) | 0.875741 | − | 3.20246i | 0.0392429 | − | 0.143505i | ||||
\(499\) | 19.4061 | + | 16.2836i | 0.868734 | + | 0.728955i | 0.963831 | − | 0.266513i | \(-0.0858716\pi\) |
−0.0950968 | + | 0.995468i | \(0.530316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.04139 | − | 34.4494i | −0.403940 | − | 1.53909i | ||||
\(502\) | 0.639340 | − | 1.75657i | 0.0285352 | − | 0.0783997i | ||||
\(503\) | 3.24252 | + | 1.87207i | 0.144577 | + | 0.0834714i | 0.570543 | − | 0.821267i | \(-0.306733\pi\) |
−0.425967 | + | 0.904739i | \(0.640066\pi\) | |||||||
\(504\) | −5.48386 | + | 3.09147i | −0.244270 | + | 0.137705i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.389187 | − | 2.20719i | −0.0173015 | − | 0.0981216i | ||||
\(507\) | −1.84723 | − | 22.4402i | −0.0820382 | − | 0.996604i | ||||
\(508\) | 5.24690 | + | 14.4157i | 0.232793 | + | 0.639595i | ||||
\(509\) | −4.22831 | + | 23.9800i | −0.187417 | + | 1.06289i | 0.735394 | + | 0.677640i | \(0.236997\pi\) |
−0.922811 | + | 0.385253i | \(0.874114\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.552932 | − | 0.463965i | 0.0244603 | − | 0.0205246i | ||||
\(512\) | − | 22.7690i | − | 1.00626i | ||||||
\(513\) | −0.528954 | − | 2.10313i | −0.0233539 | − | 0.0928554i | ||||
\(514\) | 5.70660 | 0.251707 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.4623 | + | 15.1929i | 0.944824 | + | 0.668828i | ||||
\(517\) | 36.4546 | + | 6.42792i | 1.60327 | + | 0.282700i | ||||
\(518\) | 0.829715 | + | 2.27962i | 0.0364556 | + | 0.100161i | ||||
\(519\) | 10.3853 | − | 21.9760i | 0.455862 | − | 0.964639i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.81046 | − | 16.9922i | −0.429804 | − | 0.744443i | 0.567051 | − | 0.823682i | \(-0.308084\pi\) |
−0.996856 | + | 0.0792397i | \(0.974751\pi\) | |||||||
\(522\) | −9.10941 | − | 3.42188i | −0.398708 | − | 0.149772i | ||||
\(523\) | 18.0267 | + | 10.4077i | 0.788251 | + | 0.455097i | 0.839346 | − | 0.543597i | \(-0.182938\pi\) |
−0.0510956 | + | 0.998694i | \(0.516271\pi\) | |||||||
\(524\) | 26.6763 | + | 9.70937i | 1.16536 | + | 0.424156i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.70284 | + | 6.46345i | 0.335860 | + | 0.281820i | ||||
\(527\) | 7.51051 | − | 8.95067i | 0.327163 | − | 0.389897i | ||||
\(528\) | 19.0258 | + | 19.2222i | 0.827993 | + | 0.836539i | ||||
\(529\) | −20.6075 | − | 7.50052i | −0.895978 | − | 0.326109i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9559 | + | 1.81604i | −0.475447 | + | 0.0788095i | ||||
\(532\) | 0.871598 | − | 0.503217i | 0.0377886 | − | 0.0218172i | ||||
\(533\) | 0.0653558 | − | 0.0115240i | 0.00283087 | − | 0.000499159i | ||||
\(534\) | 1.03710 | − | 2.19457i | 0.0448795 | − | 0.0949685i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.04479 | + | 17.2679i | −0.131515 | + | 0.745859i | ||||
\(537\) | −10.1975 | + | 14.4055i | −0.440054 | + | 0.621645i | ||||
\(538\) | 3.20634 | + | 3.82117i | 0.138235 | + | 0.164742i | ||||
\(539\) | −27.4245 | −1.18126 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.6272 | −1.31676 | −0.658382 | − | 0.752684i | \(-0.728759\pi\) | ||||
−0.658382 | + | 0.752684i | \(0.728759\pi\) | |||||||
\(542\) | −0.992856 | − | 1.18324i | −0.0426468 | − | 0.0508245i | ||||
\(543\) | 17.4139 | + | 37.8503i | 0.747301 | + | 1.62431i | ||||
\(544\) | −2.40681 | + | 13.6497i | −0.103191 | + | 0.585227i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.0170909 | + | 0.00140688i | −0.000731421 | + | 6.02089e-5i | ||||
\(547\) | −22.3036 | + | 3.93273i | −0.953633 | + | 0.168151i | −0.628754 | − | 0.777604i | \(-0.716435\pi\) |
−0.324879 | + | 0.945756i | \(0.605324\pi\) | |||||||
\(548\) | 19.0025 | − | 10.9711i | 0.811745 | − | 0.468661i | ||||
\(549\) | −0.212980 | + | 20.7416i | −0.00908976 | + | 0.885231i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.06186 | + | 1.11443i | 0.130440 | + | 0.0474761i | ||||
\(552\) | 2.75560 | − | 0.723220i | 0.117286 | − | 0.0307823i | ||||
\(553\) | −0.414912 | + | 0.494473i | −0.0176439 | + | 0.0210271i | ||||
\(554\) | −7.47387 | − | 6.27132i | −0.317534 | − | 0.266443i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.5523 | + | 3.84072i | 0.447517 | + | 0.162883i | ||||
\(557\) | −31.5682 | − | 18.2259i | −1.33759 | − | 0.772256i | −0.351138 | − | 0.936324i | \(-0.614205\pi\) |
−0.986449 | + | 0.164067i | \(0.947539\pi\) | |||||||
\(558\) | −4.38440 | + | 1.54500i | −0.185606 | + | 0.0654049i | ||||
\(559\) | 0.0750139 | + | 0.129928i | 0.00317275 | + | 0.00549537i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.1121 | − | 23.2637i | −0.680253 | − | 0.982196i | ||||
\(562\) | −2.89478 | − | 7.95334i | −0.122109 | − | 0.335491i | ||||
\(563\) | −26.1134 | − | 4.60450i | −1.10055 | − | 0.194056i | −0.406263 | − | 0.913756i | \(-0.633168\pi\) |
−0.694285 | + | 0.719700i | \(0.744279\pi\) | |||||||
\(564\) | −2.07290 | + | 22.3700i | −0.0872847 | + | 0.941945i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.81938 | −0.202574 | ||||||||
\(567\) | 11.6514 | + | 2.30210i | 0.489313 | + | 0.0966791i | ||||
\(568\) | 9.67492i | 0.405950i | ||||||||
\(569\) | −17.5941 | + | 14.7632i | −0.737581 | + | 0.618904i | −0.932187 | − | 0.361978i | \(-0.882102\pi\) |
0.194606 | + | 0.980882i | \(0.437657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.833165 | + | 4.72511i | −0.0348669 | + | 0.197740i | −0.997266 | − | 0.0739009i | \(-0.976455\pi\) |
0.962399 | + | 0.271641i | \(0.0875662\pi\) | |||||||
\(572\) | 0.0588619 | + | 0.161722i | 0.00246114 | + | 0.00676193i | ||||
\(573\) | −15.5865 | + | 10.7949i | −0.651134 | + | 0.450965i | ||||
\(574\) | 0.349871 | + | 1.98422i | 0.0146033 | + | 0.0828197i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.10043 | + | 9.45484i | −0.337518 | + | 0.393952i | ||||
\(577\) | 3.73545 | + | 2.15666i | 0.155509 | + | 0.0897831i | 0.575735 | − | 0.817636i | \(-0.304716\pi\) |
−0.420226 | + | 0.907419i | \(0.638049\pi\) | |||||||
\(578\) | −1.02106 | + | 2.80533i | −0.0424704 | + | 0.116686i | ||||
\(579\) | −18.0536 | − | 4.93693i | −0.750283 | − | 0.205172i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.66393 | − | 3.91351i | −0.193493 | − | 0.162360i | ||||
\(582\) | 6.91954 | − | 1.81606i | 0.286824 | − | 0.0752782i | ||||
\(583\) | −2.31983 | + | 6.37369i | −0.0960777 | + | 0.263971i | ||||
\(584\) | −0.434885 | + | 0.753242i | −0.0179957 | + | 0.0311694i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.55900 | + | 11.3605i | 0.270950 | + | 0.469299i | ||||
\(587\) | −41.1868 | + | 7.26235i | −1.69996 | + | 0.299749i | −0.937681 | − | 0.347497i | \(-0.887032\pi\) |
−0.762281 | + | 0.647246i | \(0.775921\pi\) | |||||||
\(588\) | −1.36548 | − | 16.5880i | −0.0563116 | − | 0.684076i | ||||
\(589\) | 1.46271 | − | 0.532383i | 0.0602699 | − | 0.0219365i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.7326 | − | 15.9795i | 1.42871 | − | 0.657309i | ||||
\(592\) | 8.51582 | + | 10.1488i | 0.349998 | + | 0.417111i | ||||
\(593\) | 31.5370i | 1.29507i | 0.762035 | + | 0.647536i | \(0.224200\pi\) | ||||
−0.762035 | + | 0.647536i | \(0.775800\pi\) | |||||||
\(594\) | 0.808405 | + | 11.2296i | 0.0331693 | + | 0.460757i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.23583 | + | 1.03698i | −0.0506214 | + | 0.0424764i | ||||
\(597\) | −12.8962 | + | 18.2179i | −0.527807 | + | 0.745611i | ||||
\(598\) | 0.00764279 | + | 0.00134763i | 0.000312537 | + | 5.51087e-5i | ||||
\(599\) | −11.8686 | + | 4.31982i | −0.484938 | + | 0.176503i | −0.572907 | − | 0.819620i | \(-0.694184\pi\) |
0.0879695 | + | 0.996123i | \(0.471962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.56725 | + | 20.2309i | 0.145511 | + | 0.825235i | 0.966955 | + | 0.254946i | \(0.0820577\pi\) |
−0.821444 | + | 0.570289i | \(0.806831\pi\) | |||||||
\(602\) | −3.94465 | + | 2.27744i | −0.160772 | + | 0.0928216i | ||||
\(603\) | 25.5580 | − | 21.0023i | 1.04080 | − | 0.855282i | ||||
\(604\) | −7.51556 | + | 13.0173i | −0.305804 | + | 0.529668i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.05769 | + | 6.98559i | −0.286699 | + | 0.283770i | ||||
\(607\) | −8.30003 | + | 9.89160i | −0.336888 | + | 0.401487i | −0.907718 | − | 0.419581i | \(-0.862177\pi\) |
0.570830 | + | 0.821068i | \(0.306622\pi\) | |||||||
\(608\) | −1.18689 | + | 1.41448i | −0.0481348 | + | 0.0573648i | ||||
\(609\) | −12.6827 | + | 12.5532i | −0.513930 | + | 0.508680i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0640889 | + | 0.111005i | −0.00259276 | + | 0.00449079i | ||||
\(612\) | 13.2691 | − | 10.9039i | 0.536371 | − | 0.440763i | ||||
\(613\) | 26.9851 | − | 15.5799i | 1.08992 | − | 0.629265i | 0.156364 | − | 0.987699i | \(-0.450023\pi\) |
0.933555 | + | 0.358434i | \(0.116689\pi\) | |||||||
\(614\) | −0.585856 | − | 3.32255i | −0.0236432 | − | 0.134087i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.2836 | + | 3.74293i | −0.414339 | + | 0.150807i | ||||
\(617\) | −7.03230 | − | 1.23998i | −0.283110 | − | 0.0499199i | 0.0302901 | − | 0.999541i | \(-0.490357\pi\) |
−0.313400 | + | 0.949621i | \(0.601468\pi\) | |||||||
\(618\) | −1.89805 | + | 2.68129i | −0.0763506 | + | 0.107857i | ||||
\(619\) | 7.68412 | − | 6.44774i | 0.308851 | − | 0.259157i | −0.475166 | − | 0.879896i | \(-0.657612\pi\) |
0.784017 | + | 0.620740i | \(0.213168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.83569 | − | 2.34625i | −0.194049 | − | 0.0941520i | ||||
\(622\) | 9.90827i | 0.397285i | ||||||||
\(623\) | −2.86117 | − | 3.40981i | −0.114630 | − | 0.136611i | ||||
\(624\) | −0.0850787 | + | 0.0391423i | −0.00340587 | + | 0.00156695i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.5061 | − | 3.82392i | 0.419909 | − | 0.152835i | ||||
\(627\) | −0.309286 | − | 3.75722i | −0.0123517 | − | 0.150049i | ||||
\(628\) | −22.6030 | + | 3.98552i | −0.901957 | + | 0.159039i | ||||
\(629\) | −6.93093 | − | 12.0047i | −0.276354 | − | 0.478660i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.53780 | − | 6.12765i | 0.140838 | − | 0.243938i | −0.786975 | − | 0.616985i | \(-0.788354\pi\) |
0.927812 | + | 0.373047i | \(0.121687\pi\) | |||||||
\(632\) | 0.266028 | − | 0.730905i | 0.0105820 | − | 0.0290738i | ||||
\(633\) | −40.2002 | + | 10.5507i | −1.59781 | + | 0.419353i | ||||
\(634\) | −2.65189 | − | 2.22520i | −0.105320 | − | 0.0883741i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.97070 | − | 1.08582i | −0.157448 | − | 0.0430557i | ||||
\(637\) | 0.0324790 | − | 0.0892352i | 0.00128686 | − | 0.00353563i | ||||
\(638\) | −14.6498 | − | 8.45809i | −0.579993 | − | 0.334859i | ||||
\(639\) | 11.8756 | − | 13.8613i | 0.469793 | − | 0.548344i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.870188 | − | 4.93508i | −0.0343704 | − | 0.194924i | 0.962788 | − | 0.270258i | \(-0.0871089\pi\) |
−0.997158 | + | 0.0753337i | \(0.975998\pi\) | |||||||
\(642\) | 6.68277 | − | 4.62838i | 0.263748 | − | 0.182667i | ||||
\(643\) | 0.560367 | + | 1.53960i | 0.0220987 | + | 0.0607157i | 0.950251 | − | 0.311484i | \(-0.100826\pi\) |
−0.928153 | + | 0.372199i | \(0.878604\pi\) | |||||||
\(644\) | 0.433147 | − | 2.45650i | 0.0170684 | − | 0.0967997i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.416126 | − | 0.349171i | 0.0163722 | − | 0.0137379i | ||||
\(647\) | 34.4927i | 1.35605i | 0.735040 | + | 0.678024i | \(0.237164\pi\) | ||||
−0.735040 | + | 0.678024i | \(0.762836\pi\) | |||||||
\(648\) | −14.1420 | + | 2.19521i | −0.555550 | + | 0.0862359i | ||||
\(649\) | −19.3056 | −0.757813 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.786571 | + | 8.48840i | −0.0308282 | + | 0.332687i | ||||
\(652\) | −5.96515 | − | 1.05182i | −0.233613 | − | 0.0411923i | ||||
\(653\) | 13.2569 | + | 36.4230i | 0.518783 | + | 1.42534i | 0.871862 | + | 0.489751i | \(0.162912\pi\) |
−0.353080 | + | 0.935593i | \(0.614866\pi\) | |||||||
\(654\) | −5.94223 | − | 8.57980i | −0.232360 | − | 0.335497i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.50161 | + | 9.52907i | 0.214802 | + | 0.372048i | ||||
\(657\) | 1.54764 | − | 0.545365i | 0.0603792 | − | 0.0212767i | ||||
\(658\) | −3.37015 | − | 1.94575i | −0.131382 | − | 0.0758534i | ||||
\(659\) | 8.82552 | + | 3.21223i | 0.343794 | + | 0.125131i | 0.508146 | − | 0.861271i | \(-0.330331\pi\) |
−0.164352 | + | 0.986402i | \(0.552553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.4980 | − | 15.5217i | −0.719489 | − | 0.603723i | 0.207755 | − | 0.978181i | \(-0.433384\pi\) |
−0.927244 | + | 0.374458i | \(0.877829\pi\) | |||||||
\(662\) | −1.71457 | + | 2.04335i | −0.0666387 | + | 0.0794169i | ||||
\(663\) | 0.0947785 | − | 0.0248750i | 0.00368089 | − | 0.000966065i | ||||
\(664\) | 6.89399 | + | 2.50921i | 0.267539 | + | 0.0973761i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0566265 | + | 5.51472i | −0.00219423 | + | 0.213691i | ||||
\(667\) | 6.99375 | − | 4.03784i | 0.270799 | − | 0.156346i | ||||
\(668\) | 37.0057 | − | 6.52510i | 1.43179 | − | 0.252464i | ||||
\(669\) | −37.3935 | + | 3.07815i | −1.44572 | + | 0.119008i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.26159 | + | 35.5112i | −0.241726 | + | 1.37090i | ||||
\(672\) | −4.22656 | − | 9.18674i | −0.163043 | − | 0.354386i | ||||
\(673\) | 17.0121 | + | 20.2742i | 0.655768 | + | 0.781514i | 0.986772 | − | 0.162115i | \(-0.0518316\pi\) |
−0.331003 | + | 0.943630i | \(0.607387\pi\) | |||||||
\(674\) | 3.10557 | 0.119622 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.7554 | 0.913671 | ||||||||
\(677\) | 19.9694 | + | 23.7986i | 0.767486 | + | 0.914654i | 0.998296 | − | 0.0583448i | \(-0.0185823\pi\) |
−0.230811 | + | 0.972999i | \(0.574138\pi\) | |||||||
\(678\) | −5.22143 | + | 7.37609i | −0.200528 | + | 0.283277i | ||||
\(679\) | 2.27807 | − | 12.9196i | 0.0874245 | − | 0.495809i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.0160 | + | 33.8910i | −0.613734 | + | 1.29871i | ||||
\(682\) | −7.95842 | + | 1.40328i | −0.304744 | + | 0.0537345i | ||||
\(683\) | −33.0268 | + | 19.0681i | −1.26374 | + | 0.729619i | −0.973796 | − | 0.227425i | \(-0.926969\pi\) |
−0.289942 | + | 0.957044i | \(0.593636\pi\) | |||||||
\(684\) | 2.25719 | − | 0.374149i | 0.0863060 | − | 0.0143060i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.31558 | + | 2.29868i | 0.241130 | + | 0.0877642i | ||||
\(687\) | −13.1657 | − | 13.3016i | −0.502303 | − | 0.507487i | ||||
\(688\) | −15.9892 | + | 19.0552i | −0.609583 | + | 0.726472i | ||||
\(689\) | −0.0179917 | − | 0.0150968i | −0.000685428 | − | 0.000575142i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.9436 | − | 11.2626i | −1.17715 | − | 0.428448i | −0.321957 | − | 0.946754i | \(-0.604341\pi\) |
−0.855195 | + | 0.518306i | \(0.826563\pi\) | |||||||
\(692\) | 22.2085 | + | 12.8221i | 0.844242 | + | 0.487424i | ||||
\(693\) | 19.3277 | + | 7.26030i | 0.734198 | + | 0.275796i | ||||
\(694\) | 6.53414 | + | 11.3175i | 0.248033 | + | 0.429605i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.18742 | − | 19.4413i | 0.348248 | − | 0.736919i | ||||
\(697\) | −3.93762 | − | 10.8185i | −0.149148 | − | 0.409781i | ||||
\(698\) | 4.84968 | + | 0.855130i | 0.183563 | + | 0.0323672i | ||||
\(699\) | −10.7992 | − | 7.64461i | −0.408463 | − | 0.289146i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.30710 | −0.0871381 | −0.0435690 | − | 0.999050i | \(-0.513873\pi\) | ||||
−0.0435690 | + | 0.999050i | \(0.513873\pi\) | |||||||
\(702\) | −0.0374969 | − | 0.0106689i | −0.00141523 | − | 0.000402671i | ||||
\(703\) | − | 1.84668i | − | 0.0696490i | ||||||
\(704\) | −16.5800 | + | 13.9123i | −0.624881 | + | 0.524338i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.592100 | − | 3.35796i | 0.0222840 | − | 0.126379i | ||||
\(707\) | 6.22826 | + | 17.1120i | 0.234238 | + | 0.643563i | ||||
\(708\) | −0.961241 | − | 11.6772i | −0.0361257 | − | 0.438857i | ||||
\(709\) | 1.93654 | + | 10.9826i | 0.0727281 | + | 0.412462i | 0.999336 | + | 0.0364329i | \(0.0115995\pi\) |
−0.926608 | + | 0.376029i | \(0.877289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.27830 | + | 0.720629i | −0.0479400 | + | 0.0270257i | ||||
\(712\) | 4.64508 | + | 2.68184i | 0.174082 | + | 0.100506i | ||||
\(713\) | 1.31948 | − | 3.62525i | 0.0494151 | − | 0.135767i | ||||
\(714\) | 0.755212 | + | 2.87750i | 0.0282631 | + | 0.107688i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.2646 | − | 11.9694i | −0.533092 | − | 0.447317i | ||||
\(717\) | −1.47637 | + | 5.39888i | −0.0551362 | + | 0.201625i | ||||
\(718\) | 2.51901 | − | 6.92093i | 0.0940087 | − | 0.258287i | ||||
\(719\) | −16.0850 | + | 27.8600i | −0.599869 | + | 1.03900i | 0.392971 | + | 0.919551i | \(0.371447\pi\) |
−0.992840 | + | 0.119453i | \(0.961886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.01213 | + | 5.21717i | 0.112178 | + | 0.194297i | ||||
\(722\) | −7.70267 | + | 1.35819i | −0.286664 | + | 0.0505465i | ||||
\(723\) | 37.7972 | − | 26.1777i | 1.40569 | − | 0.973560i | ||||
\(724\) | −41.3064 | + | 15.0343i | −1.53514 | + | 0.558745i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.07552 | + | 11.6066i | −0.0399163 | + | 0.430762i | ||||
\(727\) | −3.44888 | − | 4.11022i | −0.127912 | − | 0.152440i | 0.698287 | − | 0.715818i | \(-0.253946\pi\) |
−0.826199 | + | 0.563378i | \(0.809501\pi\) | |||||||
\(728\) | − | 0.0378942i | − | 0.00140445i | ||||||
\(729\) | 22.9558 | + | 14.2138i | 0.850215 | + | 0.526435i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.9377 | − | 16.7297i | 0.737424 | − | 0.618772i | ||||
\(732\) | −21.7911 | − | 2.01926i | −0.805422 | − | 0.0746338i | ||||
\(733\) | 14.3746 | + | 2.53463i | 0.530938 | + | 0.0936187i | 0.432689 | − | 0.901543i | \(-0.357565\pi\) |
0.0982489 | + | 0.995162i | \(0.468676\pi\) | |||||||
\(734\) | 7.93296 | − | 2.88736i | 0.292811 | − | 0.106574i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.794682 | + | 4.50687i | 0.0292924 | + | 0.166125i | ||||
\(737\) | 49.8023 | − | 28.7534i | 1.83449 | − | 1.05915i | ||||
\(738\) | −0.841659 | + | 4.50245i | −0.0309819 | + | 0.165737i | ||||
\(739\) | −21.6083 | + | 37.4266i | −0.794873 | + | 1.37676i | 0.128047 | + | 0.991768i | \(0.459129\pi\) |
−0.922920 | + | 0.384992i | \(0.874204\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0125917 | + | 0.00344333i | 0.000462569 | + | 0.000126494i | ||||
\(742\) | 0.458343 | − | 0.546231i | 0.0168263 | − | 0.0200528i | ||||
\(743\) | 5.21443 | − | 6.21431i | 0.191299 | − | 0.227981i | −0.661866 | − | 0.749622i | \(-0.730235\pi\) |
0.853165 | + | 0.521641i | \(0.174680\pi\) | |||||||
\(744\) | −2.60770 | − | 9.93582i | −0.0956028 | − | 0.364265i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.01116 | + | 3.48342i | −0.0736336 | + | 0.127537i | ||||
\(747\) | −6.79706 | − | 12.0571i | −0.248692 | − | 0.441146i | ||||
\(748\) | 25.8561 | − | 14.9280i | 0.945393 | − | 0.545823i | ||||
\(749\) | −2.58860 | − | 14.6807i | −0.0945854 | − | 0.536420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.22744 | + | 2.99454i | −0.300223 | + | 0.109272i | −0.487740 | − | 0.872989i | \(-0.662178\pi\) |
0.187516 | + | 0.982261i | \(0.439956\pi\) | |||||||
\(752\) | −20.9291 | − | 3.69037i | −0.763207 | − | 0.134574i | ||||
\(753\) | −3.25717 | − | 7.07968i | −0.118698 | − | 0.257998i | ||||
\(754\) | 0.0448713 | − | 0.0376515i | 0.00163412 | − | 0.00137119i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.42913 | + | 12.0520i | −0.124716 | + | 0.438329i | ||||
\(757\) | − | 32.1511i | − | 1.16855i | −0.811555 | − | 0.584276i | \(-0.801378\pi\) | ||
0.811555 | − | 0.584276i | \(-0.198622\pi\) | |||||||
\(758\) | −1.10269 | − | 1.31414i | −0.0400515 | − | 0.0477316i | ||||
\(759\) | −7.62620 | − | 5.39848i | −0.276813 | − | 0.195952i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.0656 | − | 8.39520i | 0.836128 | − | 0.304326i | 0.111756 | − | 0.993736i | \(-0.464352\pi\) |
0.724371 | + | 0.689410i | \(0.242130\pi\) | |||||||
\(762\) | −5.46192 | − | 2.58116i | −0.197865 | − | 0.0935054i | ||||
\(763\) | −18.8481 | + | 3.32342i | −0.682346 | + | 0.120316i | ||||
\(764\) | −10.0016 | − | 17.3233i | −0.361846 | − | 0.626736i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.986770 | − | 1.70914i | 0.0356535 | − | 0.0617536i | ||||
\(767\) | 0.0228638 | − | 0.0628177i | 0.000825563 | − | 0.00226822i | ||||
\(768\) | −4.76119 | − | 4.81033i | −0.171805 | − | 0.173578i | ||||
\(769\) | −24.0648 | − | 20.1928i | −0.867800 | − | 0.728170i | 0.0958338 | − | 0.995397i | \(-0.469448\pi\) |
−0.963634 | + | 0.267227i | \(0.913893\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.9085 | − | 16.7358i | 0.608945 | − | 0.602725i | ||||
\(772\) | 6.75377 | − | 18.5558i | 0.243073 | − | 0.667839i | ||||
\(773\) | 24.8675 | + | 14.3573i | 0.894422 | + | 0.516395i | 0.875386 | − | 0.483424i | \(-0.160607\pi\) |
0.0190355 | + | 0.999819i | \(0.493940\pi\) | |||||||
\(774\) | −10.2155 | + | 1.69331i | −0.367190 | + | 0.0608649i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.74507 | + | 15.5681i | 0.0985424 | + | 0.558862i | ||||
\(777\) | 9.14389 | + | 4.32116i | 0.328035 | + | 0.155021i | ||||
\(778\) | 3.09962 | + | 8.51615i | 0.111127 | + | 0.305319i | ||||
\(779\) | 0.266332 | − | 1.51044i | 0.00954233 | − | 0.0541173i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.3071 | − | 20.3961i | 0.869776 | − | 0.729829i | ||||
\(782\) | − | 1.34633i | − | 0.0481446i | ||||||
\(783\) | −37.0263 | + | 16.5763i | −1.32321 | + | 0.592388i | ||||
\(784\) | 15.7448 | 0.562315 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.1558 | + | 4.67239i | −0.362245 | + | 0.166659i | ||||
\(787\) | −38.2263 | − | 6.74033i | −1.36262 | − | 0.240267i | −0.555925 | − | 0.831233i | \(-0.687636\pi\) |
−0.806697 | + | 0.590966i | \(0.798747\pi\) | |||||||
\(788\) | 13.7959 | + | 37.9040i | 0.491459 | + | 1.35027i | ||||
\(789\) | 41.7787 | − | 3.43913i | 1.48736 | − | 0.122436i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.28623 | + | 14.3522i | 0.294625 | + | 0.510305i | ||||
\(792\) | −24.8775 | − | 0.255448i | −0.883983 | − | 0.00907694i | ||||
\(793\) | −0.108133 | − | 0.0624304i | −0.00383990 | − | 0.00221697i | ||||
\(794\) | 13.6054 | + | 4.95197i | 0.482839 | + | 0.175739i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0397 | − | 15.1371i | −0.639399 | − | 0.536520i | ||||
\(797\) | 2.59307 | − | 3.09030i | 0.0918512 | − | 0.109464i | −0.718161 | − | 0.695877i | \(-0.755016\pi\) |
0.810012 | + | 0.586413i | \(0.199460\pi\) | |||||||
\(798\) | −0.104540 | + | 0.382289i | −0.00370069 | + | 0.0135329i | ||||
\(799\) | 20.8953 | + | 7.60526i | 0.739222 | + | 0.269055i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.36315 | − | 9.54397i | −0.118831 | − | 0.337220i | ||||
\(802\) | 6.77371 | − | 3.91080i | 0.239188 | − | 0.138095i | ||||
\(803\) | 2.80923 | − | 0.495343i | 0.0991355 | − | 0.0174803i | ||||
\(804\) | 19.8715 | + | 28.6918i | 0.700813 | + | 1.01188i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.00485912 | − | 0.0275575i | 0.000171155 | − | 0.000970670i | ||||
\(807\) | 20.7067 | + | 1.91877i | 0.728909 | + | 0.0675438i | ||||
\(808\) | −14.1049 | − | 16.8095i | −0.496207 | − | 0.591357i | ||||
\(809\) | 29.9454 | 1.05283 | 0.526413 | − | 0.850229i | \(-0.323537\pi\) | ||||
0.526413 | + | 0.850229i | \(0.323537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2173 | 0.709927 | 0.354963 | − | 0.934880i | \(-0.384493\pi\) | ||||
0.354963 | + | 0.934880i | \(0.384493\pi\) | |||||||
\(812\) | −12.1017 | − | 14.4223i | −0.424687 | − | 0.506122i | ||||
\(813\) | −6.41190 | − | 0.594154i | −0.224875 | − | 0.0208379i | ||||
\(814\) | −1.66481 | + | 9.44162i | −0.0583516 | + | 0.330929i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.25021 | + | 13.3561i | 0.323822 | + | 0.467557i | ||||
\(817\) | 3.41463 | − | 0.602092i | 0.119463 | − | 0.0210645i | ||||
\(818\) | −2.28834 | + | 1.32117i | −0.0800099 | + | 0.0461938i | ||||
\(819\) | −0.0465138 | + | 0.0542910i | −0.00162533 | + | 0.00189708i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.2530 | − | 9.19133i | −0.881334 | − | 0.320779i | −0.138586 | − | 0.990350i | \(-0.544256\pi\) |
−0.742748 | + | 0.669571i | \(0.766478\pi\) | |||||||
\(822\) | −2.27918 | + | 8.33461i | −0.0794954 | + | 0.290703i | ||||
\(823\) | 14.8190 | − | 17.6606i | 0.516559 | − | 0.615611i | −0.443204 | − | 0.896421i | \(-0.646158\pi\) |
0.959764 | + | 0.280809i | \(0.0906029\pi\) | |||||||
\(824\) | −5.56089 | − | 4.66614i | −0.193723 | − | 0.162553i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.90716 | + | 0.694150i | 0.0663587 | + | 0.0241526i | ||||
\(827\) | 4.42498 | + | 2.55476i | 0.153872 | + | 0.0888378i | 0.574959 | − | 0.818182i | \(-0.305018\pi\) |
−0.421087 | + | 0.907020i | \(0.638351\pi\) | |||||||
\(828\) | 2.88561 | − | 4.88158i | 0.100282 | − | 0.169647i | ||||
\(829\) | −15.2991 | − | 26.4988i | −0.531360 | − | 0.920343i | −0.999330 | − | 0.0365985i | \(-0.988348\pi\) |
0.467970 | − | 0.883744i | \(-0.344986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.5368 | + | 3.33690i | −1.40621 | + | 0.115756i | ||||
\(832\) | −0.0256327 | − | 0.0704252i | −0.000888653 | − | 0.00244155i | ||||
\(833\) | −16.2238 | − | 2.86069i | −0.562120 | − | 0.0991170i | ||||
\(834\) | −4.01731 | + | 1.84825i | −0.139108 | + | 0.0639997i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.97744 | 0.137563 | ||||||||
\(837\) | −8.45984 | + | 17.4359i | −0.292415 | + | 0.602674i | ||||
\(838\) | − | 10.1033i | − | 0.349013i | ||||||
\(839\) | 43.1350 | − | 36.1945i | 1.48918 | − | 1.24957i | 0.593539 | − | 0.804805i | \(-0.297730\pi\) |
0.895645 | − | 0.444769i | \(-0.146714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.54853 | − | 31.4673i | 0.191329 | − | 1.08508i | ||||
\(842\) | −1.13537 | − | 3.11939i | −0.0391273 | − | 0.107501i | ||||
\(843\) | −31.9020 | − | 15.0760i | −1.09876 | − | 0.519246i | ||||
\(844\) | −7.61436 | − | 43.1832i | −0.262097 | − | 1.48643i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.61674 | − | 6.83509i | −0.193108 | − | 0.234995i | ||||
\(847\) | 18.5118 | + | 10.6878i | 0.636073 | + | 0.367237i | ||||
\(848\) | 1.33185 | − | 3.65924i | 0.0457360 | − | 0.125659i | ||||
\(849\) | −14.2797 | + | 14.1338i | −0.490079 | + | 0.485072i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.50612 | − | 2.94198i | −0.120188 | − | 0.100850i | ||||
\(852\) | 13.5470 | + | 13.6869i | 0.464114 | + | 0.468904i | ||||
\(853\) | 15.5773 | − | 42.7983i | 0.533357 | − | 1.46539i | −0.321695 | − | 0.946843i | \(-0.604253\pi\) |
0.855052 | − | 0.518542i | \(-0.173525\pi\) | |||||||
\(854\) | 1.89540 | − | 3.28294i | 0.0648594 | − | 0.112340i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.98154 | + | 15.5565i | 0.306983 | + | 0.531710i | ||||
\(857\) | 17.2235 | − | 3.03696i | 0.588343 | − | 0.103741i | 0.128451 | − | 0.991716i | \(-0.458999\pi\) |
0.459892 | + | 0.887975i | \(0.347888\pi\) | |||||||
\(858\) | −0.0612742 | − | 0.0289565i | −0.00209187 | − | 0.000988559i | ||||
\(859\) | 17.2396 | − | 6.27471i | 0.588208 | − | 0.214090i | −0.0307329 | − | 0.999528i | \(-0.509784\pi\) |
0.618941 | + | 0.785437i | \(0.287562\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.85579 | + | 4.85312i | 0.233645 | + | 0.165394i | ||||
\(862\) | −2.63618 | − | 3.14167i | −0.0897886 | − | 0.107006i | ||||
\(863\) | − | 4.65373i | − | 0.158415i | −0.996858 | − | 0.0792073i | \(-0.974761\pi\) | ||
0.996858 | − | 0.0792073i | \(-0.0252389\pi\) | |||||||
\(864\) | −1.65068 | − | 22.9298i | −0.0561574 | − | 0.780087i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.94259 | − | 1.63003i | 0.0660120 | − | 0.0553907i | ||||
\(867\) | 5.20185 | + | 11.3066i | 0.176664 | + | 0.383992i | ||||
\(868\) | −8.85735 | − | 1.56179i | −0.300638 | − | 0.0530106i | ||||
\(869\) | −2.39713 | + | 0.872486i | −0.0813172 | + | 0.0295971i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0345781 | + | 0.196102i | 0.00117164 | + | 0.00664468i | ||||
\(872\) | 19.9725 | − | 11.5311i | 0.676354 | − | 0.390493i | ||||
\(873\) | 15.1765 | − | 25.6739i | 0.513645 | − | 0.868931i | ||||
\(874\) | 0.0896791 | − | 0.155329i | 0.00303344 | − | 0.00525407i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.439487 | + | 1.67453i | 0.0148489 | + | 0.0565770i | ||||
\(877\) | 2.35716 | − | 2.80916i | 0.0795958 | − | 0.0948585i | −0.724777 | − | 0.688984i | \(-0.758057\pi\) |
0.804373 | + | 0.594125i | \(0.202502\pi\) | |||||||
\(878\) | 4.04164 | − | 4.81664i | 0.136399 | − | 0.162554i | ||||
\(879\) | 52.7512 | + | 14.4253i | 1.77925 | + | 0.486554i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.1504 | + | 33.1694i | −0.645193 | + | 1.11751i | 0.339064 | + | 0.940763i | \(0.389890\pi\) |
−0.984257 | + | 0.176744i | \(0.943444\pi\) | |||||||
\(882\) | 4.97735 | + | 4.26434i | 0.167596 | + | 0.143588i | ||||
\(883\) | −19.5844 | + | 11.3071i | −0.659069 | + | 0.380513i | −0.791922 | − | 0.610622i | \(-0.790919\pi\) |
0.132853 | + | 0.991136i | \(0.457586\pi\) | |||||||
\(884\) | 0.0179521 | + | 0.101811i | 0.000603794 | + | 0.00342429i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.282186 | + | 0.102707i | −0.00948023 | + | 0.00345052i | ||||
\(887\) | −1.86774 | − | 0.329334i | −0.0627127 | − | 0.0110579i | 0.142204 | − | 0.989837i | \(-0.454581\pi\) |
−0.204916 | + | 0.978779i | \(0.565692\pi\) | |||||||
\(888\) | −12.1348 | − | 1.12446i | −0.407216 | − | 0.0377344i | ||||
\(889\) | −8.48645 | + | 7.12097i | −0.284626 | + | 0.238830i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.3285 | + | 30.9023i | 1.18355 | + | 1.03527i | ||||
\(892\) | − | 39.5852i | − | 1.32541i | ||||||
\(893\) | 1.90415 | + | 2.26928i | 0.0637199 | + | 0.0759384i | ||||
\(894\) | 0.0586171 | − | 0.632575i | 0.00196045 | − | 0.0211565i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.1107 | − | 4.77190i | 0.437997 | − | 0.159418i | ||||
\(897\) | 0.0265976 | − | 0.0184211i | 0.000888069 | − | 0.000615062i | ||||
\(898\) | −0.682653 | + | 0.120370i | −0.0227804 | + | 0.00401680i | ||||
\(899\) | −14.5592 | − | 25.2172i | −0.485575 | − | 0.841041i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.03722 | + | 3.52856i | −0.0678695 | + | 0.117553i | ||||
\(902\) | −2.72338 | + | 7.48241i | −0.0906785 | + | 0.249137i | ||||
\(903\) | −5.00882 | + | 18.3165i | −0.166683 | + | 0.609535i | ||||
\(904\) | −15.2977 | − | 12.8363i | −0.508795 | − | 0.426930i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.50261 | − | 5.72522i | −0.0499208 | − | 0.190208i | ||||
\(907\) | 2.23371 | − | 6.13708i | 0.0741693 | − | 0.203778i | −0.897068 | − | 0.441893i | \(-0.854307\pi\) |
0.971237 | + | 0.238115i | \(0.0765294\pi\) | |||||||
\(908\) | −34.2497 | − | 19.7740i | −1.13661 | − | 0.656225i | ||||
\(909\) | −0.425067 | + | 41.3963i | −0.0140986 | + | 1.37303i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.47332 | − | 42.3833i | −0.247602 | − | 1.40422i | −0.814371 | − | 0.580344i | \(-0.802918\pi\) |
0.566769 | − | 0.823877i | \(-0.308193\pi\) | |||||||
\(912\) | 0.177566 | + | 2.15708i | 0.00587980 | + | 0.0714281i | ||||
\(913\) | −8.22940 | − | 22.6101i | −0.272353 | − | 0.748285i | ||||
\(914\) | 0.799615 | − | 4.53484i | 0.0264489 | − | 0.149999i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.1260 | − | 12.6922i | 0.499777 | − | 0.419363i | ||||
\(917\) | 20.5003i | 0.676980i | ||||||||
\(918\) | −0.693143 | + | 6.72755i | −0.0228771 | + | 0.222042i | ||||
\(919\) | 16.7911 | 0.553887 | 0.276943 | − | 0.960886i | \(-0.410679\pi\) | ||||
0.276943 | + | 0.960886i | \(0.410679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4800 | − | 8.12650i | −0.378277 | − | 0.267777i | ||||
\(922\) | 8.95409 | + | 1.57885i | 0.294887 | + | 0.0519966i | ||||
\(923\) | 0.0375788 | + | 0.103247i | 0.00123692 | + | 0.00339841i | ||||
\(924\) | −9.30703 | + | 19.6944i | −0.306179 | + | 0.647897i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.16253 | + | 8.94176i | 0.169651 | + | 0.293844i | ||||
\(927\) | 2.23957 | + | 13.5110i | 0.0735570 | + | 0.443760i | ||||
\(928\) | 29.9135 | + | 17.2706i | 0.981960 | + | 0.566935i | ||||
\(929\) | −10.9004 | − | 3.96744i | −0.357632 | − | 0.130167i | 0.156955 | − | 0.987606i | \(-0.449832\pi\) |
−0.514587 | + | 0.857438i | \(0.672055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.68122 | − | 1.41071i | −0.0550998 | − | 0.0462343i | ||||
\(932\) | 8.97294 | − | 10.6935i | 0.293918 | − | 0.350278i | ||||
\(933\) | 29.0581 | + | 29.3580i | 0.951318 | + | 0.961137i | ||||
\(934\) | 4.62072 | + | 1.68180i | 0.151195 | + | 0.0550303i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0302937 | − | 0.0806452i | 0.000990182 | − | 0.00263597i | ||||
\(937\) | 41.3919 | − | 23.8976i | 1.35222 | − | 0.780702i | 0.363656 | − | 0.931533i | \(-0.381528\pi\) |
0.988559 | + | 0.150832i | \(0.0481951\pi\) | |||||||
\(938\) | −5.95372 | + | 1.04980i | −0.194396 | + | 0.0342772i | ||||
\(939\) | 19.9150 | − | 42.1416i | 0.649901 | − | 1.37524i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.95534 | − | 11.0893i | 0.0637422 | − | 0.361500i | −0.936207 | − | 0.351448i | \(-0.885689\pi\) |
0.999949 | − | 0.0100518i | \(-0.00319964\pi\) | |||||||
\(942\) | 5.22202 | − | 7.37691i | 0.170142 | − | 0.240353i | ||||
\(943\) | −2.44343 | − | 2.91197i | −0.0795691 | − | 0.0948268i | ||||
\(944\) | 11.0837 | 0.360743 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.0010 | −0.585261 | ||||||||
\(947\) | 4.71285 | + | 5.61656i | 0.153147 | + | 0.182514i | 0.837163 | − | 0.546954i | \(-0.184213\pi\) |
−0.684016 | + | 0.729467i | \(0.739768\pi\) | |||||||
\(948\) | −0.647087 | − | 1.40649i | −0.0210164 | − | 0.0456807i | ||||
\(949\) | −0.00171521 | + | 0.00972746i | −5.56782e−5 | + | 0.000315767i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.3834 | + | 1.18401i | −0.466413 | + | 0.0383940i | ||||
\(952\) | −6.47401 | + | 1.14154i | −0.209824 | + | 0.0369976i | ||||
\(953\) | 21.5427 | − | 12.4377i | 0.697835 | − | 0.402895i | −0.108705 | − | 0.994074i | \(-0.534671\pi\) |
0.806541 | + | 0.591179i | \(0.201337\pi\) | |||||||
\(954\) | 1.41210 | − | 0.796060i | 0.0457186 | − | 0.0257734i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.54906 | − | 2.01969i | −0.179469 | − | 0.0653215i | ||||
\(957\) | −68.2122 | + | 17.9026i | −2.20499 | + | 0.578708i | ||||
\(958\) | −0.771086 | + | 0.918945i | −0.0249127 | + | 0.0296898i | ||||
\(959\) | 12.1382 | + | 10.1852i | 0.391963 | + | 0.328896i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.0590 | + | 5.84499i | 0.518031 | + | 0.188548i | ||||
\(962\) | −0.0287500 | − | 0.0165988i | −0.000926937 | − | 0.000535168i | ||||
\(963\) | 6.22720 | − | 33.3124i | 0.200669 | − | 1.07348i | ||||
\(964\) | 24.2540 | + | 42.0091i | 0.781167 | + | 1.35302i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.559269 | + | 0.807511i | 0.0179942 | + | 0.0259812i | ||||
\(967\) | 11.6389 | + | 31.9777i | 0.374283 | + | 1.02833i | 0.973687 | + | 0.227888i | \(0.0731819\pi\) |
−0.599404 | + | 0.800446i | \(0.704596\pi\) | |||||||
\(968\) | −25.3662 | − | 4.47275i | −0.815301 | − | 0.143760i | ||||
\(969\) | 0.208954 | − | 2.25496i | 0.00671258 | − | 0.0724397i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.2476 | −1.09906 | −0.549530 | − | 0.835474i | \(-0.685193\pi\) | ||||
−0.549530 | + | 0.835474i | \(0.685193\pi\) | |||||||
\(972\) | −16.9325 | + | 22.9074i | −0.543111 | + | 0.734756i | ||||
\(973\) | 8.10928i | 0.259971i | ||||||||
\(974\) | 2.78770 | − | 2.33916i | 0.0893236 | − | 0.0749514i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.59488 | − | 20.3876i | 0.115069 | − | 0.652590i | ||||
\(977\) | 8.00919 | + | 22.0051i | 0.256237 | + | 0.704004i | 0.999391 | + | 0.0348848i | \(0.0111064\pi\) |
−0.743155 | + | 0.669120i | \(0.766671\pi\) | |||||||
\(978\) | 1.96089 | − | 1.35808i | 0.0627022 | − | 0.0434266i | ||||
\(979\) | −3.05467 | − | 17.3239i | −0.0976278 | − | 0.553675i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.7687 | − | 7.99491i | −1.36550 | − | 0.255258i | ||||
\(982\) | −8.12188 | − | 4.68917i | −0.259180 | − | 0.149637i | ||||
\(983\) | 11.3561 | − | 31.2007i | 0.362205 | − | 0.995149i | −0.616044 | − | 0.787712i | \(-0.711266\pi\) |
0.978248 | − | 0.207437i | \(-0.0665122\pi\) | |||||||
\(984\) | −9.76314 | − | 2.66982i | −0.311237 | − | 0.0851108i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.78428 | − | 6.53178i | −0.247902 | − | 0.208014i | ||||
\(987\) | −15.6920 | + | 4.11843i | −0.499482 | + | 0.131091i | ||||
\(988\) | −0.00471050 | + | 0.0129420i | −0.000149861 | + | 0.000411740i | ||||
\(989\) | 4.29678 | − | 7.44223i | 0.136630 | − | 0.236649i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0903 | + | 24.4051i | 0.447594 | + | 0.775255i | 0.998229 | − | 0.0594912i | \(-0.0189478\pi\) |
−0.550635 | + | 0.834746i | \(0.685614\pi\) | |||||||
\(992\) | 16.2503 | − | 2.86537i | 0.515948 | − | 0.0909755i | ||||
\(993\) | 0.912305 | + | 11.0827i | 0.0289511 | + | 0.351700i | ||||
\(994\) | −3.13460 | + | 1.14090i | −0.0994236 | + | 0.0361872i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.2662 | − | 6.10341i | 0.420355 | − | 0.193394i | ||||
\(997\) | −28.8938 | − | 34.4342i | −0.915075 | − | 1.09054i | −0.995592 | − | 0.0937901i | \(-0.970102\pi\) |
0.0805175 | − | 0.996753i | \(-0.474343\pi\) | |||||||
\(998\) | − | 10.5249i | − | 0.333161i | ||||||
\(999\) | 16.0053 | + | 16.5061i | 0.506385 | + | 0.522228i |
(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 | 675.2.u.b.49.2 | 24 | ||
5.2 | odd | 4 | 675.2.l.c.76.1 | 12 | |||
5.3 | odd | 4 | 27.2.e.a.22.2 | yes | 12 | ||
5.4 | even | 2 | inner | 675.2.u.b.49.3 | 24 | ||
15.8 | even | 4 | 81.2.e.a.37.1 | 12 | |||
20.3 | even | 4 | 432.2.u.c.49.1 | 12 | |||
27.16 | even | 9 | inner | 675.2.u.b.124.3 | 24 | ||
45.13 | odd | 12 | 243.2.e.d.28.2 | 12 | |||
45.23 | even | 12 | 243.2.e.a.28.1 | 12 | |||
45.38 | even | 12 | 243.2.e.b.190.2 | 12 | |||
45.43 | odd | 12 | 243.2.e.c.190.1 | 12 | |||
135.13 | odd | 36 | 729.2.c.e.487.3 | 12 | |||
135.23 | even | 36 | 729.2.a.d.1.3 | 6 | |||
135.38 | even | 36 | 81.2.e.a.46.1 | 12 | |||
135.43 | odd | 36 | 27.2.e.a.16.2 | ✓ | 12 | ||
135.58 | odd | 36 | 729.2.a.a.1.4 | 6 | |||
135.68 | even | 36 | 729.2.c.b.487.4 | 12 | |||
135.83 | even | 36 | 243.2.e.b.55.2 | 12 | |||
135.88 | odd | 36 | 243.2.e.d.217.2 | 12 | |||
135.97 | odd | 36 | 675.2.l.c.151.1 | 12 | |||
135.103 | odd | 36 | 729.2.c.e.244.3 | 12 | |||
135.113 | even | 36 | 729.2.c.b.244.4 | 12 | |||
135.124 | even | 18 | inner | 675.2.u.b.124.2 | 24 | ||
135.128 | even | 36 | 243.2.e.a.217.1 | 12 | |||
135.133 | odd | 36 | 243.2.e.c.55.1 | 12 | |||
540.43 | even | 36 | 432.2.u.c.97.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.16.2 | ✓ | 12 | 135.43 | odd | 36 | ||
27.2.e.a.22.2 | yes | 12 | 5.3 | odd | 4 | ||
81.2.e.a.37.1 | 12 | 15.8 | even | 4 | |||
81.2.e.a.46.1 | 12 | 135.38 | even | 36 | |||
243.2.e.a.28.1 | 12 | 45.23 | even | 12 | |||
243.2.e.a.217.1 | 12 | 135.128 | even | 36 | |||
243.2.e.b.55.2 | 12 | 135.83 | even | 36 | |||
243.2.e.b.190.2 | 12 | 45.38 | even | 12 | |||
243.2.e.c.55.1 | 12 | 135.133 | odd | 36 | |||
243.2.e.c.190.1 | 12 | 45.43 | odd | 12 | |||
243.2.e.d.28.2 | 12 | 45.13 | odd | 12 | |||
243.2.e.d.217.2 | 12 | 135.88 | odd | 36 | |||
432.2.u.c.49.1 | 12 | 20.3 | even | 4 | |||
432.2.u.c.97.1 | 12 | 540.43 | even | 36 | |||
675.2.l.c.76.1 | 12 | 5.2 | odd | 4 | |||
675.2.l.c.151.1 | 12 | 135.97 | odd | 36 | |||
675.2.u.b.49.2 | 24 | 1.1 | even | 1 | trivial | ||
675.2.u.b.49.3 | 24 | 5.4 | even | 2 | inner | ||
675.2.u.b.124.2 | 24 | 135.124 | even | 18 | inner | ||
675.2.u.b.124.3 | 24 | 27.16 | even | 9 | inner | ||
729.2.a.a.1.4 | 6 | 135.58 | odd | 36 | |||
729.2.a.d.1.3 | 6 | 135.23 | even | 36 | |||
729.2.c.b.244.4 | 12 | 135.113 | even | 36 | |||
729.2.c.b.487.4 | 12 | 135.68 | even | 36 | |||
729.2.c.e.244.3 | 12 | 135.103 | odd | 36 | |||
729.2.c.e.487.3 | 12 | 135.13 | odd | 36 |